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4 years ago

If f(x)=2x^2 +4 and g(x)=x-3,which number satisfies f(x)=(f•g) (x)

1 answer:

8 0

$(f\cdot g)(x)=f(x)\cdot g(x)\\\\
(f\cdot g)(x)=(2x^2+4)(x-3)\\
(f\cdot g)(x)=2x^3-6x^2+4x-12\\\\
2x^2+4=2x^3-6x^2+4x-12\\
2x^3-8x^2+4x-16=0\\
2x^2(x-4)+4(x-4)=0\\
(2x^2+4)(x-4)=0\\
2(x^2+2)(x-4)=0\\
\boxed{x=4}$

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The coordinates of the endpoints of line segment C D are C(3, 8) and D(6, -1). Express the length of line segment C D in simples

8_murik_8 [283]

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
C&({{ 3}}\quad ,&{{ 8}})\quad 
% (c,d)
D&({{ 6}}\quad ,&{{ -1}})
\end{array}\qquad 
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
CD=\sqrt{(6-3)^2+(-1-8)^2}\implies CD=\sqrt{3^2+(-9)^2}
\\\\\\
CD=\sqrt{9+81}\implies CD=\sqrt{90}\quad 
\begin{cases}
90=2\cdot 3\cdot 3\cdot 5\\
\qquad 2\cdot 3^2\cdot 5\\
\qquad 10\cdot 3^2
\end{cases}
\\\\\\
CD=\sqrt{10\cdot 3^2}\implies CD=3\sqrt{10}$

3 0

3 years ago

Picture with question

pochemuha

Answer:5

Step-by-step explanation:

just tryna get points but it goes down by 3 eachtime

3 0

3 years ago

Read 2 more answers

If 0.9x-1.3=-3.1, what is the value of x-0.8?

Butoxors [25]

−2.8
Okay so "0.9x-1.3=-3.1" x=-2

0.9x−1.3=−3.1

add 1.3 to both sides

0.9x−1.3+1.3=−3.1+1.3

0.9x=−1.8

divide both sides by 0.9

0.9x/0.9=−1.8/0.9

x=−2

So if you plug in -2 into "x-0.8" you get −2.8

=−2−0.8

=−2-0.8

=−2.8

Hope this helps.

3 0

3 years ago

Read 2 more answers

Linear functions can be used to find the price of a building based on its floor area below are two of these functions,

Alborosie

Answer:

Part A) see the explanation

Part B) see the explanation

Part C) see the explanation

Step-by-step explanation:

The complete question in the attached figure

Part A) Find and compare the slopes

we have

Function 1

$y=40x+15,000$

This is a linear equation in slope intercept form

$y=mx+b$

where

y is the price of the building in thousands

x is the floor area in square foot

m is the slope

b is the y-intercept

we have

$m=\$40\ per\ ft^2$

Function 2

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

take two points from the data in the table

(400,32,000) and (700,56,000)

Remember that the price in the table is in thousands

substitute

$m=\frac{56,000-32,000}{700-400}$

$m=\$80\ per\ ft^2$

The slope of the Function 2 is greater than the slope of the Function 1

The slope of the Function 2 is two times the slope of the Function 1

Part B) Find and compare the y-intercept

we know that

The y-intercept is the value of y when the value of x is equal to zero

Function 1

$y=40x+15,000$

For x=0

$y=40(0)+15,000=\$15,000$

Function 2

Find the equation in point slope form

$y-y1=m(x-x1)$

we have

$m=80\\point\ (400,32,000)$

substitute

$y-32,000=80(x-400)$

Convert to slope intercept form

isolate the variable y

$y-32,000=80x-32,000\\y=80x$

For x=0

$y=80(0)=0$

The y-intercept of the function 1 is $15,000 and the y-intercept of the function 2 is zero (the line passes through the origin)

Part C) Describe each function as proportional or non proportion

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Function 1

$y=40x+15,000$ -----> is a non proportional linear function (because the line has a y-intercept)

Function 2

$y=80x$ ----> is a proportional linear equation (the line passes through the origin)

7 0

3 years ago

here are the ingredients for making pineapple sorbet for 6 people. 800 g pineapple 4 egg whites 1/2 lemon 100 g caster sugar Dan

VikaD [51]

Answer:

30 people

Step-by-step explanation:

If you start off with 1/2 a lemon for 6 people, then 1 whole would be 12. 1 1/2 would be 18 people and 2 whole lemons would be 24. so 2 1/2 is 30 people.

6 0

4 years ago