Find the volume of the solid. Round your answer to the nearest hundredth.

Answer:

5.4 units

Step-by-step explanation:

Hi there!

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (1,5) and (3,0)

[tex]d=\sqrt{(3-1)^2+(0-5)^2}\\d=\sqrt{(2)^2+(-5)^2}\\d=\sqrt{4+25}\\d=\sqrt{29}\\d=5.4[/tex]

Therefore, the distance between the two points when rounded to the nearest tenth is 5.4 units.

I hope this helps!

Answer:

h=rt.96=4 rt.6

Step-by-step explanation:

r=2 inches

therefore 100= root over h + 4

          =>h=rt.96=4 rt.6

Answer:

[tex]{ \tt{ {(5 {z}^{2} + 3z + 2)}^{2} }} \\ = (5 {z}^{2} + 3z + 2)(5 {z}^{2} + 3z + 2) \\ = (25 {z}^{4} + 30 {z}^{3} + 29 {z}^{2} + 12z + 4)[/tex]

Answer:

C and G

Step-by-step explanation:

Given

(x - 2)² = - 3x + 6 ← expand left side using FOIL

x² - 4x + 4 = - 3x + 6 ( subtract - 3x + 6 from both sides )

x² - x - 2 = 0 ← in standard form

(x - 2)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2 → G

x + 1 = 0 ⇒ x = - 1 → C

Answer:

2/15

Step-by-step explanation:

1/5 + 2/3

= 3/15 + 10/15

= 13/15

15/15 - 13/15

= 2/15

Step-by-step explanation:

14 gallons bought for $34.72

1 gallon bought for

[tex] \frac{34.72}{14} [/tex]

=$2.48

Step-by-step explanation:

the answer is in the image above

Answer:

12

Step-by-step explanation:

[tex]\sqrt{0^{2} + 12^{2} }[/tex]

12

Answer:

[tex]x=7\\y=128\\z=128[/tex]

Step-by-step explanation:

Value of x:-

Form an equation:

[tex]4x+24=7x+3[/tex]  {opposite / vertical angles are equal}

Subtract 7x from both sides:

[tex]4x+24-7x=7x+3-7x[/tex]

[tex]-3x+24=3[/tex]

Subtract 24 from both sides:

[tex]-3x+24-24=3-24[/tex]

[tex]-3x=-21[/tex]

Divide both sides by -3

[tex]-3x/-3=-21/-3[/tex]

[tex]x=7[/tex]

Value of y and z:-

Value of x is 7 so replace x in the equations:

[tex]4(x)+24=52\\7(7)+3=52[/tex]

Now that we have the value of x, its easy to find y and z

[tex]52+52+y+z=360[/tex]

{complete circle makes 360°}

[tex]104+y+z=360[/tex]

[tex]y+z=360-104[/tex]

[tex]y+z=256[/tex]

Divide 256 by 2 to get value of each variable:

vertically opposite angles (y & z) are equal

[tex]256/2 = 128[/tex]

[tex]y=128\\z=128[/tex]

∴ CHECK: 128 + 128 + 52 + 52 = 360°

hope this helps...

Answer:

X=7

Y and Z = 128

Step-by-step explanation:

7X+3=4X+24

it is equal coz by the opposite angle

find the value of X

7x+3=4x+24--------------collect like term

3x=21----------divided by 3

x=7

then 7x+3=52

4x+24=52

SR is the line that measure 180°

that means (7x+3)+Z=180°

use the value of X into the equation

Z=180-52

Z=128

it means Z and Y are equal so Y= 128

Given:

Principal value = $2300

Rate of interest = 14% compounded continuously.

To find:

The time taken by Brad's investment to triple.

Solution:

The formula for amount after the compound interest (Continuously) is:

[tex]A=Pe^{rt}[/tex]

Where, P is the principal, r is the rate of interest in decimal and t is the time period.

Triple of Brad's investment is

[tex]3\times \$ 2300=\$ 6900[/tex]

Substituting [tex]A=6900,P=2300\ r=0.14[/tex], we get

[tex]6900=2300e^{0.14t}[/tex]

[tex]\dfrac{6900}{2300}=e^{0.14t}[/tex]

[tex]3=e^{0.14t}[/tex]

Taking natural log on both sides, we get

[tex]\ln 3=\ln e^{0.14t}[/tex]

[tex]1.0986=0.14t[/tex]                [tex][\because \ln e^x=x][/tex]

[tex]\dfrac{1.0986}{0.14}=t[/tex]

[tex]7.84714=t[/tex]

After approximating the value, we get

[tex]t\approx 7.85[/tex]

Therefore, Brad's investment will take 7.85 years to triple.

Answer:

D

Step-by-step explanation:

its just rabdom numbers

Answer:

D thats just a number no sequence or any thing

Step-by-step explanation:

Answer:

1/12 of the area of the circle

Step-by-step explanation:

Since the total angle measure of a circle is 360 degrees, a 30 degree sector is 30/360=1/12

Answer:

Probability[Random choose marble is green] = 5 / 13

Step-by-step explanation:

Given:

Number of yellow marble in bag = 4

Number of white marble in bag = 4

Number of green marble in bag = 5

Find:

Probability[Random choose marble is green]

Computation:

Probability of an event = Number of favourable outcome / Number of total outcome

Probability[Random choose marble is green] = 5 / [4 + 4 + 5]

Probability[Random choose marble is green] = 5 / 13

6576 cm2

See the image encrypted above.

Answer:

[tex]\text{1. }2.53^{\circ},\\\text{2. }792,772.98\:\mathrm{ft}[/tex]

Step-by-step explanation:

Start by converting miles to feet:

[tex]150\text{ miles}=150\cdot 5280\text{ feet}=792000\text{ feet}[/tex]

Form a right triangle with the plane's displacement marking the hypotenuse of this triangle. We can now use basic trig for a right triangle to solve for the angle of descent.

Let the angle of descent be [tex]\theta[/tex]. In a right triangle, the tangent of an angle is equal to its opposite side divide by its adjacent side.

Therefore, we have:

[tex]\tan \theta=\frac{35000}{792000},\\\\\theta =\arctan(\frac{35000}{792000})=2.53036411\approx \boxed{2.53^{\circ}}[/tex]

In all right triangles, [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle (Pythagorean Theorem).

Therefore, the length of the plane's path is:

[tex]35,000^2+792,000^2=c^2,\\c^2=628489000000,\\c=\sqrt{628489000000}=792772.981376\approx \boxed{792,772.98\:\mathrm{ft}}[/tex]

Answer:

C) 75

Step-by-step explanation:

If January corresponds to x=0 then June corresponds to x=5.

Knowing this we can replace all values of x with 5.

[tex]v=x^4-50x^2+700[/tex]

[tex]v=5^4-50(5)^2+700[/tex]

[tex]v=625-1250+700[/tex]

[tex]v=75[/tex]

Answer:

C'(-1,1)

Step-by-step explanation:

The coordinates of C are (-2,4).

The translation is (x+1,y-3), so we take the x value -2 and the y value 4 and plug it in.

(-2+1,4-3)

=(-1,1)

C' has the coordinates (-1,1)

Answer:

Step-by-step explanation:

By (x+1, y-3), the trapezoid wll move 1 point to the right, and 3 points down.

Answer:

Simultaneous equations

Step-by-step explanation:

4a + 7m = 17.75

2a + 5m = 10.75

Double the 2nd equation and then subtract the two equations to cancel the 4a out

Work with the 'm' terms and find the value of m

After finding the value of 'm', substitute it into one of the original equations (the ones given in the question) and solve to find the value of 'a'

Hope this helped

Answer:

- 10p2

Step-by-step explanation:

p(8p - 18 p)

p x -10p

ans = -10p2

Answer:  -10p²

This is the same as saying -10p^2

============================================

Explanation:

Both terms 8p² and -18p² are like terms.

We combine them in much the same way as 8-18 = -10, just with a p² attached to everything.

So 8p² - 18p²  = (8-18)p² = -10p²

The coefficient -10 is negative because we're subtracting small minus big. If it was the other way around, then we'd get a positive value.

Answer:

(0.5, -3.5)

Step-by-step explanation:

(x1 + x2/2,   y1 + y2/2)

(-2 + 3 / 2,   -5 - 2 / 2)

(1/2, -7/2)

Answer:

(12,0)

Step-by-step explanation:

So whenever you are asked for an "intercept" it is the point where a line crosses the axis. The x intercept is where the line crosses at the x axis (horizontal line on the graph) and the y intercept is where the y axis crosses (vertical axis).

So this question is really asking where is the point when y = 0

The x values in the chart are 5 apart-- 22 +5 = 27, 27+ 5 = 32

The y values are 18 apart --> 36 + 18 = 54, 54+ 18 = 72

Make a little chart where y = 0 (this is where the x crosses) and you can see

there is a point at (17, 18) and then (12, 0) and that point is the x intercept.

Answer:

(12, 0)

Step-by-step explanation:

the x-intercept is the point, where y=0.

so, the second coordinate is therefore 0, no matter what.

now, at what x is that ?

let's find the line function.

a line is

y = a×x + b

let's use the first point (22, 36)

36 = a×22 + b

a = (36 - b)/22

let's use the second point (27, 54)

54 = a×27 + b

now we use the first expression describing a in terms of b and insert that into the second expression.

54 = 27×(36 - b)/22 + b

54×22 = 27×(36 - b) + 22b = 972 - 27b + 22b

1188 = 972 - 5b

216 = -5b

b = -43.2

=>

a = (36 - -43.2)/22 = (36 + 43.2)/22 =79.2/22 = 3.6

our line is

y = 3.6x - 43.2

so, now back to the question, at what x is y=0 ?

0 = 3.6x - 43.2

3.6x = 43.2

x = 12

Answer:

The answer is going to be the general form for e^x = 1 + x/(1!) + + x^2/(2!) + x^3/(3!) +.....,. till infinity so : e^4 = 1 + 4/1 + 16/ 2 + 64/6 + 256/24 + 1024/ 120 + 4096/720 + 16384/5040 +...till the fraction is<0.1 = 54.6

Answer:

A

Step-by-step explanation:

i don't know the real answer but i have learned it before so it's an educated guess

Answer:

25+40x=195

Step-by-step explanation:

If he already has $25, you need to add that to 40x (40 times the amount of weeks it takes to get to 195, added with 25).

Answer:

0.13347022587

Step-by-step explanation:

Answer:

7 R 32

Step-by-step explanation:

   0 0 7

6 5 4 8 7

 − 0    

   4 8  

 −   0  

   4 8 7

 − 4 5 5

     3 2

Answer:

PQ = 46

Step-by-step explanation:

The midsegment ST is half the length of the third side PQ , that is

ST = [tex]\frac{1}{2}[/tex] PQ , so

5x - 22 = [tex]\frac{1}{2}[/tex] (3x + 19) ← multiply both sides by 2 to clear the fraction

10x - 44 = 3x + 19 ( subtract 3x from both sides )

7x - 44 = 19 ( add 44 to both sides )

7x = 63 ( divide both sides by 7 )

x = 9

Then

PQ = 3x + 19 = 3(9) + 19 = 27 + 19 = 46

Answer:91%

Step-by-step explanation:

Answer:

3 1/25

Step-by-step explanation:

3.04

Do the decimal part first

.04 = 4/100

Reduce - cancel out 4

1/25

Put back the whole number

3 1/25

Answer:

3 [tex]\frac{1}{25}[/tex]

Step-by-step explanation:

I agree with the previous answer :

You need to do it part by part.

0.04 is equal to [tex]\frac{4}{100}[/tex]

[tex]\frac{4}{100}[/tex] simplified (we divide by 4 with both the denomantor and the numerator.) =

[tex]\frac{1}{25}[/tex]

And we still have those 3 wholes that we had in the beginning.

Now we add.

3 + [tex]\frac{1}{25}[/tex] = 3 [tex]\frac{1}{25}[/tex]

Answer:

Step-by-step explanation:

Lateral area, Al = a√(a² + 4h²)

Where,

a = base edge = 5 in

h = height = 10 in

Lateral area, Al = a√(a² + 4h²)

= 5√(5² + 4*10²)

= 5√(25 + 4*100)

= 5√(25 + 400)

= 5√425

= 5 * 20.615528128088

= 103.07764064044

Approximately,

Lateral area = 103.08 in²

Answer: 100

Step-by-step explanation: each side has an area of 10*5/2, or 25, and there are 4 lateral sides, so times 4, it's 100