Write the equation in vertex form for the
parabola with vertex (-1, 3) and that
passes through the point (2, -5).

Answers

Answer 1

Answer: The general equation of a parabola with vertex (h,k) is y=a(x−h)2+k y = a ( x - h ) 2 + k . In this case we have (1,3) as the vertex (h,k) and (2,6) is a point (x,y) on the parabola. To find a , substitute the two points in y=a(x−h)2+k y = a ( x - h ) 2 + k .

Related Questions

solve the following equation 23 + 23 = 5y + 11

Answers

Answer:

Step-by-step explanation:

Since 23 + 23 = 46

We just have to multiply 5 by something. 11 + 5 x 7 = 46

Y is = 7

btw im in middle school

your answer could be 72

i did a lot of math

and if you have what y means to me its y = 3 so i did 5*3

Alvin's
age Is three times Elga's age. The sum of their ages Is 96. What Is Elga's age?
years old

Answers

Answer: Elga is 16 years old

Step-by-step explanation: so first you divide 96 by 2 and get 48, 48 divided by 3=16,

please mark brainliest if this helps :)

Answer: 24 years old

Work Shown:

x = Elga's age

3x = Alvin's age since he is 3 times older

x+3x = 4x = sum of their ages

4x = 96

x = 96/4

x = 24 is Elga's age

3x = 3*24 = 72 is Alvin's age

Check: 24+72 = 96 which confirms the answer.

Congruent triangles
Please answer this question

Answers

A.Congruent triangles)

A restaurant customer left $1.05 as a tip. The tax was 8% and the tip was 15% of the cost including tax.
a. Which information is not needed to compute the bill after tax and tip?
b. What was the total bill?

Answers

well, the bill was actually "x", which oddly enough is the 100%, but we also know that the tip was $1.05 and that's 15% of the whole bill plus tax.

so if we know that 1.05 is 15% of "x", what the dickens is "x"?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 1.05 & 15\\ x& 100 \end{array} \implies \cfrac{1.05}{x}~~=~~\cfrac{15}{100} \\\\\\ 105=15x\implies \cfrac{105}{15}=x\implies 7=x[/tex]

well, as you can see, we know the tax was 8%, but, it doesn't really matter if it had been 25% or who knows, so long we know that 1.05 is 15% of the whole smack.

if f(x)=8-5x find f(4-+3)

Answers

The required value of the function at x = 4 and 3 is f(4) = -12 and f(3) = -7.

What are functions?

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given function ,

f(x) = 8 - 5x
put x = 4
f(4) = 8 - 5(4)
f(4) = 8 - 20
f(4) = -12

Again,
put x = 3
f(3) = 8 - 5(3)
f(3) = 8 - 15
f(3) = -7

Thus, the required value of the function at x = 4 and 3 is f(4) = -12 and f(3) = -7.

learn more about function here:

brainly.com/question/21145944

#SPJ1

ABC is rotated 90° counterclockwise around the origin to form A'B'C'. Then
AA'B'C' is dilated using a scale factor of with a center of dilation at vertex A'
to form A"B"C". What are the coordinates of A"B"C"? Show your work.

Answers

The coordinates of A"B"C" are as follows :

A = 1 1/2,3

B = 1 1/2,0

C = -4 1/2, 3.

What are coordinates?

Using one or more numbers, or coordinates, a coordinate system in geometry establishes a unique way to locate points or other geometrical objects on a manifold, such Euclidean space. a group of numbers representing a precise place. On graphs, there are typically two numbers: the first one indicates the length along, and the second one indicates the length up or down. For instance, the value of the point (12,5) is 12 units. In general, alphanumeric characters are used to express GPS coordinates, which are a distinctive identifier of a certain geographic location on the globe. Points of intersection in a grid system are referred to as coordinates in this context. Typically, the latitude and longitude coordinates are used to represent GPS coordinates.

Five units up and along.

90degrees clockwise is x, y, y, -x.

A = 1,2

B = 1,0

C = -3, 2.

Times everything by 3/2 now.

A = 1 1/2,3

B = 1 1/2,0

C = -4 1/2, 3.

To know more about coordinate ,visit:

https://brainly.com/question/18269861

#SPJ13

Solve for X.
Help please!!!

Answers

Answer:

x=17

Step-by-step explanation:

2x-3+3x+8=90

5x=85

x=17

Given f(x) = -x - 1, find ƒ (1).

Answers

Answer:

You've gotta be kidding me...It's easy come on

-2 is the answer

Step-by-step explanation:

f(x)= -x-1 JUST SUBSTITUTE 1 FOR X

f(1)= -(1)-1

f(1)= -2

Suppose Alex wants to kick a ball over a 10-foot fence. Assuming that gravity has no effect, at what angle would he have to kick the ball if he were standing 6 feet away from the fence?

a.
36.9°
c.
53.1°
b.
59.0°
d.
31.0°

Answers

You would take Alex's distance from the fence, which is 10 feet, and the length of the fence to get the angle.

Finding the angle using the right triangle's trig formulas, sine, cosine, or tangent

neighboring side = 6 feet

obverse side = 10 feet

employ a tangent because

[tex]tan^{-1}\frac{opposite}{adjacent} = tan^{-1}\frac{10}{6} = 59.0[/tex]

About Right triangle's

The formula for a right triangle's area, perimeter, and hypotenuse length are all included in the formula for a right triangle.

In geometry, there are several figure kinds that are distinguished from one another by their unique characteristics. A triangle is one of the shapes they frequently use. A triangle is a closed, three-sided polygonal shape. It has three vertices and three sides that contain the triangle's three interior angles. A triangle's three inner angles always add up to 180 degrees.

Equilateral, isosceles, scalene and right-angled triangles are the most typical triangle types we examine. The right triangle formula, commonly known as the right-angled triangle formulae, will be discussed in this section.

Any interior angle that is 90 degrees in length is said to be in a right triangle. It should be remembered that only one of the three angles may be a right angle because the total interior angle of a triangle is 180 degrees.

Continue reading: Right Angle Triangle

The triangle is referred to as an isosceles right-angled triangle if the other two angles are equal, or 45 degrees each. A scalene right-angled triangle, on the other hand, results from the other two angles being uneven.

Trigonometry is where right-angled triangles are used the most frequently. In reality, trigonometry's foundation is the relationship between its angles and sides.

Learn more about Right triangles https://brainly.com/question/4364353

#SPJ1

In a solar system, two comets pass near the sun, which is located at the origin. Comet E is modeled by quantity y plus 16 end quantity squared over 400 plus x squared over 144 equals 1 and Comet H is modeled by quantity y plus 13 end quantity squared over 144 minus x squared over 25 equals 1 comma where all measurements are in astronomical units.

Part A: What are the vertices for the path of Comet E? Show your work. (4 points)

Part B: Which comet travels closer to the sun? Give evidence to support your answer. (5 points)

Part C: What key feature does the sun represent for both comets? Give evidence to support your answer. (6 points)

Answers

The vertices of the path of the comet E are; (-12,0) and (+12,0) as it is moving an elliptical path.

What are the vertices of the path of the comet E?

Comet 'E' is modeled by

((y + 16)²)/400 + (x²)/144 = 1

This is an equation of an ellipse. So, the path traveled by Comet E will be an elliptic path.

Comparing with the equation of ellipse;

((y - k)²)/(b²)+ ((x - h) ²)/(a ²) = 1

whose; Centre is (h,k) and Vertex is (h±a, 0)

On Comparing Centre (h, k), h= 0 and k = -16,

a²=144

a = 12

b²=400

b=20

So, Centre (0, -16),

The Vertex (-12,0) and (+12,0)

So, the vertices of the path of the comet E are; (-12,0) and (+12,0).

Part B: The path of Comet H has been modeled as; a horizontal hyperbola.

Thus, The Comet H travels closer to the sun.

Part C: The sun represents the one of the foci of both the Comet E and Comet H.

Learn more about ellipse here:

brainly.com/question/16904744

#SPJ1

Eric orders 3 large cheese pizzas. There is a $2 delivery fee for each pizza. He pays a total of $42. Which equation can be used to find the price, r, of each pizza?

Answers

we have that he paid 4 dollars due the delivery. So each pizza costs

[tex]\frac{38}{2}=19[/tex]

so the equation to find the price r is

[tex]r=\frac{42-4}{2}[/tex]

Draw the graph of each circle given its equation below.

Answers

Step 1:

First, write the general equation of a circle

[tex]\begin{gathered} (x-a)^a+(y-b)^2=r^2 \\ r\text{ is the radius} \\ (a,\text{ b) is the center} \end{gathered}[/tex]

Step 2:

Question 1

[tex]\begin{gathered} x^2+y^2\text{ = 121} \\ x^2+y^2=11^2 \\ \text{radius r = 11} \\ \text{center = (0 , 0)} \end{gathered}[/tex]

Question 2

[tex]\begin{gathered} (x-2)^2+y^2\text{ = 64} \\ (x-2)^2+y^2=8^2 \\ \text{Center = (2, 0)} \\ r\text{ = 8} \end{gathered}[/tex]

Question 3

[tex]\begin{gathered} (x\text{ + }\frac{3}{2})^2\text{ + (y + }\frac{5}{8})^2\text{ = 36} \\ (x\text{ + }\frac{3}{2})^2\text{ + (y + }\frac{5}{8})^2\text{ = }6^2 \\ \text{Center = (-}\frac{3}{2}\text{ , -}\frac{5}{8}) \\ r\text{ = 6} \end{gathered}[/tex]

Question 4

[tex]\begin{gathered} (x-1)^2+(y+7)^2\text{ = 9} \\ (x-1)^2+(y+7)^2\text{ = }3^2 \\ \text{Center = (1, -7)} \\ r\text{ = 3} \end{gathered}[/tex]

Question 5

[tex]\begin{gathered} (x+8)^2+(y-3)^2\text{ = 7} \\ (x+8)^2+(y-3)^2\text{ = (}\sqrt[]{7})^2 \\ \text{Center = (-8, 3)} \\ \text{radius r = }\sqrt[]{7} \end{gathered}[/tex]

(3,-8) with a slope of -1

Answers

Answer:

See below

Step-by-step explanation:

Point slope form

y - - 8 = (-1)(x -3) re-arrange

y + 8 = -x+3

y = -x - 5

Use the table to answer the question. HELP PLS

Number of cases ordered

1

3

5

10

Number of rolls of paper towels

12

36

60

120.

A restaurant is placing an order for paper towels. The data table shows the amount of paper towel rolls compared to the number of cases. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair.

Answers

The constant of proportionality when the restaurant is placing an order for paper towels is 12.

How to calculate the value?

It should be noted that the constant of proportionality simply means the ratio that is important to show the proportional relationship between the two given values.

This will be illustrated as:

y = kx

y = Number of paper roll

x = Number of cases ordered

From the table, this will be:

y = kx

12 = k × 1

k = 12

Therefore, the constant of proportionality is 12.

Learn more about constant of proportionality on:

brainly.com/question/28413384

#SPJ1

Which equation has the solution x= 9? Select each correct answer. 4 + 5x = 18 0 24 - 2x – 13 DE O +7=8 – 0 3x + 2 = 25 81 si - 3 = 6 3 = V 2x - 3= 15

Answers

Equations with solution x = 9 are:

81/x - 3 = 6

2x - 3 = 15

Explanation:

To determine the equation whose result ives x = 9, we need to solve each of the equation in the question

a) 4 + 5x = 18

5x = 18 - 4

5x = 14

x = 14/5

This is not x = 9 (option is wrong)

b) 24 - 2x = 13

24 - 2x + 2x = 13 + 2x

24 = 13 + 2x

24 - 13 = 2x

11 = 2x

x = 11/2

This is not x = 9 (option is wrong)

c) x/3 + 7 = 8

x/3 = 8 - 7

x/3 = 1

x = 3(1) = 3

This is not x = 9 (option is wrong)

d) 3x + 2 = 25

3x = 25 - 2

3x = 23

x = 23/3

This is not x = 9 (option is wrong)

e) 81/x - 3 = 6

81/x = 6 + 3

81/x = 9

81 = 9x

x = 81/9

x = 9

This equation has the sloution x = 9

f) 2x - 3 = 15

2x = 15 + 3

2x = 18

x = 18/2

x = 9

This equation has the sloution x = 9

Simplify to create an equivalent expression 10+4(−8q−4)

Answers

Answer:

-32q-6

Step-by-step explanation:

Please look at the attachment! Hope this helps! ~~

Answer : -0.3125 + q + 0.5

1) Distribute

10 - 32q - 16

2) Divide all terms by -32

-0.3125 + q + 0.5

C is the center of the circle with a diameter whose endpoints are the points A(-2, 1) and B(6, 9).
What is the equation of circle C?

Answers

well, the midpoint of segment AB is the center of the circle, so

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 -2}{2}~~~ ,~~~ \cfrac{ 9 +1}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ 10 }{2} \right)\implies \stackrel{center}{(2~~,~~5)}[/tex]

now since we know AB is the diameter, so half that distance AB is its radius, so

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}[/tex]

[tex]AB=\sqrt{(~~6 - (-2)~~)^2 + (~~9 - 1~~)^2} \implies AB=\sqrt{(6 +2)^2 + (9 -1)^2} \\\\\\ AB=\sqrt{( 8 )^2 + ( 8 )^2} \implies AB=\sqrt{ 64 + 64 } \implies AB=\sqrt{ 128 } \\\\\\ AB=8\sqrt{2}\hspace{5em}\stackrel{\textit{half that is the radius}}{\cfrac{8\sqrt{2}}{2}\implies 4\sqrt{2}\implies \sqrt{32}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{2}{h}~~,~~\underset{5}{k})}\qquad \stackrel{radius}{\underset{\sqrt{32}}{r}} \\\\\\ (x-2)^2~~ + ~~(y-5)^2~~ = ~~(\sqrt{32})^2\implies {\large \begin{array}{llll} (x-2)^2~ + ~(y-5)^2~ = ~32 \end{array}}[/tex]

ANSWER QUICK I WILL GIVE BRAINLIEST
Determine which expression is equivalent to the expression 2 over 3 times g minus 5 minus 11 over 15 times g minus the expression one over 5 times g plus 12. 4 over 15 times g plus negative 17 negative 4 over 15 times g plus negative 17 2 over 15 times g plus negative 7 negative 4 over 15 times g plus negative 7

Answers

Answer:

-4/15 - 17

negative 4 over 15 plus negative 17

Step-by-step explanation:

2/3g - 5 - 11/15g - (1/5g +12)

Your wording is extremely confusing but I tried :]

-4/15 - 17

is the correct answer (I think)

The required simplified value of the given expression is -4/15 - 17.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
2 over 3 times g minus 5 minus 11 over 15 times g minus the expression one over 5 times g plus 12 is given as

= 2/3g - 5 - 11/15g - (1/5g +12)

Adding the alike terms,
= 2/3g -11/15g -1/5g -5 -12
= [10 - 11 -3] /15 g - 17
= -4g/15 -17

Thus, the required simplified value of the given expression is -4/15 - 17.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ2

x = -4z - 19
y= 5x + z - 4
-5y - z = 25

Answers

Answer:

x = 1, y = -4, z = -5

Step-by-step explanation:

Solve the following system:

{x = -4 z - 19 | (equation 1)

{y = z + 5 x - 4 | (equation 2)

{-z - 5 y = 25 | (equation 3)

Express the system in standard form:

{x + 0 y + 4 z = -19 | (equation 1)

{-(5 x) + y - z = -4 | (equation 2)

{0 x - 5 y - z = 25 | (equation 3)

Swap equation 1 with equation 2: