Cynthia Besch wants to buy a rug for a room that is 29 ft wide and 30 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 756 square feet of carpeting. What dimension should the rug have?
Answers
Answer:
Dimensions of rug:
Length = 28 ft
Width = 27 ft
Step-by-step explanation:
The given dimensions of the room is:
Length = 30 ft
Width = 29 ft
Area of carpeting = 756 sq ft
Kindly refer to the attached image.
Let the uniform strip around floor is of length = [tex]x[/tex] ft
This [tex]x[/tex] feet will be 2 times along the length and
2 times along the width of room.
So, length of rug = 30 -2 [tex]\times[/tex] [tex]x[/tex] and
Width of rug = 29 -2 [tex]\times[/tex] [tex]x[/tex]
It will be rectangular in shape.
Area of a rectangle is given as:
[tex]A = Length\times Width[/tex]
[tex]756 = (30-2x) (29-2x)\\\Rightarrow 756 = 870 - 118x+4x^2\\\Rightarrow 4x^2-118x+114=0\\\Rightarrow 2x^2-59x+57=0\\\Rightarrow 2x^2-57x-2x+57=0\\\Rightarrow x =1, -\dfrac{57}{2}[/tex]
Negative length not possible.
So,Length of strip, [tex]x = 1\ ft[/tex]
Dimensions of rug:
Length = 30 -2 = 28 ft
Width = 29 -2 = 27 ft
Related Questions
I need to answer this using dimensional analysis and the answer must be written in Scientific notation. I can't figure it out.
Answers
Answer:
3.343481472 x 10^4
Step-by-step explanation:
11.6 a = 3.25 *
6.18 * = 2.5 #
Take the first equation and solve for *
11.6 a = 3.25 *
Divide each side by 3.25
11.6 a/3.25 = *
3.569230769 a = *
Substitute this into the second equation for *
6.18 (3.569230769 a) = 2.5 #
22.05784615 a = 2.5 #
Solve for a
Divide by 22.05784615
a = 2.5 # / 22.05784615
a = .113338355
We have 2.95 x 10 ^5 a
2.95 x 10 ^5 ( .113338355)
33434.81472
Changing to scientific notation
3.343481472 x 10^4
the cost of a yard string at eleven cents per inch
Answers
Answer:$1.32
Step-by-step explanation:
3[-X + (2 x + 1)] = x - 1
X=?
Answers
Answer: -2
Step-by-step explanation: 2x/2 = -4/2
EXPLAINATION
3(-x+2x + 1)= x - 1
3(x+1) = x - 1
3x + 3 = x - 1
3x - x = -1-3
2x = -4 *DIVIDE BOTH SIDES*
x = -2
How would I solve this problem?
Answers
Answer:
(x+1)²=-1
Step-by-step explanation:
x²-7x=-9x-2
x²+2x+2=0
If you solved this using the quadratic formula, you’d end up with -1+i and -1-i.
but if you subtracted 1 from both sides, you’d have
x²+2x+1=-1
Which is:
(x+1)²=-1
Help meeeeeeeeeeeee!!!!!
Answers
Answer:
B
Step-by-step explanation:
A constant variation graph has the following format:
[tex]y=kx[/tex]
Where k is the constant of proportionality.
Let's pick a point from the graph, say, (1,5).
Substitute 1 for x and 5 for y:
[tex]5=1(k)[/tex]
Simplify:
[tex]5=k[/tex]
Therefore, the constant of proportionality is 5.
And we're done!
The quotient of 1/3 and 4/3
Answers
Answer:
1/ 4
Step-by-step explanation:
The question can also be written as [tex]\frac{1}{3} /\frac{4}{3}[/tex] .
Because it's division of fractions, you can multiply to find the answer by making 4/3 into 3/4. So
1/ 3 times 3/4 = 3/12 = 1/4
Answer:
if you're trying to find the quotient then the answer is: 4/9
if you're trying to add then the answer is: 5/3
if you're trying to divide then the answer is: 4/9
if you're trying to multiply then the answer is: 4/9
if you're trying to simplify then the answer is: 4/9
Step-by-step explanation:
Complete the description of the piecewise function graphed below. Use interval notation to indicate intervals.
Answers
Answer:
{ -2 if x ∈ -4 < x < -3
{ -5 if x ∈ -3 ≤ x < 2
[ 5 if x ∈ 2 ≤ x < 5
Step-by-step explanation:
From the graph, we have;
{ -2 if x ∈ -4 < x < -3
For the next inequality line at y = -5, we have;
1) The inequality line, starts with an open circle on the left at x = -3, which is equivalent to less than or equal to symbol, ≤ as -3 ≤ x because the point x =-3 is the left boundary. The inequality line extends to the point x = 2, where we have a closed circle (on the right), which is equivalent to a x ≤ 2 with the 2 on the right hand side because, the 2 is the right boundary of the inequality
2) The inequality can be summarized as starting from x = -3 extends to x = 2
3) As stated in point 1) the point x = 3, we have -3 ≤ x and at point x = 2, we have x ≤ 3 which can be combined as -3 ≤ x < 2, to give;
{ -5 if x ∈ -3 ≤ x < 2
For the next inequality line at y = 5, we have;
1) The inequality line, starts with an open circle on the left at x = 2, which is equivalent to less than or equal to symbol, ≤ as 2 ≤ x because the point x =2 is the left boundary. The inequality line extends to the right to reach point x = 5, where we have a closed circle (on the right), which is equivalent to a x ≤ 5 inequality, with the 5 on the right hand side because, the 5 is the right boundary of the inequality
2) The inequality can be summarized as starting from x = 2 extends to x = 5
3) As stated in point 1) the point x = 2, we have 2 ≤ x and at point x = 5, we have x ≤ 5 which can be combined as 2 ≤ x < 5, to give;
[ 5 if x ∈ 2 ≤ x < 5.
Answer:
1st box = [-4, -3]
2nd box = (-3, 2]
3rd box = (2, 5]
For f(x) = -2 we see that x is between -4 to -3 with closed endpoints.
So the interval will be [-4, -3].
For f(x) = -5 we see that x is between -3 to 2 with closed endpoint at 2 and open endpoints at -3.
So the interval will be (-3, 2].
For f(x) = 5 we see that x is between 2 to 5 with open endpoint at 2 and closed endpoint at 5.
So the interval will be (2, 5].
Learn more: https://brainly.com/question/16236436
plzz help me i need it ill mark you as brlanlest
Answers
Answer:
I believe that the answer is c or -9
Step-by-step explanation:
An absolute value is the distance from 0
F is -10 therefore |F| = |-10| = 10.
E is 1 therefore |E| = |1| = 1
10 + 1 = 11
Meaning the answer would be: B
Hope this Helped!
which point is the midpoint of AE
Answers
Midpoint is D
Point D is the midpoint of points A and E for the given number line.
What is a number line?A number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.
A horizontal number line is the most common representation and can be extended infinitely in any direction.
Given the number lines with labeled points as A, B, C, D, and E.
The midpoint of AE is the mean of AE
Mean of AE ;
(A + E )/ 2 = (- 6 + 8) / 2
2 / 2 = 1 which is point D
Therefore "D" will be the midpoint of A and E.
Hence "Point D is the midpoint of points A and E for the given number line".
To learn more about the number line,
https://brainly.com/question/13189025
#SPJ2
The quotient of a and 8 number
Answers
Answer:
a/8 or a over 8 hope this helps
Step-by-step explanation:
Answer:
n
8
→
I used
n
as the unknown number
Explanation:
The quotient is the result of division between two numbers.
The quotient of a number (I used
n
) and
8
would be
n
8
A __ is as polynomial with two terms.
Answers
Answer:
Bionominal
Step-by-step explanation:
Question:
A ____ is a polynominal with two terms.
Answer:
A Bionominal is a polynominal with two terms.
Bionominal is your answer.
Hope this helps!
the thickness of a surfboard relates to the weight of the surfer.a surfboard is 21 3/16 inch thick.write each dimension as a decimal.
Answers
Answer:
https://tex.z-dn.net/?f=%5Cunderline%7B0.1875%7D%5C%5C3%3A16%5C%5C%5Cunderline%7B0%7D%5C%5C30%5C%5C%5Cunderline%7B16%7D%5C%5C140%5C%5C%5Cunderline%7B128%7D%5C%5C.%5C%20120%5C%5C%5Cunderline%7B.%5C%20112%7D%5C%5C.%5C%20%5C%2080%5C%5C%5Cunderline%7B.%5C%20%5C%2080%7D%5C%5CR%3D0Step-by-step explanation:
The area of the surface of the largest known star is about 1015 square miles. The area of the surface of the Earth is about 1011 square miles. How many times larger is the star's area?
Answers
Answer:
The surface area of the star is approximately 1.004 times larger than the earth's surface area
Step-by-step explanation:
To find the number of times b which the area of the star is larger than that of the earth, we will divide the area of the area of the star by the area of the earth.
Area of surface of star = 1015 square miles
Area of surface of the earth = 1011 square miles
∴ (Area of star) ÷ (Area of the earth)
= 1015 ÷ 1011 = 1.00395 times
Therefore the surface area of the star is approximately 1.004 times larger than the earth's surface area
Can someone help me please
Answers
Step-by-step explanation:
kindly see attached picture
hope it helped you:)
Answer:
[tex]\sf \dfrac{{x}^{a \: (b - c)} }{ {x}^{b \: (a - c)} } \: \div \: \bigg \lgroup \dfrac{ {x}^{b} }{ {x}^{a} } \bigg \rgroup^{c} \: = \: 1[/tex]
[tex]\\[/tex]
Now,
[tex]\sf \dfrac{{x}^{ab \: - \: ac} }{ {x}^{ba \: - \: b c} } \: \div \: \bigg \lgroup \dfrac{ ({x}^{b} )}{( {x}^{a}) } \bigg \rgroup^{c} \: = \: 1[/tex]
[tex]\\[/tex]
[tex]\sf \dfrac{{x}^{ab \: - \: ac} }{ {x}^{ba \: - \: b c} } \: \div \: \dfrac{ {x}^{bc} }{{x}^{ac} } \: = \: 1[/tex]
[tex]\\[/tex]
We know that, When sign change from division to multiplication we should do reciprocal of next number.
Therefore we get,
[tex]\sf \dfrac{{x}^{ab \: - \: ac} }{ {x}^{ba \: - \: b c} } \: \times \: \dfrac{ {x}^{ac} }{{x}^{bc} } \: = \: 1[/tex]
[tex]\\[/tex]
[tex]\sf \dfrac{{x}^{ab \: - \: \cancel {ac }\: + \: \cancel{ac}} }{ {x}^{ba \: - \: \cancel{ b c} \: + \: \cancel{bc}} } \: = \: 1[/tex]
[tex]\\[/tex]
[tex]\sf \dfrac{{x} \: ^{ \cancel{ab}} }{ {x} \: ^{\cancel{ba}} } \: = \: 1[/tex]
[tex]\\[/tex]
[tex] \bigstar \: \: \underline{ \boxed{\sf x \: = \: 1}} \: \: \bigstar[/tex]
[tex]\\[/tex]
[tex] \huge\bf \dag \: \gray{RHS = LHS} \: \dag[/tex]
[tex]\\[/tex]
[tex]\large \star \: \tt Hence, Verified \: \star[/tex]
I need help please !!!!!
Answers
16- 12 cm
17- 49 mi
18- 14 ft
Three copies of this rectangle were connected along a side to make a larger rectangle. What could the perimeter of the new rectangle be? Consider all possibilities.
Answers
Answer:
388in or 202in
Step-by-step explanation:
I decided to connect three copies of this rectangle, all along the right side of the rectangle in the picture above.
When this is done the new length along the bottom and top become 45×4=180.
Now to find the perimeter, 180+180+14+14=388in
Other possibility
Connect the three copies along the top.
Now we need to do 14×4=56, which is the new side length.
Now to find the perimeter, 56+56+45+45=202in
6x + 3(x + 1.15) gfgfdgfdgdfgfdgfggfdgfdgfddfdfgdfgdf
Answers
Answer:
9x+3.45
Step-by-step explanation:
Let's simplify step-by-step.
6x+3(x+1.15)
Distribute:
=6x+(3)(x)+(3)(1.15)
=6x+3x+3.45
Combine Like Terms:
=6x+3x+3.45
=(6x+3x)+(3.45)
=9x+3.45
Answer:
6x+3x+3.45
Step-by-step explanation:9x +3.45
x=3.45/9 ans
Given f(x) = -4(6x - 5) + 60, what is the value of f(4)?
Answers
Answer:
[tex]f=-6x+20[/tex]
Step-by-step explanation:
Just solve f(4) = -4(6x - 5) + 60
After learning how to fly, Wendy reduced her daily commute time by 75\%75%75, percent. Previously, her commute took mmm minutes.
Which of the following expressions could represent Wendy's commute time, in minutes, after she learned how to fly?
Answers
Answer: 1/4 and 0.25
Step-by-step explanation:
Answer:
0.25m & 1/4
This question is incomplete, it is very signficant that the questions are complete.
Step-by-step explanation:
select the statement that is false.
•variables represent unknown values.
• variables are placeholders in math expressions and equations.
• mathematical operations can be performed on variables.
• variables cannot be represented by the letter t.
Answers
Answer:
number 3 is incorrect the rest are correct
What is p-^m divided by p^n equal to? Answers p-^m + n P-^m• n p-^m - n P-^m divided by n
Answers
Answer:
The answer is
[tex] {p}^{ - m - n} [/tex]Step-by-step explanation:
[tex] \frac{ {p}^{ - m} }{ {p}^{n} } [/tex]Using the rules of indices.
Since the bases are the same and are dividing we subtract the exponents
That's
[tex] \frac{ {x}^{y} }{ {x}^{z} } = {x}^{y - z} [/tex]So from the question we have
[tex] \frac{ {p}^{ - m} }{ {p}^{n} } = {p}^{ - m - n} [/tex]Hope this helps you
Jen had 7 blocks that each weighed 5 kg. How much did the blocks weigh all together
Answers
Answer:
35kg
Step-by-step explanation:
HELP ME!!
1. What is a variable?
2. Solve the following equations:
3x + 6 - X + 82 = 44
Show your work for the equations.
Answers
A variable is a letter that represents another number or thing.
Steps to solve:
3x + 6 - x + 82 = 44
~Combine like terms
2x + 88 = 44
~Subtract 88 to both sides
2x = -44
~Divide 2 to both sides
x = -22
Best of Luck!
Which ordered pair is on the inverse of f(x)?
Answers
Answer: (-1,-2)
Step-by-step explanation: I just did it
I need the percentage of the shaded area.
Answers
Answer:
1.22
Step-by-step explanation:
Since there is one whole shaded. And 2 tens, and 2 ones. Its 1.22.
Help me please!!!!!!!!
Answers
Answer:
The first part/question sounds like a Division problem because theirs 18 guests and each slice feeds 6 people. Therefore, Laura orders 3 boxes of Pizzas. But make sure you try Photomath,V3, or Khan Academy apps before you write down the answer to the first question.
What’s the right anwser?
Answers
-8x-104=2x-14+4x
-8x-104=2x+4x-14
-8x-104=6x-14
Hope this can help.
the 3rd option
-8(x+13)=2(x-7)+4x
-8x - 104 = 2x - 14 + 4x
-8x - 104 = 2x + 4x - 14
-8x - 104 = 6x - 14
find the width, height, and area of a 50 inch TV with a 16:9 aspect ratio
Answers
Answer:
50
Step-by-step explanation:
what is 8+8-2X5-1+22 ????
Answers
Answer:
27
Step-by-step explanation:
8+8+(-2x5)-1+22
8+8+(-10)-1+22
16+22-11
27
Evaluate this expression for c=6, and a=2. c-a
Answers
Answer:
4
Step-by-step explanation:
6-2 = 4
Answer:
4Step-by-step explanation:
[tex]c = 6 \\ a = 2 \\ c - a = [/tex]
Plug in the given values into the equation
[tex]6 - 2 = 4[/tex]