MATHEMATICS
MIDDLE SCHOOL

Answer: X is equal to 2 because 40 divided by 4/5 gives you 2 which is x

HIGH SCHOOL

The function y=-2+5sin(pi/12(x-2)), what is the minimum value?

Answer:

-7

Step-by-step explanation:

We are given that a function

We have to find the minimum value of y.

We know that range of sin x is [-1,1].

Maximum value of y=3

Minimum value of y=-7

Hence, the minimum value of given function =-7

Answer:

-7

Step-by-step explanation:

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HIGH SCHOOL

Round to the nearest ten 756

760 beause anything over five round up under5 round down

MIDDLE SCHOOL

x2y - 2xy - 24y = y(x2 - 2x - 24) What is the completely factored form of x2y – 2xy – 24y? (xy + 4)(x – 6) xy(x + 4)(x – 6) y(x + 4)(x – 6) y(x + 4)(xy – 6)

The required factorized form of the given expression is y(x - 6)(x + 4), where y is the greatest common factor (GCF).

What is the Factorization?

Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original.

We have been given that the expression below as

x²y - 2xy - 24y

We have to determine the factor of the expression 50x + 100

First, we have to find the Greatest Common Factor (GCF).

GCF = y

y Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

y(x² - 2x - 24)

Simplify each term in parentheses.

y(x² - 2x - 4x - 24)

y(x - 6)(x + 4)

Therefore, the required factorized form of the given expression is y(x² - y(x - 6)(x + 4)

Learn more about the Factorization here:

brainly.com/question/4184435

#SPJ2

we are given

now, we can factor out right side term

now, we can plug back

and we get

so,

.............Answer

HIGH SCHOOL

At a meeting of 3 representatives from each of 6 different companies, each person shook hands once with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place? A. 45B. 135C. 144D. 270E. 288

Answer: B. 135

Step-by-step explanation:

Given : Number of representatives from each company = 3

Number of companies =6

Total number of people there :

The total number of ways that 18 people shake hands with each other :-

The number of ways that representatives shake hands with people from their own company :-

If the representatives did not shake hands with people from their own company , then the total number of ways for handshake :-

Hence, the total number of handshakes will be 135.

MIDDLE SCHOOL

Item 8 Question 1

In June, a runner ran a mile in 7:45. In September, the runner ran a mile in 5:51.

Is the percent of change in time an increase or a decrease?

response - correct

Increase

Decrease

Question 2

Find the percent of change from June to September. Round to the nearest hundredth of a percent.

The percent of change is about

%.

So, I didn't quite understand your question clearly, but I'll try my best to answer it.

So, the first question is quite simple: Did the runner have a % decrease in his time or an increase.

Well, 7:45 is minor than 5:51. So, his time decreased.

2nd question:

The percent of change. Well, first things first 7:45 has 2 different units, wich are minutes and seconds, I suppose. Same goes for 5:51.

So let's put everything in seconds. multiply both the 7 and 5 for 60(for every minute has 60 seconds.)

That means:

7*60= 420+45 = 465.

5*60=300+51=351.

Now, let's do the math itself:

465 -> 100%

351 -> x%

Is equal to about 75,5%

How much did it decrease then?

(75,5-100)%= 24,5%, approximately

So, the first question is quite simple: Did the runner have a % decrease in his time or an increase.

Well, 7:45 is minor than 5:51. So, his time decreased.

2nd question:

The percent of change. Well, first things first 7:45 has 2 different units, wich are minutes and seconds, I suppose. Same goes for 5:51.

So let's put everything in seconds. multiply both the 7 and 5 for 60(for every minute has 60 seconds.)

That means:

7*60= 420+45 = 465.

5*60=300+51=351.

Now, let's do the math itself:

465 -> 100%

351 -> x%

Is equal to about 75,5%

How much did it decrease then?

(75,5-100)%= 24,5%, approximately

MIDDLE SCHOOL

The equation of a line containing one leg of a right triangle is y=-4x. Write equations could represent the line contains the other leg??

Answer:

Explanation:

The general form of the equation of the linear line is:

y = mx + c

where:

m is the slope

c is the y-intercept

1- getting the slope:

We know that our line is perpendicular to the line y = -4x

This means that:

m₁ * m₂ = -1

m₁ * -4 = -1

m₁ = 1/4

The equation now becomes:

y = (1/4) x + c

2- getting the y-intercept:

Since we are not given any points that belong to the line or any conditions regarding the value of the c, therefore, we can simply assume that the y-intercept is zero

Based on the above, the equation of the line is:

Hope this helps :)

Explanation:

The general form of the equation of the linear line is:

y = mx + c

where:

m is the slope

c is the y-intercept

1- getting the slope:

We know that our line is perpendicular to the line y = -4x

This means that:

m₁ * m₂ = -1

m₁ * -4 = -1

m₁ = 1/4

The equation now becomes:

y = (1/4) x + c

2- getting the y-intercept:

Since we are not given any points that belong to the line or any conditions regarding the value of the c, therefore, we can simply assume that the y-intercept is zero

Based on the above, the equation of the line is:

Hope this helps :)

MIDDLE SCHOOL

Soren has two jobs. During the day , he works as an office clerk, and in the evening he works as a cashier. His office job pays him$11 per hour, and his cashier job pays him $8.75 per hour . In one week Soren worked 46 hours, and earned a total of $470.. How many hours did he work in each job.

Answer:

Office clerk - 30 hours

Cashier - 16 hours

Step-by-step explanation:

We are given that Soren's office job pays him $11 per hour while his cashier job pays him $8.75 per hour.

If he has worked for a total of 46 hours and earned $470, we have to find the number of hours he worked in each job.

Assuming x represent the number of hours that Soren works as an office clerk, we can write the following equation:

11x + 8.75(46 - x) = 470

11x + 402.5 - 8.75x = 470

11x - 8.75x = 470 - 402.5

2.25x = 67.5

x = 67.5/2.25

x = 30

Number of hours Soren worked as office clerk = 30 hours

Number of hours Soren worked as a cashier = 46 - 30 = 16 hours

MIDDLE SCHOOL

there are 156 students in 6 different classrooms. What is the ratio of students that classrooms? If there are 80 boys what is the ratio of boys to girls?

156-80=numb of girls

numb of girls: 76

Ratio of boys to girls=80:76

=20:19

Ratio of students in classrooms= 156:6

=26:1

(assuming that each classroom has the same number of students)

numb of girls: 76

Ratio of boys to girls=80:76

=20:19

Ratio of students in classrooms= 156:6

=26:1

(assuming that each classroom has the same number of students)

The easiest way to find out ratios is to divide the total (in this case, students) by the divider (in this case, the classrooms).

156 ÷ 6 = 26

The ratio of students to classrooms is 26 students per classroom, or 26 : 1.

In this case, you need to figure out how many girls there are first.

156 - 80 = 76

Because you don't want to end up with a decimal, you need to find the GCF.

The factors of 76 are: 1, 2, 4, 19, 38, 76

The factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

Your GCF is 4, which is number you divide your total number of boys and total number of girls by.

80 ÷ 4 = 20

76 ÷ 4 = 19

The simplest ratio of boys to girl is 20 boys for every 19 girls, or 20 : 19

156 ÷ 6 = 26

The ratio of students to classrooms is 26 students per classroom, or 26 : 1.

In this case, you need to figure out how many girls there are first.

156 - 80 = 76

Because you don't want to end up with a decimal, you need to find the GCF.

The factors of 76 are: 1, 2, 4, 19, 38, 76

The factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

Your GCF is 4, which is number you divide your total number of boys and total number of girls by.

80 ÷ 4 = 20

76 ÷ 4 = 19

The simplest ratio of boys to girl is 20 boys for every 19 girls, or 20 : 19

MIDDLE SCHOOL

The area of a rectangle is 30 square meters. Find the length and width if the length is 1.45 times the width.

The length and the width of the rectangle will be 6.6 meters and 4.55 meters respectively.

- Let the width be x
- Let the length be = 1.45 × x = 1.45x

Therefore, the equation to solve the question will be:

Length × Width = Area

x × 1.45x = 30

1.45x² = 30

x² = 30/1.45

x² = 20.69

x = ✓20.69 = 4.55

Length = 4.55 × 1.45 = 6.60

Read related link on:

brainly.com/question/14153907

Answer:

The length of the rectangle is 14.5√6/29 or 6.6 meters and the width is 10√6/29 or 4.55 meters.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Area of a rectangle = 30 square meters

2. Find the length and width if the length is 1.45 times the width.

Width of the rectangle = x

Length of the rectangle = 1.45x

Now substituting in the formula of the area of a rectangle, this way:

30 = x * 1.45x

30 = 1.45x²

x² = 30/1.45

x = √30/1.45

x = 10 √6/29 or 4.55 (Rounding to two decimal places)

1.45 x = 14.5 √6/29 or 6.6

The length of the rectangle is 14.5√6/29 or 6.6 meters and the width is 10√6/29 or 4.55 meters.