A rectangular plece of carpet covers 180 yd². The width is 7 yd less than the length. Find the length and width.
Round your answers to the nearest tenth of a yard.
The length is approximately
yd.

The width?

The value of f(-2) in the function f(x) = 3x² + 2x + 4 is 12.

A function is defined as a relation between a set of inputs having one output each. In a simpler term a function relates input and output.

In other words, a function relates each element of a set with exactly one element of another set (possibly the same set).

Therefore, let's solve the function below:

f(x) = 3x² + 2x + 4

Let's find f(-2) as follows;

To solve f(-2), we have to substitute the value of x in the function f(x) = 3x² + 2x + 4 with -2.

Therefore,

f(x) = 3x² + 2x + 4

f(-2) =  3(-2)² + 2(-2) + 4

f(-2) = 3(4)  - 4 + 4

f(-2) = 12 - 4 + 4

f(-2) = 12

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Answer:

P = 84

Step-by-step explanation:

Area = length* width or A = lw

We know that the length is 5 times its width which can also mean

[tex]l = 5*w[/tex] or [tex]l=5w[/tex]

Use the formula for area and replace [tex]l[/tex] with [tex]5w[/tex] and the total area with 245

[tex]A = lw\\245=5w(w)[/tex]

Multiply:

[tex]245=5w^{2}[/tex]

Divide by 5

[tex]49=w^2[/tex]

Square root of [tex]w^2[/tex]

[tex]\sqrt{49}=\sqrt{w^2}[/tex]

Simplify

[tex]7=w[/tex]

Now that we know w = 7 we can input this into the Perimeter formula

(P = 2l +2w)

P = 2(5*7)+2(7)   // Note: Remember [tex]l[/tex] = 5*w and w = 7

P = 84

There is also a formula for this type of problem, but this explanation is for when you forget. Hope that explains things :)  

Answer:

  3.36 km

Step-by-step explanation:

You want the distance P east of a refinery so that the cost of laying pipe from the refinery 1 km north of a river and under a 3 km wide river to storage on the south bank is minimized. The cost of under-river pipe is double the cost of overland pipe.

Let p represent the distance east of the refinery where the river crossing starts. Then the distance in km from the refinery to the river crossing is ...

  d1 = √(1² +p²)

The storage facility is 5 km east of the refinery, so is (5-p) km east of the north-bank point where the river crossing starts. The length of the pipe under the 3 km-wide river is ...

  d2 = √(3² +(5-p)²) = √(p² -10p +34)

The cost is the sum of costs of laying pipe for each segment. The cost for each unit of distance is double for the under-river pipe, so the total cost can be described by ...

  c ∝ d1 + 2×d2

  c ∝ √(1² +p²) +2√(p² -10p +34)

The cost is minimize for the value of p that makes dc/dp = 0. The implicit derivative is ...

  c' = p/√(p² +1) +(2p -10)/√(p² -10p +34) = 0

Subtracting the second term and squaring gives ...

  p²/(p² +1) = (4p² -40p +100)/(p² -10p +34)

Cross-multiplying gives the 4th-degee equation ...

  p⁴ -10p³ +34p² = 4p⁴ -40p³ +104p² -40p +100

In standard form, this is ...

  3p⁴ -30p³ +70p² -40p +100 = 0

The only positive real solution in the domain (0, 5) is p ≈ 3.362.

P should be located about 3.36 km downriver from the refinery.

__

Additional comment

This problem does not ask for the cost, so we only need to know the relative cost of two routes.

The solution of the quartic equation is found using a graphing calculator in the first attachment.

The same graphing calculator can find the minimum of 'c' without bothering with differentiation and reducing the equation to a polynomial. This is shown in the second attachment. Note that graph also shows the cost in units of $300,000. That is, the cost of the pipeline will be about $3.1 million.

A system of linear equations to describe this situation is given by:

A + O = 11.

0.80A + 0.95O = 9.95.

Harry bought six (6) apples and five (5) oranges from this store.

In order to write a system of linear equations to describe this situation, we would assign variables to the amount of apples and oranges respectively, and then translate the word problem into algebraic equation as follows:

Since Harry bought a total of 11 pieces of fruit, we have:

A + O = 11              .....equation 1.

Since the cost of apples is $0.80 each and oranges cost $0.95 each, we have:

0.80A + 0.95O = 9.95      .....equation 2.

From equation 1, we have:

O = 11 - A                   .....equation 3.

Substituting equation 3 into equation 2, we have:

0.80A + 0.95O = 9.95

0.80A + 0.95(11 - O) = 9.95

Apples, A = 0.90/0.15

Apples, A = 6.

For the number of oranges, we have:

Oranges, O = 11 - A

Oranges, O = 11 - 6

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Complete Question:

At a store, apples cost $0.80 each and oranges cost $0.95 each. Harry buys some apples and oranges and spends $9.55 . He buys a total of 11 pieces of fruit.

Part a. Write a system of linear equations to describe this situation.

Part b. How many of each fruit did Harry buy?

The fraction of the shops t-shirt are blue t-shirt that are on sale and are size medium can be explained by

"Multiplying the fraction of T-shirt that are blue by the fraction of T-shirt that are on sale. Then, multiply the result by the fraction of the blue T-shirt that are on sale that are size medium".

The correct answer option is option C.

A fraction is a number which consists of a numerator and a denominator.

A numerator is the upper value of a fraction while a denominator is the lower value of a fraction.

Fraction of blue T-shirt = 2/3

Fraction of blue t-shirt on sale = 3/7 × 2/3

= 2/7

Fraction of the blue T-shirts that are on sale are size medium = 1/2 × 2/7

= 2/14

= 1/7

Therefore, Multiply the fraction of T-shirt that are blue by the fraction of T-shirt that are on sale. Then, multiply the result by the fraction of the blue T-shirt that are on sale that are size medium".

= 2/3 × 3/7 × 1/2

= 1/7

Complete question:

Two-thirds of the T-shirts in a T-shirt shop are blue. Three-sevenths of those T-shirts are on sale.

One-half of the blue T-shirts that are on sale are size medium. What fraction of the shop's T-shirts are blue T-shirts that are on sale and are size medium?5 Explain

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The equation of line in slope intercept form is y=−9/8x+7.

In the given question we have to write the equation of the graph line in slope intercept form.

The give points are(0,7) and (8,−2)

Let x(1)=0, y(1)=7, x(2)=8 and y(2)=−2.

The slope intercept form of equation is

y−y(1)=m(x−x(1))+c.........(1)

Before finding the equation we find the slope of equation.

Slope(m)={y(2)−y(1)}/{x(2)−x(1)}

Now putting the value

m=(−2−7)/(8−0)

m= −9/8

Now putting the value in equation 1

y−7=−9/8(x−0)

Now the equation is

y−7=−9/8x

Add 7 on both side

y−7+7=−9/8x+7

y=−9/8x+7

Hence, the equation of line in slope intercept form is y=−9/8x+7.

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Step-by-step explanation:

The total price of sneakers including tax will be equal to $20.75.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

Price of sneakers = $20

Tax on sneakers = 3.75%

Then, the amount of tax will be,

(20 × 3.75)/100

= 75/100

= $0.75

Then, the total price of the sneakers will be,

$20 + $0.75

= $20.75

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The distance between the points (-5,4) and (1,0) is  7.21 .

In the question ,

it is given that ,

the two points are (-5,4) and (1,0) ,

we  have to find the distance between them .

we know that the distance between the points (x₁ , y₁) and (x₂ , y₂) is calculated using the distance formula

distance = √(y₂ - y₁)² + (x₂ - x₁)²

Substituting the values of the points , we get

distance = √(0 - 4)² + (1 -(-5))²

= √(-4)² + (1 + 5)²

= √16 + (6)²

= √16 + 36

= √52

= 7.21111

≈ 7.21

Therefore , The distance between the points (-5,4) and (1,0) is  7.21  .

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Answer:

whole triangle 180 degrees

y = 84 degrees

x = 36 degrees

Step-by-step explanation:

y = 180 - 96

x = y - 48. Reason: Exterior angle theorem

Substitute: x = 84 - 48

Answer:

180

36

84

Step-by-step explanation:

→ Find x

180 - (96 + 48) = 36

→ Find y

180 - 96 = 84

The money spent on the plates which are very expensive is: $133.44

Given,

The plates that mom bought are very fragile and expensive.

Each  plate costs $16.68.

Total plates bought by her mom are = 8

we are asked to determine the total cost of the plates bought = ?

let y represent the total cost of the plates.

and x represent the number of plates bought.

based on the conditions, we can formulate:

total cost pf plates = 16.38(number of plates bought)

⇒ y = 16.68x

we know that plates bought = 8

⇒ total cost is:

⇒ y = 16.68(8)

⇒ y = 133.44

Hence total cost of 8 plates is $133.44

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The amount of the first application that has been downloaded is 6.48 megabytes

The size of the second application is 7.35 megabytes

The first application has a size of 10.8 megabytes and out of this 10.8 megabytes, only 60% has completely downloaded. The amount that has already downloaded is therefore:

= Size of application x Percentage downloaded

= 10. 8 x 60%

= 6.48 megabytes

The second application is sized such that it is 3.45 MB less than the first application. The size of the application is therefore:

= 10.8 - 3.45

= 7.35 megabytes

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The time that it took Zane to reach the edge of the volcano is of:

35 seconds.

The variables that are graphed in this problem are listed as follows:

The edge of the volcano is the point at which the elevation relative to the volcano is of 0, hence the coordinate is:

y = 0.

y = 0 is the x-intercept of the function, which is the value of x at which the function crosses the x-axis.

Hence, looking at the graph, the time that it took Zane to reach the edge of the volcano is of:

35 seconds.

(as 35 is the x-intercept of the graph, and we previously explained that the edge of the volcano is the x-intercept).

The question is:

How long did it take Zane to reach the edge of the volcano?

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The graph of the polar curve r = 3 – 2cos(θ) is in the attachment

A graph is a diagram representation on a coordinate system.

A polar curve is a curve represented by the equation r = a + bcosθ where

To find the graph of the polar curve r = 3 – 2cos(θ), we need to determine its maximum and minimum values and also the value as it crosses the axis.

Since r = 3 – 2cos(θ), the maximum value of r is obtained at the minimum value of cos(θ) = -1 at θ = π

So, substituting this into the equation, we have

r = 3 – 2cos(θ)

r = 3 – 2(-1)

r = 3 + 2

r = 5

Since r = 3 – 2cos(θ), the minimum value of r is obtained at the maximum value of cos(θ) = 1 at θ = 0

So, substituting this into the equation, we have

r = 3 – 2cos(θ)

r = 3 – 2(1)

r = 3 - 2

r = 1

Since r = 3 – 2cos(θ), the value of r at the origin is when θ = π/2 and θ = 3π/2

So, substituting this into the equation, we have

r = 3 – 2cos(θ)

r = 3 – 2cos(π/2)

r = 3 – 2(0)

r = 3 - 0

r = 3

So, in polar form, the points we require for the polar curve graph are

Find the graph of the polar curve in the attachment

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Answer:

C: The third graph.

Step-by-step explanation:

Took the quiz

Answer:

-40

Step-by-step explanation:

The y-intercept occurs when x is equal to 0. In order to find the y-coordinate, you would just plug in x with 0:

2(5x² − 2)(x − 5) (4x² − 2)

2(5[0]^2 - 2)(0 - 5)(4[0]^2 - 2)

2(-2)(-5)(-2)

-40

The positive co-terminal is 9π/4 and negative co-terminal is 25π/4 for the given angle 17π/4.

Coterminal angles are those with a common terminal side that are in standard position (angles with the initial side on the positive x-axis). Angles with the same initial side and terminal side are said to be coterminal angles. Depending on whether the given angle is in degrees or radians, finding coterminal angles is as easy as adding or subtracting 360° or 2 to each angle. Coterminal angles can be found in an infinite number of ways.

The negative co-terminal=17π/4-2π

=9π/4

The positive co-terminal=17π/4+2π

=25π/4

For the given angle 17π/4, positive co-terminal is 9π/4 and negative co-terminal is 25π/4.

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Answer:

18 in. x 10 in.

Step-by-step explanation:

Squares will always have equal lengths. So, you need to figure out what will multiple by itself to get 196, and it’s 14.

Since you know in the equation that if 4 were to be taken away from the length and added to the width, it would make the 14 x 14 square, you can subtract 4 from one of the 14’s and add 4 to the other 14.

So, then you get (14-4) 10 in. x (14+4) 18 in.

46 Days the number of days that the funds were on deposit on Interest rate.

What exactly does "interest rate" mean?

Interest earned = Principal*Interest rate*Time period

155.27 = 20,000 * 0.06 * Time period

Time period = 155.27/(20,000*0.06)

                      = 0.129339 years

                     =(0.129339 * 360)

                     = 46.56204 days

                     = 46 days(Approx)

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Answer:804,000,000,000 & 8.0e+11

Step-by-step explanation:

logic

h(n) = -17·0.2^(n-1)

Step-by-step explanation:

The explicit formula for a geometric sequence with first term a1 and common ratio r is ...

an = a1·r^(n-1)

Your sequence h has first term a1 = -17 and common ratio r = 0.2. Then the explicit formula is ...

h(n) = -17·0.2^(n-1)

Answer:

-1    x     120

-2    x     60

-3    x     40

-4    x     30

-5    x     24

-6    x     20

-8    x     15

-10    x     12

1    x     -120

2    x     -60

3    x     -40

4    x     -30

5    x     -24

6    x     -20

8    x     -15

10    x     -12

Answer:

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

Step-by-step explanation:

The area of the given trapezium is 16x + 8

Area of trapezium:

The general formula to calculate the area (A) of a trapezium is written as,

A = ½ (a + b) h where,

where

a, b = bases of trapezium, and,

h = height

Given,

Here we have the figure of trapezium and the measures are written in it.

Now, we have to find the area of the trapezium.

According to the formula of the area of the trapezium,

We need the value of base and height.

By looking into the given figure, we have identified the value of

a = x cm

b = 3x + 2 cm

h = 8 cm.

Then the area of the trapezium is calculated as,

A = ½ (x + (3x +2)) 8

A = ½ (4x + 2) 8

A = 4 (4x + 2)

A = 16x + 8

Therefore, the area of the trapezium is 16x + 8.

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Answer:37 number

Step-by-step explanation:

The equation of the line in point slope form that passes through  the point (2, 6) and has a slope of 5 is y - 6 = 5(x - 2) .

The equation of a line can be represented in different form such as standard form, general form, point slope form and slope intercept form.

Therefore,

y - y₁ = m(x - x₁)

where

The line passes through (2, 6) and has a slope of 5.

Hence,

m = 5

The equation of the line in point slope form is as follows;

y - 6 = 5(x - 2)

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The equation of the line will be y = 12x -3 and the graph of the line with the given y-intercept and slope is shown below.

First, let us understand the slope intercept form of a line:

The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept.

We are given:

(0, −3), m = 12.

We need to determine the graph of the line with the given y-intercept and slope.

To find the value of b;

substitute the given values in the equation of the line, we will get;

y = mx + b

-3 = 12 *0  + b

b = -3

So, the equation of the line will be:

y = 12x -3

Thus, the equation of the line will be y = 12x -3 and the graph of the line with the given y-intercept and slope is shown below.

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Answer:

Step-by-step explanation:

Let the required amount of 5% milk is x quartz, then the amount of 2% milk is 90 - x quartz.

Set equation for the fat content:

A number line which represents the given inequality (-1 ≥ x) is: number line C.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Next, we would determine a solution for the given inequality (-1 ≥ x) in order to graph it on a number line:

-1 ≥ x

x ≤ -1

In conclusion, we can logically deduce that the value of x is less than or equal to -1 as shown in number line C, which is shaded because of the less than or equal inequality symbol.

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The width of Lewis´s rectangular cage as a mixed number in simplest form is equal to 14.86 inches.

Mathematically, the perimeter of a rectangle can be calculated by using this formula;

P = 2(L + W)

Where:

For the perimeter of Becky's rectangular cage, we have:

Perimeter, P = 2(L + W)

Perimeter, P = 2(15 + 11)

Perimeter, P = 2(26)

Perimeter, P = 52 inches.

For the perimeter of Lewis's rectangular cage, we have:

Length, L = 0.75W

Perimeter, P = 2(L + W)

52 = 2(0.75W + W)

26 = (0.75W + W)

1.75W = 26

Width, W = 26/1.75

Width, W = 14.86 inches.

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