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3 years ago

Which congruence theorem can be used to prove ABR = RCA?

1 answer:

8 0

Answer: The HL Theorem can be used to prove ABR ≅ RCA because both triangles share the same hypotenuse and a leg. The HL theorem states that If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

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Every female bear has 3 baby cubs. What is the constant of proportionality for the ratio of cubs to female bears? (4 points)

andrezito [222]

Answer:

3:1 ratio

Step-by-step explanation:

5 0

3 years ago

Solve for x. Round to the nearest tenth, if necessary.

Sphinxa [80]

Answer:

2.8

Step-by-step explanation:

tan = opposite / adjacent

( opposite = side opposite of the angle and adjacent = side length that is not the opposite nor the hypotenuse ( longest side ) )

we are given an angle, ∠E = 26°

tanE = x / 5.7

tan26 = x / 5.7

==> multiply both sides by 5.7

5.7tan26 = x

==> simplify

x = 2.8 ( rounded )

3 0

2 years ago

The smith family walked 2/3 of a mile in 2/7 of an hour? What is their unit rate in miles per hour? Explain how this is determin

frez [133]

Answer: $2\dfrac13\text{ miles per hour}$

Step-by-step explanation:

Given: Distance traveled by Smith = $\dfrac23$ mile.

Time taken = $\dfrac27$ hour

Unit rate in miles per hour = ( Distance traveled by Smith) ÷ (Time taken)

$=\dfrac23\div\dfrac27$

$\\\\=\dfrac23\times\dfrac72\\\\=\dfrac73\\\\=2\dfrac13\text{ miles per hour}$

Unit rate = $2\dfrac13\text{ miles per hour}$

6 0

3 years ago

9sin(2x) sin (x) = 9cos(x)

nikdorinn [45]

Answer:

$\sin(2x) = 2 \sin(x) \cos(x) \\ 9( 2 \sin(x) \cos(x) ) \sin(x) = 9 \cos(x) \\ 18 { \sin}^{2} (x)9 \cos(x) - 9 \cos(x) = 0 \\ 9 \cos(x) (2{ \sin}^{2} (x) - 1) = 0 \\ 9 \cos(x) = 0 \: or \: 2{ \sin}^{2} (x) - 1 = 0 \\ \sin(x) = \pm \frac{1}{ \sqrt{2} } \\ \cos(x) = 0 \\ x = { \cos}^{ - 1} (0) \\ x = \frac{ \pi}{2} = 90 \degree \\ x = \frac{ \pi}{2} + 2\pi \: n \: \forall \: n \: \in \: \Z \\ = 90 \degree + 360\degree\: n \: \forall \: n \: \in \: \Z \\ = \pm\frac{ \pi}{4} \pm2\pi \: n \: \forall \: n \: \in \: \Z \\ x = \pm45\degree \pm 360\degree\: n \: \forall \: n \: \in \: \Z$

8 0

2 years ago

A half-filled cylindrical water tank has a water level of 20 feet high. The tank can hold 6000 cubic feet of water. Find the dia

Anettt [7]

Answer:

d = 13.8 feet

Step-by-step explanation:

Because we are talking about cubic feet of water, we need the formula for the VOLUME of a cylinder. That formula is

$V=\pi r^2h$

We will use 3.141592654 for pi; if the tank HALF filled with water is at 20 feet, then the height of the tank is 40 feet, so h = 40; and the volume it can hold in total is 6000 cubic feet. Filling in then gives us:

$6000=(3.141592654)(r^2)(40)$

Simplify on the right to get

$6000=125.6637061r^2$

Divide both sides by 125.6637061 to get that

$r^2=47.74648294$

Taking the square root of both sides gives you

r = 6.90988299

But the diameter is twice the radius, so multiply that r value by 2 to get that the diameter to the nearest tenth of a foot is 13.8

5 0

4 years ago