Isaac was comparing the price of pineapple juice at two stores. Isaac can buy 3 bottles
of pineapple juice at Store A for a total cost of $7.32. The graph below represents
what Isaac would pay in dollars and cents, y, for z bottles of pineapple juice at store
B.
How much more is a bottle of pineapple juice at Store A than
at Store B?

Arial's claim that the graphs of the two lines will be parallel if the coefficients are equal.

If the coefficients of the y-terms are equal and the coefficients of the x-terms are equal, the two lines represented by the equations will be parallel. Parallel lines have the same slope and do not intersect, meaning that their graphs will never cross.

To prove Arial's claim, here is an example:

y = 2x + 1 and y = 2x + 3

The coefficients of the y-terms are equal in both equations, since they both have a coefficient of 2 in front of the x-term. The coefficients of the x - terms are also equal, since they both have a coefficient of 1 in front of the constant term thereby making them parallel.

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Answer:

Step-by-step explanation:

1/6 ÷ 8

1/6 × 1/8

1/48

for each batch

Answer:

See below

Step-by-step explanation:

This is a triangular prism:

h = Perpendicular height of prism

Base shape = Triangle

t = Perpendicular height of triangle

Volume of triangular prism = Base Area × h

                  = Area of triangle × h

                  = [[tex]\frac{1}{2}[/tex] × Base of triangle × t] × h

                  = [[tex]\frac{1}{2}[/tex] × 5 in × 1.7 in] × 10 in

                  = 42.5 cubic inches

Total Surface Area = [2 × Base Area] + Lateral Surface Area

             = [2 × Area of triangle] + [(Perimeter of triangle) × h]

             = {2× [[tex]\frac{1}{2}[/tex] × 5 in × 1.7 in]} + [(5 in + 3 in + 3 in) × 10 in]
             = 8.5 [tex]in^{2}[/tex]  + 110 [tex]in^{2}[/tex]

              = 118.5 square inches

Possible answer: 9

Step-by-step explanation:

9 doubled is 18, and that is 9 more than the original number itself.

Unless I'm wrong.

Answer: T= 5 and s =17

Step-by-step explanation: Use the midpoint formula

Solve for T

^xm=^xC+^xD/2

15+t/2=10

15+t=20

Solve for S

^ym=^yC+^yD/2

s+3/2=10

s+3=20

Answer:

(x, y) = (4, 1)

i don't have an explanation lol

The system of linear inequalities (x, y) has a solution that is (-1, 2)

A system of linear inequalities is identical to a system of linear equations, but instead of equations, it is made up of inequalities. Many constraint scenarios are modeled using sets of linear inequalities.

We may determine the values of x and y in the above problem as;

x + y > 1 ...eq(i)

-x + y <= 3 ...eq(ii)

Solving both inequalities;

The solution is;

1 - x < y ≤ 3 + x

This is simple to plot on a graph, and the intersection will provide the answer;

The graph below shows the inequality's (x, y) solution, which is (-1, 2)

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Answer:871

Step-by-step explanation:If he drove 603 miles in 9 hours, he drove 67 miles per hour. So in 13 hours he will drive 67x13, which is 871.

Answer:

Step-by-step explanation:

David would drive 871 miles. This is because 603 ÷ 9 = 67.

So, you'd have to multiply 67 times 13. Because 67 is the average mph.

In  linear equation, 60m  is the height of flagpole c .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Height/ Shadow

Shadow of the pole = 12 m

Height of the pole = x m

Tim's shadow = Height of the pole - Tim's distance

12 m - 10 m =  2 m

Tim's height = 2 m

Hence:

x/12 = 2/10

Cross Multiply

2x = 12 × 10

x = 120/2

x = 60 m

Approximately = 60m

Hence, the height of the flagpole = 60m

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Answer:

x=5, y=51

Step-by-step explanation:

y = x + 46

y = 7x + 16   substitute equation 1 into equation 2 to get an expression all in terms of x, then solve for x

7x + 16 = x + 46

6x = 30

x = 30/6 = 5     substitute this into either equation and solve for y

y = 5 + 46 = 51

The area of this figure with radius 20.8 ft include the following: D. 432.64π ft² ≈ 1358.5 ft².

Mathematically, the area of a circle can be calculated by using this mathematical expression:

Area = πr²

Where:

r represents the radius of a circle.

By substituting the radius into the formula for the area of a circle, we have the following;

Area of circle = π × 20.8²

Area of circle = 432.64π square feet.

Area of circle = 1358.5 square feet.

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Answer:

Step-by-step explanation:

square root of 100 is 10 and the only point that is on 10 is f so f = 10 or square root of 100

square root of 80 equals about 8.9 and the only point on 8.9 d so d is equal to square root of 80

3 * pi is about 9.4 and the only option left is e so e = 3 * pi

The value of angle L, x and angle M is 55°, 35 and 60° respectively

An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.

From the triangle:

∠OLM + ∠MLN = 180° (sum of angles in a straight line)

125 + ∠MLN = 180°

∠MLN = 55°

Also:

∠MLN + ∠MNL + ∠LMN = 180 (sum of angle in a triangle)

substituting:

55 + (2x - 10) + 65 = 180

2x + 110 = 180

2x = 70

x = 35°

∠LMN = 2x - 10 = 2(35) - 10 = 60°

The value of angle M is 60°

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Answer:

  (c)  3

Step-by-step explanation:

You want the y-value of the solution to the equations ...

We are interested in the value of y, so it can be useful to eliminate x from the equation(s). The x² term appears in both, so it is convenient to subtract the first equation from the second.

  (x² +y²) -(x² -y) = (9) -(-3)

  y² +y = 12

  y² +y -12 = 0 . . . . . . subtract 12

  (y +4)(y -3) = 0 . . . . . factor

  y = -4 or +3 . . . . . . . . values that make the factors zero

Solving the first equation for y, we find ...

  x² +3 = y . . . . . . . add y+3

We know that x² cannot be negative, so this tells us the values of y will be ...

  y ≥ 3

Of the two solutions we found above, the value -4 is extraneous (not in the domain of y).

The y-coordinate of the solution is 3, choice C.

__

Additional comment

The solution is the point of intersection of the two curves shown in the attachment. The y-coordinate of that point is 3.

<95141404393>

For the given right triangle, the value of z is approximately 16.155 cm.

To find the value of z in a right triangle with sides 6 cm and 15 cm, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (z) is equal to the sum of the squares of the lengths of the other two sides (6 cm and 15 cm).

So we can write the equation:

z^2 = 6^2 + 15^2

Simplifying the equation:

z^2 = 36 + 225

Adding the numbers on the right side of the equation:

z^2 = 261

Taking the square root of both sides of the equation:

z = √261

Approximating the square root:

z ≈ 16.155

Therefore, the value of z is approximately 16.155 cm.

Note: The question is incomplete. The complete question probably is: Find the value of z (hypotenuse) if the other dimensions are 6cm, 15cm and right angle in triangle.

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62 kilograms was found to be equal to approximately 136.7 pounds using conversion formula.

To convert kilograms to pounds, the following formula is used:

Pounds = Kilograms x 2.20462

Plugging in 62 kilograms, we get:

Pounds = 62 x 2.20462

Pounds ≈ 136.7

Therefore, 62 kilograms is approximately equal to 136.7 pounds.

The pound (symbol: lb) is defined as exactly 0.45359237 kilograms, or approximately 16 ounces. There are also different types of pounds, such as the avoirdupois pound (used for general purposes) and the troy pound (used for precious metals).

The kilogram (symbol: kg) is used to measure the mass of an object or substance. For example, it can be used to measure your own body weight, the weight of a bag of groceries, or the mass of a planet. The prefix "kilo-" means "one thousand", so a kilogram is equal to 1,000 grams.

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Answer:

h(2)=12

Step-by-step explanation:

Given:

h(x)=4x+4

Find:

h(2)

Substitute 2 into x.

[tex]h(2)=4(2)+4[/tex]

Solve:

[tex]h(2)=12[/tex]

1) values are 15, 16 and 17

2) Drawn in the graph (2)

3)  [tex]x \geq 6[/tex] and graph (3)

Question 6)  [tex]m > 4[/tex] and graph (6)

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

1)

As per the given data:

Values are: 12, 13, 14, 15, 16, 17

Given inequality:

[tex]\frac{x}{5} \geq 3\\= x \geq 5\times3\\= x \geq 15[/tex]

The values of [tex]x[/tex] greater than or equal to 15 out of the given values are:

15, 16 and 17

15, 16, 17 are the solutions of the given equality.

2)

Given inequality:

[tex]x < 8[/tex]

For making the graph, first draw the point [tex]x=8[/tex]

The region to the left of the point [tex]x=8[/tex] will represent the graph as shown in the diagram.

3)

Given inequality:

[tex]x-5\geq 1[/tex]

= [tex]x \geq 1 + 5[/tex]

=  [tex]x \geq 6[/tex]

For making the graph, first draw the point [tex]x=6[/tex]

The region to the right and including the point  [tex]x=6[/tex] will represent the graph as shown in the diagram.

6)

Given inequality:

[tex]6m > 24[/tex]

= [tex]m > \frac{24}{6}[/tex]

= [tex]m > 4[/tex]

For making the graph, first the plot the point m = 4.

The region to the right of the point m = 4 will represent the graph as shown in the diagram.

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The ACT Math section tests a wide range of mathematical concepts and skills, so there are many formulas and concepts that you should be familiar with.

Here are some of the most important ACT math formulas that you should know:

1. Basic operations: addition, subtraction, multiplication, and division.

2. Exponents and roots: [tex]a^n[/tex] means a multiplied by itself n times; the nth root of a is the number that, when raised to the nth power, gives a.

3. Order of operations: parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).

4. Fractions: converting between fractions, decimals, and percents; adding, subtracting, multiplying, and dividing fractions.

5. Algebra: solving equations and inequalities; simplifying algebraic expressions; factoring quadratics; understanding linear and quadratic functions.

6. Geometry: properties of lines, angles, and polygons; Pythagorean theorem; trigonometric functions; volume and surface area of 3D shapes.

7. Probability and statistics: calculating probabilities; mean, median, and mode; standard deviation.

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Answer:Let the magnitude of smaller force is P, the magnitude of larger force is Q and the resultant force is R.

As the resultant force makes 90

∘

 with the smaller force P then Q forms the hypotenuse of the triangle.

Thus, it can be written as,

Q

2

−P

2

=R

2

Q

2

−P

2

=(12)

2

Q

2

−P

2

=144                                (1)

The sum of magnitudes of two forces is given as,

P+Q=18

Q=18−P                                     (2)

Substituting the value from equation (2) in equation (1), we get

(18−P)

2

−P

2

=144

P=5N

Substituting the value of P in equation (1), we get

Q=18−5

=13N

Thus, the magnitude of the forces are 5N and 13N.

Step-by-step explanation:

Answer:operation

Step-by-step explanation:

2.45 BTUs/ft³ is produced in 2 hours.

It is given that a human body that is performing light work generates about 700 BTUs.

Total heat generated by 3 peoples in 1 hour -

Q{heat} = 3 x 700

Q{heat} = 2100 BTUs/hr

For the two hours -

Q{T} = 2100 x 2

Q{T} = 4200 BTUs                                              ... { 1 }

Volume of the room -

V{R} = 12 x 13 x 11

V{R} = 1716 ft³                                                  ... { 2 }

So, we can write as -

BTUs per cubic foot produced in 2 hours is -

{r} = Q{T}/V{R}

{r} = 4200/1716

{r} = 2.45 ft³

Therefore, 2.45 BTUs/ft³ is produced in 2 hours.

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20

Step-by-step explanation:

cause 565-65 is 500 and divide that by 25 is 20.

Answer:

20 weeks

Step-by-step explanation:

starting with an initial 65 adding money each week after 20 weeks he would've added 500

Answer:

x = 64.6 degrees

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adjacent side / hypotenuse

cos x = 3/7

Taking the inverse cos of each side

x = cos^-1 ( 3/7)

x = 64.6 degrees

The function rule that models this situation is that increase in the number of tickets would lead to an increase in the total cost charged for each individual.

A direct relationship between two values is said to exist when the increase in one value leads to the increase of the other.

The cost of 1 ticket = $.75

The cost to enter the carnival = $ 6

Therefore the total cost for each individual = 6+0.75 = $6.75

The cost for two tickets for two individuals = 2× 6.75 = $13.5.

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The best explanation of how to find the experimental probability of rolling a 3:

To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

We have the Data as:

Number    Frequency     Probability

1                      4                  0.13

2                      6                  0.20

3                      5                  0.17

4                      7                  0.23

5                      3                  0.10

6                      5                  0.17

total                30                 1.00

To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials.

= 5/30

= 1/6

= 0.166

= 16.6% or 17%.

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Expression for actual length and actual width of the concrete patio are

30x inches and 30y inches respectively.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Given,

A blueprint of a concrete patio has a scale of 2 inches=5 feet.

2 inches = 60 inches

scale factor = 60/2 = 30

Let length of the patio on the blue print is x inches

width of the patio on the blue print is y inches

then actual length of the 30x inches

actual width of the patio = 30y inches

Hence, 30x inches is actual length and 30y inches is actual width of the concrete patio.

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