Answer:
m = -4
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (-3,12) (-2,8)
We see the y decrease by -4, and the x increase by 1, so the slope is
m = -4
So, the slope of the line representing by the data is -4.
For the acute angles in a right triangle, sin(5x)° = cos(3x + 2)°.
What is the number of degrees in the measure of the smaller
angle?
Answer is The smaller angle is 35°.
To solve for the acute angles in a right triangle when sin(5x)° = cos(3x + 2)°, we need to use trigonometric identities.
Recall that sin(x) = cos(90 - x) for any angle x. Using this identity, we can rewrite sin(5x)° as cos(90 - 5x)°.
Similarly, cos(x) = sin(90 - x) for any angle x. Using this identity, we can rewrite cos(3x + 2)° as sin(90 - (3x + 2))°, which simplifies to sin(88 - 3x)°.
Now we have cos(90 - 5x)° = sin(88 - 3x)°. Since these two expressions are equal, we can set them equal to each other and solve for x:
cos(90 - 5x)° = sin(88 - 3x)°
sin(5x)° = sin(88 - 3x)°
5x = 88 - 3x
8x = 88
x = 11
Therefore, the acute angles in the right triangle are 5x° and 90 - 5x°, or 55° and 35°. The smaller angle is 35°.
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Select the correct answer.
given a prism with a right triangle base and the dimensions and what is a correct expression for the volume of the prism?
The correct expression for the volume of a prism with a right triangle base can be obtained by multiplying the area of the base by the height of the prism. For a right triangle base, the area can be calculated as half the product of the base and height of the triangle, given by the formula A = (1/2)bh.
Let's say the dimensions of the right triangle base are b and h, and the height of the prism is denoted by H. Then, the volume of the prism can be expressed as V = A × H = (1/2)bh × H = (bhH)/2.
This expression represents the volume of the prism in terms of its base dimensions and height. It is important to note that the units of the dimensions should be consistent in order to get the volume in a suitable unit. For example, if the base dimensions are in centimeters and the height is in meters, the volume should be converted to cubic meters or cubic centimeters depending on the required accuracy.
In conclusion, the volume of a prism with a right triangle base can be calculated by multiplying the area of the base by the height of the prism. For a right triangle base, the area is given by (1/2)bh, and the volume can be expressed as (bhH)/2.
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what is the volume of a cylinder with a radius of 2.5 and a height of 4 answer in terms of pi
options:
-20 5/6π
-25π
-8 1/3π
-15 5/8π
Step-by-step explanation:
volume of a cylinder is pi × r² × height
r = 2.5
height= 4
volume = pi × 2.5² × 4
volume = 25 pi
Juliet wants to know if the chicken broth in this beaker will fit into this rectangular food storage container. Explain how you would figure it out without pouring the contents in. If it will fit, how much more broth could the storage container hold? If it will not fit, how much broth will be left over? (Remember: 1 cm = 1 mL. )
The container could hold an additional 870 mL of broth if it is already holding the 90 mL of broth from the beaker.
To figure out if the chicken broth in the beaker will fit into the rectangular food storage container, we need to compare the volume of the beaker to the volume of the container.
The volume of the beaker can be calculated by multiplying its base area (which is the same as the area of the circle at the bottom of the beaker) by its height. The volume of the container can be calculated by multiplying its length, width, and height.
If the volume of the beaker is less than or equal to the volume of the container, then the chicken broth will fit. If it is greater, then the chicken broth will not fit.
To find out how much more broth the container could hold if it fits, we can subtract the volume of the beaker from the volume of the container.
For example, if the beaker has a diameter of 6 cm and a height of 10 cm, then its volume would be:
V_beaker = πr^2h = π(3^2)(10) = 90π cm^3 = 90 mL
If the rectangular food storage container has dimensions of 12 cm x 8 cm x 10 cm, then its volume would be:
V_container = lwh = 12(8)(10) = 960 cm^3 = 960 mL
Since 90 mL (the volume of the beaker) is less than 960 mL (the volume of the container), the chicken broth will fit in the container. The amount of broth the container can hold in addition to the beaker's contents would be: 960 mL - 90 mL = 870 mL
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Solid cylinders A and B are similar and made from metal. 72.8% more metal is used to make cylinder B than cylinder A. The surface area of cylinder A is 700cm². Work out the surface area of cylinder B
If the surface area of cylinder A is 700cm², the surface area of cylinder B is 1612.8cm².
Since the two cylinders are similar, their dimensions are proportional to each other. Let the height and radius of cylinder A be h and r, respectively, and let the height and radius of cylinder B be kh and kr, respectively, where k is the scale factor.
Since cylinder B uses 72.8% more metal than cylinder A, we have:
Volume of cylinder B = 1.728 times the volume of cylinder A
Using the formula for the volume of a cylinder, we have:
π(kr)²(kh) = 1.728πr²h
Simplifying the equation, we get:
k³ = 1.728
k = 1.2
So the scale factor is 1.2. Therefore, the height and radius of cylinder B are 1.2 times those of cylinder A. Hence, we have:
Surface area of cylinder B = 2π(1.2r)² + 2π(1.2r)(1.2h)
= 2.304(2πrh)
= 2.304(700cm²)
= 1612.8cm²
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Jerry has the following assets a house with equity of $15. 0. A car with equity of $2. 500, and household goods worth $6,000 (no single item over $400). He also has tools worth $5. 800 that he needs for his business. Using the federal list, the total amount of exemptions that Jerry would be allowed is $____. 0. Using the state list, the total amount of exemptions that jerry would be allowed is $____. 0.
00. Using the state list the total amount of exemptions that Jerry would be allowed is s
. 0. The state
list will be more favorable for him
tially Connect
Using the federal list, the total amount of exemptions that Jerry would be allowed is $25,150.
Jerry's assets include a house with equity of $15,000, a car with equity of $2,500, household goods worth $6,000 (no single item over $400), and tools worth $5,800 that he needs for his business.
Using the state list, the total amount of exemptions that Jerry would be allowed varies depending on the state in which he resides. Without knowing the state, it is impossible to provide an accurate answer. However, it is worth noting that the state list is often more favorable for individuals than the federal list.
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Latoya has a bag with 8 balls numbered 1 through 8. She is playing a game of chance. This game is this: Latoya chooses one ball from the bag at random. She wins $1 if the number 1 is selected, $2 if the number 2 is selected, $3 if the number 3 is selected, $4 if the number 4 is selected, and $5 if the number 5 is selected. She loses $1 if 6, 7, or 8 is selected.
(a) Find the expected value of playing the game. Dollars
(b) What can Latoya expect in the long run, after playing the game many times? (She replaces the ball in the bag each time. ) Latoya can expect to gain money. She can expect to win dollars per selection. Latoya can expect to lose money. She can expect to lose dollars per selection. Latoya can expect to break even (neither gain nor lose money)
Latoya may experience some fluctuations in her winnings and losses in the short run, in the long run, her average winnings will approach $0.50 per selection.
What is the expected value of playing the game and what Latoya can expect after playing the game many times?
(a) To find the expected value of playing the game, we need to multiply the amount that Latoya can win or lose by the probability of each outcome, and then add up the results. Let p(i) be the probability of selecting the ball with the number i. Since there are 8 balls in total and each ball is equally likely to be selected, we have:
p(i) = 1/8 for i = 1, 2, ..., 8
Now we can calculate the expected value:
E(X) = ∑[i=1 to 5] (i * p(i)) + ∑[i=6 to 8] (-1 * p(i))
= (1/8)(1) + (1/8)(2) + (1/8)(3) + (1/8)(4) + (1/8)(5)
- (1/8)(1) - (1/8)(1) - (1/8)(1)
= 0.5
Therefore, the expected value of playing the game is $0.50.
(b) In the long run, after playing the game many times, Latoya can expect to break even (neither gain nor lose money) on average per selection. This means that over a large number of selections, she can expect to win some money on some selections and lose some money on others, but on average, her total winnings and losses will balance out to zero.
To see why this is the case, consider that the expected value of a single selection is $0.50. If Latoya plays the game many times, the law of large numbers tells us that the average winnings per selection will converge to the expected value of $0.50. So even though Latoya may experience some fluctuations in her winnings and losses in the short run, in the long run, her average winnings will approach $0.50 per selection.
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A student at a local high school claimed that three-
quarters of 17-year-old students in her high school had
their driver's licenses. To test this claim, a friend of hers
sent an email survey to 45 of the 17-year-olds in her
school, and 34 of those students had their driver's
license. The computer output shows the significance test
and a 95% confidence interval based on the survey data.
Test and Cl for One Proportion
Test of p = 0. 75 vs p +0. 75
Sample X N Sample p 95% CI Z-Value P-Value
1
34 45 0. 755556 (0. 6300, 0. 086 0. 9315
0. 8811)
Based on the computer output, is there convincing
evidence that p, the true proportion of 17-year olds at this
high school with driver's licenses, is not 0. 75?
O No, the P-value of 0. 9315 is very large.
Yes, the P-value of 0. 9315 is very large.
O Yes, the 95% confidence interval contains 0. 75.
No, the incorrect significance test was performed.
The alternative hypothesis should be p > 0. 75.
No, the incorrect significance test was performed.
The alternative hypothesis should be p<0. 75.
The results of the survey suggest that the student's claim of three-quarters of 17-year-olds having their driver's licenses may be accurate, but further research would be necessary to confirm this with a larger and more representative sample.
Based on the computer output, there is no convincing evidence that the true proportion of 17-year-olds at this high school with driver's licenses is not 0.75. This is because the P-value of 0.9315 is very large, indicating that the results of the survey are not statistically significant. Additionally, the 95% confidence interval for the sample proportion of 0.755556 includes 0.75, further supporting the claim that the true proportion may be close to 0.75.
It is important to note that the correct significance test was performed, testing the null hypothesis that p = 0.75 against the alternative hypothesis that p ≠ 0.75. This is the appropriate test when the claim being tested is about a specific value of the proportion, as in this case. The alternative hypothesis being p > 0.75 or p < 0.75 would be incorrect, as it assumes a one-sided test rather than a two-sided test.
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Find the area of the parallelogram.
The figure shows a parallelogram. The length of the base is 20 centimeters. The length of the sides is 17 centimeters. The overhang of the base is 8 centimeters long. The angle between the overhang and the height is a right angle.
The area of the parallelogram is 300 centimetres squared.
How to find the area of a parallelogram?The length of the base is 20 centimetres. The length of the sides is 17 centimetres. The overhang of the base is 8 centimetres long. The angle between the overhang and the height is a right angle.
Therefore,
area of a parallelogram = b × h
where
b = baseh= heightTherefore, let's use Pythagoras's theorem to find the height of the parallelogram as follows
17² - 8² = h²
289 - 64 = h²
h = √225
h = 15 centimetres
Therefore,
area of the parallelogram = 20 × 15
area of the parallelogram = 300 cm squared
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Ghost riders co. has an eps of $1.65 that is expected to grow at 8.5 percent per year. if the pe ratio is 19.15 times, what is the projected stock price in 4 years?
The projected stock price of Ghost Rider Co. in 4 years is $45.24.
First, we need to calculate the future EPS of Ghost Rider Co. in 4 years. We can do this using the formula for the future value of an annuity:
[tex]FV = PV x (1 + r)^n[/tex]
where FV is the future value, PV is the present value, r is the growth rate, and n is the number of years.
Using this formula, we get:
[tex]FV = $1.65 x (1 + 0.085)^4 = $2.36[/tex]
Next, we can use the following formula to determine the anticipated stock price:
Estimated stock price = EPS x PE ratio
When we enter the values we have, we obtain:
Projected stock price = $2.36 x 19.15 = $45.24
Therefore, the projected stock price of Ghost Rider Co. in 4 years is $45.24.
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A survey asked 3, 800 students how they are likely
to spend their money. The original results of the
survey are shown.
Category
Food
Drinks
Clothing
Shoes
Accessories
Video
Games
Electronics
Personal
Care
Other
Number of
Students
967
895
816
455
59
143
237
105
123
Complete the statement.
Based on the results of the survey, a circle graph
would have [DROP DOWN 1] sectors that are labeled
as 10% or less and [DROP DOWN 21 sectors that are are labeled as
or less and [DROP DOWN 2] sectors that are labeled as
or more.
Based on the results of the survey, a circle graph would have 6 sectors that are labeled as 10% or less and 3 sectors that are labeled as more than 10%.
What would be the results of the survey?The survey results are as follows:
there are a total of 10 categories, 6 of which (Food, Drinks, Clothing, Shoes, Personal Care, and Other) have percentages equal to or below 10% while the other 4 (Accessories, Video Games, Electronics, and Other) have percentages above 10%.
Since the complete circle in a circle graph reflects 100% of the data, categories with a percentage of less than or equal to 10% will have smaller sectors in the graph than those with a percentage of more than 10%.
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2 Liam bought too much fencing and had 26 feet of it left over. He and his brother
decided to make a rectangle-shaped garden patch for their little sister. They wanted
to use all the extra fencing to outline her garden patch. What could be the dimen-
sions of the patch they make for their sister? (Use only whole numbers of feet. )
Show all your work.
The perimeter is indeed 26 feet, which means they have used all the extra fencing.
Let's start by assuming that the length and width of the garden patch are whole numbers of feet, since we are asked to use only whole numbers.
Let's call the length of the garden patch "L" and the width "W".
We know that Liam has 26 feet of fencing left over. This fencing will be used to make the perimeter of the garden patch, which is given by:
Perimeter = 2L + 2W
We can substitute the value of the perimeter with the amount of fencing that Liam has:
26 = 2L + 2W
Simplifying this equation, we get:
13 = L + W
Since we want to use all the extra fencing, we know that the perimeter of the garden patch must be 26 feet. We can use this information to write another equation:
Perimeter = 2L + 2W = 26
We can substitute the value of 13 for L + W in this equation:
2L + 2W = 26
2L + 2(13-L) = 26
2L + 26 - 2L = 26
26 = 26
This equation is true, which means that our assumption that L and W are whole numbers is correct.
Therefore, the dimensions of the garden patch that Liam and his brother can make for their sister are 6 feet by 7 feet.
To check, we can calculate the perimeter:
Perimeter = 2L + 2W = 2(6) + 2(7) = 12 + 14 = 26
So the perimeter is indeed 26 feet, which means they have used all the extra fencing.
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70°
is the same as
radians. Round your answer to the nearest thousandth.
70 degrees to radian is 1.22 radian.
How to convert from degree to radian?In mathematics,, both degree and radian represent the measure of an angle. One complete anticlockwise revolution can be represented by 2π (in radians) or 360° (in degrees).
Therefore,
360 degrees = 2π radian
where
π = 3.14Therefore, let's find 70 degrees in radian.
Hence,
360 degrees = 2π radian
70 degrees = ?
cross multiply
angle in radian = 70 × 2π / 360
angle in radian = 140π / 360
angle in radian = 0.38888888888 × 3.14
angle in radian = 1.22 radian
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at the three points 1. Sketch the vector field 7 (x,y) = xî + xyî (1,3), (-1,2), (3,-2)
The vector field for 7 (x,y) = xî + xyî (1,3), (-1,2), (3,-2) can be plotted with arrows with magnitude 4 at point (1,3), magnitude 3 at point (-1,2), and magnitude 3 at point (3,-2).
The given vector field 7 (x,y) = xî + xyî (1,3), (-1,2), (3,-2) can be drawn by plotting arrows at each point (x,y) in the plane with the direction and magnitude of each arrow presented by the vector
7 (x,y) = xî + xyî.
over point (1,3),
the vector is 7(1,3) = 1î + 3î = 4î.
over point (-1,2),
the vector is 7(-1,2) = -1î - 2î = -3î.
Over point (3,-2),
the vector is 7(3,-2) = 3î - 6î = -3î.
The vector field for 7 (x,y) = xî + xyî (1,3), (-1,2), (3,-2) can be plotted with arrows with magnitude 4 at point (1,3), magnitude 3 at point (-1,2), and magnitude 3 at point (3,-2).
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Write the coordinates of the vertices after a rotation 180° clockwise around the origin.
Answer:
it will be P'(y,-x) since it is clockwise direction and I anti clockwise the formula to find the coordinates will be (-y,x)
PLEASE ANSWER PLEASE PLEASE DUE IN 8 MINS PLEASE
“The window has the shape of a kite. How many square meters of glass were used to make the window?”
The area of glass value is 0.18 square meters.
The longer diagonal of the kite-shaped window has a measure of 25 cm + 35 cm = 60 cm.
The shorter diagonal has a measure of 30 cm + 30 cm = 60 cm as well.
To find the area of the window, we can use the formula -
Area = (1/2) × d1 × d2
where d1 and d2 are the lengths of the longer and shorter diagonals, respectively.
Substituting the values, we get -
Area = (1/2) × 60 cm × 60 cm
Area = 1800 square cm
However, the question asks for the area in square meters, so we need to convert square centimeters to square meters by dividing by 10,000 -
Area = 1800 / 10,000 square meters
Area = 0.18 square meters
Therefore, the area of glass value is 0.18 square meters.
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A velociraptor runs 5m [e] , 10 m [w], 3m [s], & 2m [w] in 10 seconds. calculate speed & velocity.
The velociraptor's speed is 2 m/s, and its velocity is -0.3 m/s [w].
What is the total distance covered?
To calculate the speed and velocity of the velociraptor, we need to first find the total distance it covered and the displacement.
Total distance = 5m + 10m + 3m + 2m = 20m
Displacement = Final position - Initial position
Displacement = (2m [w]) - (5m [e])
Displacement = -3m [w]
Velocity is defined as displacement per unit time, while speed is defined as distance per unit time.
Velocity = Displacement / Time
Velocity = -3m [w] / 10s
Velocity = -0.3 m/s [w]
Speed = Total distance / Time
Speed = 20m / 10s
Speed = 2 m/s
Therefore, the velociraptor's speed is 2 m/s, and its velocity is -0.3 m/s [w].
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What is the volume of a rectangle when the length is 3 1/3 the width is 4 2/3 and the height is 25
To find the volume of a rectangle APR prism, you need to multiply its length, width, and height. In this case, the length is 3 1/3 (or 10/3) units, the width is 4 2/3 (or 14/3) units, and the height is 25 units.
So, the volume of the rectangle can be calculated as:
Volume = length x width x height
Volume = (10/3) x (14/3) x 25
Volume = 1166.67 cubic units (rounded to two decimal places)
Therefore, the volume of the rectangle with a length of 3 1/3, a width of 4 2/3, and a height of 25 is approximately 1166.67 cubic units.
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URGENT !Tricia has 10 quarters, 17 dimes, 40 nickels, and 15 pennies.
How much money does Tricia have in all?
O A. $5. 15
B. $5. 85
OC. $6. 20
D. $6. 35
Tricia has a total of $6.35. The answer is D.
Tricia has 10 quarters, which is equivalent to $2.50 (since 1 quarter is $0.25).
She also has 17 dimes, which is equivalent to $1.70 (since 1 dime is $0.10).
Tricia has 40 nickels, which is equivalent to $2.00 (since 1 nickel is $0.05).
Finally, she has 15 pennies, which is equivalent to $0.15 (since 1 penny is $0.01).
To find the total amount of money Tricia has, we can add up the values of each coin:
$2.50 + $1.70 + $2.00 + $0.15 = $6.35
Therefore, Tricia has a total of $6.35. The answer is option D.
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Mathetmatics
Class - 6 question
Topic - Roman Numerals :-
Question:-
The number VCX is incorrect. Explain why?
Answer as fast as you can. I'l mark you as brainliest
In Roman Numerals, smaller numbers can be subtracted from larger numbers, but only to a certain extent.
The number VCX is incorrect in Roman Numerals because V (5) cannot be subtracted from X (10) to make 5, and C (100) cannot be subtracted from X (10) to make 90.
In Roman Numerals, smaller numbers can be subtracted from larger numbers, but only to a certain extent.
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given m||n, find the value of x
Answer:
Step-by-step explanation:
The value of x is 19 if the lines l and m are parallel.
The lines l and m are parallel
The corresponding angles are equal
We have to find the value of x
6x-9 = 5x+10
Let us take all the variable terms on one side
6x-5x=10+9
x=19
Hence, the value of x is 19 if the lines l and m are parallel.
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A tabletop in the shape of a trapezoid has an area of 7,021 square centimeters. its longer base measures 131 centimeters, and the shorter base is 105 centimeters. what is the height?
urgent
The height of the trapezoidal tabletop is approximately 59.5 centimeters.
To calculate the height of a trapezoid with the given measurements, we need to use the formula for the area of a trapezoid: A = (b1 + b2)h / 2, where A is the area, b1 and b2 are the lengths of the two bases, and h is the height.
In this problem, the area (A) is 7,021 square centimeters, the longer base (b1) is 131 centimeters, and the shorter base (b2) is 105 centimeters. Our task is to find the height (h).
First, let's plug the given values into the formula:
7,021 = (131 + 105)h / 2
Now, simplify the equation:
7,021 = 236h / 2
To solve for h, multiply both sides of the equation by 2:
14,042 = 236h
Finally, divide both sides by 236:
h ≈ 59.5
Thus, the height is approximately 59.5 centimeters.
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Looking at the spread of your data best fits which step of the statistical process?
Looking at the spread of your data is part of the data analysis step in the statistical process.
In this step, the data is examined to identify patterns, relationships, and trends in the data.
One aspect of data analysis is understanding the distribution and spread of the data, which can be done through measures of central tendency and measures of variability.
Understanding the spread of the data can help in making decisions about what statistical analyses are appropriate and how to interpret the results.
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Ms. paquette put one coat of paint on a rectangular wall that measured 25 1/2 feet by 10 feet. the paint that she bought was sold in 1-gallon containers.
Ms. Paquette used approximately 0.73 gallons of paint for one coat on the rectangular wall.
To determine how many gallons of paint Ms. Paquette used for one coat on the rectangular wall, we first need to calculate the total area of the wall.
Area of the wall = length x width
= 25.5 feet x 10 feet
= 255 square feet
Now, to find out how many gallons of paint are needed for one coat, we need to know the coverage rate of the paint. This information is usually provided on the paint can label. Let's assume that the coverage rate for the paint Ms. Paquette used is 350 square feet per gallon.
To calculate how many gallons of paint are needed, we can divide the total area of the wall by the coverage rate of the paint:
255 square feet ÷ 350 square feet per gallon = 0.7286 gallons
This means that Ms. Paquette used approximately 0.73 gallons of paint for one coat on the rectangular wall. Since paint is typically sold in 1-gallon containers, she would need to purchase at least one gallon of paint to complete one coat on this wall.
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50 POINTS AND BRAINLYEST Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over x = −1.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−5, 5), M′(−2, 3), O′(−3, 7)
N′(3, 2), M′(0, 1), O′(1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)
Answer:
N'(3, 2), M'(0, 1), O'(1, 3)
Step-by-step explanation:
Please sketch the graphs of the two triangles and the line of reflection to confirm my answer.
Since NMO is reflected over the line
x = -1, the y-coordinates of N'M'O' will remain the same. Since the x-coordinate of N is at -5, which is 4 units to the left of the line of reflection, the x-coordinate of N' is at -1 + 4 = 3. Since the x-coordinate of M is at -2, which is 1 unit to the left of from the line of reflection, the x-coordinate of M' is at -1 + 1 = 0. Since the x-coordinate of O is at -3, which is 2 units to the left of the line of reflection, the x-coordinate of O' is at -1 + 2 = 1. So the vertices of N'M'O' are at (3, 2), (0, 1), and (1, 3).
Find the particular solution for:
f"(x) = 0.25x⁻³/², f'(4) = - 1/8 and f(0) = 2.
The particular solution for f(x) is:
f(x) = (2/3)x³/² - (17/8)x + 2
How to find the particular solution of f(x)?We will integrate the given differential equation twice and use the initial conditions to find the constants of integration.
Given: f"(x) = 0.25x⁻³/²
Integrating once, we get:
f'(x) = ∫(0.25x⁻³/²) dx = 0.5x¹/² + C₁
where C₁ is the constant of integration.
Using the initial condition f'(4) = -1/8, we can solve for C₁:
f'(4) = 0.5(4)¹/² + C₁ = 2 + C₁ = -1/8
C₁ = -1/8 - 2 = -17/8
So,
f'(x) = 0.5x¹/² - 17/8
Integrating again, we get:
f(x) = ∫(0.5x¹/² - 17/8) dx = (2/3)x³/² - (17/8)x + C₂
where C₂ is the second constant of integration.
Using the initial condition f(0) = 2, we can solve for C₂:
f(0) = (2/3)(0)³/² - (17/8)(0) + C₂ = 2
C₂ = 2
So, the particular solution for f(x) is:
f(x) = (2/3)x³/² - (17/8)x + 2
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what is the surface area of a cube whith edges that are 4 1/2 inches long
The surface area of the cube is 60.75 in²
What is surface area of cube?Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. The sides and surfaces of a cube are equal. A cube can also be called square prism.
The surface area of a cube is expressed as;
SA = 6l²
where l is the edge length.
l = 4 1/2 = 9/2
SA = 6(9/2)²
SA = 6 × 81/4
SA = 243/4
= 60.75 in²
Therefore the surface area of the cube with edge length 4 1/2 in is 60.75 in²
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The equation of the line of best fit is M(t)=-0.15t+3.70 where M (t) represents the average retail cost in dollars of whole milk in the united state
The function M(2) from the equation of the line of best fit M(t)=-0.15t+3.70 is M(2) = 3.4
The equation of the line of best fit is given as
M(t) = -0.15t + 3.70
The function M(2) means the value of the variable t is 2
i.e. t = 2
To calculate M(2), we substitute the known values of t = 2 in the equation M(t) = -0.15t + 3.70
So, we have
M(2) = -0.15 * 2 + 3.70
Evaluate the product in the expression
This gives
M(2) = -0.30 + 3.70
Evaluate the sum/difference in the expression
This gives
M(2) = 3.4
The above is the value of M(2)
Hence, the calculated value of M(2) is 3.4
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Ben makes orange paint by mixing red, yellow and white paint in the ratio 20 : 16 : 1. 5. How much of each colour does he need to make 1. 5 litres of orange paint?
Using the ratio, we solve and get, Ben needs 0.8 litres of red paint, 0.64 litres of yellow paint, and 0.06 litres of white paint to make 1.5 litres of orange paint.
To make 1.5 litres of orange paint, Ben needs to mix the red, yellow, and white paint in the ratio of 20 : 16 : 1.5.
To calculate the amount of each color needed, you first need to find the total number of parts in the ratio.
The total number of parts is 20 + 16 + 1.5 = 37.5.
Next, you can calculate the amount of each color needed by dividing 1.5 litres by the total number of parts in the ratio, and then multiplying by the respective parts for each color.
So, the amount of red paint needed is:
(1.5/37.5) x 20 = 0.8 litres
The amount of yellow paint needed is:
(1.5/37.5) x 16 = 0.64 litres
And the amount of white paint needed is:
(1.5/37.5) x 1.5 = 0.06 litres
Therefore, Ben needs 0.8 litres of red paint, 0.64 litres of yellow paint, and 0.06 litres of white paint to make 1.5 litres of orange paint.
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Draw the image of ABC under the translation by 1 unit to the right and 4 units up
The image of ABC under the translation by 1 unit to the right and 4 units up is the triangle with vertices A', B', and C'.
What is Triangle?A triangle is a closed two-dimensional geometric shape with three straight sides and three angles. It is one of the basic shapes in geometry and has been studied since ancient times. To translate a figure by a given vector, you need to move each point of the figure by the same amount and in the same direction as the vector. In this case, we want to translate ABC by a vector of (1, 4), which means we need to move each point of ABC one unit to the right and four units up.
Let's say the coordinates of the points of ABC are:
A = [tex]\rm (x_1, y_1)[/tex]
B = [tex]\rm (x_2, y_2)[/tex]
C = [tex]\rm (x_3, y_3)[/tex]
To translate ABC by the vector (1, 4), we add 1 to each x-coordinate and 4 to each y-coordinate:
A' = [tex]\rm (x_1 + 1, y_1 + 4)[/tex] (x₁ + 1, y₁ + 4)
B' = [tex]\rm (x_2 + 1, y_2 + 4)[/tex] (x₂ + 1, y₂ + 4)
[tex]\rm C' = (x_3 + 1, y_3 + 4)[/tex] (x₃ + 1, y₃ + 4)
Therefore, The image of ABC under the translation by 1 unit to the right and 4 units up is the triangle with vertices A', B', and C'.
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