Write the expression “the sum of seven times a number and five, divided by the sum of negative two times the number and eleven” using algebra. Choose the correct phrase below.

Finding the x-coordinate of the turning point of a quadratic equation requires knowledge of its coefficients. Given a function y = x^2 + bx + c, and points (2,0) and (0,14), we need further calculations or information to precisely identify b to use the vertex formula -b/2a effectively.

To find the x-coordinate of the turning point of the graph of the quadratic equation y = x^2 + bx + c, we can use the fact that the vertex of a parabola given by the general form ax^2 + bx + c is at x = -b/2a. Since the quadratic intersects the x-axis at (2,0), we can plug x = 2 into the equation to find one relation between b and c.

Another given point is (0,14), which when plugged in gives c = 14. To find b, we need more information from the question or an understanding of quadratic functions more deeply. However, without b, we can use the vertex formula derivatively, knowing that a in our equation is 1 (since the coefficient of x^2 is 1).

We also know that for any quadratic function, the x-coordinate of the vertex (turning point) can be found using -b/2a. Without the exact value of b, we cannot find the exact x-coordinate directly from the information given.

However, the general methodology would involve using the known points to first find equation coefficients and then apply the vertex formula. This highlights the importance of understanding quadratic functions and their graphical representations, such as vertices and intercepts, to solve these types of problems efficiently.

The x-coordinate of the turning point of the graph is 4.5

How to determine the x-coordinate of the turning point of the graph

From the question, we have the following parameters that can be used in our computation:

[tex]y = x^2 + bx + c[/tex]

It intersects the y-axis at (0, 14)

This means that

[tex]0^2 + b(0) + c = 14[/tex]

c = 14

So, we have

[tex]y = x^2 + bx + 14[/tex]

It intersects the x-axis at (2, 0)

So, we have

[tex]2^2 + 2b + 14 = 0[/tex]

4 + 2b + 14 = 0

2b = -18

b = -9

So, we have

[tex]y = x^2 - 9x + 14[/tex]

The x-coordinate of the turning point of the graph is then calculated as

x = -b/2a

So, we have

x = 9/2

x = 4.5

Hence, the x-coordinate of the turning point of the graph is 4.5

Final answer:

Calculate the difference in the number of dimes and nickels to find out how many more dimes Courtney has. The solution involves determining the total value of quarters and nickels, finding the number of dimes, and subtracting to get the difference. There are 6 more dimes than nickels.

Explanation:

To find how many more dimes Courtney has than nickels:

Calculate the value of quarters: 12 quarters * $0.25 = $3.00

Calculate the value of nickels: 9 nickels * $0.05 = $0.45

Subtract the total value of quarters and nickels from the total amount: $4.95 - $3.00 - $0.45 = $1.50

Since each dime is $0.10, divide $1.50 by $0.10 to find the number of dimes Courtney has: $1.50 / $0.10 = 15 dimes

Calculate the difference between the number of dimes and nickels: 15 dimes - 9 nickels = 6 more dimes than nickels

Therefore, Courtney has 6 more dimes than nickels.

Answer: C: 17

Step-by-step explanation:

Answer:

Each side of the garden should be 186.67 feet

Step-by-step explanation:

We know that the biggest area of a rectangular prism is when it closer to a square, and we know that a square is a special kind of rectangle with all equal sides, so we want all the sides to be equal.

To do this we know that the Gardener has 560 feet of fencing and he is only going to fence 3 sides because the other side is bordered by a river.

So we have to divide the fencing by the sides to have equal sides:

560 feet / 3 sides = 186.67 feet per side.

So the garden will be a square with each side of 186.67 feet, and the area will be:

186.67 * 186.67 = 34,845.70 square feet.

Answer:

{x|x ∈ U and 2x is prime}

Step-by-step explanation:

got 100%

Since she only needs to make the same amount of money, if she works for 4 times as many weeks, she can work 4 times fewer hours per week, meaning she can work 1/4*48= 12 hours per week.

During the academic year, Julie needs to put in about 12 hours per week of work to earn an additional $5,000 at the same rate of compensation.

To find out how many hours per week Julie must work during the school year to make another $5000,

set up a proportion using the information we already have.

Let's use the ratio of her earnings to the number of hours worked to create the proportion.

During the summer:

Earnings = $5000

Hours worked = 48 hours/week

Weeks worked = 12 weeks

Summer rate of pay = Earnings / (Hours worked × Weeks worked)

Summer rate of pay = $5000 / (48 hours/week × 12 weeks)

Summer rate of pay = $5000 / 576 hours

Summer rate of pay ≈ $8.68 per hour (rounded to two decimal places)

Now, during the school year, she needs to make another $5000.

So, set up the proportion:

School year earnings = $5000

School year rate of pay = $8.68 per hour (same as the summer rate)

School year rate of pay = School year earnings / (Hours worked × Weeks worked)

$8.68 per hour = $5000 / (Hours worked × 48 weeks)

Now, solve for the number of hours worked per week during the school year:

Hours worked × 48 weeks = $5000 / $8.68 per hour

Hours worked × 48 weeks = 576.036

Hours worked ≈ 12 hours per week (rounded to the nearest whole number)

Therefore, Julie must work approximately 12 hours per week during the school year to make another $5000 at the same rate of pay.

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The answer is A) .85 inches

Step-by-step explanation:

A =  

1 /2 πr2 4.5 =  1 2 πr2  1.6926 = r

  thus, 0.50 in  

1 ft  =  x in 1.6926 ft x = 0.8463

Final answer:

To find the radius of the bay window on the floor plan, calculate the radius of the actual bay window first, apply the scale factor, resulting in a radius of 3.4 inches that is option D is correct.

Explanation:

To find the radius of the bay window on the floor plan, you need to calculate the radius of the actual bay window first. Given the area of the bay window as 4.5 square feet in a semicircle shape, you can use the formula for the area of a semicircle, A = 1/2 * π * r².

Once you find the actual radius, you can then convert it to the scale of 0.5 inch = 1 ft to determine the radius on the floor plan. Remember, the scale factor is the ratio of a length on the drawing to the actual length it represents.

After the calculation, the radius of the bay window on the floor plan is 3.4 inches (Option D).

Final answer:

Choose the best units of measurement for a variety of items based on benchmarks and size considerations.

Explanation:

When considering the size of a bathtub, the best unit for measuring capacity would be liters.

To choose the best unit of measurement for each item:

The volume of a water balloon: Milliliters

The length of a basketball court: Yards

The weight of an apple: Ounces or grams

The volume of a milk carton: Cubic centimeters

For the height of a light switch, the appropriate unit would be inches.

For the width of a refrigerator, the appropriate unit would be feet.

The required fraction of the job that remains to be done is 2x / 5.

Given that,
A painting crew reported that a job is 3/5 completed. what fraction of the job remains to be done is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Let the whole fraction of the job be x.
A painting crew reported that a job is 3/5 completed = 3/5x
The job remains to be done = x - 3/5x
                                         = 2x / 5

Thus, the required fraction of the job that remains to be done is 2x / 5.

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The three values that make this inequality true 3n ≤ 18 are 6, 5, and 4.

We have,

To find three values that make the inequality 3n ≤ 18 true, we can simply substitute different values of n and check if the resulting statement is true or false.

Here are three values that satisfy the inequality:

n = 6:

3n = 3(6) = 18, which is equal to the upper bound of the inequality. Therefore, 3n ≤ 18 is true for n = 6.

n = 5:

3n = 3(5) = 15, which is less than 18. Therefore, 3n ≤ 18 is true for n = 5.

n = 4:

3n = 3(4) = 12, which is less than 18. Therefore, 3n ≤ 18 is true for n = 4.

Note that there are infinitely many values of n that satisfy this inequality, but these three values are enough to demonstrate that the inequality is true for at least three specific values of n.

Thus,

The three values that make this inequality true 3n ≤ 18 are 6, 5, and 4.

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we are given

[tex] p=v*i [/tex]

Since, we have to solve for i

so, we will isolate i on anyone side

we can divide both sides by v

[tex] \frac{p}{v}= \frac{vi}{v} [/tex]

[tex] \frac{p}{v}= i [/tex]

[tex] i=\frac{p}{v} [/tex]..............Answer

Answer:

p/v=I

Step-by-step explanation:

hope i helped. :} its also on edge