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3 years ago

An end behavior model for f(x) =

Mathematics

1 answer:

oksian1 [2.3K]3 years ago

3 0

<h3>Answer: Choice C) 2x^4</h3>

=====================================================

As x gets larger and larger, all we really care about is the leading terms. This is because 8x^6 is much larger than -16x^3 and 8 for very very large x values. The larger the exponent, the larger the result will be.

So effectively, the leading term 8x^6 dictates the end behavior for the numerator.

In a similar way, the leading term 4x^2 dictates the end behavior for the denominator polynomial.

Divide the two leading terms:

(8x^6)/(4x^2) = (8/4)*x^(6-2) = 2x^4

The rule used here is (a^b)/(a^c) = a^(b-c)

So as x goes to infinity or negative infinity, it's slowly approaching the asymptote y = 2x^4.

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what is the theorem states that if two inscribed angles of a circle intercept the same arc, then the angles are congruent?

marusya05 [52]

In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant<span> from the center. States that the measure of an inscribed angle is one half the measure of its intercepted arc. States that if two inscribed angles of a circle intercept the same arc, then the angles are congruent.

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6 0

3 years ago

Given the function f(x)= 2|x+6|-4, for what values of x is f(x)=6?

Paraphin [41]

Answer:

x = -1 or x = -11

Step-by-step explanation:

f(x)= 2|x+6|-4

2|x+6|-4 = 6

2|x+6| = 6+4

2|x+6|=10

|x+6| = 10/2

|x+6| = 5

x+6 = ±5

x = ±5 - 6

x = -1 or x = -11

7 0

4 years ago

The breaking strength of a fiber is required to be at least 150 psi. Past experience has indicated that the standard deviation o

aleksley [76]

Answer:

(a) Null hypothesis: The breaking strength of a fiber is required to be 150 psi

Alternate hypothesis: The breaking strength of a fiber is required to be 150 psi or greater than 150 psi

(b) Fail to reject the null hypothesis. The breaking strength of a fiber is required to be 150 psi

(d) 95% confidence interval for the mean breaking strength is between 145.227 psi and 154.773 psi

Step-by-step explanation:

(a) The null hypothesis is a statement from the population parameter which is subject to testing. The alternate hypothesis is also a statement from the population parameter that negates the null hypothesis.

(b) Z = (sample mean - population mean) ÷ sd/√n

sample mean = 145+153+150+147/4 = 148.75 psi, population mean = 150 psi, sd = 3 psi, n= 4

Z = (148.75 - 150) ÷ 3/√4 = -1.25 ÷ 1.5 = -0.833

This test is a two tailed test. The critical value at 0.05 significance level is 1.96. The region of no rejection of the null hypothesis lies between -1.96 and 1.96 since it is a two tailed test.

Conclusion: since -0.833 falls within the region bounded by -1.96 and 1.96, fail to reject the null hypothesis. The breaking strength of a fiber is required to be 150 psi

P-value = 1 - 0.9750 = 0.025

(d) Confidence Interval = mean + or - error margin (E)

E = t×sd/√n

n = 4, degree of freedom = n-1 = 4-1 = 3, t-value corresponding to 3 degrees of freedom and 95% confidence level is 3.182

E = 3.182×3/√4 = 4.773

Lower limit = mean - E = 150 - 4.773 = 145.227

Upper limit = mean + E = 150 + 4.773 = 154.773

95% confidence interval is (145.227 psi, 154.773 psi)

7 0

3 years ago

If DE = 7x + 3 and EF = 9x - 19,<br> then EF = ?

ANEK [815]

Answer:

Step-by-step explanation:

7x + 3 = 9x - 19

-2x + 3 = -19

-2x = -22

x = 11

DE= 7(11) + 3 = 77 + 3 = 80

EF = 9(11) - 19 = 99 - 19 = 80

80 + 80 = 160 for DF

6 0

3 years ago

What is the slope of the line that passes through the points (8,-8) and (5,-1)?

dezoksy [38]

Hey there!

Answer :

$\sf{ \purple{ \boxed{\bold{m = - \dfrac{7}{3} }}}}$

$\\$

Explanation :

We are given the points $\sf{P_1(\overbrace{ \blue{8}}^{\blue{x_1}} ,\underbrace{\orange{-8}}_{ \orange{y_1}}) \: and \: P_2(\overbrace{ \green{5}}^{\green{x_2}} ,\underbrace{\red{-1}}_{\red{y_2} })}$ . To find the slope $\sf{\purple{m}}$ of such a line, we use the slope formula which is the following:

$\sf{ \purple{m} }= \dfrac{\Delta y}{\Delta x} = \dfrac{ \red{y_2} - \orange{y_1}}{ \green{x_2 }- \blue{x_1}}$

$\\$

⇢Now, by plugging in our values, we get :

$\sf{ \purple{m}} = \dfrac{ \red{ - 1} - \orange{( - 8)}}{ \green{5} \: - \: \blue{8}} = \dfrac{ \: \: 7 \: }{ - 3 \: } \\ \\ \implies \sf{ \purple{ \boxed{m = - \dfrac{7}{3} }}}$

Therefore, the slope of the line is $\sf{ \purple{ \boxed{m = - \dfrac{7}{3} }}}$

8 0

2 years ago

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An end behavior model for f(x) =​

An end behavior model for f(x) =