Write an equation in intercept form of the parabola that passes through the point (1,32) and has x-intercepts −7 and 3?

Answers

Answer 1

Given that the parabola passes through points (1,32) and the x-intercepts are (-7,0) and (3,0)
thus the equation will be as follows:
y=a(x-k)(x-h)
where:
(x-k) and (x-h) are the factors:
thus
y=a(x+7)(x-3)
y=a(x^2+4x-21)
But, when x=1, y=32
plugging this in the equation we get:
32=a(1^2+4(1)-21)
32=a(1+4-21)
32=-16a
hence:
a=-2
thus the eqiation will be:
y=-2(x^2+4x-21)
hence the equation is:
y=-2x^2-8x+42

Answer 2

The correct equation of the parabola in intercept form is [tex]2 (x+2)^2 -50[/tex].

To derive this equation, we will use the fact that the parabola passes through the given point (1,32) and has x-intercepts at -7 and 3.

[tex]y = k*(x+7)(x-3)[/tex]

[tex]y = k *(x^2 + 4x - 21)[/tex]

[tex]32 = k ( 8 * -2)32 = -16* kk = 32/-16 = -2[/tex]

[tex]y = -2(x+7)(x-3)[/tex]

[tex]= -2(x^2 + 4x - 21)[/tex]

[tex]= -2(x^2 +4x ) -42[/tex]

[tex]= 2(x^2 + 4x + 4) - 42 - 8[/tex]

[tex]= 2 (x+2)^2 -50[/tex]

Related Questions

Which kind of function best models the data in the table? Use differences or ratios.

x y
0 1.7
1 6.8
2 27.2
3 108.8
4 435.2

Answers

To obtain the suitable function that will model the set of data, we begin by plotting the data. The graph is shown in the attachment. From the given graph we see it's an exponential growth curve. Therefore the best function that fits the data is exponential growth.

Mei puts 600.00 in an account to use for school expenses . The account earns 10% interest , compound quarterly. How much interest will he have earned after 6 years

Answers

She would have $960.

Hope this helped:D

A fence on a hill uses vertical posts L and M to hold parallel rails N and P. If m∠1 = 6x and m∠12 = 4x, then what is the measure of ∠5?

Answers

Answer;

D: 108 degrees

Answer:

Measure of ∠5 is 108°

Step-by-step explanation:

Given m∠1 = 6x and m∠12 = 4x, we have to find the measure of ∠5.

As ∠1 and ∠5 are alternate exterior angle hence equal i.e ∠1=∠5

Also, ∠5 and ∠12 are co-interior angles ∴these are supplementary

⇒ m∠5+m∠12=180°

⇒ 6x+4x=180°

⇒ 10x = 180° ⇒ x=18

∴ m∠5 = 6x = 6(18) = 108°

Hence, measure of ∠5 is 108°

WILL GIVE BRAINLIEST
FIND VOLUME
60 is the area of the base

Answers

Hey so yeah this can be a challenging problem, Vol (V) is much easier to solve than surface area (SA), but I'll show you how it's done, my friend.
First of all, V (prism) = area of base (B) × h
We know that the height (h) of this prism is given, which we'll need later on: h = 5 ft, and area of base (B) is given as 60 ft2
So V = 60 ft2 × 5 ft = 300 ft3

So now for the hard part... how to calculate the SA of this prism

IF YOU DON'T NEED SA FOR THIS TYPE OF PROBLEM, DO NOT PROCEED!!!
[VERY DETAILED]

means solving the dimensions (sides) of that pesky polygon base (B) or lid.
The most important things about polygons are:
1) is it regular (same angle ° and side length)??
2) How many sides or angles??

This has to be regular, because they give you no other info so it has to be, in order to solve. And then it has 5 sides and angles = regular pentagon. ("penta" means 5).

Now there are 360° in any circle, so:
take the central angles of where the sides meet at the center forming triangles (see drawing above), each of those (5) central <'s = 360/5 = 72°
Now the apex of each of these triangles = 72°
but with our 5 triangles, we need to find the height of each triangle -- which is the midpoint of the side (base (b) of triangle), and h is perpendicular to this b. By bisecting that apex angle of 72, it forms 2 equal right triangles of
72/2 = 36°. So each right triangle has 36, 90, and?? 180-36-90 = 90-36 = 54°
let's call the base (b) = 1 side of pentagon
= side (s)
Therefore (see 2nd image drawn above) tangent (tan) of € = opposite/adjacent, or
tan (54) = h÷1/2b --> h = [tan (54)]×(1/2)b
1/2b = h/[tan (54)] = h/1.38

Also the area of each of the larger 5 triangles A(t) = 1/2b×h, and that area A(t) × 5 = area of whole pentagon base A(B)
So now after all that... our A(B) given at beginning = 60ft2. let's put it all together:
1/2b = h/[tan (54)] = h/1.38
A(t) = 1/2b×h, and A(B) = 5×A(t)
which means that A(B) = 5×(1/2b×h)
AND since the other calculation shows that 1/2b = h/1.38, plug that value into the A(B) formula...
.
.
.

now that we have height (h) of each triangle, we can go back to our tan equation for the triangle: tan (54) = 1.38 = h/(1/2b)
--> 1/2×b = h/1.38 --> base (b) = 2h/1.38
b = 2(4.06 ft)/1.38 = 8.12 ft/1.38 = 5.90 ft, for which b us also the width of each rectangular side panel (w)
length (l) of these sides was given as height of the whole prism = 5 ft

NOW FINALLY... THE FINAL SURFACE AREA OF THE PRISM (SA) = (2×A(B)) + (5×rectangular side)
SA = (2×60 ft2) + (5×(l×w)) = 120 ft2 + 5×5ft×5.9ft
SA = 120 ft2 + 147.62 ft2 = 267.62 ft2

Answer:

300 ft³

Step-by-step explanation:

Volume = Area of base × height

Volume = 60ft² × 5ft

Volume = 300 ft³

A number is multiplied by 6. If 8 is subtracted from the product you get 34.
What is the number?
A-4
B-6
C-7
D-8

Answers

Hello!

You can make an equation based on what you know

A number multiplied by 6

x * 6

Subtracted by 8

x * 6 - 8

You get 34

x * 6 - 8 = 34

Now you solve it algebraically

Add 8 to both sides

x * 6 = 42

Divide both sides by 6

x = 7

The answer is C) 7

Hope this helps!

The surface area of a sphere is 200.96 square centimeters. What is the approximate volume of the sphere?

Answers

The approximate volume of the sphere is 266.19 cubic centimeters.

To find the approximate volume of a sphere from its surface area, we will use the relationship between the surface area and radius of the sphere and then apply the formula for the volume. The surface area (A) of a sphere is given by the formula A = 4πr2, and the volume (V) is given by the formula V = (4/3)πr3. Given that the surface area of the sphere is 200.96 square centimeters, we can solve for the radius (r) first:

A = 4πr2
=> r2 = A / (4π)
=> r2 = 200.96 / (4π)
=> r = √(200.96 / (4π))
=> r ≈ 3.99 cm (after calculating using a calculator)

Now that we have the radius, we can find the volume:

V = (4/3)πr3
=> V = (4/3)π(3.99 cm)3
=> V ≈ 266.19 cm3 (after calculating using a calculator)

Therefore, the approximate volume of the sphere is 266.19 cubic centimeters.

do banks always charge the same interest rate on new and used cars

Answers

Yes they do they charge interest on everything
even a house home everything yeah cars espically if your taking out a loan or that type of thing yeah your gonna have a big hard time with i would try this app offer up for a car its really cheap

Final answer:

Banks generally do not charge the same interest rate on new and used cars. Factors including the type of car, borrower's credit history, length of the loan, and market conditions can affect the interest rate. Usually, used cars have higher interest rates due to higher perceived risk.

Explanation:

No, banks do not always charge the same interest rate on new and used cars. Interest rates are based on numerous factors that include the type of car (new or used), the borrower's credit history, the length of the loan, and the existing market conditions. Typically, used cars have higher interest rates because they are viewed by the bank as more risky investments. Therefore, individuals with excellent credit may secure lower interest rates on both new and used car loans, but the rate for used cars will still generally be higher than for new cars.

Learn more about Interest Rates here:

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Delia measured a doorway to be 1 meter wide. Which of these is a nearly equivalent measurement
A: 15 mi
B: 10.5 yrds
C: 3.3 ft
D: 98.7 in

Answers

Final answer:

To find a nearly equivalent measurement to 1 meter wide, the correct answer is C: 3.3 feet, as it is very close to 39.37 inches, the length of 1 meter in inches.

Explanation:

To find a nearly equivalent measurement, we can examine the conversion between meters and other units of length. Based on the provided information, 1 meter is equivalent to 1.094 yards or 39.37 inches.

When comparing the options given:

15 miles (mi) is much larger than a meter and, therefore, not equivalent.10.5 yards (yrds) is significantly more than 1 meter, so it is not a close match either.3.3 feet (ft) can be checked by knowing that there are 12 inches in a foot, which would be equivalent to 39.6 inches, making this measurement very close to 1 meter.98.7 inches (in) would be more than twice the length of 1 meter since we know 1 meter is about 39.37 inches.

Therefore, the answer that is nearly equivalent to 1 meter is C: 3.3 feet.

This is because 3.3 feet, when converted to inches (3.3 ft x 12 in/ft), is approximately 39.6 inches, which is very close to the 39.37 inches that make up 1 meter.

Final answer:

The most nearly equivalent measurement to 1 meter wide, among the provided options, is 98.7 inches (option D), as 1 meter equals approximately 39.37 inches.

Explanation:

Delia measured a doorway to be 1 meter wide. To find a nearly equivalent measurement in a different unit, we must look at the options provided and use unit conversion reference information:

1 m = 1.094 yd = 39.37 inches1 in. = 2.54 cm

Comparing the given options against the meter measurement:

A: 15 mi – This is substantially larger than a meter.B: 10.5 yrds – This is also considerably larger than a meter.C: 3.3 ft – This is approximately 1 meter since 1 yard (3 feet) is slightly less than a meter (1 m = 1.094 yd).D: 98.7 in – This is close to a meter (1 m = 39.37 inches).

Thus, the most nearly equivalent measurement to 1 meter wide is option D: 98.7 inches.

The price of buying gasoline varies directly with the number of gallons bought.If five gallons of gas cost $17.50,what is the rate of change of this linear equation.

Answers

every 1 gallon is 3.5

I WAS ONLY ABLE TO SELECT 40 PTS THIS TIME, PLS ANSWER THIS ONE IT HAS THE PICTURE WITH IT.
In the figure, lines a and b are parallel.

Which statements are true?

Select each correct answer.
MORE THAN ONE ANSWER

m∠2=m∠1

m∠2=105°

m∠1=75°

m∠3=m∠1

Answers

Okay so the first one is right.
The second one is wrong.
the third one is right.
The forth one is wrong.

∠1 and 105° are supplementary angles. (supplementary = 180°)

180 - 105 = 75°

∠1 = 75°

∠1 and ∠2 are corresponding angles, and so there measurements will be the same

∠1 = ∠2
∠1 = 75°
∠2 = 75°

105° and ∠3 are same side, and are corresponding angles. Therefore, ∠3 = 105°

m∠1=75°

180° (the measurement of a straight angle).

Subtract the 105° (given) from the straight angle

180 - 105 = 75

m∠1=75°

hope this helps

Which of the following expressions shows the number of 8 character passwords that can be formed using letters and digits if the password must begin with a letter?

a. 21x36 to the 7th power

b.26x36 to the 7th power

c.26 to the 5th power x 10 to the 3rd

d.36 to the 8th power

Answers

Answer:

26x36 to the 7th power

Step-by-step explanation:

Answer:

its B my boys!!!!!!!

Step-by-step explanation:

What is the smallest integer greater than the square root of 148?
A.)13
B.)15
C.)14
D.)12
E.)11

Answers

EXPLAINED ANSWER:

The square root of 148 is 12.1655250606.

Now with the options, you provided which are 13, 15, 14, 12, and 11, we can represent our known numbers on a number line.

----- | ----- | ----- | -*---- | ----- | ----- | ----- | -----
10 11 12 13 14 15 16

* = 12.1655250606

Now we can use the process of elimination to determine the smallest integer greater than the square root of 148.

15 is obviously too far to be the smallest integer greater than the square root of 148, so that is not the correct answer.

14 is pretty close to 12.1655250606, but we have three other options that are even closer so that cannot be the correct answer.

11 is also incredibly close to our square root, but there are two other options that are even closer. Therefore 11 will not be our answer.

Now that we have eliminated all other options but two of them, we have made it easy to determine which is correct.

12 is closer to 12.1655250606 than the number 13, so this would be the correct answer if the question was asking for the smallest integer of the square root of 148. But it is not.

The question asks for the smallest integer GREATER THAN the square root of 148. Therefore the correct answer to this question is 13.

QUICK ANSWER:

The smallest integer greater than the square root of 148 is 13.

The square root of 148 is 12.16. The smallest integer greater than the square root of 148 is 13.

The given number is 148.

What is the square root?

The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.

The square root of the given number is

√148 = 12.16

12<12.16>13

The square root of 148 is 12.16. The smallest integer greater than the square root of 148 is 13.

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The length of a rectangle is increase by 25%. to keep the area of the rectangle the same, by what percent must the width be decreased

Answers

are there any answer choices

The line represented by y = 3x − 6 and a line perpendicular to it intersect at R(3, 3). What is the equation of the perpendicular line?

A)y=-1/3x +4
B)y=1/3x + 7/3
C)y=-1/2x +5/2
D)y=-3x + 5

Answers

The answer is (A)
opposite slop

Flip the original slop and change the sign
The equation gonna be like (A)

y-intercept is doesn't matter same or different

hope it's help

It takes a ship 4 hours to cover 420 km with the current and 6 hours against the current. Find the speed of the ship in still water and the speed of the current.

Answers

Let s be the speed of the ship, and c be the speed of the current.

We know that distance equals speed multiplied by the time.

With the current
[tex]\left(s+c\right)\left(4\:hours\right)=420\:km[/tex]
or
[tex]s+c=105[/tex]
This is our first equation.

Now, against the current, we have
[tex]\left(s-c\right)\left(6\right)=420[/tex]
or
[tex]s-c=70[/tex]
This is our second equation.

We solve the equations simultaneously, by adding them together
[tex]2s-0c=175[/tex]

[tex]s=87.5\:km/hr[/tex]

Substitute s=87.5 to the first equation to solve for c.
[tex]87.5+c=105[/tex]

[tex]c=17.5\:km/hr[/tex]

The speed of the ship is 87.5 km/hr and the speed of the current is 17.5 km/hr.

The speed of the ship is 87.5 km/hr and the speed of the current is 17.5 km/hr.

What is the speed of the current?

The actual propagation speed depends on the size of the wire and electrical parameters such as its inductance, but it is normally approximately 90% of the speed of light—about 270,000 km/s.

Let x be the speed of the ship, and y be the speed of the current.

It takes a ship 4 hours to cover 420 km with the current and 6 hours against the current.

[tex]\rm (x+y)4=420\\\\x+y=\dfrac{420}{4}\\\\x+y=105[/tex]

And the second equation is;

[tex]\rm (x-y)6=420\\\\x-y=\dfrac{420}{6}\\\\x-y=70[/tex]

Adding both the equation

[tex]\rm x+y+x-y=105+70\\\\2x=175\\\\x=\dfrac{175}{2}\\\\x=87.5[/tex]

Substitute the value of x in equation 1

[tex]\rm x+y=105\\\\87.5 +y=105\\\\y=105-87.5 \\\\y= 17.5[/tex]

Hence, the speed of the ship is 87.5 km/hr and the speed of the current is 17.5 km/hr.

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I got 4/7s + 5/7 But I’m not sure if that’s correct

Answers

Hey there! :)

2/7(2s + 3)

Simplify by by using the rainbow tactic.

(2/7 × 2s) + (2/7 × 3)

Simplify.

**Remember : 2s is the same as 2/1s and 3 is the same as 3/1**

(2/7 × 2/1s) + (2/7 × 3/1)

Simplify.

4/7s + 6/7

~Hope I helped!~

Javier and Kyle work installing windows and can earn extra money by installing doors. Last week, Javier earned $56 more than Kyle because of door installations. The expression below represents Javier's pay for the week: 14w + 56 What does the first term of the expression represent?

Answers

We can comprehend that Javier and Kyle work installing windows and can earn extra money by installing doors. Last week, Javier earned $56 more than Kyle because of door installations.

The expression below represents Javier's pay for the week: 14w + 56

As it states in the question Javier earned $56 more than Kyle because of door installations. Therefore, the $56 in the equation would represent the door installation.

The 14w would represent the amount of windows that have been installed.

Answer:

[tex]14w[/tex] represents Kyle's pay for the week.

Step-by-step explanation:

"Javier earned $56 more than Kyle because of door installations"

In other words, this means if we take out 56 from Javier's total amount of pay, we get what Kyle earned last week.

Javier's pay is [tex]14w+56[/tex] , so if we subtract 56 from this expression we will get what Kyle earned last week.

[tex]14w+56-56=14w[/tex]

So, the first term of the expression 14w + 56, which is 14w, represents earnings of Kyle last week.

Find k if 64 ÷ k = 4

Answers

Hi there! The answer is k = 16.

Let's solve this problem step by step!
[tex]64 \div k = 4[/tex]

Multiply both sides by k.
[tex]64 = 4k[/tex]

Switch sides.
[tex]4k = 64[/tex]

Divide both sides by 4.
[tex]k = \frac{64}{4} = 16[/tex]

~ Hope this helps you!

sally is comparing the prices of two window cleaning companies. company A charges $7 per window and ajbadditional $12 as service charges. company B charges $5 per window and an additional $15 as service charges. Part A: write an equation to represent each company’s total charges for cleaning a certain number of windows, for both equations (one for company A and one for company B), define the variable used . Part b: how much would company A AND company B each charge for cleaning 8 windows ?

Very quick please

Answers

part a : company A : 7w+12
Company B: 5w+15

Part B:::
company a would charge $68
and company B would charge $55

find the three arithmetic means in this sequence 14 and 26

Answers

We subtract them and divide by four to find the common difference d. The intermediate means implies that there are four increments, thus we shall have:
(26-14)=12
hence
12/4=3
thus
d=2 and the missing means are:
26, 23,20,17,14

On average, for every 15 points scored by his basketball team, Riley scores 4 of them. About how many points would you expect Riley to score in a game where his team had a final score of 90 points?

Answers

She would have made 24 points

Find the LCD of the pair of expressions.

8/5b; 12/7b^3c

A) 7b^3c
B) 12b^3c^2
C) 35b^3c^2
D)'35b^3c

Answers

The correct answer is D.

The LCD, least common denominator, is the smallest denominator that both denominators will go into. The LCD of 5 and 7 will be 35; the variable portion will be b³c, since that is the smallest thing the second fraction can go into.

This gives us a denominator of 35b³c.

Jim surveys a random sample of 150 students from his middle school to learn what type of school lunch is preferred. The table below shows the result of the survey: Lunch Type Sandwich Hot Dog Salad Number of students 70 69 11 Which of the following inferences can be made based on the data? (5 points) A hot dog is two times more popular than salad. A salad is two times more popular than sandwich. Sandwiches and hot dogs are almost equally preferred. A hot dog is the most preferred lunch.

Answers

Sandwiches and hot dogs are almost equally preferred. A hot dog is the most preferred lunch because its obvious

Answer:

Sandwiches and hot dogs are almost equally preferred.

Step-by-step explanation:

Given data is :

Lunch Type Sandwich Hot Dog Salad

Number of students 70 69 11

The total students are = [tex]70+69+11=150[/tex]

The following inferences can be made:

A hot dog is two times more popular than salad. False. It is more than 5 times popular.

A salad is two times more popular than sandwich. False. Salad is only 11 and sandwiches are 70.

Sandwiches and hot dogs are almost equally preferred. True. Both have almost same number.

A hot dog is the most preferred lunch. False. Sandwich is most preferred.

Therefore, the correct answer is - Sandwiches and hot dogs are almost equally preferred.

PLSSSSS HELP :(

Determine whether the following pair of lines are parallel, perpendicular, or neither.

3x + 4y = 7 y = −2 − 34x

Answers

convert each one to slope-intercept form

y = -34x - 2

4y = -3x + 7

y = (-3/4)x + 7/4

if the first equation is meant to b -3/4x - 2 then they are parallel

Solve for x. Round your answer to 2 decimal places.

Select one:
a. 7.55
b. 15.44
c. 19.07
d. 9.33

Answers

[tex]\cos (51) = \dfrac{12}{x} [/tex]

[tex]x = \dfrac{12}{ \cos (51)} [/tex]

[tex]x = 19.07[/tex]

Answer: x = 19.07 (Answer C)

For the function y = -2x + 20, what is the output when the input is 50.

Answers

y=-2x+20
Input 50
Y=-2(50)+20
Y=-100+20
y=-80

I hope this helps :) feel free to ask if you need anything cleared up

Sal wants to know if he has enough money to buy 4 gallons of gas if he has 15$ and each gallon of gas costs 3.29$ which is a good estimate for weather sal will be able to afford 4 gallons of gas ?

Answers

In order to make an equation to find out whether or not he can afford the gas,, we must know that since $3.29 is changing so it must have a variable. Our equation also needs to equal to $15,, so it will look like the following:
15 = 3.29x
Before we start solving,, we need to plug the 4 gallons in for x.
15 = 3.29(4)
Now multiply the numbers on the right side.
15 = 13.16
This show us that the cost of 4 gallons is less than $15,, which means that Sal will be able to afford 4 gallons of gas.
Let me know if you have any further questions.
:)

What is the volume of the triangular prism below?

Answers

we know that
volume of triangular prism=area of the base*height

step 1
find the area of the base
area of triangle=b*h/2
is a right triangle
b=18 in----> convert to ft-----> 18*0.0833----> 1.50 ft
h=2 ft
area of triangle=1.5*2/2----> 1.5 ft²

volume of triangular prism=1.5*3----> 4.5 ft³

the answer is 4.5 ft³

For the function shown below, find f(3): f(x)=2x^4-8x^2+5x-7

Answers

98 is your answer plug the three in for any x value

We have been given the function

[tex]f(x)=2x^4-8x^2+5x-7[/tex]

We have to find the value of f(3). In order to find the same, substitute x=3 in the given function.

[tex]f(3)=2(3)^4-8(3)^2+5(3)-7[/tex]

Now, we simplify this step by step.

First of all [tex]3^4=81\text{ and }3^2=9[/tex]. Thus, we have

[tex]f(3)=2\times 81 -8\times 9+5(3)-7[/tex]

Now, we can easily simplify it by PEMDAS

[tex]f(3)=162-72+15-7[/tex]

[tex]f(3)=98[/tex]

Therefore, the value of f(3) is 98.

Please help asap!!!!!!!!!!!!!

Answers

The answer is B. 1.3

The answer is 1.3 hope this helps good luck

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