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2 years ago

The following table represents a function.

Mathematics

2 answers:

ivanzaharov [21]2 years ago

6 0

The answer is B. Plug in the x values to check the y values.

netineya [11]2 years ago

4 0

Answer:

Step-by-step explanation:

To find the right exponential function, we can just take x-values an replace them into the given functions. The one that give the correct y-values will be the answer.

For $x=-2$ , let's see which function gives $y=-\frac{1}{8}$

$y=8(4)^{x-1} \\y=8(4)^{-2-1}\\ y=8(4)^{-3}\\ y=\frac{8}{4^{3} }=\frac{1}{8}$

You can observe that function A is not the correct one, because it gives a positive result. However, function B can actually be the answer, because it woud give the same y-value than A but negative, as we need. Let's see

$y=-8(4)^{x-1}\\ y=-8(4)^{-2-1}\\ y=-8(4)^{-3}\\ y=-\frac{8}{4^{3} }=-\frac{1}{8}$

Let's evalute for $x=0$

$y=-8(4)^{0-1}=-8(4)^{-1}= -\frac{8}{4}=-2$

Which is right.

Therefore, the right answer is B.

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Find the area of each figure

Anon25 [30]

Area of trapezoid = a + b/2 * h
a = 20, b = 9, h = 21/-16
20+9/2 * (21-16) = 29/2 * 5 = 72.5
The area of the trapezoid = 72.5 in^2

Area of the rectangle = l * w
l = 16, w = 20
16 * 20 = 320
The area of the rectangle: 320 in^2

7 0

2 years ago

Please help with this question, thank you :)

vovikov84 [41]

Answer:

1/2

((-2)^2-(4*2)^1/3)/abs(-2*2)

-2^2 = 4

4*2 = 8

-2*2 = -4 and abs of that is 4

4-(8)^1/3/4

8^1/3 = 2

4-2 = 2

2/4 = 1/2

Step-by-step explanation:

4 0

2 years ago

Express the fractions 2/3, 3//4 and 5/6 as equivalent fractions with a denominator of<br>12

lina2011 [118]

Answer:

like 2/3 or 15/16; Mixed number - like 1 1/2 or 4 5/6; Integer - like 5 or 28

Step-by-step explanation:

6 0

3 years ago

Evaluate the following integral using trigonometric substitution

serg [7]

Answer:

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

Step-by-step explanation:

We are given the following integral:

$\int \frac{dx}{\sqrt{9-x^2}}$

Trigonometric substitution:

We have the term in the following format: $a^2 - x^2$ , in which a = 3.

In this case, the substitution is given by:

$x = a\sin{\theta}$

$dx = a\cos{\theta}d\theta$

In this question:

$a = 3$

$x = 3\sin{\theta}$

$dx = 3\cos{\theta}d\theta$

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9-(3\sin{\theta})^2}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9 - 9\sin^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{\theta})}}$

We have the following trigonometric identity:

$\sin^{2}{\theta} + \cos^{2}{\theta} = 1$

$1 - \sin^{2}{\theta} = \cos^{2}{\theta}$

Replacing into the integral:

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{2}{\theta})}} = \int{\frac{3\cos{\theta}d\theta}{\sqrt{9\cos^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{3\cos{\theta}} = \int d\theta = \theta + C$

Coming back to x:

We have that:

$x = 3\sin{\theta}$

$\sin{\theta} = \frac{x}{3}$

Applying the arcsine(inverse sine) function to both sides, we get that:

$\theta = \arcsin{(\frac{x}{3})}$

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

8 0

2 years ago

a shape is randomly selected from the following quadrilaterals: parallelogram, rhomus, trapaziod, rectangle, square. what is pro

Artyom0805 [142]

Answer:

Step-by-step explanation:

So, it's hard to know if the sides on the parallelogram are equal or not, but both a rhombus and square have four congruent sides, but only a square has four right angles.

So 1/2 shapes fit both parameters. Therefore there is a 50% probability it has four right angles, given that it has four congruent sides.

5 0

3 years ago