•Marble City has a population of 52,348 and covers an area of 125 square miles.


•Pebble City has the same population density as Marble City.


•The shape of Pebble City resembles a rectangle with a width of 11.8 miles and a length of x miles.


•The population of Pebble City is 85,312.


–Which measure is closest to the value of x?


Answer Choices:

A) 11

B) 17

C) 36

D) 77

"3 miles below sea level" may be written as -3. The negative indicates you are below sea level. Going above sea level means the value would be positive.

"earning 45 dollars" can be written as +45 or simply 45. If you lost 45 dollars, then it would be -45. If you are in debt 45 dollars, then it would be -45.

"moving back 5 spaces" is represented by -5 whereas moving forward 5 spaces is +5 or simply 5.

Answer:  $637

Step-by-step explanation:

Find the amount she makes in commission 4,800 x 0.065=312

add the weekly salary and commission to get her total earnings

325+312= 637

Answer:

Income = 637

Step-by-step explanation:

Income = weekly salary + commission

commission = 6.5% * sales

commission = .065* 4800

                    = 312

Income = weekly salary + commission

Income = 325+312

Income = 637

Answer:

C

Step-by-step explanation:

You automatically know that it is not A. The dot is filled in on the number line, so it must have a line under the inequality mark.

The number line says that x is greater than or equal to 2.5

Key:

gtoet means greater than or equal to

ltoet means less than or equal to.

B:

3x + 2 gtoet 17

3x gtoet 15

x gtoet 5

This is incorrect. X is not gtoet 5.

C:

12 + 4x gtoet 22

4x gtoet 10

x gtoet 2.5

This is correct. X is gtoet 2.5

D:

-6x - 15 gtoet 0

-6x gtoet 15

(The sign switches in this one because you are dividing by a negative)

x ltoet 2.5

Incorrect. X is not ltoet 2.5

Answer:

The equation of this line would be y = 35x - 517

Step-by-step explanation:

In order to find this equation we must first find the slope of the original line. The original slope (the coefficient of x) is 35, which means the new slope will also be 35 because parallel lines have the same slope. Now, we can use this slope along with the point in point-slope form to find the equation of the line.

y - y1 = m(x - x1)

y - 8 = 35(x - 15)

y - 8 = 35x - 525

y = 35x - 517

The equation of the line parallel to y = 35x - 7 and passing through the point (15, 8) is y = 35x - 517.

To find the equation of a line that is parallel to y = 35x - 7 and passes through the point (15, 8), we need to determine the slope of the original line.

Since the given line is in the form y = mx + b, where m is the slope, we can see that the slope of the given line is 35.

Since parallel lines have the same slope, the slope of the line we're looking for is also 35.

Now we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Plugging in the values, we have y - 8 = 35(x - 15).

Expanding and simplifying, we get y - 8 = 35x - 525.

Finally, rearranging the equation, we find the equation of the line is y = 35x - 517.

To find the area of KLMN, we need to determine the length and width of the quadrilateral. We can do this by setting up and solving equations using the given information. By substituting the values and solving the equations, we find that the area of KLMN is 90 square units.

To find the area of KLMN, we need to determine the length and width of the quadrilateral. Since LM is parallel to KN, we know that LM = KN. Similarly, KL is parallel to NM, so KL = NM. Let's call the length of KLMN as L and the width as W. The perimeter of KLMN is 42, so we have L + KL + KN + NM = 42. Since KL = NM, we can rewrite the equation as L + 2KL + 2NM = 42.

We are also given the heights h1 and h2, which represents the vertical distance between the parallel sides. In this case, h1 = 5 and h2 = 6. The formula for the area of a quadrilateral is A = L * h1. Therefore, A = L * 5. We need to find the value of L to calculate the area.

Using the information given, we can set up the following equations:
L + 2KL + 2NM = 42
KL = NM
L * 5 = A

To solve these equations, we'll use substitution. Since KL = NM, we can substitute KL as NM in the first equation. This gives us:
L + 2NM + 2NM = 42
Simplifying the equation, we get:
L + 4NM = 42
Since h2 = 6 and h2 = NM, we can substitute NM as 6 in the equation:
L + 4(6) = 42
Simplifying further, we get:
L + 24 = 42
Subtracting 24 from both sides:
L = 18

Now that we know the value of L, we can calculate the area using the formula: A = L * h1. Substituting the values we have:
A = 18 * 5 = 90

Therefore, the area of KLMN is 90 square units.

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We can see here that the function can be written as:

f(x) = 66 + (12 × x)

To determine how many water bottles Lakita will buy, we need to consider the number of water bottles she already has (66) and the number of boxes she can afford to buy (up to 5). Each box contains 12 water bottles.

We can create a function to represent this situation:

Let's define:

x = the number of boxes Lakita will buy

The total number of water bottles Lakita will have is:

Total number of water bottles = 66 + (12 × x)

The reasonable domain for this function is 0 ≤ x ≤ 5, as Lakita can buy up to 5 boxes of water bottles.

The range of the function represents the total number of water bottles Lakita will have, which depends on the value of x. The range can be expressed as:

Range: 66 ≤ Total number of water bottles ≤ 126

So, the function can be written as:

f(x) = 66 + (12 × x)

Where:

x = the number of boxes Lakita will buy, and

f(x) = the total number of water bottles she will have.

Answer:

height

Step-by-step explanation:

the volume (V) of a cylinder is calculated using the formula

V = πr²h

where r is the radius and h the height

given the radius then the height is the required measurement needed

Answer:

Given the statement:Suppose that 216 students attended school one day, and 62 percent of them ate the school's breakfast.

Total number of students attended school = 216 students.

and 62% of them ate the school breakfast that day.

Now, to calculate the number of students ate the breakfast that day.

Proportion states that the two ratios or fraction are equal.

Let x represents the number of students ate the breakfast that day.

then, by using proportion;

[tex]\frac{62}{100}=\frac{x}{216}[/tex]

Multiply both sides by 216 we get;

[tex]x = \frac{62}{100} \times 216[/tex]

Simplify:

[tex]x = 133.92[/tex]

therefore, the number of students ate the school breakfast that day(to the nearest whole number) is, 134 students.

Answer:

The probability is 1/2.

Step-by-step explanation:

There are a total of 40 girls that are surveyed and 20 prefer chocolate. If you write that as a fraction 20/40, it simplifies to 1/2.

After withdrawing $40 from a checking account with a balance of -$30, Selene's checking account balance becomes -$70.

Selene's checking account balance is initially at -$30. When she withdraws an additional $40, the balance goes further negative.

To find Selene's checking account balance after the withdrawal, we need to subtract the withdrawal amount from the initial balance. Her initial balance is -$30, and she withdrew $40 more.

To find the new balance, you subtract $40 from -$30.

Account Balance Calculation:

Therefore, Selene's checking account balance after the withdrawal is -$70.

Final answer:

After withdrawing an additional $40 from an initial balance of -$30, Selene's checking account balance is -$70.

Explanation:

Selene's checking account balance after the withdrawal can be determined by subtracting the amount withdrawn from her initial balance. She starts with a balance of -$30. After withdrawing an additional $40, the new balance can be calculated as follows:

Initial balance: -$30
Withdrawal: -$40
New balance: -$30 - $40 = -$70

Thus, Selene's checking account balance after the withdrawal is -$70.

Answer:

x = 4

Step-by-step explanation:

3x = 48

Divide both sides by 3

x = 16

Then do 16/4 since 4 of the sides equal the same amount

x = 4

Answer:

1.5 - 1 1/5 = 3

10

= 0.3

Step-by-step explanation:

Answer:

The value of k is 4.

Step-by-step explanation:

To find the missing coordinate, we can use the slope equation and plug in all known values.

m(slope) = (y2 - y1)/(x2 - x1)

-1 = (k - 0)/(-2 - 2)

-1 = k/-4

Now we can solve using cross multiplication.

-1 = k/-4

k*1 = -1*-4

k = 4

Answer:

see explanation

Step-by-step explanation:

using  A = bh with b = 2x + 1 and h = x + 1, then

(2x + 1)(x + 1) = 28 ← expand factors on left

2x² + 3x + 1 = 28 ( subtract 28 from both sides )

2x² + 3x - 27 = 0 ← in standard form

To factorise, consider the factors of the product of the coefficient of the x² term and the constant term that sum to give the coefficient of the x term

product = 2 × - 27 = - 54 and sum = + 3

The factors are - 6 and + 9

Use these factors to split the middle term

2x² - 6x + 9x - 27 = 0 ( factor first/second and third/fourth terms )

2x(x - 3) + 9(x - 3) = 0 ( take out the factor (x - 3) )

(x - 3)(2x + 9) = 0

equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

2x + 9 = 0 ⇒ x = - [tex]\frac{9}{2}[/tex]

however x > 0 ⇒ x = 3

base = 2x + 1 = (2 × 3) + 1 = 7 units and height = x + 1 = 3 + 1 = 4 units

Answer:

80%

Step-by-step explanation:

to find the percentage of tickets sold to sixth grade students

percent sold = [tex]\frac{numbersold}{numberof tickets}[/tex] × 100%

                     = [tex]\frac{240}{300}[/tex] × 100% = 80%

Answer:

80%

Step-by-step explanation:

To find the percentage sold to sixth graders, take the number sold to sixth graders over the total

percentage to sixth graders =  tickets sold to sixth graders/ total tickets

The total tickets are 300

Tickets to sixth graders is 240

Substitute it in

percentage to sixth graders = 240/300

                                               =24/30

                                                =4/5

                                                =.8

Multiply this by 100 to give the percent

80%

Answer:

503 $1 tickets sold.

Step-by-step explanation:

Use two equations  

Let x = number of $1 tickets sold  

Let y = number of $1.50 tickets sold  

x + y = 739  

1x + (1.5)y = 857  

First equation ==> y = 739 - x  

Plug this into the second equation  

x + (1.5)(739 - x) = 857  

x + 1108.5 - 1.5x = 857  

- 0.5x = -251.5  

x = 503  

There were 503 $1 tickets sold.  

To find the number of $1.50 tickets, just plug this value of x into either one of the equations.  

(503) + y = 739       (739 - 503 = 236)

y = 236  

There were 236 $1.50 tickets sold.

A system of linear equations and using the elimination method, we found out that 503 $1 tickets were sold for the school play.

To solve the problem involving the tickets sold for the school play, we need to set up a system of linear equations.
First, let’s define our variables: let x be the number of $1 tickets and y be the number of $1.50 tickets sold. Based on the problem, we can create the following equations:

x + y = 739 (total number of tickets sold)

1×x + 1.5×y = $857 (total amount of money collected)

We can solve this system of equations using either the substitution method or the elimination method. For this example, let's use the elimination method and multiply equation (1) by -1.5 to eliminate y when we add the two equations:

-1.5x - 1.5y = -1108.5 (After multiplying equation (1) by -1.5)

1x + 1.5y = 857 (Original equation (2))

By adding the two equations, we get:

-0.5x = -251.5

Now we divide both sides by -0.5 to find the value of x:

x = 503

So, 503 $1 tickets were sold for the school play.

Answer:

$2.44

Step-by-step explanation:

Change the percentage into a decimal. Move the decimal point to the left two place values.

25% = 25/100 = 0.25

Multiply the two numbers:

3.25 x 0.25 = 0.8125

Subtract the number gotten from the original number. Remember to first simplify.

0.8125 = 0.81

3.25 - 0.81 = 2.44

$2.44 is your new price.

~

Answer:

The answer is 2 times x.

Step-by-step explanation:

X is the number of students. If each of the student received 2 pencils then you multiply 2 by the number of students.

Answer:

The answer is 2 times x.

Step-by-step explanation:

X represents the number of students. If each of her student received 2 pencils, you would multiply 2 by the number of students.

Answer:

3[tex]x^{2}[/tex]

Step-by-step explanation:

Jake's canvas is x times x,

which is [tex]x^{2}[/tex].

Jerome's canvas is 2x times 2x,

which is [tex](2x)^{2}[/tex] = [tex]4x^{2}[/tex].

The difference in area would be

[tex]4x^{2} -x^{2}=3x^{2}[/tex]

Answer:

I believe it is a 1040 tax form

Step-by-step explanation:

Final answer:

A married couple should use IRS Form 1040 to file their taxes jointly, claim dependents like children, and deduct medical expenses.

Explanation:

A married couple wishing to file their taxes jointly, claim their children, and deduct medical expenses should use the IRS Form 1040. This is the standard Income Tax Return form for individuals in the US. The Form 1040 allows taxpayers to report their income, claim tax deductions and credits, and calculate the amount of tax owed or refund due.

When filing a joint return, you are also able to claim dependents, which may include children, and report medical expenses that can be deducted if they exceed a certain percentage of your adjusted gross income. While there are different variations, such as 1040A or 1040EZ, the full 1040 form is necessary when claiming detailed deductions such as medical expenses.

Answer:

y = - 5x - 1

Step-by-step explanation:

The first thing to do (always) is pay attention to x =0. That at least gives you a partial answer. y = y' - 1. when you put 0 in for whatever y' is you get 0. What about the other numbers? How did they come about.

We have another clue. Whenever you put in a positive number for x, you get a negative answer for y. That's interesting. So y' has a minus sign associated with it.

y = -ax - 1    Make a>0 so there is only 1 minus sign. x cannot have an even power, because an even power would make everything positive except the -1.  

So we'll start with y= - ax - 1 We'll also make the assumption that a = 1

y = - x - 1 That won't work. a >1 otherwise x = 2 won't give - 11

y = -ax - 1

let x = 2

let y = - 11 Solve for a

y = - ax - 1

- 11 = -a*-2 - 1       add   1  to both sides

-11 + 1 = - a(-2) - 1 + 1

- 10 = -2a             Divide by - 2

- 10/-2 = -2a/-2

a = 5

Answer: y = - 5x - 1

Answer:

1.03

Step-by-step explanation:

I think the pattern is adding .1 So then next one is 1.03

Answer:

+0.10

Step-by-step explanation:

0.73+0.10= 0.83+0.10=0.93 etc

have a great day!

Answer:

Step-by-step explanation:

Hammers and Wrenches

I have included the graph to the first one. C is the best answer, but I don't think it is quite correct, although it is true. The actual fact is that there is no y intercept as near as I can get. That's an unusual occurrence for this kind of graph. There is no other answer that will satisfy or rectify that condition. I think you are likely to answer C, but be careful. It could turn out to be another answer.

f(x) and g(x)

I agree with your answer

Answer:

John > Gil > Sami > Hank > Tammy

Step-by-step explanation:

It might help if we draw a number line  like the one below.

Then we can see that John > Gil > Sami > Hank > Tammy.

Final answer:

The golf scores from greatest to least are John (2), Gil (1), Sami (0), Hank (-1), Tammy (-2).

Explanation:

The student is asking to order the golf scores from greatest to least. When comparing numbers, the higher a number's value, the greater it is. In this context, negative scores are lower than zero or positive scores. Here's how the scores are ordered:

John: 2

Gil: 1

Sami: 0

Hank: -1

Tammy: -2

This order reflects the scores from highest to lowest, with John having the highest score and Tammy the lowest.

Answer:

A) slope of f(x) = 3 , slope of g(x) = 7

B) y intercept of f(x) is  0  and g(x)  is 2

So g(x) has greater y intercept

Step-by-step explanation:

Lets find equation of f(x) using the given table

LEts take two points from the table (0,0) (1,3)

[tex]slope = \frac{y_2-y_1}{x_2-x_1} = \frac{3-0}{1-0} = 3[/tex]

we use equation y=mx+b

where m is the slope and b is the y intercept

we got m = 3, we use (0,0) and find out b

y=mx+b

0 = 3(0) + b

so b=0

So equation for f(x)= 3x +0

slope =3  and y intercept = 0

For equation g(x) = 7x +2 , slope = 7  and y intercept = 2

Answer:

y - 3 = 4(x - 1)

Step-by-step explanation:

This is point slope form, which looks like this:

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

Because a 3 is used for the y value, we know the coordinate point we are using is (1, 3). All we need to do is plug the x value in.

y - 3 = 4(x - 1)

Use the Pythagorean theorem:

[tex]x^2+4^2=10^2[/tex]

[tex]x^2+16=100[/tex]        subtract 16 from both sides

[tex]x^2=84\to x=\sqrt{84}\\\\x=\sqrt{4\cdot21}\\\\x=\sqrt4\cdot\sqrt{21}\\\\\boxed{2\sqrt{21}}[/tex]

The quantity y is directly proportional to x, indicated by the equation y = (5/3)x, found by determining the constant of proportionality (k = 5/3) given that y=10 when x=6.

The problem states that the quantity, y, varies directly as x.

In mathematical terms, this relationship can be represented as y = kx, where k is the constant of proportionality.

Given that when y=10, x=6, we can find k by substituting these values into our formula, yielding 10 = k*6.

Solving for k, we get k = 10/6 or k = 5/3.

Therefore, the equation that describes how y varies directly as x is y = (5/3)x.

This equation tells us that for every unit increase in x, y increases by 5/3 units, illustrating a direct proportionality relationship between the two quantities.

This relationship can be depicted as a straight line through the origin (0,0) on a graph, where k also represents the slope of the line.

Answer:

128

Step-by-step explanation:

Method A.

The volume of the prism is 2 cubic units.

Each cube has side length of 1/4 unit.

The volume of each cube is (1/4)^3 cubic unit.

The volume of each cube is 1/64 cubic unit.

To find the number of cubes that fit in the prism, we divide the volume of the prism by the volume of one cube.

(2 cubic units)/(1/64 cubic units) =

= 2/(1/64)

= 2 * 64

= 128

Method B.

Imagine that the prism has side lengths 1 unit, 1 unit, and 2 units (which does result in a 2 cubic unit volume.) Since each cube has side length 1/4 unit, then you can fit 4 cubes by 4 cubes by 8 cubes in the prism. Then the number of cubes is: 4 * 4 * 8 = 128

Answer:

128 cubes.

Step-by-step explanation:

Volume of each cube = (1/4)^3 = 1/64  cubic units.

Number of cubes that will fill the prism

= 2 /  1/64

= 2*42

= 128   answer