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3 years ago

If the function y = xa − 31 is a linear function, what is the value of a?

1 answer:

6 0

If we are to assume that a is an exponent on the x, then a would have to be 1, because x^1 is the same thing as just plain old x. If we put an exponent other than a 1 on that x, it is no longer linear. If we put an exponent of 2, the function would be a quadratic. If we put an exponent of 3, the function would be a cubic. If we put an exponent of 4, the function would be a quartic. Linear is just a plain line in the form y = mx + b.

You might be interested in

Integrate x <img src="https://tex.z-dn.net/?f=x4" id="TexFormula1" title="x4" alt="x4" align="absmiddle" class="latex-formula

Dmitrij [34]

Answer:

The result of the integration is $\frac{x^5}{5}$

Step-by-step explanation:

Integration of a power of x:

The integration of a power of x is:

$\int x^{n} dx = \frac{x^{n+1}}{n+1}$

In this question:

$n = 4$ . So

$\int x^{4} dx = \frac{x^{4+1}}{4+1} = \frac{x^5}{5}$

The result of the integration is $\frac{x^5}{5}$

4 0

3 years ago

In ΔBCD, the measure of ∠D=90°, the measure of ∠C=77°, and CD = 41 feet. Find the length of BC to the nearest foot.

OLga [1]

Answer:

182 ft

Step-by-step explanation:

When you are not given a diagram, always draw one for yourself (see diagram).

When you have a right triangle (triangle with 90° angle), you can use the trigonometry ratios, You can remember them using SohCahToa. It is read like this:

sinθ = opposite/hypotenuse Soh

cosθ = adjacent/hypotenuse Cah

tanθ = opposite/adjacent Toa

"θ" means the angle of reference (the angle you are talking about).

We are looking for the length of BC, which is the hypotenuse. I labelled it "d" (lowercase D) because it is opposite to ∠D.

We know ∠C = 77°. This will be our angle of reference (replace θ).

The side we know is DC, also known as "b" (lowercase B) because it's opposite to ∠B. "b" is the adjacent side when θ = C because "b" is touching ∠C.

Take the general trig. formula that has hypotenuse and adjacent: (cosine ratio)

cosθ = adjacent/hypotenuse

Substitute the variables specific for this problem.

cosC = b/d

Substitute the values you know.

cos77° = (41 ft) / d

Isolate "d" to the left side

dcos77° = $d*\frac{41ft}{d}$ Multiply both sides by "d"

dcos77° = 41 ft

dcos77° / cos77° = 41 ft / cos77° Divide both sides by cos77°

d = 41 ft / cos77° Input into calculator

d = 182.261874....... ft Unrounded answer

d ≈ 182 ft Rounded to nearest foot (whole number)

Remember d = BC. It's often easier to use one letter for calculations.

Therefore the length of BC is about 182 feet.

8 0

3 years ago

If EG = 59, and EF = 8x - 14, while FG = 4x + 1

lyudmila [28]

Answer:

x = 6

Step-by-step explanation:

EG = 59

EF = 8x - 14

FG = 4x + 1

to find the value of x

EF + FG = EG (same line)

8x - 14 + 4x + 1 = 59

12x -13 = 59

12x = 59 + 13

12x = 72

x = 72 ÷ 12

x = 6

You can even cross check for correct answer

EF + FG = EG

instead of x place the x's value we got

8x - 14 + 4x + 1 = 59

8 (6) - 14 + 4 (6) + 1 = 59

48 - 14 + 24 + 1 = 59

34 + 25 = 59

59 = 59

CROSS - CHECKED

4 0

3 years ago

Please help me!!!!!!!

Helen [10]

First we will find the value of x.

To find the value of x we can add angle Q and angle O and set them equal to 180 and solve for x.

We will be setting them equal to 180 since the opposite angles of an inscribed quadrilateral are supplementary.

angle Q + angle O = 180
6x - 5 + x + 17 = 180
7x +12 = 180
7x = 168
x = 24

Now we can use 24 for x and find the value of angle QRO

angle QRO = 2x + 19
angle QRO = 2(24) + 19
angle QRO = 48 + 19
angle QRO = 67

So the answer choice B is the right answer.

Hope this helps :)

6 0

4 years ago

Please someone answer this please

gladu [14]

Option C:

$\frac{3 a^{2} b^{11}}{2 }$ is equivalent to the given expression.