Answers
Answer:
(a) h = 160 - 5·x
(b) V = 4·x² × h = 4·x² × (160 - 5·x) = 640·x² - 20·x³ = 20·x²·(32 - x)
∴ V = 20·x²·(32 - x)
Step-by-step explanation:
(a) The given dimensions of the cuboid (rectangular prism) are;
'4·x' meters by 'x' meters by 'h' meters
Let the 4·x meters represent the length, 'l', of the cuboid, let the x meters represent the width, 'w', of the cuboid, and let the h meters represent the height 'h' of the cuboid
Therefore, we are given that the cuboid is a wire cage, with the total length of the sides (edges) of the cuboid equal to 640 meters
Therefore, the sum of the edges are;
Top(4·x + x + 4·x + x) + Side(h + h + h + h) + Bottom(4·x + x + 4·x + x) = 640
20·x + 4·h = 640
∴ h = (640 - 20·x)/4 = 160 - 5·x
h = 160 - 5·x
(b) The volume of a cuboid, V, is given as follows;
V = The area of the base of the cuboid × The height of the cuboid
The area of the base of the cuboid = l × w = 4·x × x = 4·x²
The height of the cuboid = h = 160 - 5·x
∴ V = 4·x² × (160 - 5·x) = 640·x² - 20·x³
V = 640·x² - 20·x³ = 20·x²·(32 - x)
∴ V = 20·x²·(32 - x) QED.
Related Questions
4 3/8 ÷ 1 3/8 = answer asap plsssss.
Answers
Answer:
3.1
Step-by-step explanation:
Answer:
1 2/3 : 4 3/8 = 8/ 21 ≅ 0.3809524
Step-by-step explanation:
Have A Wonderful Day !!
Simplify 6^7/6^5 in index form
Answers
Answer:
6²
Step-by-step explanation:
Using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex] , then
[tex]\frac{6^{7} }{6^{5} }[/tex]
= [tex]6^{(7-5)}[/tex]
= 6²
Step-by-step explanation:
[tex] {6}^{7 } - 5 \\ 6 { }^{2} [/tex]
=36PLS HELP WITH MATH WILL MARK BRAINLIEST 30 POINTS!!
Emily is encouraged to read more than 4 hours each week. It takes her 45 minutes to finish her first book. She divides the remainder of the time equally amongst the other six days. What is the minimum number of minutes she should read each day?
A. x > 32.5 minutes
B. x > 40 minutes
C. x \leq 32.5 minutes
D. x[\leq 40 minutes
Answers
Answer: D
Step-by-step explanation:
40+40= 1 hour 20 min
40+40= 1 hour 20 min
40+40 = 1 hour 20 min
40————-> 40 min
Add all together you get 4 hours in one week
Your welcome !
The sum of a number, n, and -2 is multiplied by -4. The result is at most 36. Which shows the inequality that represents this situation and its solution?
The answer choices given are
1.−4(n+2)≤36; n≤7
2.−4(n−2)≤36; n≥−7
3.−4(n−2)≤36; n≥−11
4.−4(n+2)≤36; n≤−11
Answers
Answer:
Step-by-step explanation:
-4(n+3) <36;n<7
Will give brainliest. Explain in detail, please and thank you.
You went to lunch with your friend, and the bill was $19.00. Your lunch is $3.00 more than your friend's. How much was your friend's lunch?
f+ 3 = 19; $8.00
3f + 2 = 19; $8.00
2 + 3 = 19; $8.00
2 - 3 = 19; $8.00
Answers
Step-by-step explanation:
f, your friends lunch
f + 3, your lunch
f + f + 3 = 19
2f + 3 = 19
2f = 16
f = 8
Your friends lunch was $8
I hope this helped!!!!
Write the equation in slope intercept form of a line that has a slope of 1/2 and passes through the point (-8,-4).
Answers
m(slope)=1/2
(x,y)—->(-8,-4) so x=-8 and y=-4 substitute and solve for b
-4=1/2(-8)+b
-4=-4+b
+4=+4
0=b
Find the greatest common factor of 9n and 7n^3
Answers
Explanation:
9 = 3^2
+7 = +7×7
3 = 3
GCF = 1
9 / 1 = 9
+7 / 1 = 7
3 / 1 = 3
Please hurry this is due at 11:59
Answers
Answer:
y=5
x=30
Step-by-step explanation:
the triangle with all congruent angles is an equilateral triangle, which means all side and angles are congruent, so 8y has to equal to 40 by dividing 40 by 8.
x and the angle about forms a complementary angle, so it has to be 30 degrees to add up to 90.
Ruben swims several times per week in a lake near his home. Last summer, the average water temperature was 20 °C. This summer, the average water temperature was 16 °C. What was the percent of decrease in the temperature?
Answers
0.8*100= 80
100-80= 20%
Peter has a 25 acre field. He 20.5 acres with sweet corn . What fraction of his field does Peter plant with sweet corn
Answers
Answer:
82%
Step-by-step explanation:
Multiply 25*4 to get 100.
Then multiply 20.5*4 because what you do to one side you have to do for the other.
You end up with 0.82 or 82%
Based on the length of the field and the amount of the field that was planted the fraction of the field planted is 4.1/5.
The field has a length of 25 acres and Peter plants in 20.5 acres of them.
The fraction that is planted is:
= Amount of field planted on / Total area of field
Solving will give:
= 20.5 / 25
Take to the simplest form by dividing both by 5:
= 4.1 / 5
In conclusion, the fraction planted on is 4.1/ 5.
Find out more on fractions at https://brainly.com/question/11289219.
X decreased by 61% I need the right answer
Answers
Answer:
X-61=100
X=100-61
X=39%
Step-by-step explanation:
I really need help with this question
Answers
Help due soon will give brainliest
Answers
Answer:
46
Step-by-step explanation:
So if angle 4 is the same as angle 5 then 180-134=46
if the two angles make a flat line then the total of both angles is 180.
Answer:
the anwer is 46
Step-by-step explanation:
find the m 1 if m 5 +134
Who can answer this?
Answers
R = {5,7,9,10}
It is not a function since for the 6 value of x, there are two different y outputs
Range={5,7,9,10}
Function= No because the x value repeats (6)
Hope this helps
Have a great day/night
you are rolling a die number 1-6. What is the theoretical probability that you roll a 6?
Answers
Answer:
16.7 percent
So to get a 6 when rolling a six-sided die, probability = 1 ÷ 6 = 0.167, or 16.7 percent chance. So to get two 6s when rolling two dice, probability = 1/6 × 1/6 = 1/36 = 1 ÷ 36 = 0.0278, or 2.78 percent.
........................................ ....,....
.....
Answers
Have a great day/night
Shelly deposited $8,000 into a savings
account that earns 4% simple interest.
How much interest did she earn after
three years?
Answers
Answer:
Shelly earned $8,960 in interest.
Step-by-step explanation:
The formula for simple interest is A=P(1+rt). For this problem, the equation is A=8,000(1+0.04x3). 8,000 is the initial balance, 0.04 is the annual interest rate, and 3 is the time in years. Following the order of operations, 0.04 multiplied by 3 is 0.12. 0.12 plus 1 is 1.12. 8,000 multiplied by 1.12 is 8,960.
Answer:
£960
Step-by-step explanation:
So you start of by calculating the interest for one year.
8,000 × 0.04 = 320
Because the interest rate is 4% you will write it as 0.04
And because it is simple interest, you will need to multiply 320 by 3 to get the amount of interest she will get after 3 years.
320 × 3 = 960
If you wanted the total amount of money she would have after receving the interest, you just have to add 960 to the starting amount of 8,000.
8,000 + 960 = 8,960
In this, you are assuming that she doesn't take any money out or put any money in for those 3 years.
I think that's right anyway.
How do you solve for x/3 - x/5
Answers
Answer:
x/3 - x/5 = 2/15x
Step-by-step explanation:
Please mark brainlliest if you want.
505 u
225 u
What is the Scale Factor? Show the work for the equation method
to solve, please.
Answers
Answer:
1.5
Step-by-step explanation:
A company is installing a new ski lift at a height of 225
meters above the mountain, to ascend at an angle of 48
degre.
Determine the length of the rope the elevator will require
to run from the base to the top of the mountain
Answers
Answer:
4.6875
Step-by-step explanation:
225 divided by 48 = 4.6875
Order least to greatest: -7.5, 5.3, -5.2, -8.4, 3.1
Answers
Answer: -8.4, -7.5, -5.2, 3.1, 5.3
Step-by-step explanation: First, lets separate the negative numbers and the positive numbers,
-7.5, -8.4, - 5,2 5.3, 3.1
Now, we order from least to greatest!
-8.4, -7.5, -5.2, 3.1, 5.3
Done!
I'll give u brainless if u do!
Answers
Answer:
9. 5×5×5= 125
10.2×2×2×2=16
11. 8×8= 64
12. 4×4×4×4=256
13. 6×6×6= 216
14. 1×1×1×1×1×1= 1
is 4(x+1) - 3 and 4x + 1 equivalent and why ??
Answers
Step-by-step explanation:
Hey there!
Given;
4(X+1) -3 and 4x+1.
No, they are equivalent.
Reason:
Solving 1st expression.
4(x+1) = 4x + 4 - 3
Now, next expression is: 4x+1.
So, 4x + 4 = 4x+1
So, they are equivalent to eachother.
Hope it helps...
is 4(x+1) - 3 and 4x + 1 equivalent and why?
Step-by-step explanation:
Hey there!
Given;
4(X+1) -3 and 4x+1.
No, they are equivalent.
Reason:
Solving 1st expression.
4(x+1) = 4x + 4 - 3
Now, next expression is: 4x+1.
So, 4x + 4 = 4x+1
So, they are equivalent to eachother.
Hope it helps...
What is the surface area of the box if its 5 1/2 by 3
Answers
Answer:
I think 30
Step-by-step explanation:
please help with 6-8 ! will give brainliest !! :)
Answers
Answer:
6:6=x
7:16=y
8:20=z
Step-by-step explanation:
For 6, since BD is a perpendicuar bisector, that means 15x=90. Divide 90 by 15 and you get 6
for 7, if bd is a angle bisector, you can set 3y=48. divide 48 by 3 and you get 16
for 8, since Bd is a median, you can set 2z-3=z+17. Isolate the variable and you will get 2z-z=17+3. Add like terms together and you get z=20
Just so you know, a perpendicular bisector will make both angles equal to 90, an angle bisector make both angles equal to each other, and medians make it so that it hit a line in the center therefor you can set both sides of the line to be equal
Plzz i need help i'm stuck at this problem
Answers
Answer:
y = $19.50
x = $17.17
z = $20.67
Step-by-step explanation:
Notice that $13.50 of $22.50 is 60% (in math decimal form 0.6). The same is true for $16.20 of $27.00. Therefore, the value of y is going to be :
0.6 * $32.50 = $19.50
We notice as well that the added taxes to the discount price $13.50 is:
14.31 - 13.5 = $0.81, which at a time is a percent of the discounted sales price. Such percentage is calculated as shown below:
0.81/13.5 = 0.06 (or 6%)
we can then add 0.06 * 16.20 = 0.972 to 16.20 to find the total price "x"that includes tax:
x = $16.20 + $0.97 = $17.17
And we do something similar to find z:
z = $20.67
A skateboarding club randomly surveyed 200 people who visited the club's website about their favorite skateboard brand. The data collected is shown in the table.
Answers
Answer: 36/200 = 18/100 = 18%
Step-by-step explanation:
What is the solution to the system of equations?
0 (3,2
0 (2, 3)
0 (2, 2)
(2,-2)
Answers
Answer:
What are the equations?
6(15 + 12)
Rewrite that with distributive property for crown!!!
Answers
Answer:
90 + 72 -> 162
Step-by-step explanation:
15 times 6 equals 90 and 12 times 6 equals 72, the distributive property equation is 90 + 72 in which can be added to 162 as a result.
Hey there!
The formula is: a(b + c) = a(b) + a(c) = ab + ac
“6(15 + 12)”
6(15 + 12)
6(15) + 6(12)
6(15) = 90
6(12) = 72
NEW EQUATION: 90 + 72
ANSWER: 90 + 72 = 162 ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Rewrite the expression as square of a monomial.
0.09a^2
EXTRA POINTS!!!
Answers
Answer:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
0.3
Step-by-step explanation:
Brainliest?
We want to rewrite the given expression as a square of a monomial. We will get:
0.09*a^2 = (0.3*a)^2
So we have the expression:
0.09*a^2
We want to write this as a square of a monomial like:
(c*a)^2 = 0.09*a^2
Basically, we must find a number c such that:
c^2 = 0.09
c = √(0.09) = 0.3
Then the monomial is:
0.3*a
And we can rewrite the given expression as:
(0.3*a)^2
If you want to learn more, you can read:
https://brainly.com/question/11363511