every month ben spends $350 on groceries, $150 on gas, and $250 on clothes. write abd evaluate ab expression to predict how much money he will spend on these items over the next 12 months

28000 + 3000x = 36000 + 2000x

Subtract 2000x from both sides: 28000 + 1000x = 36000

Subtract 28000 from both sides: 1000x = 8000

Divide both sides by 1000: x = 8.

Let me know if there is more to the problem!

28,000+3,000=31,000+2000=33000

the coordinates of the point of intersection of the graphs of lines with

y=−2x+7 and y=0.5x−5.5

to find intersection we solve for x  and y

We replace -2x+7 for y in the second equation

−2x+7 =0.5x−5.5

Subtract 0.5x from both sides

-2.5x + 7 = -5.5

Subtract 7 on both sides

-2.5x = -5.5 - 7

-2.5x = -12.5

divide by -2.5 from both sides

x = 5

Plug in 5 for x in y=−2x+7

y=−2(5)+7

y = -10 + 7

y = -3

The point of intersection is (5,-3)

The answer demonstrates the associative property through the multiplication of 4x6x10, resulting in 240.

Multiplication Properties Illustrated in 4x6x10:

The property of associative property is illustrated in 4x6x10. This means that changing the grouping of the numbers being multiplied does not change the result.

It will take 1000 days to spend 1,000,000 if you spend 1,000 per day.

1000 days

Hope it helps ❤️

The factors of 8 are...

8 is a composite number because has more numbers than itself and 1. A prime number like 5, only has 2 factors ( 1 and 5).

The slope is 4 and the Y-Intercept is 0.

Answer:

225, 225 and 252 meters

Step-by-step explanation:

Let  length of the 2 equal parts be each x m, then:-

2x + x + 27 = 702

3x = 702 - 27 =    675

x = 675/3

x = 225

So lengths of each parts are  225, 225, 252

To find the lengths of the three parts, we let the length of each of the two equal parts be 'x' and set up the equation 3x + 27 = 702. Solving for 'x' gives us that each of the two equal parts is 225 m, and the third part is 252 m.

The student is asking to find the lengths of three parts of a fence that has been cut, with two parts being equal in length and the third part being 27 m longer than the other two. Let's assume each of the two parts that are the same length is 'x' meters. Since the third part is 27 m longer, it would be 'x + 27' meters. According to the problem, the total length of the fence is 702 m.

Therefore, the sum of all three parts is:

x + x + (x + 27) = 702

Simplifying this, we get:

3x + 27 = 702

Subtract 27 from both sides:

3x = 675

Now, divide both sides by 3:

x = 225

So, the two equal parts are each 225 m long, and the third part is 225 + 27 = 252 m long.

331 total students. 7 traveled by car.

331 - 7 = 324 were on buses.

There were 6 buses:

324 / 6 = 54 students on each bus.

Hey there!!

What are the factors of 36?

Ans :- 1 , 36 , 2 , 18 , 3 , 12 , 4 , 9 , 6

Which of these numbers add up to 15 ?

... 12 + 3 = 15

The number are 15.

They add up to 15 and both of these are factors of 36.

Hope my answer helps!!

24 + (8·10)

24 + 80

104 dollars after ten weeks

2 and 3/5 is equal to 2.6.

Being as the 2 is in front of the fraction, it is the whole number. This means in decimal form, it is to the left of the decimal point. Since there is no "fifths place" in a decimal, you must make it so it can go under the tenths, hundreths, thousanths or another place within the right side of the deciamal point. Simply multiplying 3/5 by 2/2 will give you 6/10. 6/10 as a decimal, is 0.6. Finally, add 0.6 and 2 together. Thus making 2.6 the answer.

I hope this helps!

Answer:

6

Step-by-step explanation:

The x-intercept is the x-coordinate of the point on the line that intersects the x-axis. At the x-axis, all y-coordinates are 0. Let y = 0, and solve for x.

2x – 3y = 12

2x - 3(0) = 12

2x = 12

x = 6

The x- intercept of the graph is 6

The problem can be solved by following steps

2x-3(0)=12

2x=12

x=6

Hence the x-intercept is 6

Learn more about X-intercept here

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The slope would be b.2

This problem would be best modeled by an inequality.

Let t = the number of hours.

18 + 5t < 78

5t < 60

t < 12

The way the question sounds, it would not be a lessthan or equal to, because they want to spend less than 78.  It would be a less than or equal problem if they said "no more than 78"

Yoko would drive 754 miles in 13 hours.

First you would have to find how many miles Yoko drives per hour so you divide 522 miles/9 hours to get 58 miles per 1 hour. Then you multiply 58 * 13 to get 754 miles.

Final answer:

The number of pages decreased from 32 to 28, which is a difference of 4 pages. Dividing by the initial number of pages and multiplying by 100 gives a decrease of 12.5%.

Explanation:

To calculate the percentage change when the number of pages in a document decreases from 32 to 28, we follow these steps:

Therefore, there is a 12.5% decrease when a document goes from 32 pages to 28 pages.

Let's x represents the first odd integer

The next consecutive integer would be represented as x+2.

So x and x+2 being multiplied together will give us 1443:

(x)(x+2)=1443

x^2+2x=1443

x^2+2x-1443=0

By solving the quadratic equation using the quadratic formula, x will equal to 37 and -39.

Since the problem says "integers", so I'm assuming two pairs of consecutive integers would be ok.

With that said you 1st pair will be: 37,39

Your second pair will be: -37,-39.

Anna picked 6 apples

Sabrina picked 7 times as many apples.

Multiply the two numbers together

6 x 7 = 42

Sabrina picked 42 apples

hope this helps

~Rise Above the Ordinary

Anna picked 6 apples. Sabrina picked 7 times as many apples. How many apples did Sabrina pick?

Times, means to multiply, take the only two numbers in the problem and multiply them together.

6 x 7 = 42  

~

Answer:

Option A is the important variable.

Step-by-step explanation:

Given is - At 9:45 a.m. a patient’s temperature was 101.5 degrees at 10:41, the nurse took the patients temperature again and found it was 105.8 degrees, the highest ever recorded.

The variable that is most important here is A: the number of minutes it took for the to reach its peak.

Firstly it is not mentioned if 10:41 is am or pm.

If its am, then such a temperature rise in less than an hour is very dangerous.

So, the important variable is option A.

Answer:

The answer is B: the number of degrees that the temperature changed.

Step-by-step explanation:

Just took the test

Answer:

No, the two events "being in high school" and "GPA above 3.0" are not independent.

Step-by-step explanation:

If two events A,B are independent [tex]P(A|B)=P(A)[/tex]

P(high school | above 3.0) = [tex]\frac{14}{40}=0.35[/tex]

P(high school) = [tex]\frac{60}{100}=0.6[/tex]                                                                                                

So,0.35 ≠ 0.6

Since P(high school | above 3.0) ≠ P(high school), the events "being in high school" and "GPA above 3.0" are not independent.

The proportion of high school students with a GPA above 3.0 differs from the proportion of college students with a GPA above 3.0. Therefore, the events 'being in high school' and 'GPA above 3.0' are not independent according to the data provided.

To determine if "being in high school" and "GPA above 3.0" are independent events, we can check if the proportion of high school students with a GPA above 3.0 is the same as the proportion for college students. If the events are independent, the proportions should be equal.

From the two-way frequency table provided, we can calculate the proportions. There are 60 high school students and 40 college students. Among these, 14 high school students and 26 college students have a GPA above 3.0.

The proportion of high school students with a GPA above 3.0 is 14 out of 60, which simplifies to about 0.233.

The proportion of college students with a GPA above 3.0 is 26 out of 40, which simplifies to about 0.650.

Because these proportions are not equal, we can conclude that the events are not independent. Being in high school appears to have an impact on whether a student has a GPA above 3.0, based on this data set.

Therefore, the events 'being in high school' and 'GPA above 3.0' are not independent according to the data provided.

The LCM of 5/9 and 11/12

is 36

9*4=36

12*3=36

20/36

&

33/36

For this case we have:

By definition, two points are needed to find the equation of a line. We have a series of points given by:

[tex](x, y) = (time, cost)[/tex]

We chose two points:

[tex](t1, c1) = (1,180)\\(t2, c2) = (2,240)[/tex]

By definition, the formula of the slope is given by:

[tex]m =\frac{(c2-c1)}{(t2-t1)}[/tex]

Substituting:

[tex]m =\frac{240-180}{2-1}[/tex]

[tex]m =\frac{60}{1}\\m = 60[/tex]

Being a line of the form [tex]y = ax + b[/tex], we substitute a point and the slope found to find the cut point b.

[tex]180 = 60 * 1 + b\\180 = 60 + b\\b = 180-60\\b = 120[/tex]

Thus, the equation of the line is given by:

[tex]y = 60x + 120[/tex]

Answer:

Option C

Part (A):

The area of the penalty box.

The dimensions of the penalty box are (15x-1) and (5x-7)

The area of rectangle = length * width

∴ The area of the penalty box = (15x-1) * (5x-7) = 75 x² - 110 x + 7

===================================================

Part (B):

The area of the goal box.

The dimensions of the goal box are (7x-1) and (x+3)

The area of rectangle = length * width

∴ The area of the goal box = (7x-1) * (x+3) = 7x² + 20x - 3

=======================================================

Part (C):

The area of the penalty box not coverd by the goal box =

The area of the penalty box - The area of the goal box =

(75 x² - 110 x + 7) - (7x² + 20x - 3) = 68 x² - 130 x + 10

Answer:

41 MPH

Step-by-step explanation:

Let's assume the original speed with or without, is around 82 miles, within 2 hours.

So in this case, it'd be half the miles, half the hours!

Solution:

Let the speed of cyclist without any wind = x miles per hour

   Speed of cyclist when speed of wind increases by 2 miles per hour =              (x + 2 )miles per hour

Also , relation that is given between speed of cyclist without wind and with wind is :Riding with the wind at her back, a cyclist takes an hour less time to cover 80 miles than without any wind.

Converting this statement into terms of equation:

[tex]\frac{80}{x}-\frac{80}{x+2}=1  \\\\ 160 = x^2 + 2x \\\\ x^2 + 2x - 160=0 \\\\ x= \frac{-2\pm\sqrt{4+640}}{2}, {\text {As speed can't be negative, so taking positive value of x}} Gives,  x =11.68[/tex]→→→To solve the Quadratic equation of type : a x² + b x + c=0, I have used discriminant method, to find the roots, which is x= [tex]\frac{-b\pm\sqrt{D=b^2-4ac}}{2a}[/tex]

Speed of cyclist without wind = 11.68 miles per hour

Speed of cyclist when wind is flowing = 11.68 +2 = 13.68 miles per hour

Ok, so first you have to take the 5/6th off. This would be 24 4/6 - 5/6th which would be 23 and 5/6ths. The next step would be to turn the 5/6 into a decimal. That would be 0.83333 so 23.83 divided by 11.  The answer would be 2.166363664 according the the calculator. HOPE THIS HELPS!!!

Answer:

[tex]2\frac{1}{6}[/tex] foot

Step-by-step explanation:

John has a roll containing  [tex]24\frac{2}{3}[/tex] feet of wrapping paper.

He must cut off  [tex]\frac{5}{6}[/tex] feet.

Now the left over wrapping paper =  [tex]24\frac{2}{3}[/tex] -  [tex]\frac{5}{6}[/tex]

                                                      =  [tex]\frac{74}{3}[/tex] -  [tex]\frac{5}{6}[/tex]

                                                      =  [tex]\frac{148-5}{6}[/tex]

                                                      =  [tex]\frac{143}{6}[/tex]

                                                      =  [tex]23\frac{5}{6}[/tex]

He wants to divide the left over wrapping paper into 11 pieces.

[tex]23\frac{5}{6}[/tex] ÷ 11

[tex]\frac{143}{6}[/tex] ÷ 11

[tex]\frac{143}{6}[/tex] ×  [tex]\frac{1}{11}[/tex]

[tex]\frac{143}{66}[/tex]

[tex]\frac{13}{6}[/tex]

[tex]2\frac{1}{6}[/tex] foot

Each piece would be  [tex]2\frac{1}{6}[/tex] foot long.

x=3

multiply 2 to both sides to cancel denominator

subtract 8x from both sides and then divide by 2

[tex]\dfrac{6+8x}{2}=5x\\\\\dfrac{6}{2}+\dfrac{8x}{2}=5x\\\\3+4x=5x\qquad|\text{subtract 4x from both sides}\\\\3=x\to x=3[/tex]

Repeating decimals are considered rational numbers because they can be represented as a ratio of two integers. If a number is terminating or repeating, it must be rational if a decimal is both non terminating and non repeating, the number is irrational.

So yes.

Yes, 5.3 repeating is a rational number. It can be written as the fraction 53/9.

Yes, 5.3 repeating is a rational number. A rational number is a number that can be expressed as a fraction, where both the numerator and denominator are integers. In this case, we can write 5.3 repeating as the fraction 53/9. The decimal 5.3 repeating means that the digit 3 repeats infinitely, so it can be written as 5.3333... In fraction form, this becomes 53/10 + 53/100 + 53/1000 + ...

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Answer:

x = 6

Step-by-step explanation:

(x)(4) +3 -11 = 24

6 x 4 = 32

32 + 3 = 35

35 - 11 = 24