Billy is creating a rectangular patio in his backyard using square cement tiles. The length of the patio, in feet, is represented by the function l(x) = x + 5, and the width of the patio is represented by the function w(x) = x + 3. Write the standard form of the function which describes the total area of the patio, a(x) in terms of x, the side length of each tile.

Answers

Answer 1
The area of a rectangle by definition is given by:
 a = (l) * (w)
 Where,
 w: width
 l: long
 Substituting the values we have:
 a (x) = (x + 5) * (x + 3)
 Rewriting:
 a (x) = (x ^ 2 + 3x + 5x + 15)
 a (x) = x ^ 2 + 8x + 15
 Answer: 
 The standard form of the function which describes the total area of the patio, a (x) in terms of x is: 
 a (x) = x ^ 2 + 8x + 15
Answer 2

To find the function for the total area of Billy's patio, a(x), we multiply the length function, l(x) = x + 5, by the width function, w(x) = x + 3. Expanding this multiplication gives us the standard form a(x) = x² + 8x + 15.

Billy is creating a rectangular patio in his backyard using square cement tiles. The function for the length of the patio is l(x) = x + 5, and the function for the width is w(x) = x + 3. To find the function that describes the total area of the patio, a(x), in terms of x, we can multiply the length function by the width function.

First, let's define the area of a rectangle as the product of its length and width: a = l x w. Substituting our functions in, we get:

a(x) = (x + 5) x (x + 3)

Now we will expand this to write it in standard form:

a(x) = x² + 3x + 5x + 15
a(x) = x² + 8x + 15

Therefore, the standard form of the function describing the total area of the patio in terms of x, the side length of each tile, is a(x) = x² + 8x + 15.


Related Questions

ellen flipped a coin 80 times. the coin landed heads up 44 times and tails up 36 times. what is the theoretical probability of labding tails up

Answers

1/2 or 50% because each flip of a coin is independent from the last and a fair coin has an equal probably of landing on either side

Answer:

50%

Step-by-step explanation:

A customer bought $329.69 worth of building materials for a home remodeling project. They returned some of the unused materials worth $59.63. Estimate to determine how much the customer spent on building materials by rounding to the nearest $10. Estimate to determine how much the customer spent on building materials by rounding to the nearest $10.

Answers

Use ft math it will help you as well as photo math

What is the answer for the equation 4|x+1/3|=20 ? A.x=411/12or-411/12 B.x=411/12 C.x=42/3or-51/3D.no solution

Answers

Selection C is appropriate.

Divide by 4, unfold, subtract 1/3.
.. |x +1/3| = 5
.. -5 = x +1/3 . . . . one choice for the sign of the content of |x +1/3|
.. -5 1/3 = x

.. x +1/3 = 5 . . . . the other choice
.. x = 4 2/3

_____
If this were an inequality |x +1/3| < 5, I would "unfold" it as
.. -5 < x +1/3 < 5 . . . . . . . copy the right side expression to the left with reversed sign.
The above is an approximation of that. You can't really write -5 = ( ) = 5, because it is a gross violation of the equal sign. But you can write the two versions:
.. -5 = ( )
.. ( ) = 5

Answer:

C. x = 4 2/3  or x = -5 1/3

Step-by-step explanation:

4|x + 1/3| = 20

Divide both sides by 4.

|x + 1/3| = 5

Deal with the absolute sign symbol.

x + 1/3 = 5  or  x + 1/3 = -5

x = 4 2/3  or x = -5 1/3

Answer: C. x = 4 2/3  or x = -5 1/3

A piece of stained glass in the shape of a right triangle has sides measuring 8 centimeters, 15 centimeters, and 17 centimeters.What is the area of the piece?

Answers

For a right triangle, it is convenient to use the leg lengths as the base and altitude. The formula for the area of a triangle is
  A = (1/2)bh
  A = (1/2)(8 cm)(15 cm)
  A = 60 cm²

The diameter of a circle is 2 yards. What is the circle's radius?
d

Answers

The circle's radius is 1 yard. You take half of the diameter to get this value. 
The diameter of a circle refers to a straight line passing from side to side through the center connecting to points in the circumference.
In the other hand the radius is a line passing through the center of the circle to the circumference, and it is the half of the measure of the diameter.

On this question is given that the diameter of a circle is 2 yards and it is asked to find the radius.

Radius=1/2diameter
Radius=1/2(2)
Radius=1

The radius of a the circle is 1 yard.

Kirby drew a quadrilateral with four right angles, a side that measures 9 centimeters, and a side that measures 6 centimeters. What is the figure? What is its perimeter

Answers

the figure is a rectangle and the perimeter would be 30 because 9+9+6+6=30

Answer:

Perimeter of the rectangle is 30 cm.

Step-by-step explanation:

Kirby drew a quadrilateral with 4 right angles, a side that measures 9 centimeters and a side that measure 6 centimeters.

Since quadrilateral has all its sides equal to 90° and opposite side equal in size.

Therefore, the quadrilateral is a rectangle.

Perimeter of rectangle =  sum of all sides

                                      = [ 9 + 9 ] + [ 6 + 6 ]

                                      = [ 18 ] + [ 12 ]

                                      = 30

Perimeter of the rectangle is 30 cm.

Drag the tiles to the correct boxes to complete the pairs.
Model each problem as an equation, and then match it to its solution.
Tiles
The sum of the squares
of two positive integers is
185. If one integer is 3
less than the other, find
the larger integer.
The numerator of a
fraction is 1 more than
twice its denominator. If 4
is added to both the
numerator and the
denominator, the fraction
reduces to . Find the
denominator.
The difference of a
positive integer and its
inverse is . Find the
integer.

Answers

Final answer:

The questions are solved by setting up equations based on the information provided, and then solving. The equations help identify the larger integer, the denominator, and the positive integer in the various problems.

Explanation:

The first question talks about two integers, hence we can express them as x and y. It is stated that one is 3 less than the other, so we let y = x - 3. The sum of their squares is 185, so we can write this as x² + y² = 185. Replacing y in the equation, we get x² + (x - 3)² = 185. Solve this quadratic equation for its roots, one of which is the larger integer.

In the second question, the numerator of a fraction is described to be 1 more than twice its denominator. If the denominator is x, the numerator becomes 2x + 1. We're also told that when 4 is added to both, the fraction reduces to 1/2. Thus, we have: (2x + 1 + 4) / (x + 4) = 1/2. Solve this equation to find the denominator.

The third question talks about a positive integer and its inverse (1/x if x is the integer). It is mentioned that their difference is 1/4. Hence, we get the equation: x - 1/x = 1/4. Solving this equation gives the required integer.

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what equation has a solution of 4/5 for n?

Answers

One of them is 2/5 + 2/5 = 4/5

what is the value x?

Answers

check the picture below.

The population of city A is 18% less than the population of city B so city A population is what percent of city B

Answers

The population of city A is 82% of the population of city B.

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Let y be the population of the city A.

and, x be the population of city B.

As, the population of city A is 18% less than the population of city B.

So, (100- 18) = 82% = 0.82

Thus, the relation is y= 0.82 x

Hence, The population of city A is 82% of the population of city B.

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Final answer:

City A's population is 82% of city B's population, which is calculated by subtracting the decrease percentage (18%) from 100%.

Explanation:

The question focuses on finding the percentage of city A's population relative to city B's population. Given that city A's population is 18% less than city B's population, it means that city A has 82% (100% - 18%) of the population of city B. Therefore, if city B is considered 100% in terms of population size, city A's population is 82% of city B's population. This is calculated by understanding that subtracting the percentage decrease from 100% gives us the remaining percentage.

Hence, City A's population is 82% of City B's population, indicating that City A's population is 82/100 or 0.82 times the population of City B.

Yan Yan Corp. has a $3,000 par value bond outstanding with a coupon rate of 5 percent paid semiannually and 12 years to maturity. The yield to maturity of the bond is 5.6 percent.

Answers

The price of the bond will be given by:
P=total sum (c/(1+ytm)^t)+(per value)/(1+ytm)^n
ytm=0.056
c=coupon=2.5%=0.025×3000=75
t=12 years
this can be written as follows using continous compounding
Bond price, P will be:
P=75e^(0.056*2*1)+75e^(0.056*2*2)+75e^(0.056*3*2)+75e^(0.056*4*2)+...............+75e^(0.056*11*2)+3075e^(0.56*12*2)
=$2844.24

need to know what the right answer is

Answers

You're right because they are corresponding angles and corresponding angles are congruent.

triangle ABC is an abtuse triangle with the abtuse angle at vertex B. Angle A must be : less than 90 greater than 90. congruent to angle B congruent to angle C

Answers

If angle B of the triangle is obtuse, the two remaining angles, A and C, must both be acute--less than 90°. They are not necessarily congruent.

The 1st selection is the correct one: Angle A must be less than 90°.

WILL MARK BRAINIEST!!
Find the slope of the line that passes through each pair of points.

C(7, -3), D(11, -4)

R(-2, -3), S(-2, -5)

T(-13, 8), U(21, 8)

E(5, 2), F(12, -3)

Answers

You know the formula. It is simply a matter of putting in the numbers. When the calculations are repetitive, it is convenient to let a machine do them.

CD: -1/4
RS: undefined (a vertical line at x=-2)
TU: 0 (a horizontal line at y=8)
EF: -5/7

Point A located at (-2,4) is translated down 6 units what are the coordinates of A

Answers

(-2, -2) The first point is negative two, four. So translated down 6 units would be (-2, -2), If i did it right

5.301 times 10^7 standard form

Answers

the answer is 53010000

A potato chips manufacturing facility uses 1/6 of a barrel of oil in each batch. The facility used 2/3 of a barrel of oil yesterday. How many batches of potato chips did the facility make? A. 2/3 B. 1/4 C.2 D.4

Answers

The answer is D. 2/3 = 4/6 4/6 divided by 1/6 = 4

Answer:

Option D. 4 batches

Step-by-step explanation:

A potato chips manufacturing facility uses 1/6 barrel of oil in each batch and we have to find the batches of potato chips manufactured in 2/3 of a barrel.

We will use unitary method to solve this question.

∵ [tex]\frac{1}{6}[/tex] barrel is required to manufacture batch = 1

∴ 1 barrel is required to manufacture batches = 1 ÷ [tex]\frac{1}{6}[/tex]

∴ [tex]\frac{2}{3}[/tex] barrel is required to manufacture batches = [tex](\frac{1}{\frac{1}{6}})(\frac{2}{3})=(\frac{6}{1})(\frac{2}{3})=6.\frac{2}{3}=4[/tex]

Therefore Option D.4 is the correct option.

Can anyone help me out with this?? I dont Understand

Answers

The arc length (s) is given in terms of the radius (r) and central angle (θ) by
  s = r*θ . . . . . . . where θ is in radians

For your arc, the length is
  s = (15 ft)*(π/4) ≈ 11.78 ft

_____
45° can be converted to radians by multiplying by π/180°.
  45° * (π/180°) = π*(45/180) = π/4 . . . . radians

On the test with 25 problems, Grace got 88% correct. How many problems did Grace get correct?

Answers

Convert the percentage into a decimal (divide by 100).

88/100 is .88

Then multiply that by the number of problems.

.88 x 25 is 22

Your answer is 22!!

Hope this helped!!!
~xox Melis

There are 22 problems Grace get correct.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

Total number of questions = 25

And, Grace got 88% correct.

Now,

Since, Total number of questions = 25

And, Grace got 88% correct.

Hence, The correct questions = 88% of 25

                                              = 88/100 x 25

                                              = 88/4

                                              = 22

Thus, There are 22 problems Grace get correct.

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A sphere has a diameter of 5 inches.

What is the volume of the sphere rounded to the nearest tenth?

Use 3.14 for pi.

16.4 in³
65.4 in³
130.8 in³
523.3 in³

Answers

By definition, the volume of a sphere is given by:
 [tex]V = (4/3) * ( \pi ) * (r ^ 3) [/tex]
 Where,
 r: is the radius of the sphere
 The radius of the sphere is:
 [tex]r = d / 2 [/tex]
 Where,
 d: diameter of the sphere
 Substituting values we have:
 [tex]r = 5/2 r = 2.5[/tex]
 Then, the nolumen is given by:
 [tex]V = (4/3) * (3.14) * (2.5 ^ 3) V = 65.4 in ^ 3[/tex]
 Answer: 
 
the volume of the sphere is:
 65.4 in³

Answer:

65.4 in³

Step-by-step explanation:

Please halp!This is very important to me!

Answers

39. FALSE
40. Where is the answer?

first you subtract 4,724 - 300. that gives you 4,424. then you multiply that by 5.


5(4,424) = 22,120


Available seats are:
4724 - 300 = 4424 seats


the total number of tickets sold for 5 games:
4424(5) = 22,120 tickets


therefore your answer will be: (C) my friend.





hope this helps!!!!!!

If you complete the entire question I'll give you 1000 points!

Answers

The path is symmetrical, so the problem already gives you 2 of the 3 numbers you need.
  A = E = 25.02 feet

  B = D = 31.11 feet

  C = ║(37, 65) -(63, 39)║ = √((-26)² +26²) = √1352 ≈ 36.77 . . . feet

 A = E = 25.02 feet


 B = D = 31.11 feet


 C = ║(37, 65) -(63, 39)║ = √((-26)² +26²) = √1352 ≈ 36.77 . . . feet


i litterly need just 49 points lol thank man XD




Plastic bags used for packaging produce are manufactured so that the breaking strength of the bag is normally distributed with a mean of 5 pounds per square inch and a standard deviation of 2 pounds per square inch. what is the probability that a sample of 16 such bags will have an average breaking strength less than 6 pounds per square inch? (choose the closest answer. answers are rounded to the fourth decimal place).

Answers

The answer is 2/6 in the fourth decimal place

A traveler has $50 in United States bills and wishes to convert them to Swiss Francs. The traveler checks a newspaper for the exchange rate and finds the figure "1.6465" under "Dollar in Foreign Currency."

At this rate he receives -__ francs.
51.65
82.33
30.37
will report if answer is wrong or you just reply "sorry idk"

Answers

The answer is $82.33.

First answer, but any other questions i answer will be short and sweet and the answer itself will be in bold

Answer:

At this rate traveler receives 82.33 Swiss Francs.

Step-by-step explanation:

A traveler has $50 United States bills. He wishes to convert them to Swiss Francs.

The current exchange rate : 1 Dollar = 1.6465 Swiss Francs

50 Dollars = 1.6465 x 50 = 82.325 Swiss Francs  rounded to 82.33.

At this rate traveler receives 82.33 Swiss Francs.

The area of a rectangular classroom is given by the trinomial a - 4a - 21. The length of the rectangle is a+3. What is the expression for the width of the classroom?

Answers

I am assuming you wrote the problem wrong. Is it a^2?
A^2 -4A-21=0
(A-7)(A+3)=0
A=7 A=-3, ignore the negative number because it doesn't make sense if you plug in for a.
length=a+3=7+3=10
Width=7=a

Final answer:

To find the width of the rectangular classroom, we divide the area, expressed as -3a - 21, by the length, expressed as a+3. Simplifying the trinomial by binomial division, we find that the width is represented by the expression (a - 7).

Explanation:

To find the expression for the width of the classroom, we need to divide the area of the rectangle by its length. The area of the rectangular classroom is given by the trinomial a - 4a - 21, which simplifies to -3a - 21. Since we are given that the length of the rectangle is a+3, we divide the area by the length to get the width.

Width = Area / Length

Width = (-3a - 21) / (a + 3)

Now, to divide the trinomial by the binomial, we look for a binomial that when multiplied by the length gives us the area. The factors of -21 that add up to -4 (the coefficient of 'a' in the area expression) are -7 and 3. So, the binomial that we seek can be written as (a - 7) because:

(a+3)(a-7) = a² - 7a + 3a - 21 = a² - 4a - 21

Which matches our area expression. Therefore, the expression for the width of the classroom is (a - 7).

Emma is going camping each side triangle of hurt it is 5 feet tall the square base 4 feet wide what is the surface area of her tent

Answers

we know that
[total surface area]= [surface area of the base]+[surface area of triangle sides]

[surface area of the base]= 4*4=16 ft²
[surface area of one triangle side] = (base*height)/2 = 4*5/2------> 10 ft²
[surface area of four triangle sides]=4*10----------> 40 ft²

[total surface area]=16+40-------> 56 ft²

the answer is 56 ft²

Draw a number line and show all numbers that …

are solutions of the equations (x−1)(x+1)=0.

on a number line that is -5 through 5

Answers

(x-1)(x+1) = 0
x = 1 or x = -1

Ans : -1 and 1

-5 -4 -3 -2 -1  0 2  3 4  5
--|--|--|---|---|--|---|--|--|--|--|--


The solution to the above equation:

(x-1)(x+1)=0

is x=1 and x= -1

Therefore, there should be points on the line at 1 and -1

A swimmer swims 4 laps in 3 minuets. What is the swimmers unit rate?

Answers

Hello there! Your answer to this question is (4/3 laps per min) hope it helps and have a wonderful day!
His unit rate is 1.3 Laps per minute or 4/3 or if you want it simplified over 1 it’s would be 1.333/1

Johannes buys a bag of dried fruit in 10 ounce bags. If he plans to take 5 pounds of dried fruit on a camping trip, how many bags should he take?

A. 5
B. 8
C. 32
D. 50

Answers

Hello! In case you don't know, 16 ounces = 1 pound. We are talking about 5 pounds of fruit being brought. Let's convert pounds into ounces. 16 * 5 is 80. That's 80 ounces being brought. To find the amount of bags that should be taken, all you have to dis is divide the amount being brought by the amount per bag. The fruit will each be in 10 ounce bags. 80/10 is 8. There. Johannes should take 8 bags with him. The answer is B: 8.

Tracy is cleaning up after tiling a bathroom there are four open boxes of tile Each box has 5/8 of tile remaining how many boxes of tile are left

Answers

Hm...boxes, tiles...math!

This is multiplication. But instead of crossing our fingers and multiplying the first two numbers you see, let me explain: it says that there are FOUR open boxes of tile. Ok...what else? EACH box has 5/8 of tile remaining. EACH!!! That means, to find how much is left for FOUR boxes, multiply 4 by (5/8)

(4/1) • (5/8)

(20/8)

2.5

Or 2 (1/2) [two and a half] boxes

Tracy has the equivalent of 2 and 1/2 full boxes of tile left after tiling the bathroom, as each of the four boxes has 5/8 of tile remaining.

The question involves a scenario where Tracy is cleaning up after tiling a bathroom and assessing how much tile is remaining. With four open boxes of tile and each box containing 5/8 of tile remaining, we can calculate the total amount of tile left. To do this, we simply multiply the number of boxes by the fraction representing the remaining tiles in each box. This gives us:

4 boxes 5/8 of tile per box

4 boxes × 5/8 tile per box = 20/8 (or 2 and 1/2 boxes when simplified).

Therefore, Tracy has the equivalent of 2 and 1/2 full boxes of tile left after tiling the bathroom. The small gaps mentioned in another context are typically recommended to accommodate expansion and contraction of the tiles due to changes in temperature and humidity, which is an important concept in laying tile.

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