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3 years ago

Building a is 180 feet shorter than building

2 answers:

8 0

Here is the set up:

a = b - 180
a + b = 1520

We have a systems of linear equations in two variables.

b - 180 + b = 1520

2b = 1520 + 180

2b = 1700

b = 1700/2

b = 850

Plug b = 850 into either equation.

I will use a + b = 1520.

a + 850 = 1520

a = 1520 - 850

a = 670

Answer:

Building a is 670 feet. Building b is 850 feet.

Fofino [41]3 years ago

7 0

B= 850 ft
a= 670 ft

b + (b-80) =1,520
2b=1700
b=850 a=670 =(1,520-850)
850-670=180 ( difference between a and b)

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Answer:

Part 1) Option B: 0 ≤ x ≤ 4

Part 2) Option C: (5x − 1)(2x − 3)

Part 3) Option C: The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Part 4) Option B: f(x) = (2x + 1)(2x − 1)

Part 5) Option A: The company earned 85 billion dollars in 2008

Part 6) Option C: (3, 0) and (5, 0)

Step-by-step explanation:

Part 1) we have

$h(t)=-5t^{2}+20t$

This is a vertical parabola open downward

The vertex is a maximum

The x-intercepts are the points (0,0) and (4,0)

The vertex is the point (2,20) ---> The x-coordinate of the vertex is the midpoint of the x-intercepts

The domain is the interval ----> [0,4]

$0\leq t\leq 4$

The range is the interval ----> [0,20]

$0\leq h(t)\leq 20$

Part 2) we have

$V=10x^{2} -17x+13$

where

x is the time in minutes

V is the volume in gallons

we know that

When the trough is empty, the volume is equal to zero

For V=0

$10x^{2} -17x+3=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$10x^{2} -17x+3=0$

$a=10\\b=-17\\c=3$

substitute in the formula

$x=\frac{-(-17)(+/-)\sqrt{-17^{2}-4(10)(3)}} {2(10)}$

$x=\frac{17(+/-)\sqrt{169}} {20}$

$x=\frac{17(+/-)13} {20}$

$x=\frac{17(+)13} {20}=\frac{3}{2}$

$x=\frac{17(-)13} {20}=\frac{1}{5}$

$10x^{2} -17x+3=10(x-\frac{3}{2})(x-\frac{1}{5})$

simplify

$10(x-\frac{3}{2})(x-\frac{1}{5})=(2x-3)(5x-1)$

Part 3) we have

$f(x)=-x^{2}+20x+100$

we know that

To find the average rate of change, we divide the change in the output value by the change in the input value

the average rate of change is equal to

$\frac{f(b)-f(a)}{b-a}$

In this problem we have

$f(a)=f(10)=-(10)^{2}+20(10)+100=200$

$f(b)=f(20)=-(20)^{2}+20(20)+100=100$

$a=10$

$b=20$

Substitute

$\frac{100-200}{20-10}$

$-\frac{100}{10}=-10$ ----> is a decreasing function

therefore

The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Part 4) we have

$f(x)=4x^{2} -1$

<em>Find out the x-intercepts</em>

Remember that the x-intercepts are the values of x when the value of the function is equal to zero

For f(x)=0

$4x^{2} -1=0$

Solve for x

$4x^{2}=1$

$x^{2}=\frac{1}{4}$

take square root both sides

$x=(+/-)\frac{1}{2}$

$f(x)=4x^{2} -1=4(x-\frac{1}{2})(x+\frac{1}{2})=(2x-1)(2x+1)$

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$t^{2}+14t+85$

Remember that

The y-intercept of a function is the value of the function (output value) when the value of x (input value) is equal to zero

In this problem

The expression represent a company's net sales, in billions, from 2008 to 2018

t is the number of years since the end of 2008

For t=0 -----> represent the end of 2008

$(0)^{2}+14(0)+85=85\ billion\ dollars$

therefore

The company earned 85 billion dollars in 2008.

Part 6) What are the x-intercepts of the parabola?

we have the points (2,3),(4,-1),(6,3)

This is a vertical parabola open upward

The vertex represent a minimum

In this problem the vertex is the point (4,-1)

The equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^2+k$

where

a is a coefficient

(h,k) is the vertex

we have

(h,k)=(4,-1)

substitute

$y=a(x-4)^2-1$

take the point (2,3) and substitute in the quadratic equation to solve for a

For x=2, y=3

$3=a(2-4)^2-1$

$3=4a-1$

$4a=4$

$a=1$

The quadratic equation is

$y=(x-4)^2-1$

Find out the x-intercepts

Remember that the x-intercepts are the values of x when the value of the function is equal to zero

For y=0

$(x-4)^2-1=0$

Solve for x

$(x-4)^2=1$

take square root both sides

$(x-4)=(+/-)1$

$x=4(+/-)1$

$x=4+1=5\\x=4-1=3$

therefore

The x-intercepts are the points (3,0) and (5,0)

7 0

3 years ago

Read 2 more answers