the number of home theatres a company sells varies directly as the money spent on advertising. How many home theatres does the company sell for each $500 spent advertising? [ direct variations ] ​

Solution:

A.) [tex](-4-\sqrt{13},-4+\sqrt{13})[/tex]

Hope this helps!

Answer:

Let

x--------> the number

we know that

solve for x

Adds  both sides

Multiply by  both sides

therefore

the answer is

the number is 12

Step-by-step explanation:

The value of x and y by using the given expressions is x = -5/2 and y = -15/2.

What is an expression?

An expression can be defined as the combination of variables and constants with two or more operations applied to it. The operation can be addition, subtraction, multiplication and division.

Simplifying the expressions for x and y

The given expressions are:

x - y = 5           —--- 1

x + y = -10             —---- 2

Adding the expression 1 and 2, we get,

2x = -5

x = -5/2

Subtracting the expression 1 and 2, we get,

-2y = 15

y = -15/2

Hence, the value of x and y by using the given expressions is x = -5/2 and y = -15/2.

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The equation of the line that passes through the point (0,0) and is perpendicular to the line y=-2x+10 is .

We will be using the concept of slope and equation of straight line for this question. Here it has been said that the line passes through (0,0) which is the origin, so we know the point ([tex]x_{1},y_{1}[/tex]) is (0,0).This point will be required while solving the equation for the straight line. The line is said to be perpendicular to another line given by y=-2x+10. When two lines are parallel their slopes are equal and when two lines are perpendicular the product of their slopes is equal to -1. The slope of a line can be found from the equation of the line by dividing the coeeficient of x by the coefficient of y.

Slope of y=-2x+10 is -2

mx-2=-1⇒m=1/2

equation of a straight line,

[tex](y-y_{1} )=m(x-x_{1} )\\[/tex]

⇒y-0=[tex]\frac{1}{2}[/tex](x-0)

⇒y=[tex]\frac{x}{2}[/tex]

⇒2y=x

⇒2y-x=0

Thus the equation of the line that passes through (0,0) and is perpendicular to y=-2x+10 is 2y-x=0.

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Answer:

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Answer:

570

Step-by-step explanation:

570

The absolute difference that is between the loans paid as 570

We have the following details:

Po = $15000

loan a 5 year loan, interest = 8 percent and repayments = 304.15 dollars

Loan b

3 year loan, interest = 11 percent repayments = $491.08

Total number of repayments = 5 x 12 = 60

Total repayments = 304.15 dollars x 60

= $18249

The total interest that is paid for A would be

$18249 - $15000

= $3249

For the second loan

Total number of repayments = 3 x 12 months = 36

Total repayment = 36 x 491.08 = $17678.88

The total interest for the loan B would be: $17678.88 - $15,000

= $2678.88

Then the absolute difference between the paid loan would be

$3249 -  $2678.88 = 570.12

Hence we would have the absolute difference that is between the loans paid as 570.

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Answer:

[tex]\frac{341}{10} =34\frac{1}{10}[/tex]

Step-by-step explanation:

[tex]7\frac{3}{4} *4\frac{2}{5}[/tex]

→ Convert both fractions into improper

[tex]\frac{31}{4} *\frac{22}{5}[/tex]

→ Simplify

[tex]\frac{31}{2} *\frac{11}{5}[/tex]

→ Calculate

[tex]\frac{341}{10} =34\frac{1}{10}[/tex]

Answer:  The answer is -1

Step-by-step explanation:

-28/-4+-48/6

7-8

-1

Answer: -1

Step-by-step explanation:

-28 divided by -4 is 7

-48 divided by 6 is -8

7 - 8 would be a total of -1

Using the expected value of a discrete distribution, it is found that:

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

For the probabilities, we consider that it is given by the number of desired outcomes divided by the number of total outcomes.

For one bet, the distribution is given as follows:

Hence the expected value is given by:

E(X) = 578 x 5/6 - 300 x 1/6 = $431.67.

For two bets, the distribution is given as follows:

Hence the expected value is given by:

E(X) = 682 x 2/3 - 300 x 1/3 = $354.67.

For three bets, the distribution is given as follows:

Hence the expected value is given by:

E(X) = 945 x 1/2 - 300 x 1/2 = $322.5.

For four bets, the distribution is given as follows:

Hence the expected value is given by:

E(X) = 1312 x 1/3 - 300 x 2/3 = $237.33.

Hence, considering the greatest and the smallest expected values, we have that:

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Dots sold 65 T-shirts and 13 shorts

let the x represent the number of T-shirts and y and shorts

7x + 9y= 572.......equation 1

x= 5y........equation 2

substitute 4y for x in the equation

7(5y) + 9y = 572

35y  + 9y= 572

44y= 572
y= 572/44

y= 13

substitute 13 for y in equation 2

x= 5(13)

x= 65

Hence there 65 T-shirts and 13 shorts

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Answer:

h(10) = -25

Step-by-step explanation:

h(x) = -3x + 5

h(10) = -3(10) + 5

        = -30 + 5

        = -25

I hope this helps!

Answer:

9x

Step-by-step explanation:

=9x+8x+9x-8x-9x

=9x

Since the pairs of y values have singular and unique x values, the following set of points are a function.

Since an increase in one unit in the x value, yields an increase in one unit in the the y value, there exists a relation between these set of points.

[tex]y (x)= x + 3 \\ D_{f} ∈ [1,3][/tex]

Option: C

Th elastic potential energy of two decimal places is    k=60×1^2 N/M

Given that,

Spring has a potential energy of =30 J

we know that,

Energy of a spring=1/2 kx^2

here, x=1cm

x^2=0.01m

30=1/2 kx^2

30=1/2 k(0.01)^2

60=k(0.01)^2

k=60/(0.01)^2

k=60×1^2N/M

Hence the potential energy of two decimal places is k= 60×1^2 N/M

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Answer:

4 + -1 = 3, 3 - 5 = -2.

Step-by-step explanation:

Hope this helps!!

Answer:

1.5 pounds

Step-by-step explanation:

3/2 = 1.5

The scale drawing which is equal to 9 yards in real time is 12 cm.

Given that 4cm on the scale, drawing is equal to 3 yards in real-time

we have to find the scale drawing which is equal to 9 yards in real-time.

Let the scale drawing be 'x'

Now it can be written as

4 cm ------ 3 yards

x cm ------- 9 yards

Now we can divide this as

4/x = 3/9

By cross multiplication, we get

4 * 9 = 3 * x

x = 4 * 9 / 3

x = 12

Therefore, the scale drawing which is equal to 9 yards in real time is 12 cm.

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Answer:

[tex] \large \sf \: x=30[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

5/9 = x/54

Step 1: Cross-multiply.

5/9 = x/54

(5)*(54)=x*(9)

270=9x

Step 2: Flip the equation.

9x=270

Step 3: Divide both sides by 9.

9x/9 = 270/9

x=30

Answer: 40

Step-by-step explanation:

if 6 games = 24 tokens

then 1 game = 24/6=4

so 10 games = 4*10=40

Answer:

40

Step-by-step explanation:

24/6 = 4 tokens per game

4*10 games = 40

The equation when solved for t gives d/r

Subject of formula can be defined as a variable or element expressed in terms of other variables in an equation.

Iris also known as the variable that is being worked out in equation.

From the information given, we have the equation as;

d = rt

Where;

Now, let's make 't' the subject

Divide both sides by the coefficient of t

d/r = rt/r

t = d/r

Thus, the equation when solved for t gives d/r

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The complete question:

The formula below relates distance, rate, and time. Solve this formula for t.

d = rt

Answer: Irrational Number

Step-by-step explanation: It's Irrational because it cant be represented as a simple fraction.

1683 доллара - 102% . Найдем 1  процент и умножим его на 100%, тем самым получив ответ:

1) 1683 / 102 = 16.5 доллара - 1 % от всей зарплаты

2) 16.5 * 100 = 1650 - изначальная сумма, которую получал Андрей до повышения.

Ответ : 1650 $

Answer:

the answer is 7+1-7+0/xx{12

Step-by-step explanation:

the answer above stated is correctly corrected correct

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

For the given function :

[tex]\qquad \sf  \dashrightarrow \: f(x) = \dfrac{7}{x - 10} - 7[/tex]

f(x) is defined for all real values of x, except the value of x for which the denominator becomes 0, because if denominator is 0, the function at that instant will be undefined.

that is : f(x) is not defined when :

[tex]\qquad \sf  \dashrightarrow \: x - 10 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 10[/tex]

Hence, f (x) is defined for all real values of x except 10

It can be represented as :

[tex]\qquad \sf  \dashrightarrow \: f(x) : x \in R \sim \{10 \}[/tex]

Answer:

He now has 64 marbles.

Step-by-step explanation:

This is because 1/5 of 80 is 16.

The trip cost per person is 6 pounds.

Unit rate is the ratio of two different units, with the denominator as 1.

It means a rate for one of something.

We have,

Total members = 40

Each minibus cost = 30 pounds

Leisure centre cost = 150 pounds

Each minibus can carry = 15 people

The number of minibusses needed to carry 40 members:

= 40 / 15

= 2.67

= 3 minibusses.

This means we need  3 minibusses to carry 40 members.

Now,

The total cost for the trip:

= 150 pounds + 3 x 30 pounds

= 150 + 90

= 240 pounds

The cost per person:

= 240 / 40

= 6 pounds

Thus the trip cost per person is 6 pounds.

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The translation of the points as Z' ( - 8 , - 3 ), K' ( - 7 , 0 ) and K' ( - 5 , 0 ).

We are given the translation as:

(x , y)  → (x - 5 , y + 1)

Now we have some points:

Z (−3, –4)

K (−2, −1)

M (0, -1)

We need to translate these points.

For Z (−3, –4), we get the translation as:

Z (−3, –4) = Z' ( - 3 - 5 , - 4 + 1)

Z (−3, –4) = Z' ( - 8 , - 3 )

For K (−2, −1), we get the translation as:

K (−2, −1) = K' ( - 2 - 5 , - 1 + 1)

K (−2, −1) = K' ( - 7 , 0 )

For M (0, -1), we get the translation as:

M (0, -1) = K' ( 0 - 5 , - 1 + 1)

M (0, -1) = K' ( - 5 , 0 )

Therefore, we get the translation of the points as Z' ( - 8 , - 3 ), K' ( - 7 , 0 ) and K' ( - 5 , 0 ).

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Answer:

Step-by-step explanation: