The area of a rectangle is 36 square centimeters and its length is 9 centimeters A. What is the width of the rectangle? B. Elsa wants to draw a second rectangle that is the same length but 3x as wide. C.What is the perimeter of Elsa's second rectangle?

QUESTION POSTED AT 05/12/2019 - 09:16 PM

Related questions

A box has dimensions of 19 inches long, 1.7 feet wide, and 6 inches high. What is the volume of the box?

The volume is 139.80 cubic inches. Solution:

Volume = L x W x H
Volume  = 19 x 1.7 x 6
Volume= 139.80 cubic inches

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

Which sentence fully illustrates that polygon ABCD is congruent to polygon PQRS? A. Corresponding pairs of angles on ABCD and PQRS are equal in measure. / B. Corresponding pairs of sides on ABCD and PQRS are equal in length./ C. Polygon ABCD maps to polygon PQRS through a reflection only. / D. Polygon ABCD maps to polygon PQRS through a translation only.

Two figures are said to be congruent when they have the same shape and size or if one object is a mirror image of the other object. I think, from the choices given, the best answer to illustrate that ABCD is congruent with PQRS is option B. Corresponding pairs of sides on ABCD and PQRS are equal in length.

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

A guy wire is attached to the top of a radio antenna and to a point on horizontal ground that is 40.0 meters from the base of the antenna. If the wire makes an angle of 55° with the ground, approximate the length l of the wire. (Round your answer to the nearest tenth.)

It is useful to start by drawing a picture to visualize this problem. 

In this case we are going to use the trigonometric function cosine, which is Cos(theta) = adjacent / hypotenuse. 

Cos(55) = 40 / x 

After simplifying we reach the equation: X = 40 /  cos(55)

which would then make the length of the wire 69.7 meters long. 

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


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

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

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

What is the axis of symmetry for the function? y = x2 + 3x - 4 y = -2 x = -2 x = -1.5 y = -1.5 What is the vertex for the function? y = x2 - 4x - 3 (-1, 2) (0, -3) (1, -6) (2, -7) The vertex of y = 9 - 8x - x2 is (-4, 25) False True

Axis of symmetry is a line passing through the vertex which divides the curge into two parts such tha each part looks the same.
For y= x^{2} +3x-4, the 'x' part is squared and the coefficient of x^{2} is positive. Hence, the curve will be a parabola facing up which means that the axis of symmetry will be a vertical line. i.e. x = m.
Investigating, f(-1) == (-1)^{2} +3(-1)-4=1-3-4=-6
f(-1.5) = = (-1.5)^{2} +3(-1.5)-4=2.25-4.5-4=-6.25
f(-2) = = (-2)^{2} +3(-2)-4=4-6-4=-6
From these, the curve has a vertex at point (-1.5, -6)
Therefore the axis of symmetry is line x = -1.5 (i.e. the third option)

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


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

The motion of a simple spring hanging from the ceiling can be modeled with a cosine function. The bottom of the spring has a maximum height of 7 feet 4 inches and a minimum height of 6 feet 2 inches from the floor. It takes 2 seconds for the spring to expand from its minimum length to its maximum length. What is a cosine function that models the spring’s length in inches above and below its average, resting position? Express the model as a function of time in seconds

To get the average resting position of the spring, we must subtract the minimum from the maximum height of the spring with respect to the floor.
So,
7 + (4/12) - [ 6 + (2/12) ] = 1.5 ft

Half of this is where the resting position of the spring is located with respect to the minimum height. If the resting position of the spring is set at 0, then the amplitude of the wave is:
A = 1.5 / 2 = 0.75

Since it takes 2 seconds for the spring to expand from minimum to maximum,
Period = 2 = 2π / n
n = π

The cosine function is:
 y = A cos nt

where y is the distance from the resting position and t is the time in seconds.
y = 0.75 cos πt

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


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

Help me understand please ;-; Which shows the equation in standard form? 6y - 12 = -3x Which shows the equation in standard form? 10 - 2(x - y) = 3x + 1

Standard form for first one is
ax+by=c

6y-12=-3x
add 3x both sides
3x+6y-12=0
add 12
3x+6y=12


second one
distribute (don't forget double negative y)
10-2x+2y=3x+1
minus 3x both sides
10-5x+2y=1
minus 10 both sides
-5x+2y=-9



the equations are
3x+6y=12
-5x+2y=-9

ANSWERED AT 20/01/2020 - 01:17 PM


QUESTION POSTED AT 20/01/2020 - 01:17 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

Which of the following is a solution to the equation y = 3x - 1 ? A. (4,1) B. (2,5) C. (4,3) D. (0, -3)

B. (2,5) you would substitute the x coordinate in for x, which is 2, and the y coordinate in for y, which is 5. So it would be 5=3(2)-1

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


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

1.What is the correct reason for statement 2? Prove: 2(w + 6) + 4 = 2w + 16 Statements Reasons 1. 2(w + 6) + 4 1. Given 2. (2w + 12) + 4 2. ? 3. 2w + (12 + 4) 3. Associative Property 4. 2w + 16 4. Addition 2.What is the correct reason for statement 2? Prove: 4 + 3x + (x ∙ 2) = 5x + 4 Statements Reasons 1. 4 + 3x + (x ∙ 2) 1. Given 2. 4 + 3x + 2x 2. ? 3. 4 + 5x 3. Addition 4. 5x + 4 4. Commutative Property 3.What is the correct reason for statement 3? Prove: (11m) ∙ 4 + m = 45m Statements Reasons 1. (11m) ∙ 4 + m 1. Given 2. 4 ∙ (11m) + m 2. Commutative Property 3. (4 ∙ 11) ∙ m + m 3. ? 4. 44m + m 4. Commutative Property 5. 45m 5. Addition 4.What is the correct reason for statement 5? Prove: k + 4 + 6(1 + k) = 11k + 10 Statements Reasons 1. k + 4 + 6(1 + k) 1. Given 2. k + 4 + (6+ 6k) 2. Distributive Property 3. k + (4 + 6) + 6k 3. Associative Property 4. k + 10 + 6k 4. Addition 5. k + 6k + 10 5. ? 6. 7k + 10 6. Addition 5.Select the correct reasons for statements 1 and 3 to complete the proof. Prove: 3x + 2 • x • 11 = 25x. 1. 3x + 2 • x • 11 = 3x + 2 • 11 • x 1. ? 2. 3x + 2 • x • 11 = 3x + 22x 2. Multiplication 3. 3x + 2 • x • 11 = 25x 3. ?

1. The reason for statement 2 is
Distributive Property

2. The reason for statement 2 is
Commutative Property

3. The reason for statement 3 is
Associative Property

4. The reason for statement 5 is
Commutative Property

5. The reason for statement 1 is
Associative Property
The reason for statement 3 is
Addition

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


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

If cos Θ = negative two over five and tan Θ > 0, what is the value of sin Θ? negative square root / 21 negative square root / 21 over 5 square root / 21 over 5 square root of 21 over 2

Answer:  The correct option is (B) negative square root 21 over 5.

Step-by-step explanation:  Given that for an angle \theta,

\cos \theta=-\dfrac{2}{5},~~~\tan \theta>0.

We are to find the value of \sin \theta.

We know that

Cosine is negative in Quadrant II and Quadrant III.

Tangent is positive in Quadrant 1 and Quadrant III.

So, the given angle \theta lies in the Quadrant III.

We will be using the following trigonometric identity:

\cos^2\theta+\sin^2\theta=1.

We have

\cos \theta=-\dfrac{2}{5}\\\\\\\Rightarrow \sqrt{1-\sin^2\theta}=-\dfrac{2}{5}\\\\\\\Rightarrow 1-\sin^2\theta=\dfrac{4}{25}\\\\\\\Rightarrow \sin^2\theta=1-\dfrac{4}{25}\\\\\\\Rightarrow \sin^2\theta=\dfrac{21}{25}\\\\\\\Rightarrow \sin \theta=\pm\dfrac{\sqrt{21}}{5}.

Since the angle \theta lies in Quadrant III and sine is negative in that quadrant, so

\sin\theta=-\dfrac{\sqrt{21}}{5}.

Thus, option (B) is correct.

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


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

#1. Given the binomials (x - 2), (x - 1), (x + 2), and (x - 4), which one is a factor of f(x) = x3 + 7x2 + 14x + 8? (x - 2) (x - 1) (x + 2) (x - 4) Given the binomials (x + 1), (x + 4), (x - 5), and (x - 2), which one is a factor of f(x) = 3x3 - 12x2 - 4x - 55? (x + 1) (x + 4) (x - 5) (x - 2) #2. What is the f of x over the g of x when f(x) = 6x3 - 19x2 + 16x - 4 and g(x) = x - 2? 6x2 - 7x + 2/3x2 - 9x + 8/ 6x2 - 7x + 2 - 8 over the quantity of x minus 2/3x2 - 9x + 8 - 8 over the quantity of x minus 2 #3. What is the f of x over the g of x when f(x) = 6x3 - 19x2 + 16x - 4 and g(x) = x - 2? #4.What is the quotient when -3x3 + 5x + 14 is divided by x - 2? -3x2 - 6x - 7/- 3x2 - x + 12/-3x2 + 6x - 7 + 28 over the quantity of x minus 2/ -3x2 - x + 12 + 28 over the quantity of x minus 2. #4. What is the quotient when x3 - 5x2 + 2x + 5 is divided by x - 2? x2 - 3x - 4/ x2 - 7x + 16/x2 - 3x - 4 - 3 over the quantity of x minus 2 x2 - 7x + 16 - 3 over the quantity of x minus 2

#1
Factoring the function:

f(x) = x3 + 7x2 + 14x + 8
f(x) = (x + 4) (x + 1) (x + 2)

From the options, (x + 2) is the factor

#2
f(x) / g(x) = (
6x3 - 19x2 + 16x - 4) / (x - 2)
This can be solved by factoring the numerator, by synthetic division or using the remainder theorem.

The result is:
6x^2 - 7x + 2 or (x - 2/3)(x - 1/2)
 
#3 same with #2

#4
(x3 - 5x2 + 2x + 5) / (x - 2)
Again, this can be solved by a number of methods, the result is:
x2 -3x - 4 - (3/x-2)

ANSWERED AT 20/01/2020 - 01:02 PM


QUESTION POSTED AT 20/01/2020 - 01:02 PM

The diameter of a round dinner plate is 10 inches. What's the area of the plate?

The area is ten inches

ANSWERED AT 20/01/2020 - 01:00 PM


QUESTION POSTED AT 20/01/2020 - 01:00 PM

Find the measure of Angle 8. measure of angle 7 = 2x+15 measure of angle 8 = 3x

I do not understand the context of your question, you need extra information to find this out like a picture or a word problem.
If the angles equal each other you would have to solve for x when angle 7 and 8 equal each other. SO... based on that, x would equal 15. This means measure of angle 7 would equal 45 and measure of angle 8 would equal 45. This may not be true because I have no idea what you are asking

ANSWERED AT 20/01/2020 - 12:55 PM


QUESTION POSTED AT 20/01/2020 - 12:55 PM

Analyze the function f(x) = - 2 cot 3x. Include: - Domain and range - Period - Two Vertical Asymptotes

Answer and Explanation :

Given : Function f(x)=-2\cot 3x

To find :

1) Domain and range

2) Period  

3) Two Vertical Asymptotes    

Solution :

1) Domain is defined as the set of possible values of x where function is defined.

f(x)=-2\cot 3x

f(x)=-2(\frac{\cos 3x}{\sin 3x})

For domain, \sin3x\neq 0

So, \sin3x\neq \sin n\pi

3x\neq n\pi

x\neq \frac{n\pi}{3}

The value of x is define as x\neq n\pi+(-1)^n\frac{\pi}{3}

The domain of the function is all real numbers except x\neq n\pi+(-1)^n\frac{\pi}{3}

The range is defined as all the y values for every x.

So, The range of the function is all real numbers.

2) The general form of the cot function is y=A\cot (Bx-C)+D

Where, Period is P=\frac{\pi}{|B|}

On comparing, B=3

So, The period of the given function is P=\frac{\pi}{|3|}

3) Vertical asymptote is defined as the line which approaches to infinity but never touches the line.

The vertical asymptote is at x= n\pi+(-1)^n\frac{\pi}{3} where function is not defined.

The two vertical asymptote is

Put n=0,

x= (0)\pi+(-1)^{0}\frac{\pi}{3}

x=\frac{\pi}{3}

Put n=1,

x= (1)\pi+(-1)^{1}\frac{\pi}{3}

x=\pi-\frac{\pi}{3}

x=\frac{2\pi}{3}

So, The two vertical asymptote are x=\frac{\pi}{3},\frac{2\pi}{3}

ANSWERED AT 20/01/2020 - 12:55 PM


QUESTION POSTED AT 20/01/2020 - 12:55 PM

What's the length of side b in the figure below? I posted a picture so you can view the actual problem. Please help.

we know that

in the right triangle of the figure

Applying the Pythagorean Theorem

 13^{2} =b^{2} +7^{2} \\ b^{2} =13^{2}-7^{2}\\ b^{2}=120\\ b=\sqrt{120} \ cm

therefore

the answer is the option

C)  b=\sqrt{120} \ centimeters

ANSWERED AT 20/01/2020 - 12:54 PM


QUESTION POSTED AT 20/01/2020 - 12:54 PM