Draw at least six different sized rectangles that have an area of 64 square units then find the perimeter of each rectangle.
Answers
Six different sized rectangles that have an area of 64 square units:
1) 64 units x 1 unit
2) 32 units x 2 units
3) 16 units x 4 units
4) 40 units x 1.4 units
5) 20 units x 3.2 unit
6) 10 units x 6.4 units
For given question,
Let l be the length of the rectangle and w be the width of the rectangle.
We know that, the area of a rectangle is equal to
A = l × w
Here, A = 64 square units
So, we get an equation
l × w = 64 ...............................(1)
let's assume different values of l to get the different values of w.
Case 1) For l = 64 units
substitute in the equation 1
⇒ 64 × w = 64
⇒ w = 64/64
⇒ w = 1 units
The dimensions of the rectangle are 64 units x 1 unit
See the draw in the attached figure 1
Case 2) For l = 32 units
substitute in the equation 1
⇒ 32 × w = 64
⇒ w = 64/32
⇒ w = 2 units
The dimensions of the rectangle are 32 units x 2 unit
See the draw in the attached figure 2
Case 3) For l = 16 units
substitute in the equation 1
⇒ 16 × w = 64
⇒ w = 64/16
⇒ w = 4 units
The dimensions of the rectangle are 16 units x 4 unit
See the draw in the attached figure 3
Case 4) For l = 40 units
substitute in the equation 1
⇒ 40 × w = 64
⇒ w = 64/40
⇒ w = 1.4 units
The dimensions of the rectangle are 40 units x 1.4 unit
See the draw in the attached figure 4
Case 5) For l = 20 units
substitute in the equation 1
⇒ 20 × w = 64
⇒ w = 64/20
⇒ w = 3.2 units
The dimensions of the rectangle are 20 units x 3.2 unit
See the draw in the attached figure 5
Case 6) For l = 10 units
substitute in the equation 1
⇒ 10 × w = 64
⇒ w = 64/10
⇒ w = 6.4 units
The dimensions of the rectangle are 10 units x 6.4 unit
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Related Questions
Function a (b) relates the area of a trapeze with a given height of 14 and a base length of 5 with the length of its other base. it takes the other base value as input and returns the trapeze area as output. what equation below represents the inverse function b (a), which takes the trapeze area as input and returns the length of the other base as an output?
Answers
The function accepts the trapezoid's area as input and returns as output the length of the other base exists A(x)/7-5=x.
What is an area of a trapezoid?The function of the trapezoid area exists:
[tex]A(x)=(B+b)*h/2[/tex]
where B exists the bases
h stands the height.
Given a height of 14 and one base length of 5 with the length of its other base
With the given data:
h = 14B and b =5 and x (it may vary which one exists bigger)
So that function becomes:
[tex]$A(x)=(5+x)*14/2[/tex]
A(x) = (5 + x) [tex]*[/tex] 7
So if you want the inverse function, to find the value of x:
A(x) / 7 = 5 + x
A(x )/ 7 - 5 = x
Therefore, the function accepts the trapezoid's area as input and returns as output the length of the other base exists A(x)/7-5=x.
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True or False: When x-coordinates are selected to create a table of values for a function, negative values of x may not be used.
Answers
[tex] \sf \blue{True✅}[/tex]
Step-by-step explanation:Yes, it's true sometimes we don't use negative value of 'x'.
So, we conclude it's True.
Hope it help youRachel is having chocolate cake for dessert. The cake is 12 inches in diameter and she plans to cut it into 12 pieces. What is the area of each slice of Rachel's cake?
Answers
The area of each slice of the cake is 3π square inches
How to find the area of a circle?The cake is 12 inches in diameter. The cake top is circular.
Therefore, the area of a circle is as follows;
area of a circle = πr²
where
r = radiusTherefore,
r = diameter / 2
r = 12 / 2
r = 6 inches
Hence,
area of a circle = π × 6²
area of a circle = 36π
area of each sliced cake = 36π / 12
area of each sliced cake = 3π square inches
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Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the 6 months before the exercise program began and in the 6 months following the exercise program. Following are the results.
Employee Before After
1 7 7
2 7 1
3 2 6
4 5 4
5 7 3
6 6 3
7 4 1
8 1 4
At the .05 significance level, can he conclude that the number of absences has declined? Estimate the p-value.
a. State the decision rule for 0.1 significance level: H0 : μd ≤ 0; H1 : μd > 0. b. Compute the value of the test statistic.
c. Estimate the p-value? d. What is your decision regarding H0?
Answers
The hypothesis is given as
H0: μd< 0
H1: μd > 0
How to solve for the hypothesis.The null hypothesis is given as
H0: μd< 0
The alternative hypothesis is given asH1: μd > 0
SWe have to find the value of s
we would use this formula s = sqrt [ (Σ(di - d)^2 / (n - 1) ]
This gives us 3.454
Next we have to determine the standard error
s / √(n)
3.454/2.8284
= 1.22
Degree of freedom = 8 - 1
= 7
t = (x1 - x2) - D / S.E
= 1.025
Find t critical at 0.10
= 1.895
P-value = 0.1697
d. Given that p value is greater thatn 0.1 we fail to reject the null hypothesis.
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What is the quotient of the given values to the correct level of precision? 16.017 in. ÷ 0.370 in. 43 43.289 43.29 43.3
Answers
Answer:43.289
Step-by-step explana
Ashley spent 3x + 2hours on her science project and Adam spent 4x - 6 hours on his science project. If they spent a total of 31 hours on their projects, find the value of x
Answers
Answer:
x = 5
Step-by-step explanation:
Ashley and Adam spent a total of 31 hours on their projects so: 3x+2+4x-6 = 31
3x+2+4x-6 = 31
7x-4 = 31
7x = 35
x = 5
What transformation of the parent function f(x) is made to get 4f(x+2)?
A. a vertical stretch by 4 and 2 units in the x-direction
B. a vertical stretch by 4 and horizontal shrink by 1/2
C. a vertical stretch by 4 and -2 units in the x-direction
D. a vertical stretch by 4 and horizontal shrink by 2
Answers
The correct transformation of f(x) to get 4f(x+2) is by a vertical shift by 4 and 2 units in the x direction.
Given a function f(x) and other function 4f(x+2).
We are required to choose a transformation that will give 4f(x+2) from a function f(x).
Function is like a relationship between two or more variables that are expressed in equal to form. The values which we enter in a function is known as domain and the value that we get as a result are known as range.
So, we have to reach 4f(x+2) from f(x).
The value of function is usually expressed on y axis and variable x on x axis.
To increase the value of x by 2 we have to stretch it in x direction.To find the 4 times value of function we have to stretch the y axis to 4 units.
Hence the correct transformation of f(x) to get 4f(x+2) is by a vertical shift by 4 and 2 units in the x direction.
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Brett needs to put this equation x − 2y = 16 into function notation so that he can identify the rate of change and the y-intercept. How should he display it?
Answers
Rewrite x − 2y = 16 in slope-intercept form as y = 1/2x - 8.
Slope (m) = 1/2
Y-intercept (b) = -8.
What is the Slope Intercept Equation?The slope-intercept equation helps us to easily identify the rate of change/slope (m) and the y-intercept (b) of an equation. It is given as y = mx + b.
Given, x − 2y = 16, in order to identify the slope (m) and y-intercept (b), rewrite the equation in slope-intercept form:
x − 2y = 16
-2y = - x + 16
Divide both sides by -2
-2y/-2 = -x/-2 + 16/-2
y = 1/2x - 8
As a function it would be written as y = 1/2x - 8.
Slope (m) = 1/2
Y-intercept (b) = -8.
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If y = -9 when x = 3, find y when x = -6. when x = -5.
Answers
Answer:
When x is -6, y will be 18
When x is -5 y will be 15
Step-by-step explanation:
Create a proportion
y/x
-9/3 = x/-6 What do we need to multiply 3 by to get 6? -2, so we will multiply -9 by -2 to get 18
Some people like to solve by cross multiplying.
That would give us
(-9)(-6) = 3x
54 = 3x divide both sides by 3
18 = x
Set up the second problem as a proportion
-9/3 = x/-5 This is a little trickier. I am trying to think what I have to multiply 3 by to get -5. 3(-5/3) will give me -5, so I will multiply the top number that I know (-9) by (-5/3) to find my x.
(-9)(-5/3) = 45/3 or 15
What is the twentieth term in the sequence 23, 43, 63, 83 …?
Answers
Answer:
403 (hope this helps)
Step-by-step explanation:
Laura completed the following steps to find a product.
Multiply: Three-sevenths times 8
Step 1: 8 times three-sevenths
Step 2: StartFraction (8 plus 3) over 7 EndFraction
Step 3: Eleven-sevenths
Step 4: 1 and four-sevenths
In which step did Laura make her first mistake?
Step 1
Step 2
Step 3
Step 4
Answers
The solution to the product of 8 and three-seventh is 2 2/7. According to Laura, she made mistake in step 2 by adding 8 and 3 instead of multiplying
Multiplication of fractions and integers
Fractions are written as a ratio of two integers. For instance a/b is a fraction where a and b are integers.
Given the following equation
Multiply 3/7 and 8
This is expressed mathematically as;
3/7 * 8
Step 1: Swap to have;
8 * 3/7
Step 2: Group the numerator
(8*2)/7
Step 3; Simplify
16/7
Step 4; Convert to mixed fraction
16/7= 2 2/7
The solution to the product of 8 and three-seventh is 2 2/7. According to Laura, she made mistake in step 2 by adding 8 and 3 instead of multiplying
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Urgent Help please: My neighbor just got two new cats and now she has more than 5 cats. How many cats did she have before?
Answers
Answer:
Wouldn't she have had 5 cats before? Adding 2 other cats would make it 7, which fits the "more than 5 cats" requirement.
A regular hexagon has an apothem measuring 14 cm and an approximate perimeter of 96 cm. a regular hexagon has an apothem with length 14 centimeters and a perimeter of 96 centimeters. what is the approximate area of the hexagon?
Answers
The approximate area of the hexagon = 672 cm²
What is hexagon ?
In geometry, hexagon is a polygon with 6 sides. If the lengths of all the sides and the measurement of all the angles are equal, such hexagon is called a regular hexagon. In other words, sides of a regular hexagon are congruent.apothem of the hexagon = 14 cm
perimeter of the hexagon = 96 cm
Area of the hexagon = [(3√3) / 2] a² ; where a is the measure of the side
hexagon has 6 sides.
Perimeter = 6a
96 cm = 6a
96 cm / 6 = a
16 = a
There are 6 triangles in the hexagon .
Area of a triangle = (height * base) / 2
A = (14 cm * 16 cm) / 2
A = 224 / 2
A = 112 cm²
The approximate area of the hexagon = 112 cm² * 6 triangles = 672 cm²
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Answer: D). 672 cm2
Step-by-step explanation:
PLEASE ANSWER!!
A soccer team won only 10 of their first 30 games. How many of their remaining 20 games will they have to win to have a .500 record??
Answers
Answer: 5 games
Step-by-step explanation: They need to win half their games for a .500 record and half or 30 is 15. They already won 10 so they need to win 15- 10 = 5 more games to have a .500 record.
Find the limit, if it exists, or show that the limit does not exist. lim(,)→(0,0) 2 2 4
Answers
The limit does not exist.
What is a limit?A limit in mathematics is the value that a function approaches when its input approaches some value. Limits are used to define continuity, derivatives, and integrals in calculus and mathematical analysis.In order for such a limit to occur, the fraction [tex]\frac{x^{2} }{x^{2} +y^{2} }[/tex] must be comparable to the same value [tex]L[/tex], regardless of the way we take to get there [tex](0,0)[/tex].
Try approaching [tex](0,0)[/tex] along the x-axis.
This means setting [tex]y=0[/tex] and finding the limit [tex]lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex].
We obtain:
[tex]lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1[/tex]
Now evaluate approaching [tex](0,0)[/tex] along the y-axis.
This means setting [tex]x=0[/tex] and finding the limit [tex]lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex].
[tex]lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0[/tex]
Approaching the origin via these two methods results in distinct limits.
[tex]lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex] ≠ [tex]lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }[/tex]
Therefore the limit does not exist.
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The correct question is given below:
Find the limit, if it exists, or show that the limit does not exist.
[tex]lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }[/tex]
Phillippe wants to drink at least 72 ounces of water every day while at work. He works 6 hours a day. How many ounces of water must Phillippe drink each hour? Write and solve an inequality to answer the question.
Answers
Answer:
the answer to this question is 12
Step-by-step explanation:
72÷6=12
Which monomial is a perfect cube
Answers
Answer:
A perfect cube monomial must have three identical root , such that the product of the roots equal the perfect square monomial . The coefficient of the monomial must be divisible by 3 . Any monomial can be a perfect cube root .
Step-by-step explanation:
1.)1000=10 cube
2.) 729=9 cube
3.) 512=8 cube
4.) 343=7 cube
5.) 216=6 cube
6.) 125=5 cube
7.) 64=4 cube
8.) 27=3 cube
9.) 8=2cube
10.) 1=1 cube
Among Davids classmates, there are twice as many boys as girls. Which of the following numbers may represent the number of all the children in his class?
Answers
The number that could represent the number of students in class is = X + 2x
Calculation and f the total number of studentsLet us take the number of boys to be = X
Then the number of girls is twice that of the boys. That is, y = 2x
Therefore the total number of students in the class z = X + 2x
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How many solutions does the equation 4y − 4y − 12 = 14 − 2 have? one zero two many
Answers
Answer:Many
Step-by-step explanation:
As the unknown cancels itself out, it could be absolutely any number. So there are many solutions.
My neighbor just got two new cats and now she has more than 5 cats. How many cats did she have before?
Answers
The number of cats is an illustration of inequalities and your neighbor has 4 cats before she bought the 2 new cats
What are inequalities?Inequalities are expressions, numbers and mathematical statements that have unequal values when compared and/or evaluated
How to determine the number of cats?We start by representing the initial number of cats with x.
From the question, the new cats she bought are
New = 2
So, we have
x + New greater than 5
Rewrite properly as
x + New > 5
Substitute known values in the above inequality
x + 2 > 5
Subtract 2 from both sides
x + 2 - 2 > 5 - 2
Evaluate the right-hand side
x + 2 - 2 > 3
Evaluate the left-hand side
x > 3
The smallest integer number greater than 3 is 4
Hence, your neighbor has 4 cats before she bought the 2 new cats
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_______ 14. What is the value of x?
A. 11°
B. 22°
C. 32°
D. 43°
E. 86°
Answers
Answer: Choice D
Reason:
Add up the arc measures, then divide by 2
x = (32 + 54)/2
x = 86/2
x= 43 degrees
i need help with this ;n;
Answers
Latoya has a lot of doctor’s visits coming up, and her children all need vaccinations for the upcoming school year. which type of insurance would be most helpful to her in this situation?
Answers
Health insurance would be most helpful to Latoya.
What is Health insurance?Health insurance, often known as medical insurance in South Africa, is a type of insurance that covers all or part of the risk of a person incurring medical expenses. Risk, like other types of insurance, is shared among many people. An insurer can design a routine finance structure, such as a monthly premium or payroll tax, to provide the money to pay for the health care benefits stipulated in the insurance agreement by calculating the overall risk of health risk and health system expenses over the risk pool.The benefit is managed by a central institution, such as a government agency, a private company, or a non-profit organization.Therefore, health insurance would be most helpful to Latoya.
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. What is the midpoint of a line segment connecting the points (−4,6) and (8,2)?
Answers
What is the general form of the equation for the given circle centered at o(0, 0)? a. x2 y2 41 = 0 b. x2 y2 − 41 = 0 c. x2 y2 x y − 41 = 0 d. x2 y2 x − y − 41 = 0
Answers
The general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.
According to the question,
The general form of the equation for the given circle centered at o(0, 0) is (x-h)² + (y-k)² = r².
The given equation is x² + y² - 41 = 0 which is also represented by(x-0)² + (y-0)² = -(√41)². This is not possible.
The given equation is x² + y² - 41 = 0 which is also represented by (x-0)² + (y-0)² = (√41)²This means that the circle is centered at (0,0). Thus, the equation is correct The given equation is x² + y² +x+ y- 41 = 0 which is also represented by (x+1/2)² + (y+1/2)² = (√(83/2))²This means that the circle is centered at (-1/2,-1/2). Thus, this equation is incorrect. The given equation is x² + y² +x- y- 41 = 0 which is also represented by (x+1/2)² + (y-1/2)² = (√(83/2))²This means that the circle is centered at (1/2,-1/2). Thus, this equation is incorrect.Hence, the general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.
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Si y es la temperatura y x hora ¿A que horade registro la menor temperatura
Answers
Answer:
0
Step-by-step explanation:
A 0 horas, la temperature era 9.
Find the volume of the following cubes: (b) 15 m 18.4 ft Find the volume of each of cubes whose a side length is given as: (b) (c) 5.6 ft (f) 12 m 80 cm (a) 5 cm (d) 4.5m Solve (e) (c) 4.2 inch 4 m 20 cm
Answers
Answer:
Step-by-step explanation:
Nancy Pelosi's Husband Found Drugs in His System after D.U.I. Arrest: Kill His Elder Brother : Other "past Skeletons in Closet" Exposed.
Paul Pelosi, the husband of US House Speaker Nancy Pelosi, was found to have drugs in his system during his drink-driving arrest in May, Fox News reported on Tuesday, citing a court document.
Paul Pelosi was slurring and unsteady on his feet as he spoke to police officers and tried to show them a membership card for a foundation that has long provided money to local police officers and their children.
According to Fox News, the Napa County District Attorney's Office in California said on Monday that Paul Pelosi, the husband of House Speaker Nancy Pelosi, will be arraigned on Wednesday morning. The charges are driving under the influence and causing injury while driving with a blood-alcohol level of 0.08 percent or higher.
Answer:
Step-by-step explanation:
Nancy Pelosi's Husband Found Drugs in His System after D.U.I. Arrest: Kill His Elder Brother : Other "past Skeletons in Closet" Exposed.
Paul Pelosi, the husband of US House Speaker Nancy Pelosi, was found to have drugs in his system during his drink-driving arrest in May, Fox News reported on Tuesday, citing a court document.
Paul Pelosi was slurring and unsteady on his feet as he spoke to police officers and tried to show them a membership card for a foundation that has long provided money to local police officers and their children.
According to Fox News, the Napa County District Attorney's Office in California said on Monday that Paul Pelosi, the husband of House Speaker Nancy Pelosi, will be arraigned on Wednesday morning. The charges are driving under the influence and causing injury while driving with a blood-alcohol level of 0.08 percent or higher.
The district attorney said the misdemeanor charges against Paul Pelosi were filed "based on the extent of the injuries sustained by the victims."
Us media said that either Paul Pelosi or his lawyer would enter a plea at his arraignment on Wednesday. According to the Napa County District Attorney's Office, misdemeanor penalties for driving while intoxicated and causing injury include up to five years of probation, a minimum of five days in jail, a fine, completion of a court-ordered DUI course, and more.
After her husband s car accident, the US media reported that her brother was killed in a car collision when she was still a teenager. In 1957, Paul reportedly crashed his car near SAN Mateo County at 16. Paul suffered a broken collarbone in the crash, while his elder brother was pronounced dead on arrival at the hospital. Paul, then 16, was acquitted by a jury.
His past skeletons in closet don't stop there. Public data shows that Nancy Pelosi has more than $114 million net worth. Reports indicate that much of that comes from Mr. Paul's holdings of stocks, options, and investments.
Use the elimination method to solve each linear system.
1) 2x-9y=-55 and x+2y=18
2) 3x+2y=7 and 6x-6y=-6
3) 6x+10y=2 and 7x+4y=-13
4) 3x+2y=5 and x-2y=-1
Abby mixes cinnamon and nutmeg to make 25g of a spice mix. Cinnamon costs 9 cents per gram, and nutmeg costs 12.5 cent per gram. The spice mix costs 9.7 cents per gram. How much of each spice does Abby need to use?
Answers
Answer:
1) x=4, y=7
2) x=1, y=2
3) x=-3, y=2
4) x=1, y=1
word problem) 5g of nutmeg and 20g of cinnamon
Step-by-step explanation:
1)
2x-9y=-55
2(x+2y) = 2x+4y = 36
(2x+4y)-(2x-9y)=36-(-55)
13y = 91
y = 7 so x = 4
2)
2(3x+2y) = 6x+4y = 14
6x-6y=-6
(6x+4y)-(6x-6y) = 14-(-6)
10y = 20
y = 2 so x = 1
3)
2(6x+10y) = 12x+20y = 4
5(7x+4y) = 35x+20y = -65
(35x+20y) - (12x+20y) = -65-4
23x = -69
x = -3 so y = 2
4)
just add them
(3x+2y)+(x-2y) = 5+(-1)
4x = 4
x = 1 so y= 1
last)
c+n = 25
9c + 12.5n = 25*9.7 = 242.5
9(c+n) = 9*25
9c+9n=225
9c+12.5n - 9c-9n = 242.5-225
3.5n = 17.5
n = 5 so c = 20
5g of nutmeg and 20g of cinnamon
Write the algebraic expression that represents the following: Forty more than a number
Answers
Answer:
x+40
Step-by-step explanation:
Let's say the the "number" is x.
"Forty more than a number" would be x+40
[tex]\Large\texttt{Answer}[/tex]
[tex]\bold{40+n}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]
[tex]\Large\texttt{Process}[/tex]
⇨ Letting n be the number
[tex]\bold n[/tex]
⇨ Add 40 to n (40 more)
[tex]\bold{40+n}[/tex] (or n+40; you can swap these numbers, they'll still add up to the same amount)
Hope that helped
Which graph shows the solution to this system of inequalities y < - 1/3 x + 1
Answers
Answer:
See attached image.
Step-by-step explanation:
The image does not show the graph options. The attachment sjhhows the graph of y < - 1/3 x + 1.