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3 years ago

Find the zeros of the function. f(x) = 3x2 – 8x – 16

Mathematics

1 answer:

Vlad1618 [11]3 years ago

5 0

Answer:

amusing you mean 3x^2-8x-16 the answer is when x is equal to -4/3 and 4

Step-by-step explanation:

3x^2-8x-16 ------> (3x+4)(x-4)

3x+4=0 ----> 3x=-4 ----> x=-4/3

x-4=0 ----> x=4

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PLS ANSWER ASAP 30 POINTS!!! CHECK PHOTO! WILL MARK BRAINLIEST TO WHO ANSWERS

Sveta_85 [38]

I'll do Problem 8 to get you started

a = 4 and c = 7 are the two given sides

Use these values in the pythagorean theorem to find side b

$a^2 + b^2 = c^2\\\\4^2 + b^2 = 7^2\\\\16 + b^2 = 49\\\\b^2 = 49 - 16\\\\b^2 = 33\\\\b = \sqrt{33}\\\\$

With respect to reference angle A, we have:

opposite side = a = 4
adjacent side = b = $\sqrt{33}$
hypotenuse = c = 7

Now let's compute the 6 trig ratios for the angle A.

We'll start with the sine ratio which is opposite over hypotenuse.

$\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(A) = \frac{a}{c}\\\\\sin(A) = \frac{4}{7}\\\\$

Then cosine which is adjacent over hypotenuse

$\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(A) = \frac{b}{c}\\\\\cos(A) = \frac{\sqrt{33}}{7}\\\\$

Tangent is the ratio of opposite over adjacent

$\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(A) = \frac{a}{b}\\\\\tan(A) = \frac{4}{\sqrt{33}}\\\\\tan(A) = \frac{4\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\tan(A) = \frac{4\sqrt{33}}{(\sqrt{33})^2}\\\\\tan(A) = \frac{4\sqrt{33}}{33}\\\\$

Rationalizing the denominator may be optional, so I would ask your teacher for clarification.

So far we've taken care of 3 trig functions. The remaining 3 are reciprocals of the ones mentioned so far.

cosecant, abbreviated as csc, is the reciprocal of sine
secant, abbreviated as sec, is the reciprocal of cosine
cotangent, abbreviated as cot, is the reciprocal of tangent

So we'll flip the fraction of each like so:

$\csc(\text{angle}) = \frac{\text{hypotenuse}}{\text{opposite}} \ \text{ ... reciprocal of sine}\\\\\csc(A) = \frac{c}{a}\\\\\csc(A) = \frac{7}{4}\\\\\sec(\text{angle}) = \frac{\text{hypotenuse}}{\text{adjacent}} \ \text{ ... reciprocal of cosine}\\\\\sec(A) = \frac{c}{b}\\\\\sec(A) = \frac{7}{\sqrt{33}} = \frac{7\sqrt{33}}{33}\\\\\cot(\text{angle}) = \frac{\text{adjacent}}{\text{opposite}} \ \text{ ... reciprocal of tangent}\\\\\cot(A) = \frac{b}{a}\\\\\cot(A) = \frac{\sqrt{33}}{4}\\\\$

------------------------------------------------------

Summary:

The missing side is $b = \sqrt{33}$

The 6 trig functions have these results

$\sin(A) = \frac{4}{7}\\\\\cos(A) = \frac{\sqrt{33}}{7}\\\\\tan(A) = \frac{4}{\sqrt{33}} = \frac{4\sqrt{33}}{33}\\\\\csc(A) = \frac{7}{4}\\\\\sec(A) = \frac{7}{\sqrt{33}} = \frac{7\sqrt{33}}{33}\\\\\cot(A) = \frac{\sqrt{33}}{4}\\\\$

Rationalizing the denominator may be optional, but I would ask your teacher to be sure.

7 0

1 year ago

Name the side of the triangle that is opposite angle A *<br> Captionless Image<br> AB<br> AC<br> BC

Olenka [21]

Answer:

Step-by-step explanation:

because it is what it is

7 0

3 years ago

Use the remainder theorem to determine if x = 2 is a zero of the following polynomial, and find the quotient and the remainder.

Fofino [41]

Answer:

(A) Yes, x = 2 is a zero of the polynomial.

The quotient is x² + 26x + 160 and the remainder is 0

Step-by-step explanation:

Given;

p(x) = x³ + 24x² + 108x - 320

Using remainder theorem to test if x = 2 is a zero of the given function

p(2) = (2)³ + 24(2)² + 108(2) - 320

= 8 + 96 + 216 - 320

= 0

Thus, x = 2 is zero of the function

(ii) to get the quotient and the remainder of the given function, divide the function by 'x - 2'

x² + 26x + 160

x - 2 √ x³ + 24x² + 108x - 320

- (x³ - 2x²)

0 + 26x² + 108x - 320

- (26x² - 52x)

0 + 160x - 320

- (160x - 320)

0 + 0

The quotient is x² + 26x + 160

The remainder is 0

Thus, the correct option is A.

Yes, x = 2 is a zero of the polynomial.

The quotient is x² + 26x + 160 and the remainder is 0

3 0

3 years ago

What is x? Can you please help?

Goryan [66]

Answer:

The answer to your question is: x = 2

Step-by-step explanation:

Data

LM = 6x

MN = 10x + 4

LN = 20x - 4

x = ?

Process

LM + MN = LN

Then

6x + 10x + 4 = 20x - 4

Solve for x 16x + 4 = 20x -4

16x - 20x = -4 - 4

-4x = -8

x = -8/-4

x = 2

6(2) + 10(2) + 4 = 20(2) - 4

12 + 20 + 4 = 40 -4

36 = 36

4 0

3 years ago

HELP ASAP AGAIN (FIXED)!!!!!!!

larisa [96]

Answer:

help with what

Step-by-step explanation:

can you kindly give me brainliest i need this for Expert rank

7 0

3 years ago