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3 years ago

Find the domain and range of the relation, and determine whether it is a function.

1 answer:

7 0

The domain is all the x values so {2,-4, 1, 2, -1}
The range is all the y values so {1, 5, 7, -3, 2}

Yes, it is a function because each item in the domain matches one item in the ranges.

You might be interested in

Which of the following shows (2x + y) 4 (4 is small) In expanded notation?

professor190 [17]

Answer:

8x+4y

Step-by-step explanation:

so use the distributive property and multiply 4 into (2x+y), so you get

(2x*4) + (y*4) = 8x + 4y

hope this helped

7 0

2 years ago

For positive acute angles AA and B,B, it is known that \tan A=\frac{28}{45}tanA= 45 28 and \cos B=\frac{3}{5}.CosB= 5 3 . Fi

MrRa [10]

Answer:

$\cos(A + B) = \frac{23}{265}$

Step-by-step explanation:

Given

$\tan A=\frac{28}{45}$

$\cos B=\frac{3}{5}$

Required

$\cos(A+B)$

In trigonometry:

$\cos(A+B) = \cos\ A\ cosB - sinA\ sinB$

We need to solve for cosA, sinA and sinB

Given that:

$\tan A=\frac{28}{45}$ and the tangent of an angle is a ratio of the opposite side (x) to the adjacent side (y),

So, we have:

$x =28$ and $y = 45$

For this angle A, we need t calculate its hypotenuse (z).

Using Pythagoras,

$z^2 = x^2 + y^2$

$z = \sqrt{x^2 + y^2$

$z = \sqrt{28^2 + 45^2$

$z = \sqrt{2809$

$z = 53$

From here, we can calculate sin and cos A

$\sin A= \frac{opposite}{hypotenuse}$ and $\cos A= \frac{adjacent}{hypotenuse}$

$\sin A= \frac{x}{z}$

$\sin A= \frac{28}{53}$

$\cos A= \frac{y}{z}$

$\cos A= \frac{45}{53}$

To angle B.

Give that

$\cos B=\frac{3}{5}$ and the cosine of an angle is a ratio of the adjacent side (a) to the hypotenuse side (c),

So, we have:

$a = 3$ and $b = 5$

For this angle B, we need to calculate its opposite (b).

Using Pythagoras,

$c^2 = a^2 + b^2$

$5^2 = 3^2 + b^2$

$25 = 9 + b^2$

Collect like terms

$b^2 = 25 - 9$

$b^2 = 16$

$b = \sqrt{16$

$b = 4$

From here, we can calculate sin B

$\sin B= \frac{opposite}{hypotenuse}$

$\sin B = \frac{b}{c}$

$\sin B = \frac{4}{5}$

Recall that:

$\cos(A+B) = \cos\ A\ cosB - sinA\ sinB$

and

$\cos B=\frac{3}{5}$ $\sin B = \frac{4}{5}$ $\sin A= \frac{28}{53}$ $\cos A= \frac{45}{53}$

$\cos(A + B) = \frac{45}{53} * \frac{3}{5} - \frac{28}{53} * \frac{4}{5}$

$\cos(A + B) = \frac{135}{265} - \frac{112}{265}$

$\cos(A + B) = \frac{135-112}{265}$

$\cos(A + B) = \frac{23}{265}$

7 0

2 years ago

Find the value of 2 in the following equation: 8z=64

mariarad [96]

Altho' 2 is a factor of both 8 and 64, we cannot "find the value of 2" because that's already given.

I believe you may have meant "<span>Find the value of z in the following equation: 8z=64".

We can solve that equation for z: z = 64/8, or z = 8 (answer).</span>

5 0

3 years ago

Refer to the data above. What number represents the slope of the line, if the points on the graph above were joined?

Dmitrij [34]

Answer:

slope = 40

Step-by-step explanation:

Calculate the slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$