francine wants to join a health club and has narrowed it down to two choices. the sportshaus charges an initiation fee of $ 500 and $ 10 per month. fitness first has an initiation fee of $ 50 and charges $ 25 month.

Jane made a mistake in her third step. The solution of the equation is x = - 13 / 18

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

The solve the equation to detect where Jane made the mistake in her solution.

-3(4x - 5) = 6(x + 3) + 10

open the brackets on both sides of the equation

-3(4x - 5) = 6(x + 3) + 10

- 12x + 15 = 6x + 18 + 10

- 12x + 15 = 6x + 28

subtract 6x from both sides of the equation

- 12x + 15 = 6x + 28

- 12x - 6x + 15 = 6x - 6x + 28

-18x + 15 = 28

subtract 15 from both sides of the equation

-18x + 15 = 28

-18x + 15 - 15 = 28 - 15

-18x = 13

divide both sides by - 18

x = 13 / -18

x = - 13 / 18

Therefore, jane made a mistake in her third step. She didn't add 18 and 10 together on the right side of the equation.

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Step-by-step explanation:

The square mural in Olivia's classroom has dimensions x by x.

Then she paints a mural of dimensions: x+5 (the length) by x-2 (the width).

Thus the second mural (the hallway mural) has the shape of a rectangle with dimensions (x+5) by (x-2), so the area of the second mural is

(x+5)(x-2).

each side of the classroom mural is 7 feet means that x = 7 ft,

thus the area of the hallway mural is :

(x+5)(x-2)=(7+5)(7-2)=12*5=60 (square feet)

So the answer is 60 square feet.

1a) The number of whole servings Susan can make from 4.25 pounds of flour if one serving uses ²/₃ is 6.

1b) The quantity of flour Susan has after making 6 servings is ¹/₄ pounds.

2) Garrison can drink ⁷/₈ gallons of lemonade each of the next six days.

3) The student council sold 122 bags of chips.

4) If a container can hold 3¹/₃ ounces of peanuts, 5 containers will hold 16²/₃ ounces.

5) The number of people at the football game (400) last night who were not wearing orange and black is 240.

6) The number of long sleeves in Jordan's outfits is 45.

The numbers and values can be determined using suitable mathematical operations.

The basic mathematical operations used include division, subtraction, and multiplication.

1) The total quantity of flour available = 4.25 pounds

The amount of flour required per serving = ²/₃ pounds

The number of servings from 4.25 pounds = 6³/₈ servings (4.25 ÷ ²/₃)

= 6 servings.

Quantity of flour left = ¹/₄ pounds [4 - 6(²/₃)]

2) The number of lemonades available = 5.5 gallons

The quantity Garrison took on Monday = ¹/₄ gallons (0.25)

The remaining number of gallons = 5.25 gallons (5.5 - 0.25)

The gallons for the remaining 6 days = ⁷/₈ gallons (5¹/₄ ÷ 6)

3) The total amount realized from sales = $73.20

The unit price per bag of chips = $0.60

The units sold = 122 ($73.20 ÷ $0.60)

4) The ounces of peanuts per container = 3¹/₃

The number of containers = 5

The ounces of peanuts for 5 containers = 16²/₃ ounces (3¹/₃ x 5)

5) The total number of people at the game = 400

The proportion of people wearing orange and black = ²/₅

The proportion of people not wearing orange and black = ³/₅ (1 - ²/₅)

The number of people not wearing orange and black = 240 (400 x ³/₅)

6) The total number of outfits in Jordan's closet = 200

The proportion of shirts = ³/₄

The proportion of long sleeve shirts = ³/₁₀

The number of long sleeve shirts = 45 (200 x ³/₄ x ³/₁₀)

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The relation is shown in the graph is not a function. Two points have different y-values for the same x-value of 2.

What is a relation?

A relation in mathematics describes the connection between two sets of values for ordered pairs. The set of items in the first set are referred to as domain, and they are connected to the set of elements in the second set, referred to as range.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

A relation becomes a function if there is an unique output for each input.

The given ordered pairs are (0, 0), (2, 0), (2, 2), and (3, 4).

First element of each ordered pair is the input and second element is output.

The inputs are 0, 2, 2,3. The outputs are 0, 0, 2, 4 .

For the input 2, there are 2 outputs 0 and 2.

The given relation is not a function.

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Answer: A loss of 6 dollars

Step-by-step explanation:

Step 1 is to determine how many eggs she purchased:

3 dozen eggs * 12 eggs per dozen = 36 eggs purchased

Step 2 is to find the cost of the eggs purchased using the information you gave:

(36 eggs / 6) * 10 dollars = $60 purchase price

Step 3 is to find out how many eggs broke which is calculated like this:

36 total eggs * .25 = 9 broken eggs

Step 4 is to find how much money she made from selling the remaining eggs:

(36 total eggs - 9 broken eggs) * $2 per egg = $54 resale

Step 5 is finding the profit or loss:

$54 resale price - $60 purchase price = $ -6 (aka a 6 dollar loss)

[tex]=\sqrt{2} *\sqrt{2} *\sqrt{2} *\sqrt{2} \\=(\sqrt{2} *\sqrt{2})(\sqrt{2} *\sqrt{2})\\=2*2\\=4[/tex]

The answer is 4

The value of [tex](\sqrt2)^4[/tex] is 4.

The number of times a number has been multiplied by itself is referred to as its exponent. The rules of multiplying exponents are of different types. The given equation can be calculated using the Power of a Power rule.

According to this rule, when a base has an exponent, and that entire term has an exponent, the exponents are multiplied together. This is written as

[tex](a^x)^y=a^{xy}[/tex]

Here, both exponents are multiplied together.

Therefore, using the above rule the given square root with an exponent can be written as,

[tex]\begin{aligned}\left(\sqrt2\right)^4&=\left(2^{\frac{1}{2}\right)^4\\&=2^{\frac{1}{2}\times4}\\&=2^2\\&=4\end{aligned}[/tex]

The value is 4.

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The equation for the function described, using the translations, is given as follows:

f(x) = 2^(x - 4) + 5.

There are four cases for the translation of a parent function, and they can be represented as follows:

In the context of this problem, the parent function is defined as follows:

f(x) = 2^x

The definitions for each translation are given as follows:

Hence the translated function is defined as follows:

f(x) = 2^(x - 4) + 5.

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Answer:

x = 30 degrees

y = 15 degrees

z = 150 degrees

Step-by-step explanation:

Finding x:

2x + 90 + x = 180

3x + 90 = 180

3x = 90

x = 30

x and 2y are alternate interior angles, which means that they are congruent:

x = 2y

30 = 2y

15 = y

x and z are same side interior angles, which means that they are supplementary:

x + z = 180

30 + z = 180

z = 180 - 30

z = 150

The equilateral triangle shown has three sides and three angles that are all the same. This should be the equilateral triangle theorem, however the answer selections do not cover it.

An equilateral triangle is a triangle with three equal-length sides in geometry. An equilateral triangle's sides are congruent, which indicates that all sides are the same length. All of the inner angles are also identical (60 degrees). An equilateral triangle is a triangle with all of its sides equal in length. Because the three sides are equal, the three angles opposing the equal sides are also equal in size. As a result, it is also known as an equiangular triangle, with each angle measuring 60 degrees.

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The solutions to the rectangles located on the coordinate plane questions in the first page are;

1. Jordan ran a total distance of 6 miles

2. The fourth vertex is located at (5.5, -3.5)

3. The area of the pool is 48 square yards

The area of a figure is the region covered by the closed boundary of the shape or figure.

1. The coordinates of the points expressed as decimals are;

H(-0.75, 0.5), B(1, 0.5), L(1, -0.25), (0.5, -0.25), C(0.5, -0.75), S(-0.75, -0.75)

The distances between the points Jordan visited are;

HB = 1 - (-0.75) = 1.75

BL = |-0.25 - 0.5| = 0.75

LP = |0.5 - 1| = 0.5

PC = |-0.75 - (-0.25)| = 0.5

SC = |-0.75 - 0.5| = 1.25

SH = 0.5 - (-0.75) = 1.25

The total distance Jordan ran = 1.75 + 0.75 + 0.5 + 0.5 + 1.25 + 1.25 = 6

The total distance Jordan ran is 6 miles

2. The shape of the piece of material = A rectangle

The vertices of the rectangle are; (-1.2, -3.5), (-1.2, 4.4) and (5.5, 4.4)

The above vertices indicates that the sides of the rectangle are parallel to the x and y-axis as each two of the three points share a common coordinate

(-1.2, -3.5) and (-1.2, 4.4) represent a vertical side

(-1.2, 4.4) and (5.5, 4.4) represent a horizontal side

Therefore, based on plotting the points on the coordinate plane using MS Excel, we have;

(-1.2, -3.5) and (5.5 ,-3.5) will represent the other horizontal side

(5.5, 4.4) and (5.5, -3.5) represents the other vertical side

The coordinates of the fourth vertex is (5.5, -3.5)

3. The vertices of the pool are;

A(-5, 7), B(1, 7), C(1, -1), and D(-5, -1)

The length of the sides of the pool are;

AB = 1 - (-5) = 6

BC = 7 - (-1) = 8

CD = 1 - (-5) = 6

AD = 7 - (-1) = 8

The length of the rectangular pool = 8 yards

The width = 6 yards

The area of a rectangle = Length × Width

Area of the pool = 8 yard × 6 yards = 48 square yards

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The equation that passes through the point (7, -2) and (11, 5) is y = 4/7x - 9

Equation of the line:

The standard form of the equation of the line is written as

y = mx + b

here

x and y represents the coordinates of the equation

m refers the slope of the equation

b refers the y intercept of the equation

Given,

Here we have the points (7, -2) and (11, 5).

Now we have to find the equation that passes through this points.

If you want to find the equation of the line, we have to find the slope and the intercept of the line.

The slope of the line is calculated by using the given point (7, -2) and (11, 5),

=> m = (11 - 7) / ( 5 - (-2))

=> m = 4/7

Now, we have to use the slope and the point (11, 5) to find the value of y intercept of the equation,

=> 5 = (4/7) (11) + b

=> 35 = 44 + b

=> b = -9

Therefore, the equation that passes through the points is y = 4/7x - 9

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Answer:

[tex]15\sqrt{5}[/tex]

Step-by-step explanation:

simplify [tex]\sqrt{20}[/tex] and [tex]3\sqrt{50}[/tex]

 [tex]\sqrt{20}[/tex] simplifies into [tex]\sqrt{5}[/tex]

 so [tex]\sqrt{20}[/tex] =  [tex]\sqrt{4} \sqrt{5}[/tex]

we can simplify [tex]\sqrt{4[/tex] into a whole number

[tex]\sqrt{4[/tex] =2

          =   2[tex]\sqrt{5}[/tex]

   [tex]\sqrt{50[/tex] simplifies into [tex]\sqrt{2[/tex]

   so [tex]\sqrt{50[/tex] =3( [tex]\sqrt{25} \sqrt{2}[/tex])

we can simplify [tex]\sqrt{25}[/tex] into a whole number

[tex]\sqrt{25[/tex] = 5

= 15[tex]\sqrt{2[/tex]

then we add these simplified roots back into the question

2[tex]\sqrt{5}[/tex] + [tex]5\sqrt{2[/tex] -[tex]2\sqrt{5[/tex]

we simplify again as [tex]2\sqrt{5[/tex] cancels out

to get a final answer of:
[tex]15\sqrt{5}[/tex]

Answer:

Step-by-step explanation:We can find the sum of interior angles of any polygon using the following formula: where nis the number of sides of the polygon. For example, we use $latex n = 5$ for a pentagon. This formula works regardless of whether the polygon is regular or irregular.

Step-by-step explanation:

below -2°

that means

-2 - 5 = -7° C

Answer:

-7 degrees

Step-by-step explanation:

Answer:

x= 6/7 - 2y/7

y= 3 - 7x/2

Step-by-step explanation:

I said so

Answer:

2

Step-by-step explanation:

the rate of change is the coefficient of x

Answer:

x>-4

Step-by-step explanation:

If the agency has 3 cities, 1 month, and 3 airlines to choose from. then there are 9 different vacation packages they can offer.

What is the multiplication rule in permutation and combination?

1. Using the multiplication principle, we can count the number of ways to complete a sequence of tasks by multiplying the number of ways to complete each task together.

2. A permutation is a particular arrangement of objects.

Peaceful Travel Agency offers vacation packages.

If the agency has 3 cities, 1 month, and 3 airlines to choose from.

then by using the multiplication rule,

      The number of different packages = 3 × 1 × 3

                                                                 = 9 packages

Hence, If the agency has 3 cities, 1 month, and 3 airlines to choose from. then there are 9 different vacation packages they can offer.

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If x = -7 and y = 3, the value of the expression (x+y/x-y)²  is​  4/25  .

In the question ,

it is given that ,

the algebraic expression is given as  (x+y/x-y)² ,

we need to find the value of the given expression when the value of x = -7 and y = 3 .

Substituting the values of x = -7 and y = 3 in the expression ,

we get

= (x+y/x-y)²

= ((-7+3)/(-7-3))²

= (-4/(-10))²

= 16/100      

cancelling out the common factor 4 , from the numerator and denominator .

= 4/25

Therefore  , the value of the given expression at x = -7 and y = 3 is 4/25  .

The given question is incomplete , the complete question is

Calculate the value of the expression (x+y/x-y)²​ at x = -7 and y = 3 ?

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a. The angle fact that Mohammed can use to find angle g is alternate angles

b) The angle fact that he then use to find angle h is alternate interior angles.

When two parallel lines are cut by a transversal, the resulting alternate interior angles or alternate exterior angles are congruent, according to the alternate angle theorem. To demonstrate: If a transversal cuts two parallel lines, the alternate interior angles are equal.

When two parallel lines are intersected by a transversal, the angles formed inside them are equal to their alternate pairs. These are known as alternate interior angles.

In this case, it should be noted that the angles will be 137° based on the illustration.

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Answer:

D.

18x-54

Step-by-step explanation:

9*2x - 9*6

18x - 54

Answer: 12-(28/4)=5

Step-by-step explanation:

12-7=5 I hope it helps :)

The stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.

It is the true statement.

Given,

In the question:

Stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.

To check the above statement is true or false.

Now, According to the question:

Let's know about

Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In stratified random sampling, or stratification, the strata are formed based on members' shared attributes or characteristics, such as income or educational attainment.

In stratified random sampling, the strata are formed based on member's shared characteristics (e.g. female or male, occupation, education) or attribute (e.g. black or white).

Hence, The stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.

It is the true statement.

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Interest will the charity have received after 3 years is £60

Jenny opens a "Charity Bank Account". Any interest gained goes to a local charity.

It pays 2% per annum simple interest.

She puts £1500 into the account.

interest will the charity have received after 3 years

Interest = PRT/100

Interest = 1500 x 2 x 3/100

Interest = 60

Therefore,  interest will the charity have received after 3 years is £60

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The input of a function that can be controlled is the independent variable while the output is the dependent variable thus "Number of hours" and "D" are independent while the amount of muscle mass is the dependent variable.

A certain kind of relationship called a function binds inputs to essentially one output.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

An input variable that we can control and manage is said to be an independent variable.

For example in function y = f(x) here we can control variable x so it will be an independent variable.

As per the given,

The number of hours we can spend so will be an independent variable.

The input D will be the independent variable.

The amount of mass muscles depends on age so it will be the dependent variable.

Hence "Number of hours" and "D" are independent while the amount of muscle mass is the dependent variable".

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Answer:  its c

Step-by-step explanation:

The equations that are equivalent include:

2 + x = 5

x + 1 = 4

-5 + x = -2

It is important to note that an equation is used to illustrate the relationship between the variables that are given.

In this case, the given equation is illustrated as:

2 + x = 5

Collect like terms

x = 5 - 2

x = 3

x + 1 = 4

Collect like terms

x = 4 - 1

x = 3

-5 + x = -2

Collect like terms

x = -2 + 5

x = 3

Therefore, the three equations illustrated are equal.

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Answer:

y = -2x-13

1) plot the coordinate you have on a graph (starting at (0,0) move to the left until you hit -8 and then up until you are at +3)

2) Since your slope is negative the line will be higher on the left and lower on the right, so starting at the point you have plotted move down 2 units and to the right one unit.

3) Do this until you intersect with the y-axis (at -13), this is your value for 'b'

4) Plug your values for 'b' and 'm' into the slope-intercept equation

Answer:

Have you finished this question? I don't understand.

Step-by-step explanation: