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vesna_86 [32]
3 years ago
10

Factor the quadratic expression in the equation y=2x^2+28x+96 and use the factors to find the zeros of the equation. Then, use t

he zeros to find the line of symmetry of the parabola represented by the equation.
What is the equation for the line of symmetry of the parabola represented by the equation y=2x^2+28x+96?


Enter your answer as the correct equation, like this: x = 42
Mathematics
1 answer:
gavmur [86]3 years ago
4 0

Answer:

x=-7

Step-by-step explanation:

We have been given an equation y=2x^2+28x+96. We are asked to find the zeros of equation by factoring and then find the line of symmetry of the parabola.

Let us factor our given equation as:

2x^2+28x+96=0

Dividing both sides by 2:

x^2+14x+48=0

Splitting the middle term:

x^2+6x+8x+48=0

(x^2+6x)+(8x+48)=0

x(x+6)+8(x+6)=0

(x+8)(x+6)=0

Using zero product property:

(x+8)=0\text{ (or) }(x+6)=0

x+8=0\text{ (or) }x+6=0

x=-8\text{ (or) }x=-6

Therefore, the zeros of the given equation are x=-8\text{ (or) }x=-6.

We know that the line of symmetry of a parabola is equal to the x-coordinate of vertex of parabola.

We also know that x-coordinate of vertex of parabola is equal to the average of zeros. So x-coordinate of vertex of parabola would be:

\frac{-8+(-6)}{2}=\frac{-14}{2}=-7

Therefore, the equation x=-7 represents the line of symmetry of the given parabola.

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0=(1x+1)(1x-3) if m(x) =10, find the value of x
Anna11 [10]

Answer:

x=1+sqrt(14) & 1-sqrt(14).

Step-by-step explanation:

(1x+1)(1x-3)=0

(x+1)(x-3)=0

m(x)=(x+1)(x-3)=10

(x+1)(x-3)=10

x^2+x-3x-3=10

x^2-2x-3=10

x^2-2x-3-10=0

x^2-2x-13=0

Apply the quadratic formula with a=1, b=-2 and c=-13.

The answer is x=1+sqrt(14) & 1-sqrt(14).

6 0
3 years ago
Desmond spends $800 per month on fixed expenses. Desmond earns $10,00 per hour,
Elis [28]

Answer:  160 hours

============================================================

Explanation:

He earns $10.00 an hour. Let x be the number of hours worked in a month. So 10x represents how much he earns after working x hours.

If he spends $800 per month on fixed expenses, and wants this to be 50% of his total earnings, then this must mean that the other 50% is for other things (eg: spending on a vacation or putting it to savings). So his goal is to earn 800+800 = 1600 dollars per month.

Set 10x equal to this and solve for x

10x = 1600

x = 1600/10

x = 160

He needs to work 160 hours a month.

-------------------------------

Extra info:

Divide 160 over 4 (the approximate number of weeks in a month) and we see that he'll need to work 160/4 = 40 hours a week

If he only works Monday through Friday, that's 5 days of the week. So he'll put in 40/5 = 8 hours per day.

So his goal of working 160 hours per month is reasonable. Keep in mind that this doesn't include factors like him missing time from work due to being sick (unless he has paid sick leave).

7 0
2 years ago
Solve for b. 13/b = 8/1 A. b=1.25 B. b=1.26 C. b=16.25 D. b=1.625
Sati [7]

Answer: b=13/8

<u>Cross multiply</u>

<u></u>(13)*(1)=8*b\\13=8b<u></u>

<u></u>

<u>Flip the equation</u>

<u></u>8b=13<u></u>

<u></u>

<u>Divide both sides by 8</u>

<u></u>8b/8=13/8\\b=13/8<u></u>

6 0
3 years ago
Which of the following statements is true about the sequence? Select all that apply.
oksano4ka [1.4K]

Answer:

f(5)=33f of 5 is equal to 33

Step-by-step explanation:

f(5)=33f of 5 is equal to 33ieieieuejehrdjdjhdhhrhd

7 0
2 years ago
Correct answers only please!
blagie [28]

Answer: $86.25

Step-by-step explanation:

For this problem, we are given p, r, t.

p=70 (starting amount)

r=0.11 (11%)

t=2 (years)

We can plug this into the equation B=p(1+r)^t

B=70(1+0.11)^2

B=86.247

Sam would have $86.25

6 0
3 years ago
Read 2 more answers
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