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3 years ago

Which is a solution to the equation y = 2x – 5? A.(3, 11) B.(2, 1) C.(1, –3) D.(5, –5)

1 answer:

8 0

The correct answer is C. (1, -3).

In the brackets, the first number refers to x, and the second to y (like when you write coordinates).

So we can check what is y ineach of the options and compare whether both of the sided of the equasion are equal:
A. 2x-5=-1, should be 11, false
B. 2x-5=4-9=-5, should be 1, false
C. 2x-5=2-5=-3, should be -3, correct
D. 2x-5=10-5=5, should be -5, false

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Find area of the shaded region.

Monica [59]

Answer:

The area of the shaded region is about 38.1 square centimeters.

Step-by-step explanation:

We want to find the area of the shaded region.

To do so, we can first find the area of the sector and then subtract the area of the triangle from the sector.

The given circle has a radius of 6 cm.

And the given sector has a central angle of 150°.

The area for a sector is given by the formula:

$\displaystyle A=\pi r^2\cdot \frac{\theta}{360^\circ}$

In this case, r = 6 and θ = 150°. Hence, the area of the sector is:

$\displaystyle \begin{aligned}A&=\pi(6)^2\cdot \frac{150}{360}\\ &=36\pi\cdot \frac{5}{12}\\&=3\pi \cdot 5\\&=15\pi \text{ cm}^2\end{aligned}$

Now, we can find the area of the triangle. We can use an alternative formula:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

Where a and b are the side lengths, and C is the angle between them.

Both side lengths of the triangle are the radii of the circle. So, both side lengths are 6.

And the angle C is 150°. Hence, the area of the triangle is:

$\displaystyle A=\frac{1}{2}(6)(6)\sin(150)=18\sin(150)$

The area of the shaded region is equivalent to the sector minus the triangle:

$A_{\text{shaded}}=A_{\text{sector}}-A_{\text{triangle}}$

Therefore:

$A_{\text{shaded}}=15\pi -18\sin(150)$

Use a calculator:

$A_{\text{shaded}}=38.1238...\approx 38.1\text{ cm}^2$

The area of the shaded region is about 38.1 square centimeters.

6 0

3 years ago

A percent is a ratio of the ________ to the _______.

riadik2000 [5.3K]

Answer:

A percent is a ratio of the parts to the whole

Step-by-step explanation:

If you had 30/100, 30% as a percentage, 30 would be the parts and 100 would be the whole

7 0

3 years ago

(PLEASE HELP) Evaluate the expression 2(8 − 4)^2 − 10 ÷ 2.

SOVA2 [1]

To answer your question (PLEASE HELP) Evaluate the expression 2(8 − 4)^2 − 10 ÷ 2.

The answer would be B:27

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3 years ago

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At the honda dealership,45% of all cars sold include a sunroof. If this sold 247 cars last week, about how many would you expect

sertanlavr [38]

It is 45% of 247 move the the decimal on the 45% two places to the right, then you should get .45. Of means multiply so .45*247 should get you the answer of 111.15 that's how you find the percent of this number. If you round the answer you would get 111 so about 111cars had a sunroof

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3 years ago

How many days will a bottle of 294 blue pills last if a patient takes 6 blue pills per day?

creativ13 [48]

Answer: It'll take a patient 49 days to consume 294 pills.

6 × 49 = 294.

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3 years ago

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