A cylindrical milk storage tank needs to be built to hold 84.78 cubic feet of milk. The foundation for the tank has already been poured out of 6 foot thick concrete. The radius of the tank will be 3 feet. What is the minium height that the tank can be (in feet)?

Answer:

= (y - 4x) (y - 7)

Step-by-step explanation:

y^2-4xy-7y+28x

--

factor out y from y^2 - 4x : y(y - 4x)

factor out 7 from 28x - 7y : 7(4x - y)

= y (y - 4x) + 7(4x - y)

7 (4x - y) + 7(y - 4x)

= y (y - 4x) - 7(y - 4x)

= (y - 4x) (y - 7)

Work Shown:

(2/3)*60 = (2*60)/3 = 120/3 = 40

Notice how 40/60 = 2/3

period (T): the time it takes to travel one wave

= 2π - (-10π)

= 12π

5 / ( 2 / 3 ) = 7.5

7 full jars

The product of the two terms [tex]\dfrac{4n}{(4n-4)} \times \dfrac{(n-1)}{(n+1)}[/tex] is [tex]\dfrac{n}{(n+1)}[/tex].

A fraction is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25.

The product of the two fractions can be written as,

[tex]\dfrac{4n}{(4n-4)} \times \dfrac{(n-1)}{(n+1)}[/tex]

Taking 4 as the common term from both numerator and denominator of the first fraction, therefore,

[tex]\dfrac{4n}{4(n-1)} \times \dfrac{(n-1)}{(n+1)}\\\\=\dfrac{n}{(n-1)} \times \dfrac{(n-1)}{(n+1)}\\\\[/tex]

Now, cancelling the common factor from the numerator and the denominator, we will get,

[tex]=\dfrac{n}{(n-1)} \times \dfrac{(n-1)}{(n+1)}\\\\\\=\dfrac{n}{(n+1)}[/tex]

Hence, the product of the two terms [tex]\dfrac{4n}{(4n-4)} \times \dfrac{(n-1)}{(n+1)}[/tex] is [tex]\dfrac{n}{(n+1)}[/tex].

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Answer:

803.84 millimeters²

Step-by-step explanation:

How do we find the area of a circle?

Solving

Therefore, the area is 803.84 square millimeters.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Solution:

We know that:

Finding the area of the circle:

Answer:

22

Step-by-step explanation:

Formula : total divide by every hour

13.2/0.6 = 22

Thus, There will be 22 highways sign on the road trip.

[RevyBreeze]

Answer: m<D = 30

Step-by-step explanation: In the third step of the problem, it says that E is next to itself and equals 90. However, this is not true. Angle BEA and angle CED are vertical angles and are both equal to 65°. This means that to find the measurement of angle D, subtract 65 and 85 from 180, which equals 30.

Answer:

3/ 4/5=3.75

Step-by-step explanation:

3/ 4/5

3/ 0.80

= 3.75

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Answer:

85 points

Step-by-step explanation:

His total points will be 235+x

Number of tests will be 4

(235+x)/4 = 80

multiply by 4

235+x= 4*80

235+x= 320

x=320-235

x= 85

He has to get 85 points to average 80

1. Turn x+3y=6 into slope intercept form:

3y = 6 - x

y = 2 - 1/3x

2. The perpendicular slope is always the negative reciprocal.

-1/3 becomes 3/1

3. Find the intercept

5 = (3/1)1 +b

b = 2

Answer: y = 3x + 2, or y = 3/1x + 2

Answer:

x = 5

Step-by-step explanation:

21 - 3x = 6

21 - 6 = 3x

15 = 3x

5 = x

therefore x=5

Answer:

Number of the houses as x =35

Step-by-step explanation:

The number of houses is 1, 2, 3, ..., 49

By observation, the numbers of houses are in an A.P.

Hence

First-term, a = 1

Common difference, d = 1

Let us assume that the number of xth house can be expressed as below:

We know that sum of n terms in an A.P. is given by the formula Sₙ = n/2 [2a + (n - 1) d]

Sum of number of houses preceding xth house = Sₓ ₋ ₁

Sₓ ₋ ₁ = (x - 1) / 2 [2a + ((x - 1) - 1)d]

= (x - 1) / 2 [2 × 1 + ( x - 2) × 1]

= (x - 1) / 2 [2 + x - 2]

= [x (x - 1)] / 2 ---------- (1)

By the given information we know that, sum of number of houses following xth house = S₄₉ - Sₓ

S₄₉ - Sₓ = 49 / 2 [2 × 1 + (49 - 1) × 1] - x / 2 [2 × 1 + (x - 1) × 1]

= 49 / 2 [2 + 48] - x / 2 (2 + x - 1)

= (49 / 2) × 50 - (x / 2) (x + 1)

= 1225 - [x (x + 1)] / 2 ---------- (2)

It is given that these sums are equal, that is equation (1) = equation(2)

x (x - 1) / 2 = 1225 - x (x + 1) / 2

x² / 2 - x / 2 = 1225 - x² / 2 - x / 2

On solving further we get,

x² = 1225

x = ± 35

As the number of houses cannot be a negative number, we consider the number of houses as x = 35

35 is the correct answer

Step-by-step explanation:

Given that the houses in a row are numbered consecutively from 1 to 49. We need to show that there exists a value of x such that the sum of numbers of houses preceding the house numbered x is equal to sum of the number of houses following x. Making it more simple for you; sum of (1, 2, 3, 4.... upto x - 1) is equal to sum of (x + 1), (x + 2), (x + 3).... upto 49.

→ Sum of (x - 1) terms = Sum of (49 - x) terms

"x" is the number of houses required. The sum of houses are in AP where the value of a is 1 and d is also 1; where 'a' is first term and 'd' is common difference. We know that sum of nth term of an AP is given by: T(n) = a + (n - 1)d and upto nth term by S(n) = n/2 (2a + (n - 1)d). And also by T(n) = S(n) - S(n - 1).

As per given problem:

→ (x - 1)/2 (Sum of first and last term) = (49 - x)/2 (Sum of first and last term)

→ (x - 1)(Sum of first and last term) = (49 - x) (Sum of first and last term)

Where first term and last term in LHS is 1 and (x - 1) & in RHS is (x + 1) and 49. Substitute them.

→ (x - 1) (1 + (x - 1)) = (49 - x) ((x + 1) + 49)

→ (x - 1) (1 + x - 1) = (49 - x) (x + 1 + 49)

→ (x - 1) (x) = (49 - x) (x + 50)

→ x² - x = 49x + 2450 - x² - 50x

On solving we get,

→ 2x² - 2450 = 0

→ 2x² = 2450

→ x² = 1225

→ x = ± 35

The number of houses is a positive integer. So negative value neglected. We left with x = 35. Therefore, the value of x is 35.

11/2 so 15 inches high cubic box will get more high I guess

Answer:

STEP 1:Equation at the end of step 1 ((3 • (p3)) + 32p2) - 210p

STEP 2 :Equation at the end of step 2: (3p3 + 32p2) - 210p

STEP 3:STEP 4:

Pulling out like terms  4.1     Pull out like factors :   3p3 + 9p2 - 210p  =   3p • (p2 + 3p - 70) 

Trying to factor by splitting the middle term 4.2     Factoring  p2 + 3p - 70 The first term is,  p2  its coefficient is  1 .The middle term is,  +3p  its coefficient is  3 .The last term, "the constant", is  -70 Step-1 : Multiply the coefficient of the first term by the constant   1 • -70 = -70 Step-2 : Find two factors of  -70  whose sum equals the coefficient of the middle term,

which is   3 .     -70   +   1   =   -69     -35   +   2   =   -33     -14   +   5   =   -9     -10   +   7   =   -3     -7   +   10   =   3   That's itStep-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  10                      p2 - 7p + 10p - 70

Step-4 : Add up the first 2 terms, pulling out like factors :                    p • (p-7)              Add up the last 2 terms, pulling out common factors :                    10 • (p-7)Step-5 : Add up the four terms of step 4 :                    (p+10)  •  (p-7)             Which is the desired factorization

Final result : 3p • (p + 10) • (p - 7)

Step-by-step explanation:

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Answer:

x=45

Step-by-step explanation:

Answer:

-2, -10, and -3

Step-by-step explanation:

-2, -10, and -3 are all colder than -1.

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Answer:

a , d , e

Step-by-step explanation:

Answer:

i dont know can u help me

Step-by-step explanation:

Answer:

2x+3

Step-by-step explanation:

factor into [tex](2x+3)^{2}[/tex]

then square root it [tex]\sqrt{(2x+3)^{2} }[/tex]

We know that,

[tex]{ \longrightarrow \bf \qquad \: {(a + b)}^{2} = {a}^{2} + 2.a.b + {b}^{2} }[/tex]

Solution :

[tex]{ \longrightarrow \sf \qquad \: {4x}^{2} + 12x + 9 }[/tex]

We can also write it as,

[tex]{ \longrightarrow \sf \qquad \: {4x}^{2} + 12x + {3}^{2} }[/tex]

Now, using the formula, we'll solve the expression.

[tex]{ \longrightarrow \sf \qquad \: {2x}^{2} + 2.2x.3 + {3}^{2} }[/tex]

[tex]{ \longrightarrow \sf \qquad \: (2x + 3)^{2} }[/tex]

Since,

Therefore,

Answer:

x = 29°, y = 61°

Step-by-step explanation:

x + 61 = 90

Because of the right angle symbol

x = 90 - 61

x = 29°

x + y = 90

Because vertically opposite angles are equal

29 + y = 90

y = 90 - 29

y = 61°

16 answer correct

80×20

_______. =16

100

Brainliest

Answer:

[tex]9 \frac{4}{5} [/tex]

Step-by-step explanation:

[tex] \frac{7}{5} \times 7 = \frac{7}{5} \times \frac{7}{1} [/tex]

[tex] \frac{7}{5} \times \frac{7}{1} = \frac{49}{5} = 9 \frac{4}{5} [/tex]

Explanation:

One method is to do the steps like this

15% of 60 = 0.15*60 = 9

Or you can solve like this

part/whole = percent/100

x/60 = 15/100

100x = 60*15

100x = 900

x = 900/100

x = 9

Answer:

B

Step-by-step explanation:

The Law of Sines states that

sinA/a = sinB/b = sinC/c

We know A, a, and b. Given this, we can solve for B, and given that, we can solve for C and then c.

First, we solve for B.

sinA/a = sinB/b

sin(15°)/6 = sinB/8

sin(15°)/6 * 8 = sinB

arcsin(sin(15°)/6 * 8) = B ≈ 20.187

Note that there can be a second B value. We can check if there is a second B value by first subtracting the B value we got from 180.

180 - 20.187 = 159.813

Next, we can add that to our existing angle, A = 15°. If that is less than 180, then we do have a second solution. 159.813 + 15 = 174.813 < 180 so there does exist a second solution where B = 159.813

Next, we can solve for C.

We know that the angles in a triangle add to 180°, so A + B + C = 180. Therefore, for the first solution:

15 + 20.187 + C = 180

C = 180 - 15 - 20.187 = 144.813°

and for the second:

15 + 159.813 + C = 180

C = 180 - 15 - 159.813 = 5.187

Finally,

sinA/a = sinC/c

multiply both sides by c to no longer have it as a denominator

sinA * c / a = sinC

divide both sides by (sinA/a) to isolate c

for the first solution:

c = sinC*a/sinA = 13.35868 ≈ 13.36

and for the second:

c = sinC*a/sinA ≈ 2.10

Answer:

900

Step-by-step explanation:

1.analyze problem

2. 30/13*390

3.900

Answer:

96

Step-by-step explanation:

Answer:

942ft^2

Step-by-step explanation:

Use the equation (θ/360)*[tex]\pi[/tex][tex]r^{2}[/tex] to get the area of the shaded sector.

(120/360)*[tex]\pi[/tex]*[tex]30^{2}[/tex]

(1/3)*[tex]\pi[/tex]*900

≈942[tex]ft^{2}[/tex]

The area of the shaded region is 942 square ft if the radius of the circle is 30 ft option (G) is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)

We have a circle shown in the picture.

The area of the shaded region:

[tex]\rm A = \dfrac{120}{360}\pi (30)^2[/tex]

A = 942.47 ≈ 942 square ft

Thus, the area of the shaded region is 942 square ft if the radius of the circle is 30 ft option (G) is correct.

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Answer:

10.6 all white marbles

Step-by-step explanation:

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