Rectangular prism A measures 2 inches by 7 inches by 8 inches. Rectangular prism B measures 1 inches by 5 inches by 10 inches.


Rectangular Prism A:


Surface Area: __inches²

Volume: __inches³

Surface Area to Volume Ratio: (Enter as an improper fraction)


Rectangular Prism B:


Surface Area: __inches²

Volume: __inches³

Surface Area to Volume Ratio: (Enter as an improper fraction)

Answer:

[tex]\huge\boxed{\sf |AB|=10 \ units}[/tex]

Step-by-step explanation:

Coordinate of A = [tex](x_1,y_1)[/tex] = (-7,-6)

Coordinate of B = [tex](x_2,y_2)[/tex] = (1,0)

We will use distance formula to find the length of AB.

[tex]|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\|AB|=\sqrt{(1-(-7))^2+(0-(-6))^2} \\\\|AB|=\sqrt{(1+7)^2+(6)^2} \\\\|AB|=\sqrt{(8)^2+36} \\\\|AB|=\sqrt{64+36} \\\\|AB|=\sqrt{100} \\\\\boxed{|AB|=10 \ units}\\\\\rule[225]{225}{2}[/tex]

Considering that 12 is a root of the function, the value of coefficient Q is of 12.

It means that f(x) = 0.

In this problem, the function is given by:

f(x) = x² - 13x + q.

Since 12 is a root, we have that f(12) = 0, hence:

12² - 13 x 12 + q = 0

q - 12 = 0.

q = 12.

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Answer:

13.2 Kilometers an Minute, or 220 Kilometers an Hour

Step-by-step explanation:

26,400 divided by 2 = 13.2 (Minutes) Divided by 60 = 220 (Hours).

The system of linear equations that best represents the situation are:

z+y=18

3z +2y=44

In order to determine the values of the two types of cheese, two set of linear equations can be formed from the question. The equations have to be solved together using either the elimination , substitution or graphical methods.

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Answer:

f(-2) = 14

Step-by-step explanation:

put -2 where x is

f(x) = 3x²-x

f(-2) = 3(-2)²-(-2)

f(-2) = 3(4)+2

f(-2) = 12+2

f(-2) = 14

Answer:

B

Step-by-step explanation:

the symbol in the x < 0 has a line under it meaning it is a closed circle, and the other equation does not, so it is an open circle. And since the question has (or) in it, it means that the arrows should be facing away from eachother.

Answer: 13.7 ft

Step-by-step explanation:

Use Pythagorean theory to find radius

C^2 - B^2 = A^2

We know the hypotenuse (cone to edge) is 15

We will call that C

We know the height is 6

We will call that B

We are looking for A or radius

15^2 - 6^2 = A^2

225 - 36 = A^2

189 = A^2

Take square root of both sides

13.7 = A (radius)

Answer:

4 units

Step-by-step explanation:

formula

d = √(x2-x1)^2 + (y2-y1)^2

then fill in the spots

d = √(-5.4+5.4)^2 + (-5.5+9.5)^2

the subtraction sign became an addition sign due to it being a double negative

Hope this helped

Answer:

You count the cat's ears as the area of a right triangle, the middle as the area of a rectangle, and the cat's chin as the area of a semi-ellipse.

The equation is x² + 11x = 12. Here x represents the width of the decorative border and no, it is not reasonable to be 2.5 inches wide.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have an area of border  48 square inches.

Menu dimensions without border =  13-inch by 9-inch

The area of the border can be expressed by the equation:

area of border = area of rectangle with border—area of rectangle without

                            border

48 = (13 + 2x)(9 + 2x) - 13×9

[tex]\rm 48=4x^2+44x[/tex]

After simplification:

[tex]\rm 4x^2+44x-48=0[/tex]

or

x² + 11x = 12

Find the solution of the above quadratic equation:

x = 1 or x = -12(width cannot be negative)

Width should be 1 inches.

We have given x = 2.5 it is not reasonable for the border to be 2.5 inches wide. Due to the cost of printing, the border should have an area of 48 square inches.

Thus, the equation is x² + 11x = 12 here x represents the width of the decorative border and no, it is not reasonable to be 2.5 inches wide.

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See below for the proof that ∠1 and ∠14 are supplementary angles

The attached diagram represents the missing information in the question.

The given parameters are:

The next step in the proof is as follows:

∠2 and ∠14 are corresponding angles.

This means that:

∠2 = ∠14

Recall that:

∠1 and ∠2 are supplementary angles

This means that:

∠1 + ∠2 = 180

Substitute ∠2 = ∠14

∠1 + ∠14 = 180

Supplementary angles add up to 180

Hence, ∠1 and ∠14 are supplementary angles

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Answer:

Step-by-step explanation:

the answer is D

Answer:

B: A square is a quadrilateral

Step-by-step explanation:

Using it's concept, it is found that the probability that everyone in a simple random sample of 100 young adults owns a landline is given by:

[tex]p = (0.25)^{100}[/tex]

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 25% of the adults own a landline, and the probabilities for each adult are independent, hence the probability that everyone in a simple random sample of 100 young adults owns a landline is given by:

[tex]p = (0.25)^{100}[/tex]

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Answer:

a

Step-by-step explanation:

The volume of each individual brick is 72 cubic inches.

The volume of a rectangular prism of height H, width W, and length L is given by:

V = L*H*W

In this case we have:

Then, replacing these in the volume equation, we get:

V = (8 in)*(4 in)*(2.25 in) = 72in³

So the correct option is the second one.

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Answer:

The volume of each individual brick is 72 cubic inches.

Step-by-step explanation:

How to get the volume of each brick?

The volume of a rectangular prism of height H, width W, and length L is given by:

V = L*H*W

In this case we have:

L = 8in

W = 4in

H = 2.25 in

Then, replacing these in the volume equation, we get:

V = (8 in)*(4 in)*(2.25 in) = 72in³

So the correct option is the second one.

Answer:

D.) 7 and -4

Step-by-step explanation:

Coefficients are numbers placed directly before a variable.

(7) is a coefficient because it is placed before x².

(-4) is a coefficient because it is placed before x. The negative is included.

(6) is not a coefficient because it is not altering any variable through multiplication/division.

The value of the digit 5 in the tenths place of 3.545 is 100 times the value of the digit 5 in the thousandths place.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We have:

Evan has a bag of apples that weighs 3.545 pounds.

The value of the digit 5 in the tenths place of 3.545 is 0.500

The value of the digit 5 in the thousandths place of 3.545 is  0.005

Take the ratio of both values:

tenths place value/thousandths place value =  0.500/0.005

tenths place value/thousandths place value =  100

tenths place value = 100(thousandths place value)

Thus, the value of the digit 5 in the tenths place of 3.545 is 100 times the value of the digit 5 in the thousandths place.

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The better deal based on the information is mortgage A as it's cheaper.

From the information given, the loan amount for mortgage A will be:

= 3% × $4500

= $135

The loan amount for mortgage B will be:

= 6% × $7500

= $450

From the information, the better deal is mortgage A.

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The ratio of any side and hypotenuse is always less than 1.

The question seems incomplete

The options are not given the options are

a. 1

b. 0.5

c. 2

[tex]sin\theta=\frac{Opposite side}{hypotenuse}[/tex]

Therefore, the ratio of any side and hypotenuse is always less than 1. Now, in the case of 0 or 90 degrees, the figure is no longer a triangle because one of the sides ceases to exist while the other side coincides with the hypotenuse.

This is the reason that in these extreme cases, sin and cosine take values 0 or 1.

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Answer:

Hey!

Your Answer Is,

No Triangles: A, C

One Triangle, F, D

Many Triangles: B,E

I hope this helps you!

Step-by-step explanation:

Answer:

Your answer is 3282.34

Step-by-step explanation:

1/3 x 3.14 x 14 ^2 x 16

this is all you have to do really.

Answer: ~96.83°

Step-by-step explanation:

1) It's obvious that the largest angle is the opposite to the largest side.

▪︎ QR = 18 (the largest side)

=> <QPR is the largest angle

2) Cosine Rule:

▪︎ QR^2 = QP^2 + PR^2 - 2*QP*PR*cos(QPR)

▪︎ 18*18 = 13*13 + 11*11 - 2*13*11*cos(QPR)

▪︎ 324 = 169 + 121 - 286*cos(QPR)

▪︎ 34 = -286*cos(QPR)

▪︎ cos(QPR) = -34/286

▪︎ <QPR = arccos(-34/286) = 96.827...°

Answer:

7

Step-by-step explanation:

m=pendiente

por lo tanto:

pendiente=7

Hii!

__________________________________________________________

Answer:

Slope = 7! ^^

Step-by-step explanation:

Note that the equation is given to us in slope intercept form.

The slope intercept formula is y=mx+c.

m denotes the slope

c denotes the y intercept.

/--------------\

The slope of the line that we are working with is 7.

Remember how I said that the slope of the line y=mx+c is m?

Similarly, the slope of the line y=7x-3 is 7! ^^

--

Hope that this helped! Best wishes.

--

The quotient of the expression [tex]\frac{3y+2}{3y} divided \frac{6y^{2} + 4y}{3y + 2}[/tex]  is 3y + 2 / 6y

The quotient of the expression can be found as follows:

3y + 2 / 3y ÷ 6y² + 4y / 3y + 2

Therefore,

3y + 2 / 3y × 3y + 2 / 6y² + 4y

Hence,

3y + 2 / 3y × 3y + 2 / 2y(3y + 2)

Therefore,

1 / 3y × 3y + 2 / 2

Hence,

3y + 2 / 2(3y)

3y + 2 / 6y

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Answer: (0, 1), (-1, -3)

Given two equation's:

Solve them simultaneously:

[tex]\sf 2x^2 + 6x + 1 = -4x^2 + 1[/tex]

[tex]\sf 2x^2 + 4x^2 = 1 - 1[/tex]

[tex]\sf 6x^2 + 6x = 0[/tex]

[tex]\sf 6x(x + 1) = 0[/tex]

[tex]\sf 6x = 0, \ x + 1 = 0[/tex]

[tex]\sf x = 0, \ x = -1[/tex]

(a) When x = 0,     y = −4(0)² + 1 = 1

(b) When x = -1,    y = -4(-1)² + 1 = -3

Solution: (x, y) → (0, 1), (-1, -3)

Answer:

System of equations

[tex]\large \begin{cases}y=2x^2+6x+1\\y = -4x^2+1\end{cases}[/tex]

To solve the given system of equations, use the substitution method:

[tex]\large\begin{aligned}2x^2+6x+1 & = -4x^2+1\\2x^2+6x+1+4x^2-1 & = 0\\6x^2+6x & = 0 \\6x(x+1) & = 0\\\implies x+1 & = 0 \implies x=-1\\\implies 6x & = 0 \implies x=0\end{aligned}[/tex]

Therefore the x-values of the solutions are:

        [tex]\large \begin{aligned}x & =-1\\x & =0\end{aligned}[/tex]

Substitute the found values of x into the second equation to find the y-values:

[tex]\large \begin{aligned}x & =-1 & \implies &-4(-1)^2+1 =-3 & \implies & (-1,-3)\\x & =0 & \implies & -4(0)^2+1 =1 & \implies & (0,1)\end{aligned}[/tex]

Therefore, the solutions of the system of equations are:

(-1, -3) and (0, 1)

Answer:

g= 6.5

Step-by-step explanation:

O.25(g+1.5) = 2

(g+1.5) = 2/0.25 divide both sides with 0.25

g+1.5 = 8

g = 8-1.5

g = 6.5

Answer:

Step-by-step explanation:

(15 - 5)/(19 + 19)= 10/38= 5/19 is the slope

y - 5 = 5/19(x + 19)

y - 5 = 5/19x + 5

y = 5/19x + 10

The commission on the sales will be $118.2.

The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.

Given that:-

Elijah Henson sold $1,576 worth of merchandise. his commission rate is 7 1/2%

The commission amount will be:-

7.5 % of $1576 will be calculated as:-

Commission = 1576 x 0.075

Commission = $118.2

Therefore the commission on the sales will be $118.2.

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