Find the volume of the rectangular prism.
8 cm
8 cm
3 cm

Answer:

x + 7y = 34

Step-by-step explanation:

the altitude through C meets the opposite side AB at right angles

calculate the slope of AB using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A (2, - 4 ) and (x₂, y₂ ) = B (3, 3 )

[tex]m_{AB}[/tex] = [tex]\frac{3-(-4)}{3-2}[/tex] = [tex]\frac{3+4}{1}[/tex] = [tex]\frac{7}{1}[/tex] = 7

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{7}[/tex] , then

y = - [tex]\frac{1}{7}[/tex] x + c ← partial equation of the altitude

to find c substitute C (- 1, 5 ) into the partial equation

5 = [tex]\frac{1}{7}[/tex] + c ⇒ c = 5 - [tex]\frac{1}{7}[/tex] = [tex]\frac{35}{7}[/tex] - [tex]\frac{1}{7}[/tex] = [tex]\frac{34}{7}[/tex]

y = - [tex]\frac{1}{7}[/tex] x + [tex]\frac{34}{7}[/tex] ( multiply through by 7 )

7y = - x + 34 ( add x to both sides )

x + 7y = 34 ← equation of altitude in standard form

Answer:

Find the slope by putting your rise over your run. Make sure to label your points.

Step-by-step explanation:

Step 1:

First count the number of stickers on a page

There are 12 stickers in a page

Step 2

There are 30 pages,

Hence, the number of stickers in 30 pages = 30 x 12 = 360

Final answer

Dana has 360 stickers in all

A function is defined as a relation between a set of inputs having one output each.

The value of y when x = 48 is 96.

A function is defined as a relation between a set of inputs having one output each.

The inputs are called the domain of the function.

The outputs are called the range of the function.

We have,

The value of y varies directly with x.

y = 8, when x = 4.

Domain = input = 4

Range = output = 8

Now,

We can say that y is a function.

i.e y = 2x.

Where x = input = domain and y = range = output.

The value of y when x = 48:

y = 2x

y = 2 x 48

y = 96

Thus,

The value of y when x = 48 is 96.

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Answer:

2.6

Step-by-step explanation:

cause it is 2.6299999999

2.629 to the nearest tenth is 2.6.

Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.

Given:

A decimal number,

2.629.

Here, 2 is the whole number component and 0.629 is the fractional component part.

To round the number to the nearest tenth:

The number in tenth place is 6.

And the value right next to 6 is 2.

6 > 2.

So, the number will stay the same.

2.629 = 2.63

Then 2.63 = 2.6 to the nearest tenth.

Therefore, 2.6 is the required decimal.

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Answer:

b = [tex]\frac{g}{(d^{2}+4) }[/tex]

Step-by-step explanation:

([tex]d^{2}[/tex] + 4)b = g  Divide both sides by ([tex]d^{2}[/tex] + 4)

b = [tex]\frac{g}{(d^{2}+4) }[/tex]

Solutions are given below:

1. (14x^(5))/(5y^(2))=(2x^(4))/(10y) → x=y/14

2. ((x)/(y))((4y)/(3x))=((6y^(2))/(8x^(3))) → [tex]x=\frac{\sqrt[3]{36y^{2} } }{4}[/tex]

3. (5(y+6))/(2(xy-3))]=((y+6)/(4(xy-3))) → (-∞,∞)

4. ((x^(2)-4)/(x^(2)+5x+4))=((x+2)/(x+1)) → x=-2

What is a solution?

Solutions are given below:

1. (14x^(5))/(5y^(2))=(2x^(4))/(10y) → x=y/14

2. ((x)/(y))((4y)/(3x))=((6y^(2))/(8x^(3))) → [tex]x=\frac{\sqrt[3]{36y^{2} } }{4}[/tex]

3. (5(y+6))/(2(xy-3))]=((y+6)/(4(xy-3))) → (-∞,∞)

4. ((x^(2)-4)/(x^(2)+5x+4))=((x+2)/(x+1)) → x=-2

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Answer:

AC=KM

AB=KL

BC=LM

Step-by-step explanation:

Answer:

AC=MK

AB=KL

BC=LM

This are corresponding sides

Answer:

2, 9, 12

Step-by-step explanation:

We know that the first number is ten less than the third number and that the third number is one more than the first number and second number combined. Because of this, our third number has to be one away than the combination of the first two numbers. Now, we just have to see the numbers of the first two values and the first number is 10 less than the third number. You can mostly guess the numbers once you understand. I hope that this didn't confuse you more. Hope this helps!

Answer:

y=2(x−3)

Step-by-step explanation:

The height of the pyramid = BC = 14 units

It is a three-dimensional shape that has a polygonal base and flat triangular faces which joins at the apex at the top of the pyramid.

We have,

Base edge length = 14 units

From the figure below,

The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 14 units so,

We get,

AC = CD = AD = 14 units _____(1)

All sides in an equilateral triangle are equal.

In the right triangle ABC,

tan 45° = BC / AC

tan 45° = 1

1 = BC / AC _____(2)

From (1) and (2) we get,

1 = BC / 14

BC = 14 units

The height of the pyramid = BC = 14 units

Thus,

The height of the pyramid is 14 units.

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Answer: C 14 UNITS

Step-by-step explanation:

Answer:

y=3x+15

Step-by-step explanation:

she can make 3 a day so 3x and she already has 15 so the line crosses the y-axis  at 15

Answer:

wait, its r + 0.5

Step-by-step explanation:

∠1 and ∠8 are supplementary angles,  ∠5 and ∠6 are Congruent, ∠6 and ∠8  are Congruent .

Supplementary angles are those angles that sum up to 180 degrees. Two or more angles that are identical to each other are referred to as Congruent angles.

We are provided with the figure shown in the question. We need to name the angles provided or need to tell the relation between two angles.

∠1 and ∠8 are supplementary angles as there sum is 180°.

∠1 + ∠8 = 180°

So, angle ∠1 and ∠8 are supplementary.

∠5 and ∠6 are Congruent as they  are identical to each other.

∠5 = ∠6

∠6 and ∠8  are Congruent as they  are identical to each other.

∠6 = ∠8

Thus, we can conclude that ∠1 and ∠8 are supplementary angles, ∠6 and ∠8  are Congruent , ∠5 and ∠6 are Congruent.

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The solution is x ≤ -2 or x ≥ 10.

The inequalities are given in two parts which can be combined to form a single inequality as follows,

13 ≤ -5x + 3 or -47 ≥ -5x + 3

⇒ 13 ≤ -5x + 3 ≤ -47

Let's solve this.

First subtract 3 from all terms,

⇒ 10 ≤ -5x ≤ -50

Divide by 5 on all terms,

⇒ 2 ≤ -x ≤ -10

Multiply with (-1) on all terms, but then the inequality gets reversed as,

⇒ -2 ≥ x ≥ 10

We can now split the inequalities into two to make sense,

⇒ x ≤ -2 or x ≥ 10.

This solution can be graphed on a number line by darkening a line on the number line from 10, extended to the right of it. Then darken the line from -2, extend it to the left side.

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The augmented matrices for each system are given as follows:

1.

[ -9 4 | 1 ]

[ 7 0 | 14]

2.

[ -5 6 | 1 ]

[ 5 -2 | 9]

For a system of n variables, the first n columns of the matrix are composed by the coefficients of the variable of the system.

The two systems in this problem have variables x and y, hence:

Then the last column is composed by the values on the right side of the equations, that is, the results of the operations.

The second equation of the first system is:

7x - 9 = 5 -> 7x + 0y = 14 (this format is needed to build the augment matrix.

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The equation is 15 + 0.5x = 25 + 0.25x and number of miles is 40.

While writing the equation for green and blue cars, one time fee will be added with cost of driving for miles. Let us assume the number of miles to be x.

Firstly writing the equation for green car -

Cost = 15 + 0.5×x

Now writing the equation for blue car -

Cost = 25 + 0.25×x

The number of miles for same cost will be calculated by equating the expressions.

15 + 0.5x = 25 + 0.25x

0.5x - 0.25x = 25 - 15

Performing subtraction on Left Hand Side and Right Hand Side of the equation

0.25x = 10

Shifting 0.25 to Right Hand Side of the equation

x = 10 ÷ 0.25

Performing division on Right Hand Side of the equation

x = 40

So, if both the cars travel 40 miles, the rental cost will be same. The correct equation for calculation is 15 + 0.5x = 25 + 0.25x.

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Answer:37.5

Step-by-step explanation:

so basically a square has four sides so 150 divided by 4

The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m, then the mass of one the bodies is

[tex]m_{1} = 1.88(10)^{-7}[/tex]

The amount of matter that makes up every object or body is the greatest way to understand mass. Everything that we can see has mass. Examples of objects with mass include a table, a chair, your bed, a football, a glass, and even air. The mass of a thing determines whether it is light or heavy.

Given that : The mass of two bodies are attracted with a force of 745N.if their distance of separation is 70.3m

F=[tex]G\frac{m_{1} .m_{2} }{r^{2} }[/tex]

[tex]m_{1} =\frac{F.r^{2} }{Gm_{2} }\\ m_{1} =\frac{745.(70.3)^{2} }{6.7(10)^{-11}.2050 }\\\\[/tex]

[tex]m_{1} =\frac{26881.3(10^{7} )}{13735}[/tex]

[tex]m_{1} = 1.88(10)^{-7}[/tex]

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Carly needs to perform 33 additional sales to earn 100 this week.

Firstly forming the expression as per the weekly earning and individual payment on extra sale. Writing the expression -

Amount earned = 35 + 2×number of sales

Keep the value of amount earned in mentioned formula to find the number of sales.

100 = 35 + 2×number of sales

2×Number of sales = 100 - 35

Performing subtraction on Right Hand Side of the equation

2×Number of sales = 65

Shifting 2 to Right Hand Side of the equation

Number of sales = 65/2

Performing division on Right Hand Side of the equation

Number of sales = 32.5

Round off the number

Number of sales = 33

Therefore, she needs to make 33 additional sales.

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Answer:

Let the length be x. The breadth be y Area=xy. On reducing breadth by 4 new breadth will be (y-4). X(y-4)=xy-240. Xy-4x=xy-240. -4x=-240. X=60. Hence rectangle is 60cm long

Step-by-step explanation:

hope it will help

Hello!

What is the standard form of the parabola:

 [tex]\hookrightarrow y=(x-h)^2+k[/tex]

          => h: x-coordinate of vertex

          => k: y-coordinate of vertex

Since our vertex is (1,-8)

 [tex]\hookrightarrow \text{Our equation is }y=(x-1)^2}-8[/tex]  <== Answer

Hope that helps!

If [tex]$f(x)=4^x$[/tex] and [tex]$g(x)=4^{x+1}-3$[/tex] be the two functions then Horizontal translation 1 units right.

An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Let [tex]$f(x)=4^x$[/tex] and [tex]$g(x)=4^{x+1}-3$[/tex]

We can see that in place x , we have x + 1

so, f(x) exists shifted right side by 1 unit

and we can see that 2 exists added to y-value

so, it exists shifted upside by 2 units

horizontal translation 1 unit right

vertical translation 2 units up

Therefore, the correct answer is option e) Horizontal translation 1 units right.

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Answer:

-1

Step-by-step explanation:

-8+10÷(-2)

2÷(-2)

-1

Answer:

The answer is 18^4

Step-by-step explanation:

Its the answer

Answer:

a = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

since (2, - 3 ) lies on the graph then it makes the equation true.

substitute x = 2 and y = - 3 into the equation and solve for a

2(- 3) = a(2) - 7 , that is

- 6 = 2a - 7 ( add 7 to both sides )

1 = 2a ( divide both sides by 2 )

[tex]\frac{1}{2}[/tex] = a

Answer:

See below

Step-by-step explanation:

To find pole height

for a right triangle

sin 38 = opposite leg / hypotenuse = height /15 m

sin 38 = height / 15

15 sin 38 = height = 9.2 meters

To find rope DC

  Use pythagorean theorem ( you have leg1 = height and leg 2 = 10.7)

     DC ^2 = 9.2^2  + 10.7^2

     DC = 14.1 m

1) We can solve this problem by setting up a System of Linear Equations. So, based on this text, we can write out the following equations:

Note that the first equation relates itself to the total cost, and the second one to the amount of blend.

2) Now, we can solve this system of Linear Equations by the Elimination Method. Let's multiply the second equation by -5.65 so that we can add them both and eliminate "a"

Now, we can plug into the second equation b=90 and then solve it for a:

Thus, the answer is:

13 + √85/3 is the perimeter of triangle .

Explain what a triangle is.

The points P ( - 3 , -8 ) Q ( - 3, - 1) R ( -9,-8)

Distance between PQ = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]

                                      = [tex]\sqrt{( - 1 + 8)^{2} + ( -3 + 3)^{2} }[/tex]

                                      = [tex]\sqrt{( -7 )^{2} +0 }[/tex]

                                       = √49  ⇒ 7

Distance between QR = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]

                                     = [tex]\sqrt{( -9 + 3 )^{2} + ( -8 + 1)^{2} }[/tex]

                                     = [tex]\sqrt{(- 6)^{2} + ( - 7)^{2} }[/tex]

                                     = [tex]\sqrt{36 + 49}[/tex]

                                   = √85

Distance between RP = [tex]\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]

                                     = [tex]\sqrt{( - 3 + 9)^{2} + ( -8 + 8)^{2} }[/tex]

                                     = [tex]\sqrt{(6)^{2} }[/tex]

                                     = √36

                                    = 6

perimeter = PQ + QR+RP/3

                = 7 + √85 + 6/3

              = 13 + √85/3

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