13. Town officials are putting a pathway around a pool as shown below.
(4x+3)
pool
(2x-5) ft
deck
a) Determine the perimeter of the pool in terms of x. Write your answer in simple form and
include units. Show or explain your work.
b) Determine the area of the pool in terms of x. Write your answers as a trinomial and include
units. Show or explain your work.

I will do the first example, by explaining how to graph it. Then you can do the second example.

[tex]f(x) = x^3-10x^2+28x-24[/tex]

We start by determining the the x-intercepts, by letting y = 0:

[tex]x^3-10x^2+28x-24=0,\\\left(x-2\right)^2\left(x-6\right)=0,\\x=2,\:x=6[/tex]

The x-intercepts of the graph are (2, 0) and (6, 0) respectively. Now we determine the y-intercepts by letting x = 0:

[tex]f\left(x\right)=\left(0\right)^3-10\left(0\right)^2+28\left(0\right)-24 = - 24[/tex]

So the y-intercept is (0, -24). But remember we need one more point, as there has to be a transition between the x-intercepts. This is the minimum of the graph. To determine this, we take the derivative of the function, and then equate it to 0 to find the "critical points." :

[tex]\frac{d}{dx}\left(x^3-10x^2+28x-24\right)\\\\ =>\frac{d}{dx}\left(x^3\right)-\frac{d}{dx}\left(10x^2\right)+\frac{d}{dx}\left(28x\right)-\frac{d}{dx}\left(24\right)\\\\=> 3x^2-20x+28-0\\=> 3x^2-20x+28[/tex]

Now we equate this to 0, and apply the quadratic equation. In this case we can actually factor it :

[tex]3x^2-20x+28=0,\\\left(x-2\right)\left(3x-14\right)=0,\\\\x=2,\:x=\frac{14}{3}[/tex]

x = 2 is our maximum, or our x-intercept (2, 0). Therefore we have to take 14/3 as our minimum, and determine the y-value:

[tex]f\left(x\right)=\left(\frac{14}{3}\right)^3-10\left(\frac{14}{3}\right)^2+28\left(\frac{14}{3}\right)-24\\\\= -\frac{256}{27}[/tex]

Minimum: (14/3, -256/27)

Graph is in the attachment below -

Answer:30 percent something like that

Step-by-step explanation:

Step-by-step explanation:

y-13<6

y<6+13

y<19

hope it helps.

Answer:

y<19

Step-by-step explanation:

Add 13 to both sides.

y<6+13

Simplify  6+13  to  19.

y<19

Answer: He completes 2 4/5 rows per hour

if he completed 140 rows, how many hours did it take?

We should divide the work completed by the amount of work done per hour.

So, 140/(2 4/5) =  

2 4/5 is equivalent to 2.8  

so 140/2.8 = 50 hours

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

Find the ratio 1500 to 2000; it is 0.75.

75% of the population is Spanish speaking.

Answer:

75%

Step-by-step explanation:

1500 ÷ 200 = 0.75

Answer:10

Step-by-step explanation:

12 x 30 to see how many bottles per hour

360 x 8 to see how many it makes in a day

Divide 28,000 by 2,800 to see how many days it would take.

Step-by-step explanation:

first u will find how much bottles in 8 hours so that will be 60/2minutes =30so 30*12ottles=to 360 bottles per hour so 8*360=2,880 so u will do 28,000/2,880 it will be. 10 days of work.

Answer:

y-axis

Step-by-step explanation:

points are (x,y)

since the y-coordinate does not change, but the x-coordinate does, it rotates around the y-axis.

reflection just means it rotates 180 degrees (out of the paper, not around)

Answer:

7% of $33.00 is $2.31

total $35.31

18% of $35.31 is $6.35

The total with tax and tip is $41.66

Brainly plz :))

The total cost of the meal after tax and tip will be $41.67.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

This feast costs $33.00. A 7% deals charge is applied, trailed by a programmed tip of 18%.

The cost after tax is given as,

⇒ $33 x 1.07

⇒ $35.31

The cost after the tip is given as,

⇒ $35.31 x 1.18

⇒ $41.67

The total cost of the meal after tax and tip will be $41.67.

More about the percentage link is given below.

https://brainly.com/question/8011401

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Answer:

2.85kg

Step-by-step explanation:

3/5kg = 0.6kg

2 1/4 kg = 2.25 kg

0.6kg + 2.25kg = 2.85kg

Answer:

C

Step-by-step explanation:

Given the tables of H(t) an r(t), we want to find:

[tex](H\circ r)(3.0)[/tex]

As stated, this is equivalent to:

[tex]=H(r(3.0))[/tex]

Using the r(t) table, we can determine that:

[tex]r(3.0)=2.0[/tex]

Therefore:

[tex]H(r(3.0))=H(2.0)[/tex]

And by using the H(t) table, we can determine that:

[tex]H(2.0)=2.5[/tex]

So, our answer is C.

Answer: Choice B) Investment decreases by 3% each month

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

Explanation:

We won't use the value 2500 at all.

The base of the exponential is 0.97

Set this equal to 1+r and solve for r

1+r = 0.97

r = 0.97-1

r = -0.03

The negative r value indicates we have exponential decay, so the value of the investment decreases by 3% each month.

Let's say you had $100 to start off. This would mean the investment would be worth $97 after one month is up.

Answer:

74 pesos

Step-by-step explanation:

Let us assume the one peso coins be x

so, number of five peso would be x + 4

And, the total coins is 22

Now the equation is

x + x + 4 = 22

2x + 4 = 22

2x = 22 - 4

2x = 18

x = 9

Five peso coins is 9 + 4 = 13

Now

= 9(1) + 13(5)

= 9 + 65

= 74 pesos

Answer:

20

Step-by-step explanation:

When you simply the improper fractions, you will get this

[tex]9 + 11 = 20[/tex]

Which is 20

Hope this helped

Answer: 20 or 20 1/2

Step-by-step explanation:

I don’t know really but the real answer is 20 1/18

Answer:

8

Step-by-step explanation:

Answer:

Too blurry to read

Step-by-step explanation:

The values of given bases is 1559, 3139, 648 and 170.

We are given that;

The four equations

Now,

a) 66+9t9+48 (base twelve)

[tex]= 6×12¹+6×12⁰ + 9×12²+10×12¹+9×12⁰ + 4×12¹+8×12⁰[/tex]

= 72+6+1296+120+9+48+8

= 1559 (base twelve)

b) 5117-324 (base eight)

[tex]= 5×8³+1×8²+1×8¹+7×8⁰ - (3×8²+2×8¹+4×8⁰)[/tex]

= 3272 + 64 + 8 + 7 - (192 + 16 + 4)

= 3139 (base eight)

c) 242 x 14 (base five)

[tex]= (2x5² + 4x5¹ + 2x5⁰) x (1x5¹ + 4x5⁰)[/tex]

= (50 + 20 + 2) x (5 + 4)

= 72 x 9 =648 (base ten) = 10130(base five)

d) 101010111 (base two)

[tex]= 1x2⁷ + 0x2⁶ +1x2⁵ +0x2⁴ +1x2³ +0x2² +1x2¹ +0x2⁰[/tex]

=128+32+8+2=170 (base ten)

Therefore, by algebra the answer will be 1559, 3139, 648 and 170.

More about the Algebra link is given below.

brainly.com/question/953809

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Answer:

If rotated clockwise, then (3, -1)

If rotated counterclockwise, then (-3,1)

Step-by-step explanation:

Hope that helps!

Answer:

The answer is proportional

Step-by-step explanation:

I took the test and got 5/5

The given relationship is a proportional relation.

In mathematics, proportionality indicates that two quantities or variables are related linearly. If one quantity doubles in size, so does the other; if one of the variables diminishes to 1/10 of its former value, so does the other.

Given that, Steven went to play video games in Games Galore arcade. Games Galore charges $1.50 for each game played

Establishing the equation, we get,

y = 1.50x

Where 1.50 is the slope of the line, and, y is total cost and x is the number of game played.

When x = 2,

y = 1.50X2

y = 3

(2, 3)

When x = 4

y = 1.5X4

y = 6

(4, 6)

When x = 6

y = 1.5X6

y = 9

(6, 9)

Here we see that the value of y is varying from the value of x by 1.5 times.

Hence, The relation is a proportional relation.

For more references on proportional, click;

https://brainly.com/question/3254974

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Answer:

ocean eyes i looked this up

Step-by-step explanation:

Answer:

(-2,0)

Step-by-step explanation:

(-2,0) is the midpoint I believe!

Hope that helps!

the mid point of AB is 1 and -1

Answer:

You can do it maybe ask you teacher for help! thats always okay!

Step-by-step explanation:

Answer:

Your answer : x1= 0

x2=-4.95

Mark my answer as brainlist.

Answer:

439kg of strawberries in the afternoon

Step-by-step explanation:

This is simply 314+125

Answer:

they are both correct and also what is the question

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{3-2a}{a^2}[/tex]

Step-by-step explanation:

Before we can subtract the fractions we require them to have a common denominator.

Multiply the numerator/ denominator of [tex]\frac{2}{a}[/tex] by a , then

[tex]\frac{3}{a^2}[/tex] - [tex]\frac{2a}{a^2}[/tex] ← with common denominator a²

Add numerators leaving the denominator

= [tex]\frac{3-2a}{a^2}[/tex]

Answer:

27.8 degrees

Step-by-step explanation:

Answer:  the answer is going to be 64m hope this helped :)

Step-by-step explanation: