A store sells
79 virtual reality headsets. How much
money does the store collect?

Hint (headset cost $125)

[tex]6 {x}^{2} - 5x - 6 = 0 \\ 6 {x}^{2} - 9x + 4x - 6 = 0 \\ (6 {x}^{2} - 9x) + (4x - 6) = 0 \\ 3x(2x - 3) + 2(2x - 3) = 0 \\ (3x + 2)(2x - 3) = 0 \\ 3x + 2 = 0 \\ \\ \\ or \\ 2x - 3 = 0 \\ x = \frac{ - 2}{3} \\ \\ or \\ \\ x = \frac{3}{2} [/tex]

I FACTORISED THE EQUATION FIRST WITH A SIMPLE METHOD OF MULTIPLYING THE COEFFICIENT OF

[tex] {x}^{2} [/tex]

and the constant number then find the factors that will give me the coefficient of x.

ATTACHED IS THE SOLUTION

Step-by-step explanation:

are you sure this is the whole information ?

because

6² = 5x + 6

is not called a quadratic equation.

it is a quadratic equation, when there is one term in x² involved.

I assume therefore, that your problem is

6x² = 5x + 6

that is then as basic quadratic equation

6x² - 5x - 6 = 0

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

a = 6

b = -5

c = -6

x = (5 ± sqrt((-5)² - 4×6×-6))/(2×6) =

= (5 ± sqrt(25 + 144))/12 = (5 ± sqrt(169))/12 =

= (5 ± 13)/12

x1 = (5 + 13)/12 = 18/12 = 3/2

x2 = (5 - 13)/12 = -8/12 = -2/3

so, the 2 solutions for the quadratic equation are

x = 3/2 and x = -2/3

Answer:

y + 2 = -2(x - 2) (point-slope form)

y = -2x + 2 (slope-intercept form)

2x + y = 2 (standard form)

Step-by-step explanation:

[tex]m = \frac{ - 4 - ( - 2)}{3 - 2} = - \frac{2}{1} = - 2[/tex]

[tex]y + 2 = - 2(x - 2)[/tex]

[tex]y + 2 = - 2x + 4[/tex]

[tex]y = - 2x + 2[/tex]

[tex]2x + y = 2[/tex]

The original price of the motorcycle is approximately $7,987.

Here, we are given that p represent the motorcycle’s original price.

The sale price of Dealer A will be-

7.5% less that the original price

= 92.5% of p

= 0.925p

Similarly, the sale price of dealer B will be-

$599 less than original price

= (p - 599)

Now, these two prices are equal, so we can equate the two-

0.925p = (p - 599)

0.925p = p - 599

0.925p - p = -599

-0.075p = -599

p = -599/-0.075

p = 599/0.075

p = 599000/75

p = 7,986.67

Thus, the original price of the motorcycle comes out to be approximately $7,987.

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Answer:

[tex]g(x)=\dfrac{x^2+1}{3}[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=3x-1\\(f \circ g)(x)=x^2\end{cases}[/tex]

Composite functions are when the output of one function is used as the input of another.

Therefore, the given composite function (f o g)(x) means to substitute function g(x) in place of the x in function f(x).

[tex]\begin{aligned}(f \circ g)(x) & = x^2\\f(g(x)) & = x^2\\\implies 3(g(x))-1 & = x^2\\3(g(x))-1+1 & = x^2+1\\3(g(x))&=x^2+1\\\dfrac{3(g(x))}{3}&=\dfrac{x^2+1}{3}\\\implies g(x)&=\dfrac{x^2+1}{3}\end{aligned}[/tex]

Therefore:

[tex]\boxed{g(x)=\dfrac{x^2+1}{3}}[/tex]

Answer:

5

Step-by-step explanation:

he needs $85 and he has $25,

so it will be 85-25=60

that means he would need $60 more. if he saves $13 every week, it will 60÷13= 4.6 weeks or approximately 5.

If the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units

The length of the hypotenuse = 13.5 units

The angle = 41 degrees

Here we have to use the trigonometric function

sin θ = Opposite side / Hypotenuse

cos θ = Adjacent side / Hypotenuse

tan θ = Opposite side / Adjacent side

In this question hypotenuse and angles are given and we have to find the opposite side.

sin θ= opposite side /  Hypotenuse

Substitute the values in the equation

sin 41 = Opposite side / 13.5

Opposite side = sin 41×13.5

= 8.86 units

Hence, if the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units.

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Answer:

the formula for the vertex is f(x)=a(x-h)²+k

so if you replace -4= a(0-5)²+-2

so a=-0.08

The formula would end up like this f(x)=-0.08(x-5)²+-2

Step-by-step explanation:

Let Bailey drive x miles.

So, Kacie drove 2x miles.

Kaiden drove 2x + 10 miles.

According to the question,

x + 2x + 2x + 10 = 50

x = 8

Therefore, Bailey drove 8 miles and Kacie drove 16 miles, while Kaiden 36 miles.

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Answer:

[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

2([tex]\frac{2}{5}[/tex] ) + 2(- [tex]\frac{1}{5}[/tex] )

= [tex]\frac{4}{5}[/tex] + (- [tex]\frac{2}{5}[/tex] )

= [tex]\frac{4}{5}[/tex] - [tex]\frac{2}{5}[/tex]

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

The description that represents a sample is A. The first 5,000 people who downloaded its No. 1 hit song.

Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.

It should be noted that all people who downloaded its No. 1 hit song represents the entire population. The sample is a subset of the population.

In conclusion, the correct option is A.

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Answer:

This is the most optimal way to resolve the problem:

Step-by-step explanation:

15/n+2 = 3n/n

15/n+2 = 3

3 (n+2) = 15

n = 5 - 2

n = 3

We have to find the side of a square with a diagonal with length 12√10 ft.

We can sketch this as:

We can apply the Pythagorean theorem as:

Answer: the square side length is 12√5

a.) In Line 1 Kylie made her error.

b.) Kylie's error is that she opened the bracket -2(x - 5) in the first line and did not change the negative sign to a positive sign as she multiplied -2 and -5 as a negative number multiplied by a negative number is a positive number.

c.) The correct solution to the problem is given by,

Given: 6x - 2(x - 5) = 22

6x - 2x + 10 = 22

4x = 22 - 10

4x = 12

x = 12/4

x = 3

Hence, the value of x is 3 and not 8.

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The interval where the product will at least break even is [tex]$\left[\begin{array}{cc}\text { Solution: } & x \leq-5 \\ \text { Interval Notation: } & (-\infty,-5]\end{array}\right]$[/tex]

Given C= 305 x+1350C

R=60 x

To find the interval where the product will at least break even we must have [tex]$R(x) \geq c(x)$[/tex]

[tex]$\Rightarrow \quad 35 x \geq 305 x+1350$[/tex]

[tex]$$35 x \geq 305 x+1350$$[/tex]

Subtract 305 x from both sides

[tex]$$35 x-305 x \geq 305 x+1350-305 x$$[/tex]

Simplify

[tex]$$-270 x \geq 1350$$[/tex]

Multiply both sides by - 1 (reverse the inequality)

[tex]$$(-270 x)(-1) \leq 1350(-1)$$[/tex]

Simplify

[tex]$$270 x \leq-1350$$[/tex]

Divide both sides by 270

[tex]\frac{270 x}{270} \leq \frac{-1350}{270}$$[/tex]

Simplify

[tex]$$x \leq-5$$[/tex]

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

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The best plot for these results is given by:

C. Plot C.

The mean result for each group is given as follows:

Then we have to look at the vertical bars of each plot, and see the scores given.

For plot A, the scores are given as follows:

For plot B, the scores are given as follows:

For plot C, the scores are given as follows:

For plot D, the scores are given as follows:

Plot C has the closest value readings to the actual values of 36.8 and 52.4, hence it is the best option to plot the scores for each group.

The problem is missing and is given by the image at the end of the answer.

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Answer: C

Step-by-step explanation:

Starting off we need to understand what the circles are in inequalities.

A closed circle means that the number on the inequality is included in the solution. An open circle means that the number in the inequality is not included in the solution. A closed circle would use [tex]\leq or \geq[/tex]. An open circle would use < or >.

So, using these processes, -2<x[tex]\leq[/tex]7 would be the answer.

In a case whereby triangle ABC is congruent to triangle DEC, angle B = 2x + 31 and angle E = 7x - 24, the X is 11.

It should be noted that when a Triangles are exactly the same in term of size and shape then it is congruent.

Since the angle E and angle B is the same, then we can equate it so that we can find the value of X , then this can be calculated as

(2x + 31) = (7x - 24)

The we have

(7x - 2x) = (31 +24)

The we will have

(5x) =( 55)

Then

x = 11

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To solve this question, find the 4 first terms of the sequence.

The first term is a₁

a₁ is given and a₁ = 7

The second term is a₂

Given:

Then, let's find a₂ using the value of a₁

The third term is a₃

let's find a₃ using the value of a₂

The fourth term is a₄

let's find a₄ using the value of a₃

Answer:

The four first terms are:

a₁ = 7

a₃ = 12

a₃ = 17

a₄ = 22

Step-by-step explanation:

the set of prime numbers that, when multiplied together, give

13824:

2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3

Answer:

24

Step-by-step explanation:

Each person gets 1/12 fraction of the original cake.

What is a fraction?

A fraction, which derives from the Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal pieces. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. A common, vulgar, or simple fraction is one that has a non-zero denominator shown below (or after) the line that separates the numerator from the denominator. Composite fractions, complicated fractions, and combined numeral fractions are examples of uncommon fractions that use numerators and denominators.

Each person gets = 1/2 x 1/6 = 1/12

Hence, each person gets 1/12 fraction of the original cake.

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The Zero Product Property simply notes that if ab = 0, then either a = 0 or b = 0. The solutions exists x = -4, x = -2, x = 1.

The zero-product property in algebra asserts that two nonzero items cannot be multiplied together to produce zero.

The Zero Product Property simply notes that if ab = 0, then either a = 0 or b = 0 (or both). A product of factors exists zero if and only if one or more of the factors exists zero.

Let the given equation be (x+4)(x+2)(x-1)=0

By using the Zero Factor Principle, we get

If ab = 0 then a = 0 or b = 0

then x + 4 = 0 or x + 2 = 0 or x - 1 = 0

Solve x + 4 = 0

⇒ x = -4

Solve x + 2 = 0

⇒ x = -2

Solve x - 1 = 0

⇒ x = 1

The solutions are x = -4, x = -2, x = 1

Therefore, the correct options exists:

b) 1

c) -4

e) -2

The complete question is:

An equation is shown below.

(x + 4)(x + 2)(x - 1) = 0

Select all of the following values that make the equation true.

a) 4

b) 1

c) -4

d) 0

e) -2

f) 2

g) -1

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0.020 is a probability for student selects at least 6 .

What is a probability simple definition?

There are two ways to do it. You can either interpret this as

One minus the probability that the student will guess 5 or fewer

correct answers with a probability of a correct answer being = 1/4  ⇒      

0.0197277069

The probability that the student will guess 4 or fewer wrong answers

with a probability of a wrong answer being = 3/4

  binomcdf (10,3/4,4)

     = 0.0197277069

Either way it rounds to 0.020

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The expression that represents the distance is |-1/4 - 3/4|

From the question, the endpoints are given as

-1/4 and 3/4

Rewrite the endpoints properly

This is done as follows

Endpoint 1 =  -1/4

Endpoint 2 =  3/4

The distance expression between the endpoints is then calculated as

Distance = |Endpoint 1 - Endpoint 2 |

Substitute the known values in the above equation

So, we have the following equation

Distance = |-1/4 - 3/4|

Hence, the disance expression is |-1/4 - 3/4|

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Answer:

A, 9100 210 C 1520 99144 NO ES PERO BUENO MIRA AVER SI

Due to the fact that the line does not pass through the origin, the equation does not represent a proportionate relationship.

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.

Given Data

The remaining length (L) of 120-inch rope after x inches have been cut off: 120- x = L.

The fact that

If a relationship between two variables, x and y, can be written as or, then it represents a proportionate variation.

y = kx

The line passes through the origin, and the constant of proportionality, k, is equal to the slope of the line, m.

There are

The length (L) of a 120-inch rope that is left after x inches have been removed.

There are

The dependent variable is L —->. (output variable)

The independent variable is x. (input variable)

The linear formula is

L = 120-x

Due to the fact that the line does not pass through the origin, the equation does not represent a proportionate relationship.

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Answer: y=x2+3x−1

Hope this helps! :)

The mathematical sentence can be written as:

3 = x/6

And the solution is x = 18.

Here we have the following mathematical sentence:

"three is a number divided by 6"

If we define x as the "number", then we can write this as:

3 = x/6

So we have a simple linear equation, to solve this, we just need to multiply both sides of the equation by 6, we will get:

3*6 = (x/6)*6

18 = x

We conclude that the solution is 6.

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Suppose a life insurance company sells a $280,000 one year term life insurance policy to a 24 year old female for $290.Then The expected value of this policy to the insurance company is $168.76

Probability that Person doesn't die = 0.999567. Profit = Revenue - Cost; Profit = $290 - 0 = $290

Probability that Person dies = 1 - 0.999567 = 0.000433. Profit = Revenue - Cost; Profit = $290 - $280000 = -$279710

Expected Value E(X) = ∑xp(x)

E(X) = $290*(0.999567) + (-$279,710* 0.000433)

E(X) = $289.87443 - $121.11443

E(X) = $168.76

Thus, the expected value of this policy to the insurance company is $168.76

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Diameter = 13.93771776 cm