What is the approximate volume of the cylinder? Use 3.14 for T.
5 in.
16 in.


A. 126 in.
B. 153.86 in.
C. 1,256 in.
D. 7,121.52 in.

Answer:

Part A 1 solution

Part B 1,4

Answer:

Part A : It has one solution because the lines intersect at one point

Part B : The solution is the points where the lines intersect

Which is (3,4)

Answer:

-3, 4

Explanation:

x² + x - 12

factorize

x² + 4x -3x - 12

take out common terms

x(x + 4) -3(x + 4)

collect into groups

(x-3)(x+4)

p = -3, q = 4

Answer:

C.  -3 and 4

Step-by-step explanation:

In order to factor a quadratic equation in the form [tex]ax^2+bx+c[/tex]
we need to find a pair of numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].

Therefore, in order to factor [tex]x^2+x-12[/tex] we need to find a pair of numbers that multiply to -12 and sum to 1.

The only pair of numbers in the table that sum to 1 are:

p = -3 and q = 4

Therefore, the solution is option C.

Answer:

option B

Explanation:

Recursive Formula: aₙ = aₙ₋₁ + d

Given Sequence: 7, 4, 1, -2, -5,....

Identify the common difference:

second term - first term

4 - 7 = -3  or 1 - 4 = -3 or -2 - 1 = -3

So formula:

[tex]\sf a_n = a_{n-1}-3[/tex], where [tex]\sf a_1 = 7[/tex]

Find next term:

[tex]\sf a_6 = a_{6-1}-3 = -5-3 = -8[/tex]

Answer:

[tex] \frac{m}{h} = \frac{165}{7} [/tex]

Answer:

[tex](x-4)(x^2+1)[/tex]

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Prime factorization

36 = 3 * 3 *2 * 2

15 = 3 * 5                 The biggest difference is   5 -2 = 3

Answer:

Step-by-step explanation:

cos^-1(√(111))/2√(37) = 30°

m<C = 30°

Answer:

x = 35,000

y = 30,000

Step-by-step explanation:

5x + 2y = 235,000

2x + 3y = 160,000

Have a nice day! :)

Answer:

791,800

Step-by-step explanation:

Answer: 791800

Step-by-step explanation:

Answer:

  $3181.42

Step-by-step explanation:

The balance of an account earning compound interest is given by the formula ...

  A = P(1 +r/n)^(nt)

where P is the principal invested at annual rate r for t years, compounded n times per year.

__

You have P=1580, r=0.10, n=365, t=7, so the balance is ...

  A = $1580(1 +0.10/365)^(365×7) ≈ $3181.42

_____

Additional comment

Your graphing calculator may have a financial function that will calculate this for you.

The height of the guest in inches will be 68.93 and in feet is 5.7.

It states that in the right angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.

By applying the Pythagorean theorem:-

P²  =  H²  - B²

P²  = 84²  -   48²

P²  =  4725

P = √4725

P = 68.73 inches

Now the height in feet will be 68.73  /  12  = 5.7 feet.

Therefore the height of the guest in inches will be 68.93 and in feet is 5.7.

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Answer:

The value of x is 64.

Step-by-step explanation:

The base angles of an isoceles triangle are congruent.

[tex]x + 58 + 58 = 180[/tex]

[tex]x + 116 = 180[/tex]

[tex]x = 64[/tex]

Answer:

216 degrees

Step-by-step explanation:

To convert radian measure to a degree, substitute 180 degrees in for pi.

6(180)/5=216 degrees

Therefore, your answer is 216 degrees

Answer:

purple

Step-by-step explanation:

Answer:

2 feet

Step-by-step explanation:

The shoreline is eroding at 1/3 foot per 2 months. There are 12 months in a year so you multiply 1/3 x 6 and you get 2.

Answer:

Iris is a saleswoman whose base pay plus commissions amounted to $69,464 last year. If her base pay was $39,710 and she made $78,300 in sales last year,

what was her rate of commission?

Commissions were $29,590 against sales of $78,300

Her rate of commission was 37.79%

Step-by-step explanation:

multiply 30% by 210

210 x 0.30 = 63

answer: 63

Answer:

x=16

Step-by-step explanation:

The opposite angles will always be supplementary

<K + < M = 180

47+ 7x+21 = 180

Combine like terms

7x+68 = 180

Subtract 68

7x = 180-68

7x = 112

Divide by 7

7x/7 = 116/7

x =16

The length of arc UT in the diagram given, to the nearest tenth, is calculated as: 3.9 meters.

Length of arc = ∅/360 × 2πr

Given the following:

Radius = 1/2(VS) = 1/2(12) = 6 meters

∅ = 90 - (180 - 127) = 37°

Length of arc UT = ∅/360 × 2πr = 37/360 × 2π(6) = 3.9 meters

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The velocity that the coaster must have at the top of a 50-foot hill to achieve a velocity of 57 feet per second is 7 feet/second.

Velocity is the rate of change of its position with respect to time.

[tex]V = \dfrac{dy}{dt}[/tex]

Given the velocity(v) in feet per second of a roller coaster at the bottom of a hill is related to the vertical drop(h) in feet and the velocity(v°) in feet per second of the coaster at the top of the hill by the formula v°=√(v²-64h).

Therefore, the velocity of the coaster at the top should be,

[tex]v^o=\sqrt{(v^2-64h)}\\\\v^o=\sqrt{[57^2-(64\times 50)]}\\\\v^o=\sqrt{49}\\\\v^o = 7\rm\ feet/second[/tex]

Hence, the velocity that the coaster must have at the top of a 50-foot hill to achieve a velocity of 57 feet per second is 7 feet/second.

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Answer:

but good luck with that man

Answer:

A = 16

Step-by-step explanation:

Formula b*h/2

b =8

h =4

so

A= 8*4/2

A = 16

Answer:

$4742.10

Step-by-step explanation:

Exponential depreciation formula :-

, where y is the value of good after t years , r is rate of depreciation and A is the initial value.

Given : A= $20800  ; r=10.75%=0.1075  

The equation models this situation:

Then, the value of car after t=13 years :-

Hence, the value of car after 13 years = $4742.10

4v points in the same direction as v, so all you need to do is normalize v.

Simply multiply it by the reciprocal of its magnitude:

[tex]v = (-1, 4, 2) \implies \|v\| = \sqrt{(-1)^2 + 4^2 + 2^2} = \sqrt{21}[/tex]

[tex]\implies \dfrac{v}{\|v\|} = \dfrac{(-1,4,2)}{\sqrt{21}} = \left(-\dfrac1{\sqrt{21}}, \dfrac4{\sqrt{21}}, \dfrac2{\sqrt{21}}\right)[/tex]

Answer:

m=5

Step-by-step explanation:

If the triangles are similar, the ratios of the side lengths are the same

AB        AC  

-----  = -------

QR         QS

6         3

----  = -----

10        m

Using cross products

6m = 3*10

6m = 30

Divide each side by 6

6m/6 = 30/6

m = 5

Answer: 15.095$

Step-by-step explanation: