A carpet installer charges a flat rate of $40 + $1.50 per square foot for labor so the total cost for the labor depends on the amount of carpet installed the relationship between the total cost for labor and the amount of corporate installed is the domain of the relation is the range of the relation is

The expression written in equivalent form with a common denominator is -1/6

Fractions are written as ratio of two integers. For instance a/b is a fraction.

Given the sum of the fractions shown;

-3/4 and 5/8

Sum = -3/4 + 5/8

Sum = 5/8 - 3/4

Sum = 5-6/8

Sum  = -1/8

Hence the sum of the given fraction -1/3 and 5/8 is -1/6

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Both Amy and Laura increased their gas mileage in the first two weeks.

Option B is the correct answer.

The missing graph is attached with the answer.

A graph is a statistical way of showing data , it is used to show relation between the points.

A graph is useful in understanding the nature of a function.

From the data given in the question

The statements that can be concluded is , Option B

Both Amy and Laura increased their gas mileage in the first two weeks.

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Answer:

0.42 dollar per pint

2.36 pints per dollar

The speed of the rabbit in miles per hour is 50.33 mi/h.

We know that the speed of the jackrabbit is:

1.35 km/min.

Now we need to use the relations:

1 hour = 60 minutes.

So, in one hour, the rabit runs 60 times the distance that it runs in one minute, then:

1.35 km/min = 60*(1.35 km/h) = 81km/h

Now we need to change kilometers for miles.

1km = 0.6214 mi

Then we can rewrite:

81km/h = 81*0.6214mi/h = 50.33 mi/h

The speed of the rabbit in miles per hour is 50.33 mi/h.

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Answer:

angle ACB=45º

Step-by-step explanation:

angle 135º lies on a straight line

a straight line = 180º

thus, angle ACB= 180-135=45º

Answer:

Formula of Trapezoid:

A = (a + b) × h / 2

The formula can be derived in different ways. for now, we have discussed two ways:

1. By using the formula of a triangle

2. By dividing into different sections

Step-by-step explanation:

1. By using the formula of a triangle

One of the ways to explain a formula for an area of a trapezoid using a formula for a triangle can be as follows.

Assume a trapezoid PQRS with lower base SR and upper base PQ (they are parallel) and sides PS and QR.

The image is attached below.

Connect vertices P and R with a diagonal.

Consider triangle ΔPQR as having a base PQ and an altitude from vertex R down to point M on base PQ (RM⊥PQ).

Its area is

S1=[tex]\frac{1}{2} *PQ*RM[/tex]

Consider triangle ΔPRS as having a base SR and an altitude from vertex P up to point N on-base SR (PN⊥SR).

Its area is

S2=[tex]\frac{1}{2} *SR*PN[/tex]

Altitudes RM and PN are equal and constitute the distance between two parallel bases PQ and SR.

They both are equal to the altitude of the trapezoid h.

Therefore, we can represent areas of our two triangles as

S1=[tex]\frac{1}{2}*PQ*h[/tex]

S2=[tex]\frac{1}{2}*SR*h[/tex]

Adding them together, we get the area of the whole trapezoid:

S=S1+S2=[tex]\frac{1}{2} (PQ+SR)h,[/tex]

which is usually represented in words as "half-sum of the bases times the altitude".

2. By dividing into different sections

Trapezoid PQRS is shown below, with PQ parallel to RS.

Figure 1 - Trapezoid PQRS with PQ parallel to RS(image is attached below.)

We are going to derive the area of a trapezoid by dividing it into different sections.

If we drop another line from Q, then we will have two altitudes namely PT and QU.

Figure 2 - Trapezoid PQRS divided into two triangles and a rectangle. (image is attached below.)

From Figure 2, it is clear that Area of PQRS = Area of PST + Area of PQUT + Area of QRU. We have learned that the area of a triangle is the product of its base and altitude divided by 2, and the area of a rectangle is the product of its length and width. Hence, we can easily compute the area of PQRS. It is clear that

=> [tex]A_{PQRS} = (\frac{ah}{2}) + b_{1}h + \frac{ch}{2}[/tex]

Simplifying, we have

=>[tex]A= \frac{ah+2b_{1+C} }{2}[/tex]

Factoring we have,

=> [tex]A_{PQRS} = (a+ 2b_{1} + c)\frac{h}{2} \\= > {(a+ b_{1} + c) + b_{1} }\frac{h}{2}[/tex]

 But, [tex]a+ b_{1} + c[/tex]  is equal to [tex]b_{2}[/tex], the longer base of our trapezoid.

Hence, [tex]A_{PQRS}= (b_{1} + b_{2} )\frac{h}{2}[/tex]

We have discussed two ways by which we can derive area of a trapezoid.

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The value of the integral over limit is 20,  the average is 1.73

The signed area is shown in the graph attached.

A function is a mathematical statement used to find a relation between two variable.

To Evaluate the definite integral between

f(x) = 5 if 4≤x ≤9

f(x) = -1 if 9≤x≤14

[tex]\rm \int_{4}^{14}f(x) dx = \int_{4}^{9} 5 dx +\int_{9}^{14} (-1)dx\\\\\int_{4}^{14}f(x) dx = (5x)^{9}_{4} -(x)^{14}_{9}\\\\\int_{4}^{14}f(x) dx = 5*(9-4) - (14-9)\\\\\int_{4}^{14}f(x) dx = 20[/tex]

The average value of the interval is

= (5+5+5+5+5-1-1-1-1-1-1)/ 11 = 1.73

Therefore the average is 1.73.

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The true option about the system of linear equation is that the system can only be independent and consistent.

It should be noted that the system is consistent as it can illustrate more than a solution.

Also, it can't be independent and dependent at the same time as depicted in some of the option given.

In this case, true option about the system is that the system can only be independent and consistent.

The complete question is:

Given that (1, 0, 1) is a solution to a system of three linear equations, which of the following is true about the system?

The system can be either inconsistent or consistent.

The system can be either independent or dependent.

The system can only be independent and consistent.

The system can only be dependent and inconsistent.

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Answer:

its 80

Step-by-step explanation:

the ratio is 80 hope this helps!

The company needs 41 labels on average, each minute.

The perimeter of a circle (circumference): 2 π radius

Replacing with the values given:

C = 2 (3.14) 2 = 12.56 cm

So, the area of one label is:

Area of a rectangle: length x width = 12.56 x 7 = 87.92 cm sq.

Now, the number of label be n

87.92 x n = 3612.64 cm2

n = 3612.64 / 87.92

n = 41.09

Hence, The company needs 41 labels on average, each minute.

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(a)

421₅ = 4×5² + 2×5¹ + 1×5⁰

… = 100 + 10 + 1

… = 111

(b)

11101₂ = 1×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰

… = 16 + 8 + 4 + 0 + 1

… = 29

(c)

13T₁₂ = 1×12² + 3×12¹ + 10×12⁰

… = 144 + 36 + 10

… = 190

Answer:

  B.  2x = y; 2x +1.5y = 20

Step-by-step explanation:

The two given relations can be written as two equations, one for the numbers of fish, and one for their cost.

__

The number of goldfish (y) is twice the number of tetras (x), so one equation can be ...

  2x = y

The tetras (x) are $2 each, and the goldfish (y) are $1.50 each. Their total cost is the sum of products of the number of fish and the cost of each. That total is given as $20, so the other equation could be ...

  2x +1.5y = 20

Then the appropriate system of equations is ...

_____

Additional comment

The solution can be found by substituting for 2x to get ...

  y +1.5y = 20 . . . . . . substitute for 2x

  y = 20/2.5 = 8 . . . . divide by the coefficient of y

  x = y/2 = 4 . . . . . . . find the number of tetras

Rick bought 4 tetras and 8 goldfish.

__

The wording "twice as many goldfish as tetras" easily causes confusion. It is helpful to reword it as "goldfish were twice the number of tetras."

Answer:

Step-by-step explanation:

The angles are: A =24.7° ; B = 40.6° ; C =114.7°.

The law of cosine helps in establishing a relationship between the lengths of sides of a triangle and the cosine of its angles. The cosine law in trigonometry generalizes the Pythagoras theorem, which applies to a right triangle.

Cosine Law

a² = b²+c²-2bc cos A

b² = c²+a² -2ca cos B

Sum of three angles of a triangle is 180°.

a = 34 ; b= 53; c = 74

Substituting the given values in the cosine law, we have

34² = 53² + 74² - 2*53 *74 * cos A

7844 cos A = 2809 + 5476 - 1156 = 7129

cos A = 7129/7844 = 0.9088

A = cos⁻¹ (0.9088) = 24.6600° = 24.7°

53² = 74² + 34² - 2 (74)(34) cos B

5032 cos B = 5476 + 1156 - 2809 = 3823

cos B = 3823/5032 = 0.7597

B = cos⁻¹ (0.7597) = 40.5622° = 40.6°

Also, A + B + C = 180°

24.7 + 40.6 + C =180

C =180 -  65.3 = 114.7°

Thus, the angles are: A =24.7° ; B = 40.6° ; C =114.7°

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An equation is formed of two equal expressions. The number of infections in 6 weeks is 456.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The general equation of an exponential function is written as,

y = A(B)ˣ

Since the infection is increasing at a rate of 50%, therefore, the rate of growth will be,

B = 1.50

Substitute any value then we will get,

40 = A(1.50)⁰

A = 40

Thus, the exponential equation of the growth will be,

y = 40(1.50)ˣ

Now, the number of infections in 6 weeks will be,

y = 40(1.50)⁶

y = 455.625 ≈ 456

Hence, the number of infections in 6 weeks is 456.

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Answer:

Step-by-step explanation:

If a = 0, f(a) = f(0) = 0 + 0 + 7 = 7;

If a = 1, f(1) = 3(1^2) + 2(1) + 7 = 12;

and so on.  Normally an 'a' value would be given as part of this problem.

Actually, the value of f(a) is given and is  f(a) = 3a^2+2a+7 for input value a.

Answer:

( 1, - 1 )

Step-by-step explanation:

When decomposing into prime factors, it is when a number is taken out of its half, third, fifth and seventh, and it is also possible for the same number number.

         [tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{10692 }\\ \ 5346\\ \ 2673\\ \ \ \ 891\\ \ \ \ 297\\ \ \ \ \ 99\\ \ \ \ \ 33\\ \ \ \ \ 11\\ \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 3\\ 3\\ 3\\ 3\\ 3\\ 11\\ \: \end{matrix} \end{gathered}$}[/tex]

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Substitute [tex]y = \sqrt x[/tex], so that [tex]y^2 = x[/tex] and [tex]2y\,dy = dx[/tex]. Then the integral becomes

[tex]\displaystyle \int \frac{dx}{\sqrt{1 + \sqrt x}} = 2 \int \frac y{\sqrt{1+y}} \, dy[/tex]

Now substitute [tex]z=1+y[/tex], so [tex]dz=dy[/tex]. The integral transforms to

[tex]\displaystyle 2 \int \frac y{\sqrt{1+y}} \, dy = 2 \int \frac{z-1}{\sqrt z} \, dz = 2 \int \left(\sqrt z - \frac1{\sqrt z}\right) \, dz[/tex]

The rest is trivial. By the power rule,

[tex]\displaystyle \int \left(\sqrt z - \frac1{\sqrt z}\right) \, dz = \frac23 z^{3/2} - 2z^{1/2} + C = \frac23 \sqrt z (z - 3) + C[/tex]

Put everything back in terms of [tex]y[/tex], then [tex]x[/tex] :

[tex]\displaystyle 2 \int \frac y{\sqrt{1+y}} \, dy = \frac43 \sqrt{1+y} (y - 2) + C[/tex]

[tex]\displaystyle \int \frac{dx}{\sqrt{1+\sqrt x}} = \boxed{\frac43 \sqrt{1+\sqrt x} (\sqrt x - 2) + C}[/tex]

Answer:

- 1

Step-by-step explanation:

note there is a common difference of 6 between consecutive terms , that is

23 - 29 = 29 - 35 = 35 - 41 = 41 - 47 = - 6

by subtracting 6 from the previous term we get

23 - 6 = 17

17 - 6 = 11

11 - 6 = 5

5 - 6 = - 1

the first negative number in the sequence is - 1

Triangle ABC and triangle XYZ are similar based on angle-side-angle criterion.

Triangle ABC and triangle RQP are similar based on side-angle-side criterion.

An equation is an expression that shows the relationship between two or more numbers and variables.

Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent.

Triangle ABC and triangle XYZ are similar based on angle-side-angle criterion.

Triangle ABC and triangle RQP are similar based on side-angle-side criterion.

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The time it will take the money to reach $8,838.51 is 14years

The formula for calculating compound interest is expressed as:

A = P(1+r)^t

where

P = $6,680

A = $8,838.51?

r = 2% = 0.02

Substitute and calculate the time 't"

8,838.51 = 6680(1+0.02)^t
1.3231 = 1.02^t

t = ln1.3231/ln1.02

t = 14years

Hence the time it will take the money to reach $8,838.51 is 14years

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The incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

[tex]\rm a^b = c\\log_ac =b[/tex]

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

2ln(x) = In(3x) - [In(9) - 2ln(3)]

In(x²) = In(3x) - [In(9) - In(9)]

ln(x²) = ln(3x) - 0

ln(x²) = ln(3x/0)   (incorrect step)

ln(x²) = ln(3x)

x² = 3x  (correct step)

x² - 3x =0

x(x - 3) = 0

x = 0, 3

Thus, the incorrect step is ln(x²) = ln(3x/0) because ln(x/y) = lnx - lny and the solutions are x = 0, 3

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An equation is formed of two equal expressions. The value of x that maximizes the area of the printed region of the billboard is 9.655 ft.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given x is the left-right width of the billboard and y is the height of the billboard. Therefore,

The total area of the billboard, A= x·y

The total printed area of the billboard, [tex]A_p=(x-2)(y-8)[/tex]

Given in problem that the area of the billboard is 3600 ft².

x·y = 3600

y = (3600)/x

Substituting the value of y in the equation of the total printed area of the billboard,

[tex]A_p = (x-2)(\dfrac{3600}{x}-8)\\\\A_p = 3600 -8x -\dfrac{7200}{x} + 16\\\\A_p =3616-8x - \dfrac{7200}{x}[/tex]

Now, the value of x is needed to be minimum, therefore, differentiating the given function,

[tex]\dfrac{d}{dx}A_p =\dfrac{d}{dx}3616-8x - \dfrac{7200}{x}\\\\\dfrac{d}{dx}A_p =-8 - \dfrac{7200}{x^2}[/tex]

Equate the differentiated function with 0,

[tex]0=-8x - \dfrac{7200}{x^2}\\\\8x = - \dfrac{7200}{x^2}\\\\x^3 = 900\\\\x = 9.655 ft.[/tex]

Hence, the value of x that maximizes the area of the printed region of the billboard is 9.655 ft.

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The measure of angle OED is the measure of angle OBD. Then the correct option is C.

It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Circle O is shown.

Line segment JE is a diameter and line segment OB is a radius.

A line is drawn from point J to point B to form a chord.

Tangents BD and ED intersect at point D outside the circle.

The radius and tangent are orthogonal to each other.

∠OED = ∠OBD = 90°

Then the correct option is C.

The complete question is given below.

Circle O is shown. Line segment J E is a diameter and line segment O B is a radius. A line is drawn from point J to point B to form a chord. Tangents B D and E D intersect at point D outside of the circle.

Use the diagram to complete the statements.

The measure of angle EJB is the measure of angle BOE.

The measure of angle BDE is the measure of angle BOE.

The measure of angle OED is the measure of angle OBD.

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Answer:

one-half, 180 minus, equal to

Step-by-step explanation:

Answer:

$4,000.343

Step-by-step explanation:

Divided the months of the year and caculate the intrest.

Answer: Read attachment.

Step-by-step explanation: Attached below is my work. Hope it helps!

A description of how the pattern is growing is that the pattern is growing by the addition of two blocks every time.

A numerical description of the pattern is:

1 - 2 blocks.

2 - 4 blocks.

3 - 6 blocks

4 - 8 blocks.

The formula that can be used to calculate the number if building blocks in any term will be 2n. For example, the number of blocks for the 5th term will be:

= 2n = 2 × 5 = 10

The value for the 10th frame will be:

= 2n

= 2 × 10 = 20

The value for the 100th frame will be:

= 2n

= 2 × 100 = 200

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