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Answer:

The value of each T-shirt is $ 3 and the value of each sweatshirt is $ 10.

Step-by-step explanation:

Given that our school is selling T-shirts and sweatshirts as a fundraiser, and one student buys 2 Tt-shirts and 2 sweatshirts for $ 26, while another student buys 1 T-shirt and 3 sweatshirts for $ 33, to determine the value of the T-shirts and sweatshirts the following calculation must be made:

2X + 2Y = 26

X + 3Y = 33

Y - X = 7

2 x 3 + 2 x 10 = X

6 + 20 = X

26 = X

Therefore, the value of each T-shirt is $ 3 and the value of each sweatshirt is $ 10.

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Explanation:

For now, focus on triangle ABD. This is a right triangle due to BD being an altitude.

Use the pythagorean theorem to find that...

(AD)^2 + (BD)^2 = (AB)^2

(1)^2 + (BD)^2 = (3)^2

1 + (BD)^2 = 9

(BD)^2 = 9-1

(BD)^2 = 8

Normally we would isolate BD itself, but I'll stop short and use that last line instead.

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The triangles ABD and BCD are similar triangles (we can prove this using the AA similarity theorem).

Since we have similar triangles, we can form the proportion shown below

AD/BD = BD/CD

This cross multiplies to

AD*CD = (BD)^2

We know that AD = 1 and (BD)^2 = 8, so,

AD*CD = (BD)^2

1*CD = 8

CD = 8

This then means,

x = CD+DA

x = 8+1

x = 9

AC is 9 units long.

Answer:

2

Step-by-step explanation:

add 5/4 and 1/4 to get 6/4 or 3/2

(4^3/2 ÷ 4^1/2)^1/2 = 4^3/4 ÷ 4^1/4

4^3/4 ÷ 4^1/4 = 4^2/4 or 4^1/2

4^1/2 is the square root of 4, which is 2

Answer:

2

Step-by-step explanation:

In first step use the product rule of exponents .

so exponents going to add up.

Then in the second step simplified exponents.

After that Its division rule of exponents. and according to division to the exponents get subtracted.

In the end he would be left with four to the power half. which means square root of 4. which is 2.

Answer:

b

Step-by-step explanation:

8×19= 152  

1 : 4.5  

152×4.5=684  

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Work Shown:

area = base*height

area = 16*7

area = 112 square cm

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Extra info (optional section):

The area formula for a parallelogram is the same as the formula for a rectangle. Imagine tilting a rectangle so that it's slanted. The area has not changed.

Or another thing to imagine is that let's say we had a stack of 2 by 4s. If the stack is perfectly vertical, aka forming a rectangle, then we can nudge the beams so that we can form a slanted parallelogram instead. Both configurations involve the same amount of wood, and therefore would lead to the same frontal surface area.

Answer:

0.5

Step-by-step explanation:

From the graph given ;

The vertical distance ; y - axis :

(y2 - y1) ; y2 = 2 ; y1 = 1

y2 - y1 = 2 - 1 = 1

The horizontal distance ; the x - axis :

(x2 - x1) ; x2 = 4 ; x1 = 2

x2 - x1 = 4 - 2 = 2

The slope ; the rate of change :

Change in y / change in x

The rate of change ;

(y2 - y1) / (x2 - x1) = 1 / 2

Answer:

[tex]482.5\:\mathrm{in^2}[/tex]

Step-by-step explanation:

The area of the figure consists of a rectangle with a triangle removed from the corner of it. Therefore, the area of the composite of the figure can be found by subtracting the area of the triangle from the area of the rectangle.

Area of the rectangle: [tex]25\cdot 20=500\:\mathrm{in^2}[/tex]

Area of the triangle: [tex]\frac{1}{2}\cdot 5\cdot 7=17.5\:\mathrm{in^2}[/tex]

Thus, the area of the figure is [tex]500-17.5=\boxed{482.5\:\mathrm{in^2}}[/tex]

Answer:

3(b+2)balls

Step-by-step explanation:

Given data

number of bags of golf balls= 3

number of balls in each bag=b

total number of balls in all three bags= 3b

His friend gave him 6 more= 3b+6

Hence the total balls is = 3b+6

= 3(b+2)balls

Answer:

The answer is 37

Step-by-step explanatio

Answer: 17 square inches.

Step-by-step explanation: Area of a triangle is 1/2 x b x h. We can just take the area of half of the whole triangle, and double it. In this case, half of the triangle has an area of 1/2 x 3.4 x 5 = 8.5. Doubling it is the same is doing 8.5 x 2, which equals 17.

Given:

Radius of a cylinder = 5 units.

Surface area of the cylinder = [tex]160\pi[/tex]

To find:

The height of the right cylinder.

Solution:

Surface area of a cylinder is:

[tex]A=2\pi rh+2\pi r^2[/tex]

Where, r is radius and h is the height of the cylinder.

Putting [tex]r=5, A=160\pi[/tex] in the above formula, we get

[tex]160\pi =2\pi (5)(h)+2\pi (5)^2[/tex]

[tex]160\pi =10\pi h+2\pi (25)[/tex]

[tex]160\pi =10\pi h+50\pi [/tex]

Subtract [tex]50\pi[/tex] from both sides.

[tex]160\pi -50\pi=10\pi h [/tex]

[tex]110\pi=10\pi h [/tex]

Divide both sides by [tex]10\pi[/tex].

[tex]\dfrac{110\pi}{10\pi}=h[/tex]

[tex]11=h[/tex]

Therefore, the height of the cylinder is 11 units.

Answer:

360 meters

Step-by-step explanation:

[tex]\sqrt{8100}[/tex] = 90

one edge = 90 meters

90 x 4 = 360

360 meters

Answer:

96 cm^2

Step-by-step explanation:

the diagonal bisect in the point of intersection, so their length is 12 cm and 16 cm

Area = (12 * 16)/2 = 96 cm^2

Answer:

24 cm^2

Step-by-step explanation:

rhombus -.-

Answer:

23 thousandths. = 23 ÷ 10^3

9+4 × (6÷3) > (9+4×6) ÷ 3

5 tens + 2 hundredths. < 50.20

810.6 ÷ 10. = 8.106 × 10

Answer:

49 in the first box and 7 in the second one

25 in the 3rd box and 5 in the 4th

Answer:

Step-by-step explanation:

Total hours:

Answer:the one to the left

Step-by-step explanation:

Answer:

6) 62.5%

7) 54

8) B

Step-by-step explanation:

For number 6, just add 96 and 160 and then do 160/(96+160), which is equal to 0. 625, or 62.5%.

for number 7, x is always equal to 1/3 of y, so if x is 18, we know that 18 is 1/3 of y. 18x3 is equal to 54, which is your answer.

For number 8, you can see that B is right because it uses the greatest common factor of 32 and 48, which is 16. All the other answers can be simplified more.

Answer:

6. C) 62.5%

7. D) 54

8. B) 16(2c + 3d)

Step-by-step explanation:

160 + 96 = 256

[tex]\frac{160}{256}=\frac{160/32}{256/32}=\frac{5}{8}[/tex]

5 ÷ 8 = 0.625

0.625 × 100

62.5%

GCF = 32

The factors of 160: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160

The factors of 256: 1, 2, 4, 8, 16, 32, 64, 128, 256

The GCF is 32.

1:3 = 7:21 = 9:27 = 13:39 = 18:y

[tex]\frac{1}{3}: \frac{18}{y}[/tex]

1 × y = 18 × 3

y = 54

GCF(32, 48)

32 = 2 × 2 × 2 × 2 × 2

48 = 2 × 2 × 2 × 2 × 3

GCF = 2 × 2 × 2 × 2

GCF = 16

16(2c + 3d)

Answer:

gotta be  answer A

Step-by-step explanation:

you can search up f(x) = square root of x

Answer:

Step-by-step explanation:

Triangles are similar if their corresponding angles are congruent and corresponding sides are proportional.

Answer:

39

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

52-(20+20+8)

Answer:

Point X

Step-by-step explanation:

Okay so to find the answer to this one simply go to the origin (0,0), then go over 4 and then up 3

The point located at point (4,3) would be point X

Answer:20.75

Step-by-step explanation:

Trust me gangsta

Answer:

(1,-1)

Step-by-step explanation:

y = -1

5x+7y = -2

Substitute the first equation into the second

5x + 7(-1) =-2

5x -7 = -2

Add 7 to each side

5x-7+7 = -2+7

5x= 5

Divide by 5

5x/5 = 5/5

x =1

(1,-1)