On graph paper, draw four different rectangles that each have an area of 24 square units. Then find the perimeter of each one.

QUESTION POSTED AT 05/12/2019 - 03:46 PM

Answered by admin AT 05/12/2019 - 03:46 PM


My first rectangle is 1 unit wide and 24 units long. Its area
is 24 square units and its perimeter is 50 units.

My second rectangle is 2 units wide and 12 units long. Its area
is 24 square units and its perimeter is 28 units.

My third rectangle is 3 units wide and 8 units long. Its area
is 24 square units and its perimeter is 22 units.

My fourth rectangle is 4 units wide and 6 units long. Its area
is 24 square units and its perimeter is 20 units.

Post your answer

Related questions

If a sphere’s radius is quadrupled, what is the corresponding change in surface area?

The surface area of a sphere is four times the area of the largest circle that can be formed out of it. Mathematically, the surface area SA = 4πr^2. There is a direct variation between the surface area and radius. 

                                       SA = 4
π(4r)^2

                                       SA = 64
πr^2

Thus, the surface area is multiplied 16 times if the radius is quadrupled. 

ANSWERED AT 20/01/2020 - 01:48 PM


QUESTION POSTED AT 20/01/2020 - 01:48 PM

Graph y = 5x and y = log5x on a sheet of paper using the same set of axes. Use the graph to describe the domain and range of each function. Then identify the y-intercept of each function and any asymptotes of each function. Explain also.

Answer:

1) For  y=5x

A)  Domain= (-\infty,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x\varepsilon \mathbb{R}]

B) Range= (-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]

C) y-intercept = 0

D) Asymptote= No asymptote

2) For   y=log_5x

A)  Domain=Domain=  (0,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x>0]

B) Range= (-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]

C) y-intercept =  None

D) Vertical Asymptote:   x=0

Step-by-step explanation:

Given : y=5x and y=log_5x

Refer the graph attached.

1)  In equation (1)  y=5x

The domain is the set of all possible values in which function is defined.  

y=5x is a linear polynomial defined on all real numbers.

Domain= (-\infty,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x\varepsilon \mathbb{R}]

Range is the set of all values that function takes.

It also include all real numbers.

Range= (-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]

→y-intercept- Value of y at the point where the line crosses the y axis.

put x=0 in equation y=5x we get, y=0

Therefore, y-intercept = 0 (We can see in the graph also)

→An asymptote is a line that a curve approaches, but never touches.

Asymptote= No asymptote

2) Now in equation (2) y=log_5x

Domain=  (0,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x>0]

because log function is not defined in negative.

Range=  (-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]

y-intercept - None

Vertical Asymptote:   x=0

ANSWERED AT 20/01/2020 - 01:46 PM


QUESTION POSTED AT 20/01/2020 - 01:46 PM

Find the integral of 1/sqrt(x^2-9)

Let x = 3secβ, then dx = 3secβtanβ

∫dx/√(x²-9) = ∫[(3secβtanβ)/(3tanβ)]dβ
                 = ∫secβdβ
                 = ln |tanβ - secβ| + c
                 = ln |√(x² - 9)/3 - x/3| + C
                 = ln |√(x² - 9)/x| + C

ANSWERED AT 20/01/2020 - 01:46 PM


QUESTION POSTED AT 20/01/2020 - 01:46 PM

Find the coordinates of the other endpoint when you are given the midpoint (point M) and one of the endpoints (point P). P = (3, 5) and M =(-2, 0)

I'll try to explain. The trouble is that I do not know English :)
About Points
S = (x,y)        searched point (it will be in the third quadrant )
M = (-2,0)      Midpoint | SP |
P = (3,5)        one end of the segment | SP |

You have to draw Cartesian.

 
we set in a point M and P. We both points by a simple and we extend it for the third quarter of the system. Compass measure the distance from the point M to the point P. From the point M we set a compass point S. Figure attached. Received point S = ( -7 , -5 ) . It sought a point that calculate .

We use the information that | SM | = | MP |

 x_{S}  -  x_{M} =  x_{M} -  x_{P}  \\  \\  x_{S} - (-2) = -2 - 3 \\  \\  x_{S} +2 = -5 \\  \\  x_{S} = -5 - 2 = -7

 y_{S} - y_{M}  =  y_{M}  -  y_{P}  \\  \\  y_{S}  - 0 = 0 - 5 \\  \\  y_{S}  = -5

Answer : S = (-7,-5)

as soon as I had a good range will add drawing


ANSWERED AT 20/01/2020 - 01:45 PM


QUESTION POSTED AT 20/01/2020 - 01:45 PM

The sum of the measures of two complementary angles exceeds the difference of their measures by 72°. Find the measure of the smaller angle. A. 18° B. 36° C. 54° D. 58°

First we need to define our conditions. Since the angles are complimentary, the sum of the angles must be equal to 90 degrees.

let x = first angle
y = second angle

x + y = 90

from the second condition in the problem 

x + y =72 + x -y
solving for x

x= 54

therefore the shorter side is 90 - 54 = y

y = 36 degree, the shorter side

ANSWERED AT 20/01/2020 - 01:44 PM


QUESTION POSTED AT 20/01/2020 - 01:44 PM

As the marketing designer for Burger King, you are given a 4 in by 6 in logo and have been told to create an advertisement with sides six times larger. What is the area of your advertisement (in feet)? [12 inches = 1 ft]

The area would be 144 square inches. Solution:

Area of logo
Area = L x W
Area = 4 x 6
Area = 24 square inches

Area of Ads
Area = 6 x Logo
Area = 6 x 24
Area = 144 square inches

ANSWERED AT 20/01/2020 - 01:44 PM


QUESTION POSTED AT 20/01/2020 - 01:44 PM

The length of a rectangle is 12 in. more than its width. The perimeter is 64 in. Calculate the length of the rectangle in inches.

Let x = width
x+12 = length

Perimeter of a rectangle, P = 2x+2(x+12) = 64
2x+2x+24=64
4x = 40
x=10
x+12 = 22

therefore, length is 22 in.

ANSWERED AT 20/01/2020 - 01:41 PM


QUESTION POSTED AT 20/01/2020 - 01:41 PM

The graph of a function never has two different points with the same x-coordinate because.. A. the graph of a function cannot be a straight line. B. each input value is mapped to a single output value. C. each input value is mapped to more than one output value. D. the graph of a function is a vertical line.

Answer:  The correct reason is (B) each input value is mapped to a single output value.

Step-by-step explanation:  The given statement is:

"The graph of a function never has two different points with the same x-coordinate."

We are to select the correct reason for the above statement.

The definition of a FUNCTION is as follows:

In simple language, a function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

That is, if y = f(x) is a function of a variable 'x', then we have

x_1=x_2~~~~\Rightarrow f(x_1)=f(x_2).

(A) The first statement is "the graph of a function cannot be a straight line."

The statement is false. For example, let us consider y = x + 2. Obviously, it is a function because every value of 'x' will result in only one value of 'y'.

Also, the graph here will be a straight line as shown in the attached figure (1).

(B) The first statement is "each input value is mapped to a single output value."

The statement is true according to the definition of a function.

(C) The third statement is "each input value is mapped to more than one output value."

The statement is false by the definition of a function.

(D) The fourth statement is "the graph of a function is a vertical line."

The statement is false. For example, if we consider the vertical line x = 2. Then, we see from the attached figure (2) that the points (x, y) = (2, 1), (2, 0), (2, 3), etc. all lie on the line.

This shows that one input value leads to infinitely many values of 'y'. Hence, this vertical line cannot be the graph of a function.

Thus, (B) is the correct statement.

ANSWERED AT 20/01/2020 - 01:38 PM


QUESTION POSTED AT 20/01/2020 - 01:38 PM

The perimeter of a rectangle is 146 cm. The width is 10 cm longer than twice the length. Find the width

Perimeter of a rectangle = 2L + 2W = 146

"width is 10 longer than twice the length"
translates to
W = 2L + 10
this can be rearranged to be
2L = W - 10

we can plug that into the first equation and get
(W - 10) + 2W = 146

add like terms
3W - 10 = 146

add 10 to both sides
3W = 156

divide both sides by 3
W = 52

therefore the width is 52 cm

ANSWERED AT 20/01/2020 - 01:36 PM


QUESTION POSTED AT 20/01/2020 - 01:36 PM

Let theta be an angle in quadrant III such that cos theta=-3/5 . Find the exact values of csc theta and tan theta .

Answer:

cosec\theta=-\frac{5}{4}

tan\theta=\frac{4}{3}.

Step-by-step explanation:

Given, let \theta  be the angle in the III quadrant .

cos\theta=-\frac{3}{5}......    (given)

In III quadrant cosec\theta is negative  and tan\theta is positive .

because , cosec\theta=reciprocal of sin\theta

it means , cosec\theta=\frac{1}{sin\theta}

Therefore,  first we find value of sin\theta

 We know that

sin^2\theta=1-cos^2\theta

sin\theta=\sqrt{1-cos^2\theta}

sin\theta=\sqrt{1-(\frac{-3}{5} )^2

sin\theta=\sqrt{1-\frac{9}{25}}

sin\theta=\sqrt{\frac{16} {25}

sin\theta=\frac{-4}{5}

Because sin\theta lies in III quadrant and in III quadrant it is negative.

Now, we know that

tan\theta=\sqrt{sec^2\theta-1}

therefore,  first we find sec\theta

sec\theta=\frac{1}{cos\theta}

sec\theta=-\frac{5}{3}

tan\theta=\sqrt{(\frac{5}{3})^2-1

tan\theta=\sqrt{\frac{25} {9}-1

tan\theta=\frac{4}{3}

Because it lies in III quadrant, therefore it take positive.

Hence,cosec\theta=-\frac{5}{4} and tan\theta=\frac{4}{3}

ANSWERED AT 20/01/2020 - 01:33 PM


QUESTION POSTED AT 20/01/2020 - 01:33 PM

Find cos(sin-1(3/5))

Sin-1 (3/5) = 36.869
cos 3/5 = 0.999

ANSWERED AT 20/01/2020 - 01:30 PM


QUESTION POSTED AT 20/01/2020 - 01:30 PM

Which function below has the smallest slope? A Graph with a line going through -5 on the Y Axis and Postive 2 and a half on the X axis. f(x) f(x) = 2x - 3 h(x) x h(x) -1 3 1 7 3 11

For the first line:
m = (-5 - 0) / (0 - 2.5) = 2

For the second line:
From the given equation,
m = 2

For the third, using the given coordinates (-1,3) (1,7)
m = (7 - 3) / (1 - (-1)) = 2

Therefore, all the slopes of the lines are 2 and none of them have the smallest slope compared to the others.

ANSWERED AT 20/01/2020 - 01:28 PM


QUESTION POSTED AT 20/01/2020 - 01:28 PM

Find the exact value of sec(5pi/ 3) and and sin(7pi/6)

I know the equation is 1/cos
but is it negative sqrt(3)/2 or positive?
or is it negative 1/2 or positive?
This makes the reference angle π/6 or 30º which gives cos 30º=√3/2 or a sec value of 2/√3=2√3/3
sec(-5pi/6)=-2√3/3

ANSWERED AT 20/01/2020 - 01:27 PM


QUESTION POSTED AT 20/01/2020 - 01:27 PM

A community college enrolled 96,000 students in 2007, and the enrollment has increased by 7% every year since then. Graph the exponential function, y, that gives the number of students enrolled in terms of t, where t is the number of years since 2007. -The graph of the function begins at y = 96,000. -The graph of the function does not have any asymptotes. -The graph of the function shows the exponential growth. -As t increases in the exponential function, the value of y approaches zero.

The formula of the function would be:
y = 96000(1.07)^t

The graph is an exponential function with y-intercept of 9600. The curve goes upward indefinitely as the value of time increases.

Therefore, from the choices, the statements that apply to the graph are:
-The graph of the function begins at y = 96,000.
-The graph of the function shows the exponential growth.

ANSWERED AT 20/01/2020 - 01:25 PM


QUESTION POSTED AT 20/01/2020 - 01:25 PM

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.

Hello,

a(2)=-6
a(3)=-6*r
a(4)=-6*r²
a(5)=-6*r^3=162
a(5)/a(2)=r^3=162/(-6)=-27==>r=-3

a(1)=-6/(-3)=2
a(2)=2*(-3)
a(3)=2*(-3)²
a(4)=2*(-3)^3
a(5)=2*(-3)^4

a(n)=2*(-3)^(n-1)




Answer

ANSWERED AT 20/01/2020 - 01:24 PM


QUESTION POSTED AT 20/01/2020 - 01:24 PM

Find an integer, x, such that 5, 10, and x represent the lengths of the sides of an obtuse triangle. A. 4 B. 5 C. 6 D. 11

Hello,

5<10+x ==> -5<x realized
10<5+x ==> x>5
x<5+10 ==> x<15
==> 5<x<15
==>x=6 or x=11 but for x=11 angle none obtus
==> 1solution x=6 (angle = 130.5416...°)




ANSWERED AT 20/01/2020 - 01:23 PM


QUESTION POSTED AT 20/01/2020 - 01:23 PM

The graph of a certain quadratic function does not cross the x-axis. Which of the following are possible values for the discriminant?a) 18 b) 0 c) -25 d) -7

As the function is quadratic, it must be positive or equal 0. 
Therefore B and D are possible values.

ANSWERED AT 20/01/2020 - 01:22 PM


QUESTION POSTED AT 20/01/2020 - 01:22 PM

4x^2-x-3=0 solve by completing the square x= ??

Hello,

4x²-x-3=0
==>(2x)²-2*1/2*x+1/4-3-1/4=0
==>(2x-1/2)²-13/4=0
==>(4x-1)²-13=0
==>(4x-1-√13)(4x-1+√13)=0
==> x=(1+√13)/4 or x=(1-√13)/4



ANSWERED AT 20/01/2020 - 01:22 PM


QUESTION POSTED AT 20/01/2020 - 01:22 PM

Which sequence is modeled by the graph below? coordinate plane showing the points 2, 1; 3, 2; 4, 4; and 5, 8 an = one half(2)n − 1 an = 2(2)n − 1 an = 4(−2)n − 1 an = 2(one half)n − 1

First, we inspect what type of sequence is the order of the coordinates:
a2 = 1
a3 = 2
a4 = 4

Getting the difference,
a3 - a2 = 1
a4 - a3 = 2

The differences are not equal; hence, the sequence is not arithmetic.

Getting the ratio:
a3/a2 = 2
a4/a3 = 2

The common ratio is 2. Using the general form for a geometric series:
an = a1 r^(n-1)
If n = 2
1 = a1 (2)^(2-1)
a1 = 1/2

So,
an = (1/2) (2)^(n-1)

The answer is the first option.

ANSWERED AT 20/01/2020 - 01:22 PM


QUESTION POSTED AT 20/01/2020 - 01:22 PM

f(x)=x2-3x-7 find f(-3) a- -7 b- 8 c- 11 d- 22

Hello,

f(-3)=(-3)²-3*(-3)-7=9+9-7=11
Answer C

ANSWERED AT 20/01/2020 - 01:21 PM


QUESTION POSTED AT 20/01/2020 - 01:21 PM

Find functions f and g so that h(x) = (f ∘ g)(x). h(x) = (6x - 14)^8 A. f(x) = 6x - 14, g(x) = x^8 B. f(x) = 6x^8 - 14, g(x) = -14 C. f(x) = x^8, g(x) = 6x - 14 D. f(x) = (6x)^8, g(x) = -14

Hello,

Answer C

Be carefull

A: is (gof)(x)=g(f(x))=g(x^8)=6x^8-14

C: fog(x)=f((g(x))=f(6x-14)=(6x-14)^8

ANSWERED AT 20/01/2020 - 01:19 PM


QUESTION POSTED AT 20/01/2020 - 01:19 PM

Sam leases a car for 24 months. The car will cost him $7,000 if he decides to buy it at the end of the lease. What term describes the $7,000? A. interest B. residual value C. lease amount

Answer:

Term that describes  $7,000 is:

B. residual value

Step-by-step explanation:

We are given that:

Sam leases a car for 24 months. The car will cost him $7,000 if he decides to buy it at the end of the lease.

Then the term that describes $7000 is

B. residual value

(Since,  The residual value is the estimated value of a fixed asset at the end of its lease or at the end of its useful life.)

ANSWERED AT 20/01/2020 - 01:16 PM


QUESTION POSTED AT 20/01/2020 - 01:16 PM

A researcher finds that 15% of all commuters in a metropolitan area take the train to work. The researcher polls 250 people in the area and asks them whether they take the train to work. What is the number of trials for this binomial experiment?

Answer:

Number of trials are 250.

Step-by-step explanation:

A researcher finds 15% of all commuters in a metropolitan area take the train to work.

The researcher polls 250 people in the area to ask them whether they take the train to work or not.

We have tell the number of trials for this binomial experiment.

Researcher will do 250 trials to confirm whether they take the train work and this irrespective of their response.

ANSWERED AT 20/01/2020 - 01:16 PM


QUESTION POSTED AT 20/01/2020 - 01:16 PM

Find a number that is between 7/11 and 0.75 . A. 25/44 B. 77/99 C.23/33 D.76/99

Hello,

Answer C
23/33=0.69 69 69 .....
7/11=0.63 63 63 ....

ANSWERED AT 20/01/2020 - 01:15 PM


QUESTION POSTED AT 20/01/2020 - 01:15 PM

GEOMETRY QUESTION! Please Help 9. A design on the surface of a balloon is 5 cm wide when the balloon holds 71 cm of air. How much air does the balloon hold when the design is 10 cm wide? Explain the method you use to find the amount of air.

142cm of air I think... I divided 142 buy 2. also then added 71 and 71 and multiplied buy 2 all were same answer

ANSWERED AT 20/01/2020 - 01:14 PM


QUESTION POSTED AT 20/01/2020 - 01:14 PM

Find the value of cos(sin-1(3/5))

cos( sin^{-1}  \frac{3}{5} ) \\ =cos(sin^{-1} 0.6) \\ =cos36.87 \\ =0.8

ANSWERED AT 20/01/2020 - 01:14 PM


QUESTION POSTED AT 20/01/2020 - 01:14 PM

Every Saturday, Heather goes mountain biking. It takes Heather 32 minutes to bike 6 miles. The distance is a function of the time. Which is a reasonable range in the context of the problem? 1. 0 ≤ f(t) ≤ 6 2. 0 ≤ f(t) ≤ 32 3. 6 ≤ f(t) ≤ 32 4. 12 ≤ f(t) ≤ 24

Since distance is a function of time, then the range must be the possible time that Heather could spend with her mountain bike.

Given that she can travel for period 32 minutes and that there can be no negative time. The answer is:
2. 0 ≤ f(t) ≤ 32

ANSWERED AT 20/01/2020 - 01:14 PM


QUESTION POSTED AT 20/01/2020 - 01:14 PM

Solve the quadratic equation by completing the square. x2 + 6x + 7 = 0

Hello,

x²+2*3x+3²+7-9=0
==>(x+3)²-2=0
==>(x+3-√2)(x+3+√2)=0
==> x=-3+√2 or x=-3-√2

ANSWERED AT 20/01/2020 - 01:12 PM


QUESTION POSTED AT 20/01/2020 - 01:12 PM

List L consists of numbers 1, square root of 2, x, and x^2 , where x>0, and the range of the numbers in list L is 4. Which quantity is larger? A. x B. 2

If the range of the numbers in the list L is 4, then x can't be 4 since there is an element in the list that is x^2. Therefore,
0 ≤ x^2 ≤ 4 so that it would be the highest number and
0 ≤x ≤ 2

So, the value of x can be equal to 2 but not higher. So, 2 is always greater or equal to x.

ANSWERED AT 20/01/2020 - 01:11 PM


QUESTION POSTED AT 20/01/2020 - 01:11 PM