The dimensions of a rectangular building used to store tools for electrical lineman has a length of 12x + 24 feet and a width of 20x - 10 feet.


Write the expression that represents the area of the building, in terms of x.

Write the expression that represents the perimeter of the building, in terms of x.

If the perimeter is going to be 220 feet, what are the dimensions of the building

Answer:

50ft by 120ft

Step-by-step explanation:

Area of a rectangle = L × W

6000ft² = L × W

L = 6000/W

When a diagonal line divides a rectangle into 2 right angled triangles, the diagonal line = Hypotenuse of either of the triangle and it is the longest side.

The formula for a right angle triangle =

a² + b² = c²( c = hypotenuse)

We are told in the question that:

A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel

Let us assume the side that the hypotenuse is longer than = Width

Hence, the Diagonal = (W + 10)²

Therefore

L² + W² = (W + 10)²

Since L = 6000/W

W² + (6000/W)² = (W + 10)²

W² + (6000/W)² = (W + 10) (W + 10)

W² + (6000/W)² = W² + 10W + 10W + 100

W² + (6000/W)² = W² + 20W + 100

W² - W² + (6000/W)² = 20W+ 100

6000²/W² = 20W + 100

6000² = W²( 20W + 100)

6000² = 20W³ + 100W²

20W³ + 100W² - 6000² = 0

20W³ + 100W² - 36000000 = 0

20(W³ + 5W² - 1800000) = 0

Factorising the quadratic equation,

20(W − 120)(W² + 125W + 15000) = 0

W - 120 = 0

W = 120

Therefore,

W(Width) = 120feet

Since the Width = 120 feet

We can find the length

6000ft² = L × W

L = 6000/W

L = 6000/120

L = 50 feet

The dimensions of the land, correct to the nearest foot is 50ft by 120ft

Using proportions, it is found that one sandwich costs $4.25.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Considering x as the cost of a sandwich, the total cost is given as follows:

1.08(3x + 1.75) + 5 = 20.66.

The multiplication by 1.08 is because of the sales tax. We solve for x to find the cost of one sandwich, hence:

1.08(3x + 1.75) = 15.66

3x + 1.75 = 14.5

3x = 12.75

x = 12.75/3

x = 4.25.

Hence one sandwich costs $4.25.

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Answer:

There is one solution. The solution is 2, 18, 19.

Step-by-step explanation:

If you want me to show working tell me in the comments and I'll edit the answer

Answer:

A. (2, 18, -19)

Step-by-step explanation:

To solve:

Z is the most suitable variable to remove first

Add the first equation to the second equation: (this conveniently removes both y and z)

(x+y-z) + (4x-y+z) = 1+9

Simplify

5x = 10

Solve

x = 2

Multiply the second equation by 2 and minus it to the third equation: (Solve for y)

2(4x-y+z) - (x-3y+2z) = 2(9) - (-14)

Simplify

8x-2y+2z-x+3y-2z=18+14

7x+y=32

Substitute using x=2

7(2) + y = 32

y = 32 - 14

y = 18

Now substitute x and y for their respective values into Equation 1

2 + (-18) - z = 1

Simplify

-z = 19

z = -19

So :

x = 2, y = 18 , z = -19

Answer:

1 in 13.5

The odds of drawing a Jack from a 54 card deck are 1 in 13.5 or 4/54. The standard odds of drawing a jack, king, etc is always 1 in 13 from a shuffled 52 card deck. 4 suits,13 cards each, 1 jack for each suit

Step-by-step explanation:

Answer: 25

Step-by-step explanation: When you divide exponents with the same base, you can subtract the exponents. It becomes 5^4-2, which is 5^2, which is 25

As given that Material A has a higher thermal conductivity than Material B, the material that will transfer energy by conduction faster is the Material A because it is a good thermal conductor.

A thermal conductivity means the rate at which heat is transferred by conduction through a unit of a material when a temperature gradient exits perpendicular to the area.

By having a high thermal conductivity means that the material can effectively transfer heat and readily take up heat from their environment. An example of these materials are copper and aluminum.

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The standard deviation of the data sample is 2.55.

The standard deviation of the data sample is calculated by applying the following formula;

S.D = √ (x -  μ)²/(n - 1)

where;

The given parameters;

mean,  μ = 64

x, = 12

number of samples = 9

The standard deviation of the data sample is calculated as;

S.D = √ (12 -  64)²/(9 - 1)

S.D = 2.55

Thus, the standard deviation of the data sample is calculated by applying the formula for standard deviation.

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Answer:

80

Step-by-step explanation:

Here’s how you can estimate the product of 8 × 9.82 using rounding:

So, by rounding to the nearest whole number, we can estimate that the product of 8 × 9.82 is approximately 80.

PLS MRK ME BRAINLIEST I NEED TO GET THE NEXT RANK

Answer:

For question 2:

x=-5 then f(x)=0

x=0 then f(x)-15

x=3 then f(x)-24

x=5 then f(x)=-30

For question 3:

x=-20 then y=2

x=0 then y=-2

x=15 then y=-7

Let me know if you want an explanation

The term n is the initial amount that the television is to be sold.

We are told that the television in this case is to be sold at a discount piece. The implication of this is that there is something that has to be removed from the price of the television as it is sold.

We are told that what they are to remove from the price of the television is about $75  and that when this is done, the price of the television would be about $300. Thus n is the original price of the television.

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The variable n represents the initial value of the television

From the question, we have the following parameters that can be used in our computation:

Amount off = $75

New price = $300

When represented as the equation, we have

n - 75 = 300

Add 75 to both sides of the equation

So, we have the following representation

n = 375

This means that the initial price of the television is $375

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The domain of the square root function is x greater-than-or-equal-to 0, since the function is defined for all non-negative x-values or x-values greater than or equal to zero.

The domain of the square root function graphed below can be determined by looking at the x-values of the points on the graph.

From the given information, we can see that the curve starts at (0, -1) and goes through (1, -2) and (4, -3).

The x-values of these points are 0, 1, and 4.

Since the square root function is defined for any non-negative x-values or x-values more than or equal to zero, its domain is x greater-than-or-equal-to 0.

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Answer:

x=3

Step-by-step explanation:

Log base 5 of 125=x

that is equal to 5x5x5 which is 125

5 is multiplied 3 times so x is 3

After considering the given data we come to the conclusion that the length of AB is 12.124 units, under the condition that A (-3, 5) and B (4, -2) are the given coordinates.

The distance between two points in a plane can be found using the distance formula which is an application of the Pythagorean theorem. The formula is given by d=√ ( ((x₂ – x₁ )² + (y₂ – y₁ )²)

Here (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Applying the given coordinates of A (-3, 5) and B (4, -2), we can evaluate the distance between them as follows:

d = √( (4 - (-3))² + (-2 - 5)² )

 = √(7² + (-7)²)

 = √(98 + 49)

 = √147

 = 12.124

Therefore, the length of AB is approximately 12.124 units.

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9514 1404 393

Answer:

  A. the x-coordinate of the intersection point

Step-by-step explanation:

If you are solving ...

  f(x) = g(x)

the solution is one or more values of x. That is still true if you rewrite the equation to be a system of equations ...

  y = f(x)

  y = g(x)

The value of y tells you the value of each side of the original equation where the solution causes the functions to be equal. That is largely irrelevant. What you're looking for is the value of x.

The solution is the x-coordinate of the intersection point.

9514 1404 393

Answer:

  not possible

Step-by-step explanation:

Among the first 20 natural numbers, the numbers 10, 11, 13, 14, 18, 19 are not possible to make using four 4s and the four basic arithmetic operations.

__

Below are listed the numbers that can be made and one possible way to do it.

{1, ((4*4)/4)/4}, {2, (4/(4+4))*4}, {3, ((4*4)-4)/4}, {4, ((4-4)*4)+4},

{5, ((4*4)+4)/4}, {6, ((4+4)/4)+4}, {7, (4-(4/4))+4}, {8, ((4*4)-4)-4},

{9, ((4/4)+4)+4}, {12, (4-(4/4))*4}, {15, (4*4)-(4/4)}, {16, ((4*4)*4)/4},

{17, (4*4)+(4/4)}, {20, ((4/4)+4)*4}

Answer:

C

Step-by-step explanation:

just did it and got right

Answer and Step-by-step explanation: the doc is below for how i did the problem

Answer: x = 10

Step-by-step explanation:

     To solve, we will isolate the variable x.

Given:

     2x + 7 = 5x - 23

Add 23 to both sides of the equation:

     2x + 30 = 5x

Subtract 2x from both sides of the equation:

     30 = 3x

Divide both sides of the equation by 3:

     10 = x

Reflexive property:

     x = 10

Answer:

D.

Step-by-step explanation:

0 - 84 / 6

= -14 ft / hour.

Answer: 84 divided by 6= 14ft

Step-by-step explanation:

Answer:

Answer is in the attachment.

Answer: 3

Step-by-step explanation:

The location of point A''' after the three transformations would be (-4, 1).

To determine the location of point A''', we need to apply the three transformations (reflection over the y-axis, reflection over the x-axis, and rotation of 180°) to point A.

When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the same.

So, the reflection of point A (-4, 1) over the y-axis would be (4, 1).

When a point is reflected over the x-axis, the y-coordinate is negated while the x-coordinate remains the same. So, the reflection of point (4, 1) over the x-axis would be (4, -1).

When a point is rotated 180°, the x-coordinate and y-coordinate are both negated. So, the rotation of point (4, -1) by 180° would be (-4, 1).

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Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

The wrap has an area of  1.12π square inches.

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

Given, The net of a cylinder with a diameter of both circles labeled 1.6 inches.

So, The complete circle or the circumference of the circle will be the length of the wrap which is,

= 2π×0.8.

= 1.6π and the height of the wrap is 0.7 inches.

Therefore, the area of the wrap is 1.6π×0.7 square inches.

= 1.12π square inches.

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Answer: The real answer is 2.4π square inches (B)

Step-by-step explanation:

(Get ready for a long explanation)

So, we are trying to find the Surface Area of the cylinder.

We need to use the formula (SA = 2πr^2 + 2πrh)

Looks like a very long formula, but let do it in parts.

So the first part is just finding the area of the circle and multiplying by 2 because there are two bases. The area formula for circles is (πr^2)

But this time put a 2 in there. (2πr^2)

Okay lets get started. The diameter is 1.6. The radius is half the diameter, so divide 1.6 by 2 and you will get 0.8 which is the radius.

Now times the radius by itself (0.8 * 0.8 = 0.64) Now times that by 2 (0.64 * 2 = 1.28) The answer should be in terms of pi so just put the pi symbol next to 1.28  (1.28π)

On to the next part, (2πrh) you are basically taking the circumference of either circle base, and multiplying that by the height, which is (0.7)

The formula for Circumference is (2πr)

We already have the diameter so we don't need times the radius by 2.

So take the diameter of the circle base (1.6) and multiply that by the height, which is (0.7)
(1.6 * 0.7 = 1.12π)

Now for the last part, we need to add the two values together to find the surface area.

The first value we found is (1.28π ) and the second is (1.12π)

Now add (1.28π  + 1.12π = 2.4π)

Answer: 2.4π square inches

Sorry for the really long explanation. I took the same test and I got it right so here is proof that it is correct. Have a great day y'all.

Answer:

1.847

Step-by-step explanation:

divide 2.45 and 1.75 dats ur ans

Answer:

3 3/16

Step-by-step explanation:

Length of the box L= 2 1/2m= 1 9/16 W

Width of box W = W

Height H=?

Volume V= 12 3/4m3

If L= 5/2 = 25/16 W

W= 16 × 5/2× 25

W= 80/50= 8/5 = 1 3/5

V= LWH

Hence height =

51/4 = 5/2 × 8/5 × H

H= 51/4 × 10/40 =51/16

H= 3 3/16

Answer:

it equals 33

Step-by-step explanation:

hope this helps and have a blessed day

Answer:

no because there is a 10 which make it not proportional

Step-by-step explanation:

hope that helps.

Answer: No they are not proportional because the last row has -10 which obstructs the whole relationship.

Answer:

\(\huge\boxed{x=\pm4.5}\)

Step-by-step explanation:

The quadratic formula of

\(ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

We have:

\(y=4x^2-81\to 4x^2-81=0\\\\a=4;\ b=0;\ c=-81\)

substitute

\(x=\dfrac{-0\pm\sqrt{0^2-4(4)(-81)}}{2(4)}=\dfrac{\pm\sqrt{1296}}{8}=\dfrac{\pm36}{8}=\pm4.5\)

The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

Answer:

2x^7

Step-by-step explanation:

add the exponents because they both are x

2x^4*x^3=2x^7