find the radius of cylinder with a volume of 108pi ft3 and height of 12 ft​

Answer:

a=10 and c=20

Step-by-step explanation:

This is a system of equations. I will solve using the substitution method.

a+c=30

12a+8c=280

Solving for a:

a+c-c=30-c

a=30-c

Substituting a into the second equation:

12(30-c)+8c=280

360-12c+8c=280

360-4c=280

-4c=-80

c=20

Substituting into the original equation:

a+20=30

a+20-20=30-20

a=10

To prove this answer is correct, I will plug the solutions back in to the original equation.

a+c=30

10+20=30

30=30, True

12a+8c=280

12*10+8*20=280

120+160=280

280=280, True

Therefore, a=10 and c=20.

Answer:

Janelle can ride her bike at a rate of 9.32 miles per hour

Step-by-step explanation:

15 kilometers is 9.32 miles

Answer:

30%

Step-by-step explanation:

Purchases:

Coat £20

Hat £15

Gloves for £5

Total amount of purchases: £20 + £15 + £5 = £40

Sales:

Coat at 50% profit: 150% × £20 = 1.5 × £20 = £30

Hat: £18

Gloves at a 20% loss: 80% of £5 = £4

Total amount of sales: £30 + £18 + £4 = £52

Amount of profit: £52 - £40 = £12

Percent of profit: £12 / £40 × 100% = 30%

Answer:

y = [tex]\frac{4}{3} x + 2[/tex]

Answer:

Y=4/3x+2

Step-by-step explanation:

The slope is 4/3 because i counted 3 spaces to the right and 4 spaces up which is 4/3 and the starting point is 2 which is where it crosses on the y intercept hope this helps! :)

The dilation which represented by the line is enlargement and the scale factor of dilation is 2.

Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.

The distance from O to A is 3. Therefore,

[tex]OA=3[/tex]

The distance from A to A prime is 3. Therefore,

[tex]AA'=3[/tex]

Here, the new length of the line segment is,

[tex]OA'=OA+AA'\\OA'=3+3\\OA'=6[/tex]

The scale factor of dilation is,

[tex]r=\dfrac{OA'}{OA}\\r=\dfrac{6}{3}\\r=2[/tex]

The scale factor is 2 and the image is enlarged.

Hence, the dilation which represented by the line is enlargement and the scale factor of dilation is 2.

Learn more about the dilation of the figure here;

https://brainly.com/question/3457976

Answer:

enlargement

2

Step-by-step explanation:

Answer:

Michaela gets 3.45$ back.

Step-by-step explanation:

1 carton of eggs = 1.58$

she buys 2, so 2 times 1.58= 3.16$

1 pound of turkey = 6.99$

she buys 4.15 pounds, so 4.15 times 6.99= 29.01$

she buys a jar of jam for 4.38$

4.38 + 3.16 + 29.01 = 36.55$

4 times 10= 40

40 - 36.55 = 3.45$

Answer:

  $3.10

Step-by-step explanation:

The cost of the goods Michaela buys is ...

  2 cartons eggs at $1.58 per carton = $3.16

  4 1/5 pounds turkey at $6.99 per pound = $29.36

  1 jar of jam at $4.38 per jar = $4.38

The total is then ...

  $3.16 +29.36 +4.38 = $36.90

Four $10 bills will be $40, so the change is ...

  $40 -36.90 = $3.10

Michaela will receive $3.10 in change.

_____

Additional comment

We know that Brainly often mangles mixed numbers, so we have assumed that "415" is intended to be 4 1/5. If it is intended to be 4.15 pounds, then the price of the turkey, and the change, will be different by about $0.35. Michaela's change will increase by that amount.

Answer:

(-2/3, 4)

Step-by-step explanation:

3x+2y=10

-12x-2y=-4

-9x=6

x=-6/9=-2/3

-2+2y=10

y=4

Answer:

$2.25

Step-by-step explanation:

last year price = $3.00

this year price = $3.00 - (25% × $3.00)

= $3.00 - $0.75

= $2.25

Answer:

Zachary invests $470 into the account that earns 5% simple interest. At the end of 2 years, the account balance is $517

Step-by-step explanation:

I took the test

The new account balance at the end of 2 years is $517.

5 years

Using this formula

I= (P+r×t)

Where:

I=Interest=?

P=Principal=$400

r=Interest rate=3.5%

t=Time=5 years

Hence:

I= ($400×0.035 x 5)

I= $70

2 years

I=Interest=?

P=Principal=$470

r=Interest rate=5%

t=Time=2 years

I=($470+0.05×2)

I=$47

New balance:

New balance=$400+$70+$47

New balance=$517

Inconclusion the new account balance at the end of 2 years is $517.

Learn more about simple interest here:https://brainly.com/question/2294792

Step-by-step explanation:

opp angles are equal in kite

so x = 48°

bigger diagonal bisects smaller diagonal

w=1.6cm

take ∆rey

r= 90°

angle rye = 48°

90+48+y = 180

y= 90-48=42°

Answer:

80

Step-by-step explanation:

(x + 45) - (1.5x - 12) = 17

x + 45 - 1.5x + 12 = 17

-0.5x+57=17

-0.5x=-40

-40/-0.5=80

Using sampling concepts, it is found that the sampled is biased because only parents who attend the school's musical show are surveyed, hence they are not very likely to support the decrease, and the population proportion should be greater than the one found in the show.

Samples may be classified as:

A sample has to take into account all aspects of the population, otherwise it is biased. In this problem, either people support the decrease, or they do not. Only people that went to the show were surveyed, that is, people who are unlikely to support the decrease, which generates bias, as the population proportion should be greater than the one found in the show.

More can be learned about sampling concepts at https://brainly.com/question/25122507

Answer:

1800-35%=1170

1170-35%=760,5

760,5-35%=494,325

494,325-35%=321,31

311,31-35%=208,85

after round it is 209

Answer:

$209

Step-by-step explanation:

1800-(1800*.35)=1170

1170-(1170*.35)=760.5

760.5-(760.5*.35)=494.325

494.325-(494.325*.35)=321.31125

321.31125-(321.31125*.35)=208.8523125

$209 after 5 years

Hope this helps

Answer:

18.90

Step-by-step explanation:

Answer:

a    8 parts     b    8    3|4 =  3×2|4×2=b|8

Step-by-step explanation:

Answer:

3 solutions

Step-by-step explanation:

x = 0; x = 2; x = -6

As we are given with an equation as follows :

[tex]{:\implies \quad \sf x^{2}(x+2)(x+6)=0}[/tex]

As product of these three factors is equal . So , any of these factor can be 0 as product is 0 only when one of the expressions which are multiplied is 0. So , 3 cases arises as follows ;

[tex]{:\implies \quad \sf x^{2}=0}[/tex]

On raising ½ power to both sides we have ;

[tex]{:\implies \quad \sf x=\pm \: 0}[/tex]

Now , as +0 and -0 have no difference in them . So , it's simply 0

[tex]{:\implies \quad \sf So\quad x=0}[/tex]

[tex]{:\implies \quad \sf x+2=0}[/tex]

[tex]{:\implies \quad \sf So\quad x=-2}[/tex]

[tex]{:\implies \quad \sf x+6=0}[/tex]

[tex]{:\implies \quad \sf So\quad x=-6}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{Hence \:\: x\in \{0,\: -6,\: -2\}}}}[/tex]

Answer:

  x = 3

Step-by-step explanation:

The Pythagorean theorem tells you the sum of squares of the legs is equal to the square of the hypotenuse. In this geometry, a radius from the circle center to point T is length x, and is one leg of the right triangle.

  x^2 +4^2 = (x +2)^2

  x^2 +16 = x^2 +4x +4 . . . . . expand

  12 = 4x . . . . . . . . . . . . . subtract (x^2 +4)

  3 = x . . . . . . . divide by 4

The radius of the circle is 3 cm.

Answer:

false

Step-by-step explanation:

it cannot possibly be 180 because when you add up the other two together and then add 180 it is over 360 degrees

Answer:

x < 38 represents that there is less than 38 cubic meters of water in the pool.

Step-by-step explanation:

" < " sign represents less than.

" > " sign represents more than.

" ≥ " sign represents at least or more than.

" ≤ "sign represents at least or less than.

Answer:

B

Step-by-step explanation:

The sign < means less than

Given x is the volume of the pool

Therefore, x < 38 means the volume of the pool is less than 38 m³

For information, the statements written as inequalities would be

A: x > 38

B: x < 38

C: x ≥ 38

D: x ≤ 38

Answer:

8

Step-by-step explanation:

If we write this as an expression it looks like [tex]16^{\frac{3}{4} }[/tex]

Multiply the top number of the fraction by itself to find its square. Write the result and place the fraction line below it.

Answer:

55

Step-by-step explanation:

The Distance between (-2, -5) and (-2, 6) is 11 and the distance between (-2, 5) and (3, 5) [the altitiude] is 5. 11 x 5 is 55 so therefore the area is 55 :)

Answer:

105% ?

Step-by-step explanation:

I'm not entirely sure if the 1 yard 'squared' is considered in the 30% but assuming it's not ... 1yd =30% 1yd^2=60% and 2yd=45% so 60%+45%=100%

Answer: A

Step-by-step explanation:

Looks like A, since it's the altitude.

Answer:

the answer is twenty four

-5a²+13ab should be subtracted.

Based on the given conditions, formulate,

[tex]→- {a}^{2} - 4 {a}^{2} + 13ab[/tex]

[tex]→-({a}^{2} - 4 {a}^{2}) + 13ab[/tex]

Taking the coefficients or numbers, we get,

[tex]→(- 1 - 4) {a}^{2} + 13ab[/tex]

[tex]→ - 5 {a}^{2} + 13ab[/tex]

Given :

What should be subtracted from a² – 7ab + 3b² to get – 4a² + 6ab + 3b² ?

Solution :

Let the required expression to be subtracted be x

⇢ a² – 7ab + 3b² – x = – 4a² + 6ab + 3b²

⇢ a² – 7ab + 3b² – (– 4a² + 6ab + 3b²) = x

⇢ a² – 7ab + 3b² + 4a² – 6ab – 3b² = x

Combining the like terms :

⇢ a² + 4a² – 7ab – 6ab + 3b² – 3b² = x

⇢ 5a² – 13ab = x

⇢ x = 5a² – 13ab

Therefore,

5a² – 13ab should be subtracted from a² – 7ab + 3b² to get – 4a² + 6ab + 3b².

Answer: 9sqrt(3)

Step-by-step explanation:

First, we can prime factorize 243.

243 = 3^5

Therefore we are computing the square root of 3^5

3^5 = 3^4 * 3^1; 3^4 = (3^2)^2

Therefore, sqrt(3^5) = sqrt((3^2)^2))*3^1)

= 3^2*sqrt(3)

= 9sqrt(3)