How can you solve, write and graph inequalities on a number line?

Answer:

12

Step-by-step explanation:

First, get all of the x values to one side of the equation so that we can solve for x. One way to do this is subtract 5x from both sides.

Now we have this:

4x - 5x = -12.

Simplify:

-x = -12.

We need positive x, so divide both sides by -1.

x = 12.

Hope this helps! :)

The given system of equation:

y = 3x - 5 (1)

y = -6x + 4 (2)

We can solve the system of equation by using elimination method :

Elimination Method: In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

Subtract the equation (1) & (2)

So, we get x = 1

Substitute the value of x in the equation (1)

y = (-2)

So, the solution of the system of equations are : (x,y) = (1,-2)

Answer: (x,y) = (1,-2)

The area under a standard normal distribution, which we get on a standard normal table, is the same as the probability on that area.

Thus if the area is 0.125, the probability is 0.125, that is, 12.5%.

Given the function

To find the inverse, we must recall that the domain of the function becomes the range of the inverse function and vice-versa.

We are already given the domain of f, all the real numbers equal or greater than zero.

The domain of the function is exactly the same because x squared is always positive or zero, thus the domain and range of the inverse should be x≥0.

Once we find the inverse function, we'll use this concept.

Step 1: Substitute f(x) for y:

Step 2: Swap the variables:

Step 3: Solve for y:

But as said above, the range of this function cannot include the negative numbers, thus the inverse function is:

Mr. Thompson weighs 260 pounds and he loses 4 pounds each month.

The equation will be :

w = 260 - 4m

where w is the weight after m months

when w = 220 pounds, the number of months will be :

220 = 260 - 4m

4m = 260 - 220

4m = 40

m = 40/4

m = 10

The answer is 10 months

The answer is 75%

The length of the rafter when the architect design a house is 12.778m.

The information illustrates that the architect designs a house that is 10 m wide and that the rafters holding up the roof are equal length and meet at an angle of 65°.

The rafters extend 0.4 m beyond the supporting wall. Then, the length will be:

cos65° = BC / AC

cos 65° = (5 + 0.4)/x

cos 65° = 5.4/x

x = 5.4 / 0.4226

x = 12.778m

The length is 12.778m

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Answer:

Step-by-step explanation:

the equation is written in slope intercept form

y= mx + b with m= slope and b= y-intercept

so in your equation

y=2/3x + 1,

the slope is 2/3 and the y-intercept is (0,1)

slope is also known as rise/run

so to move from one point to another, starting at (0,1) (since you know that point is on the line) you would move up 2 units and to the left 3 units.

hope this helped!

Total number of students = 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30

The probability that a student is female given that it is a junior is computed as follows:

The probability that a student is female and junior is:

The probability that a student is a junior is:

Finally, The probability that a student is female given that it is a junior is:

Given:

To find: The value of x (box)

Explanation:

Multiplying 30 on both sides. We get,

Solving we get,

Thus, the value of x is 24.

Final answer: The missing value is 24.

Answer:

  x = 3

Step-by-step explanation:

Given the sequence x, 7, 11, 15, ... 399, where 399 is the 100th term, you want to know the first term, x.

The differences of the first few terms are ...

  11 -7 = 4

  15 -11 = 4

This suggests an arithmetic sequence with a common difference of 4.

The first term, x, will be 4 less than the second term:

  x +4 = 7

  x = 7 -4 = 3

The value of x is 3.

__

Check

The n-th term of an arithmetic sequence with first term a1 = 3 and common difference d = 4 is ...

  an = a1 +d(n -1)

  an = 3 +4(n -1) = 4n -1

Then the 100th term is ...

  a100 = 4(100) -1 = 399 . . . . consistent with the given information

Given the data that we have here where the number of people in the survey is 10, s = 2 and mean = 49, the margin of error is given as 0.76

The margin of error can be used to provide the data that has to do with the amount of sampling error that would be in a given data statistic.

We would have to calculate the amount of error using the data that we have below.

We have the following values

number n = 10

mean u = 49

standard deviation sd = 2

The level of confidence c i = 80% = 0.80

we have to find the critical value

degree of freedom = 1 - 0.80

= 0.20

zα/2

= 0.20 / 2 = 0.10

= 1.383

The margin of error

= zα / 2 * s / √n

= 1.383 * 2/√10

= 1.383 x 2 / 3.623

= 1.383 x 0.552028

= 0.7634

The calculated margin of error is given as  0.7634

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Using it's concepts, the point estimates for the population are given as follows:

a) Mean: 97 units sold per month.

b) Standard deviation: 16.06 units sold per month.

In the context of this problem, the 5 observations are given as follows:

97, 110, 89, 97, 92.

Hence the mean is given by:

M = (97 + 110 + 89 + 97 + 92)/5 = 97.

Considering the mean of 97 found above, the standard deviation is given as follows:

[tex]S(X) = \sqrt{\frac{(97 - 97)^2 + (110 - 97)^2 + (89 - 97)^2 + (97 - 97)^2 + (92 - 97)^2}{5}} = 16.06[/tex]

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Answer:

P = 80 units

Explanation:

Let's label some points in the triangle as:

Since the sides of the triangles are tangent to the circumference, we can write the following relationships:

XC = YC

AZ = AY

BX = ZB

So, the length of the missing side XC is equal to:

XC = YC = 14

On the other hand, the length of AB is the sum of the length of AZ and ZB, so we can calculate ZB as:

AB = AZ + ZB

26 = AY + ZB

26 = 18 + ZB

26 - 18 = ZB

8 = ZB

Because AZ and AY have the same length.

Finally, the measure of BX is equal to:

BX = ZB

BX = 8

Therefore, the perimeter of the triangle is:

Perimeter = AY + YC + AZ + ZB + BX + XC

Perimeter = 18 + 14 + 18 + 8 + 8 + 14

Perimeter = 80

So, the answer is 80 units.

Answer:

75?

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

3 divided by 5

0.6x125

in this problem we have a vertical line

The equation of a vertical line is equal to the x-coordinate of the point that passes through it

so

in this case

the equation of the line is

x=-1

In a case whereby joeita sees on her activity tracker that it took her 58 minutes to run 6.25 hours miles  the distance she can she run in 40 minutes is  4.31 miles.

This can be solved by the cross multiplication using the rate that given in the question.

We were told that joeita took  58 minutes  of her time to run 6.25 hours miles , then to know the distance she can cover within 40 minutes is

58 minutes  = 6.25 miles

40 minutes = X miles

Let X be the number of miles she want to cover in 40 minutes

we ca cross multiply the expression above as :

( 40 minutes *  6.25 miles ) = (58 minutes  *  X miles)

the X = 4.31 miles

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Answer:

B

Step-by-step explanation:

None

Meal prepared a day = 80 meals

Vegetarian meals will be

Non vegetarian meals = 80 - 30 = 50 meals

Solution

step 1

Explain similarity

Both triangles are similar therefore the ratio of their corresponding sides must be equal.

Step2

State the corresponding sides

Step 3

Find x

Hence option A

There is the required value would be 6 in the box.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

If you are in the partition XY in the ratio 3 to 4 from point X to point Y

To determine multiply the length of XY.

XY = 14 units then 3/7 of 14

= 3/7 × 14

Apply the multiplication operation,

= 42/7

Apply the division operation,

= 6

Hence, the required value would be 6 in the box.

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Sebastian buy 134 cookies.  

Given,

He bought 4 boxes of shortbread cookies

and, 3 boxes of peanut butter cookies.

There are 20 shortbread cookies in each box.

but only 18 peanut butter cookies in each box.

To find the how many cookies did Sebastian buy in all?

Now, According to the question:

Formulate the above conditions:

18 x 3 + 20 x 4

Calculate the product or quotient

54 + 20 x 4

54 + 80

= 134

Hence, Sebastian buy 134 cookies.  

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Here is the completed table:

Number of bags purchased           Total weight                  Total Cost

1                                                                 4                                  8

2                                                                8                                  16

3                                                                 12                               24

4                                                                  16                              32

5                                                                   20                             40

One bag of cat food weighs 4 pounds. This means that as the bag increases by 1, the weight of the bag increases by 4.

Weight of 1 bag of cat food = 4

Weight of 2 bags of cat food = 4 x 2 = 8

Weight of 3 bags of cat food = 4 x 3 = 12

Weight of 4 bags of cat food = 4 x 4 = 16

Weight of 5 bags of cat food = 4 x 5 = 20

The cost of cat food is $2 per pound.

Cost of a bag of cat food = number of bags bought x weight of one bag x cost per pound

Cost of 1 bag of cat food = 1 x 4 x 2 = 8

Cost of 2 bags of cat food = 2 x 4 x 2  = 16

Cost of 3 bags of cat food = 3 x 4 x 2  = 24

Cost of 4 bags of cat food = 4 x 4 x 2  = 32

Cost of 5 bags of cat food = 5 x 4 x 2  = 40

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Answer:

15

Explanation:

Note that a regular dodecagon is a 12 sided polygon with internal angles that are equal and sides of the same length.

So determine at what angle the architect should cut to frame the base, we have to divide 360 by 12 and divide the result by 2 as seen below;

The angle that the architect should cut to frame the base is 15 degrees

The exponential equation which represents the amount of raw sugar t hours after the process begins is; A = 1,000 (0.8)^(t/5).

It follows from the task content that the amount of raw sugar left after the process begins is to be determined according to the information given.

Since, 20% of the available raw sugar is changed to a refined sugar every 5 hrs, it follows that only 80% of the raw sugar is left after each successive time interval period.

Hence, the exponential model of the situation is such that;

A = 1,000(0.8)^(t/5).

Where t = number of hours after the process begins.

Therefore, the required equation is; A = 1,000(0.8)^(t/5).

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Part A

If Emily needs 24 feet of wire, then she has to spend $14.4

Part B

If Andy needs 13 yards of wire, then he has to spend $23.4

From the given graph choose one option

The length of the wire = 120 inches

The cost of 120 inches of wire = $6

Cost of 1 inch of wire = 6/120

= $0.05

Part A

The length of the wire = 24 feet

Convert the feet to inches

24 feet = 288  inches

The cost of 288 inches of wire = 0.05×288

= $14.4

Part B

The length of the wire = 13 yards

Convert the yards to inches

13 yards = 468 inches

The cost of 468 inches of wire = 0.05×468

= $23.4

Hence,

Part A

If Emily needs 24 feet of wire, then she has to spend $14.4

Part B

If Andy needs 13 yards of wire, then he has to spend $23.4

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SOLUTION:

Step 1:

In this question, we are given the following:

The following two right triangles are similar.If side DE = 45, side HI = 36, and side DF = 30, what is the length of side HJ?

Step 2:

The details of the solution are as follows:

Since side DE = 45, side HI = 36, and side DF = 30.

Then, the length of side HJ =

Explanations:

Given the following parameters

An initial deposit of Gerard is "d" dollars

For the savings with 5% interest, the interest on "d" dollars will be expressed as;

Get the total savings plus interest in the first account

Hence the $1.05d will be in the first savings account if Gerard's initial deposit were d dollars

For the other account:

Initial deposit = "d" dollars

Interest = $100

Since the interest will be added to the first deposit, hence;

In Tabulated form: