1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
jeka57 [31]
3 years ago
10

What is the equation of the parabola with vertex (-2,5) and an x-intercept of x = 3

Mathematics
1 answer:
Maslowich3 years ago
3 0

Step-by-step explanation:

if parabola has a vertex not in x-axis, it should have 2 x intercept

x-vertex = -2

first x intercept = 3

second x intercept should -7

so the equation will like this

y = a(x-x1)(x-x2)

y = a (x-3)(x+7)

y = a(x² + 4x - 21)

5 = a((-2)² + 4(-2) - 21)

5 = a(4 - 8 - 21)

5 = a(-25)

a = 5/(-25)

a = -1/5

then the equation is

y = (-1/5)(x² - 4x - 21)

or you can write as

y = -x²/5 + 4x/5 + 21/5

or as this one

5y = -x² + 4x + 21

You might be interested in
Jennifer earned $1000 babysitting over the summer. She spent $250 of her earnings on new clothes. What percent of her earnings d
emmainna [20.7K]

Answer:

25%

Step-by-step explanation:

she earned $1,000

she spent $250

250/1000 = 0.25

0.25 x 100 = 25%

4 0
3 years ago
Read 2 more answers
What are zeros of the function? What are there multiples? f(x) = 4x^3 -20x2 + 24x
bixtya [17]
When X=0, the function would be:

<span>f(x) = 4x^3 -20x2 + 24x
0= </span><span>4x^3 -20x2 + 24x       ----->divide all by x
</span>x(4x^2 -20x + 24)  =0     ------> split -20x into -12x and -8x
x(4x^2 -12x -8x + 24)
x{4x(x-3)  - 8(x -3}
x(4x-8) (x-3)
x1= 0
x2= 8/4= 2
x3= 3
7 0
3 years ago
Point T has coordinates (10,20). To calculate the coordinates of point T′ in the image,
Hatshy [7]

Answer: T'(18,36)

Step-by-step explanation:

For this exercise it is important to know the definition of "Dilation".

 A Dilation is defined as a transformation in which the Image (The figure obtained after the transformation) and the Pre-Image (The original figure before the transformation) have the same shape but have different sizes.

If the Dilation is centered at the origin, and knowing the scale factor of \frac{9}{5}, you need to multiply each coordinate of the point T by the scale factor in order to find the coordinates of the Image T'.

Knowing that the point T has the following coordinates:

T(10,20)

You get that the coordinates of the Image T' are the shown below:

T'=(\frac{9}{5}*10,\frac{9}{5}*20)\\\\T'=(18,36)

6 0
3 years ago
Giving 100 points.
Nitella [24]

Answer:

1.   <u>Cost per customer</u>:  10 + x

     <u>Average number of customers</u>:  16 - 2x

\textsf{2.} \quad  -2x^2-4x+160\geq 130

3.    $10, $11, $12 and $13

Step-by-step explanation:

<u>Given information</u>:

  • $10 = cost of buffet per customer
  • 16 customers choose the buffet per hour
  • Every $1 increase in the cost of the buffet = loss of 2 customers per hour
  • $130 = minimum revenue needed per hour

Let x = the number of $1 increases in the cost of the buffet

<u>Part 1</u>

<u></u>

<u>Cost per customer</u>:  10 + x

<u>Average number of customers</u>:  16 - 2x

<u>Part 2</u>

The cost per customer multiplied by the number of customers needs to be <u>at least</u> $130.  Therefore, we can use the expressions found in part 1 to write the <u>inequality</u>:

(10 + x)(16 - 2x)\geq  130

\implies 160-20x+16x-2x^2\geq 130

\implies -2x^2-4x+160\geq 130

<u>Part 3</u>

To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:

\implies -2x^2-4x+160\geq 130

\implies -2x^2-4x+30\geq 0

\implies -2(x^2+2x-15)\geq 0

\implies x^2+2x-15\leq  0

\implies (x-3)(x+5)\leq  0

Find the roots by equating to zero:

\implies (x-3)(x+5)=0

x-3=0 \implies x=3

x+5=0 \implies x=-5

Therefore, the roots are x = 3 and x = -5.

<u>Test the roots</u> by choosing a value between the roots and substituting it into the original inequality:

\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144

As 144 ≥ 130, the <u>solution</u> to the inequality is <u>between the roots</u>:  

-5 ≤ x ≤ 3

To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.  

[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an <em>increase </em>in cost.  It does not confirm that if the cost is reduced (less than $10) the number of customers <em>increases </em>per hour.]

<u>Cost per customer</u>:  

x =0 \implies 10 + 0=\$10

x=3 \implies 10+3=\$13

Therefore, the possible buffet prices Noah could charge are:

$10, $11, $12 and $13.

8 0
2 years ago
Help me with this yes im lazy 2 pages thats it.
valentinak56 [21]

Answer:

2.)\frac{1}{4}/3=\frac{1}{4}*\frac{1}{3}=\frac{1}{12} s yes she is correct

3.)\frac{1}{5}*\frac{1}{7}

4.)C\frac{1}{5}/2= \frac{2}{5},D\frac{1}{12}/5=\frac{1}{60},E

6.)\frac{1}{8}/3=\frac{1}{24}

Step-by-step explanation:

im not very good at word problems so i didnt do the secnd page sorry

5 0
3 years ago
Other questions:
  • A rectangle has vertices (-1, 1), (-4, 1), (-1, 3), and (-4, 3). If the
    10·1 answer
  • PLEASE HELP ME !!!!!!!!!!!!!!!!!<br>LET ME KNOW IF ITS RIGHT
    11·1 answer
  • What is 9xy+x+2+x+y+xy+4
    13·2 answers
  • The number of patients treated at Dr. White's dentist office each day for nine days is 10, 6, 4, 15, 6, 8, 6, 15, 4. Find the me
    7·1 answer
  • Brad is putting up a 14 foot diameter circular flower garden in his yard. What is the area of brads garden ?
    13·1 answer
  • Whats the answer? How do I understand it?
    10·1 answer
  • HOW DO YOU DO THIS? PLEASE HELP
    5·1 answer
  • I NNNNNEDDDDD HHHHEEELLLLLPPPPPPPP
    13·2 answers
  • Nerissa has 5 pink bows, 1 blue bow, and 4 purple bows in a box. She will randomly choose 1 bow from the box. What is the probab
    10·1 answer
  • Need help struggling with this question
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!