The length of a rectangle is half the width. The area is 25 square meters. Find the perimeter

Final answer:

The student's question can be solved by setting up a system of equations from the given information and finding that the two numbers are 25 and 20.

Explanation:

Solution to the Given Problem

The student's question involves solving a system of equations. They are given that the sum of two numbers is 45 and their difference is 5. To solve this, we can set up two equations based on the information given:

Let the two numbers be x and y.

The sum of the two numbers is 45: x + y = 45

The difference of the two numbers is 5: x - y = 5

To find the values of x and y, we can solve this system of equations. By adding the two equations, we cancel out y, giving us:

2x = 50

Dividing both sides by 2, we find that x = 25. Substituting x = 25 into one of the original equations, for instance, x + y = 45, we get:

25 + y = 45

Subtracting 25 from both sides gives us y = 20.

Therefore, the two numbers are 25 and 20.

Answer:

a. (1,14) and (7,7)

b. slope = -1.2

Step-by-step explanation:

a. Use the points that are actually on the drawn line

(1,14) and (7,7)

b. Slope formula is :

[tex]slope = ( y_{2} - y_{1}) \div ( x_{2} - x_{1})[/tex]

It doesnt matter which one is 1 or 2. I will take (1,14) as (x1, y1) and (7,7) as (x2, y2)

[tex]slope = \frac{(7 - 14)}{(7 - 1)} \\ = \frac{ - 7}{6} = - 1.1667 = - 1.2[/tex]

Answer:

(A) (1, 14) and (7, 7)

(B) -1.17

Step-by-step explanation:

(A) the 2 points that should be used are: (1, 14) and (7, 7). The reason is that these 2 points are the closest to the trend line.

(B) With 2 points - (x1, y1) and (x2, y2) - a linear equation can be obtained. The slope (m) of the line is computed as follows:

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

m = (7 - 14)/(7 - 1) = -1.17

Step-by-step explanation:

5(x+2)-7=5(x-3)

5x + 10 -7 = 5x -15

5x - 5x ..... this question must have an error

Answer:

Undefined

Step-by-step explanation:

5(x+2)-7=5x-3

5x+10-7=5x-3

5x+3=5x-3

5x=5x

can't solve, so it is undefined.

Answer:

=4(x−3)(x+6)

Step-by-step explanation:

4x^2+12x-72

=4(x−3)(x+6)

The factorized form of the equation 4x² + 12x - 72 is

A = 4 ( x + 6 ) ( x - 3 )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be A = 4x² + 12x - 72

Now , the equation can be simplified by

A = 4 ( x² + 3x - 18 )

Now , on simplifying the equation , we get

A = 4 ( x² - 3x + 6x - 18 )

Now , on grouping the similar terms in the equation , we get

A = 4 ( x ( x - 3 ) + 6 ( x - 3 ) )

A = 4 ( x + 6 ) ( x - 3 )

So , the factorized form of the equation is

A = 4 ( x + 6 ) ( x - 3 )

Hence , The factorized form of the equation 4x² + 12x - 72 is

A = 4 ( x + 6 ) ( x - 3 )

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Answer:

The answer to your question is: -116

Step-by-step explanation:

   2⁻²(12 x 3) - 5³

  =  1 /2² (36) - 125

  = 1/4 (36) -125

  =  36/ 4 -125

   = 9 - 125

    = - 116

Answer:

[tex]\frac{3}{2}[/tex] c

Step-by-step explanation:

Given

[tex]\frac{3a+3b}{2a-2b}[/tex] ← factor numerator and denominator

= [tex]\frac{3(a+b)}{2(a-b)}[/tex]

= [tex]\frac{3}{2}[/tex] × [tex]\frac{a+b}{a-b}[/tex] ← this = c

= [tex]\frac{3}{2}[/tex] × c = [tex]\frac{3}{2}[/tex] c

Answer:

solving

Step-by-step explanation:

Answer:

[tex]v = 3[/tex]

Step-by-step explanation:

-(v-1)=-6v+16

-v+1=-6v+16

grouping like terms

-v+6v=16-1

5v=15

dividing through by 5

[tex] \frac{5v}{5} = \frac{15}{5} [/tex]

[tex]v = \frac{15}{5} [/tex]

[tex]v = 3[/tex]

Answer:

Please read the answer to Parts A and B below.

Correct statement, question and data:

Lucas and Brianna read three books each last month. The table shows the number of pages in each book and the length of time it took to read the entire book.

Pages Lucas Read 208 156 234  

Time (hours)          8      6     9

Pages Brianna Read 168 120 348  

Time (hours)               6     4      12

a. How many observations can you make about any similarities or difference that exist between the reading rates  of the two students.

b. Both Lucas and Brianna had specific reading goals they needed to accomplish. What different strategies did  each person employ in reaching those goals?

Source:

Grade 7, Module 1 - Student material of New York State

Step-by-step explanation:

Part A.

We notice that Lucas read at a constant reading rate of 26 pages per hour and he read for a total of 23 hours. On the other hand, Brianna, does not follow a constant reading rate, she read the first book at a rate of 28 pages per hour, the second at a rate of 30 pages per hour and the third book at a rate of 29 pages per hour, adding up to 22 hours.

Part B.

Lucas followed at a constant rate of 26 pages per hour and Brianna was not constant but she reads faster than Lucas with an average rate of 29 pages per hour (636 pages in 22 hours).

Answer: 1760

Step-by-step explanation:

[tex]\dfrac{5280\ feet}{1\ mile}\times \dfrac{1\ yard}{3\ feet}\quad =\dfrac{5280\ yard}{3\ feet}\quad =\large\boxed{1760\ yard\ per\ mile}[/tex]

Answer: -3(15m-4)/40

(All the numbers are above the fraction bar, then 40 is under the fraction bar)

- 9/8 m + 3/10

Answer

The difficulty of the permit test can vary, but with proper preparation and study of the driver's handbook, most individuals can pass the test.

The difficulty of the permit test can vary depending on the individual's level of preparation and understanding of the rules of the road, traffic laws, and safe driving practices. The test typically consists of multiple-choice questions based on information found in the state's driver's handbook.

To pass the permit test, one should:

1. Study the driver's handbook thoroughly, as it contains all the necessary information.

2. Take practice tests to become familiar with the format and types of questions that may be asked.

3. Understand traffic signs, signals, and markings, as well as the rules for sharing the road with other drivers, pedestrians, and cyclists.

4. Learn about the consequences of driving under the influence of alcohol or drugs.

5. Be aware of the laws regarding distracted driving, such as texting while driving.

By dedicating time to study and understand these concepts, most individuals find that they can pass the permit test. It is designed to ensure that new drivers have the knowledge required to drive safely and responsibly.

The difficulty of the permit test can vary, but with proper preparation and study of the driver's handbook, most individuals can pass the test.

Answer:

They would have the same area.

Step-by-step explanation:

The area of a circle = pi x the circumfrence.  or pi x the radious squared.  so if they had the same circumfrence they would have the same area.

Given ST = 12 and RT = 49, we apply the basic principle of part-whole relationships in a line to find RS. By subtracting the length of ST from RT, we determine that RS equals 37.

The question asks to find the length of RS given that ST = 12 and RT = 49. To find the length of RS, we can apply the concept that in a linear situation, if S is a point between R and T, then RS + ST = RT. This concept is based on the principle of the sum of parts of a whole.

Given:

To find RS, we use the equation:

RS + ST = RT

Plugging in the given values:

RS + 12 = 49

Solving for RS, we subtract 12 from both sides:

RS = 49 - 12

RS = 37

Therefore, the length of RS is 37.

To calculate the change in volume of a box when cutout length increases from 0.3 inches to 1.2 inches using function notation, use the formula ΔV=f(l2)-f(l1), where f(l) represents the volume of the box given the length of the edge.

The change in volume when the cutout length increases from 0.3 inches to 1.2 inches can be represented in function notation as ΔV=f(l2)-f(l1), where f(l) represents the volume of the box as a function of the length (l) of the edge. Here, l1=0.3 and l2=1.2.

Given the formula for the volume of the box V = Length x Width x Height. Let's assume Width and Height remain constant. If initially the volume was V1=f(l1) and finally it became V2=f(l2), the change in volume will be ΔV=V2-V1 which equals f(l2)-f(l1).

For example, if the width and height of the box are 6 inches and 3 inches respectively, then the initial volume is V1 = 0.3 x 6 x 3 cubic inches and the final volume is V2 = 1.2 x 6 x 3 cubic inches. Therefore, ΔV = (1.2 x 6 x 3) - (0.3 x 6 x 3) cubic inches.

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The change in the volume of the box when the cutout length increases from 0.3 inches to 1.2 inches can be calculated using the function ΔV = V(1.2) - V(0.3). Assuming the rest of the box's dimensions are constant, this results in a change in volume of 16.2 cubic inches.

To use function notation to represent how the volume of the box changes by if the cutout length increases from 0.3 inches to 1.2 inches, let us first define a function V(l) that represents the volume of the box as a function of the cutout length 'l'. If the initial cutout length is 0.3 inches and the final cutout is 1.2 inches, the change in length Δl would be 1.2 inches - 0.3 inches = 0.9 inches. We can express the change in volume, ΔV, as the function of the change in cutout length as follows: ΔV = V(1.2) - V(0.3).

Given that the volume of a rectangular box can be calculated by the formula volume = length × width × height, and assuming other dimensions of the box do not change, the function V(l) becomes:

V(l) = length × width × l

Let's consider an example where the dimensions of the box remain constant at 6 inches by 3 inches. The volume function would then be:

V(l) = 6 in. × 3 in. × l in.

The change in volume for an increase in cutout from 0.3 to 1.2 inches is then:

ΔV = V(1.2) - V(0.3) = (6 × 3 × 1.2) - (6 × 3 × 0.3) = 21.6 in.³ - 5.4 in.³ = 16.2 in.³.

Answer:

7a - 2

Step-by-step explanation:

A perimeter is just the sum of all sides added together, so just put all the expressions together into a big equation.

2a - 3 + 2a + 3a + 1

Combine like terms

7a - 2

Answer:

7800

add 1 to the tens place as grater than 5

7765 rounded to the nearest hundred would be 7800

Answer:

f= .75 or 3/4

Step-by-step explanation:

13/4 = 3 1/4 or 3.25

4-3.25= .75

Or

3/4

Answer:

f = 3/4

Step-by-step explanation:

f+(13/4)= 4

subtract (13/4) from both sides

⇒f + (13/4)- (13/4) = 4 -(13/4)        

⇒f =(16-13) /4

∴f = 3/4

Answer:

whats equivelent to 6x4?

Step-by-step explanation:

6 x 4 = 24

8 x 2 = 16 so 8 x 3 = 24 because 8 x 4 would be

8 x 2 = 16

16 x 2 =

6 + 6 = 12

carry the one.

2

1 + 1 + 1 (We now have three ones from carrying that 1) and our answer is

32.

So N = 3

Answer:

6x4=8xN N=8x3

Step-by-step explanation: N=8x3 because 6x4=24 so if you multiply 8x3 it =  

24

Answer:

1/24

Step-by-step explanation:

First, multiply the two fractions together.

3/8 * 1/9

Multiply the numerators:

3*1=3

And the denominators:

8*9=72

So, the fraction ends up being 3/72.

I need simplify the fraction by dividing both the numerator and the denominator by 3:

3/3=1

72/3=24

Simplified fraction is 1/24.

Answer: [tex]\frac{1}{24}[/tex]

Step-by-step explanation: To multiply fractions, first multiply across the numerators and then multiply across the denominators.

[tex](\frac{3}{8}) (\frac{1}{9}) = \frac{3}{72}[/tex]

[tex]\frac{3}{72} = \frac{1}{24}[/tex]

Answer:

52.50/5.8= $9 per hour

Answer:

C

Step-by-step explanation:

This is a linear equation in one variable and has 1 solution

12x + 6 = 5x ( subtract 5x from both sides )

7x + 6 = 0 ( subtract 6 from both sides )

7x = - 6 ( divide both sides by 7 )

x = - [tex]\frac{6}{7}[/tex] ← 1 solution

The equation has a single solution for x, which is -6/7. The correct answer is: C. 1

To determine the number of solutions to the equation 12x + 6 = 5x, let’s solve the equation step by step.
First, we need to get all terms with the variable x on one side of the equation and constants on the other side. To do this, we can subtract 5x from both sides of the equation:
12x + 6 - 5x = 5x - 5x
This simplifies to:
7x + 6 = 0
Now we need to isolate the term with the x variable, so we subtract 6 from both sides of the equation:
7x + 6 - 6 = 0 - 6
This further simplifies to:
7x = -6
Finally, to solve for x, we divide both sides by 7:
7x / 7 = -6 / 7
x = -6/7
Therefore, the equation has a single solution for x, which is -6/7.
The correct answer is:
C. 1

Answer:

greater than

Step-by-step explanation:

it is largee

Answer:  greater then

Step-by-step explanation:

cause 546 is greater then 540

Answer:

Well this isn't a grammatically correct question but if you're asking how they would split the money it would be $5 for each person.

Step-by-step explanation:

1. The 10 people buy the cups of Lemonade.

2. One cup of lemonade is $1, so that means 10 cups would be $10.

3. Then you would give half to your friend which would be $5.

Answer:

Trapezoid Area = (Sum of Bases / 2) * Height =

(6 + 14 / 2) * Height =

10 * 8 =

80

Step-by-step explanation:

Answer:

-24x+2

Step-by-step explanation:

7x(-3) = -21x

x(-2) = -2x

x

2

-24x+2

Answer: Your answer would have to be x= 29

Answer:

x=29

Step-by-step explanation:

43+ 15 is 58

58 divided by 2 is 29

2*29= 58

58-15=43