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3 years ago

Enter the equation of the line in slope-intercept form. Slope is 1 3 , and (6, 3) is on the line.

Mathematics

1 answer:

Jlenok [28]3 years ago

7 0

Answer:

would it be zero because when you try to find the equation its just 0 so it would be y=3

Step-by-step explanation:

as you can see both the points are at 3. so i would say y=3

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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

19,129 divided by 37

Marina CMI [18]

Answer: 517

Step-by-step explanation:

8 0

3 years ago

Write the equation of the line in slope intercept form.

sergey [27]

Answer:

see below

Step-by-step explanation:

slope intercept form: y=mx+b

you are given the slope, and can plug the points in to find b.

a) -3=2/3(6)+b --> b=-7

y=2/3x+7

b)10=-8(1/2)+b --> b=14

y=1/2x+13

c)4=-3(2)+b --> b=10

y=-3x+10

6 0

3 years ago

Read 2 more answers

At a track meet 2/7of the 756 competing athletes are sophomores. How many of the competing

kkurt [141]

Answer:

Step-by-step explanation:

700/7= 100

100*2= 200

200+ (756-700)= 256

256 closest to 216 than to 204 or any other answer.

5 0

3 years ago

Which expression is equivalent to the expression shown?

Kaylis [27]

Answer:

the answer is 7^12

Step-by-step explanation:

7^14 ÷ 7^2

14 - 2

8 0

3 years ago