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shutvik [7]
3 years ago
15

Given that the triangles shown below are simiar, what is the value of x?

Mathematics
1 answer:
mrs_skeptik [129]3 years ago
3 0

Answer:

C) 14

Step-by-step explanation:

Both triangles are the same as far as angles, DEF is however half of ABC. Therefore x is half of 28

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Items for a fundraiser are packaged in small boxes shaped like rectangular prisms that are inches long, inches wide, and 8 inche
allochka39001 [22]

Answer:

- The number of small boxes that will fill the large box 1 = 64

- The number of small boxes that will fill the large box 2 = 56

Step-by-step explanation:

Complete Question

Items for a fundraiser are packaged in small boxes shaped like rectangular prisms that are 4.5 inches long, 4.5 inches wide, and 8 inches tall. To transport the items to an event, you want to know how many of the small boxes will fit in larger boxes. The larger boxes are available in two sizes. Large Box 1 is 24.25 inches long, 18 inches wide, and 24 inches tall. Large Box 2 is 20.5 inches long, 18.5 inches wide, and 24 inches tall. Both the small and large boxes must remain upright.

Solution

To know how many of the small boxes will fit in larger boxes, we need to obtain the volumes of the small box, large box 1 and large box 2.

Volume of a cuboid = L × W × H

For the small box,

Length = L = 4.5 inches

Width = W = 4.5 inches

Height = H = 8 inches

Volume of the small box = 4.5 × 4.5 × 8 = 162 in³

For large box 1,

Length = L = 24.25 inches

Width = W = 18 inches

Height = H = 24 inches

Volume of the large box 1 = 24.25 × 18 × 24 = 10,476 in³

For large box 2

Length = L = 20.5 inches

Width = W = 18.5 inches

Height = H = 24 inches

Volume of the large box 2 = 20.5 × 18.5 × 24 = 9,102 in³

The number of small boxes that'll fill the large box 1 = (10,476/162) = 64.667 = 64 small boxes (rounded down because the fraction cannot be forced into the large box 1.

The number of small boxes that will fill the large box 2 = (9,102/162) = 56.185 = 56 small boxes.

Hope this Helps!!!

7 0
3 years ago
On Monday, 341 students went on a trip to the zoo. All 6 buses were filled and 5 students had to travel in cars. How many studen
Otrada [13]

Answer:

If 4 students travelled in cars, then 341 - 5 = 336students travelled by bus.

 There were 5 buses.  336÷ 6 = 56

 There were 56 students on each bus.

3 0
3 years ago
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The area of a sail is 4012
bezimeni [28]

Answer:

2006 sorry if I’m wrong I divided it by 2

Step-by-step explanation:

6 0
3 years ago
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the three sides of a triangle are n, 3n+2, and 4n−4. If the perimeter of the triangle is 54cm, what is the length of each side?
taurus [48]

The lengths of the sides are 7, 23 and 24.

In order to find this, we need to add all of the side lengths together and set equa to 54. This will allow us to solve for n.

n + 3n + 2 + 4n - 4 = 52

8n - 2 = 52

8n = 54

n = 7

This gives us the length of the first side. To solve for the others, plug 7 into the equations.

3n + 2

3(7) + 2

21 + 2

23

Then the next one.

4n - 4

4(7) - 4

28 - 4

24

8 0
3 years ago
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Write an equation of a line in slope intercept form that is perpendicular to the line 2x -3y = 12 and passes through the point (
Scilla [17]

Answer:

The equation of the line would be y = -3/2x + 9

Step-by-step explanation:

In order to solve this, start by finding the slope of the original line. You can do this by solving for y.

2x - 3y = 12

-3y = -2x + 12

y = 2/3x - 4

Now that we have a slope of 2/3, we know that the perpendicular slope is -3/2 (since perpendicular lines have opposite and reciprocal slopes). We can use this and the new point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 6 = -3/2(x - 2)

y - 6 = -3/2x + 3

y = -3/2x + 9

4 0
3 years ago
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