Simplify the expression. 5(x - z) + 4(y

A quadratic function is defined by f(x) = 3x^2 + 4x - 2. A linear function is defined by g(x) = mx-5. What values of the slope o

irakobra [83]

You need to find points where the line g(x) intercepts the quadratic function f(x) in one and only one point.

Then 3x^2 + 4x -2 = mx - 5

solve 3x^2 + 4x - mx -2 + 5 = 0

3x^2 + (4 - m)x + 3 = 0

In order to there be only one solution (one intersection point) the radicand of the quadratic formula must be 0 =>

b^2 - 4ac = (4 - m)^2 - 4(3)(3) = 0

(4 - m)^2 = 24

4 - m = +/- √(24)

m = 4 +/- √(24) = 4 +/- 2√(6)

Then m, the slope of the line, may be 4 + 2√6 and 4 - 2√6

7 0

3 years ago

A school wishes to enclose its rectangular playground using 480 meters of fencing.

Harlamova29_29 [7]

Answer:

Part a) $A(x)=(-x^2+240x)\ m^2$

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

$P=2(L+W)$

we have

$P=480\ m\\L=x\ m$

substitute

$480=2(x+W)$

solve for W

$240=x+W\\W=(240-x)\ m$

Find the area of the rectangular playground

The area is given by

$A=LW$

we have

$L=x\ m\\W=(240-x)\ m$

substitute

$A=x(240-x)\\A=-x^2+240x$

Convert to function notation

$A(x)=(-x^2+240x)\ m^2$

Part b) What side length x gives the maximum area that the playground can have?

we have

$A(x)=-x^2+240x$

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

$A(x)=-x^2+240x$

Factor -1

$A(x)=-(x^2-240x)$

Complete the square

$A(x)=-(x^2-240x+120^2)+120^2$

$A(x)=-(x^2-240x+14,400)+14,400$

$A(x)=-(x-120)^2+14,400$

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

$x=120\ m$

$W=(240-120)=120\ m$

The playground is a square

$A=120^2=14,400\ m^2$

8 0

3 years ago

Points X and Y are in plane Z. Any point collinear with X and Y is also in plane Z

mars1129 [50]

Answer:

yes above statement is true

Step-by-step explanation:

mark me as brainliest ❤️

8 0

3 years ago

Read 2 more answers

destiny sells pencil cases for $5 each and mechanical pencils for $2 each at the school supply store. she sells p pencil cases a

Andrew [12]

Answer:

Step-by-step explanation:

5p + 2(p + 4) .......because pencil cases (p) sell for 5 bucks a piece....and mechanical pencils (p + 4), sell for 2 bucks a piece. She is basically selling 4 more mechanical pencils then she is pencil cases.

8 0

3 years ago

PLEASE HELP ME

yuradex [85]

The answer is C because it’s going back 5 times meaning it’s -5

8 0

3 years ago

Read 2 more answers

Simplify the expression. 5(x - z) + 4(y - x)