Determine the equation, in both factored and standard forms, of a parabola with zeros at (-2, 0) and (5, 0) and passes through the point (-1, -4)

Answers

Answer 1

The parabola equation in the factored and standard form are f(x) = (x + 2)(x - 5), and f(x) = (x - 3/2)² - 49/4 respectivly.

What is a parabola?

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have:
Parabola with zeros at (-2, 0) and (5, 0) and passes through the point (-1, -4)

In factored forms:

f(x) = (x + 2)(x - 5)

Because zeros at (-2, 0) and (5, 0)

In the standard form:

f(x) = x² - 3x - 10 or

f(x) = (x - 3/2)² - 49/4

Thus, the parabola equation in the factored and standard form are f(x) = (x + 2)(x - 5), and f(x) = (x - 3/2)² - 49/4 respectivly.

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Related Questions

PLEASE HELP!!!!!!!!!!!!!!ASAP, I MEAN THAT AS NICE AS POSSIBLE, THANKS!!!!!!!!!!!!

Answers

34 degrees is the measurement of angel ABC
Answer 34
ABD - CBD = ABC
64-30 = 34

What is DF=
Help me please thank you :)

Answers

The value of DF = 20.

What is similarity?

Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.

Given:

Using theorem

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

ΔSDF/Δ RTY = (SD/RT)= (DF/TY)=  (FS/ YR)

ar ΔSDF² / ar  ΔRTY² = 16/81

SD/ RT = 4/9

SD = 4x,  RT= 9x

SD= 8

4x = 8

x = 2

So,

RT=  9*2 = 18

SF = RT -2

SF = 16

(SD/RT)= (FS/ YR)

8 / 18 = 16/ YR

YR= 36

TY= 9 +RY = 45

(DF/TY)=  (FS/ YR)

DF / 45= 16/ 36

DF=20

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If I have 8$and something 3$ how many change wil I get?

Answers

If you have $8 and something’s cost $3 you will be getting $5 dollars back

pls help me in this i really need help :( :)

Answers

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

First off, let's write the line in point-slope form:

  [tex]\rm \hookrightarrow (y-y_0)=m(x-x_0)[/tex]

(x₀, y₀) any random point on the line'm' is the value of the slope

Let's calculate the slope:

 [tex]\rm \hookrightarrow Slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

(x₁, y₁): any random point on the line                                     ⇒   (-2, -6)(x₂,y₂): any random point on the line that is not (x₁, y₁)         ⇒   (2, -3)

                 [tex]\rm \hookrightarrow slope = \frac{-3--6}{2--2} =\frac{3}{4}[/tex]

Now that we found the slope, let's put it into the point-slope form

  ⇒ we need (x₀, y₀) ⇒ let's use (2,-3)

     [tex](y-(-3))=\frac{3}{4} (x-2)\\y+3=\frac{3}{4} (x-2)[/tex]

The equation, however, could also be put into 'slope-intercept form'

     ⇒ gotten by isolating the 'y' variable to the left

          [tex]y = \frac{3}{4}x-\frac{9}{2}[/tex]  

Answer:[tex]y = \frac{3}{4}x-\frac{9}{2}[/tex] or [tex]y+3=\frac{3}{4} (x-2)[/tex]

   *Either equations work, put the one that you are the most familiar with

Hope that helps!

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N= ???
Please help asap

Answers

Answer:

N=[tex]\sqrt{61}[/tex]

Step-by-step explanation:

We have the first point as (2,4), and the second point as (-3,-2). This means that [tex]x_1=2, y_1=4,x_2=-3,y_2=-2.[/tex] Using the distance formula, we get [tex]\sqrt{(2-(-3))^2+(4-(-2))^2} \\\sqrt{(2+3)^2+(4+2)^2}\\\sqrt{25+36}=\sqrt{61}[/tex]

Answer:

[tex]\sqrt{61}[/tex]

Step-by-step explanation:

ASAP PLS HELP
Which function is the inverse of f(x)=12x+5?
f−1(x)=2x+10
f−1(x)=2x−5
f−1(x)=2x−10
f−1(x)=2x+5

Answers

Answer:

Step-by-step explanation:

what’s the slope and y-int of, [-1,7] and [0,4]

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What is the formula for finding slope?}[/tex]

[tex]\mathbf{\dfrac{y_2 - y_1}{x_2 - x_1} = slope}[/tex]

[tex]\huge\textbf{Often people understand it better by:}[/tex]

[tex]\mathbf{\dfrac{rise}{run} = slope}[/tex]

[tex]\huge\textbf{Answering the given question:}[/tex]

[tex]\mathbf{y_2 \rightarrow 4}\\\\\mathbf{y_1 \rightarrow 7}\\\\\mathbf{x_2\rightarrow 0}\\\\\mathbf{x_1 \rightarrow -1}[/tex]

[tex]\huge\textbf{Now, that we have that information out}\\\huge\textbf{the way, we can answer the question.}[/tex]

[tex]\huge\textbf{Solving for the answer:}[/tex]

[tex]\mathbf{\dfrac{4 - 7}{0 - (-1)} = slope}[/tex]

[tex]\mathbf{\rightarrow \dfrac{4 - 7}{0 + 1} = slope}[/tex]

[tex]\mathbf{\rightarrow \dfrac{-3}{1} = slope}[/tex]

[tex]\mathbf{-3\div 1 = slope}[/tex]

[tex]\mathbf{\rightarrow -3 = slope}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\textsf{S}\frak{lope \rightarrow -3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Solve the triangle.
Round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".

Answers

The value of the side b and c will be 58.57 units and 36.86 units, and angle ∠B will be 107°.

What is law of sines?

Let the triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c.

Then by the sine law, we have

[tex]\rm \dfrac{\sin\angle A}{a} = \dfrac{\sin\angle B}{b} = \dfrac{\sin\angle C}{c}[/tex]

The sum of angles of triangle is 180°.

∠A + ∠B + ∠C = 180°

36° + ∠B + 37° = 180°

                  ∠B = 107°

Then the side b will be

sin 36° / 36 = sin 107° / b

                b = 58.57 units

Then the side c will be

sin 36° / 36 = sin 37° / c

                c = 36.86 units

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Adrian brought snacks for his team's practice. He bought a bag of apples for $1.68 and a 12-pack of juice bottles. The total cost before tax was $10.92. How much was each bottle of juice

Answers

Answer:

x = 77/100

Step-by-step explanation:

When you solve this equation: 1.68+ 12x = 10.92

The answer is x = 77/100

The cost of each bottle of juice will be $0.77.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Adrian brought snacks for his team's practice. He bought a bag of apples for $1.68 and a 12-pack of juice bottles. The total cost before tax was $10.92.

From the given data the expression will be formed as below:-

1.68+ 12x = 10.92

12x = 10.92 - 1.68

12x = 9.24

x =9.24 / 12

x = $0.77

Therefore, the cost of each bottle of juice will be $0.77.

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Having some trouble here

Answers

Answer:

None of them are correct i believe

Step-by-step explanation:

its sideways lol

The length of a picture is 10.5cm and the diagonal is 18.2cm . What width must have to meet a right angle ?

Answers

The width that must meet a right angle is 14.87 cm

How to determine the width?

The given parameters are:

Length = 10.5 cmDiagonal = 18.2 cm

The width is calculated using the following Pythagoras theorem.

Width^2 = Diagonal^2 - Length^2

So, we have:

Width^2 = 18.2^2 - 10.5^2

Evaluate

Width^2 = 220.99

Take the square root of both sides

Width = 14.87

Hence, the width that must meet a right angle is 14.87 cm

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What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)?
f(x)=2x²+x+4

Answers

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is (1, 7)

How to solve system of equation?

The solution to the linear and quadratic equation is as follows:

For the linear, a solution is 1 and 7.

This is because when x = 1, f(x) = 7

For the quadratic equation, 1 and 7 also works.

2x² + x + 4

2(1)² + 1 + 4

2 + 1 + 4 = 7

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X=
Help me please thanks

Answers

The value of x will be equal to 6 units.

What is trigonometry?

Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.

Given that:-

Given that the radius of the circle is 9 which is SO= 9 and SG = 9.

Now the value of x will be calculated by using the Pythagorean theorem.

H² = P ² + B ²

OG² = 12² + 9 ²

OG = √225

OG = 15

Since, OG = OH + HG

HG = OG - OH

x  = 15 - 9

x = 6 units

Therefore the value of x will be equal to 6 units.

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In a sale, the cost of a car is
reduced by 20%. In the sale it
costs £4,500. How much was it
before the sale?

Answers

5400

4500 multiplied by 1.2

Answer:

The original price would be $5,625

Step-by-step explanation:

The formula to finding out the original price is -

OP = SP/1 - P

- OP = Original Price

- SP = Sale Price

- P = Percent Discount

Now just put in the respected values and you'll get -

OP = 4500/1 - 0.20

Now solve :D

OP = 4500/1 - 0.20

= 4500/0.8

= 5625

So the original price is $5,625

Hope this helped! :D

Find the surface area of the composite figure.​

Answers

The surface area of the composite figure shown in the image is 952 ft²

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Surface area of composite is the sum of the individual areas of the surface.

Hence:

Surface area of composite = 2(14 * 9) + 2(0.5 * 10 * 8) + 2(10 * 10) + 2(10 * 14) + (10 * 14) = 952 ft²

The surface area of the composite figure shown in the image is 952 ft²

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PLSSS HELP!!!
Which equation is represented by the graph below?

Answers

Answer:

hope it will help you to

hope it will help you

It would be y = ex - 4

As a suggestion, I would recommend using the desmos calculator online. It's an entirely free graphing calculator and helps with questions like this. I hope that helps!

Suppose that the linear probability model yields a predicted value of Y that is equal to 1.3. Explain why this is nonsensical. A. The predicted value of Y must be between 0 and 1. B. The predicted value of Y is a positive number. C. The predicted value of Y is too low. D. The predicted value of Y is not an integer.

Answers

The predicted value of Y must be between 0 and 1.

A linear probability model (LPM) is a regression model where the outcome variable is a binary variable, and one or more explanatory variables are used to predict the outcome. Explanatory variables can themselves be binary, or continuous.

Suppose, that the linear probability model yields a predicted value of Y that is equal to 1.3.

This is nonsensical because

The predicted value of Y must be between 0 and 1.

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Suppose that two fair dice have been tossed and the total of their top faces is found to be divisible by 5. What is the probability that both of them have landed 5

Answers

The probability that both of them have landed 5 is 1/7.

Two fair dice have been tossed,

The total of their top faces is found to be divisible by 5,

Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0.

The probability that both of them have landed 5 is

E={(x,y)|x+y=5 or x+y=10, 1≤x,y≤6},

F={(5,5)}.

P(F|E)= 1/7.

Hence, The probability that both of them have landed 5 is 1/7.

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The equations in this sytem were added to solve for x. What is the value of x?
-6x+4y=-8
6x-12y=14

.-16y=6
.-8y=6
.-8y=-22
.-16y=-22

Answers

Answer:

x=5/6 but since you gave options in terms of y: -8y=6

Step-by-step explanation:

When you add equations together to solve for a systems of equations, it because you want to cancel out one of the values, and in this case it's the 6x, since the 6x + (-6x) = 0

Now all you need to do is add the -12 and 4y and you get -8y which is going to be the left side of the equation

Now add the -8 and 14 and you get 6 which is going to be the right side of the equation. This gives you the equation:

-8y = 6

Divide both sides by -8

y =  -0.75

Now plug this into either original equation but in this case I'll just use the -6x+4y=-8

Plug in -0.75 as y

-6x+4(-0.75) = -8

-6x-3=-8

-6x=-5

Divide both sides by -6

x=5/6

If Jamari pays $25 at the beginning of the month, he will pay only $5 per hour for using Vic Sporting facility. The information is recorded in the table on the image inserted. Write an equation for y, the cost of spending x hours at the sporting facility each month.

Answers

Answer:

Y = 5x + 25

Step-by-step explanation:

$25 is the constant, meaning regardless of the time he spends, he will not pay more or less.

However, he pays 5 dollars for every hours (x) = 5x

use an exponential expression to calculate the area covered by purple loosestrife seven years from now. is this a valid prediction? What does this result tell you about the constraints on the exponential model?

Answers

The area of the wetland that will be covered in purple loosestrife 7 years from now is modeled by this expression 500(1.2)^7

How to illustrate the information?

The exponential expression to calculate the area covered by purple loosestrife seven years from now will be:

= 500 × 1.2^7

After evaluating the expression, the model predicts that approximately 1,792 acres of the wetland will be covered in purple loosestrife 7 years from now.

This is not a valid prediction because the total area of the wetland is only 1,240 acres. Therefore, a constraint on the model is that the value of the expression 500(1.2)^t must be less than or equal to 1,240.

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Copy the figure below onto a separate sheet of paper. Find the image of the figure under reflections in line m and then line t. In the box below, describe the rotation equivalent to the composition of reflections with respect to lines m and t.

Answers

The reflection of the triangle DEFG will be given in the figure.

What is a transformation of geometry?

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Reflection does not change the size and shape of the geometry.

The image of the figure under reflections in line m and then line t.

The reflection of the triangle DEF will be given in the figure.

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The sum of 5 consecutive even integers is 4 less than the sum of the first 8 consecutive odd counting numbers. What is the smallest of the even integers

Answers

The smallest of the even integers is 8.

It is a well-known fact that the sum of the first n odd numbers is n^2. This makes the sum of the first 8 odd numbers equal to 64.

Let n be equal to the smallest of the 5 even integers. Then (n+2) is the next highest, (n+4) even higher, and so on.

This sets up the equation n+(n+2)+(n+4)+(n+6)+(n+8)+4=64

Now we solve:

5n+24 = 64

5n = 40

n = 8

The smallest of the even integers is 8.

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You have several numbers in a data set: 5, 7, 9, 11, 13, 15, 17. What is the z Score for the number 7

Answers

The z score for the number 7 is -0.92.

The standard deviation is 4.32

X is the score that is 7 given.

We have to calculate the z score for doing so we need the mean also.

Mean is obtained by dividing the sum of numbers / total frequency.

Mean = Summation of numbers / total numbers

= 5, 7, 9, 11, 13, 15, 17 / 7

= 77/7

= 11

Formula of z-score, Z= x - mean /S.D.

x is the number that is 7.

S D is the standard deviation.

Z= 7-11 / 4.32

= -4/4.32

Z score = -0.92

In data, the standard deviation is a degree of the quantity of version or dispersion of a fixed of values. A low fashionable deviation suggests that the values have a tendency to be near the suggest of the set, while a high widespread deviation shows that the values are spread out over a much broader range.

Standard deviation is vital because it is able to assist users check chance. Bear in mind a funding option with a median annual return of 10% in line with the year. However, this average changed into derived from the past three-year returns of 50%, -15%, and -5%. with the aid of calculating the same old deviation and understanding your low likelihood of really averaging 10% in any single given 12 months, you're better armed to make knowledgeable decisions and apprehend underlying risk.

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When two variables are being examined, and one variable moves one way and the other variable moves in the opposite direction, this is called a(n):

Answers

When two variables are being examined, and one variable moves one way and the other variable moves in the opposite direction, this is called an inverse relation.

Correlation is a statistical degree (expressed as various) that describes the size and path of a courting among or extra variables. A correlation between variables, however, does now not robotically suggest that the trade in a single variable is the purpose of the alternate inside the values of the opposite variable.

A positive correlation is clear while variables move within an equal course. An inverse correlation is clear whilst variables circulate inside the opposite route.

A negative correlation is a relationship among variables that pass in contrary instructions. In other phrases, while variable A increases, variable B decreases. A poor correlation is likewise known as an inverse correlation.

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When two variables are being examined, and one variable moves one way and the other variable moves in the opposite direction, this is called a(n): Inverse Relationship.

Consumption is subject to diminishing marginal utility. -A lower price increases the purchasing power of a buyer's income, enabling a buyer to purchase more of a product.

The law of supply and demand is a keystone of modern economics. According to this theory, the price of goods is inversely related to the quantity offered. This makes sense for many goods, since the more costly it becomes, fewer people will be able to afford them and demand will subsequently drop.

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At which of the given values is the graph discontinuous?
a. 7
b. -2
C. -4
d. 0

Answers

According to the
figure when ×<7. fx<0..


Here are six number cards.
9 7 5 -4 -2 0
Arrange the cards into three pairs with the same total.
Note: Please write each pair on separate lines and
use the word 'and' between the numbers (eg. 7 and -3).

Answers

9 and -4
7 and -2
5 and 0

Each and every pair has a total of 5.

Answer:

9 and-4

7 and -2

5 and 0

Step-by-step explanation:

When ya subtract 4 from 9 you get 5

the same applies to the rest.

Write the correct postulate, theorem, property, or definition that justifies the statement below the diagram.

Answers

The correct theorem or definition that justifies the given statement for the diagram is; Definition of a Right angle Triangle

What is the angle postulate?

We are given that;

∠MRS ≅ ∠MRO

Now, what that means is that ∠MRS is congruent to ∠MRO. Thus, to understand this concept of equality or congruence, we can prove it since  from the given image, we see that;

m∠MRS = m∠MRO = 90°

Since they are both right angles then we can say that the correct theorem is the definition of a right angle triangle.

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send help lol confused

Answers

Answer:

C. 0≤x≤7

Step-by-step explanation:

It is not choice D. because it has y instead of x. It is supposed to be x because it is asking for domain.

Hope this helps!

3/a times x -4 equals 20

Answers

Answer:

a = -5/3

Step-by-step explanation:

3/a × -4 = 20

3a × -4/-4 = 20/-4

3a = -5

a = -5/3

Check:

3/(-5/3) × - 4 = 20

-5 × - 4 = 20

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