A square rug lies in the middle of a rectangular room. There are 7 feet of uncovered floor on 2 sides of the rug and 2 feet of uncovered floor on the other 2 sides. Find a polynomial expression for the area of the room in terms of x, the side length of the rug.
Answers
A=(x+10)(x+12)
A=x²+22x+120
Polynomial expression of area of room in terms of x is A = x² + 9x + 14.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Area of rectangle(room) = Length × width
So,
A = (x + 7)(x + 2)
A = x² + 20x + 7x + 14
A = x² + 9x + 14
Hence "Polynomial expression of area of room in terms of x is A = x² + 9x + 14".
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Related Questions
Solutions for the system 10x^2 -y=48
2y=16x^2+48
Answers
Solutions are (x, y) = (-6, 312) and (6, 312).
_____
Divide the second equation by 2, then substitute the expression for y into the first equation. Solve the quadratic for x.
.. 10x^2 -(8x^2 +24) = 48
.. 2x^2 -72 = 0
.. 2(x -6)(x +6) = 0
.. x = -6 or 6
.. y = 8x^2 +24 = 8*36 +24 = 312 . . . for either value of x
Answer:
Solutions are (x, y) = (-6, 312) and (6, 312).
Step-by-step explanation:
How do I convert 12 ounces into grams. Please help
Answers
To find out how many grams equals 12 ounces, multiply 28.35 by 12.
Final answer should be 340.2 grams = 12 oz.
Hopefully this helps!
:)
Find the equation of the plane which has intercepts of (4,0,0) and (0,−2,0) and no z-intercept.
Answers
First step: find direction vector of the two points:
V = <4-0, 0-(-2), 0-0> = <4,2,0>
Since there is no z-intercept, Π must be orthogonal to the z-axis, hence the unit normal vector is Z=<0,0,1>.
To find the normal vector of the plane Π, we take the cross-product of V & Z, i.e.
Π =
i j k
4 2 0
0 0 1
= <2*1, -4*1, 0>
= <2,-4,0>
The corresponding equation of the plane through (4,0,0) is then
2(x-4)-4y+0(z-0)=0 => 2x-4y=8
Answer: The equation of the plane is 2x-4y=8
The equation of the plane which has intercepts of (4, 0, 0) and (0, -2, 0) and no z-intercept is [tex]\frac{1}{4}\cdot x -\frac{1}{2}\cdot y = 1[/tex].
A plane is represented by the following expression:
[tex]A\cdot x + B\cdot y + C\cdot z = 1[/tex] (1)
Where [tex]A,B, C[/tex] are real coefficients.
We need three distinct points to determine all coefficients of the plane. If we know that [tex](x_{1}, y_{1}, z_{1}) = (4,0,0)[/tex], [tex](x_{2}, y_{2}, z_{2}) = (0,-2,0)[/tex] and [tex](x_{3}, y_{3}, z_{3}) = (0, 0, 0)[/tex], then we have the following system of linear equations:
[tex]4\cdot A = 1[/tex] (2)
[tex]-2\cdot B = 1[/tex] (3)
[tex]0 \cdot C = 1[/tex] (4)
Then, the solution of this system is [tex]A = \frac{1}{4}[/tex], [tex]B = -\frac{1}{2}[/tex] and [tex]C = 0[/tex].
And the equation of the plane which has intercepts of (4, 0, 0) and (0, -2, 0) and no z-intercept is [tex]\frac{1}{4}\cdot x -\frac{1}{2}\cdot y = 1[/tex].
We kindly invite to check this question of planes: https://brainly.com/question/16900259
which of the following function is f(x) if f^-1(x)=5x-19
Answers
Answer: F(x)=x-19/5
Step-by-step explanation:
Tyrone’s hourly wage is $18 and his net pay is 72% of his earnings. Tyrone spends about $1,800 on his monthly expenses. If Tyrone works 40 hours per week and has no other sources of income, what is his total monthly cash inflow? (Hint: Assume that there are 4 pay periods per month.)
a. $273.60
b. $1,080.00
c. $1,800.00
d. $2,073.60
Would It Be D?
Answers
Read more on Brainly - https://brainly.com/sf/question/2415896
Answer:
Yes the Answer is
"D" $2,073.60
Step-by-step explanation:
Correct on edg. 2021
Michael has a total of 15 bills that are either $1 bills or $5 bills. If the total amount of money he has is $47, how many $5 bills does he have?
Answers
Luke purchased a motorcycle for $8,765. It depreciates about 5.3% each year. What is the value of the motorcycle after five years?
Answers
△FSB∼△ZDR .
What is the value of x?
Enter your answer.
How many units?
Answers
---------------------------------------------------------
Explanation:
The triangles are similar, so we know the corresponding sides form ratios that are equal.
Note how...
FS and ZD are the first two letters of FSB and ZDR respectively
FB and ZR are the first & last letters of FSB and ZDR respectively
Based on those two facts above, we can form this proportion
FS/ZD = FB/ZR
38/15.2 = 55/x
Solve for x
38/15.2 = 55/x
38*x = 15.2*55
38*x = 836
x = 836/38
x = 22
△FSB∼△ZDR
What is the value of x?
Enter your answer in the box.
____UNITS
Luis wants to buy a home priced at $315,000. He plans to finance this amount less the down payment required. His mortgage payment would then be $2100. Luis has an annual income of $91,500 and $65,000 in savings. Luis has a car payment of $370, a student loan payment of $165 and a credit card payment of $45. Use a 20% down payment and the 28/36 ratio to determine if Luis is eligible for a loan. What would you advise him to do if he is not eligible?
Answers
Solution:
Annual income of Luis= $ 91,500
[tex]\frac{28}{36}[/tex] ratio states that maximum of 28 % of your gross monthly income should be spent on housing finances and not more than 36% of your total monthly income should be spent on loans.
36% of $ 91,500= 0.36 × 91,500=$ 32,940(Annualy)
Total money that luis can use for loan as a monthly payment =$ [tex]\frac{32940}{12}=2745[/tex] $
Amount that Luis spent on loan Monthly =car payment of $370, a st udent loan payment of $165 and a credit card payment of $45= $ 370 + $ 165 + $ 45=$ 580
Amount that can be used for housing debt = $ 2745 - $ 580= $2165
Down Payment =
20 % of $315,000=0.20 × 315,000 =$ 63,000
Remaining amount for home that Luis has to pay = $ 315,000 - $ 63,000= $252,000 (not given in how many months or years Luis has to pay this amount )
Mortgage payment = $ 2100
Calculated Mortgage payment on $ 91,500 using 28% rule = 0.28 × 91,500=$25620 (Yearly)
Amount that Luis can use for Mortgage payment monthly=$ [tex]\frac{25620}{12}=2135[/tex] $(Calculated) Monthly
So, Money saved = 2135-2100=$ 35
If Monthly income allowable for Debt(i.e if $ 252,000 is divided into months) > or exceeds $ 2165, then Luis is not eligible for Loan.
If Monthly income allowable for Debt (i.e if $ 252,000 is divided into months )< or Less than $ 2165, then Luis is eligible for Loan.
The advise that i will give to Luis is that he should make full payment of his car debt, and stop being Extravagant i.e start saving more money if he wants to Possess a home.
A picture shows that 3 cans have the same mass as 9 identical boxes. Each can has a mass of 30 grams. What is the mass, in grams, of each box.
Answers
Final answer:
To find the mass of each box in this scenario, calculate the total mass of the cans first, then divide by the number of boxes. Each box weighs 10 grams.
Explanation:
A picture shows that 3 cans have the same mass as 9 identical boxes. Each can has a mass of 30 grams. What is the mass, in grams, of each box.
To find the mass of each box, we first calculate the total mass of the 3 cans: 3 cans * 30 grams/can = 90 grams. Since the 3 cans have the same mass as 9 identical boxes, each box's mass is: 90 grams / 9 boxes = 10 grams per box.
HELP PLEASE! −3.64⋅|−5.3|−1.53
^
Absolute value of -5.3
Answers
To solve −3.64⋅|−5.3|−1.53, calculate the absolute value of −5.3, which is 5.3, then multiply by −3.64 to get −19.292, and finally, subtract 1.53 to result in −20.822.
Explanation:You have presented a mathematical expression involving absolute value and multiplication: −3.64⋅|−5.3|−1.53. Let's solve this step by step:
First, determine the absolute value of −5.3, which is 5.3 because absolute value represents the distance of a number from zero without considering direction.Next, multiply −3.64 by the absolute value you just calculated: −3.64 * 5.3.Once you have the result of that multiplication, subtract 1.53 from it to get the final answer.
Now performing the operations:
−3.64 * 5.3 = −19.292−19.292 - 1.53 = −20.822Therefore, the result of the given expression −3.64⋅|−5.3|−1.53 is −20.822.
find the length of arc ac, cb=60degrees, ab=12ft(diameter)
Answers
Radius= diameter ÷2 =12÷2=6
And put in ur values to obtain the answer
Final answer: arc ac = 120
what is the factored form of 64g^3+8
Answers
how many different combinations of 1 odd number and 1 shape are possible
Answers
Cheryl paid 37.20 for 12 gallons of ice cream for a school picnic. How much would 1 quart of ice cream cost?
Answers
Answer:
A quart of ice cream costs $0.775
Step-by-step explanation:
This problem can be solved by a rule of three problem.
Rule of three problem:
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.
In this problem, the measures are:
- The number of gallons of ice cream
- The cost
As the number of gallons increases, so will the cost that Cheryl paid. So, the relationship between the measures is direct and we have the following rule of three.
12 gallons - $37.20
1 gallon - $x
12x = 37.20
[tex]x = \frac{37.20}{12}[/tex]
x = $3.1
Each gallon cost $3.1. Each gallon also has 4 quarts, so the cost of 4 quarts is $3.1. To find the cost of a quart of ice cream
4 quarts - $3.1
1 quart - $x
4x = 3.1
[tex]x = \frac{3.1}{4}[/tex]
x = $0.775
A quart of ice cream costs $0.775
Jen has 2 meters of taffy. She wants to give each of her 3 best friends an equal amount of taffy. How many centimeters of taffy will each friend get?
Write your answer as a mixed number in the form a b/c.
Answers
Answer:
[tex]66\frac{2}{3}[/tex] centimeters.
Step-by-step explanation:
Jen has 2 meters of taffy.
She wants to give each of her 3 best friends an equal amount of taffy.
First we convert 2 meters to centimeters.
1 meter = 100 centimeters
2 meters = 100 × 2 = 200 centimeters.
Now divide 200 cm to 3 friends
Each friend get = [tex]\frac{200}{3}[/tex]
= [tex]66\frac{2}{3}[/tex]
Each friend will get [tex]66\frac{2}{3}[/tex] centimeters of taffy.
math hw..................
Answers
One factor of f(x)= 4x^3-4x^2-16x+16 is (x – 2). What are all the roots of the function? Use the Remainder Theorem.
Answers
f(x)=4x^3-4x^2-16x+16=x^3-x^2-4x+4.
We could divide f(x) by (x-2) and solve the resulting quadratic equation.
We could, however, use another property of f(x).
We are given that.................................................... (x-2) is a factor
Knowing that the constant term is +4, and using the factor theorem, we can try (x+2) as a factor.
f(-2)=-8-4+8+4=0......................................................(x+2) is a factor
We note that f(x) has a sum of coefficients 1-1-4+4=0, equal to zero, this means that f(1)=0, or (x-1) is a factor...................................................(x-1)
Therefore all the factors of the function are (x+2)(x-2)(x-1)
and the roots are x={1,2,-2}
Is the answer to your problem
What is the slope of a line that is perpendicular to the line shown? (0, 2) (3, 0)
Answers
slope = (2-0)/(0-3) = -2/3
perpendicular lines, slope is opposite and reciprocal
so the slope of a line that is perpendicular to the line is 3/2
answer
3/2
What is the measure of
Answers
<ABC = 120 / 2
<ABC = 60
answer
A. 60
m∠ABC = (75+45)/2 = 60°
suppose a new car that cost 20 000 depreciates by 15% each year. in how many year till the car costs 7500. use the equation 7500=(20,000)(0.85)^x
Answers
3 = 8 * (0.85)^x => 0.85^x = 3/8
next, we can take the log() on both sides, and use the fact that log(a^b)=b*log(a)
log(3/8) = log(0.85^x) => log(3/8) / log(0.85) = x
If you calculate this, you find x ≈ 6.03
Two cylinders are similar. The radius of cylinder A is 5.6 inches. The radius of cylinder B is 1.4 inches. If the height of cylinder B is 4 inches, what is the height of cylinder A
Answers
Answer:
C ✔️
Step-by-step explanation:
"16 inches"
One is dollar is currently worth 84.1 Japanese yen. If you exchange 4,205 for US dollars, how much will you have?
Answers
yen/yen per dollar=dollar
Mr Richards science class is conducting a variety of expirements with projectiles and falling objects DROP DOWN ANSWERS ARE GROUPS A-D
Answers
a = g
vf = g * t + vo
rf = (1/2) * g * t ^ 2 + vo * t + ro
g: gravity
t: time
vf: final speed
Vo: initial speed
For this case what we should do is to choose the equation that best suits each statement.
We have then:
GroupA: h (t) = - 4.9 * t ^ 2 + 19 * t
Group B: h (t) = - 16 * t ^ 2 + 50 * t
Group C: h (t) = - 4.9 * t ^ 2 +19
Group D: h (t) = - 16 * t ^ 2 +50
What is the least whole number that has exactly 9 factors, including 1 and itself?
Answers
All squares of primes have exactly three factors.
So start with perfect squares (skipping perfect squares of primes)
4^2=16 {1,2,4,8,16} 5 factors.
6^2=36 {1,2,3,4,6,9,12,18,36} 9 factors.
Answer: 36 is the least whole number that has exactly 9 factors.
The volume of a cylinder is 224π cubic centimeters and its radius is 4 centimeters. What is the height of the cylinder? Enter your answer in the box.
Answers
.. V = π*r^2*h
.. 224π = π*4^2*h
.. 224π/(16π) = h = 14
The height of the cylinder is 14 cm.
_____
You have not provided a box for me to enter my answer. (Please omit such directions.)
The height of the cylinder is 14 centimetres.
To find the height of the cylinder, we use the formula for the volume of a cylinder, which is given by [tex]\( V = \pi r^2 h \),[/tex] where V is the volume, r is the radius, and h is the height.
Given that the volume V is [tex]224\pi[/tex] cubic centimetres and the radius r is 4 centimetres, we can substitute these values into the formula to solve for the height h:
[tex]\[ 224\pi = \pi (4)^2 h \][/tex]
Simplifying the equation by dividing both sides [tex]\( \pi \) and \( (4)^2 \),[/tex]we get:
[tex]\[ \frac{224\pi}{\pi \cdot 16} = h \][/tex]
[tex]\[ \frac{224}{16} = h \][/tex]
[tex]\[ 14 = h \][/tex]
Therefore, the height h of the cylinder is 14 centimetres.
A culture started with 6000 bacteria after 3 hours ot grew to 7200 bacteria Predict how many bacteria will be present after 19 hours
Answers
Answer:
19038
Step-by-step explanation:
Given : A culture started with 6000 bacteria after 3 hours to grew to 7200 bacteria
To Find: Predict how many bacteria will be present after 19 hours
Solution:
General Form of exponential function: [tex]y=ab^x[/tex]
where y is the amount after x hours
x is the time
a is the initial amount
b is the growth factor
Bacteria initial amount= a = 6000
Time = x = 3 hours
Amount of bacteria after 3 hours = 7200
Substitute the values in the general form
[tex]7200=6000(b)^3[/tex]
[tex]\frac{7200}{6000}=(b)^3[/tex]
[tex]\sqrt[3]{\frac{7200}{6000}}=b[/tex]
[tex]1.06265856918=b[/tex]
Now we are supposed to find how many bacteria will be present after 19 hours
So, Bacteria initial amount= a = 6000
Time = x = 19 hours
Amount of bacteria after 19 hours = y
Substitute the values in the formula:
[tex]y=6000(1.06265856918)^{19}[/tex]
[tex]y=19038.488[/tex]
Hence there will be approximately 19038 bacteria present after 19 hours
How many possible outcomes exist when two fair coins are flipped and a three-section spinner is spun?
Answers
The spinner can have the outcomes 1, 2, 3.
The total number of outcomes is the product of the individual numbers of outcomes.
2 * 2 * 3 = 12
Here's a way of thinking about it:
The coins can have these four outcomes:
HH
HT
TH
TT
For each of the 4 outcomes of the two coins, there are 3 different outcomes of the spinner, so the total number of possible outcomes is 4 * 3 = 12.
Answer:
12
Step-by-step explanation:
At sea, the distance D to the horizon is directly proportional to the square root of the elevation E of the observer. If a person who is 36 feet above the water can see 7.4 miles, find how far a person 49 feet above the water can see.
Answers
The person who is 36 feet above the water ⇒ √36=6
A person 49 feet above the water ⇒ √49=7
So, by proportions, you have:
(7/6)x7.4= 8.63 miles
Therefore, the answer is: a person 49 feet above the water can see 8.63 miles
#8 surface area please explain
Answers
Solving for the surface area:
Surface area of 2 triangles (top and bottom) + Surface area of 3 rectangles (sides)
2 [1/2 (2.6)(3.9)] + [ (4.3)(3.9) + (4.3)(2.6) + (4.3)(5.2) ] = 60.45 cm^2 surface area