Mathematics College

Write a quadratic function in standard form whose graph passes through (-5,0), (0,-8), and (4,0)

Answers

Answer 1

The quadratic equation y = (2 / 5) · x² + (2 / 5) · x - 8 contains the points (- 5, 0), (0, - 8) and (4, 0).

How to derive the equation of a parabola

In this problem we find the case of a parabola, parabolae are defined by quadratic equations of the form:

y = a · x² + b · x + c

Where:

a, b, c - Real coefficients.x - Independent variable.y - Dependent variable.

First, write the points associated with the parabola:

(x₁, y₁) = (- 5, 0), (x₂, y₂) = (0, - 8), (x₃, y₃) = (4, 0)

Second, create a system of linear equations:

25 · a - 5 · b + c = 0

c = - 8

16 · a + 4 · b + c = 0

Third, resolve the system by numerical methods:

(a, b, c) = (2 / 5, 2 / 5, - 8)

Fourth, write the resulting quadratic equation:

y = (2 / 5) · x² + (2 / 5) · x - 8

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Write A Quadratic Function In Standard Form Whose Graph Passes Through (-5,0), (0,-8), And (4,0)

Related Questions

Suppose X varies directly with YX equals 29 when Y equals -87 what is the constant variation and what is the value of x when y = -187
A. Constant variation -1/3, x= 63
B. constant variation -1/3, x= -63
C. Constant variation -3, x= 63
D. Constant variation -3, x = 567

Answers

The constant variation and the value of x are (a) Constant variation -1/3, x= 63

How to determine the constant variation and the value of x

From the question, we have the following parameters that can be used in our computation:

X varies directly with Y

X equals 29 when Y equals -87

This means that

Constant of variation = X/Y

Substitute the known values in the above equation, so, we have the following representation

Constant of variation = 29/-87

Evaluate

Constant of variation = -1/3

From the question, we have

y = -187

This means that

Constant of variation = X/-187

So, we have

X = -187 * Constant of variation

This gives

X = -187 * -1/3

Evaluate

X = 63

Hence, the solution is (a)

Answers

Answer: -1 - (-0.25) = -0.75

Step-by-step explanation:

The way you would do that is by first pretending as the negative sign (-), isn't present.

Then do "1 - 0.25".

1.00 - 0.25 = 0.75

After you solved the equation, then we can add the negative sign (-), back into the equation = -1 - (-0.25) = -0.75 ✅

Total students in a class are 120. 40% of them are female students. 70 male students passed with 100% pass rate. What is the pass rate of female students at 100 percent rate?

Answers

Answer:

Here is the answer

Step-by-step explanation:

If 40% of the students in the class are female, then there are 40/100 * 120 = 48 female students.

If 70 male students passed with a 100% pass rate, then the pass rate for male students is 100%.

If the pass rate for male students is 100%, then the pass rate for female students must also be 100%. This is because the pass rate is calculated as the number of students who pass divided by the total number of students, and if all the male students pass, then the pass rate for male students must be 100%.

Therefore, the pass rate for female students at a 100% rate is also 100%.

if you apply demorgan's theorem to the expression overbar(overbar((overbar(a) overbar(b))) (overbar(c d))), you get:

Answers

Applying DeMorgan's theorem to the expression overbar(overbar((overbar(a) overbar(b))) (overbar(c d))) results in (a b) + (c + d).

DeMorgan's theorem states that when two terms are combined with an AND operator (such as overbar(a) overbar(b)), the result is the two terms combined with an OR operator (such as a + b).

Similarly, when two terms are combined with an OR operator (such as overbar(c d)), the result is the two terms combined with an AND operator (such as c overbar(d)). Applying this theorem to the expression above results in (a b) + (c + d).

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An air traffic controller is tracking two planes. To start, plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second. How many seconds will pass before the planes are at the same altitude? What will their altitudes be when they’re at the same altitude?

Answers

44 seconds will pass before the planes are at the same altitude.

What do you mean by algebraic expression?

An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.

There are three main types of algebraic expressions:

Monomial Expression

Binomial Expression

Polynomial Expression

An algebraic expression with only one term is called a monomial.

It is given that plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second.

Let x seconds will pass before the planes are at the same altitude.

Plane A, 3500 + 45.5x

Plane B, 2609 + 65.75x

x is number of seconds of time

When altitudes equal

3500 + 45.5x = 2609 + 65.75x

3500 - 2609 = 65.75x - 45.5x

891 = 20.25x

891/20.25 = x

44 = x

Therefore, 44 seconds will pass before the planes are at the same altitude.

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I need help with this please help me

Answers

The picture of the (5, -1) beneath the same translation, in accordance with the stated statement, is (9, 6).

What does a math translation mean?

Each point in a graphic is moved the same distance within the same direction using a sort of transformation known as translation.

What does math formula translation mean?

Translation in mathematics is the movement of a form in any direction—left, right, up, or down—without turning. They are congruent if the translated forms appear to be of the same size as that of the original ones. They have only changed their direction or directions.

Briefing:

The image of the translation is (9,-2).

The point is given as: P = (-6, -4)

The image of the point is: P' = (-2, 3)

The translation rule is calculated as:

T = x - 2 - (-6), y+3-(-4)

so, T = x + 4, y + 7

So, the image of (5, -1) is:

the Image of the translation = 5 + 4, -1 + 7

Hence, the image of the translation is (9, 6).

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Can anyone help me ASAP?

Answers

A cheeseburger costs 4 and a taco costs 2

- At a bake sale, the Math Club raised $225 by selling 300 baked goods. If the amount
raised varies directly with the baked goods sold, how much money will be raised for
selling 450 baked goods?
Record your answer on the answer document.
5x3

Answers

The amount of money for selling 450 baked goods will be

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

At a bake sale, the Math Club raised $225 by selling 300 baked goods.

And, The amount raised varies directly with the baked goods sold.

Now,

Let the amount of money for selling 450 baked goods = x

Since, At a bake sale, the Math Club raised $225 by selling 300 baked goods.

And, The amount raised varies directly with the baked goods sold.

Hence, By definition of proportion we get;

⇒ $225/300 = x / 450

⇒ x = 225 × 450 / 300

⇒ x = $337.5

Thus, The amount of money for selling 450 baked goods = $337.5

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Solve 0=sin1/2x+cosx−1

Answers

The value of x = 2nπ, (n ∈ Z) and

[tex]x=2(n\pi+(-1)^{n} \pi /6)[/tex], (n ∈ Z)

What are Trigonometric Identities?

Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Trigonometric Identities are true for every value of variables being on both sides of an equation. Geometrically, these identities involve certain trigonometric functions( similar as sine, cosine, tangent ) of one or further angles.

According to question

⇒ sin(x/2) + cos(x) - 1 = 0

{ cos(2x) = 1 - 2sin²(x) }

cos(x) = 1 - 2sin²(x/2)

⇒ sin(x/2) + cos(x) - 1 = 0

⇒ sin(x/2) + 1 - 2sin²(x/2) - 1 = 0

⇒ - 2sin²(x/2) + sin(x/2) + 1 - 1 = 0

⇒ - 2sin²(x/2) + sin(x/2) = 0

⇒ sin(x/2)(- 2sin(x/2) + 1) = 0

⇒ sin(x/2) = 0 , x = 2nπ (n ∈ Z)

and

⇒ sin(x/2) = 1/2 , [tex]x=2(n\pi+(-1)^{n} \pi /6)[/tex] (n ∈ Z)

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McDonald's has a leaking drink machine. The manager placed a cup under the leak until he
could get it fixed. After 1 1/4 hours, the manager noticed that the cup had collected 1/3 cups of
soda. What is the rate, in cups per hour, at which the drink machine is leaking?

Answers

Answer:

4/15 cups of soda per hour

Step-by-step explanation:

1 1/4 = 5/4 and if 5/4 hours yielded 1/3 cups, you would have to multiply 1/3 by the reciprocal to find the hourly rate

1 4 4

- * - = --

3 5 15

Find the angle round to the nearest degree. please help.

Answers

63 degrees is the angle.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given triangle is a right angle triangle.

The opposite side length is 85 and the adjacent side is 38.

Opposite side=85

Adjacent side=38.

Calculate Opposite/Adjacent

= 85/38= 2.236

Which is tanθ=2.236

Now tan inverse on both the sides

θ=tan⁻¹2.236

θ=tan⁻¹2

θ=63 degrees.

Hence, the angle is 63 degrees.

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You are given the figure below well as the following information.

Answers

Answer:

A. 110°

Step-by-step explanation:

according to the theorems,

m∠1=m∠6=m∠9=m∠14=110°;

m∠2=m∠5=m∠10=m∠13=70°;

m∠3=m∠8=m∠11=m∠16=70°;

m∠4=m∠7=m∠12=m∠15=110°.

all the details are in the attachment.

You install 538 feet of fencing along the perimeter of a rectangular yard. The width of the yard is 127 feet. What is the length of the yard?

Answers

so, you know that perimeter is equal to 2 times width + 2 times length. if the width is 127, then you must multiply it 2 times getting 254, then you’re gonna subtract than number from 538, getting 284 (that’s 2 times length) so simply divide by two to get the answer.

answer: 142feet

Please help me with this question

Answers

Answer:

Point of intersection is (13.72, 660)

Step-by-step explanation:

You have to use your graphing tool to answer questions 2 and 3.

Then click on the point of intersection and note the coordinates.

That's it.

This can also be solved mathematically but since the question does not ask I have not given that solution process.

Graph attached

which of the following is not a valid property of circles? a rotateangle b none of these c left d width

Answers

There is no property named 'left' for the circle. So the answer is 'c'.

What is Circle?

Circle is a two dimensional figure which has a round shape. It is formed by joining all the points which are at an equal distance from a fixed point called the center of the circle.

The line formed by joining the center to any point on the boundary of the circle is called radius. Diameter is double of the radius.

Rotate angle is the term defining the angle of rotation of the circle. Angle of rotation of a complete circle is 2π.

Width is another term for diameter of the circle, although it is not commonly used.

Left is the only term which does not have any role in the properties of circles.

Hence, the term 'left' is not a valid property of circles.

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What is an equation of the parabola

Answers

Answer:

Step-by-step explanation:

You want an equation of the parabola with directrix x = 11/4 and vertex (0, 3).

Equation

The directrix is a vertical line to the right of the vertex. This means the parabola opens to the left.

The vertex form of the equation is ...

x = 1/(4p)(y -k)² +h . . . . . . . . where (h, k) is the vertex, and p is the distance from the directrix to the vertex (also, the distance from the vertex to the focus)

Application

Here, we have ...

p = 0 -11/4 = -11/4 . . . . negative because the vertex is left of the directrix

and

(h, k) = (0, 3)

so the equation is ...

x = 1/(4(-11/4))(y -3)² +0

x = -1/11(y -3)²

MP MODELING REAL LIFE You sell instruments at a
Caribbean music festival. You earn $326 by selling 12 sets
of maracas, 6 sets of claves, and x djembe drums. Find the
number of djembe drums you sold.

Answers

The number of djembe drums you sold is 8

How to determine the number of djembe drums you sold.

From the question, we have the following parameters that can be used in our computation:

Total = 12 sets of maracas, 6 sets of claves, and x djembe drums.

Earning = $326

Also, we have:

The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.

So, we have

12 * 14 + 6 * 5 + x * 16 = 326

Evaluate the products

198 + 16x = 326

Evaluate the iike terms

16x = 128

So, we have

x = 8

Hence, the number of djembe drums is 8

Answers

Answer:

Step-by-step explanation:

Divide both sides of the equation by 4.

What are the domain and range of the function F(x) = 3/4 x + 5?
Domain (-infinite, infinite)
Range (-infinite, infinite)

Domain (3/4, infinite)
Range (-infinite, 5)

Domain (-infinite, 3/4)
Range (5, infinite)

Domain (3/4, infinite)
Range (5, infinite

Answers

The domain and range of the provided function are (-infinite, 3/4) and (5, infinite) respectively.

What is function?

A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output. A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

What is domain and range?

The domain of a function is the set of values that may be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the collection of values that the function returns when we enter an x value. To acquire the domain and range, just solve the equation y = f(x) to discover the values of the independent variable x. To compute the function's range, just define x as x=g(y) and then discover the domain of g. (y).

Here,

f(x)=3/4x+5

Domain=(-infinite, 3/4)

Range=(5, infinite)

The domain for given function is (-infinite, 3/4) and range is (5, infinite).

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Kim decided that she wanted to go bowling. The bowling alley charges $2.75 per game and $10 for shoes. If Kim has $30, how many complete games can she bowl?
Write an equation and solve it.

Answers

Answer: 2 complete games

Step-by-step explanation:

add shoes and game charge

$10.00 + 2.75 = 12.75 <— that’s 1 complete game

subtract it from $30.00

$30.00 - 12.75 = 17.25.

A complete game costs 12.75. so, Kim had enough money for one more game.

17.25 - 12.75 = $4.50 remaining after 2 complete games

Answer: 7 games

Step-by-step explanation: if it charges 10 for shoes, then you already subtract 10 from 30. 30-10=20. then, to find out how many games she can play, divide 2.75 from 20. 20/2.75=7.272727.... Since you can't pay for half of a game, it would be 7 games.

a number has the same digit in its hundreds place and in its hundreds place. how many times greater is the value of the digit in the hundreds place than the value of the digit in the hundreds place

Answers

A number has the same digit in its hundreds place and in its hundreds place. 10,000

What is the value of the digit?

Generally, Given that a number's hundreds place and its hundredths place both have the same digit, we may assume that the number is perfect.

Let's say that the digit is a 1.

Therefore, the value of the hundreds position in a number is equal to 100.

The value of the hundredth position in a number is equal to 0.01%.

The following formula may be used to determine the number of instances in which the value of the digit in the hundreds place is higher than the value of the digit in the hundredths place:

As a result, the difference between the value of the digit in the hundreds place and the value of the digit in the hundredth place is 10,000 times bigger.

Answers

Answer:

f - 36

-3f - 23

are your prime polynomials.

Write as a single fraction in its simplest form.
[tex] \frac{ {x}^{2} - 3x}{ {x}^{2} - 9 } [/tex]

Answers

Answer:

[tex]\frac{x}{x+3}[/tex]

Step-by-step explanation:

[tex]\frac{x(x-3)}{(x+3)(x-3)}[/tex]

[tex]\frac{x}{x+3}[/tex]

8w-16 how do i answer this

Answers

The factor of the expression 8w - 16 will be 8 and (w - 2).

What is factorization?

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

A frequency table displays a sequence of scores in either increasing or decreasing order together with their occurrences as a way to compactly organize raw data.

The expression is given below.

⇒ 8w - 16

The factor of each term in the expression, then we have

8w = 8 x w

16 = 8 x 2

Then the expression is written as,

⇒ 8w - 16

⇒ 8 × w - 8 × 2

⇒ 8 × (w - 2)

⇒ 8(w - 2)

The component of the articulation 8w - 16 will be 8 and (w - 2).

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x = 1/4. y = 2/3. z = 4*1/5

Work out the value of X x y x z

Give your answer as a fraction in its simplest form.

Answers

Answer:

[tex]\frac{7}{10}[/tex]

Step-by-step explanation:

At a football game, a vender sold a combined total of 244 sodas and hot dogs. The number of hot dogs sold was 42 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.

Answers

Answer:

143 sodas101 hot dogs

Step-by-step explanation:

Given a total of 244 sodas and hot dogs sold, with sodas numbering 42 more than hot dogs, you want to know the number of each that were sold.

Setup

Let s represent the number of sodas sold. Then s-42 is the number of hot dogs sold, and the total sold is ...

s +(s -42) = 244

Solution

Add 42 and simplify

2s = 286

s = 143 . . . . . divide by 2

hot dogs = 143 -42 = 101 . . . . . figure the number of hot dogs

143 sodas and 101 hot dogs were sold.

A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet. They sort the data by payment plans, as shown below. Plan A: 27 text, 21 Internet Plan B: 13 text, 10 Internet Answer the questions to determine a conditional probability. What is the probability that a randomly selected customer who is on plan B uses the phone most often to text? Give the answer in fraction form.

Answers

The probability that a randomly selected customer who is on plan B uses the phone most often to text is; 13/23

How to solve fraction word problems?

We are given that;

The data by payment plans are;

Plan A: 27 texts, 21 Internet

Plan B: 13 texts, 10 Internet

Now, the probability is defined as the ratio of the sum of all observations and the total number of observations.

The total number of observations for plan B is; 13 +10 = 23

The number of customers that are on payment plan B = 23 customers are on payment plan B.

The number of customers that are on plan B text is; 13

Thus, the probability that a randomly selected customer who is on plan B uses the phone most often to text is;

Probability = 13/23

The probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.

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PLEASE HELP

Given that x is a normal variable with mean = 47 and standard deviation = 6.4, find the following probabilities. (Round your answers to four decimal places.)

(a) P(x ≤ 60)

(b) P(x ≥ 50)

(c) P(50 ≤ x ≤ 60)

Answers

Given that x is a normal variable with mean = 47 and standard deviation = 6.4, find the following probabilities.

(a) P(x ≤ 60) = 0.9356 (b) P(x ≥ 50) = 0.6744 (c) P(50 ≤ x ≤ 60) = 0.2612

What are the probabilities?

Generally, To solve these problems, we can use the standard normal distribution table or a computer program to find the desired probabilities.

First, we need to standardize the given values of x by subtracting the mean and dividing by the standard deviation. This gives us a standard normal random variable, denoted by Z, with a mean of 0 and a standard deviation of 1.

(a) P(x ≤ 60) = P(Z ≤ (60 - 47)/6.4) = P(Z ≤ 1.5625). From the standard normal distribution table or a computer program, we find that P(Z ≤ 1.5625) = 0.9356.

(b) P(x ≥ 50) = P(Z ≥ (50 - 47)/6.4) = P(Z ≥ 0.46875). From the standard normal distribution table or a computer program, we find that P(Z ≥ 0.46875) = 0.6744.

Therefore, the probabilities are as follows:

(a) P(x ≤ 60) = 0.9356 (b) P(x ≥ 50) = 0.6744 (c) P(50 ≤ x ≤ 60) = 0.2612

Answers

x(7 - x) > 8

Steps for calculation

First solve x(7 - x) = 8

x^2 - 7x + 8 = 0

x = 5.56, 1.44

If we plug in these values into the original equation we can see that solution is

1.44 < x < 5.56

Meaning and definition of systems of inequality:The value of the variable(s) that transforms the inequality into a true statement is the solution. Think about the example (x+3>5). If we provide any real value bigger than (2) for this inequality, it will be true (x). (therefore) This inequality's answer is (x>2)A collection of two or more inequalities in one or more variables is referred to as a system of inequalities. Systems of inequalities are utilized when a scenario calls for several solutions but also places multiple restrictions on those answers.The best answer is often found by solving a set of linear inequalities. This response could be as simple as calculating the number of products that need be produced in order to maximize profit or as complex as selecting the ideal medication regimen for a patient. The different kinds of inequalities and how to solve them will be covered in this article.

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Five acres of land were divided into 4 lots of equal size. How many square feet did each lot measure? (1 acre = 43,560 sq ft)

Answers

The number of square feet each lot measure is 54, 450 square feet.

How to find the area in square feet of the lot?

Five acres of land were divided into 4 lots of equal size. The number of square feet each lot measure can be calculated as follows:

1 acre = 43,560 square ft

5 acres = ?

cross multiply

number of acres = 5 × 43,560

number of acres = 217800 square feet.

Therefore, the lots is divide into 4 equal lots.

Hence,

measure of each lot = 217800 / 4

measure of each lot = 54, 450 square feet.

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