ZA and ZB are complementary angles. If mZA = (2x + 10)° and m
ZB = (3x + 15)', then find the measure of ZB.

Answer:

the answer is 4.5 in term of the measurement because Figure A has a larger scale and B has a smaller scale

Answer:

0.25

Step-by-step explanation:

Divide one side of Figure B by the congruent side of Figure A and you would get the scale factor.

If you multipy every side of figure A by 0.25 you would get the sides of figure B.

Hope this is helpful:)

Answer: 452.16 square feet

Step-by-step explanation:

The formula that is used to calculate the area of a circle is given as:

= πr²

where π = 3.14

r = Diameter/2 = 24/2 = 12

Area = πr²

= 3.14 × 12²

= 3.14 × 144

= 452.16 feet²

Therefore, the answer is 452.16 square feet.

B) 3,026 feet

Cause 5,942 - 2,916 = 3,026 feet

Answer:

its the last one D

Step-by-step explanation:

The median is 22 and the rest dont have that as the median

Equations:

[tex]x+6=5+x[/tex]

[tex]-2(x-3)=-2x+6[/tex]

[tex]4-4x=3x+2[/tex]

[tex]4(x+1)=3(x+2)[/tex]

[tex]5-3x=-3x+4[/tex]

Answer:

[tex]x+6=5+x[/tex]

[tex]5-3x=-3x+4[/tex]

Step-by-step explanation:

Given

[tex]x+6=5+x[/tex]

[tex]-2(x-3)=-2x+6[/tex]

[tex]4-4x=3x+2[/tex]

[tex]4(x+1)=3(x+2)[/tex]

[tex]5-3x=-3x+4[/tex]

Required:

Which have no solution

[tex]x+6=5+x[/tex]

Subtract x from both sides

[tex]x -x+6 = 5 + x - x[/tex]

[tex]6 = 5[/tex]

[tex]x+6=5+x[/tex] has no solution because [tex]6 \ne 5[/tex]

[tex]-2(x-3)=-2x+6[/tex]

Open bracket

[tex]-2x + 6 = -2x + 6[/tex]

Both sides are equal.

Hence, there is an [tex]Infinite\ Number[/tex] of Solutions

[tex]4-4x=3x+2[/tex]

Collect like terms

[tex]-3x - 4x = 2 - 4[/tex]

[tex]-7x = -2[/tex]

Solve for x

[tex]x = \frac{-2}{-7}[/tex]

[tex]x = \frac{2}{7}[/tex] --- This has a solution

[tex]4(x+1)=3(x+2)[/tex]

Open brackets

[tex]4x + 4 = 3x + 6[/tex]

Collect like terms

[tex]4x-3x = 6 - 4[/tex]

[tex]x = 2[/tex] --- This has a solution

[tex]5-3x=-3x+4[/tex]

Add 3x to both sides

[tex]5 - 3x + 3x = -3x + 3x + 4[/tex]

[tex]5 = 4[/tex]

[tex]5-3x=-3x+4[/tex] has no solution because [tex]5 \ne 4[/tex]

Answer:

y = 31

Step-by-step explanation:

Given

y = [tex]x^{5}[/tex] + 32 ← substitute x = - 2

y = [tex](-2)^{5}[/tex] + 63 = - 32 + 63 = 31

Answer:

(x - 15) ( x + 3)

Step-by-step explanation:

x² - 12x - 45

= x² - (15 - 3)x - 45

= x² - 15x + 3x - 45

= x(x - 15) + 3(x - 15)

= (x - 15) ( x + 3)

Answer:

0.9043secs and 0.3456secs

Step-by-step explanation:

Given the height of an overhand volleyball modeled as h=-16t^2+20t+6.

If the height is 11feet, then;

11 = -16t^2+20t+6.

-16t^2+20t+6 - 11 = 0

-16t^2+20t-5 = 0

Multiply thriugh by -1

16t^2-20t+5 = 0

Factorize

t = 20±√20²-4(16)(5)/2(16)

t = 20 ±√400-320/32

t = 20 ±√80/32

t = 20 ±4√5/32

t = 20±8.94/32

t = 28.94/32 and 11.06/32

t = 0.9043 and 0.3456

Hence the required time are 0.9043secs and 0.3456secs

Answer:

[tex](a)[/tex] [tex]V = -H^3+ 5H^2 + 36H[/tex]

[tex](b)[/tex] [tex]Length = 5in; Width = 9in; Height = 5in[/tex] or [tex]Length = 3in; Width = 10in; Height = 6in[/tex]

Step-by-step explanation:

Let:

[tex]W=Width; L = Length; H = Height[/tex]

Given

[tex]W = 4 + H[/tex]

[tex]L = 9 - H[/tex]

Solving (a): The polynomial for the volume in terms of height

Volume (V) is calculated using:

[tex]V = L * W * H[/tex]

[tex]V = (9 - H) * (4 + H) * H[/tex]

Expand

[tex]V = (9 - H) * (4H + H^2)[/tex]

Open brackets

[tex]V = 36H + 9H^2 - 4H^2 - H^3[/tex]

[tex]V = 36H + 5H^2 - H^3[/tex]

Rewrite as:

[tex]V = -H^3+ 5H^2 + 36H[/tex]

Solving (b): The dimensions when Volume = 180

Substitute 180 for V in: [tex]V = -H^3+ 5H^2 + 36H[/tex]

[tex]180 = -H^3+ 5H^2 + 36H[/tex]

Rewrite as:

[tex]H^3 - 5H^2 - 36H + 180 = 0[/tex]

Factorize:

[tex]H^2(H - 5) - 36(H - 5) = 0[/tex]

[tex](H^2 - 36)(H - 5) = 0[/tex]

Express [tex]H^2 - 36[/tex] as difference of two squares

[tex](H - 6)(H + 6)(H - 5) =0[/tex]

This gives:

[tex]H - 6 =0==> H = 6[/tex]

[tex]H + 6 =0==> H = -6[/tex]

[tex]H - 5 =0==> H = 5[/tex]

Since the height can not be negative, then H = 5 or H = 6

Recall that:

[tex]W = 4 + H[/tex]

[tex]L = 9 - H[/tex]

When H = 5

[tex]W = 4 + 5 = 9[/tex]

[tex]L = 9 - 5 = 4[/tex]

When H = 6

[tex]W = 4 + 6 = 10[/tex]

[tex]L = 9 - 6 = 3[/tex]

Hence, the dimensions of the box are:

[tex]Length = 5in; Width = 9in; Height = 5in[/tex]

or

[tex]Length = 3in; Width = 10in; Height = 6in[/tex]

The volume of the box is given by -h³ + 5h² + 36h

Volume is the amount of space occupied by a three dimensional object. The volume (V) of a box is given by:

V = length * width * height

Let h represent the the height, hence width = h + 4, length = (9 - h)

V = h(h + 4)(9 - h) = h(5h -h² + 36) = -h³ + 5h² + 36h

For a volume of 180 in³:

180 = -h³ + 5h² + 36h

h = 5 or 6.

The volume of the box is given by -h³ + 5h² + 36h

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Answer:

Mr. Linx wages = x = $15

Mrs. Lynn wages = y = $17.50

Step-by-step explanation:

Mr. Linx wages = x

Mrs. Lynn wages = y

x + y = 32.50 (1)

35x + 37y = 1,172.50 (2)

From (1)

x = 32.50 - y

Substitute x = 32.50 - y into (2)

35x + 37y = 1,172.50

35(32.50 - y) + 37y = 1172.50

1137.5 - 35y + 37y = 1172.50

- 35y + 37y = 1172.50 - 1137.50

2y = 35

y = 35/2

y = 17.50

Substitute y = 17.50 into (1)

x + y = 32.50

x + 17.50 = 32.50

x = 32.50 - 17.50

x = 15

Mr. Linx wages = x = $15

Mrs. Lynn wages = y = $17.50

Given:

The pairs of angles are:

36°,24°

18°,72°

96°,84°

To find:

Whether each pair of angle measurements are complementary, supplementary or neither.

Solution:

Two angles are complementary if there sum is 90 degrees.

Two angles are supplementary if there sum is 180 degrees.

For 36° and 24°,

[tex]36^\circ+24^\circ =60^\circ[/tex]

So, this pair is neither complementary not supplementary.

For 18° and 72°,

[tex]18^\circ+72^\circ =90^\circ[/tex]

So, this pair is complementary.

For 96° and 84°,

[tex]96^\circ+84^\circ =180^\circ[/tex]

So, this pair is supplementary.

Answer:

B

Step-by-step explanation:

C = πd = 3.14 * 32 = 100.48in

Answer:

Look at the other question i answered it for you

Step-by-step explanation:

Answer:

The number 5 units to the left of -4 is;

[tex] - 9[/tex]

Step-by-step explanation:

We want to number 5 units to the left of -4 on a number line.

Drawing the number line we have;

Therefore, The number 5 units to the left of -4 is;

[tex] - 9[/tex]

Explanation is in the file

tinyurl.com/wpazsebu

The no of three-pointer questions is 35 and the no of six-pointer questions is 15.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given:

The total no of questions = 50,

The total marks in the test = 195.

According to the question, the equation will be,

3x + 6y = 195 and x + y = 50

Here, x is the no of three mark question and y is the no of six marks question.

Solve the equation by elimination method, and we get,

x = 35 and y = 15

Therefore, the no of three-pointer questions is 35 and the no of six-pointer questions is 15.

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Answer is in the file below

tinyurl.com/wpazsebu

Answer:

choice 4) all of the angles are supplementary to each other since any two added together = 180°

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solve the compound inequality. 6 – x > 15 or 2x – 9 ≥ 3 A. x > 9 or x ≤ 6 B. x < 9 or x ≥ –6 C. x > –9 or x ≤ –6 D. x < –9 or x ≥ 6

Answer:

F

Step-by-step explanation:

The area is equal to length times width.

Use the foil method to multiply (2x-5)(3x+3).

The volume of the cone is [tex]\frac{\pi}{4}[/tex] the volume of the pyramid

The ratio of the area is given as:

[tex]R= \frac{\pi r^2}{4r^2}[/tex]

or

[tex]R= \frac{\pi}{4}[/tex]

The volume of a cone is:

[tex]V_1 = \frac 13 \pi r^2 h[/tex]

For a pyramid, the volume is:

[tex]V_2 = \frac 43 r^2h[/tex]

Rewrite as:

[tex]V_2 = 4 * \frac 13 r^2h[/tex]

Divide by 4

[tex]\frac{V_2}{4} = \frac 13 r^2h[/tex]

Substitute [tex]\frac{V_2}{4} = \frac 13 r^2h[/tex] in [tex]V_1 = \frac 13 \pi r^2 h[/tex]

So, we have:

[tex]V_1 = \frac{V_2}{4} * \pi[/tex]

This gives

[tex]V_1 = \frac{\pi}{4} V_2[/tex]

Hence, the volume of the cone is [tex]\frac{\pi}{4}[/tex] the volume of the pyramid

Read more about volumes at:

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Answer:

1017.6

Step-by-step explanation:

i think, if it is asking for the original sales price

Answer:

Sale price of phone:  $640

Sale price including tax:  $678.40

Step-by-step explanation:

If the discount is 20%, the price actually paid is (100% - 20%), or 80% of full price.

Multiplying $800 by 0.80 results in the sale price:  $640.

The 6% sales tax is 0.06($640), or $38.40.

Paying $38.40 sales tax on the $640 purchase results in a total paid of $678.40.

Answer:

First, we have to set it from least to greatest 11, 12, 12, 13, 14, 15, 16, 17, 18

The  interqurtile range is q3 - q1

Q3 is 16.5 and the q1 is 12

16.5 - 12 = 4.5

Step-by-step explanation:

Answer is 4.5

Interquartile range (IQR) :

The interquartile range shows the range in values of the central 50% of the data. To find the interquartile range, subtract the value of the lower quartile ( or 25%) from the value of the upper quartile ( or 75%).

=>  IQR = Q3 – Q1

Here,

First Arrange the data in ascending order.

11, 12, 12, 13, 14, 15, 16, 17, 18

Median = 14.

Q1 = 12 and Q3 = 16.5

IQR = Q3 - Q1 => 16.5 - 12 = 4.5

Answer is 4.5

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Answer:

m = -1, b = 5.

Step-by-step explanation:

We can find the slope, m, by plugging in our coordinates into the slope formula: [tex]\frac{y2-y1}{x2-x1} =\frac{2-7}{3-(-2)}=\frac{-5}{5}=-\frac{5}{5}=-\frac{1}{1}=-1[/tex]. That gives us the slope. Now we can fill that in the slope intercept formula: [tex]y=-1x+b[/tex]. We know one of the coordinates and the slope, which allows to find the y-intercept. We know that for every 1 unit down on the line, we move 1 unit right, and vice versa. Meaning we can just count down (or up in this case), so, (-2, 7), (-1, 6), (0, 5). Therefore, our y intercept is 5.

Answer:

x=5 and y=16

Step-by-step explanation:

x = number of pants

y = number of shirts

Set up equations:

Set the equations up as a system:

25x+14.5y=357

x+y=21

Steps:

Solve the system by substitution.

(You can also solve this system by elimination.)

25x + 14.5y=  357

x + y = 21

Step 1: Solve x+y=21 for x:

(x + y) − y = (21) − y(Subtract y from both sides)

x = −y + 21

Step 2: Substitute −y + 21 for x in 25x + 14.5y = 357:

25x + 14.5y = 357

25(−y + 21) + 14.5y = 357

−10.5y + 525 = 357 (Simplify both sides of the equation)

(−10.5y + 525) − 525 = (357) − 525(Subtract 525 to both sides)

−10.5y =  −168

−10.5y / −10.5 = −168 / −10.5 (Divide both sides by -10.5)

y = 16

Step 3: Substitute 16 for y in x = −y + 21:

x = −y + 21

x = −16 + 21

x = 5 (Simplify both sides of the equation)

Answer:

x=5 and y=16

Answer:

9 cm

Step-by-step explanation:

Given :

Area, A = 36cm²

Height, h = 8cm

Using the relation :

Area, A of triangle :

A = 1/2 * base * height

36 = 0.5 * base * 8

36 = 4 * base

base = 36 / 4

Base = 9 cm

Length of base is 9cm