Spencer has a rectangular garden. The length and width are both odd numbers and the perimeter is 16 feet. What can be the area of his garden? Find all possible answers.

Answers

Answer 1

Area of rectangle = length x width

Perimeter of rectangle = 2 x (length + width)

Now we know that perimeter of rectangle = 16

2(length + width) = 16

Length + width = 16/2

Length + width = 8

Now the value of length and width is that if we add both values we have the answer 8.

So, here are some possible values of length and width and also that length and width are odd numbers;

Odd numbers are = 1,3,5,7,….

7 + 1 = 8

5 + 3 = 8

So, either length is 7 and with is 1 or length is 5 and width is 3

So area of rectangle = 7 x 1 = 7 or 5 x 3 = 15

Thus, the possible values of area of rectangle are 7 ft² and 15 ft².

 


Related Questions

if the population of state is 1,821,000 decreasing by 0.2% every year what will the population be in 5 years PLEASE PLEASE HELP

Answers

that would be  1,821,000(1 - 0.002)^5  = 1.802,862  answer

(Note 2%  = 0.002 as a decimal fraction.)

Answer:

1,802,862.

Step-by-step explanation:

We have been given that the population of state is 1,821,000 decreasing by 0.2% every year. We are asked to find the population of state after 5 years.

We will use exponential decay function to solve our given problem.

[tex]y=a\cdot b^x[/tex], where,

y = Amount left after x years,

a = Initial amount,

b = For decay b is in form (1-r) where r represents decay rate in decimal form.

x = Number of years.

Let us convert our given rate in decimal form.

[tex]0.2\%=\frac{0.2}{100}=0.002[/tex]

Upon substituting our given values in above formula we will get,

[tex]y=1,821,000 \cdot(1-0.002)^5[/tex]

[tex]y=1,821,000 \cdot(0.998)^5[/tex]

[tex]y=1,821,000 \cdot 0.990039920079968[/tex]

[tex]y=1,802,862.69[/tex]

Since we can not have 0.69 of a person, therefore, we will round down our answer.

[tex]y=1,802,862.69\approx 1,802,862[/tex]

Therefore, the population of state after 5 years will be 1,802,862.

The sum of the squares of two consecutive even integers is 452. find the two integers.

Answers

Hii

I m here to help u!!!


Let the two consecutive even integers are:-
x and x+2

according to the question ,we have
x^2 + (x+2)^2 =452
2x^2 + 4 + 4x =452
x^2 +2x -224=0

Now splitting the middle terms
x^2 + 16x -14x -224=0
we get
x=14
So the integers are 14 and 16.

I Hope it helps you!
Hi there! We can create a number equation to find your solution. Already, we know that two consecutive integers can be represented by [tex]x+x+1[/tex]. All we have to do is square that expression and make it equal to 452. This gives us:
[tex](x)^{2} +(x+1)^{2} =452[/tex]
We can simplify that down to [tex]2x^{2}+4x+4 =452[/tex]. Now, we can subtract 452 from both sides to make the whole left side equation equal to zero. Doing that gives us [tex]2x^{2}+4x-448=0[/tex]. We see that 2 can be factored out of the whole equation, giving us [tex] 2(x^{2}+2x-224)=0[/tex]. Next, we can factor the equation to get [tex](x-16)(x+14)=0[/tex]. We can use the Zero Product Property to find the x values of -16 and 14. Therefore, the two integers are -16 and 14. Hope this helped!

Which is the approximate solution to the system y = 0.5x + 3.5 and y = −x + shown on the graph?

Answers

I'm assuming there is a graph with both functions plotted. The solution would be the point at which these two functions intersect. That coordinates of x and y for that point will yield the solutions for x and y that solve the system of equations.

Answer:(-2.7,2.1)

Step-by-step explanation:

what is 21 1/4% expressed as a fraction

Answers

[tex] p\%=\dfrac{p}{100}=p:100\\\\21\dfrac{1}{4}\%=\dfrac{21\cdot4+1}{4}=\dfrac{85}{4}\%=\dfrac{85}{4}:100=\dfrac{85}{4}\cdot\dfrac{1}{100}=\dfrac{85}{400}=\dfrac{85:5}{400:5}=\dfrac{17}{80} [/tex]

Answer:

the answer is 17/80 hope this helps

PLEASE ANSWER ASAP !!!

Answers

Find the angle of 1, which would be the same as angle of 5 (alternate interior angles applicable to parallel lines). 

38+<1=180 degrees (<1 just represents angle one) 
<1=180-38 
<1=142 degrees 

Therefore, the angle of 5 is 142 degrees as well. 

Hope I helped :) 

True or false?

this is the equation of a horizontal hyperbola (y-2)^2/16-(x+1)^2/144=1

Answers

it's going to be false my man

False, the given equation of hyperbola is vertical hyperbola.

What is hyperbola?

Hyperbola is defined as a conic section, two-branched open curve, produced by the intersection of a circular cone.

[tex]\frac{(y-2)^2}{16} -\frac{(x+1)^2}{144}=1[/tex]

Simplify each term in the equation in order to set the right side equal to 1

The standard form of an ellipse or hyperbola requires the right side of the equation be 1

This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.

[tex]\frac{(y-k)^2}{a^2} -\frac{(x-h)^2}{b^2}=1[/tex]

Match the values in this hyperbola to those of the standard form. The variable

h represents the x-offset from the origin,

k represents the y-offset from origin, a.

a=4

b=12

k=2

h=−1

c, the distance from the center to a focus  4√10

The foci is (−1,2+4√10),(−1,2−4√10)

Hence, the hyperbola is vertical.

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The attendance at a ball game was 400 people. student tickets cost $2 and adult tickets cost $3. if $1050 was collected in ticket sales, how many of each type of tickets were sold

Answers

They sold 150 student tickets and 250 adult tickets. Hope this helps!

PLEASE ANSWER! BRAINLIESTTTTT

Ellen has $75 in her savings account. She deposits $25 every week. Her father also deposits $35 into the account every time Ellen mows the lawn. Her savings account balance can be shown with the following expression:

75 + 25w + 35m

Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points)

Part B: If Ellen saves for 8 weeks and mows the lawn 2 times, how much will she have in her account? Show your work to receive full credit. (4 points)

Part C: If Ellen had $95 in her savings account, would the coefficient, variable, or constant in the expression change? Why? (3 points)

Answers

A: coefficient 75, variable 35m, constant 25w


B:25x8=200+75=345


C:coefficient because instead of 75, it would be 95 changing the equation

Hopefully I did it right
part a: the coefficient is 25 and 35 the variable is m and w the constant is 75
part b: $345
part c: only the constant would change because her original amount is 75 so if you change 95 it should be the expression 95+25w+35m

What is Fourteen less than five times a number is three times the number and what is Twelve more than seven times a number equals the number less six?

Answers

Your first equation:
  5x - 14 = 3x
  5x (- 5x) - 14 = 3x (- 5x)
   - 14 = - 2x
   - 14 (/ - 2) = - 2x (/ - 2)
   7 = x

Your second equation:
    7x + 12 = x - 6
    7x + 12 (+ 6) = x - 6 (+ 6)
    7x + 18 = x
    7x (- 7x) + 18 = x (- 7x)
    18 = - 6x
    18 (/ - 6) = - 6x (/ - 6)
    - 3 = x

I hope this helps :)

The solution to the first algebraic equation is x = 7, and the solution to the second equation is x = -3. Both problems involve setting up and solving algebraic equations to find the value of the unknown number.

To solve the problems stated, we need to set up algebraic equations and solve for the unknown number x.

For the first one:

Fourteen less than five times a number is three times the number: 5x - 14 = 3x.

After simplifying, we get 2x = 14.

Divide both sides by 2 to find x = 7.

For the second one:

Twelve more than seven times a number equals the number less six: 7x + 12 = x - 6.

Rearrange to find 6x = -18.

Divide both sides by 6 to find x = -3.

We have found that the unknown number in the first equation is 7 and in the second equation, it is -3.

Solve the equation -2.6b + 4 = 0.9b - 17

Answers

If you are solving for b:
-2.6b+4=0.9b-17 <subtract 4 from both sides
-4 -4
-2.6b =0.9b-21 <subtract 0.9b from both sides
-0.9b -0.9b
-3.5b = -21 <divide by -3.5
--------- ------
-3.5 -3.5

b=6

How can you tell if a system of equations has infinite solutions?

Answers

To tell if an equation has infinite solutions, the equation will be equal to each other.

For example,

x = x
x + 1 = x + 1
x - y = x - y

And so on...

And in special cases,

0x = 0
0x = 0(y + 1)

They have infinite solutions because there's no constant to determine the variable.

Geraldine is picking a four-digit password by using the digits 0 through 9. She can use each digit only once. How many different passwords are possible?

Answers

0-9 = 10 numbers

 1st digit can be 1 0f 10

2nd digit can be 1 of 9

3rd digit can be 1 of 8

4th digit can be 1 of 7



10 * 9 *8*7 = 5040 different combinations

The number of different possible passwords are possible

Given that each digit can be used once, then:

The first digit can be any of the 10 digitsThe second digit can be any of the remaining 9 digitsThe third digit can be any of the remaining 8 digitsThe fourth digit can be any of the remaining 7 digits

So, the number of passwords is:

n = 10 * 9 * 8 * 7

Evaluate the products

n = 5040

Hence, there are 5040 different possible passwords

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Sarah needs 11 bottles of water from the store. sarah can only carry three at a time. what's the minimum number of trips sarah needs to make to the store?

Answers

11/3 = 3 2/3....so the minimum number of trips would be 4

Luis deposited $500 into his bank account. He now has $4732. Write and solve an equation to find how much was in his account before the deposit.

Answers

4732-500=x. X=4232.hope this helped

What's the answer to blank plus 33 equals 5?

Answers

? + 33 = 5
-28 + 33 = 5

Which term applies to numbers that cannot be written in this form a/b

Answers

Assuming 'a' and 'b' are integers, with b as nonzero, then a/b is known as a rational number. The term "ratio" is buried in "rational". A ratio is effectively a fraction of two values so that's a good way to remember the term. Some examples of rational numbers are 2/3 or 4/9. Whole numbers are rational because something like 7 is the same as 7/1

Any numbers that cannot be written as a ratio of whole numbers, we consider them irrational (aka opposite of rational, or not rational). Something like pi = 3.14 or sqrt(2) = 1.414 are irrational as we cannot express them in the form a/b. We can get close but not exact. 

In summary, the answer is irrational

Let gg be an exponential function that is changing at a rate proportional to itself, with constant of proportionality 0.60.6. (a) what's the growth factor of gg? .6 . (b) the function gg exhibits

Answers

The growth factor of g is given by [tex]A = e^{0.6t}.[/tex]

The function exhibits exponential growth.

We have,

(a)

Let's denote the growth factor as A(t), where t is the independent variable representing time.

The rate of change of g at any time t is proportional to g itself, with a constant of proportionality of 0.6.

This can be expressed as:

dA/dt = 0.6A

This is a separable differential equation, which we can solve by separating the variables and integrating them:

1/A dA = 0.6 dt

Integrating both sides,

ln|A| = 0.6t + C

Here, C is the constant of integration.

Exponentiating both sides:

[tex]|A| = e^{0.6t + C}[/tex]

Since the growth factor A is always positive, we can drop the absolute value:

[tex]A = e^{0.6t + C}[/tex]

We can do this by considering the initial condition.

Let's assume that at t = 0, the growth factor A is 1 (no growth). Substituting these values into the equation:

[tex]1 = e^{0.6(0) + C}\\1 = e^C[/tex]

Taking the natural logarithm of both sides:

[tex]ln(1) = ln{e^C}[/tex]

0 = C

So,

[tex]A = e^{0.6t}[/tex]

(b)

The function g exhibits exponential growth, as the value of g increases exponentially with time.

Thus,

The growth factor of g is given by [tex]A = e^{0.6t}.[/tex]

The function exhibits exponential growth.

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Final answer:

The growth factor of gg is 0.6. The function exhibits exponential growth.

Explanation:

(a) The growth factor of an exponential function is the base of the exponent. In this case, the growth factor is 0.6.

(b) The function gg exhibits exponential growth, meaning that as the input increases, the output increases at a proportional rate.

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suppose m < ABC = 110. what is m < DBC

Answers

I believe the answer is   A. 40.

The measurement of ∠y = ∠DBC will be 40°.

What is Angle ?

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Given is ∠ABC = 110°

Let ∠ABD = x , ∠DBC = y, ∠CBE = z

∠ABD + ∠DBC + ∠CBE = 180°

x + y + z = 180°

and

∠ABD + ∠DBC = 110°

x + y = 110°

Then -

z = 180° - (x + y)

z = 180 - 110

z = 70°

Since DB and EC are equally inclined -

x = z = 70°

Then -

x + y = 110°

y = 110° - 70°

y = 40°

Therefore, the measurement of ∠y = ∠DBC will be 40°.

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To find a baseball pitcher's earned run average (ERA), you can use the formula Ei = 9r, in which E represents ERA, i represents the number of innings pitched, and r represents the number of earned runs allowed. Solve the equation for E. What is a pitcher's ERA if he allows 57 earned runs in 63 innings pitched? If necessary, round your answer to the nearest hundredth.

Answers

Ei = 9r
E = (9r) / i

E = (9 * 57) / 63
E = 513/63
E = 8.14 <==

the intersection of the perpendicular rays below has formed which of the following?
a. 4 obtuse angles b. 4 right angles c. 4 acute angles d. 4 straight lines

Answers

b. 4 right angles

perpendicular lines always create 90° angles

during the 2009-2010 basketball season, the number of points scored in each game by the boston celtics was approximately normally distributed with a mean of 99.2 points and a standard deviation of 10.5 pthe mean number of points scored by los angeles lakers was 101.7. in what proportion of their games did the celtics score more than the lakers' mean score?

Answers

To solve this problem, we use the z statistic.  The z formula is:

z = (x – u) / s

where x is lakers score = 101.7, u is Celtics score = 99.2, s is standard dev = 10.5

z = (101.7 – 99.2) / 10.5 = 0.24

 

using the normal distribution table at z = 0.24, the P value is:

P (z = 0.24) = 0.5984 = 59.84% 

Final answer:

To find the proportion of games in which the Boston Celtics scored more than the Los Angeles Lakers' mean score, we need to standardize the Lakers' mean score, find the z-score, and then find the proportion from the standard normal distribution table.

Explanation:

To find the proportion of games in which the Boston Celtics scored more than the Los Angeles Lakers' mean score, we need to find the area under the normal distribution curve to the right of the Lakers' mean. First, we need to standardize the Lakers' mean score by finding the z-score using the formula:

z = (x - μ) / σ

where x is the mean score, μ is the mean of the Celtics' scores, and σ is the standard deviation of the Celtics' scores. Substituting the given values, we have:

z = (101.7 - 99.2) / 10.5 = 0.2381

Next, we find the proportion of scores greater than the Lakers' mean in the standard normal distribution table or using a calculator. Looking up the z-score of 0.2381 in the table, we find the proportion to be approximately 0.4069, or 40.69%.

Year (X) =2000 2001 2002 2003 2004
Cost in Dollars(Y) = 56.25 74.30 122.75 200.00 308.50

The table shows the cost of a game from 2000 to 2004, which has been increasing in a quadratic fashion. Let x = 0 in 2000, and find the best-fit quadratic equation. What will game cost in 2010?
A) $417
B) $746
C) $960
D) $1,586

Answers

Answer-

The best-fit quadratic equation is  [tex]y=14.9786x^2+3.1057x+56.2771[/tex] and the game cost in 2010 will be $1586

Solution-

Plotting a table taking year as input variable and cost as output variable.

X= year - 2000    

Y= cost in dollar.

Quadratic equation formula,

[tex]y=ax^2+bx+c[/tex]

[tex]a=\frac{(\sum x^2y\sum xx)-(\sum xy\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]

[tex]b=\frac{(\sum xy\sum x^2x^2)-(\sum x^2y\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]

[tex]c=\frac{\sum y}{n}-b\frac{\sum x}{n}-a\frac{\sum x^2}{n}[/tex]

Where,


[tex]\sum xx=\sum x^2-\frac{(\sum x)^2}{n}[/tex]

[tex]\sum xy=\sum xy-\frac{\sum x\sum y}{n}[/tex]

[tex]\sum xx^2=\sum x^3-\frac{\sum x\sum x^2}{n}[/tex]

[tex]\sum x^2y=\sum x^2y-\frac{\sum x^2\sum y}{n}[/tex]

[tex]\sum x^2x^2=\sum x^4-\frac{(\sum x^2)^2}{n}[/tex]

Putting the values, we get

[tex]a=14.9786,b=3.1057,c=56.2771[/tex]

Putting these in the quadratic equation,

[tex]y=14.9786x^2+3.1057x+56.2771[/tex]

In order to  get the cost of game in 2010, we can put x=10 to get the value of y or the cost of game.

[tex]y(10)=14.9786(10)^2+3.1057(10)+56.2771=1585.1941 \approx 1586[/tex]


The fifth period Coordinate Algebra class received their quiz grades back from Mr. Smith today. The students were offered a chance for five quiz points if they constructed a box and whisker plot using the 20 quiz scores. As Mr. Smith's teaching assistant, you are asked to create a solution key for the box and whisker plot. Mr. Smith asked you to report back to him tomorrow morning with the Q1, Q3, and IQR.Use the set of student quiz scores to complete your calculations. Complete your work in the space provided or upload a file that can display math symbols if your work requires it.Turn in the Q1, Q3, and IQR and all of the necessary steps that you took to make your calculations. Fifth Period Quiz Grades: 100, 96, 58, 95, 60, 95, 69, 88, 71, 95, 85, 93, 91, 78, 78, 85, 86, 98, 87, 100

Answers

first, we need to put the numbers in order...
58,60,69,71,78,78,85,85,86,87,88,91,93,95,95,95,96,98,100,100
and since there is an even number of numbers (20), we need to find the 2 middle numbers and divide them by 2 to find the median (Q2)
Q2 (the median) = (87 + 88) / 2 = 175/2 = 87.5
now we take all the numbers below 87.5...and find the median (middle number) and that number will be Q1...there is 2 middle numbers...so we add them and divide by 2
Q1 = (78 + 78) / 2 = 156/2 = 78
now we take all the numbers after 87.5....and find the median...there will be 2 numbers, so we add them and divide by 2..that wil be Q3
Q3 = (95 + 95) / 2 = 190/2 = 95

So in summary :
Q1 = 78 <==
Q2 = 87.5 
Q3 = 95 <==

The interquartile range (IQR) is found by subtracting Q1 from Q3.
IQR = 95 - 78 = 17 <==

"To create a box and whisker plot and calculate the Q1, Q3, and IQR for the given set of quiz grades, we must first organize the data in ascending order:

58, 60, 69, 71, 78, 78, 85, 85, 86, 87, 88, 91, 93, 95, 95, 95, 96, 98, 100, 100

Next, we find the median (Q2), which is the middle value in the ordered list. Since there are 20 scores, the median will be the average of the 10th and 11th scores:

Q2 = (87 + 88) / 2 = 175 / 2 = 87.5

Now, we need to find the first quartile (Q1), which is the median of the first half of the data (excluding the median if the number of data points is odd). Since we have an even number of scores, we take the first 10 scores and find their median:

Q1 = (71 + 78) / 2 = 149 / 2 = 74.5

For the third quartile (Q3), we take the median of the second half of the data (excluding the median if the number of data points is odd). Again, we have an even number of scores, so we take the second set of 10 scores and find their median:

Q3 = (95 + 96) / 2 = 191 / 2 = 95.5

Finally, the interquartile range (IQR) is calculated by subtracting Q1 from Q3:

IQR = Q3 - Q1 = 95.5 - 74.5 = 21

Therefore, the Q1, Q3, and IQR for the fifth period Coordinate Algebra class quiz grades are:

Q1 = 74.5

Q3 = 95.5

IQR = 21

These values are essential for constructing the box and whisker plot and for understanding the spread of the middle 50% of the quiz scores."

A box contains 10 cups of pancake mix. You use 23 cup each time you make pancakes. How many times can you make pancakes?

Answers

You can make pancakes twice, and you will have 3/10 of a cup of pancake mix. First, divide 23 and 10, then you will get 2.3.

Answer:

PANCKACKES

Step-by-step explanation:

Factor this expression completely and then place the factors in the proper location on the grid. Note: Place factors alphabetically in the grid! mr + ns - nr - ms

Answers

Greetings!

Find the GCF by Grouping.
[tex]mr+ns-nr-ms[/tex]
[tex]mr-ms-nr+ns[/tex]
[tex]m(r-s)-n(r-s)[/tex]
Find the GCF.
[tex](r-s)(m-n)[/tex]
This is the furthest you can factor.

Hope this helps.
-Benjamin

Answer:

(m-n)(r-s)

Step-by-step explanation:

We will factor this by grouping.  First we rearrange the terms so the m's are together and the n's are together:

mr-ms+ns-nr

Next we group the first two and the last two:

(mr-ms)+(ns-nr)

The GCF of the first group is m; factor this out:

m(r-s)+(ns-nr)

The GCF of the second group is n; factor this out:

m(r-s)+n(s-r)

We want to have the same thing in both sets of parentheses; to do this, we will multiply the second factor by -1:

m(r-s)+-n(r-s)

Factoring out the term now in common, r-s, we have

(r-s)(m-n) = (m-n)(r-s)

Make a conjecture about the next item in the sequence. 3, 6, 12, 24, …

Answers

48, 96, 192, 384, ....
 Each item is two times the previous item. Multiply each item by two to get the next item in the sequence.
Each term is created by multiplying THE PREVIOUS ONE by 2  so the  next item will be 24* 2   = 48

If you used 765 KWH and the power company charges 0.06354/KWH and a customer charge of $3.75, how much will you pay?

Answers

$52.36

THIS IS THE ANSWER

What are the factors of the function graphed below?

Answers

Start by finding the roots (which is everywhere y = 0.

Roots are at:
-2, 0, 1, 2

a factor is in the form (x + a) where a = the negative of a root

So the factors are:
(x+2)
(x + 0) = x
(x -1)
and
(x-2)

If angle a and angle b are complements and m angle a=36 degrees, what is angle b

Answers

Attached the solution and work.
Final answer:

Complementary angles add up to 90 degrees. Angle b can be found by subtracting the measure of angle a from 90 degrees.

Explanation:

The question states that angle a and angle b are complements, and that the measure of angle a is 36 degrees. In mathematics, complementary angles are two angles whose measures add up to 90 degrees. So, if angle a is 36 degrees, angle b can be found by subtracting 36 from 90, which gives us 54 degrees. Therefore, angle b is 54 degrees.

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Mariya is solving the quadratic equation by completing the square.

4x2 – 20x + 3 = 0

4x2 – 20x = –3

A(x2 – 5x) = –3

What is the value of A?

Answers

The value of A is 

4x2 – 20x + 3 = 0  
                 -3    -3

4x2 - 20 x = - 3

Pull out common factor which is 4 

4 ( x2 - 5x) = - 3

Answer:

The value of A is 4.

Step-by-step explanation:

Consider the provided quadratic equation.

[tex]4x^2-20x+3=0[/tex]

Subtract 3 from both sides.

[tex]4x^2-20x+3-3=-3[/tex]

[tex]4x^2-20x=-3[/tex]

Now take 4 common from the left side of the above equation.

[tex]4(x^2-5x)=-3[/tex]

Compare the above equation with [tex]A(x^2 - 5x) = -3[/tex]

By the comparison it is clear the value of A is 4.

Hence, the value of A is 4.

Other Questions
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