Which of the following is the BEST possible first step to solve for n:

The amount that Justin would have to pay the pizza shop if he bought 12 slices of pizza this month is $15.

The monthly cost for x slices of pizza is $25 + $1.5x

In order to determine the amount that Justin would have to pay the pizza shop if he bought 12 slices of pizza can be determined by multiplying the cost per pizza by the number of pizzas sold.

Multiplication is the operation used in mathematics that is used to calculate the product of two or more numbers. The sign that is used to represent multiplication is x.

Cost of 12 slices of pizza = discounted price x number of slices bought

$1.25 x 12 = $15

The monthly cost is the sum of the membership fee and the total cost of the pizzas bought

Monthly cost = monthly membership fee + cost of the slices

Monthly cost = monthly membership fee + (discounted price x number of slices bought)

$25 + (1.25 x x)

$25 + $1.25x

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Answer:

1. Slope= 2

2. [tex] \frac{b - 2}{4 - 2} = 2[/tex] or [tex] \frac{8 - 2}{a - 2} = 2[/tex]

3. a= 5

4. b= 6

Step-by-step explanation:

The slope of a straight line between any two points of the line would be the same. This means that calculating the slope of the line using point (2, 2) and (6, 10) would give us the same slope value when calculating with points (4, b) and (6, 10) for example.

Formula

[tex]\boxed{\text{slope} = \frac{y_1 - y_2}{x_1 - x_2} }[/tex]

Q1. Since we two pairs of known coordinates, let's make use of them in the slope calculation.

Slope of line

[tex] = \frac{10 - 2}{6 - 2} [/tex]

[tex] = \frac{8}{4} [/tex]

= 2

Q2-4. Since in the subsequent parts we will eventually have to find the value of a and b, let's form an equation for each of them.

Slope between (2, 2) and (4, b)= slope between (2, 2) and (6, 10)

[tex] \frac{b - 2}{4 - 2} = 2[/tex]

[tex] \frac{b - 2}{2} = 2[/tex]

Multiply both sides by 2:

b -2= 2(2)

b -2= 4

b= 4 +2

b= 6

Using (2, 2) and (a, 8):

[tex] \frac{8 - 2}{a - 2} = 2[/tex]

Multiply both sides by (a -2):

6= 2(a -2)

Expand:

6= 2a -4

Add 4 to both sides:

2a= 10

Divide both sides by 2:

a= 10 ÷2

a= 5

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The volume of the Oblique pyramid is 19 [tex]ft^{2}[/tex]

We know, the volume of a pyramid is [tex]\frac{1}{2}[/tex] × B × h

where B is the area of the base and h is the height of the pyramid.

Given:  The pentagonal base has an edge length of 2.16 ft and an area of 8 [tex]ft^{2}[/tex] and angle ACB measures 30°.

Consider triangle ACB

tan30° = [tex]\frac{AB}{CB}[/tex]

[tex]\frac{1}{\sqrt{3} }[/tex] = [tex]\frac{AB}{7\sqrt{3} }[/tex]

AB = 0.58 × [tex]7\sqrt{3}[/tex]

AB = 0.58 × 12.12

AB = 7.03

Now, the volume of the oblique pyramid will be

V = [tex]\frac{1}{2}[/tex] × 8 × 7.03

V = 18.75

V ≈ 19 [tex]ft^{2}[/tex]

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Answer:19

Step-by-step explanation:

Answer:

Slope = -1

Step-by-step explanation:

m = second y - first y / second x - first x

second y = 1

first y = 9

second x = 9

first x = 1

1 - 9 = -8

9 - 8 = 8

-8/8 = -1

Find the slope of a line.

We mark the points: (x₁ = 1, y₁=9) and (x₂ = 8, y₂ = 1)

We have that the formula is:

          [tex]\boldsymbol{\sf{m=\dfrac{Y_{2}-Y_{1} }{X_{2}-X_{1}} }}[/tex]

Now we apply the formula and solve:

                    [tex]\boldsymbol{\sf{m=\dfrac{1-9}{8-1} =\dfrac{-8}{7} }}[/tex]

                   [tex]\boldsymbol{\sf{m=\dfrac{-8}{7} }}[/tex]

The slope of the line through (1, 9) and (8, 1) is -8/7.

The fractions are divided to give 77/144. Option A

A fraction can simply be defined as the part of a whole set or element.

The types of fractions includes;

Examples of simple fractions are: 1/2 , 1/4

Examples of proper fractions are; 2/3, 5/6

Examples of improper fractions are; 5/3, 9/7

Examples of mixed fractions are; 2 1/2, 3 1/4

Given the expression as;

2 3/4 ÷ 5 1/7

Turn into improper fractions

11/4 ÷ 36/7

Take the inverse of the divisor

11/4 × 7/36

Multiply the numerators and denominators

77/144

Thus, the value is 77/144

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Answer: #1 / A

Step-by-step explanation:

Answer:

1,312.5

Step-by-step explanation:

6.25x10=62.5

3500x62.5%=2,187.5

3500-2,187.5=1,312.5

I hope this is correct :-|

we have

3500 = Pe^(0.0625) x(10)

3500= Pe^(0.625)

P = 3500 / e^(0.625) = 1873

thus 1873 Macaws remaining in 10 years

Answer:

11.4 pounds

Step-by-step explanation:

Answer: 80un^2

Step-by-step explanation:

The length of AB is 10

The length of BC is 8

The length of CD is 10

The length of DA is 8

10 x 8 = 80 and there are two pairs of 8 and ten which makes it 80un^2

The value of b that will cause the system to have an infinite number of solutions is 6.

Given the following system of equation expressed as:

y = 6x – b

-3x + 1/2 y = -3

Rewrite equation 2:

1/2 y = 3x - 3

y = 6x - 6

Equate the right hand side of both equations

6x - b = 6x - 6

For the equation to have  infinite number of solutions, the expression on both sides must be the same.

Comparing both sides;

-b = -6

b = 6

This gives the required value of b

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Gil is out purchasing CDs and books. He spends $32 on 4 books but not any CDs. A standard form equation y=-8n and x=0.

Given that,

Gil is out purchasing CDs and books. He spends $32 on 4 books but not any CDs.

We have to create a standard form equation to show the connection between the price of a book (y) and the price of a CD (x).

The equations in standard form for Gil's change in money after purchasing a book (y) and his change in money after selling a CD (x).

Gil spends $32 on 4 books.

4 books = $32

1 book = $8

If n is the total number of books bought, the change in currency equals

y=-8n.

Here, the negative sign stands for a decline in currency. Here, a slope of -8 indicates that after purchasing each book, the money declined by $8.

There are no CDs so x=0.

Therefore, y=-8n and x=0.

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The sine of the angle based on the information about the cosine is D. ✓91 / 10.

It should be noted that cos is calculated as:

= adjacent / hypothenuse.

This was given as 3/10.

It should be noted that sine = Opposite / Hypothenuse

The opposite will be:

Opp² + Adj² = Hyp²

Opp² + 3² = 10²

Opp² + 9 = 100

Opp² = 100 - 9

Opp² = 91

Opp = ✓91

Therefore, the sine of the angle will be ✓91 / 10

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[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{7}}} \implies \cfrac{ -6 }{ -3 }\implies 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{2}(x-\stackrel{x_1}{7}) \\\\\\ y-4=2x-14\implies {\Large \begin{array}{llll} y=2x-10 \end{array}}[/tex]

Answer:

-5

Step-by-step explanation:

[tex]-3t+4=19 \\ \\ -3t=15 \\ \\ t=-5[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{3c + 6d + 3d}\\\large\text{COMBINE the LIKE TERMS}\\\mathsf{= (3c) + (6d + 3d)}\\\mathsf{= 3c + 6d + 3d}\\\mathsf{= 3c + 9d}\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{3c + 9d}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

In the football club, the percentage of 15-year 12 pupils out of 46 pupils is equal to 30%.

The proportion can be found by dividing the number of 15-year pupils by the total number of pupils. Therefore;

number of 15-year pupils / total number of pupils = 12 / 46 = 0.260

Rounding it to one decimal;

0.260 = 0.3

Percentage in mathematics can be defined as a number or a rate in each hundred. A decimal value can be converted into a percentage by multiplying the decimal value by 100.

0.3 × 100 = 30%

Therefore, the proportion of the 15-year pupils in the football club is 12/46 and this proportion can be written in percentage as 30%.

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Twenty-four equals the sum of 10.5 and the quotient of a number and 4.5 is given by 24 = 10.5 + x/4.5

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number. As a general rule, the smaller the divisor (denominator) of an expression, the larger would be the quotient.

In order to translate this word problem, we would assign a variable to the unknown number and then translate the word problem into algebraic equation as follows:

Let n represent the unknown number.

Translating the word problem into an algebraic equation, we have;

24 = 10.5 + x/4.5

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Longest display is 1.125 inches longer than the shortest display.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

Given Data

Size of cell phones

5.625 inches

5[tex]\frac{1}{2}[/tex] inches = [tex]\frac{11}{2}[/tex] inches

5.5 inches

6[tex]\frac{1}{4}[/tex] inches = [tex]\frac{25}{4}[/tex] inches

6.25 inches

5.125 inches

Longest display = 6.25 inches

Shortest display = 5.125 inches

Difference = longest display - shortest display

Difference = 6.25 - 5.125

Difference = 1.125

Longest display is 1.125 inches longer than the shortest display.

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After 2.57 hours, the distance between Steve and Elsie will be 25 miles.

So, let t (hours) represent the amount of time Elsie needs to travel before they are 25 miles apart.

Steve takes longer because he is 2 hours earlier, so his time is t + 2.

So, according to the formula the distance between Steve and Elsie will be:

Solve for t as follows:

[tex]\begin{aligned}&(2(t+2))^2+(2.5 t)^2=25^2=625 \\&4(t+2)^2+6.25 t^2=625 \\&4\left(t^2+4 t+4\right)+6.25 t^2=625 \\&10.25 t^2+16 t-609=0 \\&t=\frac{-b \pm \sqrt{t^2-4 a x}}{2 a} \\&t=\frac{-16 \pm \sqrt{(16)^2-4 *(10.25) *(-109)}}{2 *(10.25)} \\&t=\frac{-16 \pm 68.74}{20.5}\end{aligned}[/tex]

So, t = 2.57 or t = -4.13.

Therefore, after 2.57 hours, the distance between Steve and Elsie will be 25 miles.

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The correct question is given below:

Steve and Elsie are camping in the desert, but have decided to part ways. Steve heads north, at 8 AM, and walks steadily at 2 miles per hour. Elsie sleeps in and starts walking west at 2.5 miles per hour starting at 10 AM. When will the distance between them be 25 miles?

Answer:

Your answer is [tex]70[/tex].

Step-by-step explanation:

[tex]10[/tex] ÷ [tex]\frac{1}{7}[/tex] [tex]= 70[/tex]

The length of the course is 480 m.

Length is used to measure distance. According to the International System of Quantities, length has the dimension of distance. In most measurement systems, length is represented by a base unit from which all other units are derived. The International System of Units (SI) system's fundamental unit of length is the meter.

From the given figure we can infer that W is the mid-point of AB. Therefore we know that AW = WB

Now the distance is given by

5x -110 = 2x +100

or, 5x - 2x = 100 + 110

or, 3x = 210

or, x = 70

Therefore total length = 5x -110 + 2x +100 = 7x - 10 = 490 - 10 = 480 m

Therefore the length is 480 m.

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Answer:

7560 meters

Step-by-step explanation:

42 meters a second -> 2520 meters a minute -> 7560 meters for 3 minutes

Answer:

The airplane will be 7560 meters after three minutes of flying.

Step-by-step explanation:

one minute= sixty seconds

42*1800=7560

3*60=1800

Not sure if I did the math right but I'm positive I got the right answer.

The coordinates of the second end point of the line is (8, -12).

For the given question;

The end point of the line segment is (0,0).

The mid-point of the line segment is at  (4,-6).

Thus,

(x₁, y₁) = (0,0)

(x₂, y₂) = ?

(xₐ, yₐ) = (4,-6)

Thus, the formula for finding the mid point is;

xₐ = (x₁ + x₂)/2

Put the values;

4 = (0 + x₂)/2

On simplification;

x₂ = 8.

For y coordinate;

Thus, the formula for finding the mid point is;

yₐ = (y₁ + y₂)/2

Put the values;

-6 = (0 + y₂)/2

On simplification;

x₂ = -12

Thus, the coordinates of the second end point of the line is (8, -12).

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New function that is a horizontal stretch of F(x)=[tex](x+2)^{3} + 5[/tex] is F([tex]\frac{x}{k}[/tex])=[tex](\frac{x}{k} +2)^{3} + 5[/tex]

The point (x, y) on the graph of f(x) is changed to the point (x/k, y) on the graph of g when the graph is stretched or contracted horizontally by a factor of 1/k (x).Only when the input value is also increased by a, can a graph be stretched horizontally by a factor of 1/a. The x-coordinates should be multiplied by a once f(x) has been stretched horizontally to f(ax). Keep the y-intercepts where they are. The resulting function might have a different domain, but it will have the same range. If a point (m, n) is stretched horizontally, it becomes (am, n).

F(x)=[tex](x+2)^{3} + 5[/tex]

F([tex]\frac{x}{k}[/tex])=[tex](\frac{x}{k} +2)^{3} + 5[/tex]ch visit :
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Answer:

x = -4

Step-by-step explanation:

3(x-5) becomes 3x-15

5x-(3-x) becomes 6x-3

3x - 15 = 6x - 3

    + 15        + 15

3x = 6x + 12

-6x  -6x

-3x = 12

    divide -3 on both sides

X = - 4

Answer:

x = -4.

Step-by-step explanation:

3(x-5) = 5x-(3-x)

3x - 15 = 5x - 3 + x

3x - 5x - x = -3 + 15

-3x = 12

x = -4.

The distance between the two points is 13 unit.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the display style for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle. All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.

Given that,

A right triangle can be drawn using the grid lines for legs and the line segment between the two points as the hypotenuse. You can count grid squares or subtract coordinates to find the vertical leg is 12 units and the horizontal leg is 5 units. The Pythagorean theorem tells you the length of the hypotenuse (distance between the points) is d² = 12² +5² = 144 +25 = 169

d = √169 = 13

The distance between the two points is 13 unit

This set of dimensions, {5, 12, 13}, is one of several "Pythagorean triples" that often show up in math problems. Other common triples are {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}, and multiples of these.

Therefore, distance between the two points is 13 unit.

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the Algebraic representation of the expression "product of 2 and the cube of a number" is 2x³

Algebra is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

The product of 2 and the cube of a number

So,

product of 2 and the cube of a number

= 2 × x³

= 2x³

For instance, if x = 2

2x³

= 2×(2)³

= 2 × (2 × 2 × 2)

= 2 × 8

= 16

Therefore, the expression "product of 2 and the cube of a number" can be written as 2x³

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Answer:

14.077 appr. 14.1

Step-by-step explanation:

183/13=

18÷13=1 remainder 5

53÷13=4 remainder 1

therefore the answer is 14.1

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