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2 years ago

This mapping shows a functional relationship. When f(x)=4, what is the value of x?

Mathematics

1 answer:

marishachu [46]2 years ago

3 0

Answer:

x=2

Step-by-step explanation:

This is a one-to-one relationship, so when the output (range) is 4, the input (domain) is 2

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If x = 10, find the value of:<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B2%20%7Bx%7D%5E%7B2%7D%28x%20-%205%29%20%7D%7B10x

vesna_86 [32]

Answer:

$10$

Step-by-step explanation:

$\frac{2(10)^2(10-5)}{10(10)}$

Square the 10.

$\frac{2(100)(10-5)}{10(10)}$

Subtract 10 with 5.

$\frac{2(100)(5)}{10(10)}$

Multiply the numbers in the numerator.

$\frac{2(500)}{100}$

$\frac{1000}{100}$

Divide 1000 with 100.

$=10$

4 0

2 years ago

Read 2 more answers

Analyze the diagram below and complete the instructions that follow.

lora16 [44]

Answer:

$\displaystyle y=2\sqrt{6}$

$\displaystyle x=2\sqrt{2}$

Step-by-step explanation:

<u>Trigonometric Ratios </u>

The ratios of the sides of a right triangle are called trigonometric ratios.

The longest side of the right triangle is called the hypotenuse and the other two sides are the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

The image provided shows a right triangle whose hypotenuse is given. We are required to find the value of both legs.

Let's pick the angle of 30°. Its adjacent side is y. We can use the cosine ration, which is defined as follows:

$\displaystyle \cos 30^\circ=\frac{\text{adjacent leg}}{\text{hypotenuse}}$

$\displaystyle \cos 30^\circ=\frac{y}{4\sqrt{2}}$

Solving for y:

$y=4\sqrt{2}\cos 30^\circ$

Since:

$\cos 30^\circ=\frac{\sqrt{3}}{2}$

$\displaystyle y=4\sqrt{2}\frac{\sqrt{3}}{2}$

Simplifying:

$\displaystyle y=2\sqrt{6}$

Now we use the sine ratio:

$\displaystyle \sin 30^\circ=\frac{\text{opposite leg}}{\text{hypotenuse}}$

$\displaystyle \sin 30^\circ=\frac{x}{4\sqrt{2}}$

Solving for x:

$x=4\sqrt{2}\sin 30^\circ$

Since:

$\sin 30^\circ=\frac{1}{2}:$

$\displaystyle x=4\sqrt{2}\frac{1}{2}$

Simplifying:

$\displaystyle x=2\sqrt{2}$

The choices are not clear, but it seems like the correct answer is C.

$\boxed{\displaystyle y=2\sqrt{6}}$

$\boxed{\displaystyle x=2\sqrt{2}}$

6 0

3 years ago

What is the volume of this composite solid?

katen-ka-za [31]

Answer: c

Step-by-step explanation:

i did the test

7 0

2 years ago

If a bowling ball is dropped out of an airplane,

Rom4ik [11]

Answer: The velocity of the ball is 108.8 ft/s downwards.

Step-by-step explanation:

When the ball is dropped, the only force acting on the ball will be the gravitational force. Then the acceleration of the ball will be the gravitational acceleration, that is something like:

g = 32 ft/s^2

To get the velocity equation we need to integrate over time, to get:

v(t) = (32ft/s^2)*t + v0

where v0 is the initial velocity of the ball. (t = 0s is when the ball is dropped)

Because it is dropped, the initial velocity is equal to zero, then we get:

v(t) = (32ft/s^2)*t

Which is the same equation that we can see in the hint.

Now we want to find the velocity 3.4 seconds after the ball is dropped, then we just replace t by 3.4s, then we get:

v(3.4s) = (32ft/s^2)*3.4s = 108.8 ft/s

The velocity of the ball is 108.8 ft/s downwards.

6 0

3 years ago

Question 4 of 5

Arturiano [62]

Answer:

D. 9 cm

Step-by-step explanation:

The radius of the sphere can be found by solving the volume equation for the radius.

V = 4/3πr³

3V/(4π) = r³

r = ∛(3V/(4π)) = ∛(3×3052/(4×π)) ≈ ∛728.611

r ≈ 9.0 cm

The radius of the sphere is about 9 cm.

4 0

2 years ago