what are the dimensions of a rectangle with an area equal to the parallelogram with the vertices (6,21) (14,15) (6,0) (-2,6)

The required function is (fog)(x) = x^2 – 5x – 19  

We have been given two functions which are:

 f(x) = x^2 – 3x – 23

 g(x) = x – 1

We need to find (fog)(x) which is also equal to f(g(x)).

In this, we have to replace x with the function g(x) in the function, f(x). numerically

    f(g(x)) = g(x)^2 – 3g(x) – 23    

Now we will write the value of g(x) in the above equation. We will get

         f(g(x)) = (x-1)^2 – 3(x-1) – 23

         f(g(x)) = x^2 + 1 – 2x – 3x + 3 – 23

         f(g(x)) = x^2 – 5x – 19

Hence  (fog)(x) = x^2 – 5x – 19  is the required function.

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Answer:

7/8

Step-by-step explanation:

This is a counting exercise. Think of the 200 persons that you have to separate into two groups:

1) A group that satisfies the condition of the question

2) A group that does not satisfy the condition

Then, count how many persons are in group 1, and divide that by the total (200). That is your probability.

For (i), you will find 175 persons in group 1. Even though there are many persons with not blue AND not fair hair, they are only in the group once, so don't count them double.

Then 175/200 = 7/8

In fact, you could reverse the question by counting how many people do not satisfy the condition. That group are the persons that have both blue eyes and fair hair. That is the only way to not satisfy the condition. That amount is 25, you can read it from the table.

The chance of being in that group is 25/200 = 1/8.

P(group 1) + P(group 2) = 1

So you now have two ways of getting your answer.

P(group 1) = 1 - 1/8 = 7/8.

Answer: x=1, AC=23

Step-by-step explanation:

ABC=AB+AC+BC

53=5x+18+5x+18+7

53=10x+36+7

53=10x+43

10x=10

x=1

AC=5x+18

AC=5(1)+18

AC=23

The value of the expression is −10,077,696

The expression is given as:

negative one sixth cubed all raised to the power of negative 3?

Rewrite properly as:

(-1/6^3)^-3

Evaluate the exponent of 6 to 3

So, we have:

(-1/216)^-3

Apply the law of negative exponent

So, we have

(-216)^3

Evaluate the exponent

−10,077,696

Hence, the value of the expression is −10,077,696

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The algebraic expression of the mathematical statement given as "The difference of a number squared and 6" is  x^2 - 6

Expressions are mathematical statements that are represented by variables, coefficients and operators

The mathematical statement is given as

The difference of a number squared and 6

Represent the number with x

So, the mathematical statement becomes

The difference of a number squared and 6 ⇒ The difference of x squared and 6

x squared implies x^2

So, the mathematical statement becomes

The difference of a number squared and 6 ⇒ The difference of x^2 and 6

difference means minus (-)

So, the mathematical statement becomes

The difference of a number squared and 6 ⇒  x^2 - 6

Hence, the algebraic expression of the mathematical statement given as "The difference of a number squared and 6" is  x^2 - 6

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For the given sample data, 42, 25, 86, 30, 25, 15, 42, 42, the mode is 42.

In statistics, the mode, denoted by Mo, refers to the most frequent value or values in the data set. If all the numbers in the data set appears only once, then the data set has no mode.

For the given sample data,

42, 25, 86, 30, 25, 15, 42, 42

the number 42 appears thrice, 25 appears twice and the rest appears only once.

The number 42 appeared the most frequent among all the other data.

Hence, the mode of the data set that contains 42, 25, 86, 30, 25, 15, 42, 42 is 42.

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Answer:

I think y is 29

Step-by-step explanation:

It's what the results gave me

Answer:

(3) 36

Step-by-step explanation:

3x + 1 = 9

Minus 1 from both sides.

3x = 8

Divide both sides by 3.

x = 2 2/3

Plug it in.

12 (2 2/3) + 4

32 + 4

36

Answer:

Not sure, is there a problem or only the rant? lol. I'd appreciate my first brainliest though.

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

If you use -7 the LHS will get cancelled.

x + 7 = 19

or, x + 7 - 7 = 19 - 7

or, x = 12

The Total number of miles that Laney walked is 65 miles.

From the information, Laney walks 13 miles to school from her house and rides the bus home and she walked five days last week.

Therefore, the total number of miles that he walked will be:

= 13 × 5

= 65 miles.

Therefore the miles is 65 miles.

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Answer:

2

Step-by-step explanation:

Because 2 goes into 24, 36 and 50.

The ratio of the volume of the cylindrical tank to its surface area will be r / 2.

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

Let r be the radius and h be the height of the cylinder.

Then the volume of the cylinder will be

V = π r²h cubic units

Then the surface area of the cylinder will be

SA = 2πrh square units

Then the ratio of the volume of the cylindrical tank to its surface area will be

V / SA = π r²h / 2πrh

V / SA = r / 2

The ratio of the volume of the cylindrical tank to its surface area will be r / 2.

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Answer:

C

Step-by-step explanation:

given the zeros x = a and x = b then the corresponding factors are

(x - a) and (x - b)

then f(x) is the product of these factors

given zeros x = 6 and x = - 4 then the factors are

(x - 6) and (x - (- 4)) , that is (x - 6 and (x + 4) , then

f(x) = (x - 6)(x + 4)

The bill for a person who uses 560 kWh in a month is $74. Therefore, option D is the correct answer.

The given functions are

b(x) = 0.15x;  x ≤ 360

b(x) = 0.10(x - 360) + 54;  x > 360

Functions are the fundamental part of calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h.

For a person who uses 560 kWh, it means that:

x > 360

So, we use the following function to determine the bill

b(x) = 0.10(x - 360) + 54

Substitute 560 for x

b(560) = 0.10(560 - 360) + 54

⇒b(560) = 74

Hence, the bill for a person who uses 560 kWh in a month is $74. Therefore, option D is the correct answer.

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Your question is incomplete, probably the complete question/missing part is:

A power company calculates a person's monthly bill from the number of kilowatt-hours ( Nh), x, used. The function b(x)= 0.15x, and x≤360. 0.10(x-360)+54, and x>360 determines the bill. How much is the bill for a person who uses 560 kWh in a month? A. $84 B. $54. $64 D. $74.

Answer:

SK: 32

Step-by-step explanation:

Subtract SY - KY to find SK

45 - 13 = 32

Answer:

5 years. Correct answer is D.

Step-by-step explanation:

The value of x from the given line segment is 1 2/3.

Given that, line segment AC = 5 and line segment AB = 3x - 5.

We need to find the value of x.

A line segment is a part of a line that has two endpoints and a fixed length. It is different from a line that does not have a beginning or an end and which can be extended in both directions.

Since point B is the midpoint of the line segment AC.

AB=BC=3x - 5

Now, AC=AB+BC

⇒5=3x - 5+3x - 5

⇒6x=15

⇒x=15/6

⇒x= 5/3

⇒x=1 2/3

Therefore, the value of x from the given line segment is 1 2/3.

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For 5 months site b be less expensive than site a.

From the given question we get to know that on-site $50 is a must and %5 will be paid per month, and on-site b $15 will be per to promote his brand and there is no start-up fee.

Let's take the n to be x.

We have to find how many months will b site be less expensive than site a.

So total expenses for site a = 50 + 5x

and total expenses for site b = 15x

We get an equation

50+5x =15x

10x=50

x=5

Therefore for 5 months site b will be less expensive than site a.

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Answer:

x = 60°

Step-by-step explanation:

See picture below.  When two parallel lines are cut by a transversal there are some special relationships.

Answer:

x = 60°

Step-by-step explanation:

∠ ABO and ∠ CBO are a linear pair and sum to 180° , that is

∠ ABO + ∠ CBO = 180°

150° + ∠ CBO = 180° ( subtract 150° from both sides )

∠ CBO = 30°

∠ XYO and ∠ CBO are alternate angles and are congruent , so

∠ XYO = 30°

∠ XOY and ∠ COY are a linear pair and sum to 180° , then

∠ XOY + ∠ COY = 180°

∠ XOY + 90° = 180° ( subtract 90° from both sides )

∠ XOY = 90°

the sum of the 3 angles in Δ XOY = 180° , that is

x + 90° + 30° = 180°

x + 120° = 180° ( subtract 120° from both sides )

x = 60°

With 70% off the regular price, a dishwasher, regularly priced at $519.89, will be $155.97 only. The answer is C.

Discount is the deduction in the price of a good or service. When this reduced price is expressed in percentage then we call it a discount rate.

If the discount is given in percent, then the amount of discount can be found by using the formula:

Amount of Discount = Regular Price × Rate of Discount

If the regular price of a dishwasher is $519.89, and the discount rate is 70%, using the formula, solve for the discount value.

Amount of Discount = $519.89 x 70%

Amount of Discount = $519.89 × 0.70

Amount of Discount = $363.92

To get the final price of the dishwasher, subtract the discount value from the original or regular price.

price = $519.89 - $363.92

price = $155.97

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Approximately 6.8 hours Alyssa spends on the train per day.

Given that, Alyssa spent 365 hours commuting on the train over the course of 54 days.

We need to find the number of did Alyssa spend on the train per day.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of hours Alyssa spends on the train per day be x.

Now, x=365/54

=6.759≈6.8 hours

Therefore, approximately 6.8 hours Alyssa spends on the train per day.

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If line PQ bisects line ST at point R and SR=3x+3 and ST=30 then the value of x = 4.

As given in the question,

Line PQ bisects ST at point R

SR=3x+3

ST=30

R is the midpoint of ST as PQ bisects ST this implies

Line SR=1/2 of line (ST)

⇒SR=ST/2

Substitute the value of SR and ST in the given condition

  3x+3=30/2

⇒3x+3=15

Subtract 3 from both the sides

⇒3x=12

Divide both the side by 3

⇒3x/3=12/3

⇒x=4

Therefore, for the  line PQ bisects line ST at point R and SR=3x+3 and

ST=30 then the value of x is equal to 4.

The complete question is:

If the line PQ bisects line ST at point R. SR=3x+3 and ST = 30. Find x.

a. x= 8      b. x =6           c. x =2          d. x= 4

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For the graphed parabola we can see that the maximum is at (3, 2), then the x-value is x = 3.

For a function f(x), we define the maximum as a value y = f(x₀), such that:

f(x₀) ≥ f(x) for every value in the domain.

In the case of the graph is really easy to identify the maximum, in this case, it is in the vertex of the parabola.

We can see that the maximum is on the point (3, 2)

Then it is at x = 3, y = 2, from that, we can see that the x-value of the graphed function is x = 3.

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Usando una función lineal, tenemos que:

Con cada año adicional, la cantidad en la cuenta es incrementada en 60.

Una función lineal es modelada por:

y = mx + b

En el cual:

En este problema, hay que la pendiente es de 60, puesto que en cada año la cantidad aumenta en $60, por eso:

Con cada año adicional, la cantidad en la cuenta es incrementada en 60.

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Answer:

The graph in the top right hand corner.

Hope this helps :)

Step-by-step explanation:

The formula y = mx + b

shows that m is the slope and b is the y-intercept.

m = 34

b = - 3

So to find the equation of the graph I looked at the y-intercept which is -3 and the graph in the right hand corner has a y-inyercept of -3 so that graph represents the equation y = 34x - 3

Reason:

The equation is y = (3/4)x - 3 which is in y = mx+b form

m = slope = 3/4

b = -3 = y intercept

The y intercept of -3 means the point (0,-3) is on the line. Start at this point and go up 3, then to the right 4 to arrive at (4,0) which is the x intercept. The motion "up 3, right 4" is directly from the slope 3/4

slope = rise/run = 3/4

rise = 3 = go up 3

run = 4 = go right 4