The graph of y = x2 –7x +12 is a parabola with x-intercepts at and a vertex that is the
point on the curve.

Answers

Answer 1

The vertex of the parabola is at the point (3.5, 0.75).

To find the x-intercepts of the given quadratic equation [tex]y = x^2 - 7x + 12,[/tex]we set y = 0 and solve for x.

[tex]0 = x^2 - 7x + 12[/tex]

Factoring the quadratic equation, we can rewrite it as:

0 = (x - 3)(x - 4)

Setting each factor equal to zero, we find the x-intercepts:

x - 3 = 0 => x = 3

x - 4 = 0 => x = 4

Therefore, the parabola represented by the equation [tex]y = x^2 - 7x + 12[/tex] has x-intercepts at x = 3 and x = 4.

To find the vertex of the parabola, we can use the formula:

x = -b / (2a)

In this case, a = 1 (coefficient of [tex]x^2[/tex]) and b = -7 (coefficient of x). Plugging these values into the formula, we get:

x = -(-7) / (2[tex]\times[/tex] 1)

x = 7 / 2

x = 3.5

To find the y-coordinate of the vertex, we substitute this value back into the original equation:

[tex]y = (3.5)^2 - 7(3.5) + 12[/tex]

y = 12.25 - 24.5 + 12

y = 0.75

Therefore, the vertex of the parabola is at the point (3.5, 0.75).

In summary, the graph of the equation [tex]y = x^2 - 7x + 12[/tex]is a parabola with x-intercepts at x = 3 and x = 4. The vertex of the parabola is located at the point (3.5, 0.75).

For similar question on parabola.

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The Graph Of Y = X2 7x +12 Is A Parabola With X-intercepts At And A Vertex That Is The Point On The Curve.

Related Questions

If f(x)=x^2+x, find f(-3)

Answers

Answer:

f(-3) = (-3)^2 + (-3) = 9 - 3 = 6

Answer:

I believe the answer is 6

Step-by-step explanation:

1) If f(-3), x is equal to -3 ( I think )

2) f(x) = -3^2 + (-3)

3) f(x) = 9 - 3

4) f(x) = 6

The answer is f(x) = 6

MULTIPLE CHOICE:

Jen and David owe $21,000 in loans for their two cars. The amount of the loan for Jen's car is $2,000 less than twice the amount of the loan for David's car. How much is each car loan? (Let j represent the amount of Jen's loan and let d represent the amount of David's loan.)


A. d + j = 21,000
2d − 2,000 = j


B. j + d = 21,000
2j − 2,000 = d



C. j + d = 21,000
2j + 23,000 = d


D. j + d = 2,000
2j − 21,000 = d


E. d + j = 2,000
2d − 21,000 = j

Answers

9514 1404 393

Answer:

  A. d + j = 21,000; 2d − 2,000 = j

  d = $7,666.67; j = $13,333.33

Step-by-step explanation:

The relationships given in the problem statement are ...

  d + j = 21,000 . . . . .  the total of the two loans is $21,000

  2d -2000 = j . . . . . . Jen's is $2000 less than twice David's

__

These equations can be solved by substituting for j:

  d +(2d -2000) = 21000

  3d = 23000 . . . . . . . . . . . add 2000, collect terms

  d = 23000/3 = 7666.67 . . . divide by the coefficient of d

  j = 21000 -d = 21000 -7666.67 = 13333.33

Jen's loan is $13,333.33; David's loan is $7,666.67.

6th grade students took a survey on their favorite subject.
The ratio of students whose favorite subject was Science to
students whose favorite subject was Math was 3:5. If 238
more students picked Math as their favorite subject, how many
students picked Science as their favorite subject?

Answers

Using a system of equations, it is found that 595 students picked Science as their favorite subject.

For our system, we suppose that x is the number of students that picked science, and y is the number of students that picked math.

Ratio of science to math of 3:5, thus:

[tex]\frac{x}{y} = \frac{3}{5}[/tex]

Then

[tex]5x = 3y[/tex]

[tex]x = \frac{3y}{5}[/tex]

238  more students picked Math as their favorite subject, thus:

[tex]y = 238 + x[/tex]

[tex]y - \frac{3y}{5} = 238[/tex]

[tex]\frac{2y}{5} = 238[/tex]

[tex]y = \frac{238(5)}{2}[/tex]

[tex]y = 595[/tex]

595 students picked Science as their favorite subject.

A similar problem is given at https://brainly.com/question/21244414

Donna Forrester's gross pay is $72,500 a year. The state income tax is 6% of
taxable wages. Donna takes a married exemption of $4,000 for herself and her
husband. How much is withheld from her gross earnings for state income tax
for the year?
A.$4,350
B.$4,110
C.$4,590
D. $3,870

Answers

I have no idea to be honest with you

Answer:

Choice B

Step-by-step explanation:

Cuz I'm smart :)

Hope this helps :]  

pls make brainliest :3  

and have an amazing day <3

what is the slope of (29,11) and (-3,-7)

Answers

Answer:

The slope is [tex]\frac{9}{16}[/tex]

Step-by-step explanation:

Hi there!

We are given the points (29, 11) and (-3, -7), and we want to find the slope of them.

The slope can be calculated from two points with the slope formula, which is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.

We have two points given, but let's label their values to avoid any confusion when we actually calculate:

[tex]x_1=29\\y_1=11\\x_2=-3\\y_2=-7[/tex]

Now substitute into the formula (m is the slope).

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-7-11}{-3-29}[/tex]

Subtract

m=[tex]\frac{-18}{-32}[/tex]

Reduce the fraction

m=[tex]\frac{9}{16}[/tex]

The slope is [tex]\frac{9}{16}[/tex]

Hope this helps!

Payton starts a lemonade stand for the summer. She thinks that she should be able to operate her business for 14 weeks. The table shows the expenses and revenue after 1 week.



Item Expenses Revenue
Cups $5
Lemonade $6
Ice $7
Income $45


Based on this, how much money will Payton make during the 14 weeks?



$__

Answers

Answer she makes $378 in 14 weeks

Payton will make money after 14 weeks is $378.

What is income and expenses?

Income is the money your business takes in and expenses are what it spends money on. Your net income is generally your revenue, or all the money coming into your business, minus all of your expenses.

For the given situation,

Item Expenses Revenue after 1 week

Number of Cups = $5

Number of Lemonade = $6

Number of Ice = $7

Total revenue, Income = $45

Formula to find the net income,

Net Income = Total Revenue - Total Expenses

⇒ Net Income = [tex]45 - ( 5+6+7 )[/tex]

⇒ Net Income = [tex]27[/tex]

Thus net income for 14 weeks = [tex]14[/tex] × [tex]27[/tex]

⇒ [tex]378[/tex]

Hence we can conclude that Payton will make money after 14 weeks is $378.

Learn more about income and expenses here

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Find x ASAP you’ll get lots of points

Answers

Answer:

x=4

Step-by-step explanation:

Its an equilateral triangle so all angles and side lengths are the same.

2x-1=x+3

x=3+1

x=4

checking the work

4+3=8-1

7=7

x=4 have a great day

0.052 x 8.17 Multiplying Decimals
(Answer and how to write it)​

Answers

Answer:

0.42484

Step-by-step explanation:

place them on top of each other but the bottom one has to leave a space and put a zero in that space also go by the order of the decimal do not do 8.17 0.052 it will not give you the correct answer so they put it in a way to give you an answer. you should write it like this     0.052

                                                                  x 8.170

                                                                    _____

I hope this helps! If you can, can I have brainlest? I really want to level up.

See photo attached (NEED SOON)

Answers

Answer:

3 m

Step-by-step explanation:

The formed triangles are similar and the ratio of corresponding sides is equal:

x/4 = 9/12x/4 = 3/4x = 3 m

The light source should be at 3 m height

Both triangles are congruent so

[tex]\\ \bull\sf\longmapsto \dfrac{x}{4}=\dfrac{9}{12}[/tex]

[tex]\\ \bull\sf\longmapsto 12x=36[/tex]

[tex]\\ \bull\sf\longmapsto x=3[/tex]

Light source should be at 3m

PLZ HELP ME!! GUYS i need help on my homework!!

Answers

Answer:

The answer is 24

Step-by-step explanation:

Answer:

The answer is 24 or D

Step-by-step explanation:

Well, first you need to figure out the equation in these [ ].

[-5 (2-4) ÷ 2]

[-5 (-2) ÷ 2] ---> -5(-2) = -5 x -2

[10 ÷ 2]

[5]

Then, you need to complete the equation in these { }

{3+[5]} OR {3+5}

{8}

Then, you need to finish the equation!

{8} · 3 OR 8 x 3

24

__________________________

Hope this helped!

please help
the answer is not 16

Answers

Answer:

18

Step-by-step explanation:

Leo is traveling to Canada for work. He is taking $2,400 with him that he wants to
convert to Canadian dollars. If the current exchange rate is 1 U.S. dollar is equal to
1.33 Canadian dollars, how many Canadian dollars will he have when he converts
his money?
2, 400 Canadian dollars
3,000 Canadian dollars
3,192 Canadian dollars
1,084 Canadian dollars

Answers

Answer:

C) 3,192 Canadian dollars

Step-by-step explanation:

$2,400 x 1.33 = $3,192

Give the slope of the graph and the unit rate. Express your answers as simplified fractions, if necessary.


Jorge: 5 miles every 7 hours

Answers

Answer:

The slope of the graph is 7/10

Solve 31-X + (2 x + 1)] = x - 1.

Answers

Answer:

x = X + 33 (I am guessing "x" and "X" are not the same. "x" is a variable and "X" is a constant.)

Step-by-step explanation:

31 - X + (2x+1) = x - 1

or, 2x+1 = x - 1 - 31 + X

or, 2x - x = -1 -31 + X -1

or, x = -2 -31 + X

or, x = X - 33

Help Asap! I will give brainliest

Answers

I think it is
Y = 2x - 6

which is greater? -1 17/20 or -1 8/10

PLSSS HELP ASAP
PLSSS SHOW WORK ASWELL

Answers

Answer:

-18/10

Step-by-step explanation:

I think that is correct

Answer:

1 17/20

Step-by-step explanation:

if you × 8/10 it by 2 = 16/10

Hi, need help on this please, will give 5 stars and a thanks if you get it correct (:

Answers

Answer:

Move the decimal point in 407.26 three places to the left = 0.407283

Step-by-step explanation:

Answer:

3, left

Step-by-step explanation:

When you're dividing a number by any power of 10 that is a whole number (10, 100, 1000, etc.), you move the decimal point to the left as many times as there are zeroes in the digit.

Examples:

30.22 ÷ 100 = 0.3022

There are two zeroes in 100, so move the decimal point two spaces to the left.

568.9 ÷ 10000 = 0.05689

There are four zeroes in 10000, so move the decimal point four spaces to the left.

The given equation in the problem is 407.26 ÷ 1000, so you move the decimal point 3 spaces to the left to find the correct answer.

What is 98,248 written as a number name?

Answers

Answer:

ninety eight thousand two hundred forty eight

Answer:

Ninety-eight-thousand-and-two-hundred-and-forty-eight

Step-by-step explanation:

A figure has been dilated from center O by a scale factor of r = 3/10 scale factor would magnify the dilated figure back to the original size?​

Answers

Answer: The new scale factor needs to be 10/3

Explanation:

Consider a line segment that is 10 units long. Apply the scale factor 3/10 to it, and now it's 3 units long because (3/10)*10 = 3.

To get it back to 10 units, we multiply by the scale factor 10/3 which is the reciprocal of the original scale factor. Note that (3/10)*(10/3) = 1. Those two scale factors multiply to 1 to indicate no change has been made overall.

Solve the following inequality: -3x > 6 or 2x + 3 > 9

Answers

Answer:

I think the first one is x < 2 and the second is x > 3

One angle of a triangle measures 112°. The other two angles are congruent.

Enter and solve an equation to find the measure x of the congruent angles.

An equation is = 180.

The congruent angles each measure
pls help

Answers

Answer:

Each of the congruent angles is 34

Step-by-step explanation:

A = 112                               A is the given angle

A + x + x = 180                   A + x + x = 180 All triangles have 180 degrees  

112 + x + x = 180                 Combine

112 + 2x = 180                     Subtract 112 from both sides

112-112 + 2x = 180 - 112       Combine

2x = 68                                Divide both sides by 2

2x/2 = 68/2

x = 34

So what’s the easiest way to get the answer? 80 = 720 divided by?

Answers

Answer:

57,600

Step-by-step explanation:

720 * 80 = 57,600

Answer:

9

Step-by-step explanation:

You divide the answer with the first number and you'll get the answer, 9.

Absolute value of -2

Answers

The absolute value is of -2 is 2 because it’s 2 away from zero hope it helps !

Someone please hurry and answer number 4!!!! Will give brainliest

Answers

Answer:

25×2.50=62.5

62.5+12=74.5

hope that helps

Answer:

$74.50

Step-by-step explanation:

M = 2.50(f) + 12

M = 2.50(25) + 12

M = 74.5

Through (4, -3); perpendicular to 3y = x-6

Answers

Answer:

its=> 3×4=-3-6(use a caculator now)

plz help me i really need help these problems are really hard for me to understand so if anybody helps it would be highly appreciated​

Answers

Answer:

51.5; the origin

Step-by-step explanation:

Translation

For the translation find the distance between corresponding points of A and A'. It is 5 units.

Dilation

We see the figures A' and A'' are symmetrical and the sides on the x-axis overlap. It means the center of dilation is the origin, the point (0, 0).

Find the scale factor by dividing the corresponding x- or y- coordinate of A'' to the one of A'.

Take points (-2, 0) of A' and (-3, 0) of A''.

The scale factor is:

k = -3/-2 = 1.5

the area of a triangle is 54cm². if the height of the triangle is 6cm, find it's base.​

Answers

Answer:

18cm

Step-by-step explanation:

triangle area = b*h/2

base = 2*area : h

2 * 54 : 6 =

18

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

18*6:2= 54

the answer is good

NO LINKS OR ASSESSMENT!!!

Part 1: Domain and Range of Graphs

Answers

Domain is the set of input valuesRange is the set of output valueFunction is passes the vertical line test#1

Domain:

- 5 < x < 5 or x ∈ (-5, 5)

Range:

-5 < y < 5 or y ∈ (-5, 5)

Function:

YES - passes the vertical line test#3

Domain:

- 5 < x ≤ 5 or x∈ (-5, 5]

Range:

-3 < y ≤ 2 or y ∈ (-3, 2]

Function:

YES - passes the vertical line test#5

Domain:

- 5 < x < 3 or x∈ (-5, 3)

Range:

0 < y < 4 or y ∈ (0, 4)

Function:

N0- doesn't pass the vertical line test

Hello! I really need help on these two questions please!

Answers

Answer:

1. y-4=1/3(x-3)

used (3,4)

2. y-7=3(x-3)

used (3,7)

If 1040-x=3y and x-880=y what is y
HELP FAST

Answers

I got the answer Y=920

y = x - 880 ==》 x = y + 880 ( ☆ )

_________________________

3y = 1040 - x =☆=》 3y = 1040 - ( y + 880 )

====》 3y = 1040 - y - 880

====》 3y + y = 1040 - 880

====》 4y = 160

====》 y = 160 ÷ 4

====》 y = 40

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