Lyle and Ming are painting an art room. They started with 44 gallons of paint. On the first day, Lyle used \frac{1}{2} 2 1 ​ gallon of paint and Ming used 1\frac{1}{4}1 4 1 ​ gallons of paint. How many gallons of paint were left when they completed their first day of painting?

c = 2.97r is the equation that describes the proportional relationship between r, the number of reams purchased and c, the total cost

Two variables have a proportional relationship if all the ratios of the variables are equivalent

In order to write an equation that describes the proportional relationship r, the number of reams purchased and c, the total cost, we need to write a proportional equation using the variables:

c α r                  (Note: α is the proportion symbol)

c = kr

k = c/r

Where k is the constant of proportionality

As shown in the image, you can see that 4 reams cost $11.88 and 6 reams cost $17.82

k = c/r

k = 11.88/4 = 2.97 or 17.82/6 = 2.97

c = kr

c = 2.97r

Therefore, the equation that describes the proportional relationship between r, the number of reams purchased and c, the total cost is c = 2.97r. Enter c = 2.97r in the box

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The relationship between the perimeter and the side length of the hexagons is proportional.

A proportional relationship is one that illustrates the constant between the data that are given.

In this case, when the side length is 2, the perimeter is 12. The constant is:

= Perimeter / Length

= 12 / 2

= 6

Also, when the length is 3, the perimeter is 18. The constant will be:

= 18 / 3

= 6

Since they have 6 as constant, it's a proportional relationship.

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There are 10 students in a class: 6 boys and 4 girls. If the teachers chooses 3 at random, then the probability that everyone in the group is a girl is 1/30

It is given that,

Total number of students = 10

Number of boys = 6

Number of girls = 4

Total number of ways to select 3 students from 10 students.

10C3= 10!/ 3!7!= 120

Total number of ways to select 3 students from 4 girls

4C3 = 4!/ 3!=4

The probability that everyone in the group is a girls is

P = 4/120

  = 1/30

Hence ,  the probability that everyone in the group is a girl is 1/30

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a. The two numbers between which the solution to the equation lies are 0 and 1.

b. The value of the variable "s" is 13/20.

The equation given to us is  one fourth plus s equals 18 over 20. This can be expressed as;

¹/₄ + s = ¹⁸/₂₀

s = ¹⁸/₂₀ - ¹/₄

s = (18/20) - (5/20)

s = (18 - 5)/20

s = 13/20

The solution is a rational number. A rational number is defined in mathematics as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

We can determine two rational numbers such that the solution is in between them. A rational number smaller than the solution is 0. A rational number larger than the solution is 1. Hence, the solution lies between 0 and 1.

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Answer:

$1925

Step-by-step explanation:

So your problem is $55,000 x 3.5%

You can rewrite this as:

55,000 x 3.5/100 or 55,000 x 35/1000

Now multiply. I will remove the /1000 for now.

55,000x35=1925000

Now, divide 1925000 by 1000.

1925/1000=$1,925

The area of the of the rectangle is 5.25square inch and the area of the square is 6.25square inch. Therefore the square has larger area.

The area of a shape is the “space enclosed within the perimeter or the boundary” of the given shape. We calculate the area for different shapes using formulas.

Area formula in rectangle is L× W and in square is L^2. This happened in square becos square has all it's sides equal. Where L and W are length and Width respectively

The area of rectangle with dimension 7inches by 3/4 inch is 7×3/4= 5.25 square inches

The area of the square with dimension 2 1/2 inches is( 5/2)^2= 25/4= 6.25m

Therefore the square has larger area

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The inequality that can be used to solve for x, the number of minutes it will take Amy to finish typing her paper is D. 38x + 1,450 > 4,000.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Since Amy types at an average speed of 38 words per minute and has already typed 1,450 words of her final paper, which will be more than 4,000 words.

Let the number of minutes be x.

This will be:

1450 + 38(x) > 400

1450 + 38x > 4000

In conclusion, the correct option is D.

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The algebraic fundamental theorem states that there are 12 zeros in the function f(x) = 15x12 + 41x9 + 13x2 10.

acc to our question-

hence,there are 12 zeros

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The graph of (y = 4x), which depicts the relationship between the quantity of tickets sold (x) and the sum of the proceeds from the sales (y), can be drawn by first formulating the linear equation and then using the transformation.

Which is the function's graph?

We have a piecewise function right here:

If x > 6, f(x) = 0.5*x - 2.

If x > 6, f(x) = -x - 1

Given:

Each ticket for the school play is $4.

There have been 'x' tickets sold in total.

The tickets generated 'y' in total revenue.

The graph showing the relationship between the quantity of tickets sold (x) and the sum of the ticket sales (y) can be drawn using the procedures below:

Form the linear equation in two variables as a first step.

y = 4x

The total revenue from the tickets is shown in the equation above.

Draw the graph of (y = x) in step two.

Step 3: In the graph of (y = x), multiply the x-axis by 4 units. The graph that is produced is (y = 4x).

You may find the graph for (y = 4x) below.

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Answer:

No

Step-by-step explanation:

Total money = €150

1 pair of sunglasses = €70

3 pairs of shorts = €15 × 3 = €45

then, Total = €70 + €45 + x

€150 = €115 + x

x = €150 - €115

x = €35

Which means Eddie got only €35 left on him which is not enough for him to buy the trainers

The value of 9 and a half will be 9 1/2.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

Here, we want to find the value of 9 and half. This will be:

= 9 + 1/2

= 9 1/2

The value is 9 1/2.

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The measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.

According to the question,

We have the following information:

We have a figure where angle MCJ is 130°.

Now, we can extend the two given lines as imaginary lines. After extending the lines, we will find that these lines are parallel and the lines are being cut by another line.

We know that in this case the alternate interior opposite angles are equal and the sum of consecutive alternate interior angles is 180°.

Now, ∠MCJ and ∠CMB are alternate interior opposite angles and thus they are equal.

Hence, the measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.

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The relation between angle 1 and angle 2 is they are equal and corresponding angle.

What are parallel lines?

Two lines are said to be parallel when they do not intersect each other. We can also say that two lines that run along and meet at infinity are called parallel lines.

What are corresponding angles?

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines and the transversal.

Given, m and l are parallel line.

Hence, m and l satisfy the condition of parallel lines.

Therefore, the angle 1 and angle 3 are equal.

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Answer:

The ratio of acid to water is 2 to 3 in the mixture of the two solutions

This can be thought of as a chemistry problem or a math problem, but both use practically the same process to find the final answer.

So, let's say 2 liters of 50% acid and 1 liter of 20% acid is mixed.
In total, there is 2*(50%) + 1*(20%) of acid, so there is 1 liter of pure acid in 2 liters of 50% acid, and 0.2 liters of pure acid in 1 liter of 20% acid. This in total is 1.2 liters of acid. The total volume is 2 + 1 liters, which is 3 liters. the percentage can be found by dividing the amount of pure acid by the total volume, so 1.2/3, which equals 0.4, or 40%. The ratio would be 40% to 100-40%, or 40% to 60%, or 2 to 3

Answer:

24

Step-by-step explanation:

lets set up the equation

x=25-(0.05x20) this is

x=25-1

x=24

Answer:

[tex]\sqrt{2}[/tex] × [tex]\sqrt{8}[/tex]   And [tex]\sqrt{2}[/tex] ×[tex]\sqrt{3}[/tex]  

Step-by-step explanation:

3x9 are both whole numbers and 0x[tex]\sqrt{5}[/tex] has only one irrational number

Answer:

---------------------------

Considering the figure of a right angle triangle, the given length is the hypotenuse,. The unknown side x is calculated to be 6.86 cm

information given in the question

hypotenuse = 9.7 cm

opposite = x

adjacent =  x

The problem is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

opposite = adjacent

plugging the values as in the problem

let x be the required distance

9.7² = x² + x²

94.09 = 2x²

47.045 = x²

x² = 47.045

x = √47.045

x = 6.8589

x = 6.86 to 3 significant figures

side x is 6.86 cm

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The domain of the given function is -∞ < x < ∞.

So, the function is:

Now, the domain of the given function is:

The domain will therefore be -∞ < x < ∞.

Therefore, the domain of the given function is -∞ < x < ∞.

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Answer: C. (2, 1)

Step-by-step explanation:

The numbers labeled are

(-5, -8)

(-2, 1)

(4, 0)

(2, 9)

Find coordinates by looking at each line. (x, y)

The x-axis is the horizontal line in the middle.

The y-axis is the vertical line going across.

The x-axis always goes first when plotting down coordinates, and y goes second.

So, the one NOT labeled is C (2, 1)

Answer:

x < 1 and x > -4 (more down below)

Step-by-step explanation:

First we have to solve the algebra
|-2x - 3| + 2 < 7
|-2x - 3| < 5
1. -2x - 3 < -5                    2.  -2x -3 < 5
-2x < -2                           -2x < 8                        

x < 1                                x > -4 (switch the expression)
Now... The two answers are x < 1 and x > -4

The interval notation is a number line with circles on the two points (answers)
Sorry I can't exactly explain what that is you might have to search it up, but you need a number line like this, and you need to draw another line above the -5 and 1 with an open circle on -5 and 1

    O-----------------------O

<---5, -4, -3, -2, -1, 0, 1, 2-->

For graphing, make a graph with 5 points on each side with 4 quadrants or whatever reasonable size, and draw a vertical line that extends all the way above and below your graph above 1 on line x and a vertical line all the way above and below your graph above above -5 on x, then shade everything in between those two lines.

This helps you to know what value you plug in for X makes the inequality true (shaded region)

The students that will like exactly one of the two sports out of football and baseball is 200.

These are the fundamental set of set theory formulas. When there are two sets P and Q, the number of elements in one of the sets P or Q is denoted by n(P U Q). The number of elements in both sets P and Q is represented by the expression n(P ⋂Q). n(P U Q) is equal to n(P) + n(Q) - n (P Q).

Here,

F=140

B=144

F∩B=42

F-B=n(F)-n(F∩B)

=140-42

F-B=98

B-F=n(B)-n(F∩B)

=144-42

=102

So, the students that will like exactly one of the two sports,

=102+98

=200

There are 200 students who will only enjoy one of the two sports—football or baseball.

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Answer:

x = 52°

y = 25°

z = 90°

Step-by-step explanation:

        We know there are 180 degrees in a triangle. The box represents 90 degrees.

90° + x + 38° = 180°

x + 128° = 180°

x = 52°

        Next, we know that a straight line is equal to 180 degrees. Again, the box represents 90 degrees.

90° + z = 180°

z = 90°

        Lastly, we will use the same process for angle x, but for angle y.

y + z + 65° = 180°

y + 90° + 65° = 180°

y + 155° = 180°

y = 25°

The solution for the system of equations -

x+3y+z=-8      

2x+y-6z=20    

x-2y+z=-13    

is x = 5.875, y = 1, z = 16.875

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line in point slope form can be also written as-

[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

We have the following set of equations -

x+3y+z=-8       ..[1]

2x+y-6z=20     ..[2]

x-2y+z=-13        ..[3]

We can write eq [3] as -

z = - 13 - x + 2y

So, eq [1] and [2], will become -

x + 3y + (-13 - x + 2y) = -8

x + 3y - 13 - x + 2y = -8

5y = - 8 + 13

5y = 5

y = 1       ..Eq[4]

AND

2x + y - 6z = 20

2x + y - 6(- 13 - x + 2y) = 20

2x + y + 78 + 6x - 12y = 20

2x + 1 + 78 + 6x - 12 = 20

8x = 47

x = 5.875      ..Eq[5]

Now -

x - 2y + z = -13

5.875 - 2 + z = - 13

z = 16.875

Therefore, the solution for the system of equations -

x+3y+z=-8      

2x+y-6z=20    

x-2y+z=-13    

is x = 5.875, y = 1, z = 16.875.

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The value a = 2 and b = 5 is makes the expression (5x²y²){-4xªy³) =−20xªyᵇ as true.

Expression:

An expression is set of numbers or variables combined using the operations +, -, * and /.

Given,

Here we have the expression (5x²y²){-4xªy³) =−20xªy°.

Now, we have to the value of a and b which make both equation as equal.

In order to get the value a and b, first, we have to solve the expression in the left hand side,

To solve this type of equation, the first step is to combine the like terms, then we get,

=> (5x²y²){-4xªy³)

=> (5 x -4) (x² xᵃ) (y² y³)

Now, we have to do the multiplication on it, then we get,

=> -20 xᵃ⁺² y²⁺³

=> -20xᵃ⁺²y⁵

Now, we have to equate both LHS and RHS, then we get,

=> -20xᵃ⁺²y⁵ = -20xᵃyᵇ

While we looking into the equation, we have identified that the value of a is 2 and the value of b is 5.

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The proof that shows that lines DC and AB are parallel is shown below.

The SSS congruence theorem states that two triangles that have three corresponding congruent sides are congruent to each other.

When two triangles are proven to be congruent triangles, invariably, we can state that the corresponding parts of both triangles are also equal to each other by CPCTC.

The following proof shows lines DC and AB are parallel lines:

Statement                                              Reasons                                                    

1. AB = CD                                             1. Given

AD = CB                                    

2. Line AC = Line AC                            2. Reflexive property

3. Triangle ADC ≅ Triangle ABC         3. SSS

4. Angle 1 ≅ Angle 4                             4. CPCTC

5. DC║AB                                              5. Converse of alternate interior ∠s theorem

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The 27.4 m² of carpet is needed for three bedrooms.

Firstly we will calculate the area of each room.

Area of bedroom a = 3.1 × 3.1

Area of bedroom a = 9.61 m²

Area of bedroom b = 2.9 × 3.2

Performing multiplication on Right Hand Side of the equation

Area of bedroom b = 9.29 m²

Area of bedroom c = 2.5 × 3.4

Area of bedroom c = 8.5 m²

Total area of all the rooms = 9.61 + 9.29 + 8.5

Performing addition on Right Hand Side of the equation

Total area of all the rooms = 27.4 m²

Hence, 27.4 m² carpet is required for three bedrooms.

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The angle-side-angle (ASA) Congruence theorem proves that

ΔABC and ΔPQR are congruent triangles.

We know that the angle-side-angle ASA Congruence theorem states that if two angles and the side between these angles of one triangle are equal to two angles and the side between then of another triangle then those two triangles are congruent.

In given triangles ABC and PQR,

∠ABC ≅ ∠PQR

BC ≅ QR

∠BCA ≅ ∠QRA

so, by ASA Congruence theorem ΔABC ≅ ΔPQR

Therefore, the angle-side-angle (ASA) Congruence theorem proves that

ΔABC and ΔPQR are congruent triangles.

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Answer:

equation: y= -2x-1

Step-by-step explanation:

y= -2x+b

-3= -2(1)+b

-3= -2+b

b= -1

equation: y= -2x-1

Answer:

686 cm^2

Step-by-step explanation:

4(7)=28

7(7)=49

49 x 28= 1372

1372/2=686

hopes this helps