All categories

3 years ago

Triangle △A′B′C′ is the image of △ABC under a dilation with a scale factor of 2.

Mathematics

1 answer:

Aloiza [94]3 years ago

6 0

Answer:

8 units if it's talking about the shown triangle, and 4 units if it's talking about the original

Step-by-step explanation:

I would guess it's talking about the original so do 4 units first

You might be interested in

In △ABC, m∠A = α, m∠B = β, m∠C = γ. AB = c, AC = b, BC = a. Find the areas of the triangles if the following parts are given.

Mazyrski [523]

A = c/sin C, and b by the proportion b/sin B = c/sin C.

a/sin 37° = 4380/sin 109°
a sin 109° = 4380 sin 37°
a = 4380 sin 37°/sin 109° ≈ 2787.8

b/sin 34° = 4380/sin 109°
b sin 109° = 4380 sin 34°
b = 4380 sin 34°/sin 109° ≈ 2590.4

6 0

3 years ago

Solve GHI. Round the answer to the nearest hundredth.

Sedaia [141]

Answer:

Part 1) $HI=15\ units$

Part 2)

Part 3) $< I=28.07\°$

The answer is the option A

Step-by-step explanation:

Part 1) Find the measure of side HI

Applying the Pythagoras Theorem

$GI^{2} =GH^{2}+HI^{2}$

substitute the values and solve for HI

$17^{2} =8^{2}+HI^{2}$

$HI^{2}=17^{2}-8^{2}$

$HI^{2}=225$

$HI=15\ units$

Part 2) Find the measure of angle G

In the right triangle GHI

$cos(G)=\frac{GH}{GI}$

substitute the values

$cos(G)=\frac{8}{17}$

$G=arccos(\frac{8}{17})=61.93\°$

Part 3) Find the measure of angle I

Remember that

The sum of the interior angles of a triangle must be equal to 180 degrees

substitute the values

$61.93\°+90\°+< I=180\°$

$< I=180\°-(61.93\°+90\°)=28.07\°$

7 0

3 years ago

Given parallelogram MNOP, MA = x + 5, AO = y + 2, PA = 3x and AN = 2y

erma4kov [3.2K]

Answer:

The values of x and y are x = 6 and y = 9

Step-by-step explanation:

MNOP is a parallelogram its diagonal MO and PN intersected at point A

In any parallelogram diagonals:

Bisect each other
Meet each other at their mid-point

In parallelogram MNOP

∵ MO and NP are its diagonal

∵ MO intersect NP at point A

- Point A is the mid-point pf them

∴ MO and NP bisect each other

∴ MA = AO

∴ PA = AN

∵ MA = x + 5

∵ AO = y + 2

- Equate them

∴ x + 5 = y + 2 ⇒ (1)

∵ PA = 3x

∵ AN = 2y

- Equate them

∴ 2y = 3x

- Divide both sides by 2

∴ y = 1.5x ⇒ (2)

Now we have a system of equations to solve it

Substitute y in equation (1) by equation (2)

∴ x + 5 = 1.5x + 2

- Subtract 1.5x from both sides

∴ - 0.5x + 5 = 2

- Subtract 5 from both sides

∴ - 0.5x = -3

- Divide both sides by - 0.5

∴ x = 6

- Substitute the value of x in equation (2) to find y

∵ y = 1.5(6)

∴ y = 9

The values of x and y are x = 6 and y = 9

4 0

3 years ago

For a party, you are cooking a large amount of stew that has meat, potatoes, and carrots. The meat costs $6 per pound, the potat

Vaselesa [24]

Answer:

6lb meat

2.5lb potatoes

5Ib carrots

Step-by-step explanation:

M + P + C = 13.5

6M + 3P + C = 48.50

OM + 2P - C = O

2P = C

Therefore, there are 6 pounds of meat, 2.5 pounds of potatoes, and 5 pounds of carrots.

7 0

3 years ago

The mass of a freight train is 9.98 ⋅ 106 kilograms. The mass of an aircraft carrier is 7.3 ⋅ 107 kilograms. Approximately how m

shutvik [7]

Mass of freight train: 9.98 • 106
= 1057.88 kg
mass of aircraft carrier: 7.3 • 107
= 781.1 kg
difference: 1057.88 - 781.1
= 276.78 kg
= 2.7678 x 10^2

8 0

3 years ago