A rug is shaped like a rectangle who's per Perimeter there's 192 feet the length is five times longer with find the length and the width

Answers

Answer 1

P = Perimeter = 2(length) + 2(width). Let the width be x; then if the length is 5 times longer than the width, the length is 5x.

Plug these values into the Perimeter equation P = 2(length) + 2(width):

P = 2(5x) + 2(x), or P = 12x, and this is known to have the value 192 units. Solve for the width, x:

(192 units) = 12x gives us x = 16 units. Then the length is 5(16 units) = 80 units.

Check: Does 2(80 units) + 2(16 units) = 192 units? If so, then our width (16) and length (80) are correct.

Related Questions

M(5, 7) is the midpoint of rs The coordinates of S are (6, 9). What are the coordinates of R?
(5.5, 8)

(7, 11)

(10, 14)

(4, 5)

Answers

the correct answer is D (4,5)

[tex]\text{Let the coordinates of R be (x, y)}[/tex]

[tex]x_M = \frac{x_R + x_S}{2}[/tex]
[tex]5 = \frac{x + 6}{2}[/tex]
[tex]10 = x + 6[/tex]
[tex]x = 4[/tex]

[tex]y_M = \frac{y_R + y_S}{2}[/tex]
[tex]7 = \frac{y + 9}{2}[/tex]
[tex]14 = y + 9[/tex]
[tex]y = 5[/tex]

[tex]\therefore R(4, 5)[/tex]

The probability that you will win a game is 0.18. if you play the game 504 times, what is the most likely number of wins?

Answers

.18 × 504 will give you the answer

Using 8(-20) in a real world situation

Answers

Maybe, the price went down $20 eight times?

Determine the order in which an inorder traversal visits the vertices of the given ordered rooted tree.

Answers

I think you forgot to include the diagram, the answer is d,b,f,e,g,a,c.

Explanation:

The left subtree of the root approaches first which is namely the tree rooted at b. There again the left subtree approaches first so the list begins with d. Afterwards that approaches b the root of this subtree and then the right subtree of b specifically in order f, e and g. At that point approaches the root of the whole tree and finally its right child. Thus the answer is d,b,f,e,g,a,c.

What key features of a polynomial can be found using the fundamental theorem of algebra and the factor theorem?

Answers

The number of zeroes the polynomial has

Answer:

The key fundamental theorem of algebra says that degree of polynomial is equal to number of zeros in a function.The Factor Theorem states that a first degree binomial is a factor of a polynomial function if the remainder, when the polynomial is divided by the binomial, is zero.

The perimeter of a rectangle is 56 feet. Describe the the possible lengths of a side if the area of the rectangle is not to exceed 132 square ft

Answers

P = 2(L + W)
56 = 2(L + W)
56/2 = L + W
28 = L + W.....L = 28 - W

A = L * W
132 = W(28 - W)
132 = -W^2 + 28W
W^2 - 28W + 132 = 0
(W - 6)(W - 22) = 0

W - 6 = 0 L = 28 - W
W = 6 L = 28 - 6
L = 22

W - 22 = 0 L = 28 - W
W = 22 L = 28 - 22
L = 6

not sure which (length or width)....one of them is 6 ft and the other is 22 ft

The possible lengths of sides of the rectangle will be [tex](6,22)[/tex] or [tex](22,6)[/tex] .

What is area ?

Area is the space which is occupied by any [tex]2D[/tex] surface.

Area of rectangle [tex]=Length\ *\ Breadth[/tex]

Perimeter of rectangle [tex]=2(Length\ +\ Breadth)[/tex]

We have,

Perimeter of rectangle [tex]=56[/tex] feet

Area of rectangle [tex]=132[/tex] squared feet

Let,

Length of rectangle [tex]=x[/tex]

Breadth of rectangle [tex]=y[/tex]

So,

Perimeter of rectangle [tex]=2(Length\ +\ Breadth)[/tex]

[tex]56=2(x+y)[/tex]

[tex]28=(x+y)[/tex]

⇒ [tex]x=28-y[/tex] [tex]........(i)[/tex]

Now,

Area of rectangle [tex]=Length\ *\ Breadth[/tex]

[tex]132=x\ *\ y[/tex] [tex]........(ii)[/tex]

Now substitute value of [tex]x[/tex] in [tex](ii)[/tex],

[tex]132=(28-y)y[/tex]

[tex]132=28y-y^2[/tex]

⇒[tex]y^2-28y+132=0[/tex]

Now using Middle term split method;

[tex]y^2-28y+132=0[/tex]

[tex]y^2-22y-6y+132=0[/tex]

[tex]y(y-22)-6(y-22)=0[/tex]

[tex](y-6)(y-22)=0[/tex]

⇒

[tex](y-6)=0[/tex]

⇒ [tex]y=6[/tex]

[tex](y-22)=0[/tex]

⇒ [tex]y=22[/tex]

So,

Now if we take [tex]y=6[/tex], then

[tex]x=28-6[/tex]

[tex]x=22[/tex]

And,

if we take [tex]y=22[/tex], then

[tex]x=28-22[/tex]

[tex]x=6[/tex]

So, the possible lengths of sides of the rectangle are [tex](6,22)[/tex] or [tex](22,6)[/tex] .

Hence, we can say that he possible lengths of sides of the rectangle are [tex](6,22)[/tex] or [tex](22,6)[/tex] .

To know more about rectangle click here

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What's 10⁄12 written as a fraction in simplest form?

A. 5⁄6
B. 10⁄6
C. 3⁄5
D. 5⁄12

Answers

That would be
A. 5/6

A. 5/6 because 10/12 divided by two would = 10 divided by 2=5 and 12 divided by 2=6

How many different committees can be formed from 10 teachers and 41 students if the committee consists of 2 teachers and 2 students?

Answers

If we define "n choose r" as C(n,r)=n!/(r!(n-r)!)
where C(n,r) represents the number of ways (order not important) we can choose r objects out of n, then

Number of ways to choose teachers = 10 choose 2 = C(10,2), and
number of ways to choose students = 41 choose 2 = C(41,2)

So the number of different committees
= C(10,2)*C(41,2)
= 45*820
= 36900

[tex]10C2\cdot41C2=\dfrac{10!}{2!8!}\cdot\dfrac{41!}{2!39!}=\dfrac{9\cdot10}{2}\cdot\dfrac{40\cdot41}{2}=36,900[/tex]

Which number is greater? 0 -1 -25 -50?

Answers

The greatest number in this group is 0.
Remember that with positive numbers, 50 is greater than 1, but with negative numbers, -1 is greater than -50.
If that confuses you, think of it like this.
If you owe someone 1 dollar, you yourself have more than if you owe someone 50 dollars. You yourself have even more if you don't owe any money.

If, on average, Bob can make a sale to every 3rd person that comes into his store, how many people must come into Bob�s store if he wanted to make approximately fifteen (15) sales?

Answers

(1/3)n = 15
n = 3 * 15 = 45

An ellipse has vertices along the major axis at (0, 8) and (0, –2). The foci of the ellipse are located at (0, 7) and (0, –1). What are the values of a, b, h, and k, given the equation below? (y-k)^2/a^2+(x+h)^2/b^2=1

Answers

check the picture below, so it looks like so.

now hmm, from the provided vertices and focus point, you can pretty much see what "a" is, half of the major axis, is just 5.

now, the center is from either vertex to half-way up, or "a" units up, so say from -2 + 5, is at 3, so the center is at 0, 3.

now, the distance from a focus point to the center, is 4 units, like say from 0, 3 up to 0,7.

[tex]\bf \textit{ellipse, vertical major axis}\\\\ \cfrac{(y-{{ h}})^2}{{{ a}}^2}+\cfrac{(x-{{ k}})^2}{{{ b}}^2}=1 \qquad \begin{cases} center\ ({{ h}},{{ k}})\\ vertices\ ({{ h}}, {{ k}}\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{{{ a }}^2-{{ b }}^2}\\ ----------\\ h=0\\ k=3\\ a=5\\c=4 \end{cases} \\\\\\ \cfrac{(y-3)^2}{5^2}+\cfrac{(x-0)^2}{b^2}=1[/tex]

now, let' s find "b".

[tex]\bf c=\sqrt{a^2-b^2}\implies c^2=a^2-b^2\implies b^2=a^2-c^2 \\\\\\ b=\sqrt{a^2-c^2}\implies b=\sqrt{5^2-4^2}\implies b=3[/tex]

so, just plug that in.

Answer: The values for a, b, h, and k are a = 5, b = 3, h = 0, k = -3.

Step-by-step explanation: In this problem, we know ellipse has vertices along the major axis at (0, 8) and (0, -2). The foci of the ellipse are located at (0, 7) and (0, -1). We are asked to determine the values of a, b, h, and k.

We were also then provided with the equation for vertical eclipse:

[tex]\frac{(x-h)^2}{b^2} + \frac{(y -k)^2}{a^2}[/tex]

Before we begin, we need to first define our values for a, b, h, and k.

a - distance to vertices from the centerb - distance to co-vertices from the center(h, k) - represents the center of the eclipse

The first step, we need to determine the center of the eclipse. We can use the midpoint formula to determine the midpoint between the vertices along the major axis: (0, 8) and (0, -2).

[tex]M = (\frac{x_{1} +x_{2} }{2} , \frac{y_{1} + y_{2} }{2} )[/tex]

[tex]M = (\frac{0 + 0}{2} , \frac{-2 + 8}{2} )\\M = (0, 3)[/tex]

We now know that our center (h, k) is (0, 3). Which means our values for h and k are 0 and 3. Next, we have to determine our values for a and b. Considering the center of our eclipse is not at the center, we can use one of our vertices to determine our value for a.

[tex]V_{1}[/tex] = (h, k±a)

(0, 8) = (0, 3±a)

3 ± a = 8

±a = 5

Now, we know that a = 5. For us to get b, we need to use this formula: [tex]c^2 = a^2 - b^2[/tex]. Let's rewrite this formula, so we can focus on getting our b-value.

[tex]c^2 - a^2 = -b^2[/tex]

For us to use this formula, we need to determine our c value. To find our c-value, we have use of our foci points: (h, k±c). C is the units away/further from the center towards our foci points.

(0, 3±c) = (0, 7)

3 + c = 7

7 - 3 = c

4 = c

Now, we know that our value for c is 4. Now, let's plug into the formula.

[tex](4)^2 - (5)^2 = -b^2\\16 - 25 = -b^2\\\frac{-9}{-1} = \frac{-b^2}{-1} \\\sqrt{b^2} = \sqrt{9} \\b = 3[/tex]

Our value for b is 3. If we put into our eclipse formula:

[tex]\frac{(x-0)^2}{3^2} + \frac{(y -(-3))^2}{5^2}[/tex]

A telephone pole cast a shadow that is 34 m long find the height of the telephone pole if a statue that is 36 cm tall cast a shadow 77 cm long ?

Answers

check the picture below

solve for "p".

Answer:

16 cm approximately

Step-by-step explanation:

We are given that a telephone pole cast shadow that is 34 m long .We are given that a statue that is 36 cm long and shadow of statue is 77 cm long.

We have to find the length of telephone pole

Let height of pole

Using direct proportion

[tex]\frac{x}{34}=\frac{36}{77}[/tex]

By multiply property of equality then we get

[tex]x=\frac{36}{77}\times 34[/tex]

x=[tex]\frac{1224}{77}[/tex]

x=15.896 cm

Hence, the height of telephone pole=15.896 cm=16 cm approximately

Guess the value of the limit (correct to six decimal places). (if an answer does not exist, enter dne.) lim hâ0 (4 + h)5 â 1024 h

Answers

[tex]\displaystyle\lim_{h\to0}\frac{(4+h)^5-1024}h=\lim_{h\to0}\frac{(4+h)^5-4^5}h[/tex]

Recall the definition of the derivative of a function [tex]f(x)[/tex] at a point [tex]x=c[/tex]:

[tex]f'(c)=\displaystyle\lim_{h\to 0}\frac{f(c+h)-f(c)}h[/tex]

We can then see that [tex]f(c)=c^5[/tex], and by the power rule we have [tex]f'(c)=5c^4[/tex]. Then replacing [tex]c=4[/tex], we arrive at

[tex]\displaystyle\lim_{h\to0}\frac{(4+h)^5-4^5}h=5\times4^4=1280[/tex]

Alternatively, we could have expanded the binomial, giving

[tex]\dfrac{(4+h)^5-4^5}h=\dfrac{(4^5+5\times4^4h+10\times4^3h^2+10\times4^2h^3+5\times4h^4+h^5)-4^5}h[/tex]
[tex]=\dfrac{1280h+640h^2+160h^3+20h^4+h^5}h[/tex]
[tex]=1280+640h+160h^2+20h^3+h^4[/tex]

and so as [tex]h\to0[/tex] we're left with 1280, as expected.

A store is offering a 20% discount on all sales over $50 if you purchase a T-shirt and a pair of jeans for $62.50 what is the amount of the discount you would receive

Answers

$12.50.

($62.50*0.2) = 12.5

Therefore, you would get a discount of $12.50. Total price would be $62.50 - $12.50.

The discount on the purchase of a T-shirt and a pair of jeans costing $62.50 with a 20% discount policy is $12.50.

A store's discount policy offers 20% off for purchases over $50. The question involves calculating the discount amount when a T-shirt and a pair of jeans are purchased together for $62.50. To determine the discount, we simply multiply the total purchase amount by the discount rate.

Step-by-Step Calculation:

First, confirm the purchase amount qualifies for the discount. The combined cost of the T-shirt and jeans is $62.50, which is above $50, so the purchase qualifies for the discount.

Calculate the discount by multiplying the total purchase amount by the discount rate: $62.50 × 0.20 (which is the same as 20%).

Discount Amount = $62.50 × 0.20 = $12.50.

Therefore, the amount of the discount the customer would receive on the purchase of the T-shirt and jeans is $12.50.

Find the length of the third Angelou a triangle given that the first two angels are 35 and 70 show your work

Answers

angles in a triangle = 180 degrees

70 +35 = 105 degrees

180-105 = 75 degrees

3rd angle = 75 degrees

Which pair of non-congruent figures must be similar? two squares two parallelograms (not rectangles) two right triangles two isosceles triangles (not equilateral)

Answers

Similar figures are figures which has the same shape however they do not always have the same size. It should not be used interchangeably with congruent figures since the latter would refer to figures which has the same size and shape. Thus, congruent figures are always similar figures but similar figures are not always congruent figures. From the choices given, I think the best choice would be the first option. The two squares would be the pair of non-congruent figures that are always similar. This is because no matter what are the side lengths of the squares, it will always have the form of the square.

The blades of a windmill turn on an axis that is 40 feet from the ground. The blades are 15 feet long and complete 3 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.

a is the .
The vertical shift, k, is the... length of a blade, height of a windmill, or numbers of rotations per minute.
a =
k =

Answers

Draw a diagram (shown below) to illustrate the problem.

The rotational speed is
ω = (3 rev/min)*(1 min/60 s)*(2π rad/rev) = π/10 rad/s
The period is
T = 2π/ω = 20 s

The amplitude of the rotational motion is equal to the radius of 15 ft.

At t=0, the height of the tip of the blade is horizontal to the right, therefore its motion relative to the ground is given by
[tex]y=15 sin( \frac{ \pi t}{10})+40 [/tex]

A plot of the motion is shown below.

Step-by-step explanation:

Let (-7, -4) be a point on the terminal side of theta. Find the exact values of Sin, CSC and COT

Answers

First you need to get the radius of the circle. We do that by using the (x,y) point. So we have (-7, -4).

To get the radius, we us the following formula.

r = √(-7)² + (-4)²

This reads:
radius = square root of -7 to the power of 2 plus -4 to the power of 2.

I am new here and I am not sure if they support latex. Other wise I would of used latex.

Ok so r (radius) = r = √(-7)² + (-4)² = √65

r = √65

Now we have our radius we can find the values for sin csc and cot

sin = y / r
csc = r / y
cot = x / y

I will do the first one for you which is sin.

sin = y / r = -4 / √65

The above is saying sin = y divided by r = -4 divided by the square root of 65.

If you need help with the others let me know.

The above is saying sin = y divided by r = -4 divided by the square root of 65.

what is the answer to 11 over 7 in improper fractions

Answers

if its improper fraction is 11/7 if you want the mixed number its 1 4/7

if u change it to a proper fraction it would be a mixed number and the mixed number is 1 4/7

How many outfits are possible from 4 pairs of jeans 6 shirts and 2 pairs of shoes? Assume that outfit consists of 1 pair of jeans, 1 shirt, and 1 pair of shoes

Answers

there would be two complete outfits
and the rest would a least be missing either pants or shoes

multiply jeans by shirts by shoes

so 4 x 6 x 2 = 48 different combinations

a total of 321 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold

Answers

Joey, divide the total of 321 by 3. that's the number of adult tickets. double that answer and that's the number of student tickets.

student tickets= adult tickets* 2

total tickets= ST + AT

subbing in ST=2*AT into total=ST+AT

Total= 2*AT + AT

Total=3AT

321=3AT

AT=321/3=107

Total= ST +AT

321= ST + 107
321-107=ST
ST=214

write an expression for the area of the rectangle

Answers

l*w or length time width

What is the median of the data set given below? 19, 22, 46, 24, 37, 16, 19, 33

Answers

u have to put tje numbers in order...
16,19,19,22,24,33,37,46....the median is the middle number. If there is an even number of numbers, like this one, there will be 2 middle numbers. Find those 2 middle numbers, divide them by 2, and that is ur median.

start from the ends and count inwards till u come to the 2 middle numbers...
(22 + 24) / 2 = 46/2 = 23

** now if there would have been an odd number of numbers, u would just have 1 middle number, and that number would be the median.

To find the median, first arrange the data in either ascending or descending order;

16,19,19, 22, 24, 33, 37, 46

If the total amount of data [let's take it as n] is odd, then the median is data on [[tex] \frac{n}{2} [/tex]].

But here the total amount of data is even [n=8], so the median is the average of the data on [[tex] \frac{n}{2} [/tex]] and [[tex] \frac{n}{2} +1[/tex]].

So the median is

[tex] \frac{22+24}{2} = \frac{46}{2} = 23[/tex]

A total of 279 tickets were sold for the school play. they were either adult or student tickets. the number of student tickets sold was two times the number of adult tickets sold. how many adult tickets were sold?

Answers

s=2a

a+s=279, using a from above in this equation gives you:

a+2a=279 combine like terms on left side

3a=279 divide both sides by 3

a=93

So 93 adult tickets were sold.

Final answer:

The number of adult tickets sold for the school play is 93, calculated by setting up an equation based on the information that the total tickets sold were 279 and student tickets were two times the number of adult tickets.

Explanation:

The question asks us to determine the number of adult tickets sold when a total of 279 tickets were sold for the school play, and the number of student tickets is two times the number of adult tickets sold. We can set up an equation to solve this problem.

Let A be the number of adult tickets, and S be the number of student tickets. The problem gives us two equations:

S = 2A (The number of student tickets is two times the number of adult tickets)

A + S = 279 (The total number of tickets sold is 279)

Substituting the first equation into the second gives us:

A + 2A = 279

3A = 279

A = 279 / 3

A = 93

Therefore, 93 adult tickets were sold for the school play.

Line segment AB is congruent to line segment CD.
A.AB overbar similar to CD overbar
B.AB overbar congruent to CD overbar
C. AB overbar equal to CD overbar
D. AB overbar element to CD overbar

Answers

When two line segments are congruent, what it really means is that the length of the line segments are equal. Congruent is usually interchanged with the word equal since it means the same: equal lengths. However, congruent is very specific in the sense that it means “equal lengths”. When we say equal alone, it may refer to different properties, congruent however is very specific.

Now the answer to this question should be:

B. AB overbar congruent to CD overbar

Not similar, not equal, and definitely not element. What we mean in this case is “equal lengths”, therefore the perfect word is congruent.

Find an ordered pair (x , y) that is a solution to the equation

Answers

4x+y = 3
if x = 0, y = 3

ordered pair (0,3)

Solve the equation by graphing. x^2+14x+45=0 First, graph the associated parabola by plotting the vertex and four additional points, two on each side of the vertex. Then, use the graph to give the solution(s) to the equation. If there is more than one solution, separate them with commas.

Points:
Solution(s):

Answers

wheres the image or graph so i can help u?

ok, we know that for
y=ax²+bx+c
the x value of the vertex is -b/(2a)
so
y=1x²+14x+45
vertex is -14/(2*1)=-14/2=-7

sub back to find y value
y=(-7)²+14(-7)+45
y=49-98+45
y=-4
the vertex is (-7,-4)

some other points are
(1,60)
(-1,32)
(-8,-3)
(-9,0)

we see that the solutions to y=0 and y=x^2+14x+45 is at x=-9 and x=-5

What is a non example of a rate

Answers

I would answer this question by addressing the opposite. A rate is any number that indicates amount of anything per unit time. The essential detail here is rates always express how fast a thing could go. Therefore, any parameter that does not indicate amount of time is a non example of a rate.

The adult child radio at a local daycare center is 3 to 16.at the same rare how many adults are needed for 48 children?

Answers

[tex]\bf \cfrac{adult}{child}\qquad \cfrac{3}{16}=\cfrac{a}{48}\implies \cfrac{48\cdot 3}{16}=a[/tex]

To find the number of adults needed for 48 children at a daycare with an adult to child ratio of 3:16, we set up a proportion and solve for the unknown number of adults. We cross-multiply and divide to find that 9 adults are required.

The question asks us to calculate how many adults are needed for 48 children in a daycare center given an adult to child ratio of 3:16. To solve this, we need to set up a proportion based on the ratio and solve for the number of adults needed.

We have the ratio of adults to children as 3:16, which means for every 3 adults, there are 16 children. To find out how many adults are needed for 48 children, we set up the proportion:

3 adults / 16 children = x adults / 48 children

Now we cross-multiply and solve for x:

(3 adults) / (48 children) = (16 children)

144 = 16x

x = 144 / 16

x = 9

Therefore, 9 adults are needed to take care of 48 children at the daycare center.

Find the percent equivalent to the ratio 8 to 20

Answers

12 to 25 ==> 12/25 = 0.48 ===> 0.48*100 = 48%

divide the ratio:

8/20 = 0.4

0.4 = 40%

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