find the x intercepts of the parabola with vertex (2,13) and y-intercept (0,5) write your answer in this form: (x1,y1),(x2,y2) if necessary, round to the nearest hundredth

Answers

Answer 1

The standard formula for a parabola are

(x-h)^2 = +/- 4a (y-k) or (y-k)^2 = +/- 4a(x-h)

where
(h,k) is the coordinates of the vertex
a is the length of the focus from the vertes
+4a if the parabola opens upwards or to the right
-4a if the parabola opens downwards or to the left

The vertex (2,13) is situated in the 1st quadrant of the Cartesian plane. It only has y-intercept. This means that it only passes the y-axis once. Therefore, the parabola must open downwards and it passes the x-axis twice. The intersections at the x-axis are the x-intercepts. If the parabola has 2 x-intercepts, then the equation would be (x-h)^2 = -4a(y-k).

Let's use the y-intercept (0,5) to determine 4a:

(0-2)^2=-4a(5-13)
4a = 0.5

Therefore, the equation of the parabola is (x-2)^2 = -1/2(y-13). To find the x-intercepts, let y=0.

(x-2)^2 = -1/2(0-13) = 6.5
x-2 = +/- √6.5 = +/- 2.55
x = 4.55 and and -0.55

The x-intercepts are (-0.55,0) and (4.55,0).

Answer 2

Answer:

(-0.55,0),(4.55,0)

Related Questions

If a train travels one mile (5,280 feet) while climbing a hill at an angle of five degrees, approximately how many vertical feet has the train climbed?

Answers

to calculate the vertical height multiply the hypotenuse ( 5280) by the sin of the angle (5)

5280 x sin(5) = 460.1823

round off to 460 feet

You are interviewing an applicant for a sales agent position in your company. Based on the company’s record, almost every company sales agent makes a total revenue of 150x-x² pesos for selling x products in a week. If the applicant confidently assures you that he/she can easily make ₱10,000 weekly revenue, how many products should he/she sell to meet this quota?

Answers

Using the revenue model for most company sales agents y = 150x - x^2, and the weekly revenue of $10,000 assured by the applicant, you get:

150x - x^2 = 10,000

From which you can solve for x:

x^2 - 150x + 10,000 = 0

When you use the quadratic equation you find that the equation does not have real solution driving to the conclusion that the agent is not tellling the true.

HELP!!!!!!! I GIVE BRAINLEST AND THANKS!!!!!! + 5 POINTS!!!!

Answers

In order for a relation to be a function, each x value must have no more than 1 corresponding y value.

Remember that the x values are the ones on the left in an ordered pair. Because each one is unique, the relation is a function in this case.

Final answer: B

Four times the sum of a number and 15 is at least 120. Find all possible solutions for x

Answers

First translate the English phrase "Four times the sum of a number and 15 is at least 120" into a mathematical inequality.

"Four times..." means we're multiplying something by 4.

"... the sum of a number and 15..." means we're adding an unknown and 15 and then multiplying the result by 4.

"... is at least 120" means when we substitute the unknown for a value, in order for that value to be in the solution set, it can only be less than or equal to 120.

So, the resulting inequality is 4(x + 15) ≤ 120.

Simplify the inequality.

4(x + 15) ≤ 120
4x + 60 ≤ 120 <-- Using the distributive property
4x ≤ 60 <-- Subtract both sides by 60
x ≤ 15 <-- Divide both sides by 4

Now that we have the inequality in a simplified form, we can easily see that in order to be in the solution set, the variable x can be no bigger than 15.

In interval notation it would look something like this:

[15, ∞)

In set builder notation it would look something like this:

{x | x ∈ R, x ≤ 15}

It is read as "the set of all x, such that x is a member of the real numbers and x is less than or equal to 15".

WILL GIVE BRAINLIST!!!!!!!!!!!!!! A group of students were surveyed to find out if they like working as a camp counselor and/or as a lifeguard during summer break. The results of the survey are shown below:

32 students like working as a camp counselor
8 students like working as a camp counselor but do not like working as a lifeguard
29 students like working as a lifeguard
8 students do not like working as a lifeguard or a camp counselor
Four students created the tables below to represent the data. CC represents camp counselor and LG represents lifeguard.

Which student's table is correct?

Answers

Answer:

I think Table C - Corralle

Answer:

Step-by-step explanation:

2(-4^2) - 2(2^4) + 3^2 - -4^2 + 2^4 = ? Please explain, I got 41 but I highly doubt I'm right.

Answers

PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction)
Parenthesis
(-4^2) - inside that we do Exponents first. That makes it (-16).

(2^4)=2*2*2*2=16

Next, we have Exponents

3^2=9, 4^2=16, and 2^4=16

Putting that all together so far, we have 2(-16) -2(16) +9 - -16 +16

Taking Multiplication next, we have 2(-16)=-32 and 2(16)=32.

Then, we have -32 - -32 +9 - -16 +16

Making the double negatives positive (-1*-1=1), we get

-32+32+9+16+16

After that, we add -32 and 32 together to get 0, add 16 and 16 to get 32, then add 9 to 32 and get 41.

Congratulations - you got it right!

Tim enlarged a picture with a width of 5.5 inches and a length of 8 inches by a scale factor of 3. What are the dimensions of the enlargement?

a. width: 24 in.; length: 16.5 in.b. width: 16.5 in.; length: 24 in.c. width: 14.5 in.; length: 22 in.d. width: 19.5 in.; length: 25 in.

Answers

It is B. 8*3 = 24. 5.5*3 = 16.5

Answer:

Option b. width = 16.5 inches and length = 24 inches

Step-by-step explanation:

Tim enlarged a picture wit a width of 5.5 inches and a length of 8 inches.

He enlarged the picture by a scale factor of 3.

We have to find the new dimensions of the picture.

Since, New dimension of the picture = Scale factor × dimensions before enlargement

So new width = 3×5.5 = 16.5 inches

new length = 3×8 = 24 inches

Therefore, option b. is the answer.

what is the value of the fourth term in a geometric sequence for which a1=15 and r=1/3
express your answer as a fraction

Answers

nth term = a1r^(n-1)

4th term = 15* (1/3)^3 = 15/27 = 5/9

Answer: The required fourth term in the given geometric sequence is [tex]\dfrac{5}{9}.[/tex]

Step-by-step explanation: We are given to find the fourth term of a geometric sequence with the following first term and common ratio :

[tex]a=15,~~r=\dfrac{1}{3}.[/tex]

We know that

the nth term of a geometric sequence with first term a and common ratio r is given by

[tex]a_n=ar^{n-1}.[/tex]

Therefore, the forth term of the given geometric sequence is

[tex]a_4=ar^{4-1}=ar^3=15\times\left(\dfrac{1}{3}\right)^3=15\times\dfrac{1}{27}=\dfrac{5}{9}.[/tex]

Thus, the required fourth term in the given geometric sequence is [tex]\dfrac{5}{9}.[/tex]

Sherita’s club is selling grapefruit to raise money. For every box they sell, they get $1.35 profit. They have sold 84 boxes already. How many more boxes must they sell to raise 270 dollars

Answers

1.35*84=113.4 dollars
to get to 270 they need 270-113.4=156.6
156.6/1.35=116 boxes

14÷420 long division

Answers

14➗ 420. 14 goes into 42 , 3 times subtract bring down the zero and your answer is 30

Find the lateral area for the prism. L.A. =
Find the total area for the prism. T.A. =

Answers

The lateral area of the prism is given by:
LA=[area of the two triangles]+[area of the lateral rectangles]
hypotenuse of the triangle will be given by Pythagorean:
c^2=a^2+b^2
c^2=6^2+4^2
c^2=52
c=sqrt52
c=7.211'
thus the lateral area will be:
L.A=2[1/2*4*6]+[6*8]+[8*7.211]
L.A=24+48+57.69
L.A=129.69 in^2

The total are will be given by:
T.A=L.A+base area
base area=length*width
=4*8
=32 in^2
thus;
T.A=32+129.69
T.A=161.69 in^2

Answer:

Part 1) [tex]LA=(80+16\sqrt{13})\ in^{2}[/tex]

Part 2) [tex]TA=(104+16\sqrt{13})\ in^{2}[/tex]

Step-by-step explanation:

Part 1) Find the lateral area of the prism

we know that

The lateral area of the prism is equal to

[tex]LA=Ph[/tex]

where

P is the perimeter of the base

h is the height of the prism

Applying the Pythagoras Theorem

Find the hypotenuse of the triangle

[tex]c^{2}=4^{2}+6^{2}\\ \\c^{2}=52\\ \\c=2\sqrt{13}\ in[/tex]

Find the perimeter of triangle

[tex]P=4+6+2\sqrt{13}=(10+2\sqrt{13})\ in[/tex]

Find the lateral area

[tex]LA=Ph[/tex]

we have

[tex]P=(10+2\sqrt{13})\ in[/tex]

[tex]h=8\ in[/tex]

substitutes

[tex]LA=(10+2\sqrt{13})*8=(80+16\sqrt{13})\ in^{2}[/tex]

Part 2) Find the total area of the prism

we know that

The total area of the prism is equal to

[tex]TA=LA+2B[/tex]

where

LA is the lateral area of the prism

B is the area of the base of the prism

Find the area of the base B

The area of the base is equal to the area of the triangle

[tex]B=\frac{1}{2}bh[/tex]

substitute

[tex]B=\frac{1}{2}(6)(4)=12\ in^{2}[/tex]

Find the total area of the prism

[tex]TA=LA+2B[/tex]

we have

[tex]B=12\ in^{2}[/tex]

[tex]LA=(80+16\sqrt{13})\ in^{2}[/tex]

substitute

[tex]TA=(80+16\sqrt{13})+2(12)=(104+16\sqrt{13})\ in^{2}[/tex]

write a numerical sentence that illustrates the commutative property of multiplication

Answers

24 x 15 = 15 x 24

I think that this is an example...

commutative property of multiplication states : ab = ba.....what it is basically saying is u can " commute " the numbers....move them around, and it will not change the result. Example : 4 * 3 = 3 * 4....even though u switched them, they will still equal the same number.

so ur answer can be : 4 * 3 = 3 * 4.....or 2(3x + 5) = (3x + 5) * 2....u get the idea, right ?

Find the probability of drawing a king from a standard deck of cards and then drawing a queen after the first card is replaced in the deck. None of the above 1/26 1/13 1/2704 2/13

Answers

52 cards in a deck

4 kings

4 queens

King = 4/52 reduces to 1/13

Queen = 4/52 reduces to 1/13

1/13 *1/13 = 1/169

so none of the above

With replacement:

P(K,Q)=(1/13)(1/13)

P(K,Q)=1/169

So none of the above.

Kenya plans to make a down payment plus monthly payments in order to buy a motorcycle. At one dealer she would pay $2,500 down and $150 each month. At another dealer, she would pay $3,000 down and $125 each month. After how many months would the total amount paid be the same for both dealers? What would that amount be?

Answers

Let us say that the total amount paid in the first dealer is P1 and the total amount paid to the second dealer is P2. So that:

P1 = 2500 + 150 t

P2 = 3000 + 125 t

Where t is the total number of months

Now we are asked when the total amount paid would be equal for the two dealers, this means P1 = P2, therefore equating the two:

2500 + 150 t = 3000 + 125 t

25 t = 500

t = 20 months

Therefore the total amount paid for both dealers would be equal after 20 months.

A circle of radius 1 centered at (4, 0) is rotated about the y-axis.

1) Draw a picture of the three-dimensional shape that is produced when the circle is rotated about the y-axis.

2) In two or more complete sentences, describe the three-dimensional shape.

please help and thank you.

Answers

Answer to part 1) is shown in the diagram below

Answer to part 2)

By rotating a circle on the y-axis we obtain a solid shape called TORUS. This shape is like a pipe with its two ends joined. In older literature, it is called 'anchor ring' as its shape does look like a ring.

According to the text, which is not a main component of drawing?

Perspective
Vanishing point
Horizon

Answers

I think it's horizon

17. For the parallelogram find the value of the variables. Show your work.

18. What is the length of the second base of a trapezoid is the length of one base is 24 and the length of the midsegment is 19? Show your work

Answers

24=3y-6 => 30=3y, y=10,

12 = 5x+2 => 10=5x, x =2

Basically parallel sides must have the same length (parallelogram)

Hope it helps!

24=3y-6= 30=5x, y=30
12=5x+2 = 10=5x x=2

Is the following expression shown the exact answer? 144π - 216√3

true or false

Answers

[tex]144\pi - 216\sqrt{3} \\\\ 144 = 2^4 \times 3^2\\\\ 216 = 2^3 \times 3^3\\\\ \Longrightarrow~~\text{Common factor } = 2^3 \times 3^2 = 8 \times 9 = 72\\\\ \Longrightarrow~~ 144\pi - 216\sqrt{3} = \boxed{72\Big(2\pi - 3\sqrt{3} \Big)}[/tex]

Find the simple interest paid for 8 years on a $850 loan at 7.5% per year.

Answers

The formula is
I=pre
I interest paid?
P principle 850
R interest rate 0.075
T time 8 years
I=850×0.075×8
I=510

The simple interest paid for 8 years on a $850 loan at a 7.5% annual interest rate is $510.

To calculate simple interest, you can use the formula:

Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

Where:

- Principal (P) is the initial amount of the loan.

- Rate (R) is the annual interest rate (in decimal form).

- Time (T) is the number of years.

In this case:

- Principal (P) = $850

- Rate (R) = 7.5% = 0.075 (decimal form)

- Time (T) = 8 years

Now, plug these values into the formula:

SI = $850 × 0.075 × 8

SI = $510

The simple interest paid for 8 years on a $850 loan at a 7.5% annual interest rate is $510.

For more such questions on Simple Interest :

https://brainly.com/question/30978175

#SPJ2

EF=5x+15, FG=53 And EG=143 find the value of x
And can you please tell me how to do it?

Answers

I'm assuming EFG is a triangle. In order to solve this problem, you do not have all the information to solve for x in a numerical form. However, if you let variable P equal the perimeter. You can solve for x in terms of P. Perimeter is the sum of all the sides of a shape. First, let's add together all the sides of the triangle. (P = 5x+15+53+143). Add together the common variables so that (5x+211=P). Our next job is to isolate the x. We start by subtracting 211 from both sides. (5x=P-211) Next we divide by 5. [x=(P-211)/5] Therefore, [x=(P-211)/5], assuming P = perimeter

Find the domain of the following piecewise function

Answers

domain is the numbers you can use

see, we have -1≤x<0 and 0≤x<5

so if it is in the range of -1 to 5, then it is in the function

it includes -1 but not 5 because we gots -1≤x but x<5

remember, in interval notation, [] is includes and () is not include
or
[] is ≤≥ and () is <>

so
[-1,5)

angle ABD and angle DBC are supplementary. Find the value of x.

A. 6
B. 8
C. 4
D. 10

Answers

Angle ABD and angle DBC are supplementary
so
14x+8x+4 = 180
22x = 176
x = 8

answer B. 8

The answer is B because if you substitute 8 to x and add them all up you will get 180 degrees.

How could you find the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,-12)

Answers

I think it should be -6, because line segment equals 12 and it's midpoint will be 12/2 = 6, so you must go down by 6 from (0,0) point on y axis which is 0-6=-6

So the point will be (0, -6)

Eighty seven decreased by three times a number is greater than one hundred sixty five

Answers

87-3x>165

-3x> (165-85)

-3x>80

80/-3 = -26.666

check;

87-3*(-26)=165

so x < -26

A lawn mower manufacturer incurs a total of $34,816 in overhead costs and $388 per lawn mower in production costs. How many lawn mowers were manufactured if the average cost of production is $660?

Answers

There are 128 law mowers manufactured.

I hoped I helped and if you need more you could always ask me :)

-Dawn

Answer:

128 lawn mowers

Step-by-step explanation:

Given,

The overhead cost = $ 34,816,

The cost for one lawn mower = $ 388,

Let x be the number of lawn mowers manufactured,

So, the total cost of x lawn mowers = 34816 + 388x,

Now, if the average cost of x mowers = $ 660,

So, the total cost = 660x

[tex]\implies 660x = 34816 + 388x[/tex]

[tex]660x - 388x = 34816[/tex]

[tex]272x= 34816[/tex]

[tex]\implies x = \frac{34816}{272}=128[/tex]

Hence, 128 lawn mowers were manufactured.

Chase makes 2 gallons of soup for a dinner party. He serves 10 cups of soup to his guests. How many cups of soup will be have left over?

Answers

2 gallons equal 32 cups

32-10= 22

22 cups will be left

He will have 22 cups left. 2 gallons = 32 cups minus 10.

What numbesr can be multiplied and added to equal the same number?

Answers

It would be 6. for an example (3+2+1=6 | 3*2*1=6)

2x2 = 4

2+2 =4

0x0=0

0+0=0

10 employees in an office were absent. Of these absentees constitutes 25% of the employees, what is the total number of employees?

Answers

25% is 1/4, it looks like 10*4 = 40 is the total number, right?

Perform Gauss-Jordan elimination on the augmented matrix shown.
Could someone please help me figure this out.

Answers

Hi! Let me help you!
Basing from the visual you provided, it can be observed that item A, item B, item C, and item D have already undergone "row operations". Therefore, to complete Gauss-Jordan elimination, all we need to do is to transform row echelon A, row echelon B, row echelon C, and row echelon D such that each element they have separately become roots of their respective linear equations.

For A:
x = 2; y = (not sure if it is -1 or -7, the visual is too blurry for me to see)

For B:
x = ; y = -1

For C:
x = 0; y = 0

For D:
x = -(26/3); y = -7

I hope this helped you!

If h(x)=6-x, what is the value of (h o h)(10)

Answers

[tex](h \circ h)(x)=6-(6-x)=6-6+x=x\\\\ (h \circ h)(10)=10[/tex]

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