The length of the rectangular prism is L = 4x/5
What is the volume of a prism?A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.
The volume of a prism is the product of its base area and height
Volume of Prism = B x h
where B = base area of prism
h = height of prism
Given data ,
The formula for the volume of a rectangular prism is V = lwh, where l, w, and h are the length, width, and height of the prism, respectively.
In this problem, we are given that the volume of the prism is 7/(x - 3/5x) and the width and height are 2/x and 4/x, respectively.
So we can substitute these values into the formula for the volume and solve for the length:
V = lwh
7/(x - 3/5x) = l * (2/x) * (4/x)
Multiplying both sides by (x - 3/5x), we get:
7 = l * 8/(5x² - 3x)
Simplifying, we get:
l = 56x²/(5x² - 3x)
Now we need to check if this solution satisfies the condition that the width is 2/x and the height is 4/x:
w = 2/x, h = 4/x
V = lwh = (56x²/(5x² - 3x)) * (2/x) * (4/x) = 7/(x - 3/5x)
So the solution is correct.
Hence , the length of the prism is 56x²/(5x² - 3x), which can be simplified to 32x²/40x or 4x/5
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Can someone solve this problem
Answer:
y = -2x + 5
Step-by-step explanation:
slope-intercept form: y = mx + b
Hope this helps:)
The sum of aanual interest and semi-annual compound interest on a sum of money for 2 years at the interest rate of 20% per annum is Rs. 18082. Find the differences.(Ans: Rs. 482)
The differences between the annual interest and semi-annual interest will be Rs 435.78.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
The same of annual interest and semi-annual compound interest on a same of money for 2 years at the interest rate of 20% per annum is Rs. 18082.
The annual interest will be
⇒ 18082(1.2)² – 18082
⇒ Rs 7956.08
The semi-annual interest will be
⇒ 18082(1.1)⁴ – 18082
⇒ Rs 8391.86
Then the differences between the annual interest and semi-annual interest will be
⇒ 8391.86 – 7956.08
⇒ Rs 435.78
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A day at the spa costs $125.
You leave a 20% tip.
How much tip did you leave?
Answer:
total cost is $150 so the tip is $25
Step-by-step explanation:
125:100=1.25
1.25 x 20 = 25
125+25=150
The NYC DOE Laptop weighs around 48 oz (ounces). Note: 1 pound 16 ounces Find this weight in pounds What would be the weight in pounds for two NYC DOE Laptop's? (Explain your thinking)
Answer:
Step-by-step explanation:
ohh i seeee
This triangle has one side that lies on an extended line segment.
Based on this triangle, what statement about x is true?
x = 43 because 71−28=43 and 28 + 43 = 71
x = 81 because 180 − 71 − 28 = 81
x = 99 because 28 + 71 = 99 and 99 − 28 = 71
x = 137 because 180 − 71 + 28 = 109 + 28 = 137
A n s w e r :
C . . .
The measure of angle x is; 137 degrees, the statement (4) x = 81 because 180 − 71 − 28 = 81 is true.
What is a triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
In a triangle, the measures of the three angles add up to 180 degrees. In this triangle, one of the angles measures 71 degrees, and another angle measures 28 degrees.
Therefore, the measure of the third angle must be 48 degrees.
Since the measure of the third angle is 48 degrees, and the measure of one of the other angles is 33 degrees, the measure of the remaining angle must be 48 - 33 = 15 degrees.
Then the measure of the third angle must be 180 − 71 - 28 = 81 degrees.
Therefore, the measure of angle x is 81 degrees.
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3x+4y=24
2x+5y=2
Please help me with this problem
Answer:
x=16
y=-6
Step-by-step explanation:
A 5.5-foot-tall woman walks at 8 ft/s toward a street light that is 22 ft above the ground. What is the rate of change of the length of her shadow when she is 20 ft from the street light? At what rate is the tip of her shadow moving?
Answer: [tex]\frac{8}{3}\ ft/s[/tex]
Step-by-step explanation:
Given
length of shadow =22 ft
height of woman =5.5 ft
speed of woman [tex]\frac{dy}{dt}=8\ ft/s[/tex]
from the figure, we can write
[tex]\frac{22}{x+y}=\frac{5.5}{x}[/tex]
at given instant
y=20 ft
so, using similar triangle properties
[tex]\frac{22}{x+20}=\frac{5.5}{x}\\22x=5.5x+110\\16.5x=110\\x=6.67\ ft[/tex]
Again we can write
[tex]\dfrac{22}{x+y}=\dfrac{5.5}{x}\\22x=5.5x+5.5y\\16.5x=5.5y\\3x=y\\\text{differentiate w.r.t time} \\3\frac{dx}{dt}=\frac{dy}{dt}\\\frac{dx}{dt}=\frac{1}{3}\times 8=\frac{8}{3}\ ft/s\ \text{away from the woman}[/tex]
Stefan sells Jin a bicycle for 138 $ and a helmet for 16 $. The total cost for Jin is 140% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answer:
its 3
Step-by-etep explanation:
please help will give brainliest if correct i know it's not C
Answer:
Table 1
Step-by-step explanation:
Table represents a function because the Input does not repeat.
Answer:
the answer would be the first one
Step-by-step explanation:
Fill in the blank with the correct inequality symbol.
If x>_5, then 4x __ 20
Answer:
4x5 = 20
Step-by-step explanation:
Im not rlly sure at all but hope this helps :)
During the month of January George worked a total of 21 days, 8 hours each day. He did not work any overtime hours during October. Henry earns $29 per hour. What was his earned wages for the month of January ?
A) $232.00
B) $4,872.00
C) $4,640.00
D) $609.00
Answer:
B
Step-by-step explanation:
21*8=168
29*168=$4,872.00
Somebody please help quickly
What is the answer to 3(2M-6)
On Monday, 414 students went on a trip to the zoo. All 9 buses were filled and 9 students had to travel in cars. Write an equation to find the number of students on each bus. Use b for your variable. Do not solve for b."
Step-by-step explanation:
let the total number of students in each bus be 'b',
Total number of students in 9 buses= 9b
Total number of students in cars= 9
Hence, Total number of students= 9b+9
= 414
Number of students in each bus = (414-9)/9
Somebody help plz i need some I’m dying inside help?
Answer:
1/3
Step-by-step explanation:
slope is just change in y over change in x
on a graph this can be found by counting the change in units
look at the point at (-3,0)
find the change in y by starting at that point and counting up or down until you reach another point.
the next point (-4,-3) is three units down (change of -3)
now go back to the first point and count left or right until you reach the other point to get change of x
the other point is one unit left (change of -1)
change of y over change of x = -1/-3=1/3
Answer:
slope = 3
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, - 3) and (x₂, y₂ ) = (- 3, 0) ← 2 points on the line
m = [tex]\frac{0-(-3)}{-3-(-4)}[/tex] = [tex]\frac{0+3}{-3+4}[/tex] = [tex]\frac{3}{1}[/tex] = 3
Which expression simplifies 6(2 + x + x + y) using only 3 terms
Answer: 6(2+2x+1y)
Step-by-step explanation:
i think that is the anwser
Can someone plz help me on number 4 plz
Answer: 6:5
Step-by-step explanation:
Let each little rectangle have the dimensions a by b (where a is the length and longer than b, the width). We find that l=3a because there are 3 lengths of a along l at the top of the crate and that l=4b because there are 4 lengths of b along l at the bottom of the crate. In addition, w=2b+a because there are 2 lengths of b and one length of a along w. Therefore, we can find b and a in terms of l and plug them into w=2b+a to find w in terms of l:
l=4b
b=l/4
l=3a
a=l/3
w=2b+a
w=2(l/4)+(l/3)
w=l/2+l/3
w=5l/6
If w=5l/6, l:w=l/(5l/6)=l(6/5l)=6/5
The correct answer is 6:5.
A rectangle is 36 m long and 25m broad .Find the cost of carpeting the floor at the rate of R.s 650 \ square meter .
Answer:
585000Rs
Step-by-step explanation:
Area=l×b
Area =total cost/rate or rate ×area
Maria Louisa looks at a sequence of shapes and records the number of vertices in each of the shapes in the sequence. The first shape has 7 vertices, the second shape has 13 vertices, and the third shape has 19 vertices. If Maria Louisa assumes that the number of vertices in the sequence of shapes follows the same pattern, how many vertices would she expect the 17 shape to have?
Answer:
103
Step-by-step explanation:
appears to be an arithmetic sequence question where sequence is 7, 13, 19 meaning the initial value is 7 and the common difference is 6 so we'll plug into this formula:
[tex]a_{17}[/tex] = 7 + (17 - 1) · 6
= 7 + (16 · 6)
= 7 + 96
'7' because that's the initial value
'6' because that the common difference
'17' because that's the position the question is asking
Ms. Chawla’s class has 35 students. On children’s day, she gave 2 chocolates to each child in her class. After that, 5 chocolates were left with her. How many chocolates did she have at the start?
Answer:
75
Step-by-step explanation:
Total number of students = 35
Nø of chocolate received by each student = 2
Number of chocolates = 35 * 2 = 70
After the distribution of chocolate, remaining chocolates = 5
Then Now
Total chocolates = 70 + 5 = 75
Hope it will help :)
Answer:
75 Chocolates.
Step-by-step explanation:
She had 35 students and she gave each 2 chocolates. That's 70, but she had 5 left over. That makes the answer 75.
Here’s!! hxhxhxbbd & thanks again
Answer:
x=2
Step-by-step explanation:
this is just like the last one. since it is vertical it only includes the x value 2
Please help it has to be in fraction form rounded all the way
Answer:
The answer to the question provided is
0 = [tex] - \frac{6}{5} [/tex]
It has no solutions.
Betty made 3:4 of the baskets she attempted in a basketball game. If she attempted 20 baskets, how many baskets did Betty make?
Answer:she would have made 15 baskets
Step-by-step explanation:She would have made 15:20 because since you had 3:4 it’s the same thing with 15:20 she is now going to make a maximum number of 15 baskets
Simplify 1 3/4 : 2 1/3
1 3/4 = 7/4 or 1.75
2 1/3= 7/3 or 2.33333333
Which of the following sets of ordered pairs represents a function?
{(-6,-1), (13,8), (1,6), (1,-10)}
{(3,5), (-17,-5), (3,-5), (-17,5)}
{(10,5), (10,-5), (5,10), (5,-10)}
{(10,5), (-10,-5), (5,10), (-5,-10)}
if 2 of the angles of a triangle are 30 and 70 degrees, the third angle measures ...
Answer:
The third angle measures 80°
Step-by-step explanation:
Let us solve the question
In any triangle
∵ The sum of the measures of the interior angles of a triangle is 180°
∵ The angle of triangles are ∠1, ∠2, and ∠3
∴ m∠1 + m∠2 + m∠3 = 180°
∵ Two of the angles of the triangle are 30° and 70°
∴ m∠1 = 30°
∴ m∠2 = 70°
→ Substitute them in the rule above
∴ 30° + 70° + m∠3 = 180°
→ Add the like terms
∵ (30 + 70) + m∠3 = 180
∴ 100 + m∠3 = 180
→ Subtract 100 from both sides
∵ 100 - 100 + m∠3 = 180 - 100
∴ m∠3 = 80°
∴ The third angle measures 80°
The cost of 5 cans of dog food is 4.35 . At this price how much do 11 cans of dog food cost?
Answer: 9.57
Step-by-step explanation:
I added 4.35 by 4.35 wich would be 10 cans and then I divided 4.35 by 5
2. A recipe calls for 1/2 cup flour for every 3 cups
of milk. If you use 1 1/2 cups of flour, how many
cups of milk will you need to use?
Answer:
9 cups of milk is used
Step-by-step explanation:
1/2 + 1/2 + 1/2 = 1 1/2
3×3 = 9
Select the graph for the solution of the open sentence lxl +3>3
No solution
Closed circle on 0 going to the right
Open circle going out left and right
Open circle only going to the right
Answer:
[tex]x>0\:or\:x<0[/tex]
As seen in graph, there is an open circle on 0, and it goes out left and right.
Option C is correct option.
Step-by-step explanation:
We need to draw the graph for the solution of the open sentence [tex]|x| +3>3[/tex]
First we will solve the inequality: [tex]|x| +3>3[/tex]
Adding -3 on both sides
[tex]|x| +3-3>3-3\\|x| >0[/tex]
We know that [tex]If\:|x|>0,\:then\:x>0\:or\:x<0[/tex]
So, we have
[tex]x>0\:or\:x<0[/tex]
Now, the graph is attached in the figure below
As seen in graph, there is an open circle on 0, and it goes out left and right.
Option C is correct option.
The number of lines shows 5/7 and 10/14. Which statement is true?
Answer:
[tex]\frac{5}{7} = \frac{10}{14}[/tex] because [tex]\frac{5}{7} = \frac{(5)(2)}{(7)(2)} = \frac{10}{14}[/tex].
Step-by-step explanation:
Looking at the number line, we can see that the highlighted parts go the same distance on the number line, therefore the fractions are equal. The number of equal parts, the size of a single equal part, or the denominators of two fractions do not matter. It's the total size made of up of those equal parts that counts.
Also, you can even convert [tex]\frac{5}{7}[/tex] into [tex]\frac{10}{14}[/tex] by multiplying BOTH the denominator and numerator by 2. When doing this with any number, regardless if it's 2, the original fraction and the converted fraction will still be equal.