Which graph shows the solutions to<br> the inequality? PLSSS HELPPP

Han earns $33.00 for babysitting 4 hours. At this rate, how much will he earn if he

Lemur [1.5K]

First you do $33.00/4 to get $8.25. Take the 8.25 and multiply it by 7 to get $57.75

8 0

3 years ago

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Write the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10).

Serjik [45]

Answer:

$\displaystyle f(x)=x^2+2x+2$

Step-by-step explanation:

<u>System Of Linear Equations </u>

In this problem, we'll need to solve a 3x3 system of linear equations because we have three unknowns and three conditions.

We are required to find the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10)

The general quadratic function can be written as

$\displaystyle f(x)=ax^2+bx+c$

We need to find the values of a,b, and c. Let's use the first condition, i.e. f(-1)=1

$\displaystyle f(-1)=a(-1)^2+b(-1)+c$

$\displaystyle f(-1)=a-b+c$

$\displaystyle a-b+c=1.....[eq\ 1]$

Now we use the second condition f(1)=5

$\displaystyle f(1)=a(1)^2+b(1)+c$

$\displaystyle f(1)=a+b+c$

$\displaystyle a+b+c=5.......[eq\ 2]$

Finally, we use the third condition f(2)=10

$\displaystyle f(2)=a(2)^2+b(2)+c$

$\displaystyle f(2)=4a+2b+c$

$\displaystyle 4a+2b+c=10....[eq\ 3]$

We put together eq 1, eq 2, and eq 3 to form the system

$\displaystyle \left\{\begin{matrix}a-b+c=1\\ a+b+c=5\\ 4a+2b+c=10\end{matrix}\right.$

Adding the first two equations we have

$\displaystyle 2a+2c=6$

$\displaystyle a+c=3$

And also

$\displaystyle b=2$

Using the above equation and the value of b in the third equation, we have

$\displaystyle \left\{\begin{matrix}a+c=3\\ 4a+c=6\end{matrix}\right.$

Subtracting the first equation from the second

$\displaystyle 3a=3$

$\displaystyle a=1$

And therefore

$\displaystyle c=2$

Now we have all the values, the quadratic function is

$\displaystyle \boxed{f(x)=x^2+2x+2}$

6 0

3 years ago

A 27-foot long wire is attached from a stake in the ground to the top of a 24-foot flagpole. Find the distance from the stake in

levacccp [35]

Answer:

the distance is 3

Step-by-step explanation:

6 0

3 years ago

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Solve for d: s=d/t<br> please help

nika2105 [10]

Where is the equation?

6 0

4 years ago

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A costume designer has 40 yards of red fabric to make costumes for a musical in which 8 performers will wear red dresses and 14

Fed [463]

Answer:

38.5 yards used

Step-by-step explanation:

Yes he has enough fabric

to get the answer you must take the total number of dresses (8) and multiply it by 3 1/2 (3.5) because thats how much it takes to create one dress.

3.5 x 8 = 28

Now take the number of scarfs (14) and multiply it by 3/4 (0.75) because thats now much it takes to create a single scarf

0.75 x 14 = 10.5

now you add both of the answers

10.5 + 28 = 38.5

since 38.5 < 40 it means that he has enough fabric to create all the costumes for the musical

7 0

3 years ago

Which graph shows the solutions to the inequality? PLSSS HELPPP