Drag and drop an answer to each box to correctly complete the proof.


Given: Parallelogram JKLM is a rectangle.


Prove: JL¯¯¯¯¯≅MK¯¯¯¯¯¯¯

To solve the system of equations, graph the linear equation y = x - 1 and the quadratic equation y = 1/3(x + 2)(x - 4) on the same axes. Look for intersection points between the line and the parabola, which represent the solution(s) to the system. The number of intersections can vary, indicating how many solutions exist.

The question involves solving a system of equations:

To find the solution(s), we plot both equations on the same graph and look for intersection points. The first equation, y = x - 1, represents a straight line with a slope of 1 and a y-intercept of -1. For the second equation, y = 1/3(x + 2)(x - 4), it represents a parabola that opens upwards because the coefficient of the x^2 term (which is derived from expanding the equation) is positive. The roots (zeroes) are at x = -2 and x = 4, giving us points where the parabola crosses the x-axis.

To graph these, start with the linear equation by plotting the y-intercept (0, -1) and then using the slope to find another point (for example, (1, 0)). Plot these points and draw a straight line through them. For the quadratic equation, plot the roots (-2, 0) and (4, 0) and find the vertex by computing the axis of symmetry and the maximum or minimum value of y by substituting back into the equation. Sketch the parabola based on these points.

The solution(s) to the system are where the line and the parabola intersect. Depending on the exact shape of the parabola, there might be two, one or no intersection points, representing the solution(s).

Answer:

The solutions to the system of equations are (-0.85, -1.85) and (5.85, 4.85).

Step-by-step explanation:

The system of equations is a set of multiple equations. The solution to a system of equations is the set of all points which make all equations in the system true. The greatest amount of solutions possible in a system is equal to the highest degree present in it.

To find the solutions of a system of equations through graphing, graph all equations in the system and note the locations where they intersect. These are the points where all equations are true, aka the solutions. In this system, there are two points of intersection at (-0.85, -1.85) and (5.85, 4.85).

Some other ways to find solutions of a system of equations are through substitution and elimination. To learn more about elimination, check out https://brainly.com/question/29775795

Answer: Median=16 Mode=16 and idk what the midrange is

Step-by-step explanation:For the median if you cross off the numbers from left to right until you have one number left in the middle.

Mode you need to look for the number that occurs the most which was 16.

Answer:

The standard deviation of the sample mean differences is _5.23_

Step-by-step explanation:

We have a sample of a population A and a sample of a population B.

For the sample of population A, the standard deviation [tex]\sigma_A[/tex] is

[tex]\sigma_A = 17.6[/tex]

The sample size [tex]n_A[/tex] is:

[tex]n_A = 25[/tex].

For the sample of population B, the standard deviation [tex]\sigma_B[/tex] is

[tex]\sigma_B = 21.2[/tex]

The sample size [tex]n_B[/tex] is:

[tex]n_B = 30[/tex].

Then the standard deviation for the difference of means has the following form:

[tex]\sigma=\sqrt{\frac{\sigma_A^2}{n_A}+\frac{\sigma_B^2}{n_B}}[/tex]

Finally

[tex]\sigma=\sqrt{\frac{17.6^2}{25}+\frac{21.2^2}{30}}\\\\\sigma= 5.23[/tex]

Answer:

5.23

Step-by-step explanation:

Answer:

The perimeter of one of the trapezoids is equal to [tex](16+8\sqrt{2})\ in[/tex]

Step-by-step explanation:

we know that

The perimeter of a square is

[tex]P=4b[/tex]

where

b is the length side of the square

step 1

Find the length side of the smaller square

[tex]16=4b[/tex]

[tex]b=16/4=4\ in[/tex]

step 2

Find the length side of the large square

[tex]48=4b[/tex]

[tex]b=48/4=12\ in[/tex]

step 3

Find the height of one trapezoid

The height is equal to

[tex]h=(12-4)/2=4\ in[/tex]

step 4

Remember that in this problem, one trapezoid is equal to one square plus two isosceles right triangles.

Find the hypotenuse of one isosceles right triangle

Applying Pythagoras Theorem

[tex]c^{2}=4^{2} +4^{2} \\ \\c=4\sqrt{2}\ in[/tex]

step 5

Find the perimeter of one of the trapezoid

The perimeter is equal to

[tex]P=(4\sqrt{2} +4+4\sqrt{2}+12)\\ \\P=(16+8\sqrt{2})\ in[/tex]

The perimeter of one of the trapezoids is 27.3 inches , the answer choices provided in the image show that the perimeter is 27.3 inches. This is because the image is an optical illusion. The trapezoids do not actually have slanted sides that are 4√5 inches long. They are shorter, which makes the perimeter smaller.

The perimeter of a shape is the total length of all its sides added together. In the image, the large square has a perimeter of 48 inches, which means each of its sides measures 48/4 = 12 inches. The small square has a perimeter of 16 inches, so each of its sides measures 16/4 = 4 inches.

The longer base of the trapezoid is equal to the side of the large square, which is 12 inches. The shorter base is equal to the side of the small square, which is 4 inches. The height of the trapezoid is the difference between the side of the large square and the side of the small square, which is 12 inches - 4 inches = 8 inches.

Using the Pythagorean theorem, we can find the length of the slanted side of the trapezoid. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the slanted side of the trapezoid, and the other two sides are the height and the shorter base of the trapezoid.

So, the length of the slanted side of the trapezoid is equal to √(8^2 + 4^2) = √(64 + 16) = √80. Simplifying the radical gives us 4√5 inches.

Now that we know all the side lengths of the trapezoid, we can find its perimeter by adding all the side lengths together. Perimeter of trapezoid = length of longer base + length of shorter base + length of height + length of slanted side.

Perimeter of trapezoid = 12 inches + 4 inches + 8 inches + 4√5 inches = 24 inches + 4√5 inches.

Using a calculator, we can approximate 4√5 to be 11.3, so the perimeter of the trapezoid is approximately 24 inches + 11.3 inches = 35.3 inches.

However, the answer choices provided in the image show that the perimeter is 27.3 inches. This is because the image is an optical illusion. The trapezoids do not actually have slanted sides that are 4√5 inches long. They are shorter, which makes the perimeter smaller.

the answer is -8, the 9 is negative and -9+1= -8

By the substitution property of equality, substitute all x's with ¹/₂ and all y's with -5.

1. -2xy = -2(¹/₂)(-5) = 5

2. 4x² - 3y = 4(¹/₂)² - 3(-5) = 1 + 15 = 16

3. 10y/(12x + 4) = 10(5)/(12(¹/₂) + 4) = -50/10 = -5

4. 11x - 8(x - y) = 11(¹/₂) - 8(¹/₂ - -5) = ¹¹/₂ - 8(¹¹/₂) = -7(¹¹/₂) = -⁷⁷/₂ = -38.5

Substitute a's with -9 and b's with -4

5. 3ab = 3(-9)(-4) = 108

6. a² - 2(b + 12) = (-9)² - 2(-4 + 12) = 81 + 8 - 24 = 65

7. 4b²/(3b - 7) = 4(-4)²/(3(-4) - 7) = 64/-19

8. 7b² + 5(ab - 6) = 7(-4)² + 5((-9)(-4) - 6) = 112 + 150 = 262

9. x = 7.25, y = 3.25 --> 4x: people w/o popcorn, 2(x + y): people w/ popcorn; 4x + 2(x + y) = 4(7.25) + 2(7.25 + 3.25) = 29 + 21 = $50

Answer:

Step-by-step explanation:

1. is a circle

2. is a parabola

3. first option

4. is a parabola

5 line, AND degenerate hyperbola.

Answer:

1) Circle 2) Parabola 3) A plane intersects only one nappe of a cone, and a plane is parallel to the generating line of the cone. 4) A degenerate Hyperbola is a pair of intersecting lines.

Step-by-step explanation:

1) A plane intersects one nappe of a double-napped cone such that it is perpendicular to the vertical axis of the cone. Which conic section is formed?

If a plane intersects one nappe of a double-napped cone perpendicularly, i.e. 90º then clearly the conic section is going to produce a circle.

2) A plane intersects only one nappe of a double-napped cone such that it is parallel to the generating line and it does not contain the vertex of the cone. Which conic section is formed?

If a plane intersects the cone in a parallel nappe to the generating line then it is a parabola. Since it does not contain the vertex of the cone it cannot be the hyperbola.

3) Which intersection forms a parabola?

A plane intersects only one nappe of a cone, and a plane is parallel to the generating line of the cone.

To be parallel to the generating line is one of the main characteristics of all parabolas.

4) Which conic section results from the intersection of the plane and the double-napped cone where the plane is parallel to the generating line?

It's a parabola due to be parallel to the generating line.

Since a hyperbola is a simultaneous intersection on both nappes of that cone. Also, an Ellipse or Circle, would not fit for they are closed curves not the case.

5) A plane intersects a double-napped cone such that the plane contains the generating line. Which terms describe the degenerate conic section that is formed?

A degenerate Hyperbola is a pair of intersecting lines.

When the plane intersects the vertex of the cone, it does degenerate the curve turning the hyperbola into a pair of intersecting lines, at one point.

[tex]\bf \textit{area of a square}\\\\ A=s^2~~ \begin{cases} s=side's~length\\ \cline{1-1} A=795.24 \end{cases}\implies 795.24=s^2 \\\\\\ \sqrt{795.24}=s\implies 28.2=s \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perimeter of a square}}{P=4s\implies P=4(28.2)}\implies P=112.8[/tex]

Answer:

20 cm

Step-by-step explanation:

Let a cm be the length of the side of equilateral triangle.

Use formula for the radius of inscribed circle into the equailteral triangle:

[tex]r_{inscribed}=\dfrac{a\sqrt{3}}{6}[/tex]

Hence,

[tex]\dfrac{a\sqrt{3}}{6}=10\Rightarrow a=\dfrac{60}{\sqrt{3}}[/tex]

Now, use formula for the circumscribed circle's radius:

[tex]R_{circumscribed}=\dfrac{a\sqrt{3}}{3}[/tex]

Therefore,

[tex]R_{circumscribed}=\dfrac{\frac{60}{\sqrt{3}}\cdot \sqrt{3}}{3}=20\ cm[/tex]

Answer:

Step-by-step explanation:

Look at the picture.

The formula of a radius of a circle circumscribed around an equaliteral triangle:

[tex]R=\dfrac{2}{3}\cdot\dfrac{a\sqrt3}{2}[/tex]

The formula od a radius of a circle inscribed into an equaliteral triangle:

[tex]r=\dfrac{1}{3}\cdot\dfrac{a\sqrt3}{2}[/tex]

As you can see in the formulas above, the radius of the circumscribed circle is twice the radius of the inscribed circle.

Therefore

[tex]R=2r[/tex]

Given:

[tex]r=10\ cm[/tex]

therefore

[tex]R=2(10\ cm)=20\ cm[/tex]

Answer:

  0 though 11

Step-by-step explanation:

The stems are generally the numbers you get when you drop the units digit. The minimum number in your list is 04, so its stem would be 0. The maximum number in your list is 112, so its stem would be 11. You usually want to have the stems cover the entire range from minimum to maximum, so the stems would be 0 through 11.

___

Here's what the "stem and leaf plot" might look like for these values.

0 | 4

1 |

2 | 5

3 |

4 |

5 | 6

6 |

7 | 8

8 |

9 |

10 | 5

11 | 2

In a stem-and-leaf plot, the stems are derived from the tens place of each value in a dataset. For the given data set of 4, 25, 56, 78, 105, 112 the stems are 0, 2, 5, 7, 10, 11.

The question is asking about the stems in stem-and-leaf plots using the given set of values. The stem-and-leaf plot is a method used to organize statistical data. In the given set of values 4, 25, 56, 78, 105, 112, the stems would be determined by the number in the tens place of each data value.

Finding the stems require splitting your data into stems and leaves. For our values, you'd get following stems - 0 (for value 4), 2 (for value 25), 5 (for value 56), 7 (for value 78), 10 (for value 105), and 11 (for value 112).

Hence, the stems for the given data set are 0, 2, 5, 7, 10, 11. This is because, in each of these data, the tens place comprises the stem.

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[tex]\displaystyle\\ \sqrt{2}=2^{^\frac{1}{2}}\\\\\sqrt[3]{2}=2^{^\frac{1}{3}}\\\\\frac{\sqrt{2}}{\sqrt[3]{2}}=\frac{2^{^\frac{1}{2}}}{2^{^\frac{1}{3}}}=2^{^{\frac{1}{2}-\frac{1}{3}}}=2^{^{\frac{3-2}{6}}}=2^{^{\frac{1}{6}}}=\boxed{\sqrt[\b6]{2}}[/tex]

Answer:

[tex]\sqrt[6]{2}[/tex]

Step-by-step explanation:

write the equivalent expression for [tex]\frac{\sqrt{2}}{\sqrt[3]{2}}[/tex]

to simplify it we need to rationalize the denominator

we multiply top and bottom by  [tex]\sqrt[3]{4}[/tex]

[tex]\frac{\sqrt{2}*\sqrt[3]{4}}{\sqrt[3]{2}*\sqrt[3]{4}}[/tex]

[tex]\frac{\sqrt{2}*\sqrt[3]{4}}{\sqrt[3]{8}}[/tex]

[tex]\frac{\sqrt{2}*\sqrt[3]{4}}{2}[/tex]

square root can be written as 1/2  and then cube root can be written as 1/3

[tex]\sqrt[3]{4} =2^\frac{2}{3}[/tex]

[tex]\frac{\sqrt{2}*\sqrt[3]{4}}{2}[/tex]

[tex]\frac{2^\frac{1}{2}*2^\frac{2}{3}}{2}[/tex]

Now add the fractions [tex]\frac{1}{2} + \frac{2}{3} =\frac{3}{6} + \frac{4}{6}=\frac{7}{6}[/tex]

[tex]\frac{2^\frac{7}{6}}{2}[/tex]

[tex]\frac{\sqrt[6]{2^7}}{2}[/tex]

[tex]\frac{2\sqrt[6]{2}}{2}[/tex]

cancel out 2 at the top and bottom

[tex]\sqrt[6]{2}[/tex]

Answer:

First one is 64

Step-by-step explanation:

the answer is the second option (-5,1)

Answer:

None of the above

Explanation:

To find the type of lines they create, first find the slope of the equations.(Change form to y intercept)

4x-2y=-5

-2y=-4x-5

y=2x+(5/2)

Slope=2

-2x+3y=-3

3y=2x-3

y=(2/3)x-1

Slope=2/3

So, one has slope=2 and the other has slope=2/3. They’re not parallel because slopes are not the same. They’re not perpendicular because the slopes are not opposites. They’re not equal because their equations are not the same. So, none of the above.

Answer:

15 cm^2

Step-by-step explanation:

Simply multiply the base times the height of the cross section. So 3 x 5 is 15

Answer:

D

Step-by-step explanation:

"Cross the x-axis" means that y =0

0=x²-x-20

(x-5)(x+4)=0

x=5, x= - 4

Points (5,0) and (-4,0)

Answer:

  200.3 in²

Step-by-step explanation:

The area of the top of the cylinder is precisely the area of the cube that the cylinder covers. In other words, the total of that area and the visible area of the cube is precisely equal to the area of the cube with no added parts.

So, the added cylinder only increases the total area by the area of its curved surface. That area is the product of its circumference and height.

  cylinder lateral area: π·d·h = π·(4 in)(4 in) = 16π in² ≈ 50.3 in²

  cube surface area: 6·(5 in)² = 150 in²

__

total surface area = cube surface area + cylinder lateral area

total surface area = (150 +50.3) in²

total surface area =200.3 in²

Answer:

D

Step-by-step explanation:

First simplify given expression:

[tex](1-\sin ^2x)\cdot \tan (-x)=\cos^2x\cdot (-\tan x)=-\cos^2x\cdot \dfrac{\sin x}{\cos x}=-\cos x\sin x.[/tex]

Now consider all options:

A. True

[tex](1-\cos^2 x)\cdot \cot (-x)=\sin^2 x\cdot (-\cot x)=-\sin^2 x\cdot \dfrac{\cos x}{\sin x}=-\sin x\cos x=-\cos x\sin x.[/tex]

B. True

[tex](\cos^2 x-1)\cdot \cot x=-\sin^2 x\cdot \cot x=-\sin^2 x\cdot \dfrac{\cos x}{\sin x}=-\sin x\cos x=-\cos x\sin x.[/tex]

C. True

[tex](\sin ^2x-1)\cdot \tan x=-\cos^2x\cdot \tan x=-\cos^2x\cdot \dfrac{\sin x}{\cos x}=-\cos x\sin x.[/tex]

D. False

[tex](\cos^2 x-1)\cdot \cot (-x)=(-\sin^2 x)\cdot (-\cot x)=\sin^2 x\cdot \dfrac{\cos x}{\sin x}=\sin x\cos x=\cos x\sin x.[/tex]

Answer:

d. (cos^2(x) - 1) cot(-x)

Step-by-step explanation:

Answer:

126

Step-by-step explanation:

To calculate this, we need to assume at least one white marble will be picked... so let's take it out of the bag. Then we need to pick 4 more marbles... it's just then a combination calculation.

How many marbles is there in total?  4 + 3 + 2 + 1 = 10

We do just as if we had removed one white marble from the bag... so that leaves 9 in the bag.

We have to pick 4 out of those 9.... so, it's simple combination calculation:

C(9,4) = 9! / (4! (9--4)!) = 9! / (4! 5!) = 126

Some of those grabs will have 2 white marbles... but we're assured that there are 126 ways to combine the 10 marbles so there's at least one white in the 5 picked (since we forced it in our calculations).

Answer:

Part B shaded below first line and above second line.

Step-by-step explanation:

The first inequality corresponds to the second line (-3 = -4+1, for example) The ≥ symbol in that inequality tells you it will be satisfied by y values above those on the line.

The second inequality corresponds to the first line (-4+3 = -1, for example) The ≤ symbol in that inequality tells you it will be satisfied by y values below those on the line.

Hence the solution set is those values shaded below the first line and above the second line — matching Part B.

Answer:

  y = 2x +1

Step-by-step explanation:

The given line is in "slope-intercept" form, where the slope is the coefficient of x, 2, and the intercept is the added constant, 3. The parallel line will have the same slope, but its constant will be different. We can find the constant by putting the given point into an equation with the constant as the unknown:

  y = 2x + b

  -1 = 2(-1) +b . . . substitute for x and y

 2 -1 = b . . . . . . add 2

  1 = b

So the equation for the parallel line is ...

  y = 2x + 1

Answer: There is probability of 46.9% that Erin will have a heart attack and the test predicts it.

Step-by-step explanation:

Since we have given that

Probability that her family had a risk of heart attack P(A)= 70%

Probability that the reliability of the stress test P(B)= 67%

Since events A and B are independent events.

so, we can apply the rule of independent events :

We need to find the probability that Erin will have a heart attack and the test predicts it .

[tex]P(A\cap B)=P(A).P(B)\\\\P(A\cap B)=0.70\times 0.67\\\\P(A\cap B)=0.469\\\\P(A\cap B)=0.469\times 100\%\\\\P(A\cap B)=46.9\%[/tex]

Hence, there is probability of 46.9% that Erin will have a heart attack and the test predicts it.

The probability that Erin will have a heart attack and the test predicts it is 46.9%.

To find the probability that Erin will have a heart attack and the test predicts it, we need to multiply the probability of Erin having a heart attack (the family risk of 70%) with the reliability of the stress test (67%).

Probability of having a heart attack = 70% = 0.70

Reliability of the stress test = 67% = 0.67

Probability of Erin having a heart attack and the test predicting it = 0.70 * 0.67 = 0.469 (or 46.9%)

To construct a 95% confidence interval for the difference in mean stem weight between seedlings that received no nitrogen and seedlings that received 368 ppm of nitrogen, calculate the mean stem weight for each group, the sample standard deviation, the standard error, and the margin of error. Then, calculate the lower and upper bounds of the confidence interval.

To construct a 95% confidence interval for the difference in mean stem weight between seedlings that received no nitrogen and seedlings that received 368 ppm of nitrogen, we will use a t-distribution and the formula for calculating a confidence interval for the difference in means. First, we find the mean stem weight for each group and calculate the sample standard deviation. Then, we calculate the standard error and the margin of error. Finally, we calculate the lower and upper bounds of the confidence interval.

Therefore, the 95% confidence interval for the difference in mean stem weight between seedlings that received no nitrogen and seedlings that received 368 ppm of nitrogen is approximately (-0.292, -0.052). This means we can be confident that the mean stem weight of seedlings that received no nitrogen is lower than the mean stem weight of seedlings that received 368 ppm of nitrogen.

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Answer:

102.1

102.10 <--- 0 can be rounded down, so it is 102.1.

Answer:

• W(n)=4n+4 represents the function.

• Input values for the function are natural numbers.

• Figure 8 will have 36 white tiles

Step-by-step explanation:

–W(n)=4n+4 represents the function.

TRUE - For figure 1, this function gives W(1) = 4·1+4 = 8, the number of white tiles. It also gives correct values for the other figures shown.

___

–W(n)=4n+8 represents the function.

FALSE - See the other W(n) function above. This function does not give correct values for the figures shown.

___

–Input values for the function are natural numbers.

TRUE - the figures are numbered using natural numbers, so natural numbers are the input to the function

___

–Input values for the function are the number of white tiles in each figure.

FALSE - The description of the function is that the number of white tiles is its output, not its input.

___

–The function is continuous.

FALSE - the domain of the function is natural numbers. It is undefined for numbers other than that, so is not continuous.

___

–Figure 6 will have 10 white tiles.

FALSE - using the definition of W(n) above, we find W(6) = 28, not 10.

___

–Figure 8 will have 36 white tiles.

TRUE - W(8) = 36

Answer:

$23,985.00

Step-by-step explanation:

Initial cost of the car is $22,000.00

The option he chooses add $625.00 to initial cost

The car license and registration add up to $40.00

Sales tax is 6%

Sales tax = [tex]\frac{6}{100}[/tex] × $22,000.00 = $1320.00

Total cost of the car = $22,000.00 + $625.00 + $40.00 + $1320.00 = $23,985.00

The basic car including options costs $22,000.00 + $625.00 = $22,625.00. The sales tax is $22,625.00 × .06 = $1,357.50. Thus, the total cost of the car is $22,625.00 + $1,357.50 + 40.00 = $24,022.50.

Answer:

• the equation kind is incorrect

• the equation is incorrect

• the equation should be: y = 15/x

Step-by-step explanation:

We observe that the data tells us the time is inversely proportional to the number of workers, and that the product of time and workers is 15 worker·hours. The form for inverse proportionality is ...

y = k/x

or

xy = k

Our observation tells us k = 15 (worker·hours), so our model equation is ...

y = 15/x . . . . . where x is the number of workers, and y is the hours to paint the room

Answer:

cos∠FHE = 4/5

Step-by-step explanation:

* Lets revise the trigonometry functions

- In ΔABC

# m∠B = 90°

# Length of AB = a , length of BC = b and length of AC = c

# The trigonometry functions of angle C are

- sin(C) = a/c ⇒ opposite side to ∠C ÷ the hypotenuse

- cos(C) = b/c ⇒ adjacent side to ∠C ÷ the hypotenuse

- tan(c) = a/b ⇒ opposite side to ∠C ÷ adjacent side to ∠C

* Now lets solve the problem

- To find cos∠FHE , we must find the length of the adjacent

 side HF and the length of the hypotenuse HE

- We can find the length of HF from ΔFGH

- In ΔFGH

∵ m∠G = 90°

∵ GF = √8

∵ m∠GHF = 45°

∵ sin∠GHF = GF/HF

∴ sin45° = √8/HF ⇒ by using cross-multiplication

∴ HF × sin45° = √8

∵ sin45° = 1/√2

∴ HF × 1/√2 = √8 ⇒ multiply each side by √2

∴ HF = √2 × √8 = √16 = 4

* Lets find the length of HE from ΔHFE

- In ΔHFE

∵ m∠HFE = 90°

∵ EF = 3 ⇒ given

∵ HF = 4

- By using Pythagoras theorem

∵ HE = √(FH² + FE²)

∴ HE = √(4² + 3²) = √(16 + 9) = √25 = 5

* Now we can find cos∠FHE

∵ cos∠FHE = HF/HE

∵ HF = 4 and HE = 5

∴ cos∠FHE = 4/5

Answer:

Step-by-step explanation:

25%:  640 X .25 =160

         640-160= $480

10%:   640 X .10= 64

        640- 64= $576

5%:     640 X .05 =32

        640- 32= $608

Answer:

the discount with rate 25%=$160,the discount with rate 10%=$64,the discount with rate 5%=$32

Step-by-step explanation:

Hello, I think I can help you with this

the discount is a percentage, a proportion of the real value, we can find that proportion using a simple rule  of three

let

100% =$640

Step 1

If

$640= 100%

x? %  = 25%    

($640/100%)=(x/25%)

isolating x

x=($640*25%)/(100%)

x=$160

the discount with rate 25%=$160

Step2

If

$640= 100%

x? %  = 10%

($640/100%)=(x/10%)

isolating x

x=($640*10%)/(100%)

x=$64

the discount with rate 10%=$64

Step 3

If

$640= 100%

x? %  = 5%

($640/100%)=(x/5%)

isolating x

x=($640*5%)/(100%)

x=$32

the discount with rate 5%=$32

Have a nice day

Answer:

• 109 lb 1 oz

• 115 gal 3 qt 1 pt

• 111 yd 8 in

Step-by-step explanation:

The relevant unit relationships are ...

1 lb = 16 oz

1 gal = 4 qt

1 qt = 2 pt

1 yd = 3 ft = 36 in

To convert from one unit to another, multiply by a fraction that has ...

(to unit)/(from unit)

For example, to convert (13 oz)×5 = 65 oz to pounds, multiply by (1 lb)/(16 oz). This will give you ...

(65 oz)·(1 lb)/(16 oz) = 65/16 lb = 4 1/16 lb

Now, if you don't already recognize that 1/16 lb = 1 oz, you can multiply the fraction by the unit conversion from lb to oz: (16 oz)/(1 lb). Doing that gives ...

(1/16 lb)·(16 oz)/(1 lb) = 16/16 oz = 1 oz

When the same units are in the numerator and denominator, they cancel, as do any factors that appear in both numerator and denominator.

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1. (21 13/16 lb)×5 = 105 65/16 lb = 109 1/16 lb = 109 lb 1 oz

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2. (12 7/8 gal)×9 = 108 63/8 gal = 115 7/8 gal = 115 gal 3 qt 1 pt

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3. ((15 2/3 +8/36) yd)×7 = (105 14/3 + 56/36) yd = 109 yd 2 ft + 1 yd 20 in

= 111 yd 8 in

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Additional explanation

7/8 gal = 7 pt = 1 pt + 3·2 pt = 1 pt + 3 qt

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14/3 yd = 4 2/3 yd = 4 yd 2 ft

56/36 yd = 1 20/36 yd = 1 yd + (12 +8)/36 yd = 1 yd + 1 ft + 8 in

Then 14/3 yd + 56/36 yd = (4 yd + 2 ft) + (1 yd + 1 ft + 8 in) = 6 yd + 8 in

X = 1/2(76 + 78)

x = 1/2(154)

x = 77