Mathematics College

Write the equation of the parabola in vertex form.
vertex (0,4), point (1,-3)

f(x)=

Answers

Answer 1
Hello,

y=k(x-0)²+4
if x=1 then y=-3
==> -3=k*1+4==>k=-7

y=-7x²+4
Answer 2
Final answer:

The equation of the parabola in vertex form is f(x) = -7x^2 + 4

Explanation:

To write the equation of a parabola in vertex form, we use the formula f(x) = a(x - h)^2 + k where (h, k) represents the vertex. In this case, the vertex is (0,4) so our equation becomes f(x) = a(x - 0)^2 + 4 which simplifies to f(x) = ax^2 + 4. To find the value of a, we substitute the coordinates of the point (1,-3) into the equation and solve for a. Plugging in these values, we get -3 = a(1)^2 + 4, which simplifies to -3 = a + 4. Solving for a, we find that a = -7. Therefore, the equation of the parabola in vertex form is f(x) = -7x^2 + 4.

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Related Questions

John bought 15 cookies and ate 3 of them. He ate ____% of the cookies.

Answers

He ate 20% of the cookies 
20 because 15/3 = 5 and 20 goes into 100 5 times

The perimeter of parallelogram ABCD is equal to 10 cm. Find the length of diagonal BD if you know that the perimeter of △ABD is 8 cm.

Answers

see the attached figure

Let
P1-------------> Perimeter of parallelogram ABCD
P2-------------> Perimeter of △ABD

we know that
P1=10 cm
P1=2*(AD)+2*(AB)=10------------> AB+AD=5-----------> equation 1
and
P2=AD+AB+DB
P2=8 cm------------>AD+AB+DB=8-------- AB+AD=8-DB-----> equation 2
I substitute 1 in 2

(5)=8-DB----------> DB=8-5-----------> DB=3 cm

the answer is DB=3 cm

The length of the diagonal BD is 3 centimeters.

Procedure - Length determination in a parallelogram side

A parallelogram is a quadrilateral where each pair of parallel sides have the same length and can be form by two congruent triangles which share the same side (diagonal).

Expressions for the parallelogram

Perimeter equations for the parallelogram are the following:

[tex]AB + BD + AD = 8\,cm[/tex] (1)

[tex]2\cdot AB + 2\cdot AD = 10\,cm[/tex] (2)

Where:

[tex]AB[/tex], [tex]AD[/tex] - Side lengths of the parallelogram, in centimeters. [tex]BD[/tex] - Diagonal length of the parallelogram, in centimeters.

Resolution of the system

By (2) we have the following conclusion:

[tex]AB + AD = 5\,cm[/tex]

And we find the length of the diagonal BD by (1):

[tex]5\,cm + BD = 8\,cm[/tex]

[tex]BD = 3\,cm[/tex]

The length of the diagonal BD is 3 centimeters. [tex]\blacksquare[/tex]

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what is the answer to the system of equations 2x+y=29 and y=1x+2.

explain why, if answer is a random answer you will be reported and lose points.

this is for free and easy points

Answers

y = x+2 means that y can be replaced by x+2
The other equation is 2x+y = 29.

2x+y = 29
2x+x+2 = 29
3x = 27
x = 9

y = x+2 = 9+2 = 11

2x+y = 29

2x+x+2 = 29

3x = 27

x = 9



Hope this helps...

a furlong is a unit of length still used today in racing and agriculture. a race that is 8 furlongs is 1 mile. a furlong is 660 feet. how many furlongs are in 1 mile?

Answers

8 furlongs are in one mile

There are 0.125 miles in one furlong.

What is unit conversion?

It is the conversion of one unit to another unit with its standard conversion.

Examples:

1 hour = 60 minutes

1 minute = 60 seconds

1 km = 1000 m

We have,

There are 8 furlongs in 1 mile.

Since a furlong is 660 feet, we can convert the number of feet into 1 mile.

Now,

1 mile = 5280 feet

Multiply 660/5280 on both sides.

660/5280 mile =  660 feet

0.125 mile = 660 feet

Therefore,

There are 0.125 miles in one furlong.

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The complete question.

A furlong is a unit of length still used today in racing and agriculture.

A race that is 8 furlongs is 1 mile.

A furlong is 660 feet. how many miles are in 1 furlong?

The sum of 5 consecutive even numbers is 200 what is the fifth term in the sequence

Answers

Try this option:
if to write the given sequence as n;n+2;n+4;n+6;n+8, then it is possible to write its sum:
n+n+2+n+4+n+6+n+8=200.
5n=180; n=36.
n=36 it means that the 1st number is 36. The 5th number is n+8=36+8=44.
all the even numbers are: 36;38;40;42;44.

answer: 44.

Two cards are drawn without replacements from a standard deck of 52 playing cards what is the probability of choosing a king for the second card drawn if the first card drawn was a queen

Answers

20% chance of drawing out of 52 because it is probly shuffeld

Answer:

Step-by-step explanation:

4

663

Explanation:

Probability of drawing a King is

4

52

Probability of drawing a queen

4

51

as the King was not put back.

So the probability of drawing one then the second would be

4

52

×

4

51

=

4

663

Will Give 100 points and brainliest!
An image of a rectangular pyramid is shown below: A right rectangular pyramid is shown. Part A: A cross section of the rectangular pyramid is cut with a plane parallel to the base. What is the name of the shape created by the cross section? Explain your answer. (5 points) Part B: If a cross section of the rectangular pyramid is cut perpendicular to the base, passing through the top vertex, what would be the shape of the resulting cross section? Explain your answer. (5 points)

Answers

Part A: Square cross-section 
Part B: Rectangle cross-section 

The Part A cross section will be rectangle and Part B cross section will be triangle .

What is rectangular pyramid ?

A rectangular pyramid is a 3-D object with a base shaped like a rectangle and triangle-shaped faces or sides that correspond to each side of the base. Like the other types of pyramids, a rectangular pyramid also has a point on top of the base of the pyramid that is joined together by bringing the top of all the sides which is known as the apx. A rectangular pyramid has a total of 5 faces, 5 vertices, and 8 edges and is of two types a right pyramid or an oblique pyramid.  

According to the question

Part A: A cross section of the rectangular pyramid is cut with a plane parallel to the base.

When we cut a cross section parallel to base of the rectangular pyramid which have rectangular base

The cross section will always be a rectangle.  

Part B: If a cross section of the rectangular pyramid is cut perpendicular to the base, passing through the top vertex .

When we cut a cross section perpendicular to the base, passing through the top vertex of the rectangular pyramid

The cross section will always be a Triangle.  

As the lateral face of a rectangular pyramid  is a triangle, so a cross section that passes through the top vertex and the base is also a triangle.

Hence , The Part A cross section will be rectangle and Part B cross section will be triangle .

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What are two items that weigh less than 1 oz

Answers

Examples are paper and feathers
Hello,

An ounce is about the weight of 11 pennies. So anything that weighs less than about 11 pennies would weigh less than 1 oz.

You could have a piece of paper, blade of grass, a pill, a quarter, etc.

I hope this helps!
MrEquation

Complete the comparison: 26 < ? A. 25 B. 54 C. 13 D. 26

Answers

the answer for that one is B, because 26<54
meaning 26 is less than 54 which is true 
The answer is B since 25 is less than 26 and 26 is equal to 26

what is a rational number between 9.6 and 9.7

Answers

The rational number between them is 9.6 1/2

A rational number between 9.6 and 9.7 is 93/20.

The given decimal numbers are 9.6 and 9.7.

What are the rational numbers?

Rational numbers are in the form of p/q, where p and q can be any integer and q ≠ 0. This means that rational numbers include natural numbers, whole numbers, integers, fractions of integers, and decimals (terminating decimals and recurring decimals).

Now, (9.6+9.7)/2

= 19.3/2

= 9.65

So, the rational number is 965/100 = 93/20

Therefore, a rational number between 9.6 and 9.7 is 93/20.

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the school gets $5 for each T-shirt they sell at a fundraiser. They have a goal of raising $150. If $45 has been raised so far, how many more T-shirts do they have to sell

Answers

21 more T-shirts they need to sell.

Chelsea dog-sits for her neighbors as a part-time job. She charges $12 a day plus an additional $2.50 for each walk she takes with the dogs. Determine which graph and which equation represent the amount of money Chelsea earns in one day, A, after taking w walks with the dogs.

Answers

The equation that would represent this situation is:

A = 2.5w + $12

To graph this you would substitute in varying numbers for w(the number of weeks) and this would be your x value in your ordered pair.

After you substitute in a number of weeks, you will get a total amount of money earned (A). This would be your y value in your ordered pair.

Here are some orders pairs you could plot to create the graph of this equation.

(1, 14.5)
(2, 17)
(3, 19.5)
(4, 22)

The equation is:

A= 2.5W + 12

The graph is

open the attachment I added AND THATS THE THE GRAPH ANSWER.

I HOPE I HELPED YOU. :)

Compare how you would model and record finding the sum difference of two rocks weighing 2/8 pound and 3/8 pound.

Answers

2/8+3/8=5/8

3/8-2/8=1/8

hope this helped

Final answer:

To find the sum or difference of two rocks weighing 2/8 pound and 3/8 pound, add or subtract their numerators while keeping the denominator the same. The sum is 5/8 pound, and if finding a difference with the second rock being lighter, it's 1/8 pound.

Explanation:

To model the sum of two rocks weighing 2/8 pound and 3/8 pound, we work with fractions with the same denominator. To find the sum, simply add the numerators together and keep the same denominator. Thus, 2/8 + 3/8 equals 5/8. To record the sum difference, you list both weights then show their combined weight, which is the sum.

The process is like this:

Write down the weights of the two rocks: 2/8 pound and 3/8 pound.Add the numerators (2 + 3 = 5) while keeping the denominator the same (8).The sum is therefore 5/8 pound.

If we were to find the difference, you would subtract the smaller numerator from the larger numerator:

Assuming we're taking the second rock's weight from the first: 3/8 - 2/8.Subtract the numerators (3 - 2 = 1) while keeping the denominator the same (8).The difference is therefore 1/8 pound.

what's a Fibonacci sequence?

Answers

Hello :)


A Fibonacci Sequence is a series of number . It is the sum of two preceding numbers.


Hope this helps <33
a Fibonacci sequence is a series of number, each number is the sum of the proccding number 
simplest sequence is 1,1,2,3,5,8 and so on

Is the price of 2/5 + 5 greater than or less than 2/5 is it greater than or less than 5 explain your reasoning

Answers

It is greater than 2/5 and 5 BC 2/5 + 5 is equal to 5 and 2/5.

The student body of a large university consists of 65% female students. a random sample of 8 students is selected. what is the probability that among the students in the sample at least 7 are female?
a. 0.1064
b. 0.0896
c. 0.1373
d. 0.1692

Answers

b. 0.0896
hope this helps x

find the distance between :(-1,5)( 3,-2)

Answers

Try this option:

distance=  [tex] \sqrt{(3+1)^2+(5+2)^2}= \sqrt{65} [/tex]

If a train is moving 72 km/h on a road of 360 km, how much time will it take to arrive?

Answers

It should 5 hours. You do 360 divided by 72 and get 5 
"I'm assuming this is just a rate problem not a more complex physics answer. Think about it this way:

72 kilometers is 72,000 meters, and an hour is 60 minutes of 60 seconds each, meaning an hour is 3600 seconds (60m*60s). This means that in 3600 seconds the car travels 72,000 meters. You can figure out how many meters are travelled per second by dividing 72,000 meters by 3,600 seconds, giving you 20 meters per second. This would give you an answer of 80 meters in 4 seconds, not 120 m. I don't know how to account for that disparity, but 80 meters would be the correct answer. If there is any other information in the problem it is probably important."

I wonder if I did #9 right and I’m having trouble with #10

Answers

Let's see....

QUESTION: Add. Write your answer as a mixed number in simplest form.

[tex]6 \frac{7}{9} + 9 \frac{8}{9} [/tex]

1. Rewriting our equation with parts separated

[tex]=6+ \frac{7}{9} +9+ \frac{8}{9} [/tex]

2. Solving the whole number parts

[tex]6+9=15[/tex]

3. Solving the fraction parts

[tex] \frac{7}{9} + \frac{8}{9} = \frac{15}{9} [/tex]

4. Reducing the fraction part, 15/9,

[tex] \frac{15}{9} = \frac{5}{3} [/tex]

5. Simplifying the fraction part, 5/3,

[tex] \frac{5}{3} = 1\frac{2}{3} [/tex]

6. Combining the whole and fraction parts

[tex]15+1+ \frac{2}{3} =16 \frac{2}{3} [/tex]

ANSWER: [tex] 16\frac{2}{3} [/tex]

Hope that helps!

9
It's correct. The only problem is entering it. Is a fraction OK or do you need to break it down to 16.6666

10
I don't wonder that you are having trouble with this.

Do it in parts. 
numerator
3/4 - 3/2 = 3/4 - 6/4 = - 3/4 Notice what happened. You multiplied top and bottom of 3/2 by 2
= 3*2 = 6
2 * 2 = 4

Now do the denominator
1/4 - 3/5 = 
5/20 - 12/20
= - 7/20

What do you have?
-3/4 // - 7/20 Now invert and multiply
- 3/4 * - 20 /7
= 60/ 28
= 15 / 7 Where did the two minus' go?  

Convert the equation 3x + 2y = 14 to slope intercept form

Answers

The answer is:
y=-3/2x+7

I have added a photo of how you show your work. 

Answer:

Step-by-step explanation:

y=-3/2x+7

HELLLPP PLLZZZ III BEEEGGG UUUU

For what value of x:

is the square of the binomial x+1 twenty greater than the square of the binomial x–3?

Answers

Asked and answered elsewhere.
https://brainly.com/question/9124477

Alice has a box that is 5 inches long, 5 inches wide, and 5 inches tall. How many 1 inch by 1 inch by 1 inch blocks can Alice fit into the box?

Answers

The volume of the box, is 5 x 5 x 5, which is equivalent to 125. The answer should be 125 1 inch blocks.
Hope this helps!:)
~Scarlett

PLEASE HELP EXPLAIN THIS!?!
(picture below)

I have part A however idk how to work out part B how would i write the equation out???

Answers

Using your approximate y-intercept on the line of best fit, your equation would be y=11/7x + 3. 

We find the slope by choosing two points that are on the line:

(9, 18) is easy to spot; and (2, 7) is fairly easy to spot as well.  The formula for slope is:
m=y₂-y₁/x₂-x₁

m=7-18/2-9 = -11/-7 = 11/7

Slope intercept form, y=mx+b, has the slope and the y-intercept.  Plugging those in we have y=11/7x+3.
The generic equation of the line is:
 y-yo = m (x-xo)
 We look for the slope:
 m = (y2-y1) / (x2-x1)
 m = (18-15) / (9-7)
 m = (3) / (2)
 m = 3/2
 We write the equation choosing any point:
 y-15 = (3/2) (x-7)
 we rewrite the equation:
 y-15 = (3/2) x-10.5
 y = (3/2) x-10.5 + 15
 y = (3/2) x + 4.5
 Then, for x = 13 we have:
 y = (3/2) * (13) +4.5
 y = 24
 Answer: 
 The equation is:
 y = (3/2) x + 4.5
 The number of matches won for 13 months is:
 y = 24

GPA calculation assignment
I need help please

Answers

total hours is 13

quality points is 76
gpa is 
gpa would be 3.20

A self-service car wash charges $4 for the initial 5 minutes plus an additional $0.75 for each minute after that. Nick only has $10 to spend on washing his car. Let m represent the number of minutes Nick spends washing his car.

Answers

the number of minutes m that Nick will spend washing his car given that he has $10 will be:
Cost for spending 5 min is $4, any additional minutes will be $0.75 per minutes.
amount of cash Nick will remain with after spending $4 will be:
10-4=$6
the total extra minutes he will spend will be:
6=0.75*m
0.75m=6
thus
m=6/0.75
m=8 min
the total number of minutes that Nick will spend with $10 will be:
8+5=13 min

Nick can spend a total of 13 minutes washing his car at the self-service car wash with his $10 budget, accounting for both the initial charge and the additional cost per minute after the first 5 minutes.

Nick is planning to use a self-service car wash that charges $4 for the initial 5 minutes and an additional $0.75 for each minute after that. With a budget of $10, he wants to calculate the number of minutes (m) he can spend washing his car. The cost for m minutes is given by the equation:

Total Cost = Initial Charge + (Additional Charge per minute * Number of extra minutes)

First, subtract the initial charge from the total amount Nick has:

$10 - $4 = $6

This is the amount remaining for the additional minutes. Next, divide this by the additional charge per minute:

$6 / $0.75 per minute = 8 minutes

Therefore, Nick can spend 8 minutes washing his car after the initial 5 minutes, for a total of 13 minutes.

Dam is rowing a boat away from a dock the graph shows the relationship between the time and sams distance from the dock. Evaluate the function for an input of 9

Answers

The answer is B.

A and C would not be correct because you are finding the distance for 9 minutes. D is not correct because the y-axis does not even have 3 meters on it, neither does the graph hit y=3.

Answer:

B. After 9 minutes Sam is 80 meters away from the dock.

Step-by-step explanation:

We have been given a graph of function that shows the relationship between the time and Sam's distance from the dock.

Let us see our given options one by one to find the correct choice.

A. After 80 minutes Sam is 9 meters away from the dock.

Upon looking at our graph we can see that y-axis is representing distance in meters and x-axis is representing time in minutes. Range of x is from 0 to 11 So our input cannot be greater than 11.    

Therefore, option A is not a correct choice.

B. After 9 minutes Sam is 80 meters away from the dock.

We can clearly see from our given graph that at 9 minutes distance is 80 meters, which means that after 9 minutes Sam is 80 meters away from the dock. Therefore, option B is the correct choice.

C. After 80 minutes Sam is 80 meters away from the dock.

We can see from our graph that range of x is from 0 to 11 minutes, So our input can not be greater than 11. Therefore, option C is not a correct choice.  

D. After 9 minutes Sam is 3 meters away from the dock.

We can see from our graph that initial value of our function is 20, which means that at time equals 0 minutes Sam was 20 meters away from dock and this distance is increasing with the time. Therefore, option D is not a correct choice.  

A segment has endpoints at (3,−4) and (3,−17) How many units long is the segment?

Answers

the segment is 13 units long.

Answer:

what the other person said

Step-by-step explanation:

Classify the following triangle. check all that apply?

Answers

we know that

the triangle of the figure is

Equilateral------> because has three equal sides and three equal angles

Acute -------> because all three angles are less than [tex]90[/tex] degrees

The measure of each angle in a equilateral triangle is [tex]60[/tex] degrees

therefore

the answer is

A equilateral

D Acute

Answer:

Step-by-step explanation:

Adf

Find the vertex of the given function.
f(x) = l x-5 l + 10
The vertex is at (___, ___)

Answers

when it comes to this "vertex form" type of expressions, the cheap way to get the vertex is, set the grouped terms to 0, namely

x - 5 = 0
x = 5

well, if we set x = 5, x - 5, turns to 0, and that happens when x  = 5, therefore, the vertex is

| x - 5 | + 10

| (5) - 5 |  (+ 10)              is at ( 5 , 10 )

The vertex of an absolute function is the highest or lowest point of the function. The vertex of the given equation is: (5,10)

Given that:

[tex]f(x) = |x - 5|+ 10[/tex]

If an absolute function is represented as:

[tex]f(x) = a|x - h|+ k[/tex]

The vertex of the function is:

[tex]Vertex = (h,k)[/tex]

By comparing [tex]f(x) = a|x - h|+ k[/tex] and [tex]f(x) = |x - 5|+ 10[/tex]

[tex]h = 5[/tex]

[tex]k =10[/tex]

So, the vertex is:

[tex]Vertex = (5,10)[/tex]

Read more about vertices at:

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What is 5x 1/2? please use any type of model to show work...

Answers

Change the fraction into a decimal, in this question it would be 5 x 0.5 which basically is asking for half of 5 which is 2.5.
You could also rearrange the question so put the fraction first and say what is:
1/2 of 5 which would equal 2.5 this would work for all questions like this. Hope I helped, have a nice day :)
5 times .5
5
 .5
----
2.5
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