What is the vertex of the function f (x) = x2 - 10x?
(5,-25)
(5.-75)
(-5,75)
(-5,25)​

Answers

Answer 1

Option A

The vertex is (h, k) = (5, -25)

Solution:

Given function is:

[tex]f(x) = x^2-10x[/tex]

The vertex form is given as:

[tex]y = a(x-h)^2+k[/tex]

where (h, k) is the vertex

Rewrite the equation in vertex form

[tex]f(x) = x^2-10x[/tex]

Complete the square for  [tex]x^2-10x[/tex]

Use the form [tex]ax^2+bx+c[/tex] to find the values of  a, b, c

a = 1 , b = -10, c = 0

Consider the vertex form of a parabola

[tex]a(x+d)^2+e[/tex]

Substitute the values of a and b into the following formula to find "d" :

[tex]d = \frac{b}{2a}\\\\d = \frac{-10}{2 \times 1}\\\\d = -5[/tex]

Find the value of "e" using the formula,

[tex]e = c - \frac{b^2}{4a}\\\\e = 0 - \frac{(-10)^2}{4 \times 1}\\\\e = -25[/tex]

Substitute the value of a, d, e into vertex form

[tex]a(x+d)^2+e\\\\1(x-5)^2-25\\\\(x-5)^2-25[/tex]

Set y equal to above equation

[tex]y = (x-5)^2-25[/tex]

Compare the above equation with vertex form

[tex]y = a(x-h)^2+k[/tex]

[tex]y = (x-5)^2-25[/tex]

We find, h = 5 and k = -25

Thus the vertex is (h, k) = (5, -25)


Related Questions

What is the inverse of f(x)=-x-1

Answers

Answer:

f^-1 (x)=-x-1

Step-by-step explanation:

y=-x-1

x=-y-1

-y=x+1

y=-x-1

3,562,185 What is the value of 3?

Answers

the value of the three would be three million, as it is in the millions place

Answer: 3 millions

Explanation: To determine what the digit "3" means in 3,562,185, if we put 3,562,185 into the place value chart, we can see that the 3 appears in the units column of the millions period so in this problem 3 refers to 3 millions.

What is the value of n?

Answers

Answer:

What is n?

Step-by-step explanation:

1. Justin divided 403 by a number and got a quotient of 26 with a remainder of 13. What was the
number Justin divided by?
a. 13
b. 14
c. 15
d. 16

Answers

Answer:

15

Step-by-step explanation:

First subtract the remainder from 403 to get 390. then divide 390 by 26 to get 15.

The number used by Justin used to divide 403 to get a quotient of 26 with a remainder of 13 is 15.

What number was used to divide 403?

Division is theartimetic process used to divide a number into equal parts using another number. The sign used to denote division is ÷.

In order to detemine the number used to divide 403, take the following steps:

Subtract 13 from 403 = 403 - 13 = 390

Now divide 390 by 26: 390 / 26 = 15

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find the value of m<1 m<2 and m<3

Answers

Answer:

i don't know

Step-by-step explanation:

Which of the following points is a solution of the inequality y < -|x|?
a) (1, -2)
b) (1, -1)
c) (1, 0)

Answers

Answer:

a) (1, -2)

Step-by-step explanation:

The given inequality is y < -|x|

We substitute the point to see which points satisfy the inequality.

For a) (1, -2), we substitute x=1 and y=-2 to get:

-2 < -|1|---------->-2<-1--------->True

For b) (1, -1), we substitute x=1 and y=-1 to get:

-1 < -|1|---------->-1<-1--------->False

For a) (1, 0), we substitute x=1 and y=0 to get:

0 < -|1|---------->0<-1--------->False

The first choice is correct.

jacob qnd jordan are training for track season. jacob did 39 sit-ups in 30 secs. jordan did 59 sit-ups in 50 secs. who will likely do more sit-ups in 2 1/2 mins

Answers

Jordan it a bigger number

Mark as Brainliest

it took Bob 55 minutes to clean the garbage. How many seconds did it take bob?there are 60 seconds in one minute please help me .​

Answers

Answer:

3,300 sec

Step-by-step explanation:

Factor each expression.
17. 5x -25

Answers

Answer:

~ 5(x-5)

Explanation:

~ Always find GCF to factorize a number, here it’s 5

~ Now inside the bracket the x stays the same but 25 divided by 5=5

~ Now we have 5(x-5)

Hii!

_________________________________________________________

Answer:

5(x-5)

Step-by-step explanation:

Both terms, 5x and -25, have something in common. This "something" is called the greatest common factor, or g.c.f.

The g.c.f. of 5x and -25 is 5, so we factor 5 out by dividing 5x and -25 by 5. Upon doing this we obtain

x-5

Now we need to put parentheses around x-5.

(x-5)

Next, we put 5 outside the parentheses.

5(x-5)

--

Hope that this helped! Best wishes.

--

Solve by using substitution. Express your answer as an ordered pair.
3x+y=10
Y=x+2
A.) 8,10
B.) 8/3,2
C.) 2,4
D.) 4,2

Answers

Answer:

c. 2,4

Step-by-step explanation:

If 5/8 = x/16 , then x is equal to

Answers

Answer:

10/16

Step-by-step explanation:

Perform the indicated operation.(7 - 11/) + (-3 + 5/)

Answers

Answer:

The correct answer is C. 4 -6

Step-by-step explanation:

Let's solve the operation given, this way:

(7 - 11/) + (-3 + 5/)

7 - 11 - 3 + 5=

12 - 14 = - 2

After resolving the parenthesis, adding and subtracting the result of thhe operation is - 2

The correct answer is C. 4 -6

If sin A is negative and cos A is positive, what
is the number of the quadrant in which angle A
terminates?

Answers

Answer:

Quadrant 4

Step-by-step explanation:

sinA < 0 in quadrants 3 and 4

cosA > 0 in quadrants 1 and 4

Thus sinA < 0 and cosA > 0 in quadrant 4

elizabeth can run 5 mils in 24 1/2 minutes Dez can run 8 miles in 32 1/3 minutes. who can run faster?

Equivalent ratio 1:

Equivalent ratio 2:

Answers

Answer:

Des can run faster than Elizabeth.

Des can run 1 mile in 4.037 minutes while Elizabeth can run 1 Mile in 4.9 minutes

Step-by-step explanation:

If Elizabeth can run 5 miles in 24.5 minutes. Elizabeth will run 1 mile in 24.5/5=4.9 minutes.

If Dez can run 8 miles in 32 1/3 minutes. Then Dez will run 1 mile in 32.3/8=4.037 minutes

Therefore if Dez can run 1 mile in 4.037 minutes and Elizabeth can run 1 mile in 4.9 minutes then Dez can run faster than Elizabeth.

What is the equation of the line that has a slope of -4 and goes through (-1,6)

Answers

Answer:

y = - 4x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 4, thus

y = - 4x + c ← is the partial equation

To find c substitute (- 1, 6) into the partial equation

6 = 4 + c ⇒ c = 6 - 4 = 2

y = - 4x + 2 ← equation of line

rectangle ABCD is graphed in the cordinate plane. The following are the verticies of the rectangle; A(-6,-4),B(-4,-4),C(-4,-2), and D (-6,-2). what is the perimiter

Answers

Answer:

Therefore Perimeter of Rectangle ABCD is 4 units

Step-by-step explanation:

Given:

ABCD is a Rectangle.

A(-6,-4),

B(-4,-4),

C(-4,-2), and

D (-6,-2).

To Find :

Perimeter of Rectangle = ?

Solution:

Perimeter of Rectangle is given as

[tex]\textrm{Perimeter of Rectangle}=2(Length+Width)[/tex]

Length = AB

Width = BC

Now By Distance Formula  we have'

[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]

Substituting the values we get

[tex]l(AB) = \sqrt{((-4-(-6))^{2}+(-4-(-4))^{2} )}[/tex]

[tex]l(AB) = \sqrt{((2)^{2}+(0)^{2} )}=2\ unit[/tex]

Similarly

[tex]l(BC) = \sqrt{((-4-(-4))^{2}+(-2-(-4))^{2} )}[/tex]

[tex]l(BC) = \sqrt{((0)^{2}+(2)^{2} )}=2\ unit[/tex]

Therefore now

Length = AB = 2 unit

Width = BC = 2 unit

Substituting the values  in Perimeter we get

[tex]\textrm{Perimeter of Rectangle}=2(2+2)=2(4)=8\ unit[/tex]

Therefore Perimeter of Rectangle ABCD is 4 units

Answer:

Therefore Perimeter of Rectangle ABCD is 4 units

Step-by-step explanation:

Given:

ABCD is a Rectangle.

A(-6,-4),

B(-4,-4),

C(-4,-2), and

D (-6,-2).

To Find :

Perimeter of Rectangle = ?

Solution:

What is the equation of the line that is parallel to the line y - 1 = 4(x + 3) and passes through the point (4, 32)?
A: y=-1/4x +33
B: y=-1/4x + 36
C: y = 4x - 16
D: y = 4x + 16

Answers

Answer:

Option D: y = 4x + 16

Step-by-step explanation:

Given the line:  y - 1 = 4(x + 3)  ⇒  y = 4x + 13

The slope of the given line = m = 4

The required line is parallel to the given line

So, the slope of the required line = m = 4

So, the general equation of the required line: y = 4x + c

Where c is constant represents y-intercept

To find the value of c, substitute with the point (4,32)

At x = 4 y = 32

∴ 32 = 4 * 4 + c

∴ c = 32 - 16 = 16

∴ y = 4x + 16

The answer is option D: y = 4x + 16

Michelle sets up a lemonade stand to make some extra money.She spends $4.75 purchasing supplies.She earns $16.50 selling lemonade.How much money does she make after she subtracts her expenses?

Answers

16.50-4.75= 11.25 Simple subtraction.

in general, f−1(f(x)) = f(f−1(x)) =

Answers

Answer:

f−1(f(x)) = f(f−1(x)) = x

Step-by-step explanation:

Follow this simple example using the function f(x) = x + 2

f(x) = x + 2

NOw we find the inverse function f^(1)(x).

y = x + 2

x = y + 2

y = x - 2

f^(-1)(x) = x - 2

The inverse function is f^(-1)(x) = x - 2

Now we do the two compositions of functions:

f^(-1)(f(x)) = x + 2 - 2 = x

f(f^(-1)(x)) = x - 2 + 2 = x

Both are equal to x.

Answer: f−1(f(x)) = f(f−1(x)) = x

The expression [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]

We are to prove the relationship;

[tex]f^{-1}(f(x)) = f(f^{-1}(x)) = ?[/tex]

To get the unknown, let f(x) = x - 2

Find its inverse:

Let y = x - 2

Replace y with x;

x = y - 2

y = x+2

Hence [tex]f^{-1}x = x+2[/tex]

Next is to get [tex]f(f^{-1}(x))[/tex]

[tex]f(f^{-1}(x))=f(x+2) = (x+2) - 2\\f(f^{-1}(x))= x\\[/tex]

We can conclude that [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]

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The line passing through (11,y) and (2,0)is parallel to the line joining (7,5) and (-2,2). Find y.

Answers

Answer: y = 3

Step-by-step explanation:

Two lines are said to be parallel if they have the same slope. All we need to do is to find the slope of each line . The formula for finding slope is given as :

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

For the first line

[tex]x_{1}[/tex] = 11

[tex]x_{2}[/tex] = 2

[tex]y_{1}[/tex] = y

[tex]y_{2}[/tex] = 0

substituting into the formula , we have

m = [tex]\frac{0 - y}{2 - 11}[/tex]

m = [tex]\frac{-y}{-9}[/tex]

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

Also Finding the slope of the second line we have

[tex]m_{2}[/tex] = [tex]\frac{2-5}{-2 - 7}[/tex]

[tex]m_{2}[/tex] = [tex]\frac{-3}{-9}[/tex]

[tex]m_{2}[/tex] = [tex]\frac{1}{3}[/tex]

Since the two lines are parallel , we will equate their slope , that is

[tex]\frac{y}{9}[/tex] = [tex]\frac{1}{3}[/tex]

3y = 9

y = 3

How can I use fractions tiles to help divide a whole number by a unit fraction

Answers

To divide a whole number by a unit fraction, you can always multiply the whole number by the unit fraction's denominator to get the answer! Example: 5 divided by 1/7 is 5*7=35. This answer of 35 makes sense: there are seven 1/7's in a 1, so there are thirty-five 1/7's in a 5.

Final answer:

To divide a whole number by a unit fraction using fraction tiles, treat the division as multiplication by the reciprocal of the unit fraction and then split the whole number tiles accordingly.

Explanation:

To use fraction tiles to help divide a whole number by a unit fraction, you can follow these steps:

Understand that dividing by a unit fraction is the same as multiplying by its reciprocal. For example, dividing by 1/2 is the same as multiplying by 2, since 2 is the reciprocal of 1/2.Start with fraction tiles that represent the whole number you want to divide. For instance, if the whole number is 6 and you're dividing by 1/2, use 6 whole tiles.Since you're multiplying by the reciprocal of the unit fraction, convert the action of dividing into multiplication. Each whole tile would be split into the number of pieces that are equivalent to the denominator of the unit fraction. If dividing by 1/2, split each whole into 2 pieces.Count all the new pieces. The result is the number of pieces you have after dividing by the unit fraction. In our example with 6 whole tiles and dividing by 1/2, you'd end up with 12 pieces since each whole tile is split into 2 pieces.

The friends now To go on the loop D loop and the roller coaster. Explain why only 1 of the friends can go on both of these rides

Answers

Are there any more instructions or information?

Final answer:

Due to requirements such as height and ride capacity, only one friend can go on both the loop and the roller coaster at the same time.

Explanation:

In order to go on the loop and the roller coaster, the friends need to meet certain requirements. For example, they need to be tall enough to ride the roller coaster and meet any age restrictions. Additionally, the roller coaster may have a limited number of seats or ride capacity. Due to these factors, it's possible that only one friend can go on both of these rides at the same time.

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Can some one help me please and explain it

Answers

Answer:

c= -2

Step-by-step explanation:

Perpendicular lines imply that the product of the gradient of the two lines is -1.

So let's find the gradient of each lines.

[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]

Gradient of 1st line

= 1-(-4)/ -3-2

= 5/-5

= -1

(gradient of 1st line)(gradient if 2nd line)= -1

(-1)(gradient of 2nd line)= -1

gradient of 2nd line= -1 ÷ (-1) =1

Now make use of the gradient formula to find an expression of the gradient of the second line.

Gradient of 2nd line= c-1/ -2-1

subst. gradient of second line and simplify:

1= c-1/-3

c-1= -3 (multiply by -3 on both sides)

c= -3+1 (add 1 on both sides)

c= -2

Linda's start up cost for her online jewelery store was $250, as she has to pay an additional $60per month to keep it running. Write an expression or equation modeling the real world

Answers

Total Cost = 250 + 60x is the equation that models the given situation

Solution:

Given that, Linda's start up cost for her online jewelery store was $250

She has to pay an additional $60 per month to keep it running

To find: Equation that models this situation

From given,

Start up cost = $ 250

Let "x" be the number of months she keeps the store running

Additional pay per month = $ 60

Thus, the total cost Linda spend to keep the store running is given as:

Total Cost = Startup cost + (Additional pay per month)(number of months)

[tex]Total\ Cost = 250 + 60x[/tex]

Thus the equation that models the given situation is found

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is twice the measure of the first angle. The third angle is 12 more than the second.

Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.

Answers

x = first angle

y = second angle

z = third angle

x + y + z = 180

The sum of the measures of the second and third angles is twice the measure of the first angle.    ---->       y + z = 2x

The third angle is 12 more than the second.  ---->    z = y + 12

Use substitution to find each variable. Since z is already isolated/by itself, plug it into the other equation

y + z = 2x    Plug in (y + 12) for z

y + (y + 12) = 2x      Simplify

2y + 12 = 2x    Divide 2 on both sides

y + 6 = x          Isolate "y"

y = x - 6         Next you could plug this into z = y + 12, so that z has the x variable

z = y + 12

z = x - 6 + 12

z = x + 6

Now that you have y and z, you can do this:

x + y + z = 180

x + (x - 6) + (x + 6) = 180     Simplify

3x = 180    Divide 3 on both sides

x = 60             Now that you found x, plug it into the other equations to find y and z

y = x - 6

y = 60 - 6

y = 54

z = x + 6

z = 60 + 6

z = 66

x = 60°

y = 54°

z = 66°          [sorry if this is confusing]

PROOF

x + y + z = 180

60 + 54 + 66 = 180

180 = 180

Final answer:

The problem can be solved by setting up and solving a system of equations based on the information given in the problem. Using these equations, we are able to establish a relationship between the angles and thus calculate their individual measures.

Explanation:

To solve this problem, we need to set up and solve a system of equations based on the information provided. We know from the problem that:

The sum of the angles of a triangle is 180 degrees, so x + y + z = 180.The sum of the measures of the second and third angles is twice the measure of the first, so y + z = 2x.The third angle is 12 more than the second, so z = y + 12.

First, let's substitute z = y + 12 into the other two equations:

In x + y + z = 180, replace z with y + 12 to get x + y + y + 12 = 180; or, simplifying further, x + 2y = 168.In y + z = 2x, replace z with y + 12 to get y + y + 12 = 2x or, simplifying further, 2x = 2y + 12 or x = y + 6.

We now substitute x = y + 6 into the equation x + 2y = 168 to find the values of x and y and hence z.

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what should be added to both sides of the equation to solve for the variables? 45=30+m

Answers

Answer: m = 15

Step-by-step explanation:

45 = 30 + m

subtract 30 , from both sides  , that is , -30 should be added to both sides to find the variable

45 - 30 = 30 + m - 30

15 = m

Therefore : m = 15

What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1?

y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1

–8
–5
0
6

Answers

Answer: 0 on edge

Step-by-step explanation:

got it correct

Answer: C

Step-by-step explanation:

took quiz

Ryder used front-end estimation to estimate the product of (–24.98)(–1.29). What was his estimate?

Answers

Answer:

20

Step-by-step explanation:

Answer:

20

Step-by-step explanation:


ASAP


Of 450 lunches sold at school on Thursday, 40% were hamburgers
and the rest were pizza. How many more pizza lunches were sold than
hamburgers? Explain how you found your answer.

Answers

Answer: 90

Step-by-step explanation:

Total number of lunches sold = 450

Number of hamburgers = 40% of the total , that is

number of hamburgers = 40/100 x 450 = 180

number of pizza = 450 - 180 = 270

Therefore , the number of pizza lunches sold more than hamburgers will be

270 - 180 = 90

Therefore : 90 more pizza lunches were sold than hamburgers.

Find fifth roots of z⁵ + 32 = 0 and draw its graph?

Answers

Answer:

Step-by-step explanation:

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