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3 years ago

Jessica rides the bus 8 and 4/5 miles each day what is the total number of miles she rides in 21 days?

Mathematics

1 answer:

Masja [62]3 years ago

5 0

Answer:

= 184/5

Step-by-step explanation:

converting mixed numbers to fractions, our initial equation becomes,

44/5 × 2/11

Applying the fractions formula for multiplication you get,

= 924/5

Simplifying 924/5, the answer is

=184 4/5

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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

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

<u><em>Find the area of the rectangular playground</em></u>

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

Which is the graph of the cube root function f(x) = RootIndex 3 StartRoot x EndRoot?

lara [203]

Answer:

<h3>On a coordinate plane, a cube root function goes through (negative 8, negative 2), has an inflection point at (0, 0), and goes thorugh (8, 2).</h3>

Step-by-step explanation:

$f(x)=\sqrt[3]{x}\\\\f(-8)=\sqrt[3]{-8}=-2\to(-8,\ -2)\\\\f(0)=\sqrt[3]{0}=0\to(0,\ 0)\\\\f(8)=\sqrt[3]{8}=2\to(8,\ 2)\\\\\\\sqrt[3]{a}=b\iff b^3=a\\\\\text{Therefore:}\\\\\sqrt[3]{-8}=-2\ \text{because}\ (-2)^3=-8\\\sqrt[3]0=0\ \text{because}\ 0^3=0\\\sqrt[3]{8}=2\ \text{because}\ 2^3=8$

7 0

3 years ago

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Distribute: -3(4a-5b+c)

kvv77 [185]

Answer:

I got it.

Step-by-step explanation:

-12a - (-15b) + (-3c)

4 0

3 years ago

Help me find x on either one of these problems please!

mash [69]

In the problem with the white circle, x=100, in the problem with the blue circle, x might equal 165, but I'm not entirely certain. But I am certain about the first one.

3 0

3 years ago

HAVE A NICE DAY <br> WILL GIVE BRAINLST :)

muminat

Answer:

1) 2 and 6 ; 4 and 8 ; 1 and 5 ; 3 and 7

2) 3 and 6 ; 4 and 5

3) 1 and 8 ; 2 and 7

7 0

3 years ago

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