Diagram shows the composite solid formed by a cuboid and a right prism. Trapezium LMNP is the uniform cross section of the prism. It is given the volume of the composite solid is 444cm³. Calculate the length, in cm of MN​

Diagram Shows The Composite Solid Formed By A Cuboid And A Right Prism. Trapezium LMNP Is The Uniform

Answers

Answer 1

Answer:

MN = 7 cm

Step-by-step explanation:

Well the volume we can separate into pieces

first the ABCDEFGH (? you know this cuboid)

which has a volume of

[tex]V = AB\cdot BC\cdot CH\\\\V = 3*6*(3+JY+4)[/tex]

if you ask where does the 4 come from

it comes from LP = KB = YC and JY + YC =JC

so

[tex]V = 18(7+MX)[/tex]

this is because JY = MX

the other volume is of BCNPKLXY (hope you understand which one)

and the volume is

[tex]V = BP*PN*NX\\\\V=8*6*4\\\\V = 192[/tex]

and the last one is KYXLMJ (the top "triangle")

the volume is

[tex]V = \frac{LX*XM}{2}*LK\\\\V = \frac{6*MX}{2}*8\\\\V= 6*4*MX\\\\V=24MX[/tex]

so now add them up

and has to equal 444

[tex]V_T = 18(7+MX)+192+24MX\\\\V_T = 126+18MX+192+24MX\\\\V_T = 318+42MX\\\\444=318+42MX\\\\444-318=42MX\\\\126=42MX\\\\MX = 3[/tex]

and finally we know that MN = MX + XN = 3+4 = 7

so here is our answer MN = 7 cm

a couple of notes

[tex]1.\:\angle LXM = 90\\\\2.\:\angle KYX = 90[/tex]

3. the units don't matter due to the fact that everything is in cm

4. see the picture below to get a better idea of which prism I am talking of

5. tell me if you have questions :D

Diagram Shows The Composite Solid Formed By A Cuboid And A Right Prism. Trapezium LMNP Is The Uniform

Related Questions

please answer my question I will mark brainliest

Answers

Answer:

Wouldn't it be A because the spinner has a 1/8th of a chance to land on a number

Step-by-step explanation:

If 3^2+4^2+12^=13^2
Then what is x+(x+1)+___=____

Answers

Answer:

Those are two different questions that aren't related isn't it?

Step-by-step explanation:

I KNOW

janelle came to the bat 262 times in 91 games. at this rate, how many times should she expect to have at bat in full season of 162 games?

Answers

Answer:

465 times

Step-by-step explanation:

[tex]r=\frac{262}{91} = 2.87[/tex]

In full season of 162 games

[tex]162r=162(2.87)[/tex] = 465

can anyone help please :)

Answers

Answer:

148°

Step-by-step explanation:

the angles are equal

Im new too this math and i could use a little help !:)

Answers

Answer:

25 degrees

Step-by-step explanation:

A right triangle is considered 90 degrees, so subtract 90 degrees by 65 degrees.

90 - 65 = 25

Hence, angle A equals 25 degrees.

what is the answe to this?

Answers

Answer:

8

Step-by-step explanation:

one half of the triangle adds up to 12. You need to make the other side equal.

9+3=4+x

x must be 8, because then it equals 12.

9+3=4+8

Answer:

answe

Step-by-step explanation:

hew answe

Find the slope (-5,-6), (3,-3) , (−5,−6), (3,−3)

Answers

Answer:

the slope or gradient is 8/2=4

You've decided to buy a printer and have narrowed it down to two choices. The laser printer costs
$150 but the average cost of each page is just 1.5 cents. The other option is an inkjet printer, which
costs $30, but each page has an average cost of 6 cents. Determine the conditions (e.g. the number
of pages) where each printer is the better buy.

Answers

Answer:

The conditions are;

Where the number of paper printed = x (x ∈ Z)

For 0 ≤ x ≤ 2,666, It costs less to own and therefore it is better to buy the ink jet printer

For 2,666 < x ≤ ∞, it costs less to own and therefore it is better to buy the lase jet printer

Step-by-step explanation:

The given parameters are'

The cost of the laser printer = $150

The average cost of each page printed with the laser printer = 1.5 cents

The cost of the inkjet printer = $30

The average cost of each page printed with the inkjet printer = 6 cents

Let 'y', represent the total cost of ownership each printer and let 'x', represent the number of paper printed, we have;

For the laser printer, we have;

[tex]y_{laser \ jet}[/tex] = 150 + 0.015·x

For the ink jet printer, we have;

[tex]y_{ink\ jet}[/tex] = 30 + 0.06·x

Therefore, the initial cost of ownership of the ink jet printer is lesser than the initial cost of ownership of the laser jet printer

However, where the cost, 'y', of the laser jet printer and the ink jet printer are equal, we have;

[tex]y_{laser \ jet}[/tex]  = [tex]y_{ink\ jet}[/tex]

∴ 150 + 0.015·x = 30 + 0.06·x

120 = 0.06·x - 0.015·x = 0.045·x

x = 120/0.045 = 2,666.[tex]\overline 6[/tex]

Therefore, given that the cost of ownership and the number of sheets printed is a straight line relationship, after printing 2,666.[tex]\overline 6[/tex] sheets or when 2,667 sheets are printed, the cost of ownership of the laser jet printer will become lesser than the cost of ownership of the ink jet printer

Therefore, the conditions where each printer is better to buy are;

For printing the number of papers in the range 0 ≤ x ≤ 2,666, the ink jet printer is better to buy

When the number of paper printed, 'x', is in the range, 2,666 < x ≤ ∞, the laser jet printer is better to buy.

We want to see when is better to buy which printer.

Printer 1 is better for 2667 pages or more.

Printer 2 is better for less than 2667 pages.

Printer 1 costs $150 pls 1.5 cents per page, so the cost for x pages is:

C₁(x) = $150 + $0.015*x

Printer 2 costs only $30, but each page costs 6 cents, so we have the cost:

C₂(x) = $30 + $0.06*x

First, we need to find the value of x such that the two costs are equal:

C₁(x) = C₂(x)

$150 + $0.015*x = $30 + $0.06*x

$150 - $30 = $0.06*x -  $0.015*x

$120 = $0.045*x

$120/$0.045 = x = 2,666.67

Rounding to the next whole number we have x = 2,667

Then, if you plan to use less than x = 2,667, you should buy the second printer because it has a smaller y-intercept.

If you plan to use 2,667 or more, you should buy the first printer, because it has a smaller slope.

If you want to learn more, you can read

https://brainly.com/question/21107621

Which line has a slope of 0.625, and which line has a slope of 1.6?
Explain why the slopes of these lines are 0.625 and 1.6.

Answers

Answer:

The answer is below

Step-by-step explanation:

The equation of a straight line is given by:

y = mx + b; where y and x are variables, b is the y intercept (i.e. value of y when x is zero), m is the slope of the line.

The slope of a line passing through the points [tex](x_1,y_1)\ and\ (x_2,y_2)\ is:[/tex]

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let the point where the two lines intersect be the origin (0, 0).

Line 1 passes through (0, 0) and (8, 5). Hence:

slope of line 1 = [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{5-0}{8-0} =0.625[/tex]

Line 2 passes through (0, 0) and (5, 8). Hence:

slope of line 2 = [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{8-0}{5-0} =1.6[/tex]

(14x + 6)
lo
52°
С C
X
A​

Answers

Answer:

thats easy

 105 not

Step-by-step explanation:

The system of equations id graphed on the coordinate plane.
y=4x +3
y=-X-2
Enter the coordinates of the solution to the system of equations
in the box

Answers

Answer:

;~; ...................IMA FAILL ;;;;;;;;;;----;;;;;;;;;;;;

Select all functions from the tables given below that show Y as a function of X.
A.
B.
C.
D.
E.

Answers

Answer: I dunnowhy are you asking me

Step-by-step explanation: the line of the perpendicular angle is non existent

help me with this chart please

Answers

Answer:

-2(0.5)^whatever number x is

Step-by-step explanation:

X      Y

-2      8

-1      4

0      2

1      -1

2      -0.5

3      -0.25

4      -0.125  

What is - 4/7 as a number?

Answers

Answer:

0.57142857142857

Step-by-step explanation:

hi -12 is less than -12.5 right? please answer quick

Answers

-12.5 is less than -12

Tania wants to go to Europe. She decided she can only spend 200 U.S. dollars. The exchange rate is 1 euro to 1.30 U.S. dollars. After exchanging her money, how many euros will she have to spend, rounded to the nearest cent?​

Answers

I think it’s around 164.93?

PLEASE help me! I’m giving all my points, please help ASAP!!!

Answers

Answer:

I have send u picture

Step-by-step explanation:

I think this will help u

help............please

Answers

Answer:

k=5

Step-by-step explanation:

subtract 14 from both sides

Answer:

19=4+k is easy that means 10-x=100+11 so the answer is 70

Step-by-step explanation:

Select the correct solution for 8x = 56.
O A. X= 1/7
O B. X = 48
O c. x = 64
O D. x = 7

Answers

D but I need at least 20 characters

A health club has a monthly membership fee of $20 and charges an additional fee of $1.50 for every exercise class attended. Write an equation that represents the total cost, y, for a month in which a member attends x exercise classes

Answers

Answer:

y=1.50x+20

20 is the fixed price for each month, so that stays the same. It's the independent variable.

y=1.5x+20 is the equation that represents the total cost, y, for a month in which a member attends x exercise classes

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given,

A health club has a monthly membership fee of $20 and charges an additional fee of $1.50 for every exercise class attended.

We need to write an equation to represent this.

Total cost per person will be y.

Total cost is sum of membership fee and x be the the number of exercise classes.

y=1.5x+20

y equal to one point five times of x plus twenty.

Hence y=1.5x+20 is the equation that represents the total cost, y, for a month in which a member attends x exercise classes

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ2

whats the quotient of -72 divided by -9?

Answers

Answer:

8

Step-by-step explanation:

  9 |08|

       72

   -    0

        72

-

         72

            00

work out the surface area of this triangular prism

Answers

I’m fairly certain it would be 958cm^2

What is the value of 100?

Answers

Answer:

10

Step-by-step explanation:

Means back the numbers into multiples of several small numbers

Like:; 1. We take LCM of 40

Just break into multiples of small number

40= 2×2×2×5

2. We take LCM of 50

50= 5×5×2

So LCM for 100 is 2×2×5×5

after that see the pairs in the LCM like 2×2 or 3×3 or 4×4(same numbers)

Then write the the single number in place of two multipled numbers

Like:; 2×2 is written as 2 // 3×3 is written as 3

So we can write 100 into 2×2×5×5 and then after selecting pairs (2×2)×(5×5)

write pairs in single number 2×5

And so we get 2×5=10

So we find root of 100 that is 10

Value of a hundred is a hundred

Check ALL of the ratios that are equivalent to 5:8 (Select al that apply) 10:16 8:5 2.5:4 40:25 15 to 24​

Answers

Answer:

10 ,16 AND 8

Step-by-step explanation:

PLEASE MARK ME AS BRAINLIEST

Top one correct thank you (mark him brainiest)


Is the following equation linear?
yes or no

Answers

Answer:

Yes the equation is Linear

Step-by-step explanation:

Answer:

Yes it is a linear equation

Combining Like Terms
-4x - 2 + 5x = -4
I know the answer is -2 but I don’t know how to get -2

Answers

You have to combine the -4x+5x first
combine the -4x and the 5x
x-2=-4
+2. +2
x=-2

hope this helps!

Determine the approximate measure of angle Y.

Answers

Answer:

45

Step-by-step explanation:

Is 361 rounded to 400?

Answers

Answer

I do not think so.

Step-by-step explanation:

Answer:yes

Step-by-step explanation:

the sum of three consecutive integers is three times the second integer. show that this is true for the three consecutive integers 7,8 and 9

Answers

Step-by-step explanation:

7+8+9=24

second integer is 8 so 8*3=24

can sum1 do number 3 for me plz i will mark brainliest

Answers

Answer:

Addition-

(9x+27)

Subraction-

(x-63)

Multiplication-

(20x-810)

Division-

(1.25x-0.4)

Step-by-step explanation:

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