The piecewise function h(x) is shown on the graph.

Find an equation in standard form of a parabola passing through the points below

EastWind [94]

Answer:

Basic parabola: y = ax2 + bx + c

We have 3 points we can plug in for (x, y) to create 3 simultaneous equations

(-2, 24): 24 = 4a - 2b + c {equation 1}

(3, -1): -1 = 9a + 3b + c {equation 2}

(-1, 15): 15 = a - b + c {equation 3}

Solve this system to find the values of a, b, c

Let's first eliminate variable c:

4a - 2b + c = 24 {equation 1}

a - b + c = 15 {equation 3}

--------------------- subtract

3a - b = 9

9a + 3b + c = -1 {equation 2}

a - b + c = 15 {equation 3}

-------------------- subtract

8a + 4b = -16

We now have two equations with 2 unknowns we can use to find a, b

3a - b = 9 {equation 4}

8a + 4b = -16 {equation 5}

Multiply equation 4 through by 4 and add equations

12a - 4b = 36

8a + 4b = -6

----------------- add

20a = 30

a = 30/20

a = 3/2

8a + 4b = -6

8(3/2) + 4b = -6

12 + 4b = -6

4b = -6- 12

4b = -18

b = -18/4

b = -9/2

Plug these 2 values into one of the original equations and solve for c

15 = a - b + c {equation 3}

15 = 3/2 + 9/2 + c

15 = 12/2 + c

15 = 6 + c

c = 15-6

c = 9

y = (3/2)x2 - (9/2)x+ 9

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Step-by-step explanation:

8 0

3 years ago

Select the favorable outcomes for rolling a sum less than five

Anvisha [2.4K]

We want the sum of the two rolls to be less that five.
Therefore, we will examine each given set of choices and choose the one where all the points have a sum less than 5.

First set: all the point are 5 added to another number. Therefore, the sum is definitely not less than 5. This choice is rejected.

Second set: We have two points having 6 added to a number. Therefore, this choice is also rejected.

Third set: We have the points (5,5) and (6,6) which have a sum greater than 5. Therefore, this set is also rejected.

Fourth set: We have:
(1,1) with sum = 2
(1,2) with sum = 3
(1,3) with sum = 4
(2,1) with sum = 3
(2,2) with sum = 4
(3,1) with sum = 4
Therefore, all sums are less than 5. This is the correct choice.

Based on the above, the correct option is the last one.

3 0

3 years ago

The quotient of a number is -5 decreased by 9?

Fofino [41]

2 the answer is two I put it in the calculator

4 0

3 years ago

celeste wants to have her hair cut and permed and also go to lunch. she knows she will need 59$. the perm cost twice as much as

miv72 [106K]

Let's first start off with an equation to represent Celeste's budget:
$h + p + l = 59$
Where:
'h' is the money in dollars that she needs to get her hair cut
'p' is the money in dollars that she needs to get her hair permed
'l' is the money in dollars that she needs for lunch

Now let's simplify this equation using the information that was given:
$l = 5$ *This must be true since it is told that she needs $5 for lunch
$0.5p = h$ *This is because the perm costs twice as much as the hair cut

Our new/updated equation is:
$0.5p + p + 5 = 59$

This is much easier to solve, let's rearrange and solve for 'p':
$0.5p + p = 59 - 5$
$1.5p = 54$
$p = 36$

Therefore the perm costs $36

I hope this helps! Let me know if you have any further questions.

5 0

3 years ago

1.

ZanzabumX [31]

Remember, you can do anything to an equationas long as you do it to both sides

1.
-6+x=-3
add 6 to both sides
6-6+x=6-3
0+x=3
x=3

2.
add like terms
-5a+5a+9=8
0a+9=8
0+9=8
9=8
false
no solution
zero solutions

8 0

3 years ago

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