The greatest of the three interior angles in the triangle is approximately 71.2 degrees.
To find out which of the three interior angles in the triangle is the greatest, we can use the fact that the largest angle is opposite the longest side. So, in this case, the longest side is 22, which means that the angle opposite it must be the greatest. We can use the Law of Cosines to find the measure of this angle:
c^2 = a^2 + b^2 - 2ab*cos(C)
where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides. Plugging in the values we know, we get:
22^2 = 12^2 + 17^2 - 2*12*17*cos(C)
484 = 144 + 289 - 408*cos(C)
51 = 408*cos(C)
cos(C) = 51/408
C = cos^-1(51/408)
C ≈ 71.2 degrees
So the greatest of the three interior angles in the triangle is approximately 71.2 degrees.
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Sikie Shoe Manufacturing Co. Was incorporated in the New York State on January 15, 2021 and received authorization to issue 100,000 shares of $25 par value, preferred stock 200,000 shares of $2 Par Value Common Stock. Prepare journal entries to record the following transactions. (40 POINTS)
1 What journal entry would you make on January 15, the authorization date?
2 On Jan. 20, 50,000 preferred stock were sold cash at $70 per share.
3 On February 1, 2021 Sikie Shoe Manufacturing Co. Issued 70,000 common shares with a Market price of $8
4 On February 15, 2021 Sikie Shoe Manufacturing Co. Issued 4,000 common shares to Delkab Consulting Co. In settlement of various Professional Services Provided at a fee of $100,000
5 On March 20, 2021 Mr. Park agreed to exchange a piece of land he owns with a fair value of $150,000 for 10,000 common shares. Sikie Shoe Manufacturing Co. Shares are actively traded at $10 per share on the stock exchange.
6 On July 1, 2021 Sikie Shoe Manufacturing Co. Issued 45,000 common shares for cash at a Market price of $25
7 As of July 31, How many common shares have been issued?
8 As of July 31, How many common shares are outstanding?
The following treasury stock transactions were made by Sikie in 2021 Prepare the necessary journal entries to record the transactions in the financial records of the company. (25 POINTS)
9 1-Aug Purchased 5,000 shares of its own $2 par value common stock at $20 per share
10 1-Sep Sold 1,500 shares of treasury stock purchased on August 1 for $30 per share
11 21-Oct Sold 700 shares of treasury stock purchased on August 1 for $27 per share
12 1-Nov Sold 900 shares of treasury stock purchased on August 1 for $13,500
13 18-Nov Sold 600 shares of treasury stock purchased on August 1 for $9,600
Prepare the stockholders' equity section of Sikie Shoe Manufacturing Co as of December 31, 2021 including disclosure of all relevant information. (Hint: Refer to Learning Objective 3 Illustration 13. 11 page 13-18 of your text book). (35 points)
To help you with the journal entries and preparation of the stockholders' equity section for Sikie Shoe Manufacturing Co, let's start with the journal entries for the given transactions:
On January 15, the authorization date:
Journal entry:
Common Stock (200,000 shares * $2 par value) $400,000
Preferred Stock (100,000 shares * $25 par value) $2,500,000
Authorized Capital Stock $2,900,000
On January 20, 50,000 preferred stock were sold for cash at $70 per share:
Journal entry:
Cash $3,500,000
Preferred Stock (50,000 shares * $25 par value) $1,250,000
Common Stock $1,250,000
Paid-in Capital in Excess of Par - Preferred Stock $2,250,000
On February 1, 70,000 common shares were issued with a market price of $8:
Journal entry:
Cash $560,000
Common Stock (70,000 shares * $2 par value) $140,000
Paid-in Capital in Excess of Par - Common Stock $420,000
On February 15, 4,000 common shares were issued to Delkab Consulting Co. in settlement of professional services provided at a fee of $100,000:
Journal entry:
Common Stock (4,000 shares * $2 par value) $8,000
Paid-in Capital in Excess of Par - Common Stock $92,000
Accounts Payable/Professional Services $100,000
On March 20, Mr. Park exchanged a piece of land with a fair value of $150,000 for 10,000 common shares:
Journal entry:
Land (fair value) $150,000
Common Stock (10,000 shares * $2 par value) $20,000
Paid-in Capital in Excess of Par - Common Stock $130,000
On July 1, 45,000 common shares were issued for cash at a market price of $25:
Journal entry:
Cash $1,125,000
Common Stock (45,000 shares * $2 par value) $90,000
Paid-in Capital in Excess of Par - Common Stock $1,035,000
Now let's move on to the questions regarding common shares issued and outstanding:
As of July 31, the number of common shares issued is:
Calculation: 70,000 (February 1) + 4,000 (February 15) + 10,000 (March 20) + 45,000 (July 1) = 129,000 common shares
As of July 31, the number of common shares outstanding is the same as the number of common shares issued since there are no repurchases or retirements mentioned.
Moving on to the treasury stock transactions:
On August 1, purchased 5,000 shares of its own $2 par value common stock at $20 per share:
Journal entry:
Treasury Stock $100,000
Cash $100,000
On September 1, sold 1,500 shares of treasury stock purchased on August 1 for $30 per share:
Journal entry:
Cash $45,000
Treasury Stock $30,000
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Q4. A. A triangle has vertices (-2, 3), (1, 1) and (-1,-2).
a. Find the length of the sides. (3mks)
b. Name this triangle. (Imks)
The length of the sides AB, BC and AC are √13, √13 and √26, hence the triangle is a isosceles triangle.
a. Points (-2, 3), (1, 1), (-1, 2) in the triangle are vertex. The distance formula for any two points is,
AB = √[(d-b)²+(c-a)²]
= √[(1 - (-2))² + (1 - 3)²]
= √[3² + (-2)²]
= √13
BC = √[(d-b)²+(c-a)²]
= √[(-1-1)²+(-2-1)²]
= √[(-2)² + (-3)²]
= √13
AC = √[(d-b)²+(c-a)²]
= √[(-1 - (-2))² + (-2 - 3)²]
= √[1² + (-5)²]
= √26
b. The triangle is an isosceles triangle because AB = BC.
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On a certain plaats moon the acceleration due to gravity is 2.9 m/sec^2 if a rock dropped into a chivaste, how fast it will be going just before it hits the bottom 31 secs later?
the rock will be going 89.9 m/s just before it hits the bottom of the chaste on a certain plaats moon.
To answer your question, we need to use the formula for the acceleration due to gravity, which is:
a = g
where a is the acceleration, and g is the gravitational constant. In this case, we know that the acceleration due to gravity on the moon is 2.9 m/sec^2, so we can substitute that into the formula:
a = 2.9 m/sec^2
Now we need to use the formula for calculating the speed of an object that is falling under the influence of gravity, which is:
v = gt
where v is the speed, g is the gravitational constant, and t is the time. We know that the rock takes 31 seconds to hit the bottom of the chivaste, so we can substitute that into the formula:
t = 31 s
Now we can calculate the speed of the rock just before it hits the bottom:
v = gt
v = 2.9 m/sec^2 x 31 s
v = 89.9 m/s
So the rock will be going 89.9 m/s just before it hits the bottom of the chivaste on the certain plaats moon.
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I need this problem solved.
The relation has been plotted on the graph where the first quadrant has (1, 2) and (2, 4), while the second quadrant contains (-1, 3) and (-2, 4).
What is a graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
You can compare various data sets using bar graphs.
In a line graph, the data is represented by tiny dots, and the line that connects them indicates what happens to the data.
So, we have the coordinates:
(-1, 3); (-2, 4); (1, 2); (2, 4)
Now, plot it on the graph as follows:
(Refer to the graph attached below.)
(-1, 3) and (-2, 4) are in the 2nd quadrant, and (1, 2) and (2, 4) are in the 1st quadrant.
Therefore, the relation has been plotted on the graph where the first quadrant has (1, 2) and (2, 4), while the second quadrant contains (-1, 3) and (-2, 4).
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Correct question:
Express the relation (-1, 3); (-2, 4); (1, 2); (2, 4) on the graph.
A street light is mounted on a pole. the tip of the shadow of a man who is standing on a street a short distance from the pole has an angle of elevation to the top of his head of 42o. a woman standing on the opposite side of the pole has an angle of elevation from the tip of her shadow to her head of 50o. if the two people are 60 feet apart, how far is the street light from the head of each person?
the man’s head is 78.3 ft away and the woman’s head is 89.6 ft away.
the man’s head is 41.2 ft away and the woman’s head is 39.5 ft away.
the man’s head is 1105.1ft away and the woman’s head is 1277.6 ft away.
the man’s head is 46.0 ft away and the woman’s head is 40.2 ft away.
The correct option is (a). The man’s head is 78.3 ft away and the woman’s head is 89.6 ft away.
How to find the distance from the street light to each person's?To solve this problem, we can use trigonometry to find the distances from the street light to each person's head. Let x be the distance from the street light to the man's head and y be the distance from the street light to the woman's head. Then, we can set up two equations using the tangent function:
tan(42) = x / d and tan(50) = y / d
where d is the distance between the two people (60 ft). Solving for x and y, we get:
x = d * tan(42) = 78.3 ft
y = d * tan(50) = 89.6 ft
Therefore, the man’s head is 78.3 ft away from the street light and the woman’s head is 89.6 ft away from the street light.
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Please upload a picture of a piece of paper with the problem worked out, and draw the graph for extra points, there will be 6 of these, so go to my profile and find the rest, and do the same, for extra points.
The solution of the system of equations is given by the ordered pair (2, 7).
How to graphically solve this system of equations?In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
3x - y = -1 ......equation 1.
x - 2y = -12 ......equation 2.
Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I, and it is given by the ordered pairs (2, 7).
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A spinner has 10 equally sized sections, 6 of which are gray and 4
of which are blue. The spinner is spun twice. What is the probability that the first spin lands on blue and the second spin lands on gray.
Step-by-step explanation:
since both spins are independent events (one does not have any impact on the other), the sequence does not matter. the probability of first blue and then gray is the same as first gray and then blue.
it is the probability of getting 1 gray and 1 blue result.
a probability is always the ratio
desired cases / totally possible cases.
since 6/10 of the area of the spine are gray, and 4/10 of the area are blue, the probability for any single spin to result in gray is 6/10 = 3/5 = 0.6.
and the probability to result in blue is 4/10 = 2/5 = 0.4
the probability to get 1 gray and 1 blue is then the product of both probabilities :
0.6 × 0.4 = 0.24
it is like rolling a die twice and asking for e.g. two 6s or any other combination of 2 specific numbers. that probability is
1/6 × 1/6 = 1/36
FYI :
the probability of getting gray twice is then
0.6 × 0.6 = 0.36
the probability of getting blue twice is
0.4 × 0.4 = 0.16
as mentioned to get gray first and blue second is
0.6 × 0.4 = 0.24
to get blue first and gray second
0.4 × 0.6 = 0.24
and these are all the possible results you can get in 2 spins.
therefore, the probability for any of them is
0.36 + 0.16 + 0.24 + 0.24 = 1
Find the reduction formula for the following integrals
In = ∫cot^n dx, then find I4
The reduction form is [tex]I_4 i= cot^3 x =ln |sin x| - 3 cot x + 3x + C[/tex].
To find the reduction formula for ∫cot^n x dx, we can use integration by parts. Let u = cot^(n-1) x and dv = cot x dx, then[tex]du = (n-1)cot^(n-2) x csc^2[/tex]x dx and v = ln |sin x|. By the formula for integration by parts, we have:
∫cot^n x dx = ∫u dv = uv - ∫v du
= [tex]cot^(n-1) x ln |sin x| - (n-1) ∫cot^(n-2) x csc^2 x ln |sin x| dx.[/tex]
This gives us the reduction formula:
[tex]I_n = ∫cot^n x dx = cot^(n-1) x ln |sin x| - (n-1) I_(n-2).[/tex]
Using this formula, we can find I_4 as follows:
[tex]I_4 = ∫cot^4 x dx = cot^3 x ln |sin x| - 3 I_2\\= cot^3 x ln |sin x| - 3 ∫cot^2 x dx\\= cot^3 x ln |sin x| - 3 (cot x - x) + C,\\[/tex]
where C is the constant of integration. Therefore, the solution for I_4 is [tex]cot^3 x ln |sin x| - 3 cot x + 3x + C.[/tex]
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22. Your choir is taking a trip. The trip has an initial cost of $500, plus $150 for
each student.
a. Estimate how many students must go on the trip for the average cost
per student to fall to $175.
b. What happens to the average cost as more students go on the trip?
a. There would be at least 20 students must go on the trip for the average cost per student to fall to $175.
b. As more students go on the trip, the total cost of the trip increases, but the cost per student decreases.
a. To find out how many students must go on the trip for the average cost per student to fall to $175, we can use the formula:
Total Cost = $500 + $150 x Number of Students
Average Cost per Student = Total Cost / Number of Students
Setting the average cost per student to $175 and solving for the number of students, we get:
$175 = ($500 + $150 x Number of Students) / Number of Students
Multiplying both sides by Number of Students, we get:
$175 x Number of Students = $500 + $150 x Number of Students
Simplifying, we get:
$25 x Number of Students = $500
Number of Students = $500 / $25 = 20
Therefore, at least 20 students must go on the trip for the average cost per student to fall to $175.
b. As more students go on the trip, the total cost of the trip increases, but the cost per student decreases. This is because the fixed cost of $500 is spread over more students, making the cost per student lower. So, as more students go on the trip, the average cost per student will continue to decrease.
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Find the area of a parallelogram with the given vertices: p(3, 3), q(5, 3), r(7, 7), s(9, 7). a. 16 units2 b. 8 units2 c. 4 units2 d. none of these
The area of the parallelogram is 8 units², which is option (b).
To find the area of a parallelogram, we need to use the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we can use the distance formula to find the base and height.
Base = distance between points P and Q
= √[(5-3)² + (3-3)²]
= √4
= 2 units
Height = distance between point P and the line containing points R and S. We can find the equation of this line by first finding its slope:
slope = (y2 - y1)/(x2 - x1)
= (7 - 7)/(9 - 7)
= 0
Since the slope is 0, the line is horizontal and has an equation of y = 7. Therefore, the height is the distance between point P and this line, which is:
Height = distance from point P to line y = 7
= |3 - 7|
= 4 units
Now we can plug in the values of b and h into the formula A = bh:
A = 2 x 4
= 8 units²
Therefore, the area of the parallelogram is 8 units², which is option (b).
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what is the answer to 8 units away from zero.
Answer:
Step-by-step explanation:
Write and solve an inequality to represent the scenario, then explain the solution.
Brianna has a $50 online gift certificate from a book store. The cost of each book is $9. There is also a shipping charge of $5 for her entire order. How many
books can Brianna buy without spending more than her gift certificate amount?
Enter the correct answers in the boxes.
Brianna can buy up to 5 books without spending more than her gift certificate amount.
We can set up the inequality: 9x + 5 <= 50. where x is the number of books Brianna can buy. To solve for x, we can start by subtracting 5 from both sides of the inequality: 9x <= 45
Divide both sides by 9: x <= 5. The inequality 9x + 5 <= 50 represents the fact that the total cost of Brianna's order (the cost of the books plus the shipping charge) should not exceed the amount of her gift certificate, which is $50.
We subtracted 5 from both sides to isolate the term 9x and then divided by 9 to solve for x, which represents the number of books she can buy. The solution, x <= 5, indicates that Brianna can buy up to 5 books without going over her gift certificate amount.
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The kinetic energy of a moving object varies directly with the square of its velocity. A bowling ball traveling at 15 meters per second has about 1000 joules of energy.
Write the equation that relates the kinetic energy, E, to its velocity, v.
Round your answer to the nearest hundredth.
About how much energy will a bowling ball have if it is moving at 11 meters per second?
Use your answer from part one. Round your answer to the nearest hundredth
A bowling ball moving at 11 meters per second will have approximately 537.64 joules of energy, rounded to the nearest hundredth.
The kinetic energy (E) of a moving object varies directly with the square of its velocity (v). To write the equation relating E to v, we can use the formula: E = k * v^2, where k is a constant of proportionality. Given a bowling ball traveling at 15 meters per second with 1000 joules of energy, we can find the value of k:
1000 = k * (15^2)
1000 = k * 225
k ≈ 4.44
So, the equation relating the kinetic energy and velocity is: E ≈ 4.44 * v^2.
Now, we want to find the energy of the bowling ball when it's moving at 11 meters per second. Using the derived equation:
E ≈ 4.44 * (11^2)
E ≈ 4.44 * 121
E ≈ 537.64
Therefore, a bowling ball moving at 11 meters per second will have approximately 537.64 joules of energy, rounded to the nearest hundredth.
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Complete question:
The kinetic energy of a moving object varies directly with the square of its velocity. A bowling ball traveling at 15 meters per second has about 1000 joules of energy.
Write the equation that relates the kinetic energy, E, to its velocity, v.
Round your answer to the nearest hundredth.
About how much energy will a bowling ball have if it is moving at 11 meters per second?
Use your answer from part one. Round your answer to the nearest hundredth
I will mark you brainliysit help
WHAT IS 2X36 DIVED BY 3 PLUS 9 -4=
HEEELPPP
Answer:
Step-by-step explanation:
2 x 36 ÷ 3 + 9 - 4
= 72 ÷ 3 + 9 - 4 (perform multiplication first)
= 24 + 9 - 4 (perform division)
= 29 (perform addition and subtraction)
Therefore, 2x36 ÷ 3 + 9 - 4 = 29.
Answer:
29
Step-by-step explanation:
2×36=72
72/3=24
24+9=33
33-4=29
How many cube ds will fit into cube a? enter the max amount.
1 cm
cm
in
сті
1
cm
1 cm
1 cm
cube a
cm
ст
2
cube b
ст
1
cm
ст
1 3
3
ст
cube c
cube d d
1 2 3
5
cinish
As per the given dimension, we need 343 small cubes to completely cover the larger cube.
To determine how many small cubes are needed to cover the larger cube, we need to think about how many of the smaller cubes can fit inside the larger cube.
We can start by looking at the dimensions of the larger cube. Each side is 7cm long, so the volume of the cube can be calculated by multiplying the length, width, and height:
7cm x 7cm x 7cm = 343 cubic centimeters
Now let's consider the dimensions of the smaller cubes. Each cube is 1cm x 1cm x 1cm, so the volume of each cube is:
1cm x 1cm x 1cm = 1 cubic centimeter
To determine how many of these smaller cubes are needed to cover the larger cube, we need to divide the volume of the larger cube by the volume of each small cube:
343 cubic centimeters ÷ 1 cubic centimeter = 343
So we need 343 small cubes to completely cover the larger cube.
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Complete Question:
How many cubes of dimensions 1cm*1cm*1cm are required to cover a cube of dimensions 7cm*7cm*7cm?
D Moon 17 The sun is composed primarily of A wat A one average star C. Three stars D. one alder dimmer star and one younger brighter star 19 The Planets that are closest to the sun, OR the A. Moon B. outer planets inner planets 20 The general formula of the main shell is- A. 2n Proto B. Proto 8. several stars spread across 21. All spin in the same direction except one. A. Mercury B. Venus 22. Which of the following is the inner planet in the solar system? 8. Jupiter C. Uranus D. Saturn 23. Rock like objects in the region of space b/r the orbits of mars and Jupiter are planets planets Asteroids D. Meteorites Asteroids A. Comets B. are rocky and are similar in
Therefore , the solution of the given problem of unitary method comes out to be space between Mars' and Jupiter's orbits contains rock-like objects.
An unitary method is defined as what?To complete the work, the well-known straightforward strategy, actual variables, and any essential components from the very first and specialised inquiries can all be utilised. In response, customers might be given another opportunity to sample the product. Otherwise, important advancements in our comprehension of algorithms will be lost.
Here,
What makes up the majority of the sun?
hydrogen a
The names of the planets nearest to the sun are:
Inner planets, B
A. 2n² is the general formula for the main shell.
Except for one planet, all of them revolve in the same direction. What planet is that?
(1) Venus
Which of the following is the solar system's inner planet?
Mercury, a.
The region of space between Mars' and Jupiter's orbits contains rock-like objects, which are known as:
Asteroid C.
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Waukegan, Illinois, had a population of 149,000 in the year 2019. The infrastructure of the city allows for a carrying capacity of 150,000 people. rmax = 0.8 for Waukegan.
What will be the population growth rate for 2019? Round to the nearest person.
What will be the population size at the start of 2020? Round to the nearest person.
The population growth rate for 2019 would be 800 people.
The population size at the start of 2020 would be 149, 800 people.
How to find the growth rate ?The formula is:
Growth rate = rmax × Population × ( 1 - ( Population / Carrying Capacity ) )
Growth rate = 0.8 × 149,000 × ( 1 - ( 149, 000 / 150, 000) )
Growth rate = 0.8 × 149, 000 × 0. 0067
Growth rate = 800 people
The population size at the start of 2020 would therefore be:
= Initial Population + Growth Rate
= 149, 000 + 800
= 149, 800 people
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Helppppp this is hard. i will give brainiest to the answer. i need it by 30 mins. please help
Of course! Please let me know what you need help with and I'll do my best to assist you within the given time frame.
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A cube is cut into two pieces by a single slice that passes through the points A, B, and C.
What shape is the cross section.
1. Rectangle
2. Triangle
3. Square
4. Trapezoid
The correct option is (2) triangle, because the slice intersects the cube face at three non-collinear points.
How many edges does a cube have?When a cube is cut by a single slice passing through three non-collinear points on a face, the shape of the cross section will be the intersection of the slice with the cube face. In this case, the slice passes through points A, B, and C, which are non-collinear, and thus the shape of the cross section will be a triangle.
This is because a triangle is the only shape that can be formed by the intersection of a plane with three non-collinear points on a flat surface, such as the face of a cube. The other options of rectangle, square, and trapezoid are not possible since they cannot be formed by the intersection of a plane with three non-collinear points on a flat surface.
A rectangle can only be formed by the intersection of a plane with four points that form a right angle, a square can only be formed by the intersection of a plane with four points that form a right angle and are equidistant from each other, and a trapezoid can only be formed by the intersection of a plane with four points that are not collinear, but only two of which are parallel.
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write the equation that gives the number of tickets sold, y, as a linear function of the number of hours, i, since the tickets have been on sale. enter your
answer in the box.
The linear function representing relation of the number of tickets sold and number of hours since tickets have been on sale is given by y = 32x.
Let us consider the two points of the linear function are,
(x₁, y₁) = (2, 64) and (x₂, y₂) = (6, 192).
Use the two-point form of the equation of a line .
Equation of linear function shows relationship between number of tickets sold y and the number of hours since tickets have been on sale x
Slope of the line is,
slope = (y₂ - y₁) / (x₂ - x₁)
= (192 - 64) / (6 - 2)
= 128 / 4
= 32
Apply the point-slope form of the equation of a line with the point (2, 64),
y - y₁= m(x - x₁)
⇒ y - 64 = 32(x - 2)
⇒ y - 64 = 32x - 64
⇒ y = 32x
Check if the equation of the line passes through the third point (18, 576),
y = 32x
⇒576 = 32(18)
⇒576 = 576
Since the equation of the line passes through all three points,
Therefore, linear function between the number of tickets sold and number of hours since tickets have been on sale is y = 32x.
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The above question is incomplete, the complete question is:
A linear function has the table of values shown. The information in the table shows the number of tickets sold on opening night of a movie as a function of the number of hours since the tickets have been on sale.
Number of Hours (x) 2 6 18
Number of Tickets Sold (y) 64 192 576
Write the equation that gives the number of tickets sold, y, as a linear function of the number of hours, x, since the tickets have been on sale. Enter your answer in the box
A municipality has budgeted r80 000 for putting up new street name boards the street name boards cost r134 each. how many new street name boards can be put up, and how much money will be left in the budget?
we first need to find out how many street name boards can be purchased with a budget of R80,000. We can do this by dividing the budget by the cost of each street name board:
R80,000 ÷ R134 = 597.01
Since we cannot purchase a fraction of a street name board, we round down to the nearest whole number. Therefore, the municipality can purchase 597 new street name boards with a budget of R80,000.
To find out how much money will be left in the budget, we can subtract the cost of the street name boards from the initial budget:
R80,000 - (597 x R134) = R1,598
Therefore, the municipality will have R1,598 left in their budget after purchasing 597 new street name boards.
Street name boards are an important part of any municipality as they help residents navigate and locate specific areas. By budgeting for and installing new street name boards, the municipality is taking a proactive approach to improve their community's infrastructure and ensure the safety and well-being of their residents.
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so if i went to park at 4:30 and it took me 24 minutes , when did i leave home
I must have left home at 4:54 PM in order to arrive at the park at 4:30 PM after 24 minutes of travel time.
When was the time I left home?Given the parameters in the question: if i went to park at 4:30 and it took me 24 minutes
Arrival time = 4 : 30PM
Travel time = 24 minutes
I can determine when i left home by simply subtracting the travel time from the time I arrived.
Hence,
Add the travel time to the time you arrived at the park.
4:30 PM (arrival time) + 24 minutes (travel time) = 4:54 PM
Therefore, I must have left home at 4:54 PM.
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What is the process of solving this?
The solution of the trigonometric equation
cos(2x) = cos(x) + 2
is x = 180°
How to solve the trigonometric equation?Here we want to solve the equation:
cos(2x) = cos(x) + 2
First, we know that:
cos(2x) = 2cos(x)² - 1
Then we can rewrite:
2cos(x)² - 1 = cos(x) + 2
We can define:
cos(x)= y
2y² - 1 = y + 2
Then we need to solve the quadratic:
2y² - 1 - y - 2 =0
2y² - y - 3 = 0
Using the quadratic formula we will get:
[tex]y = \frac{1 \pm \sqrt{(-1)^2 - 4*2*2*-3} }{2*2} \\\\y = \frac{1 \pm 5}{4}[/tex]
so the solutions are:
y = (1 + 5)/4 = 6/4
y = (1- 5)/4 = -1
And remember that y = cos(x), then y = 6/4 can be discarded.
Then the solution comes from:
cos(x) = -1
then x = pi = 180°
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Consider the following function f(x)=x^2+5
part a write a function in vertex form that shifts f(x) right 3 units
part b write a function in vertex form that shifts f(x) left 10 unites
Part a: f(x) = (x-3)^2 + 5
Part b: f(x) = (x+10)^2 + 5
Part a: To shift the function f(x) = x^2 + 5 right 3 units, we need to subtract 3 from the x-coordinate of the vertex. The vertex form of a quadratic function is given by f(x) = a(x-h)^2 + k, where (h,k) is the vertex. Thus, the function in vertex form that shifts f(x) right 3 units is:
f(x) = (x-3)^2 + 5
Part b: To shift the function f(x) = x^2 + 5 left 10 units, we need to add 10 to the x-coordinate of the vertex. Using the same vertex form as before, the function in vertex form that shifts f(x) left 10 units is:
f(x) = (x+10)^2 + 5
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2.
(03. 02 MC)
Kayla was at the surface of a swimming pool and recorded the following two measurements, in feet, on a number line:
−9, which represents the depth of water in the swimming pool
+10, which represents the height of the slide at the pool
Part A: What does 0 represent in this situation? (3 points)
Part B: Describe the height of the slide in relation to 0 in the situation. (3 points)
Part C: Kayla held a pole in the swimming pool. The bottom of the pole was at a depth of 3 feet. How should Kayla mark the level of the bottom of the pole on the number line? Explain how you determined this. (4 points)
0 represents the surface level of the swimming pool.
The height of the slide in relation to 0 is +10 feet.
Part A: In this situation, 0 represents the surface level of the swimming pool on the number line, acting as a reference point between the depth of the water and the height of the slide.
Part B: The height of the slide in relation to 0 is +10 feet. This means the slide is 10 feet above the surface level of the swimming pool.
Part C: To mark the level of the bottom of the pole on the number line, Kayla should mark it at -3 since the bottom of the pole is at a depth of 3 feet below the surface level of the pool.
This is determined by using the negative value to represent the depth below the surface (0).
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PLEASE HELP. A painting canvas has a length that measures 3( to the fifth power)mm. The width of the canvas measures 3(to the seventh power)mm. If lea wants to divide the canvas into sections that contain an area of 3( to the eighth power)mm( squared). How many sections can she create on the canvas ?
If lea wants to divide the canvas into sections that contain an area of 3 then Lea can create 81 sections on the canvas.
To find the number of sections Lea can create on the painting canvas, given the length is 3^5 mm, the width is 3^7 mm, and each section has an area of 3^8 mm^2 we should follow the steps given below:
Step 1: Calculate the total area of the canvas by multiplying the length and the width.
[tex]Total area = (3^5 mm) * (3^7 mm)[/tex]
Step 2: Use the property of exponents that states a^m * a^n = a^(m+n) to simplify the total area.
Total area = 3^(5+7) mm^2
Total area = 3^12 mm^2
Step 3: Divide the total area of the canvas by the area of each section to find the number of sections.
Number of sections = (3^12 mm^2) / (3^8 mm^2)
Step 4: Use the property of exponents that states a^m / a^n = a^(m-n) to simplify the number of sections.
Number of sections = 3^(12-8)
Number of sections = 3^4
Step 5: Calculate the numerical value of 3^4.
Number of sections = 81
Lea can create 81 sections on the canvas.
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The expedition team decides to have another practice run. Two team members head due north at a pace of 4 km/h. The second pair decide to head 60° west of north travelling at the same pace. How far from the first pair is the second pair after 2 h?
After the duration of 2 hours the distance between the first pair and the second pair is 3.07 km, under the condition that the second pair decide to head 60° west of north travelling at the same pace.
In order to evaluate the distance between two points with given coordinates, we can apply the distance formula. The distance formula is
d = √ [ (x₂ − x₁)² + (y₂ − y₁)² ]
Here,
(x₁, y₁) and (x₂, y₂) = coordinates of the two points.
For the given case, we can consider that the first pair of team members start at the origin (0, 0) and cover the distance towards north for 2 hours at a pace of 4 km/h.
Hence, their final position is (0, 8).
The second pair of team members take the origin (0, 0) and travel 60° west of north for 2 hours at a pace of 4 km/h.
Now to evaluate their final position, we have to find their coordinates. Let us consider their final position (x, y).
We can apply trigonometry to find x and y.
The angle between their direction of travel and the y-axis is 60°.
sin(60°) = y / d
cos(60°) = x / d
Here,
d = distance travelled by the second pair of team members.
It is given that they travelled for 2 hours at a pace of 4 km/h.
d = 2 hours × 4 km/h
= 8 km
Staging this value into the above equations
y = d × sin(60°) = 8 km × sin(60°)
≈ 6.93 km
x = d × cos(60°) = 8 km × cos(60°)
≈ 4 km
Hence, the final position regarding the second pair of team members is approximately (4 km, 6.93 km).
Now we can apply the distance formula to evaluate the distance between the two pairs of team members
d = √ [ (x₂ − x₁)² + (y₂ − y₁)² ]
d = √ [ (4 − 0)² + (6.93 − 8)² ]
d ≈ 3.07 km
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In triangle ABC, angle B is a right angle. Give me measures of side BC and hypotenuse AC so that the measure of Angle A is greater than 75 degrees
In triangle ABC with angle B as a right angle, if the measure of angle A is greater than 75 degrees (e.g., 80 degrees), side BC can be approximately 9.848 units, and the hypotenuse AC can be 10 units.
In triangle ABC with angle B as a right angle, to find measures of side BC and hypotenuse AC such that the measure of angle A is greater than 75 degrees, we can use the sine function.
Determine the sine of angle A. Since angle A needs to be greater than 75 degrees, let's choose 80 degrees as an example.
sin(80°) = opposite side (BC) / hypotenuse (AC)
Choose a convenient value for the hypotenuse (AC). Let's choose AC = 10 units.
Solve for the opposite side (BC).
sin(80°) = BC / 10
BC = 10 * sin(80°)
BC ≈ 9.848
If the measure of angle A is more than 75 degrees (for example, 80 degrees), side BC and the hypotenuse AC in the triangle ABC with a right angle can both be 10 units.
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Work out the size of angle h.
h
125⁰
Answer:
when it's maintain supplimentary , it means that the sum of the angles given is 180° , In this case let one of the angle be x and the other is given as 125° .
therefore
125° + x = 180°
x = 180° - 125° = 55°
the compliment of x is the angle which when added to x givens 90° , Let the angle be y.
therefore
x + y = 90°
y = 90° - x = 90° - 55° = 35°
35° is the answer
Read the following question:
Answer: 5 hours of service
Step-by-step explanation:
25 + x(15) = 20x
⇒ 25 = 20x - 15x
⇒ 25 = 5x
⇒ x = 5
