solving one step inequalities using addition subtraction multiplication and division

Problem

Kyle just graduated from college and got his first job, he has $45,000 in student loan debt, wants to buy a new car, and is considering opening up a retirement account. He has a disposable income of $300/month, what would you recommend he do with this money? Why?

Solution

For this case the best option would be put the $45000 in a bank with a compound interest

And with the earnings each month of 300$ he can put the half of this into the account and the remain to spend on other things

Answer:

50

Step-by-step explanation:

Solution for 700 is what percent of 1400:

700:1400*100 =

(700*100):1400 =

70000:1400 = 50

Now we have: 700 is what percent of 1400 = 50

Answer:{(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}

Step-by-step explanation: hope this helps

SOLUTION:

For inequalities, the solution to is usually where the two regions meet.

The graphs here are:

Final answer:

The final answer here is Option (B)

Answer:

-31, 9, 1, 5, 37

Step-by-step explanation:

f(x) = -2(-2)^2 + 1

f(x) = 4^2 + 1

f(x) = 8+1

f(x) = 9

f(x) = -2(0)^2 +1

f(x) = 0^2 + 1

f(x) = 0 + 1

f(x) = 1

f(x) = -2(1)^2 + 1

f(x) = -2^2 + 1

f(x) = 4+1

f(x) = 5

f(x) = -2(3)^2 + 1

f(x) = -6^2 + 1

f(x) = 36+1

f(x) = 37

Answer:

w = 1

Step-by-step explanation:

You have to divide 48 by 8 to get 6, so you have to divide 8 by 8 to find w.

8/8 = 1

Answer:

A) there are no outliers in this distribution.

Answer:

Step-by-step explanation:

Answer there are no outlier

68 = Diane's score x 4

Equation

68= 4d

___________________

Can you see the updates?

_________________

Diane's score

4d= 68

d= 17

ANSWER: 10 ICE-CREAM SCOOPS

There are 5 icecream flavors

For each we need 2 scoops so = 2*5 = 10 scoops

therefore ther must be 10 icecream scoops in use for five flavors.

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The slope of the line that passes through the points (-2, 2) and (-4, -1) is 3/2 i.e. 1.5 .

How can we define the slope for a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is provided by the formula m = change in y/change in x = Δy/Δx, where "m" is the slope of a line.
Mathematically, slope of a line = m = (y₂ - y₁)/(x₂ - x₁)

Given, the line passes through the points (-2, 2) and (-4, -1)
Now, using the formula established in the literature, we get:
slope = m = (y₂ - y₁)/(x₂ - x₁) = (-1 - 2)/(-4 - (-2)) = -3/-2 = 3/2 = 1.5
Therefore, the slope of the line that passes through the points (-2, 2) and (-4, -1) is 3/2 i.e. 1.5 .

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The equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3 is y = 3x - 5

We need to find the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3

The point slope form of a equation of a line is

y - y₁ = m(x - x₁)

y - (-2) = 3 (x - 1)

y + 2 = 3x - 3

y = 3x - 3 - 2

y = 3x - 5

Therefore the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3 is y = 3x - 5.

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Answer:

10.8

Step-by-step explanation:

Hello!

Once, graphed, a right triangle forms, with PQ as the hypotenuse. The other two lengths are 6 and 9.

We can use the Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]

The length of PQ is 10.8.

Answer:

D. $870; $31,320 from deposits and $3,680 from interest

Explanation:

In order to calculate the monthly payment, we use the formula below:

Given:

• The Financial Goal, A= $35,000

• Rate = 7.5% = 0.075

• Number of compounding period = 12 (Monthly)

• Time, t = 3 years

Substitute into the given formula:

The monthly payment is $870.

Option D is correct.

Answer:

B

Step-by-step explanation:

It is asking which graph show (x,y) for one line and (y,x) for the other line.

For example, the blue line shows (0,2) as a point and the red line shows ( 2,0) and so on and so on.

The distance between the ordered pairs is 4 units

What is distance formula?

Distance formula calculates the distance between two coordinates. it calculates the straight line distance between two points. The formula can be given as [tex]distance=\sqrt{(c-a)^{2}+(d-b)^{2} }[/tex] for the coordinates (a, b) (c, d)

We are given the ordered pair (w+2,m) and (2t,c-3)

We are given the value w = 6, m = 3, t = 4 and c = 10.

Substituting the values in the pairs

We get,

(6+2,3),(2(4),10-3)

(8,3),(8,7)

We use distance formula to find the distance

[tex]d=\sqrt{(8-8)^{2} +(7-3)^{2} }\\ d=\sqrt{4^{2} }\\ d=4[/tex]

Hence the distance between the ordered pairs is 4 units.

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Answer:

0.64 is 1 3/5% of 40

Step-by-step explanation:

The sample size is 1727 points for given data . Sample size is defined as the number of observations used to determine estimates for a given population. Sample size was drawn from the population .

In this question we want to find the sample size and so let's, look at the formula that is given by, the value at over 2, divided by a margin of error, whole squared times p into 1 minus p.

N= ( Z ₐ / E)² p (1-p)

In this case , Z --> Z-Score

E --> error value

P --> estimated proportion or if given standard deviations

Given that, estimate error is 2% that is margin (E) = 2% = 2/100 =0.02

Now, what we have is our confidence level and our made error, so our estimate has been given us 2 percent or confidence level is 99 percent. Now, let's get our Z values, so we use alpha(a) to find out. For alpha value 1 minus 0.99 , we get 0.01. now we are going to be 0.01 divide by 2 and get 0.005 . So, the corresponding value of Z ₀.₀₀₅ is 2.576 . The only value of p is 11.8% (year 2000 estimate ) of what is required for getting an answer

= 118/1000= 0.118

Finally, we put all these values into formula of sample size , i.e.,

N= ( 2.576 / 0.02)² (0.118 )(1- 0.118) = 1726.56 1727

Our sample size is , 1727 point.

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From this class, the teacher wishes to selected six students. 2,2,2,2,2,3 different ways are there to selected from this class of 13 students.

Given that,

From this class, the teacher wishes to selected six students. The first chosen student will assist with media, the second will assist with pledges and flags, the third will sharpen pencils, the fourth will take attendance, the fifth will wipe the board, and the sixth will assist with the calendar.

We have to find how many different ways are there to selected from this class of 13 students.

For 13 students,

We divide like 2,2,2,2,2,3.

The first 2 student will be a media helper,

The second 2 students will be a pledge/flag helper,

The third 2 students will be a pencil sharpener,

The fourth 3 students will be attendance taker,

The fifth 2 students will be a board eraser and

The sixth 2 students will be a calendar helper.

Therefore, This many ways we can selected the students.

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The most appropriate choice for distance between numbers will be given by -

Distance between 3 and 15 is 12 units

What is distance between two numbers?

At first it is important to know about number line.

A pictorial representation of real numbers has been done along a horizontal straight line. That horizontal straight line is called number line. On a number line, all the integers has been placed at equal distance apart. In between integers, fractions, decimal numbers, rational numbers and irrational numbers can be marked. Number line can be used for addition or subtraction.

Distance between two numbers indicates how far one number is situated from other number on the number line.

Here,

Distance between 3 and 15 = 15 - 3

                                              = 12 units

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Answer: Area = 126 square inches

Explanation:

The formula for calculating the area of a triangle is expressed as

Area = 1/2 x base x height

From the information in the diagram,

base = 18

height = 14

Thus,

Area = 1/2 x 18 x 14

Area = 1/2 x 252 = 252/2

Area = 126 square inches

The perimeter of the given equilateral triangle would be 28.2 cm if the sides of the triangle are 9.4 cm.

The numerical value that is rounded up to represent the supplied value's next value serves as its upper bound.

The numerical number that is rounded off for the previous value or the predicted value of the provided value is the lower bound for the supplied value.

The sides of an equilateral triangle are 9.4 cm

The perimeter of an equilateral triangle = 3 × length of the side

The perimeter of an equilateral triangle = 3 × 9.4

The perimeter of an equilateral triangle = 28.2 cm

Hence, the perimeter of the given equilateral triangle would be 28.2 cm if the sides of the triangle are 9.4 cm.

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Answer: x-3y=6

Step-by-step explanation:

so first subtract x to get -x+3y = -6 because standford is ax+by = c

and then multiply by -1 since x has to be positive

x-3y = 6 That is your answer

Answer:

Step-by-step explanation:

Slopes of parallel lines are the same. ( [tex]m_{1}[/tex] = [tex]m_{2}[/tex] )

Slopes of two perpendicular lines are opposite reciprocals. ( [tex]m_{1}[/tex] × [tex]m_{2}[/tex] = - 1 )

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

~~~~~~~~~~~~~

(9, 9)

(6, 1)

[tex]m_{m}[/tex] = [tex]\frac{1-9}{6-9}[/tex] = [tex]\frac{8}{3}[/tex]

(10, 7)

(1, 15)

[tex]m_{n}[/tex] = [tex]\frac{15-7}{1-10}[/tex] = - [tex]\frac{8}{9}[/tex]

Lines m and n neither parallel, nor perpendicular.

Given:

Yesterday:

1 female and 5 male = 52 yards

Today:

5 female and 2 male = 76 yards

Let's find the number of yards of fabric each type of costume requires.

Let F represent the number if yards for each female customer use.

Let M represent the number of yards each male customer uses.

From this situation, we have the system of equations:

1F + 5M = 52

5F + 2M = 76

Now, let's solve the system of equations simultaneously using substitution method.

Rewrite equation 1 for F:

F = 52 - 5M

Substitute 52 - 5M for F in equation 2:

Subtract 260 from both sides:

Divide both sides by -23:

Substitute 8 for M in either of the equations:

F = 52 - 5M

F = 52 - 5(8)

F = 52 - 40

F = 12

Therefore, we have the solution:

F = 12, M = 8

Each male customer requires 8 yards while each female customer requires 12 yards.

ANSWER:

• Male customer = 8 yards

• Female customer = 12 yards

x = 5

2x - 14 = -4

2x = -10

x = 5

Answer: 5

Step-by-step explanation: First I took away the 2 on the left which was multiplying the brackets.  Then because I did this I had to do the opposite to the other side. -4÷2

Then I just filled in the gaps 5-7=-2

To answer this question we need to remember that:

then:

now we need to remember that:

hence:

Therefore:

and the asnwer is A.

Answer:

area of trapezium → 1/2 × Sum of parallel sides × Distance between them.

Area → 15in² {given}

B1 → 4in

B2 → 6in

15 = 1/2 × ( 4+6 ) × h

h = 15 × 2 ÷ 10

h = 3in

I hope it's helpful

Answer:

i wouldd but likee

Step-by-step explanation:

i didnt pay a single second of attention in math

The Mean distance is 4,145,760,000  miles

The correct option is (a)

Given,

The mean distance from Venus to the sun is 67,240,000 miles.

The mean distance from Mars to the sun is 4,213,000,000 miles.

Now, According to the question

Subtract the distance of Mars to the sun from Venus to the sun :

Let's Calculate the mean distance:

= 4,213,000,000 - 67,240,000

= 4,145,760,000 miles

Hence, The Mean distance is 4,145,760,000 miles.

The correct option is (a)

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Answer:

The equation of the line is;

Explanation:

Given that

the slope of a line is -2 and it passes through the point (4,-5).

Applying the slope-intercept form of equation;

Substituting the values of the slope and coordinates;

Therefore, the equation of the line is;

Answer:

2x + y = 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (4, - 5 ) into the partial equation

- 5 = - 8 + c ⇒ c = - 5 + 8 = 3

y = - 2x + 3 ← in slope- intercept form

add 2x to both sides

2x + y = 3 ← equation in standard form

The measurement is closest to the length of the rectangle is √119 ft.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c = √( a² + b² )

Where c is the diagonal that divides the rectangle into two equal triangle, a and b are the other legs of the triangle.

Given the data in the question;

Plug the values into the formula and solve for b.

12ft = √( (5ft)² + b² )

Take the square of both sides

( 12ft )²  = (5ft)² + b²

144ft²  = 25ft² + b²

b² = 144ft² - 25ft²

b² = 119ft²

b = √( 119ft² )

b = √119 ft

Therefore, the measure of the length is √119 ft.

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