What is the volume of the prism below?

Answer: 1

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I am to determine the future value of Thomas' deposit with annual compounding

The formula for calculating future value:

FV = P (1 + r)^n

FV = Future value  

P = Present value  

R = interest rate  

N = number of years  

840 x (1.075)^5 = 1205.93

I am to determine the future value of Sherill's deposit in 5 years using simple interest

The amount that would be in the account = amount deposited + interest earned on deposit

interest earned on deposit can be determined by determining the simple interest

Simple interest = amount deposited x time x interest rate

1250 x 0.069 x 5 = 431.25

Amount that would be in her account after 5 years = 1250 +  431.25 =  1681.25

Sheril's money is higher by - 1681.25 -  1205.93 = 475.32

Answer:

See Below.

Step-by-step explanation:

We are given that ΔAPB and ΔAQC are equilateral triangles.

And we want to prove that PC = BQ.

Since ΔAPB and ΔAQC are equilateral triangles, this means that:

[tex]PA\cong AB\cong BP\text{ and } QA\cong AC\cong CQ[/tex]

Likewise:

[tex]\angle P\cong \angle PAB\cong \angle ABP\cong Q\cong \angle QAC\cong\angle ACQ[/tex]

Since they all measure 60°.

Note that ∠PAC is the addition of the angles ∠PAB and ∠BAC. So:

[tex]m\angle PAC=m\angle PAB+m\angle BAC[/tex]

Likewise:

[tex]m\angle QAB=m\angle QAC+m\angle BAC[/tex]

Since ∠QAC ≅ ∠PAB:

[tex]m\angle PAC=m\angle QAC+m\angle BAC[/tex]

And by substitution:

[tex]m\angle PAC=m\angle QAB[/tex]

Thus:

[tex]\angle PAC\cong \angle QAB[/tex]

Then by SAS Congruence:

[tex]\Delta PAC\cong \Delta BAQ[/tex]

And by CPCTC:

[tex]PC\cong BQ[/tex]

Answer:

Step-by-step explanation:

To prove PC = BQ, we need to prove triangle APC and ABQ are congruent.

AP = AB as they are part of equilateral triangle APB

AC = AQ as they are part of equilateral triangle AQC

Angle PAC = Angle PAB + Angle BAC = 60 + Angle BAC

Angle BAQ = Angle QAC + Angle BAC = 60 + Angle BAC = Angle PAC

By SAS, triangle APC and ABQ are congruent and therefore

PC = BQ

Answer:

C. 70%

Step-by-step explanation:

35 / 50 = 70/100 = 70%

So she will be 70% accurate in the next shot.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

B. 44°

Step-by-step explanation:

Central angle = 3x + 10°

Inscribed angle = 2x - 17°

Now

Central angle = 2 * inscribed angle

( Central angle is double of the inscribed angle standing on same arc)

3x + 10° = 2 ( 2x - 17°)

3x + 10° = 4x - 34°

4x - 3x = 34 ° + 10°

x = 44°

Hope it will help :)❤

Answer:

[tex]x^2+y^2=9[/tex]

Step-by-step explanation:

Equation of a circle (when centred at the origin):

[tex]x^2+y^2=r^2[/tex] where r is the radius of the circle

Plug in the point (0,3) to solve for the radius squared

[tex]0^2+3^2=r^2\\9=r^2[/tex]

Plug r² back into the original equation

[tex]x^2+y^2=9[/tex]

I hope this helps!

Question:

A particle moves along the x-axis so that its position at time t>0 is given by [tex]x(t)=\frac{t^2 -9}{3t^2 +8}[/tex]

Show that the velocity of the particle at time t is given by [tex]v(t) = \frac{70t}{(3t^2 + 8)^2}[/tex]

Answer:

[tex]v(t) = \frac{70t}{(3t^2 + 8)^2}[/tex]

Step-by-step explanation:

Given

[tex]x(t)=\frac{t^2 -9}{3t^2 +8}[/tex]

Required

Show that:

[tex]v(t) = \frac{70t}{(3t^2 +8)^2}[/tex]

To calculate v(t), we use:

[tex]v(t) = x'(t)[/tex]

So, we have:

[tex]x(t)=\frac{t^2 -9}{3t^2 +8}[/tex]

Apply quotient rule

[tex]x'(t) = \frac{vu' - uv'}{v^2}[/tex]

Where

[tex]u =t^2 - 9[/tex]

[tex]v=3t^2 + 8[/tex]

So:

[tex]u =t^2 - 9[/tex]

[tex]u' = 2t[/tex]

[tex]v=3t^2 + 8[/tex]

[tex]v' = 6t[/tex]

So, we have:

[tex]x'(t) = \frac{vu' - uv'}{v^2}[/tex]

[tex]x'(t) = \frac{(3t^2 + 8) * 2t - (t^2 - 9) * 6t}{(3t^2 + 8)^2}[/tex]

Expand the numerator

[tex]x'(t) = \frac{6t^3 + 16t - 6t^3 + 54t}{(3t^2 + 8)^2}[/tex]

Collect like terms

[tex]x'(t) = \frac{6t^3 - 6t^3+ 16t + 54t}{(3t^2 + 8)^2}[/tex]

[tex]x'(t) = \frac{70t}{(3t^2 + 8)^2}[/tex]

Recall that:

[tex]v(t) = x'(t)[/tex]

[tex]v(t) = \frac{70t}{(3t^2 + 8)^2}[/tex]

Proved

Answer:

Volume of cylinder = 12,560 feet³

Step-by-step explanation:

Given:

Height of cylinder = 40 ft

Radius of cylinder = 10 ft

Find:

Can its volume be 10 ft ?

Computation:

Volume of cylinder = πr²h

Volume of cylinder = (22/7)(10)²(40)

Volume of cylinder = (3.14)(10)²(40)

Volume of cylinder = (3.14)(100)(40)

Volume of cylinder = 12,560 feet³

Volume of this cylinder never be 10 feet

Answer:

Area:12.5663706            Circumference: 12.5663706

Step-by-step explanation:

Answer:

1. 11x + 11.  2. 3x - 4.

Step-by-step explanation:

sorry if im wrong

Answer:

C

Step-by-step explanation:

because d + Q = 19 is just counting the coins, not the monetary value

and .25q + .10d signs values per coin type.

Answer:

1/3

Step-by-step explanation:

Rewrite the 5 overtime hours as regular hours:

5 hours x 1.5 = 7.5

40 + 7.5 = 47.5

Divide total pay by hours:

926.25/47.5 = 19.50

The hourly rate is $19.50

Answer:

$20.30  plus tax

Step-by-step explanation:

You multiply 28 x .30 and that is your discount.

Answer:

$20.30

Step-by-step explanation:

Answer: 9.

Step-by-step explanation:

6 large rooms which will add up to 18

9 small rooms which will also add up to 18 totaling the 36 guests.

The no. of small and large rooms in the hotel are 9 and 6 respectively.

A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.

Given, Emily is blocking off several rooms in a hotel for guests coming to her wedding.

Let us assume that small rooms be x and large rooms to be y.

Emily booked a total of 15 rooms which is x + y = 15...(i).

which can accommodate 36 guests altogether which is 2x + 3y = 36...(ii)

Now if we multiply eqn(i) by 2 it'll be 2x + 2y = 30...(iii)

Now subtracting eqn(iii) from eqn(ii) we get y = 6.

substituting the value of y in eqn(iii) we get x = 9.

So, the number of small rooms is 9 and no. of large rooms is 6.

learn more about linear equations here :

https://brainly.com/question/13738061

#SPJ2

Answer:

540

Step-by-step explanation:

area of trapezium is b×h

Answer:

540 Sq m

Step-by-step explanation:

Area of parallelogram EFGH

= base * height

= 30 * 18

= 540 Sq m

Answer:

-3 = D

Step-by-step explanation:

A really smart freind of mine says this is the answer.

Answer: B. (10, –20)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

x = -20/11

Step-by-step explanation:

and how -(11 x)/4 - 5 = 0

1/4 (7 x - 12) = 1/2 (9 x + 4)

hope this helps

Answer:

X = 11/20

Step-by-step explanation:

7/4x-3=2+9/2x

We move all terms to the left:

7/4x-3-(2+9/2x)=0

Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R

Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R

We add all the numbers together, and all the variables

7/4x-(9/2x+2)-3=0

We get rid of parentheses

7/4x-9/2x-2-3=0

We calculate fractions

14x/8x^2+(-36x)/8x^2-2-3=0

We add all the numbers together, and all the variables

14x/8x^2+(-36x)/8x^2-5=0

We multiply all the terms by the denominator

14x+(-36x)-5*8x^2=0

Wy multiply elements

-40x^2+14x+(-36x)=0

We get rid of parentheses

-40x^2+14x-36x=0

We add all the numbers together, and all the variables

-40x^2-22x=0

a = -40; b = -22; c = 0;

Δ = b2-4ac

Δ = -222-4·(-40)·0

Δ = 484

The delta value is higher than zero, so the equation has two solutions

We use following formulas to calculate our solutions:

x1=−b−Δ√2ax2=−b+Δ√2a

Δ−−√=484−−−√=22

x1=−b−Δ√2a=−(−22)−222∗−40=0−80=0

x2=−b+Δ√2a=−(−22)+222∗−40=44−80=−11/20

Answer: I don’t understand What is the value of 3 to the power of 2 + 4(2 + 4) × 6 ÷ 8 + 4 but I can solve 2 + 4(2 + 4) × 6 ÷ 8 + 4 for you. Look at the picture

Step-by-step explanation: Hope this help :D

Answer:

Midpoint (-2,4)

distance nearest tenth = 8.9

The approximate distance = 9

Step-by-step explanation:

Formulas

PQ midpoint = (x2 + x1)/2, (y2 + y1)/2

distance d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )

Givens

x2 = -4

x1 = 0

y2 = 1

y1 = 7

Solution

M(PQ) = (-4+0)/2, (1 + 7)/2

M(PQ) = -2, 4

The midpoint is -2,4

The distance = sqrt( (4 - 0)^2 + (1 + 7)^2 )

The distance = sqrt(16 + 64)

The distance = sqrt(80)

The distance = 4√5           exactly

The distance = 8.94    

The distance = 8.9            To the nearest tenth

Question 2

The distance is rounded to the nearest whole number which is 9.

Answer:

49 votes

Step-by-step explanation:

Because 70% of the 350 is 49