John has a blueprint for a square-shaped office. He decides to change the layout and so draws a new blueprint such that the width of his office increased by 15 feet. The area of his office according to the new blueprint is given by the expression below, where x is the side length, in feet, of the original square-shaped office.

x^2+15x

Which statement best describes the term 15x?

the area of the office according to the old blueprint
the width of the office according to the new blueprint
the area added to the office according to the new blueprint
the area of the office according to the new blueprint

Answer:

2m+2n+7

Step-by-step explanation:

Given: Two polynomial

[tex]P_1=m+n+3[/tex]

[tex]P_2=m+n+4[/tex]

We need to find the sum of polynomial.

[tex]Sum=P_1+P_2[/tex]

[tex]\Rightarrow (m+n+3)+(m+n+4)[/tex]

write like term together  

[tex]\Rightarrow m+m+n+n+3+4[/tex]

Combine the like term

[tex]\Rightarrow 2m+2n+7[/tex]

Hence, The sum of two polynomial is 2m+2n+7

Final answer:

By adding 22 to -7, we find that the number 22 spaces to the right of -7 on the number line is 15.

Explanation:

The question asks for the number that is 22 spaces to the right of negative 7 on a number line. To find this, you can simply add 22 to negative 7. Here's the calculation: -7 + 22 = 15. Therefore, the number that is 22 spaces to the right of negative 7 is 15. To determine the number that is 22 spaces to the right of -7 on the number line, we need to add 22 to -7. Moving 22 spaces to the right indicates an increase in value by 22. Therefore, when we add 22 to -7, we get the final answer of 15. This calculation reflects the concept that moving to the right on the number line corresponds to increasing the numerical value, while moving to the left corresponds to decreasing it. In this case, starting from -7 and moving 22 spaces to the right results in a value of 15. Hence, 15 is the number that is 22 spaces to the right of -7.

Answer: [tex]81^{\circ}\ \text{ and }\ 9^{\circ}[/tex]

Step-by-step explanation:

We know that the sum of two complementary angles is [tex]90^{\circ}[/tex].

Given : An angle measures 72° less than the measure of a complementary angle.

Let x be the angle , then the measure of other angle will be x-72.

Since they area complementary , then we have

[tex]x+x-72=90\\\\\Rightarrow\ 2x=90+72\\\\\Rightarrow\ 2x=162\\\\\Rightarrow\ x=\dfrac{162}{2}=81[/tex]

Therefore, the measure of angles are :

[tex]81^{\circ}\ \text{ and }\ (81-72)^{\circ}=9^{\circ}[/tex]

Answer:

Zoya is 10 years old. Nelya is 40 years old.

The range of the function is {-1, 3, 15}.

The set of a function's potential output values is known as its range.

Given that, the domain of the function is {0,2,-6}.

The range is the set of the output of the functions for the given domain values.

The value of y for x = 0 is:

y = -2(0) + 3

y = 3

Similarly, the values of y for x = 2 and x = -6 are:

y = -2(2) + 3

y = -1, and

y = -2(-6) + 3

y = 15

Hence, the range of the function is {-1, 3, 15}.

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Answer:

A: x= -3

Step-by-step explanation:

The x- coordinate is of solution is -3.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

2x-3y = -12...........(1)

4x+ y= -10..............(2)

Now, multiply Equation (1) by 2 we get

4x - 6y = -24

4x + y = -10

________

 -7y = -14

y= 2

and, 4x+ y= -10

4x + 2 = -10

4x = -12

x= -12/4

x= -3.

Hence, the x- coordinate is -3.

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Answer:

decay

just answered this question.

Step-by-step explanation:

Answer:

decaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecaydecay

Step-by-step explanation:

Answer:

3 minutes polish 2 minutes hungarian

Step-by-step explanation:

I just did it on Kahn Academy, and this was correct.

Answer:

The scale factor of the dilation is [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

Let

z------> the scale factor

so

[tex]z=\frac{K'J'}{KJ}=\frac{K'H'}{KH}=\frac{J'H'}{JH}[/tex]

substitute the values

[tex]z=\frac{K'J'}{KJ}[/tex] ----->  [tex]z=\frac{1}{4}[/tex]

The scale factor is less than 1

therefore

The dilation is a reduction

The solution of  x  is √(S/6).

The formula to find the surface area of a cube with side lengths x is:

S = 6x2

To solve for x:

Divide both sides by 6: S/6 = x2

Take the square root of both sides to isolate x: x = √(S/6)

This should get you a hundred on the 4.11 quiz. :)

The correct option is the x-coordinate of the vertex representing the length.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.

It is written in the form of ax²+bx+c.

As it is given that the perimeter of the rectangular fencing is 1600 m.

Now, since the shape of the fence is rectangular, therefore, the x-coordinate of the vertex represents the length that results in the largest possible area, while the y-coordinate is the width of the rectangular fencing.

Hence, the correct option is the x-coordinate of the vertex representing the length.

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Final answer:

To find the dimensions of the barn's wall, we set up the equation w x (2w + 4) = 96 and solved for w to find the width is 8 feet. Then, we used the width to find the length, which is 20 feet.

Explanation:

To solve the problem of finding the dimensions of the rectangular wall of the barn, we need to set up and solve an algebraic equation. Let's call the width of the wall w feet. According to the problem, the length is 4 feet longer than twice the width, so we can express the length as 2w + 4 feet.

The area of the rectangle is given by multiplying the length by the width. We know the area is 96 square feet, so our equation to solve is w × (2w + 4) = 96.

Expanding this equation gives us 2w^2 + 4w - 96 = 0. This is a quadratic equation that we can solve by factoring, completing the square, or using the quadratic formula.

Factoring the quadratic equation, we look for factors of -96 that add up to 4. These factors are 12 and -8. So, we can write our equation as (2w + 12)(w - 8) = 0.

Setting each factor equal to zero gives us two possible solutions for w: w = -6 or w = 8. Since width cannot be negative, we discard w = -6 and keep w = 8 feet. The length is then 2(8) + 4 = 16 + 4 = 20 feet.

Therefore, the width of the barn's wall is 8 feet, and the length is 20 feet.