What shape is produced when slicing a right rectangular pyramid perpendicular to the base?

Answer:

(a) [tex]U_1 =5[/tex]; [tex]U_2 = 8[/tex]; [tex]U_{18} = 328[/tex]

(b) [tex]U_1 = 11[/tex]; [tex]U_2 =17[/tex]; [tex]U_{18} = 113[/tex]

Step-by-step explanation:

Required

1st, 2nd and 18th terms

To do this, we simply substitute 1, 2 or 18 for n in the given equations

Solving (a):

[tex]U_n =n^2 + 4[/tex]

1st term: n = 1

[tex]U_1 =1^2 + 4[/tex]

[tex]U_1 =1 + 4[/tex]

[tex]U_1 =5[/tex]

2nd term: n = 2

[tex]U_2 = 2^2 + 4[/tex]

[tex]U_2 = 4 + 4[/tex]

[tex]U_2 = 8[/tex]

18th term: n = 18

[tex]U_{18} = 18^2 + 4[/tex]

[tex]U_{18} = 324 + 4[/tex]

[tex]U_{18} = 328[/tex]

Solving (b):

[tex]U_n = 6n + 5[/tex]

1st term: n = 1

[tex]U_1 = 6*1 + 5[/tex]

[tex]U_1 = 6 + 5[/tex]

[tex]U_1 = 11[/tex]

2nd term: n = 2

[tex]U_2 = 6*2 + 5[/tex]

[tex]U_2 =12 + 5[/tex]

[tex]U_2 =17[/tex]

18th term: n = 18

[tex]U_{18} = 6*18 + 5[/tex]

[tex]U_{18} = 108 + 5[/tex]

[tex]U_{18} = 113[/tex]

Answer:

1 --> 26

5 --> 130

11 --> 286

24 --> 624

40 --> 1040

Step-by-step explanation:

to find unit rate divide 78 by 3 and you get 26 gallons, which means you can drive 26 miles with one gallon.

To find the amount of gallon for a certian number of miles, simply divide the number of miles by 26. Ex. 130/26 = 5 gallons

Answer:

Step-by-step explanation:

Answer:

461.97 in³

Step-by-step explanation:

Given the following measurement for the dimension of a box : 13 1/7 inches long, 7 2/5 inches wide, and 4 3/4 inches tall.

The volume of a box is calculated using the relation :

Volume = Length * width * height

Volume = 13 1/7 * 7 2/5 * 4 3/4

Volume = 92/7 * 37/5 * 19/4

Volume = (92*37*19) / (7*5*4)

Volume = 64676 / 140

Volume = 461.97 in³

Answer:

Liability insurance

Step-by-step explanation:

Liability insurance provides protection against claims resulting from injuries and damage to people and/or property. Liability insurance covers legal costs and payouts for which the insured party would be found liable. Provisions not covered include Intentional damage, contractual liabilities, and criminal prosecution.

Answer: 23 2/3 points

Step-by-step explanation:

First, we can set up an equation where Mitch's points are equal to m and Tom's are equal to t.

We can say that 79=3t-8. Next, we can subtract 8 on each side to get 71=3t. Then, we can divide by 3 to get that Tom has 23 2/3 points.

Answer:

22

Step-by-step explanation:

You can also use the radius of the circle and the arc length to find the central angle. Call the measure of the central angle θ. Then: θ = s ÷ r, where s is the arc length and r is the radius.

So...

0=31 divided by 22

0

22 remainder

0=22

22 is the arc's central angle.

:D

Answer:

$0.57

Step-by-step explanation:

20% of $2.85 =

= 0.2 * $2.85

= $0.57

2.85 x 0.2 = 0.57

Yoon saves 57 cents

Answer:

11.76

Step-by-step explanation:

j

Answer:

The rate of change is -4

Step-by-step explanation:

In slope intercept form the m value is the rate of chane/slope

Answer:

[tex]1860 - 550 = 1310 \\ = 1310[/tex]

Answer:

FV= 200*(1.07^n)

Step-by-step explanation:

Current population= 200 deer

Growth rate= 7% per year

To calculate the future value of deer in any given years, we need to use the following formula:

FV= PV*(1+g)^n

FV= future value

PV= present value

g= growth rate

n= number of years

FV= 200*(1.07^n)

For example, the population in 5 years:

FV= 200*(1.07^5)

FV= 281

Answer: X=23

<u is 75

< v is 29

<w is 76

Step-by-step explanation:

< u + < v +< w = 180

<w + 3x+35 = 180

so 3x+35= <v+ <u

3x+35=x+52+x+6

3x+35= 2x+58

x+35=58

x= 23

so each angle

U= (23+52)= 75

V= (23+6)= 29

W=180-75-29= 76

or 3(23)+35+w=180

104+w=180

w= 76

Answer:

C

Step-by-step explanation:

The greatest common factor of 8 and 10 is 2

The greatest common factor of a^4 and a^3 is a^3

The binomial whose greatest common factor is 2a³ is 8a⁴ + 10a³.

The largest number among all the common factors of the given numbers is known as the GCF (Greatest Common Factor) of two or more numbers. The greatest integer that may be used to divide two natural numbers x and y without producing any remainders is called their GCF. There are three main methods for calculating GCF: division, multiplication, and prime factorization.

Given the a³ is not common in  A and B they are wrong

C. 8a⁴ + 10a³

common factors of 8 and 10 is 2

so 8a⁴ + 10a³  has factors 2a³

Hence option C is correct.

Learn more about greatest common factor;

https://brainly.com/question/11221202

#SPJ2

Answer:

2 hours

Step-by-step explanation:

Answer:

sinB

Step-by-step explanation:

Using trigonometric sum/difference rule -

we can expand the expression to

= (sinAcosB + cosAsinB)cosA - (cosAcosB - sinAsinB)sinA

= cosAsinAcosB + cos^2(A)sinB - sinAcosAcosB + sin^2(A)sinB

= cos^2(A)sinB + sin^2(A)sinB

= (cos^2(A) + sin^2(A))sinB, (Pythagorean identity)

= (1 * sinB)

= sinB

Answer: (5/9)(v – 1)

Hope this helps!

Answer:

20x^3/4x7

20/4x^4

5/x^4

Step-by-step explanation:

Answer:

-(14 - 7x)

7(x- 2)

3x - 14 + 4x

these are correct

For this case the distance will be given by:

d ^ 2 = (12 * 1.5) ^ 2 + (8 * 1.5) ^ 2

Rewriting we have:

d ^ 2 = (18) ^ 2 + (12) ^ 2

d ^ 2 = 324 + 144

d ^ 2 = 468

d = root (468)

d = 21.63 Km

Answer:

1) She did not find the full distance each traveled in 1.5 hours.

2) She should have used 12 km for Joseph's distance and 18 km for Isabelle's distance.

Answer:

a and b

Step-by-step explanation:

The option that describes the solutions of the equation is A. Since 7 and 11 are both rational, the sum and difference are rational.

An equation simply means a statement that the values of two mathematical expressions are equal.

In this case, the solutions of the equation is that since 7 and 11 are both rational, the sum and difference are rational.

Learn more about equations on:

https://brainly.com/question/297232

Answer:

replace m with 2 and do 7(2)+9

Answer:

A Square plus B square equals

Step-by-step explanation:

T

Answer:

The answer is below

Step-by-step explanation:

The rocket is made up of square pyramid and a rectangular prism. Hence the volume of the rocket is the sum of the volume of the square pyramid and the volume of the rectangular prism.

Volume of square pyramid = a²h/3

a = base length = 1.1 in, h = height of pyramid = 2.1 in

Volume of square pyramid = a²h/3 = 1.1² * 2.1/3 = 0.847 in³

Volume of rectangular prism = length * breadth * height = 1.1 * 1.1 * 8.2 = 9.922 in³

Volume of rocket = volume of prism + volume of pyramid = 0.847 + 9.922 = 10.769 in³

Answer:

B) 5

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

B. 75.36 cubic cm

Step-by-step explanation:

We will use the formula V=π times r² times h

so, V= 3.14 times 2² times 6

so, V= 3.14 times 4 times 6

= 3.14 times 24

=75.36 cubic cm

Answer:

63076.27

Step-by-step explanation:

Answer:

KL= 14

Step-by-step explanation:

4*2=8

5*2=10

7*2=14

Function 1 Answer: 45

Function 1 Explanation: The rate of change (ROC) is basically the same thing as the slope of a graphed function. If you were to graph this table onto a coordinate plane, the slope of the line formed would be 45. (see Function 2 Explanation for more explanations, duh.)

Function 2 Answer: 40

Function 2 Explanation: Functions can be written in slope-intercept form, like this: y = mx + b. The m is the slope, or ROC (above), and the b is called the y-intercept, or where the line crosses the y-axis. The m in that equation is 40...

Hope that helps!! Sorry that took so long...