The perimeter of a rectangle is 120 feet. The ratio of the width to the length is 2:3. Find the length and width.

Answers

Answer 1

Since the ratio of width to length is 2:3, that is a total of 5 parts.
Multiply this by 2 (P = 2L + 2W) = 10 parts.
120/10 = 12
Each part = 12
W:L

12*2:12*3 = 24:36

CHECK

2(24) + 2(36) ??=?? 120

48 + 72 ??=?? 120

120 = 120 checks

Length = 36 ft
Width = 24 ft

Related Questions

Frank borrowed $400 from his neighbor. He made 3 payments of $65 each and another payment of $95. How much does Frank still owe?

Answers

Hello there!

Frank borrowed $400. He made 3 payments of $65 and an additional payment of $95.

Let's start by setting up our equation.

400 = 3(65) + 95
Multiply 3 by 65.
400 = 195 + 95
Combine like-terms.
400 = 290
Subtract 290 from both sides.
110

Frank still owes $110 to pay.

I hope this helps!

Transform both equations in each system of equations so that each coefficient is an integer.

***I also need it to be solved using substitution method.

Answers

For the first one multiply each term by the LCM of 4 and 6, which is 12:-

15x -36 = 2y..................(1)

and second multiply by 5:-

2x + y = 9..............(2)

solving:-
from equation (2) y = 9-2x, substitute in equation (1):-

15x - 36 = 2(9-2x) = 18 - 4x
19x = 54
x = 54/19 = 2.84

so y = 9 - 2(2.84) = 3.32

True or false
Two points determine a plane

Answers

False it is 3.
One up and down and add one more

false. two points only determine a side of a plane.

What is the equation of a quadratic graph with a Focus of (8,-8) and directrix of y=-6

Answers

check the picture below

so hmmm the left-side of the picture, is the focus point and the directrix, notice, the directrix is a horizontal line, that means the parabola is a vertically opening one.

also notice, the focus point is below the directrix, that means the parabola opens downwards

now, the vertex is "p" distance from either the directrix and the focus point, so that means, the vertex is half-way between those two fellows, if you notice the right-side of the picture, that's where the vertex is at.

the distance "p" is clearly just 1unit, however, since the parabola is opening downwards, "p" is negative, thus -1

[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}}) }\\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \begin{cases} h=8\\ k=-7\\ p=-1 \end{cases}\implies (x-8)^2=4(-1)(y-(-7)) \\\\\\ (x-8)^2=-4(y+7)\implies \cfrac{(x-8)^2}{-4}=y+7 \\\\\\ -\cfrac{1}{4}(x-8)^2-7=y[/tex]

FIND THE MISSING VALUE. SHOW YOUR WORK.

Answers

to find x multiply the side (24) by the tangent of the angle(13)

so 24 * tan(13) = 5.5408

to find x

divide the side (10) by the sin of the angle (20)

10/sin(20) = 29.238

Round the answers as needed.

Each week Rosario drive to an ice-skating rink that is 60 miles away. The road trip takes 2.75 hours. If he averages 55 mph on his way to the rink, which equation can be used to find X, the number of miles per hour he averages on his way home?

Answers

60(55)•60x=2.75 there's your answer

Answer: The number of miles per hour he averages on his way home is 36 mph.

Step-by-step explanation:

Since we have given that

Distance traveled by Rosario = 60 miles

Time taken for road trip = 2.75 hours

Speed at which he on his way to the rink = 55 mph

Let X be the speed at which he averages on his way home.

So, According to question, we get that,

[tex]\dfrac{60}{55}+\dfrac{60}{x}=2.75\\\\1.09+\dfrac{60}{x}=2.75\\\\\dfrac{60}{x}=2.75-1.09\\\\\dfrac{60}{x}=1.659\\\\x=\dfrac{60}{1.659}\\\\x=36.16\\\\x=36\ mph[/tex]

Hence, the number of miles per hour he averages on his way home is 36 mph.

Can someone help me with this math problem, please? Thanks!

Answers

Answer: D, -1
First, plug in the value -1 for x in f(x) first. [tex] \frac{1}{(-1)^2+1} [/tex] can then be simplified to [tex] \frac{1}{2} [/tex] because [tex](-1)^2=1[/tex]. Next, put the value -1 for x in the equation g(x). This will look like [tex]- \frac{1}{2} [/tex].

The final step is to evaluate f(x) divided by g(x). f(x) = 1/2 and g(x) = -1/2, so when divided, you get -1.

f(-1)= 1/2
g(-1) = -1/2
1/2 / -1/2 =
1/2 * -2/1 = -1
Letter D

On the blueprint of a house, 45 millimeters represents 10 meters. The length of the living room is 36 millimeters on the blueprint. What is the actual length of the living room?

Answers

45/10= 36/x

cross multiply

360/45X

360/45 = 8

the length is 8 meters

Find the missing number in the proportion. 8/56 = ?/49

Answers

Let x be the unknown quantity. First, cross multiply to get 56x=392. Then divide both sides of the equation by 56 to get x=7.

PLEASE HELP!!!! IMAGE ATTACHED FIND THE MEASURE OF ANGLE 3

Answers

m< 3 = 180 - 60 - 90
m< 3 = 30

answer
30

The data table represents the distance between a well-known lighthouse and a cruise ship over time. The cruise ship is travelling at uniform speed. Which equation represents the distance (y) from the lighthouse, based on the number of hours (x)?

Number of Hours Distance from Lighthouse
(in oceanic miles)
2 53
4 95.5
6 138
8 180.5
10 223
12 265.5
14 308
16 350.5

y = 42.5x + 10.5
y = 10.5x + 32
y = 21.5x + 10.5
y = 12.25x + 28.5
y = 12.5x + 10.5

Answers

Find the velocity first, the "slope".

m=(y2-y1)/(x2-x1)

m=(95.5-53)/(4-2)

m=21.25 ? Your equations are wrong, I'll double check with another set of points...

m=(350.5-308)/(16-14)

m=21.25 LOL, yep none of your lines has the correct slope.

Anyway...

y=21.25x+b, using any point we can solve for the y-intercept, or "b", (2, 53)

53=21.25(2)+b

53=42.5+b

10.5=b so the distance to the lighthouse as a function of time is:

y=21.25x+10.5

So essentially, you should fire your teacher or burn that book you are using :)

Answer:

y=21.5x+10.5

Step-by-step explanation:

Convert 28.7251° to degrees, minutes, and seconds. Round to the nearest second.

Answers

28.7251 =

28 degrees

then take the decimal and multiply by 60 to get the minutes

so 0.7251 *60 = 43.506, use the whole number (43)

so now you have 28 degrees, 43 minutes

now take the remaining decimal ( 0.506) and multiply by 60

0.506*60= 30.36

when you have a decimal left over for the seconds, keep that as is.

so you now have 28 degrees, 43 minutes and 30.36 seconds

use ' for minutes and " for seconds

28 degrees 43' 30.36"

Final answer:

To convert 28.7251 degrees to degrees, minutes, and seconds, take the whole number of degrees (28) and multiply the decimals (.7251) by 60 to get the minutes (43). Then multiply the remaining decimal of the minutes (.506) by 60 to get the seconds (30), resulting in 28 degrees, 43 minutes, and 30 seconds (28° 43' 30").

Explanation:

To convert 28.7251 degrees to degrees, minutes, and seconds, you follow a multi-step process which involves converting the decimal part of the degrees into minutes and then into seconds. First, identify the whole number of degrees, which is 28 in this case.

To convert the decimal part (.7251) to minutes, multiply by 60. Using the operation provided in the reference, with 0.7251 × 60, you get 43.506 minutes. The whole number part, 43, is the minutes.

To convert the remaining decimal part of minutes (.506) into seconds, again multiply by 60. This gives you (.506 imes 60) 30.36 seconds, which when rounded to the nearest second is 30 seconds.

Therefore, 28.7251 degrees is equal to 28 degrees, 43 minutes and 30 seconds (28° 43' 30").

Use the remainder theorem to determine the remainder when 3t2 + 5t − 7 is divided by t − 5. A. 93 B. 43 C. 107 D. 57

Answers

Using remainder theorem, we get:

[tex]P(t) = 3t^{2} + 5t - 7[/tex]

Substitute t = 5 into the equation:
[tex]P(5) = 3(5)^{2} + 5^{2} - 7[/tex]
[tex]P(5) = 75 + 25 - 7 = 93[/tex]

Thus, we get a remainder of 93 or (A)

The answer for your question is A. 93

The roof of a house is being reconstructed to accommodate heavy snows. the current 32 foot roofline makes an 18.2° angle with the horizontal. the owner has decided to construct the new roof so that it makes a 50° with the horizontal as shown below. what will be the length of the new roofline?

Answers

Final answer:

To find the length of the new roofline, we can use the tangent function. The length is approximately 26.9 feet.

Explanation:

To find the length of the new roofline, we can use the trigonometric function tangent. Let's call the length of the new roofline 'x'. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the roofline, which is 32 feet, and the adjacent side is the horizontal distance, which is 'x' feet. So, we can set up the equation:

tan(50°) = 32/x

To solve for 'x', we can multiply both sides of the equation by 'x' and then divide both sides by tan(50°). This gives us:

x = 32/tan(50°)

Using a calculator, we can find that tan(50°) ≈ 1.1917. So, substituting this value into the equation, we get:

x ≈ 32/1.1917

By calculating this, we find that the length of the new roofline is approximately 26.9 feet.

If the x-axis is Quantity and the y-axis is Price, which of the following is the best summarization of the supply shift from S1 to S2?
A)The supply decreased.
B) The supply stayed the same.
C) The supply increased.
D) The supply outweighed demand.

Answers

Line S1 and S2 are parallel and that shows that the rate of change in price to change in quantity stays the same. This means that the supply stays the same.

Correct answer: B

Answer:

Option B is correct.

Step-by-step explanation:

We have been given x-axis representing quantity

And y-axis representing price

S1 and S2 are supply

So, these two supply have parallel lines which means they will never intersect they will remain same throughout the domain.

Therefore, the supply stayed the same.

Option B is correct.

Which expression represents the area of triangle ABC in square meters?

Answers

Formula for area of a triangle - 1/2 bh

The base is 20 + 37 = 57.
Now here is where I am confused. I think it is 14 however. I'm sorry if I'm wrong here.

So the answer is 1/2 * 57 * 14

Answer:

the correct answer is A. 1/2 x 14 x 57

Step-by-step explanation:

i got it right on my test

simplify each expression by destributing. math problem> 3(2y-7)

Answers

The distributive property says that a(b+c)= ab+ac

3(2y-7)= 3(2y)+ 3(-7)

Final answer: 6y-21

Write the equations in graphing form, then state the vertex of the parabola or the center and radius of the circle.

x^2+y^2+y+2=8

Answers

Since it has both x and y squared, it's a circle - the graphing equation would be x^2+y^2+y-6=0 and we'd then get x^2+y^2+y=6, then (x)^2+(y+1/2)^2=6+1/4, and the center would therefore be (0, -1/2) with the radius being sqrt(6+1/4)

Write the equation of the ellipse with its center at the origin. the height of the ellipse is 12 units and the width is 14 units.

Answers

Sketch the ellipse as shown in the figure below.

The general form of the equation of an ellipse centered at (h,k), with semi -major axis of a and semi - minor axis of b is
[tex] \frac{(x-h)^{2}}{a^{2}}+ \frac{(y-k)^{2}}{b^{2}} =1[/tex]

Because the width is 14, therefore a = 7.
Because the height is 12, therefore b = 6.
Because the ellipse is centered at the origin, h=0, and k=0.

Answer:
[tex] \frac{x^{2}}{49} + \frac{y^{2}}{36} =1[/tex]

If five cakes cost 5 pounds how much do 2 cakes cost

Answers

they would cost 2 pounds.

Well, think about it...

You have five cakes, and it costs 5 pounds. What is the price of each cake?

Well.. It has to be 1! So, if you have two cakes - it will cost 2 pounds. Wanna go extra and get 30 cakes? 30 pounds!

Jenna surveyed the students at her dance class to find out if they like salsa and/or ballet. The results of her survey are shown in the two-way table below:

Like Salsa

Do Not Like Salsa

Total

Like Ballet

32

42

74

Do Not Like Ballet

22

4

26

Total

54

46

100

If a student does not like ballet, what is the probability that student also does not like salsa?
8.7%
15.4%
18.2%
84.6%

Answers

like salsa hate salsa total
like ballet 32 42 74
hate ballet 22 4 26
total 54 46 100

if a student does not like ballet (there is 26 that do not like ballet)..what is the probability that the student does not like salsa..of those 26 that do not like ballet, 4 do not like salsa...
4/26 = 0.1538 = 15.38% rounds to 15.4% <=

The answer is 15.4 because the student who don't like ballet and don't like salsa is 4 divided by the total which is 26.

I need help and I'm not sure if the answer is A so can you pls help!

Answers

The answer is not A because it less than or equal to and 1 is = 1.
The answer is D because -5 is less than 1 and its not equal to 1.

Which double-angle or half-angle identity would you use to verify that 1+cos2a=2/1+tan2a?

Answers

In this case or scenario, the double-angle identity that should be used is the one for cosine.

In totality, we shall need the following three trigonometric identities to end up with the equality:

1. cos (2a) = cos² (a) - sin² (a)
2. sin² (a) + cos² (a) = 1
3. tan² (a) + 1 = sec² (a)

Using identities 1 and 2 on the left-hand side of the equation, we get the following:

1 + cos (2a) = 1 + cos² (a) - sin² (a) = 2 cos² (a)

Recalling that cos² (a) = 1 / sec² (a) and applying identity 3, we find the following:

2 cos² (a) = 2 / sec² (a) = 2 / (1 + tan² (a))

Therefore giving us:

2 cos² (a) = 2 / (1 + tan² (a))

Answer:

Its C. cos2a=cos^2a-sin^2a on ed

ind the area of an octagon with a radius of 6 meters. Round your answer to the nearest tenth.

Answers

Area of an octagon :
A = 2 a² ( 1 + √ 2 )
and a = r √ 2
a = 6 √ 2
A = 2 * ( 6 √2 )² * ( 1 + √ 2 ) =
= 2 * 72 ( 1 + √ 2 ) =
= 144 * ( 1 + √ 2 ) m² = 144 + 144 √2 ≈ 347.65 m²

Convert the following using dimensional analysis:

13.2 cm to ft & in

Answers

Multiply (13.2 cm) by (1 inch/2.54 cm). That gives you the whole length in inches. If it's more than 12, then take as many 12s away from it as you can, and call each of those '1 foot'. When you can't take 12 away any more, then what you have left is the inches.

What is the intersection of this sphere with the yz-plane? find an equation of the sphere with center (−3, 2, 9) and radius 6?

Answers

The equation of a sphere with center (a, b, c) and radius r is given by :

[tex] (x-a)^{2} + (y-b)^{2} + (z-c)^{2} = r^{2} [/tex],

so the equation of the sphere with center (-3, 2, 9) and radius 6 is :

[tex](x-(-3))^{2} + (y-2)^{2} + (z-9)^{2} = 6^{2} [/tex]

[tex](x+3)^{2} + (y-2)^{2} + (z-9)^{2} = 36[/tex]

The yz plane is the set of all points (0, y, z), that is x is always 0.

For x=0, the plane

[tex](x+3)^{2} + (y-2)^{2} + (z-9)^{2} = 36[/tex]

becomes

[tex](0+3)^{2} + (y-2)^{2} + (z-9)^{2} = 36[/tex]

[tex](y-2)^{2} + (z-9)^{2}=36-9=25= 5^{2} [/tex]

[tex](y-2)^{2} + (z-9)^{2}=5^{2} [/tex]

This is the circle with center (y, z)=(2, 9) and radius 5.

Final answer:

The equation of the sphere with center (-3, 2, 9) and radius 6 is (x + 3)² + (y - 2)² + (z - 9)² = 6². The intersection of this sphere with the yz-plane is described by the equation (y - 2)² + (z - 9)² = 27.

Explanation:

The equation of a sphere with center (-3, 2, 9) and radius 6 is given by:

(x + 3)² + (y - 2)²+ (z - 9)² = 6²

To find the intersection of this sphere with the yz-plane, we need to set x = 0 in the equation:

(0 + 3)² + (y - 2)² + (z - 9)² = 6²

Simplifying this equation gives:

(y - 2)² + (z - 9)² = 27

So, the intersection of the sphere with the yz-plane is described by the equation (y - 2)² + (z - 9)² = 27.

If one u.s. dollars equals 5.76 egyptian pounds and one u.s. dollar equals 0.56 british pound, how many egyptian pound equal one british pound?

Answers

The task is to calculate the ratio of exchange rates. We must carefully write the equation.Let's write the equation.
0,56 p=1s=5,76 e
So
0,56 p=5,76 eWe have to show how much the Egyptian pound was equal to one British pound.
This means that we must obtain the equation 1p=.....
Of 0.56=56/100.56/100 multiply by 100/56 get 1.Multiply both parts of equation by 100/56
1 pound =10.2857 of egyptian pound.

△LMN, with vertices L(2,2), M(3,5), and N(6,1), is rotated 90° about the origin. What is the location of M′?

Answers

The rotation of triangle LMN 90° about the origin is shown in the diagram below.

The coordinate of M' is (5, -3)

How would you represent 4 eighth notes as a fraction?

Answers

It would be 4/8 which is 1/2

it would have to be either 4/8 or 1/2. 4 eighth notes are 1/8 times 4 which is 4/8 but simplified it can be 1/2

Write a point-slope equation for the line that has slope 5 and passes through the point (6, 22). Do not use parenthesis on the y side.

Answers

the equation to point-slope form is y-y1=m(x-x1) so the answer is:
y-22=5(x-6)

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