What is the volume of the pyramid below?

Answer:

First one: function

Second one: not a function

Step-by-step explanation:

A function is a relationship where each input has it's own unique output. If an input has more than one output then the relationship is not a function

For the first one no x value repeats meaning each input has it's own output therefore it is a function

For the second one the x value 8 has more than 1 output therefore the second one is not a function

Answer:

Step-by-step explanation:

a). In ΔABC and ΔEDC,

Since, AB and DE are parallel and AE is a transversal,

Therefore, ∠CAB ≅ ∠CED [Alternate interior angles]

m∠D = m∠B = 90°

ΔABC ~ ΔEDC [By AA property of similarity of two triangles]

b). Therefore, by the property of similar triangles,

"Corresponding sides of two similar triangles are proportional"

[tex]\frac{DC}{BC}= \frac{DE}{AB}[/tex]

[tex]\frac{60}{200}=\frac{40}{AB}[/tex]

AB = [tex]\frac{40\times 200}{60}[/tex]

     = 133.33

     ≈ 133.3 ft

They should use the conversion factor

1 mile = 5280 feet

To go from feet to miles, you divide by 5280

So,

4224 ft = 4224/5280 = 0.8 miles

The distance between their homes is exactly 0.8 miles

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Annual interest rate (i)= 0.055

Initial investment (PV)= $10,000

Number of years (n)= 7

To calculate the future value (FV), we need to use the following formula (except in d):

FV= PV*(1+i)^n

a.

Semiannual interest rate= 0.055/2= 0.0275

Number of semesters= 7*2= 14

FV= 10,000*(1.0275^14)

FV= $14,619.94

b.

Quarterly rate= 0.055/4= 0.01375

Number of quarters= 7*4= 28

FV= 10,000*(1.01375^28)

FV= $14,657.65

c.

Monthly interest rate= 0.055/12= 0.0045833

Number of months= 7*12= 84

FV= 10,000*(1.0045833^84)

FV= $14,683.18

d.

To calculate the future value using continuous compounding, we need to use the following formula:

FV= PV*e^(n*i)

FV= 10,000*e^(7*0.055)

FV= $14,696.14

Answer:

Step-by-step explanation:

This question is asking us to find where sin(2x + 30) has a sin of 1. If you look at the unit circle, 90 degrees has a sin of 1. Mathematically, it will be solved like this (begin by taking the inverse sin of both sides):

[tex]sin^{-1}[sin(2x+30)]=sin^{-1}(1)[/tex]

On the left, the inverse sin "undoes" or cancels the sin, leaving us with

2x + 30 = sin⁻¹(1)

The right side is asking us what angle has a sin of 1, which is 90. Sub that into the right side:

2x + 30 = 90 and

2x = 60 so

x = 30

You're welcome!

Answer:

94.5 yd^3

Step-by-step explanation:

The volume of a rectangular prism is given by the formula:

A = lwh

Where:

l = length

w = width

h = height

Volume is how much space a 3d figure occupies.

USE THE FORMULA WITH THE GIVEN DIMENSIONS:

A = (7)(4.5)(3)

= (31.5)(3)

= 94.5

Volume is measured in cubic yards, in this case.

Therefore your answer is 94.5 yd^3

I hope I helped!

Answer:

Step-by-step explanation:

length = 7 yd

Width = 4.5 yd

height = 3 yd

Volume of rectangular prism = length * width * height

                                                = 7 * 4.5 * 3 = 94.5 yd³

Answer:

8

Step-by-step explanation:

x=16

x(16)-8=8

Answer:

I solved the question step by step in the pic, and I hope it helps

Answer:

1,086,183,741,982,184

Step-by-step explanation:

998^3

 = (1,000)^3 - (2)^3 - 3 · 1,000 · 2 (1000 - 2)

 = 1,000,000,000 - 8 - 6,000 (998)

 = 999,999,992 - 5,988,000

 = 994,011,992

103^3

 = (100 + 3)^3

 = (100)^3 + (3)^3 + 3(100) (3) + (100+3)

 = 1,000,000 + 27 + 900(103)

 = 1,000,027 + 92,700

 = 1,092,727

994,011,992 · 1,092,727

 = 994,011,992 · (1,000,000 + 90,000 + 2,000 + 700 + 20 + 7)

 = (994,011,992 · 1,000,000) + (994,011,992 · 90,000) + (994,011,992 · 2,000) + (994,011,992 · 700) + (994,011,992 · 20) + (994,011,992 · 7)

= 994,011,992,000,000 + 89,461,079,280,000 + 1,988,023,984,000 + 695,808,394,400 + 19,880,239,840 + 6,958,083,944

 = 1,086,183,741,982,184

Answer:

[tex]\displaystyle lne^4 = 4[/tex]

General Formulas and Concepts:

Algebra II

Natural Logarithms ln and Euler's number e

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle lne^4[/tex]

Step 2: Evaluate

Answer:

18

Step-by-step explanation:

Find the zeros of the divisor

x-2=0

x=2

Plug 2 into the polynomial

4(2)²-2(2)+6

=16-4+6

=18

Answer:

1/4( y -2)

Step-by-step explanation:

1/4 y -1/2

Rewriting

1/4 * 1 y - 1/4*2

Factor out the 1/4

1/4( y -2)

Answer:

[tex]End = (4, 9)[/tex]

Step-by-step explanation:

Given

[tex]Start = (2,6)[/tex]

Transformation: 2 units right and 3 units down

Required

The new point

First, we take the right translation;

When a point is translated right by 2 units, the rule is:

[tex](x,y) \to (x + 2, y)[/tex]

So, we have:

[tex](2,6) \to (2 + 2, 6)[/tex]

[tex](2,6) \to (4, 6)[/tex]

Next, we take the down translation;

When a point is translated down by 3 units, the rule is:

[tex](x,y) \to (x, y + 3)[/tex]

So, we have:

[tex](4,6) \to (4, 6+3)[/tex]

[tex](4,6) \to (4, 9)[/tex]

Hence, the endpoint is:

[tex]End = (4, 9)[/tex]

Solution :

Case I :

If Collen is late on [tex]0[/tex] out of [tex]5[/tex] days.

[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} $[/tex]

[tex]$=\frac{1}{32}[/tex]

Case II :

When Collen is late on [tex]1[/tex] out of [tex]5[/tex] days.

[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times ^5C_1$[/tex]

[tex]$=\frac{1}{32} \times 5$[/tex]

[tex]$=\frac{5}{32}[/tex]

Case III :

When Collen was late on [tex]2[/tex] out of [tex]5[/tex] days.

[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times ^5C_2$[/tex]

[tex]$=\frac{1}{32} \times 10$[/tex]

[tex]$=\frac{5}{16}[/tex]

Therefore, the [tex]\text{probability}[/tex] that Collen will arrive late to work no more than [tex]\text{twice}[/tex] during a [tex]\text{five day workweek}[/tex] is :

[tex]$=\frac{1}{32} + \frac{5}{32} + \frac{5}{16} $[/tex]

[tex]$=\frac{1}{2}$[/tex]

Answer: a and d

Step-by-step explanation:

(to find all points of discontinuity, set denominator equal to zero and solve)

[tex]x^2-7x+10=0\\\\[/tex]

(to factor, find two numbers when added together equal -7 and when multiplied together equal 10)

-2 + -5 = -7

-2(-5) = 10

-2 and -5 are the two numbers

[tex](x-2)(x-5)=0\\\\x-2=0\\x=2\\\\x-5=0\\x=5\\\\x=2,5[/tex]

Answer:

Solution given:

Right angled triangle ABC is drawn where <C=[tex]\theta[/tex]

we know that

[tex]\displaystyle Sin\theta=\frac{opposite}{hypotenuse} =\frac{AB}{AC}[/tex]

[tex]\displaystyle Cos\theta=\frac{adjacent}{hypotenuse}=\frac{BC}{AC} [/tex]

Now

left hand side

[tex] \displaystyle {sin}^{2} \theta + {cos}^{2} \:\theta[/tex]

Substituting value

[tex](\frac{AB}{AC})²+(\frac{BC}{AC})²[/tex]

distributing power

[tex]\frac{AB²}{AC²}+\frac{BC²}{AC²}[/tex]

Taking L.C.M

[tex]\displaystyle \frac{AB²+BC²}{AC²}[/tex]....[I]

In ∆ABC By using Pythagoras law we get

[tex]\boxed{\green{\bold{Opposite²+adjacent²=hypotenuse²}}}[/tex]

AB²+BC²=AC²

Substituting value of AB²+BC² in equation [I]

we get

[tex]\displaystyle \frac{AC²}{AC²}[/tex]

=1

Right hand side

Answer:

x = 6/5  x = -2

Step-by-step explanation:

|5x+2| = 8

There are 2 solutions

5x+2 = 8   and 5x+2 = -8

Subtract 2 from each side

5x+2 -2 = 8-2    and 5x+2-2 = -8-2

5x= 6                           5x = -10

Divide by 5

5x/5 = 6/5                        5x/5 = -10/5

x = 6/5                                  x = -2

Answer:

b

Step-by-step explanation:

|5x+2|=8

1) |5×(-2)+2|=8

|-10+2|=8

|-8|=8

8=8

2) |5×6/5+2|=8

|6+2|=8

|8|=8

8=8

Answer:

C

Step-by-step explanation:

c

Answer:

Answer is 360 degrees

Step-by-step explanation:

The sum of the exterior angles of a triangle is 360°.

Answer: 360 degrees

Step-by-step explanation:

You know that in a triangle is 180 degrees. In the diagram, the figure shows a, b, and c, outside of the triangle. Also, the a, b, and c makes a circle. The circle is 360 degrees, so when you add a, b, and c that will equal 360.

Answer:

Step-by-step explanation:

We have 3 identical pumps working to fill a pool. If it takes them working  together 8 hours to fill the pool, the equation is:

[tex]\frac{1}{x}+\frac{1}{x}+\frac{1}{x}=\frac{1}{8}[/tex] and

[tex]\frac{3}{x}=\frac{1}{8}[/tex] . Cross multiply to get

x = 24, which is the number of hours it will take one pump to do the job all alone. If this be the case, and we have 4 pumps WORKING AT THE SAME TIME, filling the pool will be the number of hours it takes one pump divided by 4.

4 pumps can do the job in 6 hours.

so, start floor = x

x + 7 - 9 - 4 + 8 - 2 = 14

x = 14

the elevator started on the 14th floor.

to verify: 14 + 7 = 21 - 9 = 12 - 4 = 8 + 8 = 16 - 2 = 14

Answer:

The answer is n = - 4.. I hope it will help :)

Answer:

(4x4) + (6x11) = 82 for area

4+4+10+11+7+6= 42

Step-by-step explanation:

You can calculate this by calculating the two squares separately, and on the bottom line, it is 10, so just subtract 4 to make the rectangle on the right, separate from the square on the left. (for area)

Answer:

Step-by-step explanation:

The central angle of a hexagon is 60 degrees. Drop a line from the center to the middle of the side marked 7.

Use the  tan of the angle so formed (which is 30 degrees)

Tan(30)= opposite / height (which is the line you just drew).

Tan(30) = 3.5 / h

Tan(30) = 0.5774

Tan(30) = 3.5 / h                multiply both sides by h

h*Tan(30) = 3.5                  Divide by tan30

h = 3.5 / Tan(30)

h = 3.5 / 0.5774

h = 6.062

Now from both ends of the given side, draw 2 lines to the center. Find the area of that triangle.

Area of 1 triangle = 1/2 * b * h

area of 1 triangle = 1/2 * 7 * 6.062

Area of 1 triangle = 21.2176

There are 6 such triangles so multiply that number by 6

Answer:  6 * 21.2176

Answer:  127.31

Answer:

b,d

Step-by-step explanation:

Answer:

[tex]3y = 6,=> y=2[/tex]

Step-by-step explanai

on:

Answer:

h = 504, k = 65, t = -1

Step-by-step explanation:

56 = h/9

h = 56 x 9

h = 504

k/5 - 10 = 3

k/5 = 3 + 10

k/5 = 13

k = 13 x 5

k = 65

3t + 5 = 2

3t = 2 - 5

3t = -3

t = -3/3

t = -1