Answer: 5 and 2
Step-by-step explanation:
In an arithmetic sequence, the difference between consecutive terms is constant. Since the third and fourth terms are -1 and -4, the common difference is -4 - (-1) = -3. Therefore, the second term is -1 - (-3) = 2 and the first term is 2 - (-3) = 5. So the first and second terms of the sequence are 5 and 2 respectively.
Frank spends $90 on his $1800 monthly income what percent of monthly check does not go toward food
If Frank spends $90 on his $1800 monthly income, then 95 percent of monthly check does not go toward food.
Let's say Frank spends $90 on food and has a monthly income of $1800. We can calculate the percentage of his monthly check that does not go towards food as follows:
Percentage = (Total Income - Food Expenses) / Total Income
Percentage = (1800 - 90) / 1800
Percentage = 0.95 = 95%
Therefore, 95% of Frank's monthly check does not go towards food.
Here are the steps in detail:
Subtract the food expenses from the total income to get the amount of money that is not spent on food.
Divide the amount of money that is not spent on food by the total income to get the percentage.
In this case, the amount of money that is not spent on food is $1800 - $90 = $1710. The percentage of the monthly check that is not spent on food is $1710 / $1800 = 0.95 = 95%.
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What is Mine-craft Incorrect Responses Only
Mine-craft Incorrect Responses is known to be a sort of game or challenge where members are inquired to reply to Mine-craft-related questions or explanations with intentioned inaccurate answers.
What is Mine-craft?
The thought is to utilize humor and creativity to come up with reactions that are totally off-base but still somehow related to Mine-craft.
Mine-craft Incorrect Responses is an amusing way of reacting to questions or statements related to the prevalent sandbox video diversion Mine-craft with intentioned off base answers. The objective is to be as imaginative and amusing as conceivable whereas intentionally giving off-base answers to Mine-craft-related questions or comments.
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In tetrahedron $ABCO,$ $\angle AOB = \angle AOC = \angle BOC = 90^\circ.$ A cube is inscribed in the tetrahedron so that one of its vertices is at $O,$ and the opposite vertex lies on face $ABC.$ Let $a = OA,$ $b = OB,$ and $c = OC.$ Show that the side length of the cube is
\[\frac{abc}{ab + ac + bc}.\]
[asy]
import three;
size(180);
currentprojection = orthographic(6,3,2);
real a, b, c, s;
triple A, B, C, O;
a = 6;
b = 3;
c = 2;
s = a*b*c/(a*b + a*c + b*c);
A = (a,0,0);
B = (0,b,0);
C = (0,0,c);
O = (0,0,0);
draw(O--A,dashed);
draw(O--B,dashed);
draw(O--C,dashed);
draw(A--B--C--cycle);
draw((0,0,s)--(s,0,s)--(s,0,0)--(s,s,0)--(0,s,0)--(0,s,s)--cycle,dashed);
draw((s,s,0)--(s,s,s),dashed);
draw((s,0,s)--(s,s,s),dashed);
draw((0,s,s)--(s,s,s),dashed);
label("$A$", A, SW);
label("$B$", B, E);
label("$C$", C, N);
dot("$O$", O, NW);
dot((s,s,s));
[/asy]
pls help me
Answer:
Step-by-step explanation:To solve this problem, we can use similar triangles. Let the side length of the cube be s, and let the midpoints of AB, AC, and BC be P, Q, and R, respectively. Then OP, OQ, and OR are the diagonals of the faces of the cube, and so they are equal to .Consider triangle AOB. By the Pythagorean theorem, we have , so . Since angle AOB is 90 degrees, we can use similarity to see that triangle OAP is similar to triangle OAB, so . Solving, we find that .Using similar triangles, we can find that . Since the sum of the squares of the lengths of the diagonals of a cube is equal to three times the square of the side length, we have
$$(0P2 + 0Q? + OR?) = 35388 Substituting the values we found for $OP$, $OQ$, and $OR$, we haveSimplifying and solving for , we find that . Thus, the side length of the cube inscribed in the tetrahedron is .
Find the are of the shaded shape below it has two lines of symmetry (vertical and horizontal) that pass through its centre
Give your answer in cm^2
The area of the shaded shape is 62.5cm^2.
To find the area of the shaded shape, we need to break it down into simpler shapes that we can calculate the area of. From the image, we can see that the shape is composed of a rectangle and two right-angled triangles.
First, we need to find the dimensions of the rectangle. Since the shape has vertical and horizontal lines of symmetry passing through its center, we know that the rectangle is divided into four equal parts.
Therefore, the length of the rectangle is twice the length of one of the triangles, which is 5cm. So, the length of the rectangle is 2 x 5cm = 10cm. The width of the rectangle is also 5cm.
Next, we need to find the area of each of the triangles. We know that the base of each triangle is 5cm, and the height is half of the width of the rectangle, which is 2.5cm. Therefore, the area of each triangle is:
0.5 x base x height = 0.5 x 5cm x 2.5cm = 6.25cm^2
So, the total area of the two triangles is 2 x 6.25cm^2 = 12.5cm^2.
Finally, we can find the area of the shaded shape by adding the area of the rectangle and the area of the triangles:
Area = rectangle area + triangle area = 10cm x 5cm + 12.5cm^2 = 62.5cm^2.
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When doubling the dimensions of a rectangle, why does the area quadruple and the perimeter only doubles?
If you double the length and the width, you are quadrupling the area.
This is because 2 × 2 = 4.
Perimeter of new rectangle= 2 × perimeter of initial rectangle.
The perimeter will be double of if we double the length and breadth of rectangle
→ When doubling the dimensions of a rectangle, why the area is quadruple:
We know that :
Area of rectangle = l × b
where, l is length and b is breadth
A = L × W
This means area equals length times width.
if you double the length and you double the width, the formula becomes:
A = 2 × L × 2 × W
A = 2 × 2 × L × W
A = 4 × L × W
if you double the length and the width, you are quadrupling the area.
This is because 2 × 2 = 4.
→When doubling the dimensions of a rectangle, why the perimeter is doubles?
Let length be equal to ′l′
And breadth be equal to ′b′
Perimeter of rectangle = 2 (l + b) ____(equation i )
The perimeter if the length and breadth of the rectangle will increase by two, or will it double? So new parameters of rectangle when its length and breadth will get double on initial one.
Double length of rectangle of initial one= 2 × l=2l
Double breadth of rectangle of initial one = 2×b=2b
So the perimeter of new rectangle whose length and breadth are double of initial one are:
As we know that:
Perimeter of rectangle = 2 (l + b)
So,
Perimeter of new rectangle= 2(2l+2b), (by taking 2 common)
Perimeter of new rectangle = 2×2(l + b) ____ equation (ii)
As from equation (i) perimeter of initial rectangle is = 2(l + b)
So from equation (i) and (ii)
Perimeter of new rectangle= 2 × 2(l + b)
Perimeter of new rectangle= 2 × perimeter of initial rectangle.
Hence, the perimeter will be double of if we double the length and breadth of rectangle.
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PLEASE HELP SOLVE 30 PTS
Answer:
The polynomial has a unique zero in the interval [1,2] by using intermediate value theorem
What is 1 and 1/4
And 1 and 1/2
The mixed fraction 1 and 1/4 is equal to 5/4 and the mixed fraction 1 and 1/2 is equal to 3/2.
Given first number = 1 and 1/4.
1 and 1/4 is a mixed fraction so, we can write it in the form as [tex]1\frac{1}{4}[/tex] .
To find the value of [tex]1\frac{1}{4}[/tex] we have to multiply 4 with 1 and add the numerator part of the fraction which is 1 and then divide it by 4 which is the denominator. So,
[tex]1\frac{1}{4}[/tex] = ((4x1) + 1 )/4 = 5/4.
Similary, for 1 and 1/2,
[tex]1\frac{1}{2}[/tex] = ((2x1) + 1)/2 = 3/2.
From the above analysis, we can conclude that the value of 1 and 1/4 is 5/4 and the value of 1 and 1/2 is 3/2.
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Write an Equation for the ellipse. The center is (1, -3).
The standard form of the equation of the ellipse is (x - 1)² / 16 + (y + 3) / 9 = 1.
How to define the standard form of the equation of an ellipse
In this problem we find the representation of an ellipse on Cartesian plane, whose center is at (h, k) = (1, - 3), whose major semiaxis length is 4 units and whose minor semiaxis length is 3 units. The standard form of the equation of the ellipse is described below:
(x - h)² / a² + (y - k)² / b² = 1
Where:
(h, k) - Coordinates of the center.a - Length of the major semiaxis.b - Length of the minor semiaxis.If we know that (h, k) = (1, - 3), a = 4 and b = 3, then the standard form of the equation of the ellipse is:
(x - 1)² / 16 + (y + 3) / 9 = 1
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The space available for a relay race at a carnival is 92.75 yards. A rules sign is placed 5 yards before the starting line. If there are 5 sections of th
start to finish and each section covers the same distance, how long is each section of the race?
Each section of the race is (blank) yards long
If the total distance available is 92.75 yards, and there is a sign 5 yards before the starting line, the actual distance available for the race is:
92.75 - 5 = 87.75 yards
Since there are 5 sections of the race, each section covers:
87.75 / 5 = 17.55 yards
Therefore, each section of the race is 17.55 yards long.
3
Florence Griffith-Joyner was an Olympic runner who set the women's world records
for the 100- and 200-meter races in 1988. She completed the 100-meter race in
10.49 seconds and the 200-meter race in 21.34 seconds. How much faster did
Florence run in the 100-meter race than in the 200-meter race, in meters per second?
A 10.85
B 0.1085
C 0.0016
D 0.16
Florence was 0.16 m/s faster in the 100-meter race than in the 200-meter race
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
Speed is the ratio of distance travelled to time taken. It is given by:
Speed = distance / time
She completed the 100-meter race in 10.49 seconds and the 200-meter race in 21.34 seconds. Hence:
For 100 meters:
Speed = 100 m / 10.49 s = 9.53 m/s
For 200 meters:
Speed = 200 m / 21.34 s = 9.37 m/s
The speed difference = 9.53 m/s - 9.37 m/s = 0.16 m/s
Florence was 0.16 m/s faster
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PLEASE IM BEGGING HELP PLEASE!!!!!
Answer:
C
Step-by-step explanation:
Mo is running the tracks where one lap is 400m. After completing some laps, he found that he has completed 40% of the total distance. After another 2, 50% is done. What is the total distance that he needs to cover in meters?
I REALLY NEED THE ANSWER SOON,
IF YOU CAN DO IT WELL THANK YOU.
Answer:
Total distance is 8000 m------------------
According to the problem, 2 laps make a difference of 10% as:
50% - 40% = 10%Hence the total distance in terms of laps is:
100% / 10% = 10 times the 2 laps:Find the total distance:
Total distance = 10*2 = 20 lapsTotal distance = 20*400 m = 8000 mUse the quadratic formula to solve -2x^2+2x+1
The solutions for -2x²+2x+1 are x = 1 + √(3)/2 and x = 1 - √(3)/2.
To use the quadratic formula to solve -2x²+2x+1, we first identify the coefficients a, b, and c of the quadratic equation in standard form: ax²+bx+c=0. In this case, a=-2, b=2, and c=1. We then plug these values into the quadratic formula
x = (-b ± √(b²-4ac)) / 2a
Substituting the values, we get
x = (-2 ± √(2²-4(-2)(1))) / 2(-2)
Simplifying the expression inside the square root
x = (-2 ± √(4+8)) / (-4)
x = (-2 ± √12) / (-4)
Simplifying the radical
x = (-2 ± 2√3) / (-4)
Reducing the fraction
x = (1 ± √3/2)
Therefore, the two solutions are x = (1 + √3/2) and x = (1 - √3/2).
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This table shows all of the values for the function y = f(x).
y = f(x)
Checkpoint Function transformations (L
-5-28
-3
-2
0
0
7
1 26
Based on those values, complete a table for the function y=f(x)-5.
=F(x)-5
The table for the function y = f(x) - 5 is
x f(x) - 5
5 -33
-3 -5
-2 2
0 21
Creating a table for the function y = f(x) - 5From the question, we have the following parameters that can be used in our computation:
x f(x)
5 -28
-3 0
-2 7
0 26
To create a table for the function y = f(x) - 5, we subtract 5 from the values of f(x)
using the above as a guide, we have the following:
x f(x) - 5
5 -28 - 5
-3 0 - 5
-2 7 - 5
0 26 - 5
Evaluate
x f(x) - 5
5 -33
-3 -5
-2 2
0 21
This represents the table for the function y = f(x) - 5
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16
Which graph correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r?
О А.
m. All rights reserved.
2 Fr
Arc
Length
Q Search
I:
3=
IA
>
0
A graph that correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r is: C. graph C.
How to calculate the length of the arc?In Mathematics and Geometry, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.
Mathematically, the length of an arc formed by a circle can be calculated by using the following equation (formula):
Arc length = 2πr × θ/360
In this context, we can reasonably infer and logically deduce that the arc length is directly proportional to the radian measure of the central angle.
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Complete the following using compound future value. (Use the Table provided.)
Note: Do not round intermediate calculations. Round your final answers to the nearest cent.
Time
6 years
Principal
$ 15,300
Rate
8 %
Compounded
Quarterly
What is amount &
Interest?
The total is $24,947.06 plus $9,647.06 in compound interest.
Define compound interest?One way to earn or pay interest on interest is through compound interest. It denotes that interest will be charged on both the main amount and the accrued interest in the subsequent period. Savings or investments can expand over time with the aid of compound interest.
We can use the following formula to determine compound future value:
FV = P * (r/n + 1)(n*t)
where P is the principal, r is the yearly interest rate, n is the number of times interest is compounded annually, and t is the amount of time in years.
Your values have led us to:
FV = 15300 * (1 + 0.08/4)²⁴
FV = $24,947.06
The total is $24,947.06 plus $9,647.06 in interest.
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In the diagram shown, points B and D lie on sides AC and AE such that BD is parallel to CE. If AB=10, AD=16, and De=22 then find the length of AC
In triangle ACE, with BD parallel to CE, using similar triangles and ratios, we get a quadratic equation with two possible solutions. Only the positive one is chosen, so AC is approximately 30.96 units long.
Since BD is parallel to CE, we can use the property of similar triangles to find the length of AC.
Triangles ABD and ACE are similar because they have the same corresponding angles. This means that the ratios of their corresponding side lengths are equal.
We know that AB = 10, AD = 16, and DE = 22.
Let x be the length of AC. Then, we have
AB/AD = CE/EA (by similarity of triangles ABD and ACE)
10/16 = CE/(x-16+22) (substituting CE = EA - DE and simplifying)
5/8 = CE/(x-6)
CE = (5/8)(x-6)
We also know that
BD/DE = AB/AE (by similarity of triangles ABD and ADE)
BD/22 = 10/(x-22) (substituting BD = CE and AE = AC - CE - DE, and simplifying)
CE = (220 - 10x)/(x-22)
Since CE is equal in both expressions, we can equate them and solve for x
(5/8)(x-6) = (220 - 10x)/(x-22)
5x² - 196x + 1320 = 0
x² - 39.2x + 264 = 0
Using the quadratic formula, we get
x = 30.96 or x = 8.54
The length of AC must be positive, so we choose x = 30.96.
Therefore, the length of AC is approximately 30.96 units.
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--The given question is incomplete, the complete question is given
" In the diagram shown, points B and D lie on sides AC and AE such that BD is parallel to CE. If AB=10, AD=16, and De=22 then find the length of AC "--
Find the area of each of the figures
In the given diagram, the areas of the figures are as follows:
Area of the rectangle is 1/6 cm²
Area of the parallelogram is 12 m²
Calculating the area of a plane shapeFrom the question, we are to calculate the areas of the given plane shapes
From the diagram, we have a rectangle and a parallelogram
The area of a rectangle is given by the formula
Area = l × w
Where l is the length
and w is the width
From the given information,
l = 1/2 cm
w = 1/3 cm
Thus,
Area = 1/2 cm × 1/3 cm
Area = 1/6 cm²
Hence, the area of the rectangle is 1/6 cm²
For the parallelogram
The area of a parallelogram is given by the formula
Area = b × h
Where b is the base length
and h is the perpendicular height
From the given information,
b = 6 m
h = 2 m
Thus,
Area = 6 m × 2 m
Area = 12 m²
Hence, the area of the parallelogram is 12 m²
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The distance from Hans house to Priyas house is 4/5 kilometer. Han has walked 3/4 of the way already. How many kilometers has he walked?
Han has walked 3/5 km.
What is distance?Distance is the length of space between two reference points. It is a scalar quantity, and it is measured in meters.
In the given question, we have that;
distance from Han's house to Priya's house = 4/5 km
Han has walked 3/4 of the way already.
Thus,
distance walked by Han = 3/4 of 4/5
= 3/4 x 4/5
= 12/ 20
= 3/ 5
distance walked by Han is 3/5 km.
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2.1/0.7=3 but how do you work it out (I cheated and used a calculator)
Answer: To work out 2.1/0.7 without a calculator, you can use long division as follows:
0.7 | 2.1
1.4 (3 times 0.7 is 2.1)
-----
0.7
0.0 (there is no remainder)
Therefore, 2.1/0.7 = 3, which means that 2.1 is equal to 3 times 0.7.
Answer:
see below
Step-by-step explanation:
2.1
-----
.7
Multiply the top and bottom by 10 to get rid of the decimals.
2.1 *10 = 21
.7 * 10 = 7
21/7 = 3
Enter your answer by filling in the boxes to correctly complete the statements. If necessary, round to the nearest hundredth.
The practical domain of the situation is [0, ∞].
The practical range of the situation is [0, 100].
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
How to identify the domain any graph?In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [0, ∞] or 0 ≤ x ≤ ∞.
Range = [0, 100] or 0 ≤ y ≤ 100.
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A motorist travelled from Town A to Town B. After travelling for 1 1/2 hours , he passed
a cyclist travelling at an average speed of 45 Km/h in the opposite direction.
when the motorist reached Town B 2 h later, the cyclist was 30 km away from Town A.
a) Find the average speed of the motorist.
b) Find the distance between Town A and Town B.
Answer:
the formula: Speed = Distance / Time.
Let's break down the problem into two parts:
a) Find the average speed of the motorist.
Let's assume the average speed of the motorist is "v" km/h.
The distance the motorist traveled in 1 1/2 hours is given by: Distance = Speed × Time = v × (3/2) km.
The distance the cyclist traveled in 1 1/2 hours (opposite direction) is given by: Distance = Speed × Time = 45 × (3/2) km.
Since they passed each other, the sum of their distances should be equal to the distance between Town A and Town B.
So, we can set up the equation: v × (3/2) + 45 × (3/2) = Distance between Town A and Town B.
b) Find the distance between Town A and Town B.
When the motorist reached Town B 2 hours later, the cyclist was 30 km away from Town A.
We can set up the equation: Distance between Town A and Town B = v × 2 + 30.
Now, let's solve the equations:
v × (3/2) + 45 × (3/2) = v × 2 + 30.
Simplifying the equation, we have: (3v + 135)/2 = 2v + 30.
Multiplying both sides of the equation by 2 to eliminate the fraction, we get: 3v + 135 = 4v + 60.
Subtracting 3v from both sides of the equation, we have: v = 75.
Therefore, the average speed of the motorist is 75 km/h.
To find the distance between Town A and Town B, we substitute the value of v into the equation:
Distance between Town A and Town B = v × 2 + 30 = 75 × 2 + 30 = 150 + 30 = 180 km.
Therefore, the distance between Town A and Town B is 180 km.
A gas can hold 10 L of gas how many cans could we filled filled with 7 L of
Answer:
2 cans
Step-by-step explanation:
A house is purchased for $313,000 with a 15% down payment. A mortgage is secured at 7% for 25 years. Find the monthly payment.
If house is purchased for $313,000 with a 15% down payment, the monthly payment for the mortgage is $1,906.33.
To find the monthly payment for a mortgage secured at 7% for 25 years on a house purchased for $313,000 with a 15% down payment, we can use the formula for calculating mortgage payments:
P = L[c(1 + c)ⁿ]/[(1 + c)ⁿ - 1]
Where P is the monthly payment,
L is the loan amount (which is the purchase price minus the down payment),
c is the monthly interest rate (which is the annual interest rate divided by 12),
n is the total number of monthly payments (which is the number of years multiplied by 12).
Substituting the given values, we get:
L = $313,000 - 0.15($313,000) = $266,050
c = 0.07/12 = 0.00583
n = 25 x 12 = 300
Plugging these values into the formula, we get:
P = $266,050[0.00583(1 + 0.00583)³⁰⁰]/[(1 + 0.00583)³⁰⁰ - 1]
Simplifying the expression, we get:
P = $1,906.33
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What is the perimeter of the regular pentagon?
Answer:
To find the perimeter of a regular pentagon, you need to know the length of one side and the number of sides. In a regular pentagon, all sides have the same length and the shape has 5 sides.
Let's say the length of one side of the regular pentagon is 's'.
The formula for the perimeter of a regular pentagon is:
Perimeter = 5s
This is because a regular pentagon has 5 sides of equal length, so you can simply add the length of each side together 5 times.
Therefore, the perimeter of a regular pentagon with a side length 's' is 5s.
Step-by-step explanation:
Working with Formulas
HELP PLS
.
the rate of interest is 11.25%.we can use simple interest formula get answer as above
what is simple interest ?
Simple interest is a type of interest that is calculated as a percentage of the principal amount of a loan or investment, and is based only on the original amount of money that was borrowed or invested.
In the given question,
We can use the formula for simple interest to solve for the rate:
Simple Interest = (Principal x Rate x Time) / 100
Substituting the given values, we get:
$900 = (400 x Rate x 20) / 100
Multiplying both sides by 100 and dividing by 400 x 20, we get:
Rate = $900 / (400 x 20) = 0.1125 or 11.25%
Therefore, the rate of interest is 11.25%.
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A company gives a 12% discount to his customers on retail price. If the total is over $10,000 after the discount, they give an additional 3% discount on the remaining balance. A customer’s total came to $13,500 (discounted price). How much did he save?
Answer:
Therefore, the customer saved $2,448.45.
Step-by-step explanation:
To answer this question, we need to use the percentage discount formula to find the original price and the amount saved.
Let x be the original price of the product. Then, after applying the 12% discount, the price becomes 0.88x. If the total is over $10,000 after this discount, then an additional 3% discount is applied on the remaining balance, which means the final price becomes 0.97 * 0.88x.
We are given that the final price is $13,500, so we can set up an equation and solve for x:
0.97 * 0.88x = 13,500 x = 13,500 / (0.97 * 0.88) x = 15,948.45
Therefore, the original price was $15,948.45.
The amount saved is the difference between the original price and the final price:
15,948.45 - 13,500 = 2,448.45
PLEASE HELP PLEASE!!
Complete the following statement to estimate the root of 75 to the nearest tenth. Use numbers that are closest to the root of 75
Answer:
√75 =8.66.
Step-by-step explanation:
The square root of 75 is an irrational number where the numbers after the decimal point go up to infinity. √75 = 8.660.√75 cannot be written in the form of p/q, hence it is an irrational number. irrational with never-ending digits.
How to Find the Square Root of 75?Let's see how to find the square root of 75 by the long division method.
Step 1: Express 75 as 75.000000. We take the number in pairs from the right. Take 75 as the dividend.
Step 2: Now find a quotient which is the same as the divisor. Multiply quotient and the divisor and subtract the result from 75.
Step 3: Now double the quotient obtained in step 2. Here is 2 × 8 = 16. 160 becomes the new divisor.
Step 4: Apply decimal after quotient '8' and bring down two zeros. We have 1100 as the dividend now.
Step 5: We need to choose a number that while adding to 160 and multiplying the sum with the same number we get a number less than 1100. 160+ 6 = 166 and 166 × 6 = 996. Subtract 996 from 1100. We get 104
Step 6: Bring down two zeros again and place it after 104, so that it becomes 10400 which is the new dividend. Now multiply the number in the quotient by 2. Here it is 86. We get 172. Have it as 1720. Now find a number at the unit's place of 1720 multiplied by itself gives 10400 or less. We find that 1726 × 6 = = 10356. Find the remainder.
Step 7 : Repeat the process until we get the remainder equal to zero. The square root of 75 up to two places is obtained by the long division method. Thus √75 = 8.66
The sound wave of two music notes can be represented by the function y = 2sin2x and y = sin x, where x represents the time since the note is played. At what times will the frequencies of the sound waves be the same in the interval [0°, 360°)?
Group of answer choices
x = 0°, 30°, 150°, 180°
x = 0°, 180°, 210°, 330°
x = 30°, 90°, 150°, 270°
x = 90°, 210°, 270°, 330°
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
How to solveFor the frequencies to be the same, we need to find values of n and m such that:
n = m
Solving for n and m, we get:
n = m = 2
So both functions complete two cycles in the interval [0, 2π).
We can find the times when this occurs by setting the angles in radians equal to multiples of 2π/2, or π:
2sin2x = sin x
2sin2x - sin x = 0
sin x (2sin x - 1) = 0
sin x = 0 or 2sin x - 1 = 0
sin x = 0 when x is an integer multiple of π.
2sin x - 1 = 0 when sin x = 1/2, which occurs when x = π/6 or x = 5π/6.
Therefore, the frequencies of the sound waves are the same at x = π/6, x = π/2, x = 5π/6, and x = 3π/2.
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
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what is the difference between an angle bisector and a segment bisector ?
The clear difference between an angle bisector and a segment bisector is that angle bisector passes through the apex of an angle while segment bisector passes through the midpoint of the line segment.
What is an angle bisector?An angle bisector is defined as the line the divides an angle into two equal parts by passing through its apex.
A segment bisector is defined as the line that divides a segment at the midpoint into two parts.
The difference between angel bisector and segment bisector is that angle bisector passes through the apex of an angle while segment bisector passes through the midpoint of the line segment.
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