Determine the simplest expression for the area of shaded region below

Answer:

The required ratio is 1 : 3.

Step-by-step explanation:

Let the length is L, width is W and the height is H.

Volume of the prism is

V = LW H

Volume of the pyramid

V' = 1/3 L W H

Ratio of volume of pyramid to the prism is

[tex]\frac{V'}{V} = \frac{1}{3}[/tex]

Answer:

e = -1/2

Step-by-step explanation:

To solve this problem, our first step is to add 5/3 to both sides of the equation.  This gives us:

4/3 + 5/3 = -6e - 5/3 + 5/3

9/3 = -6e

We can simplify the left side of the equation by performing the division.

3 = -6e

Next, we can solve for e by dividing both sides of the equation by -6.

e = -1/2

Therefore, the correct answer is e = -1/2.

Hope this helps!

Answer:

The value of e is -1/2

Step-by-step explanation:

4/3 = - 6e - 5/3

Now, add 6e both side we get,

4/3 + 6e = + 6e - 6e - 5/3

4/3 + 6e = - 5/3

Now, subtract 4/3 from both side we get,

4/3 - 4/3 + 6e = -4/3 - 5/3

6e = -4/3 - 5/3

6e = -4 - 5/3

6e = -9/3

6e = -3

Now, divide 6 from both side we get,

6e/6 = -3/6

e = -1/2

Thus, The value of e is -1/2

-TheUnknownScientist

Answer:

C

Step-by-step explanation:

[tex]y=\sqrt{x-1} +4[/tex]

graph is shifted right 1 unit and 4 units up.

Answer:

5:15 simplified as 1:3

Step-by-step explanation:

To check:put value of m and n in both equations

Answer: n=2 and m=1

Step-by-step explanation:

m+3n=7 , 5m-n=3

m=7-3n => 5(7-3n)-n=3

=> 35-15n-n=3

=> -16n=-32

=> n=2

n=2 => 5m-2=3

=> m=1

Answer:

1

Step-by-step explanation:

February is the only month that has 28 days

Answer:

[tex]12 \: months \: have \: 28 \: days \\ thank \: you[/tex]

Answer:

C. $516

Step-by-step explanation:

His regular rate is $8 per hour.

Since it's 40 hours a week, it means from Monday to Friday his regular work time is 8 hours per day.

Thus, for the regular week work, he is to be paid;

40 × 8 = $320

Now, we are told he worked 9 hours each day from Monday through Friday.

This means that;

He worked 1 hour each day.

That is 5 hours extra from Monday to Friday.

He is paid one and one-half times the regular hourly rate.

Thus, for this 5 extra hours, he will be paid 1½ × 5 × 8 = $60

He works 6 hours on Saturday, and 4 hours on Sunday.

Thus;

For Saturday, he is also paid one and one-half of regular pay. Thus, he is due for;

1½ × 8 × 6 = $72

He is paid double the regular hourly pay for Sundays.

Thus, for 4 hours on Sunday, he is paid;

2 × 8 × 4 = $64

Total he is due = $320 + $60 + $72 + $64 = $516

Answer:

4

Step-by-step explanation:

y=3x-2

y=3(2)-2

y=6-2

y=4

Answer:

pretty sure it would be 90 degrees

Answer:

Step-by-step explanation:

The formula for this is

14(20) = 25x and

280 =25x so

x = 11.2

Answer:

x = 6[tex]\sqrt{5}[/tex]

Step-by-step explanation:

Here we need to use the Pythagorean Theorem

Pythagorean Theorem: a^2 + b^2 = c^2

STEP 1: Define your variables

The legs of the triangle are a and b, and the hypotenuse is c.

a = x

b = 4

c = 14

STEP 2: Plug your variables into the equation and solve

x^2 + 4^2 = 14^2

x^2 + 16 = 196

x^2 + 16 - 16 = 196 - 16

x^2 = 180

[tex]\sqrt{x^2}[/tex] = [tex]\sqrt{180}[/tex]

STEP 3: Simplify

Since the question asks you to put the equation in simplified radical form, you do not have to approximate the answer, but you do have to simplify the radical.

[tex]\sqrt{x^2}[/tex] = [tex]\sqrt{180}[/tex]

x = [tex]\sqrt{36}[/tex] * [tex]\sqrt{5}[/tex]

x = 6[tex]\sqrt{5}[/tex]

Work Shown:

y = 2x^3 - 4x

dy/dt = 2*3*x^2*dx/dt - 4*dx/dt

dy/dt = 2*3*1^2*4 - 4*4

dy/dt = 8

notice how I used the chain rule for step 2.

Answer:

(24-8)4

(24-8)*4

16 *4

64

We are given:

aᵇ = bᵃ

b = 2a

Finding (a+b):

Finding a:

replacing b by 2a in the first equation, we get:

(a²)ᵃ = (2a)ᵃ

(a²)ᵃ = 2ᵃ * aᵃ

a²ᵃ / aᵃ = 2ᵃ                  [dividing both sides by aᵃ]

aᵃ = 2ᵃ                          [because xᵃ / xᵇ = xᵃ⁻ᵇ]

a = 2                             [raising both sides to 1/a]

Finding b:

We are given that b = 2a

now that we know what a equals, we will plug that value here

b = 2(2)

b = 4

Finding a+b:

We found that a = 2, b = 4

a + b = 2 + 4 = 6

Answer:

the square root of 85 (so 85 is the answer)

Step-by-step explanation:

You can use the pythagorean theorem to find the height. So the sides of the triangle would contain the radius (4/2 = 2) and 9.

so, 2 squared plus 9 squared = 85

I hope this helps!

Answer:

$60 per ticket

Step-by-step explanation:

$215 is what it costs after the discount, so add the amount taken off, back on.

215+25

 240

Then, divide by 4 to find the cost of each individual ticket.

240/4

60

Hope it helps!

A

Step-by-step explanation:

because it's the only possible one

Answer:

A.) 10

Step-by-step explanation:

So the relationship here seems to be going by two. Every time the x-value decreases from -2 to +7, the y-value is decreasing by 2. Since you're looking for when x=0, the only number that could possibly do that is when y=10. Before x=1, the y-value can increase by two so it would go from 8 to 10 since we know the relationship for the y-values is 2. Therefore your answer should be A.) 10

Hope this helps!

Answer:

possibility of yellow÷ total possibilities

1÷8

1/8

Step-by-step explanation:

hope this is helpful

Answer:

first step - make x² the subject of the formula

x² = 25

second step :

find the square root of both sides

√x² = √25

x = 5

Step-by-step explanation:

Given:

The sine function is:

[tex]y=\dfrac{1}{3}\sin (2x)[/tex]

To find:

The frequency of the graph of given function.

Solution:

If a sine function is defined as:

[tex]y=A\sin(Bx+C)+D[/tex]

Then, the frequency of the sine function is:

[tex]f=\dfrac{B}{2\pi}[/tex]

We have,

[tex]y=\dfrac{1}{3}\sin (2x)[/tex]

Here, [tex]B=2[/tex]. So, the frequency of the given function is:

[tex]f=\dfrac{2}{2\pi}[/tex]

[tex]f=\dfrac{1}{\pi}[/tex]

Therefore, the correct option is D.

Answer:

[tex]x=3\\y=2[/tex]

Step-by-step explanation:

[tex]3x+2y=13\\y=x-1[/tex]

Solve for [tex]y=x-1[/tex] for y:

[tex]y=x-1[/tex]

Substitute [tex]x-1[/tex] for y in [tex]3x+2y=13[/tex]:

[tex]3x+2y=13[/tex]

[tex]3x+2(x-1)=13\\[/tex]

[tex]5x-2=13[/tex]

[tex]5x=13+2[/tex]

[tex]5x=15[/tex]

[tex]x=15/5[/tex]

[tex]x=3[/tex]

Substitute 3 for x in [tex]y=x-1[/tex]:

[tex]y=x-1[/tex]

[tex]y=(3)-1[/tex]

[tex]y=2[/tex]

[tex]x=3[/tex] and [tex]y=2[/tex]

hope this helps...

Answer:

340 ml

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

3/5

Step-by-step explanation:

Remember that odds for plus odds against must be 1. Therefore, 20 out of 50 of the DVRs are defective, so 30 out of 50 would work.

30/50

simplifies into 3/5 so that would be the probability of you picking out a DVR that works, and the probability of picking one that does not work would be the leftover 2/5 . Or, if you're answering with a percent, you would have a 60% chance of picking a working DVR.

I hope this helps, I know the explanation isn't really clear, but I can't really think of another way to explain it.

Answer:

6/4 or 1 1/2

Step-by-step explanation:

You have to use the Keep Change Flip technique.

Keep 3/4.

Change the division symbol to a multiplication one

Flipi 1/2 to 2/1

and when you multiply the answer is 6/4 = 1 1/2

Answer:

x = 0

Step-by-step explanation:

First, multiply 4 by x+1

4x + 4 = 3x + 4

Subtract 3x on both sides

x + 4 = 4

Subtract 4 from both sides

x =

this is x = 0, since x = nothing.

Answer:

x=0

Step-by-step explanation:

4(x+1)= 3x+4

Distribute

4x+4 = 3x+4

Subtract 3x from each side

4x-3x+4 =3x-3x+4

x+4 = 4

Subtract 4 from each side

x+4-4 = 4-4

x=0

Answer:

a) negative reciprocals

Step-by-step explanation: