The width of a rectangle is the length minus 1 units. The area of the rectangle is 72 units. What is the width, in units, of the rectangle?

The measure of the second largest angle in (6x-17) (4x-12) (2x+5) is 56°.

It should be noted that the value of the angle in a triangle is equal to 180°. Therefore, we will add the angle and add them to equate 180°

This will be:

(6x-17) + (4x-12) + (2x+5) = 180

6x - 17 + 4x - 12 + 2x + 5 = 180

12x -24 = 180

Collect like terms

12x = 180 + 24

12x = 204

Divide

x = 204 / 12

x = 17

First angle = 6x - 17 = 6(17) - 17 = 85°

Second angle = 4x - 12 = 4(17) - 12 = 68 - 12 = 56°

Third angle = 2x + 5 = 2(17) + 5 = 39°

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She will have to pay 1,500

Answer:

n = 49

Step-by-step explanation:

We can find the value of n by completing the square.  The general form of the quadratic equation is ax^2 + bx + c and the formula for completing the square is (b / 2)^2.  

In the question, -14 is the b value so we can do:

[tex](-14/2)^2=(-7)^2=49[/tex]

a) An equation to describe the relationship between time and the number of restaurants in the United States, with 2012 as the base, is Y = 980 + 16.5x.

b) Using this equation, we can predict that the number of restaurants in 2018 will be 1,079 thousand.

An equation is a mathematical statement or function claiming that two mathematical expressions that may combine numbers, variables, and constants are equal or equivalent.

Equations are depicted with the equation symbol (=) to establish the equality of expressions.

The number of thousands of restaurants in the United States:

2012 = 980

2016 = 1,046

4 years (2016 - 2012) = 66 more restaurants (1,046 - 980)

In 1 year = 16.5 more restaurants (66/4)

(0, 980) and (4, 1,046)

Y = 980 + 16.5x

Where Y = the number of thousands of restaurants in the year

x = the number of years past.

In 2018, the number of restaurants, Y = 980 + 16.5x

The number of years between 2018 and 2012 = 6 years

The expected number of restaurants Y = 980 + 16.5(6)

= 1,079.

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Answer:

BGHA

Step-by-step explanation:

Just look at the coordinates.

1 is at x=0 and y=4, so (0, 4), or B

2 is at x=-4 and y=3, so (-4, 3), or G

3 is at x=2 and y=0, so (2, 0), or H

4 is at x=0 and y=-1, so (0, -1), or A

The range of the function y= [tex]x^2-4[/tex] is (-4,∞)

What is range?

 The set of every output from a function is its range. Example: Let's have a look at the function f: AB, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output. Set of even natural numbers is the range.

Here the given function is ,

=> y= [tex]x^2-4[/tex]
Now we know that x>0

Then , square on both sides

=> [tex]x^2[/tex] > 0 now add -4 thwn ,

=> [tex]x^2[/tex] -4> -4

=> y > -4

We note that value of y is greater than -4 , (not including -4)

Then range of the function is ,

=> (-4,∞)

Hence the range of the function is (-4,∞).

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For the given function f(x) = x²-16 , the inverse of the function if the domain f(x) is x> 0 is equal to f⁻¹(x) = √x+16.

As given in the question,

Given function is equal to:

f(x) = x²-16

To calculate the inverse of the function if the domain f(x) is x> 0,

Let us consider f(x) = y

y = x²-16

⇒ x² = y + 16

⇒ x = √y + 16

Now, replace x by f⁻¹(x) and y by x we get,

f⁻¹(x) = √x+16

Therefore, for the given function f(x) = x²-16 , the inverse of the function if the domain f(x) is x> 0 is equal to f⁻¹(x) = √x+16.

The complete question is:

Which function is the inverse of f(x)=x²-16 if the domain of f(x) is x> 0?

a. f⁻¹(x) = √x+16

b.  f⁻¹(x) = √x + 4

c.  f⁻¹(x) =  √x -16

d.  f⁻¹(x) =  √x - 4

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Answer:

1. [tex]\frac{3}{7}[/tex] × [tex]\frac{4}{5}[/tex] = [tex]\frac{12}{35}[/tex]

2. [tex]2\frac{6}{8}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{11}{4}[/tex] × [tex]\frac{2}{3}[/tex]

             = [tex]\frac{11}{6}[/tex]

             = [tex]1\frac{5}{6}[/tex]

3. [tex]\frac{12}{5}[/tex] ÷ [tex]\frac{3}{7}[/tex] = [tex]\frac{12}{5}[/tex] × [tex]\frac{7}{3}[/tex]

             = [tex]\frac{28}{5}[/tex]

             = [tex]5\frac{3}{5}[/tex]

4. [tex]\frac{8}{18}[/tex] ÷ [tex]\frac{4}{6}[/tex] = [tex]\frac{8}{18}[/tex] × [tex]\frac{6}{4}[/tex]

             = [tex]\frac{2}{3}[/tex]

Answer: 100 x 1.05^(15x12) = $651739.184097

Step-by-step explanation:

Step-by-step explanation:

a line with undefined slope is a vertical line, because x does not change on this line at all, and therefore the shoe is y/0.

a vertical line is parallel to the y-axis.

and to go through the given point, it has to use the x- coordinate.

so, the equation is

x = -5

that's really it.

this is the line of all points with the x-coordinate = -5. any value for y is valid.

52.7gk. 1mok/39.1gk= 1.347 mol k/1133y=1 kci

The cost for each pound of chocolate chips and each pound of walnuts is: $1.25 and $9.75

Given,A store is having a sale on chocolate chips and walnuts.

For 3 pounds of chocolate chips and 5 pounds of walnuts, the total cost is 18.00 .

For 12 pounds of chocolate chips and 2 pounds of walnuts, the total cost is 45.

we are asked to determine the cost for each pound of chocolate chips and each pound of walnuts.

let x=cost/lb of walnuts

let y=cost/lb of chocolate chips

we frame the equations as:

3x+5y=16

6x+2y=22

Multiply eq 1 by 2.

we get:

6x+10y=32

6x+2y  = 22

subtract now,

8y = 10

y = 10/8

y=1.25

x = x=16-5y=9.75

cost/lb of walnuts=$1.25

cost/lb of chocolate chips=$9.75

Hence we get the required cost.

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The four sided figure formed by opposite pairs of parallel lines is called a parallelogram.

In the attached figure we can see that the quadrilateral ABCD has the following aspects:

AB || CD

AD || BC

Which states that the opposite sides are parallel.

Now ∠A + ∠B = 180° co interior angles are supplementary.

Therefore , ∠A = 180° - ∠B

Again ∠C + ∠B = 180° co interior angles are supplementary.

And , ∠C= 180° - ∠B

Therefore from the above two statements we can say that  ∠C = ∠B.

A unique sort of quadrilateral made up of parallel lines is called a parallelogram. According to definition, a parallelogram is a shape with opposite sides that are parallel and any angle between the sides on each side.

If the opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. If both pairs of opposite sides of a quadrilateral remain parallel and equal, the shape is referred to as a parallelogram.

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Springfield's population in the year 2026, based on the population in 2019, and the growth rate, would be 251, 940 people

As at the year 2019, the population of Springfield was estimated to have been 202, 628 people. This number is also growing by the year, at a rate of 0. 81%.

This means that in the year 2046, the population of Springfield can be estimated using the future value formula which is:

= Current population x ( 1 + population growth rate) ^ number of years

Find the number of years as:

= 2046 - 2019

= 27 years

The population would be:

= 202, 628 x ( 1 + 0.81 % ) ²⁷

= 251, 940 people

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The total cost per yard is $4

How do we calculate the total cost?

The average total cost formula shows the cost per unit of the quantity produced and is calculated by taking two figures where the first one is total production cost and the second one is the quantity produced in numbers and then the total cost of production is divided by the total quantity produced in numbers.

Average Total Cost = Total Cost of Production / Quantity of Units Produced

Given,

Gloria bought fabric which is = 6 3/4 yards or 27 / 4 yards

Total cost was = $27

Cost per yard is = 27 / (27/4)

                           = $4 per yard

Therefore, the total cost per yard is $4

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The compound interest rate is 54.23% for investment that triples in 2 years.

What is compound interest?

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is calculated by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:

A = P (1 + r/4)4t

Given investment triples in 2 years

3p = [tex]e^{rt}[/tex]

rt = ln(3)

r = ln(3)/2 = 0.54

Which is 54.23%

Hence the interest rate is 54.23% for investment that triples in 2 years.

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Answer:

C or third option

Step-by-step explanation:

a) The value of (g/f)(-3) is  -1/2

b)  -5 and -2 are the values that are not in the domain of g(x)/f(x)

What are domain and range of a function ?

The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

g(x)=x+4

f(x)=(x+5)(x+2)

a) g(x)/f(x) = (x+4)/ (x+5)(x+2)

(g/f)(-3) = (-3+4)/(-3+5)(-3+2)

            = 1/(2*-1)

           = 1/-2

           = -1/2

b)  

Set denominator to zero

(x+5)(x+2) = 0

=> (x+5)=0 or (x+2)=0

=> x = -5 and x=-2

=> -5 and -2 are the values that are not in the domain of g(x)/f(x)

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The point-slope form of the equation is y - 2 = -(x + 2)

From the graph, we have the following points

(-2, 2) and (2, -2)

Start by calculating the slope of the points

This is calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

This can be rewritten as

m = (y₂ - y₁)/(x₂ - x₁)

Where

slope = m

(x, y) = (-2, 2) and (2, -2)

So, we have

m = (-2 - 2)/(2 + 2)

Evaluate the expression

m = -1

From the question, we understand that:

(x₁, y₁) = (-2, 2)

The equation of the line is then calculated as

y - y₁ = m(x - x₁)

Substitute the known values in the above equation, so, we have the following representation

y - 2 = -1(x + 2)

Evaluate

y - 2 = -(x + 2)

Hence, the equation of the line is y - 2 = -(x + 2)

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On a given map each unit represnts= 100 miles

Given that the airports are located at coordinates p(1,17) and q(12,10) in this puzzle, the distance between them is given by: Since 100 miles are represented by each unit, the distance in miles is calculated as follows: D = 13.03 x 100 = 1303 miles.

Therefore the distance to the nearest whole mile between the two airports= 1303 miles.

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The height of Liberty School  in ordinary form is 8850 m and of Festus school is 5890 m , the difference of the height values is 2960 m.

In the question ,

it is given that the height of the Liberty  school is 8.85 × 10³ m.

we have to convert this height in the ordinary form ,

8.85 × 10³ = (885/100) × 1000

= 885 × 10

= 8850 m

The height of the Festus school is 5.89 × 10³ m

in ordinary form it is

= 5.89 × 10³

= (589/100) × 1000

= 589 × 10

= 5890 m

The difference in the height of the school = height of liberty school - height of Festus school .

difference = 8850 - 5890

= 2960 m

Therefore , the height of liberty school is 8850 m and height of Festus school is 5890 m, the difference of the height values is 2960 m.

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Answer: $0.576

Step-by-step explanation:

The total amount in prizes is $1800.

For there to be 60% profit, the total cost of the tickets need to be [tex]1800(1.6)=\$ 2880[/tex].

Thus, each ticket must sell for [tex]\frac{2880}{5000}=\$ 0.576[/tex]

Answer: 17/25

Step-by-step explanation:

This equals 68%, which equals 68/100.

Let's divide both sides by 2.

68/2 = 34

100/2 = 50

This gives us 34/50.

We can simplify even more!

34/2 = 17

50/2 = 25.

This gives us 17/25.

We can no longer simplify, which means 17/25 is our final answer.

The volume of the entire shape, given that the figure is a solid shape, and the unit cubes, is d. 32 cubic units.

The volume for the shape can be found by the formula:

= Length  Width x Height

Each small cube is a unit cube which means that the measurements of the dimensions are:

Length = 4 units because there are 4 unit cubs along the length

Width = 4 units for the same reason

Height = 2 units because there are 2 unit cubes needed to get the height

The volume would therefore be:

= 4 x 4 x 2

= 32 cube units

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The vertical line intercept the the graph more than once, the graph is of a relation but it is not a function

Hence, the vertical line intercept the the graph more than once, the graph is of a relation but it is not a function.

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