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2 years ago

F(x)=2x^3+2x-3 g(x)=-.5[x-4] what is the y value when f(x) = g(x)?

Mathematics

1 answer:

Charra [1.4K]2 years ago

5 0

Answer:

D. x = 0.5

Step-by-step explanation:

A graphing calculator is the quickest way to get to an answer here.

f(x) = g(x) for x = 0.5

We can find the y-intercepts of the two functions to be ...

f(0) = -3

g(0) = -2

We know the x-intercept of g(x) is x=4. The x-intercept of f(x) will be a value less than 1, because f(1) = 1. (The function crosses the x-axis between x=0 where f(x) < 0 and x=1, where f(x) > 0.)

Considering these intercept points, we know the value of x for f(x)=g(x) will be between x=0 and x=1. There is only one answer choice in that interval:

x = 0.5

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Anastaziya [24]

Answer:

$\displaystyle \frac{dy}{dx} = \frac{2x + 2}{x^3}$

Step-by-step explanation:

we would like to figure out the derivative of the following:

$\displaystyle \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }$

to do so, let,

$\displaystyle y = \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }$

By simplifying we acquire:

$\displaystyle y = 3 - \frac{2}{x} - \frac{1}{ {x}^{2} }$

use law of exponent which yields:

$\displaystyle y = 3 - 2 {x}^{ - 1} - { {x}^{ - 2} }$

take derivative in both sides:

$\displaystyle \frac{dy}{dx} = \frac{d}{dx} (3 - 2 {x}^{ - 1} - { {x}^{ - 2} } )$

use sum derivation rule which yields:

$\rm\displaystyle \frac{dy}{dx} = \frac{d}{dx} 3 - \frac{d}{dx} 2 {x}^{ - 1} - \frac{d}{dx} {x}^{ - 2}$

By constant derivation we acquire:

$\rm\displaystyle \frac{dy}{dx} = 0 - \frac{d}{dx} 2 {x}^{ - 1} - \frac{d}{dx} {x}^{ - 2}$

use exponent rule of derivation which yields:

$\rm\displaystyle \frac{dy}{dx} = 0 - ( - 2 {x}^{ - 1 -1} ) - ( - 2 {x}^{ - 2 - 1} )$

simplify exponent:

$\rm\displaystyle \frac{dy}{dx} = 0 - ( - 2 {x}^{ -2} ) - ( - 2 {x}^{ - 3} )$

two negatives make positive so,

$\displaystyle \frac{dy}{dx} = 2 {x}^{ -2} + 2 {x}^{ - 3}$

<h3>further simplification if needed:</h3>

by law of exponent we acquire:

$\displaystyle \frac{dy}{dx} = \frac{2 }{x^2}+ \frac{2}{x^3}$

simplify addition:

$\displaystyle \frac{dy}{dx} = \frac{2x + 2}{x^3}$

and we are done!

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2 years ago

Line AB contains points A(4, 5) and B(9, 7). What is the slope AB

MatroZZZ [7]

For the answer to the question, what is the slope AB if l<span>ine AB contains points A(4, 5) and B(9, 7)?
The</span> answer <span>to </span>this question is 2/5.
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2 years ago

Find the constant $a$ such that\[(x^2 - 3x + 4)(2x^2 +ax + 7) = 2x^4 -11x^3 +30x^2 -41x +28.\]

Colt1911 [192]

The value of constant a is -5

Further explanation:

We will use the comparison of co-efficient method for finding the value of a

So,

Given

$(x^2 - 3x + 4)(2x^2 +ax + 7)\\= x^2((2x^2 +ax + 7)-3x((2x^2 +ax + 7)+4(2x^2 +ax + 7)\\= 2x^4+ax^3+7x^2-6x^3-3ax^2-21x+8x^2+4ax+28\\Combining\ alike\ terms\\=2x^4+ax^3-6x^3+7x^2-3ax^2+8x^2-21x+4ax+28\\= 2x^4 +(a-6)x^3+(15-3a)x^2-(21-4a)x+28\\$

As it is given that

(x^2 - 3x + 4)(2x^2 +ax + 7) = 2x^4 -11x^3 +30x^2 -41x +28

In this case, co-efficient of variables will be equal, so we can compare the coefficients of x^3, x^2 or x

Comparing coefficient of x^3

$a-6 = -11\\a = -11+6\\a = -5$

So the value of constant a is -5

Keywords: Polynomials, factorization

Learn more about factorization at:

#LearnwithBrainly

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