Gus plans to install a handrail around a rectangular skating rink. One of the rink's sides is 40 meters long and one of the rink's width is 20 meters wide. How many meters of handrail does Gus need to cover the perimeter of the rectangular skating rink?

Answer:

[tex] x = \frac{11}{2} \\ [/tex]

Step-by-step explanation:

f(x) = 2x - 7

when x = 4

It means that equate f(x) to the value of x that's 4 and solve for x

That's

f(x) = 4

We have

[tex]2x - 7 = 4[/tex]

Add 7 to both sides of the equation

[tex]2x + 7 - 7 = 4 + 7 \\ 2x = 11[/tex]

Divide both sides by 2

[tex] \frac{2x}{2} = \frac{11}{2} \\ [/tex]

We have the final answer as

[tex]x = \frac{11}{2} \\ [/tex]

Hope this helps you

Answer:

The first term is 3. The common difference is 2.

Step-by-step explanation:

The first term is x.

The common difference is d.

The second term is x + d.

3rd term: x + 2d

4th term: x + 3d

7th term: x + 6d

"The fourth term of an Arithmetic Sequence is equal to 3 times the first term"

x + 3d = 3 * x       Eq. 1

"the seventh term exceeds twice the third term by 1"

x + 6d = 2(x + 2d) + 1       Eq. 2

Simplify Eq. 1:

2x = 3d

Simplify Eq. 2:

x + 6d = 2x + 4d + 1

x = 2d - 1

Multiply both sides of the last equation by 2.

2x = 4d - 2

2x = 3d   (simplified Eq. 1)

Since 2x = 2x, then the right sides are equal.

3d = 4d - 2

d = 2

2x = 3d

2x = 3(2)

2x = 6

x = 3

Answer: The first term is 3. The common difference is 2.

Answer:

Step-by-step explanation:

We know that:

2x + 6 = 9.

Using this we want to find the values of different expressions.

The solutions are:

a) 4x + 12

You can see that if we grab the initial equation:

2x + 6 = 9

And multiply both sides by 2 we get:

2(2x + 6) = 2*9

4x + 12 = 18

So we just found the value of the expression.

b) 2x+9

Again we start with the original equation:

2x + 6 = 9

Now we add 3 in both sides:

2x + 6 + 3 = 9 + 3

2x + 9 = 12

We just fond the value of the expression.

c) x + 3

We start with:

2x + 6 = 9

Now we divide both sides by 2:

(2x + 6)/2 = 9/2

x + 3 = 4.5

d) -6x - 18

We start with:

2x + 6 = 9

Here we need to multiply both sides by -3 to get:

(2x + 6)*-3 = 9*-3

-6x -18 = -27

e) 2x + 1

We start with:

2x + 6 = 9

Now we subtract 5 in both sides:

2x + 6 - 5 = 9 - 5

2x + 1 = 4

f) 10x + 32

We start with:

2x + 6 = 9

Now we multiply both sides by 5:

5*(2x + 6) = 5*9

10x + 30 = 45

Now we add 2 to both sides:

10x + 30 + 2 = 45 + 2

10x + 32 = 47.

If you want to learn more, you can read:

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Answer:

-166

Step-by-step explanation:

g to kk hg hg g to hg FG u

Answer:

its B,C,and E

Step-by-step explanation:

Answer:

B C and E

Step-by-step explanation:

i did it and it said it was right :)

Answer:

1) Function

2) Function

3) Not a Function

Step-by-step explanation:

Using the vertical line test, using a pen, pencil or finger to move it vertically, I determined that 2 of the 3 questions was a function because the last question would not be a function since there are two lines instead of one when doing the test. Hope this helps!

Graph A:

It is a function.

Graph B:

It is a function.

Graph C:

It is not a function.

We have,

Vertical line test:

If every vertical line intersects the graph at most once, meaning that no two different points on the graph lie on the same vertical line, then the graph represents a function.

Now,

Graph A:

Any vertical line will touch only once on the graph.

It is a function.

Graph B:

Any vertical line will touch only once on the graph.

It is a function.

Graph C:

Any vertical line will touch more than once on the graph.

It is not a function.

Thus,

Graph A:

It is a function.

Graph B:

It is a function.

Graph C:

It is not a function.

Learn more about functions here:

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Answer:

10x

Step-by-step explanation:

5x ft LONG 2x ft WIDE

cancell the x

new expression:

5 times 2

now add

5 *2=10

put back the x that we cancelled

10*x=10x

we get the answer as 10x.

Answer:

Lifegard

Step-by-step explanation:

Answer:

The Lifeguard Job

from khan academy (AKA KA)

Answer:

Given:

f(x) = 3x + 2

g(x) = 2x – 5

f(2)+g(1)

----------------------------------------------------------------

Above we have three clues that we got from the question.

First, substitute the value of f(2) for f(x)

3(2)+2

6+2

8

Second, substitute the value of g(1) for g(x)

2(1)-5

2-5

-3

Now we have to add the f(x) value which is 8 and the g(x) value which is -3.

8+-3

5

Your final answer would be 5.

Answer:

15x+10

Step-by-step explanation:

So if Mark makes $15 from selling it but he has to pay $10 he is really only making $5 per copy of his artwork

$15-$10=$5

Answer:

(x - 5)(x - 4)

Step-by-step explanation:

[tex] {x}^{2} - 9x + 20 \\ \\ = {x}^{2} - 5x - 4x + 20 \\ \\ = x(x - 5) - 4(x - 5) \\ \\ = (x - 5)(x - 4)[/tex]

Answer:

15%

Step-by-step explanation:

3÷20=0.15

0.15×100=15

95

Step-by-step explanation:

she would have to get At Least 95 or better to balance it out

Answer:750

Step-by-step explanation:

because you need to find the area of 1 tile then multiply it by 100

Answer:

x = 7

Step-by-step explanation:

Let x be the number

x+16 = 23

Subtract 16 from each side

x+16-16 =23-16

x = 7

Answer:

205.71 miles

Step-by-step explanation:

you take the miles they are going to travel minus the miles you have been given.In this case you are going to take 517.74-312.03

Answer:

Dividend=[tex](3x^4+4x^2-2x-35)[/tex]

Divisor=[tex](x+2)[/tex]

Quotient=[tex](3x^3-6x^2+16x-34)[/tex]

Remainder=43

Step-by-step explanation:

Answer:

AE = 12

Step-by-step explanation:

[tex]\triangle DAE \sim\triangle BAC.... (given) \\

\therefore \frac{AD}{AB} = \frac{AE}{AC}.. (csst) \\\\

\therefore \frac{6}{6+4} = \frac{x}{x+8} \\\\

\therefore \frac{6}{10} = \frac{x}{x+8} \\\\

\therefore \frac{3}{5} = \frac{x}{x+8} \\\\

\therefore 3(x+8) = 5x\\\\

3x + 24 = 5x \\\\

24= 5x - 3x \\\\

24= 2x \\ \\ x = \frac{24}{2} \\ \\ x = 12 \\ \\

\because \: AE = x \\ \\ \huge \red{ \boxed{\therefore \: \: AE = 12}}[/tex]

Answer: The mixed number is 5 5/8 cups of trail mix.

Step-by-step explanation:

    3. Add the numerators, 54 + 20 + 12 + 33 + 16. 54 +16 = 70. 70 + 20 = 90. 90 + 12 = 102. 102 + 33 = 135.

     4. The improper fraction is 135/24. Simplify it by 3 on both numerator and denominator which results in 45/8. 45/8 as a mixed number is 5 5/8  since 8 goes into 45, 5 times and the remainder is 5, which results the denominator to be 8.

Answer:

mixed number: 5 5/8 cups of trail mix.

Step-by-step explanation:

Hope this helped!

Answer:

The second one.

Step-by-step explanation:

Hope this helps! If it does, please mark me brainliest. Thank you! ;)

The second histogram correctly represents the prices of the dishwashers.

"Histogram is an approximate illustration of the distribution of numerical data."

Now, from the given options we can see that the prices of the dishwashers are plotted in the following range:

$200$-$399; $400-$599; $600-$799; $800-$999

Also, the data of the prices of the dishwashers are given:

$229, $260, $299, $389, $399, $439, $525, $568, $615, $629, $780, $955

From this we can calculate the number of data points for the prices of dishwashers in the given range:

$200-$399 - 5 dishwashers ($229, $260, $299, $389, $399)

$400-$599 - 3 dishwashers ($439, $525, $568)

$600-$799 - 3 dishwashers ($615, $629, $780)

$800-$999 - 1 dishwasher ($955)

Hence, the second histogram shows the correct representation of the data points of the prices of the dishwashers.

More example on the use of histogram can be found here https://brainly.com/question/14421716?referrer=searchResults

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Answer:

3:1

Step-by-step explanation:

I took this same question in a test and the correct answer was 3:1

The ratio of the driver gear to the follower gear is 3 : 1.

A ratio indicates the number of times one number contains another.

Given that, the driver gear has 15 teeth while the follower gear has 5 teeth.

The ratio of the driver gear to the follower gear is:

15 : 5

= 3:1

Hence, the ratio of the driver gear to the follower gear is 3 : 1.

To learn more about ratios, click here:

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Answer:

2k + 4 > k + 11

Step-by-step explanation:

Keywords:

more - addition

twice - multiplication

greater than - >

sum - addition

4 more than twice the number k

2k + 4

Greater than

>

Sum of k and 11

k + 11

2k + 4 > k + 11

Solve for k if needed.

2k + 4 > k + 11

2k > k + 7

k > 7

Best of Luck!

Answer:

400

Step-by-step explanation:

if its 350 or more u round up to 400 but if it was 350 or less it would be 300

Answer:

  [tex]7^{-5}[/tex]

Step-by-step explanation:

It looks like you may want an exponential representation of ...

  [tex]\dfrac{1}{7\times7\times7\times7\times7}=\dfrac{1}{7^5}=\boxed{7^{-5}}[/tex]

__

The applicable rule of exponents is ...

  1/a^b = a^-b

Answer:

First number: -39

Second number: -37

Step-by-step explanation:

An odd number can be written as [tex]2n+1[/tex] where n is a whole number.

Let's call our first number 2n+1.

Our second, consecutive number will be 2 more than our first number, since it has to be odd. All numbers go: odd -> even -> odd -> even. If we have an odd number, and add 2, we'll get the next odd number.

First number: 2n+1

Second number: 2n+1+2 = 2n+3

The sum of these two numbers, 2n+1 and 2n+3 will be -76.

(2n+1) + (2n+3) = -76

2n + 2n + 1 + 3 = -76

4n + 4 = -76

4n = -80

n = -20

Since our first number is 2n+1:

2 * (-20) + 1 = -40 + 1 = -39

First number: -39

Our second number is 2n+3, or 2 more than our first number.

-39 + 2 = -37

Second number: -37

We can double check this:

-39 + (-37) = -39 - 37 = -76

Answer:

All real numbers are solutions to this equation

Step-by-step explanation:

[tex]\frac{9x+3}{3} =3x+1\\\frac{3(3x+1)}{3} =3x+1\\3x+1=3x+1[/tex]

Answer:

The number of sides is 7

Step-by-step explanation:

Once the sum of interior angles is equal to 900º and the sum of interior angles is given by

[tex]S=(n-2) \cdot 180\º, \text{ as }n \text{ being the number of sides}[/tex]

[tex]900\º = (n-2) \cdot 180\º[/tex]

[tex]\dfrac{900\º}{180\º} = (n-2)[/tex]

[tex]5 = (n-2)[/tex]

[tex]5+2 = n-2+2[/tex]

[tex]\boxed{n=7}[/tex]

Answer:

Option (a).

Step-by-step explanation:

1) Pedro decided to build a rectangular enclosure with an area of 36 m². How many meters of canvas will he have to buy to make the enclosure considering that one side will be 3 meters more than the other?

Let the length of the rectangle be x then the width will be (3+x) m

The area of a rectangular enclosure is 36 m².

To find how may meter of canvas will he have to buy to make the enclosure, we can find its perimeter. Firstly finding length and breadth using formula of area of rectangle.

[tex]A=l\times b\\\\36=x(x+3)\\\\x^2+3x-36=0[/tex]

[tex]x=\dfrac{-3+\sqrt{3^{2}-4(1)(-36)}}{2\times(1)},\dfrac{-3-\sqrt{3^{2}-4(1)(-36)}}{2\times(1)}\\\\x=4.68\ m\ \text{and}\ -7.68\ m[/tex]

Neglecting negative value, we get the length is 4.64 m

Width, b = (3+x) = (3+4.64) = 7.64 m

The perimeter of rectangle is :

P = 2(l+b)

P = 2(4.64 m+7.64 m)

P = 24.56 m

or

P = 25 m

Hence, 25 m of canvas will he have to buy to make the enclosure.