The sum of two consecutive even integers divide by four is 189.5

The solutions of -x^2 + 4x = x - 4 are -1 and 4

The equation is given as

-x^2 + 4x = x - 4

When split, it becomes

y = -x^2 + 4x

y  = x - 4

The graph represents the above equations.

So, the solution is the point of intersection of both equations

The equations intersect at x = -1 and x = 4

Hence, the solutions of -x^2 + 4x = x - 4 are -1 and 4

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The cost of 11 baseball uniforms will be the multiplication of 11 to 124 which is $1364 thus it is enough to buy the uniforms and the team will be left with $36 so option (B) will be correct.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

Multiplication = to multiply any two or more numbers or variables called multiplication.

As per the given question,

Each uniform costs $124.

Number of uniforms needed to buy = 11

Cost of 11 uniform = 11 × 124 = $1364

The budget $1400 > $1364 therefore it is enough.

Hence "The cost of 11 baseball uniforms will be the multiplication of 11 to 124 which is $1364 thus it is enough to buy the uniforms".

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Divide the amount of each ingredient by 4.

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

100 servings of apple dumplings.

The amount of each ingredient to make just 25 servings.

Divide the amount of each ingredient by 4.

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Two expression with equal sign is an equation. To solve 2(x + 7) + 3x = 12, the first step in solving this equation for x  is 2x + 14 + 3x = 12. Option A is correct.

Two expression with equal sign is called as equation.

In given equation 2(x + 7) + 3x = 12 we need to solve the first step.

2(x + 7) + 3x = 12

For the first step, we need to multiply 2 with the expression in bracket,

So it will be

2x+14+3x=12.

Therefore option (A) is correct, For solveing 2(x + 7) + 3x = 12, 2x + 14 + 3x = 12  is the first step.

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Answer:

The slope of the line is 4.

The Y intercept of the line is -6.

Step-by-step explanation:

The slope intercept form of a line is

[tex]y=mx+b[/tex]           .... (1)

where, m is slope and b is y-intercept.

The given equation of line is

[tex]y=4x-6[/tex]             .... (2)

On comparing (1) and (2) we get

[tex]m=4[/tex]

[tex]b=-6[/tex]

It means the slope of the line is 4 , The Y intercept of the line is -6. the graph of a linear function is a straight line.

The value of y is -6 at x=0, so the line do not passes through the origin.

Therefore, the correct statements are "the slope of the line is 4  and the Y intercept of the line is -6".

The solutions are

The slope of the line is 4

The y-intercept of the line is –6

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y coordinate of second point

y₁ = y coordinate of point one

m = slope

x = x coordinate of second point

x₁ = x coordinate of point one

Given data ,

Let the equation be y = 4x - 6

Now , the equation is of the form y = mx + b where m is the slope and b is the y-intercept

Therefore , the slope of the equation is m = 4

And the y intercept is -6

Hence ,

The slope of the line and the y-intercept of the line is –6

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The correct answer for product in lowest term of the expression [tex]\dfrac{8}{15} * \dfrac{-3}{10}[/tex]  is [tex]\dfrac{-4}{25}[/tex]. The correct option is 1.

To calculate the product of fractions in lowest terms, multiply the numerators together and multiply the denominators together, Then simplify the resulting fraction.

A fraction can be simplified in it's  lower term , if both the numerator and denominator after simplification have no common factor other than 1.

The given fractions are:

[tex]\dfrac{8}{15}[/tex]   and  [tex]\dfrac{-3}{10}[/tex].

To simplify, Multiply both numerator and denominator.

[tex]\dfrac{8}{15} * \dfrac{-3}{10}[/tex]

= [tex]\dfrac{-24}{150}[/tex]

Simplify further, Divide both numerator and denominator by their greatest common divisor, which is 6.

[tex]= \dfrac{\dfrac{-24}{6}}{\dfrac{150}{6}}[/tex]

=  [tex]\dfrac{-4}{25}[/tex]

The product of  [tex]\dfrac{8}{15}[/tex]  and  [tex]\dfrac{-3}{10}[/tex] in lowest terms  is  [tex]\dfrac{-4}{25}[/tex].   The correct option is  1.

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Final answer:

Lena's garden area is calculated to be 792 square feet. She needs approximately 2.64 bags of topsoil but will purchase 3 bags since she cannot buy a fraction of a bag. The total cost for the topsoil will be $9.

Explanation:

To calculate the total cost of the topsoil Lena needs for her garden, we first need to find out the area of her garden. We do this by multiplying the garden's length by its width. The formula for area is length × width.

The garden is 36 feet long and 22 feet wide. So the area is:

Next, we calculate how many bags of topsoil Lena will require. Each bag covers 300 square feet, so she will need:

Since Lena cannot purchase a fraction of a bag, she'll need to round up to the nearest whole number. Therefore, she will purchase 3 bags of topsoil.

Finally, we find the total cost by multiplying the number of bags by the cost per bag. The cost of one bag is $3, so the total cost is:

Therefore, Lena will spend $9 on topsoil for her garden.

There are 12 beads on the bracelet and 8 of the beads are purple. What percent of the beads are purple?

The fraction [tex]\frac{8}{12}[/tex] represents the number of purple beads on the bracelet out of all the beads on the bracelet.

To find what percent of the beads are purple, we can turn the fraction [tex]\frac{8}{12}[/tex] to a percent.

We can first reduce the fraction [tex]\frac{8}{12}[/tex] by dividing both the numerator and denominator by the Greatest Common Factor of 8 and 12 using 4.

8 ÷ 4 = 2

12 ÷ 4 = 3

Our reduced fraction is [tex]\frac{2}{3}[/tex]

2 ÷ 3 = 0.66666666666667

0.66666666666667 × 100 = 66.666666666667%

Therefore, 66.666666666667% of the beads on the bracelet are purple.

The total number of apples on the tree before Bill and Sally picked any apples was [tex]\[{120}\][/tex]

Let's start by defining the total number of apples on the tree initially as [tex]\( x \).[/tex]

First, Bill picked [tex]\( \frac{1}{2} \)[/tex] of the apples. Therefore, after Bill finished picking, the number of apples left on the tree was:

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

Next, Sally picked [tex]\( \frac{1}{3} \)[/tex] of the remaining apples. After Bill picked, there were [tex]\( \frac{x}{2} \)[/tex] apples left. Thus, Sally picked:

[tex]\[\frac{1}{3} \times \frac{x}{2} = \frac{x}{6}\][/tex]

After Sally picked her apples, the number of apples left on the tree was:

[tex]\[\frac{x}{2} - \frac{x}{6}\][/tex]

To simplify this expression, find a common denominator (which is 6):

[tex]\[\frac{x}{2} - \frac{x}{6} = \frac{3x}{6} - \frac{x}{6} = \frac{2x}{6} = \frac{x}{3}\][/tex]

We are told that after Sally picked her apples, there were 40 apples left on the tree. Therefore:

[tex]\[\frac{x}{3} = 40\][/tex]

To find x, we multiply both sides by 3:

[tex]\[x = 40 \times 3 = 120\][/tex]