5. A water tank is in the shape of a right circular cylinder with a height of 20 feet and a volume of 320pi cubic feet. What is the diameter, in feet, of the water tank? ​

Answer:

There are 585 adults and children

Step-by-step explanation:

Let the number of adults be a, number of children be c and the number of seniors be a

Amount made per group;

adults; 52 * a = 52a

Children : 26 * c = 26c

Seniors = 20 * s = 20s

Adding all will give 20,490

52a + 20s + 26c = 20 490 ••••(i)

Now let us work with the ratios;

a : s = 6 : 1

a/s = 6/1

a = 6s •••••(ii)

Lastly;

a/c = 4/9

4c = 9a ••••(ii)

We want to get a + c

From the first equation , let’s substitute

52(6s) + 20s + 26c = 20,490

26c = 6.5 (4c)

but 4c = 9a; 6.5(9a)

But a = 6s

So we have; 6.5(9)(6s) = 351s

so we have;

312s + 351s + 20s = 20,490

683s = 20,490

s = 20490/683

s = 30

Recall;

a = 6s = 6 * 30 = 180

4c = 9a

4c = 9 * 180

c = (9 * 180)/4 = 405

So the total number of children and adult is a + c

405 + 180 = 585

Answer:

y-1=7(x-0)

Step-by-step explanation:

The line perpendicular to y=-1/7+1 is y=7+1 because you find the reciprocal of the slope.

Then find one point on the line since the equation has a y intercept just use (0,1) and put that into point slope

Answer:

3

Step-by-step explanation:

Answer:

4x+2

[tex] - \frac{84}{5} [/tex]

3x+5

[tex] - \frac{91}{10} [/tex]

Step-by-step explanation:

i hope its correct

Answer:

3

This is the correct answer

Answer:

[tex] a = \frac{28}{ \sqrt{2} } [/tex]

Step-by-step explanation:

[tex] \sin \: 45 \degree = \frac{a}{28} \\ \\ \frac{1}{ \sqrt{2} } = \frac{a}{28} \\ \\ a = \frac{28}{ \sqrt{2} } [/tex]

The side of "a" of right angled triangle is  [tex]\frac{28}{\sqrt{2} }[/tex] .

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.

The basic trigonometric ratios formulas are given below,

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

sec θ = Hypotenuse/Base

cosec θ = Hypotenuse/Perpendicular

cot θ      = Base/Perpendicular

According to the question

In right angle Δ

Hypotenuse = 28

Base for ∠45° = b

Perpendicular for ∠45° = a

now , Using trigonometric ratio

sin θ [tex]= \frac{Perpendicular}{Hypotenuse }[/tex]

sin 45° = [tex]= \frac{a}{28}[/tex]

[tex]\frac{1}{\sqrt{2} } = \frac{a}{28}[/tex]

a = [tex]\frac{28}{\sqrt{2} }[/tex]

Hence, side of "a" of right angled triangle is  [tex]\frac{28}{\sqrt{2} }[/tex] .

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Answer:87.68

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

x = 3

y = 4

2x + y² - 1

2(3) + 4² - 1

2(3) + 16 - 1

6 + 16 - 1

22 - 1

21

Answer:

it's totally depends on u whether you like to find the value of x or value of y

Answer:

1 mas 1 en English es 1 plus 1

Answer:

si

Step-by-step explanation:

Answer:

3,000

Step-by-step explanation:

Since the next number is less than 5 you round down

Answer:

their total collected is $135.45

Step-by-step explanation:

travis collect 20% more than Jessica

if travis collect $43 then

20% of 43

43 × 20 ÷ 100 = $8.6

Jessica collected $8.6 less than travis

$43 - $8.6 = $34.4

and Robin collect 35% more than travis

35% of 43

43 × 35 ÷ 100 = $15.05

therefore Robin collect $15.05 more than travis

$43 + $15.05 = $58.05

their total collected

Jessica collected $34.4

robin collected $58.05

travis collected $43

total

$34.4 + $58.05 + $43 = $135.45

Answer:

D = 4

Step-by-step explanation:

41 divided by 12 is 3.41666666667

then add 7 to 41 = 48

then divide 48 divided by 12 = 4

D then equals 4

Answer: Pam has -8 dollars in her piggy bank  she owns mark 12 dollars

Step-by-step explanation:

The slope is the change in y over the change in x.

The first number in the parentheses is the x value, the second number is the y value.

Slope = (0-3) / (4-0)

Slope = -3/4

The y intercept is the y value when x is 0.

The given point (0,3) has x as 0, so the y intercept would be 3

Answers: slope = -3/4, y intercept = 3

Answer:

y intercept = 3 slope = -3/4

Step-by-step explanation:

I did this on edganuity :)

Answer:

7

Step-by-step explanation:

Simplify the expression.

Answer: 78 square units

Step-by-step explanation:

(2x+1)(x+4)

calculator

Answer:

Step-by-step explanation:

Multiply co efficient of the x^2 and the constant; which will be 8

What can you multiply together that will give you 8 and add that give the co efficient of x, 9

1*8 ✓

(2x^2 +8x) + (1x + 4) = 0

Factorise

2x(x+4) +1(x+4) = 0

2x+1= 0

x+4=0

x = -1/2 or -4

Answer:

X- intercept(S) : (4,0)

Y- Intercept(S) : (0, -6)

Step-by-step explanation:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for Y.

Hopes this helps!

The x- intercept (4, 0) and y intercept ( 0, -6).

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

when the independent variable is 0 and you want to know the value of the dependent variable (zero).

Given:

Equation: 12x - 8y = 48

Now, for x- intercept put y= 0

12x - 8(0)= 48

12x= 48

x= 4

and, for y- intercept put x= 0

12(0) - 8y= 48

-8y= 48

y= -6

Hence, the x- intercept (4, 0) and y intercept ( 0, -6).

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Given:

[tex]ST=4y,TU=2y+6[/tex]

To find:

The value of  y, ST and TU.

Solution:

In triangle STV and UTV,

[tex]m\angle TSV\cong n\angle TUV[/tex]            (Given right angles)

[tex]m\angle SVT\cong n\angle UVT[/tex]            (Given)

[tex]TV\cong TV[/tex]            (Common side)

The corresponding two angles and a non included sides in both triangles are congruent. So, the triangles are congruent by using AAS congruence postulate.

[tex]\Delta STV\cong \Delta UTV[/tex]           (AAS congruence postulate)

Corresponding parts of congruent triangles are congruent. So,

[tex]ST\cong UT[/tex]              (CPCTC)

[tex]4y=2y+6[/tex]

[tex]4y-2y=6[/tex]

[tex]2y=6[/tex]

[tex]y=3[/tex]

Now,

[tex]ST=4y[/tex]

[tex]ST=4(3)[/tex]

[tex]ST=12[/tex]

And,

[tex]TU=2y+6[/tex]

[tex]TU=2(3)+6[/tex]

[tex]TU=6+6[/tex]

[tex]TU=12[/tex]

Therefore, [tex]y=3,\ ST=12\ units,\ TU=12\ units[/tex].

Answer:

The SSS theorem

Step-by-step explanation:

Answer:

SAS Theorem

Step-by-step explanation:

You can tell that the triangles are similar because of the SAS (side-angle-side) theorem.

This is because you already know that two of the sides are congruent since AB and CD were shown to be congruent in the image, and AC and CA are congruent because they're shared. You know that there are similar angles because of the Alternate Interior Angles Theorem*: because of it, you know ∠ACD and ∠CAB are similar because the lines that their transversal intersects are parallel.

*The Alternate Interior Angles Theorem states that if two lines are parallel, the alternate interior angles formed by a transversal are congruent.

Answer:

a^2-12a+35

Step-by-step explanation:

(a-7)(a-5)

a^2-7a-5a+35

a^2-12a+35

Answer:

Simply  which value you put for x  you will get some answer for y that makes x and y coordinates..

Step-by-step explanation:

Like when  x=0

y=3(0)-1=-1

when x=1

y=3(1)-1

y=3-1

y=2

When x=2

y=3(2)-1

y=6-1

y=5

When x=3

y=3(3)-1

y=8

Answer:

n=7

Step-by-step explanation:

71=10n+1

We move all terms to the left:

71-(10n+1)=0

We get rid of parentheses

-10n-1+71=0

We add all the numbers together, and all the variables

-10n+70=0

We move all terms containing n to the left, all other terms to the right

-10n=-70

n=-70/-10

n=7

Hope it helps

Answer:

The equation simplifies to n = 7.

Step-by-step explanation:

Hey there! We have an algebraic equation with the variable n. We want to solve for n. Therefore, we need to simplify the expression as much as we can.

To do this, we're going to notice we have two like terms in the equation:

These two terms can be combined to make one term. In order to do this, we're going to check which side of the equation has two terms.

We are going to then check the sign of the constant. As a reminder, constants are numbers without a variable attached to them.

We see our constant is 1 on the right side and it is positive due to it being added to 10n. Therefore, we are going to do the opposite and subtract it from 71.

This leaves us with a more simplified equation: 70 = 10n.

To make things easier, we're going to use the commutative property and switch the terms around. This will give us 10n = 70. It is easier to operate when our variable term is on the left side.

Now, we need to get our variable by itself. A coefficient is multiplying the variable by that value, so to reverse that, we must divide.

In addition to that, what we do on one side of the equation must be done on the other side of the equation.

[tex]\displaystyle \frac{10n}{10} = \frac{70}{10}[/tex]

This simplifies to n = 7, which is our final answer.

Answer:

x = 21 and y = 83

Step-by-step explanation:

Since the figures are similar, then corresponding sides and angles are congruent, that is

GE = LA

x = 21

and

∠ I = ∠ M , so

y = 83

Answer:

x<-8 is answer

Step-by-step explanation:

I got the big maths