# 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

QUESTION POSTED 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.

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 = 4π(4r)^2

SA = 64πr^2

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

SA = 4π(4r)^2

SA = 64πr^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

**Answer:**

1) For

A) **Domain=**

B) **Range= **

C)** y-intercept **= 0

D) **Asymptote= **No asymptote

2) For

A) **Domain=Domain=**

B) **Range= **

C)** y-intercept **= None

D) **Vertical Asymptote:**
x=0

**Step-by-step explanation:**

** Given : ** and

**Refer the graph attached. **

1) In equation (1)

→**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=**

→**Range is the set of all values that function takes.**

It also include all real numbers.

**Range= **

**→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)

**Domain=**

because log function is not defined in negative.

**Range=**

**y-intercept **- None

**Vertical Asymptote:**
x=0

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

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

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

∫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

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 |

Answer : S = (-7,-5)

as soon as I had a good range will add drawing

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 |

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

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

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

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

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

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.

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

**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

**(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

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**

"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

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

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

**Answer:**

**=-**

**=.**

**Step-by-step explanation:**

Given, let be the angle in the III quadrant .

=-...... (given)

In III quadrant is negative and is positive .

because , =reciprocal of

it means , =

Therefore, first we find value of

We know that

∴

Now, we know that

therefore, first we find

Hence,** and **

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

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

Sin-1 (3/5) = 36.869

cos 3/5 = 0.999

cos 3/5 = 0.999

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

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

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.

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

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

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

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.

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

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

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

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...°)

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

As the function is quadratic, it must be positive or equal 0.

Therefore B and D are possible values.

Therefore B and D are possible values.

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

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

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

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

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.

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

Hello,

f(-3)=(-3)²-3*(-3)-7=9+9-7=11

Answer C

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

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

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

**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

**Answer: 21 inches **

**Step-by-step explanation: this answer is for edge.nuity**

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

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

**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

Hello,

Answer C

23/33=0.69 69 69 .....

7/11=0.63 63 63 ....

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

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

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

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

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

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

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

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

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.

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