An architect is trying different dimensions for the room shown below. Write an algebraic expression the architect can use to find the area of the room then find the area when x is 6 m. Show your work.
Answers
Answer:
x² + 12
48m²
Step-by-step explanation:
Find the diagram attached.
The room can be segregated into two rectangles
The area of the room = Area of bottom rectangle + area of the top rectangle
Area of the bottom rectangle = x * (x-3) = x² - 3x
Area of the top rectangle = 3* (4+x) = 12 + 3x
The area of the room = x² - 3x + 12 + 3x
Area of the room = x² + 12
Hence the algebraic expression that the architect can use to find the area of the room is x² + 12
Given x = 6m
The area of the room = x² + 12
The area of the room = 6² + 12
The area of the room = 36 + 12
The area of the room = 48m²
Related Questions
HOLA IM DORA AND IM GONNA NEED YOUR HELP FIGURING OUT THIS EQUATION?..... MUCHAS GRACIAS. what are the x-intercepts of the graph of y=x^2+5x+6?
A. (-2,0) and (-3,0)
B. (6,0) and (5,0)
C. (2,0) and (3,0)
D. (-6,0) and (-5,0)
Answers
Answer:
D
Step-by-step explanation:
yeah
Which fraction names the shaded part of the set?
Answers
The answer is 1/3
The fraction of the shaded part of the set is 1/3.
Given is a figure in which there are total 12 parts with 4 parts shaded.
We need to find the fraction of the shaded part of the set,
To find the fraction of the shaded part of the set, we need to determine the ratio of the number of shaded parts to the total number of parts.
In this case, the total number of parts is 12, and the number of shaded parts is 4.
Therefore, the fraction of the shaded part can be calculated as follows:
Fraction of shaded part = Number of shaded parts / Total number of parts
Fraction of shaded part = 4 / 12
Simplifying the fraction, we get:
Fraction of shaded part = 1 / 3
So, the fraction of the shaded part of the set is 1/3.
Learn more about fraction click;
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What is the domian of the following represented by ordered pairs?
{(3, 7), (-5, 1), (2, 4), (-3, 6)}
Answers
Answer:
The Domain are 3,-5,2,-3
Step-by-step explanation:
hope that helps
Answer:
The domain is (3, -5, 2, -3
Step-by-step explanation:
Plz give brainlyest
Is the relation shown in the arrow diagram a function? Justify your answer.
Alternative text
Yes. The input 0.8 and 0.4 have only one output.
Yes. Each output has only one input.
No. Each input has only one output.
No. The input 1.2 has 2 outputs.
Answers
Answer:
No. The input 1.2 has 2 outputs.
Step-by-step explanation:
See attachment for complete question
The first circle represents the domain while the second represents the range of the function.
For a mapping to be a function, it must either be a one to one relationship or a many to one relationship.
One to one, in the sense that; there can be only one entry in the domain points to one entry in the range of the function.
Many to one, in the sense that: there can be multiple domain entries that point to one entry in the range of the function
However, from the attachment it can be seen that an entry in the domain (1.2) points to two entries in the range (6 and 8).
Hence, this does not represent a function.
The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubic meters per minute. At the instant when the radius of the cone is 99 meters and the volume is 180 cubic meters, what is the rate of change of the height? The volume of a cone can be found with the equation V=\frac{1}{3}\pi r^2 h.V= 3 1 πr 2 h. Round your answer to three decimal places.
Answers
Answer:
The rate of change of the height is 0.021 meters per minute
Step-by-step explanation:
From the formula
[tex]V = \frac{1}{3}\pi r^{2}h[/tex]
Differentiate the equation with respect to time t, such that
[tex]\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)[/tex]
[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)[/tex]
To differentiate the product,
Let r² = u, so that
[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)[/tex]
Then, using product rule
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}][/tex]
Since [tex]u = r^{2}[/tex]
Then, [tex]\frac{du}{dr} = 2r[/tex]
Using the Chain's rule
[tex]\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}[/tex]
∴ [tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})][/tex]
Then,
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]
Now,
From the question
[tex]\frac{dr}{dt} = 7 m/min[/tex]
[tex]\frac{dV}{dt} = 236 m^{3}/min[/tex]
At the instant when [tex]r = 99 m[/tex]
and [tex]V = 180 m^{3}[/tex]
We will determine the value of h, using
[tex]V = \frac{1}{3}\pi r^{2}h[/tex]
[tex]180 = \frac{1}{3}\pi (99)^{2}h[/tex]
[tex]180 \times 3 = 9801\pi h[/tex]
[tex]h =\frac{540}{9801\pi }[/tex]
[tex]h =\frac{20}{363\pi }[/tex]
Now, Putting the parameters into the equation
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]
[tex]236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)][/tex]
[tex]236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386][/tex]
[tex]708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}[/tex]
[tex]708 = 30790.75 \frac{dh}{dt} + 76.36[/tex]
[tex]708 - 76.36 = 30790.75\frac{dh}{dt}[/tex]
[tex]631.64 = 30790.75\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}= \frac{631.64}{30790.75}[/tex]
[tex]\frac{dh}{dt} = 0.021 m/min[/tex]
Hence, the rate of change of the height is 0.021 meters per minute.
y
What is the equation of the graphed line written in
standard form?
3
2+
1
X=-3
y=-3
O x + y = -3
Ox-y=-3
1 2 3 4 5 X
54-3-2-14
2
-3
N
4
Answers
Answer:
A) x = -3
the line is undefined
The equation of the graphed line written in slope-intercept form is x = -3
What is the Slope-Intercept form?The graphed line in slope-intercept form, y = mx + b
To Convert it into the standard form of the equation, ax + by = c.
Consider that the points be (0, 3) and (5,0).
A Slope exists how many units it brought to go vertically or horizontally.
Which Slope doesn't exist.
The y-intercept in slope-intercept form, y = mx + b
where, m = undefined
x = -3
Therefore, the correct answer is option (A), x = -3 because the line is undefined.
To learn more about slope-intercept form
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Keesha has 12 glue bottles and 42 craft sticks.
What is the greatest number of supply bags
she can make if she puts an equal amount of
both in each bag?
Answers
Answer:
4 i believe
Step-by-step explanation:
There is a sale at your favorite clothing store. They have their jeans priced at $49.99 with a extra 20% off. How much will you pay for three pairs of jeans, not including tax? Exlpain how you got your answer.
Answers
Answer: You need to pay $119.98 for three pairs of jeans.
Step-by-step explanation:
Market price of 1 jeans = $49.99
Discount percent = 20% = 0.20
Market price for 3 jeans = 3 x ($49.99)
= $ 149.97
Discount price = 20% of (Market price for 3 jeans )
= .0.20 x ($149.97)
= $ 29.99
Price of 3 jeans after discount = (Market price for 3 jeans ) - ( Discount price)
= $ (149.97 - 29.99)
= $ 119.98
Hence, you need to pay $119.98 for three pairs of jeans.
Determine the nth term rule and find the 45th term for the arithmetic sequence with a10=1 and d=−6.
Answers
Answer:
a(45) =-209
Step-by-step explanation:
a(n) = a +(n-1)d
d=-6
we have to get a1
By using:
a(10) = a1 +(10-1)-6=1
a(10) = a1 +(9)-6 =1
a1 =1+54=55
So:a(45) = 55 +(45-1)-6=-209
hope this helps
Please help asap- will give brainliest:
See the image attached and choose ONE
Answers
If ∠1≅∠2, then ___...
a) ∠5≅∠6, angle 5 is congruent to angle 6
b) ∠3≅∠4, angle 3 is congruent to angle 4
c) XK≅YK
d )GK≅HK
e)All of the above are true
Answers
Answer: All of thé above
Step-by-step explanation:
#1- 2 is what percent of 16 #2- 15 is what percent of 80 #3- 38 is what percent of 200
Answers
Answer:
#1 . 12.5%
#2. 18.75%
#3. 19%
Step-by-step explanation:
2 / 16 x 100% = 12.5%
15 / 80 x 100% = 18.75
38 /200 x 100%= 19%
Are the two given triangles similar? Show your work to support your answer.
Helpppp please
Answers
Answer:
no
Step-by-step explanation:
1 is obtuse one is acute
Plz help this is worth 30 points
Answers
Answer:
Choice A
Step-by-step explanation:
What is the product of 7/10 and 3 2/3?
1 3/5
1 13/15
2 17/30
3 7/15
Answers
11) Stephanie makes $ 50 a week babysitting. She spends $ 25, saves $ 15, and uses the rest to pay off a $ 100 loan from her brother. After six weeks, how much has Stephanie spent, how much has she saved, and how much still owes her brother?
Answers
Answer:
She saved 90 dollars and she owes her brother 40 still.
Step-by-step explanation:
A museum requires a minimum number of chaperones proportional to the number of students on a field trip. The museum requires a minimum of 333 chaperones for a field trip with 242424 students.
Answers
Answer: See explanation
Step-by-step explanation:
Here is the complete question:
A museum requires a minimum number of chaperones proportional to the number of students on a field trip. The museum requires a minimum of 3 chaperones for a field trip with 24 students. Which of the following could be combinations of values for the students and the minimum number of chaperones the museum requires? Choose 2 answers.
A. Students: 72
Minimum of chaperones: 9
B. Students: 16
Minimum of chaperones: 2
C. Students: 60
Minimum of chaperones: 6
D. Students: 45
Minimum of chaperones: 5
E. Students: 40
Minimum of chaperones: 8
Since the museum requires a minimum of 3 chaperones for a field trip with 24 students. This means that there will be 24/3 = 8 students per chaperone.
We then divide the number of students given in the question by the number of chaperone to know our answers. This. Will be:
Students: 72
Minimum of chaperones: 9
This will be: 72/9 = 8
Therefore, this is correct.
B. Students: 16
Minimum of chaperones: 2
This will be: 16/2 = 8
This is correct
C. Students: 60
Minimum of chaperones: 6
This will be: = 60/6 = 10.
Therefore, this is wrong
D. Students: 45
Minimum of chaperones: 5
This will be 45/5 = 9
Therefore, this is wrong.
E. Students: 40
Minimum of chaperones: 8
This will be: 40/5 = 8.
Therefore, this is wrong.
Therefore, options A and B are correct.
How to find the constant of y=3/5x
Answers
Answer:
3/5
Step-by-step explanation:
y=3/5x = 0 x both sides by 5
5y-3x=0 reorder terms (community property)
-3x+5y=0
3x-5y=0 changes the signs when you do that
[WORTH 100 WHOLE POINTS] !!
I need it soon!!
Answers
2. 3/5
3. i do not understand
4. 1/2 (even chance)
Answer:
1. 1/5 2. 3/5 4. 1/2 I dont know what 3 is
Step-by-step explanation:
4/3 ÷ 7/8 = in khan academy
Answers
Answer:
1/42
Step-by-step explanation:
1 11/21
Have a Merry Christmas!
1. Solve each equation. a. 4x = -28 b. x - -6 = -2 C.-Y + 4 = -9 d. -3x + 7 = 1 e 25% -11 = -86
Answers
Answer:
A,-7
B, 4
C,13
D,2
Step-by-step explanation:
A,Step 1: Divide both sides by 4.
[tex] \frac{4x}{4} = \frac{ - 28}{4} [/tex]
[tex] x = - 7[/tex]
B,Step 1: Add 6 to both sides.
x−6+6=−2+6
x = 4
C, Step 1: Regroup terms.
4−Y=−9
Step 2: Subtract 44 from both sides.
-Y=-9-4−Y=−9−4
Step 3:Simplify -9-4−9−4 to -13−13.
[tex] \frac{ - y}{1} = \frac{ - 13}{ - 1} [/tex]
Y = 13
D,Subtract 77 from both sides.
-3x=1-7−3x=1−7
2, Simplify 1-71−7 to -6−6.
-3x=-6−3x=−6
3,Divide both sides by −3.
[tex] x = \frac{ - 6}{ - 3} [/tex]
4,Two negatives make a positive.
x = 6/3
x = 2.
I don't understand Question E!
I hope it helps you!
a) Estimate the value of 50.75 x 0.18
Answers
Answer:9.135
Step-by-step explanation: I had have this answer
Answer:
9.135
Step-by-step explanation:
Juan needs to simplify the fraction LaTeX: \frac{32}{52}32 52. He will need to divide the numerator and the denominator by the greatest common factor. What is the greatest common factor of 32 and 52?
Answers
Answer:
4Step-by-step explanation:
Given the expression, 32/52
Juan need to divide the numerator and the denominator by the greatest common factor
For 32;
32 = 8 * 4
For 53
52 = 13 * 4
Find the ratio
32/52 = (8*4)/(13*4)
32/52 = 8/13
Since 4 is common to both factors, Hence the greatest common factor is 4
1. Solve the system of equations.
2y - 3z=0
x+3y = -4
3x + 4y = 3
Answers
Answer:
1. y = 3/2z
Step-by-step explanation:
1. ,2y-3z + 3z =0 + 3z ,2y=3z, 2y/2 =3z/2=3/2z
I’m doing a percent equation problem and the question is blank % of $50 =$35 help me plzzzz
Answers
Answer:
70
Step-by-step explanation:
blank % of $50 =$35
Let us take x in place of blank.
x % of $50 =$35
x/100 * 50 = 35
x/2 = 35
x = 35*2
x = 70
Therefore, 70% of $50 =$35
PLEASEE HELPPPP WILL GIVE BRAINLEAST IT IS URGENT!!!!
Which equation models the trend line?
A- y = –1.3x + 2
B- y = 1.3x + 2
C - y= –1.3x – 2
D- y = 1.3x – 2
Answers
sorry if i got it wrong
Answer:
B. y = 1.3 + 2
Step-by-step explanation:
The slope is positive, and the y intercept is at positive 2.
Which expression is equivalent to -44
PLease asap 12 points please dont just take them
Answers
Answer:
|44|
Those are not Ones, those are the straight lines you can type using the Shift key and the key underneath the Backspace :)
Step-by-step explanation:
-44 is 44 places away from zero, and |44| is also 44 places away from zero. For those who are wondering, this symbol: | if is placed around a certain number, the positive or negative effect on that number is taken away, and the number is just thought as of that many spaces away from zero. EX: -9 => |9| is now not negative
Answer:
One equation is -22+-22
If you were to roll a die one time, what is the probability of it landing on an odd number
Answers
Answer:
It's one half.
Step-by-step explanation:
There are six sides on a dice, three of those sides (this is half) have negative numbers. Therefore the probability is 1/2 or 0.5 or a half.
120% of __________ is 78
Answers
120% of 65 is 78.
This means that 120 times what equals 78.
120*65=78
Answer:
65
Step-by-step explanation:
Which pair of triangles MUST be similar?
A. Triangle 5 has a 25 degree angle and a 75 degree angle. Triangle 6 has a 25 degree angle and a 70 degree angle.
B. Triangles 1 and 2 each have a 40 degree angle.
C. Triangle 7 has a 40 degree angle and a 35 degree angle. Triangle 8 has a 40 degree angle and a 105 degree angle.
D.Triangles 3 and 4 are both scalene. Each have a 65 degree angle.
Answers
Answer:
C
Step-by-step explanation:
The total measurement of a triangle is 180
Triangle 7 has a 40 degree angle and 35 degree angle.
40+35=75
180-75=105
Triangle 8 has the same angle that is 40 degrees and 105. And if you do the same math, you would get 35 for the missing angle of triangle 8