What is the side length of the image if the apothem is 8.3 feet and the area is
214.14 feet squared?

Answer:

c = 3.46

Step-by-step explanation:

use tangent to find c

2 tan 60 = c

firstly label the sides

let me know if you need further explanation on how I got my answer

Answer:

x = 6 , y = 2

Step-by-step explanation:

81x + 10 = 5y + 486 ............ (1)

9x + 40 = 20y + 54 ............ (2)

(1) × 4 - (2)

315x = 1890

x = 6 -------> (2)

9(6) + 40 = 20y + 54

20y = 94 - 54

y = 2

Answer: 338 boys

1) Formulate an equation

The total students at Byrnade Junior High School is 464. Let girls equal x. If girls equal x and there are 212 more boys than girls, then boys should equal 212 + x. (212 + x) and x equal 464. Therefore, our equation would be (212 + x) + x = 464.

2) Isolate the variable

Simplify the equation to 212 + 2x = 464. Subtrac 212 on both sides to get 2x = 252. Divide 2 on both sides to get x = 126.

3) Plug the variable

Because x = 126, we can plug 126 into (212 + x) + x = 464 to get (212 + 126) + 126 = 464. We need to primarily focus on (212 + 126), because the question is asking for how many boys are there. 212 + 126 = 338. So, your answer should be 338 boys.

Answer:

-4

Step-by-step explanation:

<symbol means squared or increase and so does ( )

Answer:

(- 6, 0 )

Step-by-step explanation:

x = -2y - 6 → (1)

- 3x - 7y = 18 → (2)

substitute x = - 2y - 6 into (2)

- 3(- 2y - 6) - 7y = 18 ← distribute parenthesis and simplify left side

6y + 18 - 7y = 18

- y + 18 = 18 ( subtract 18 from both sides )

- y = 0 , then

y = 0

substitute y = 0 into (1)

x = - 2(0) - 6 = 0 - 6 = - 6

solution is (- 6, 0 )

Answer:

  (x, y) = (-6, 0)

Step-by-step explanation:

A system of equations is easily solved using a graphing calculator. The attached shows the solution to be ...

  (x, y) = (-6, 0)

__

The first equation gives a convenient expression for substituting for x in the second equation:

  -3(-2y -6) -7y = 18

  18 -y = 18 . . . . . . . . simplify

  y = 0 . . . . . . . . add y-18

  x = -2(0) -6 = -6

The solution by substitution is (x, y) = (-6, 0).

Answer:

4250

Step-by-step explanation:

0.13 = 13%

1000×0.13=130
130×25= 3250 + 1000 = 4250

What I did:

You have to turn the percent to a decimal first

Then multiply the decimal by the first investment amount (1000)

then multiply that by the years that you have before retirement
You add that amount plus the 1000 you have started with

Answer:

Four lakhs thirty eight thousand five hundred fourty three.

ii)Eight crore ten lakhs one

Follow me friend

Answer:

i)four hundred thirty eight thousand five hundred forty three

ii) eighty million one hundred thousand one

Answer:

-5

f(-1) would be the remainder

Answer:

There are 14 dimes and 17 nickels.

Step-by-step explanation:

Let x be number of nickels and let y be number of dimes.

Given that the total is $2.25 and there are 31 coins, we know that:

[tex]0.05x +0.10y = 2.25[/tex]

[tex]x+y = 31[/tex]

Solving for x yields:

[tex]x=31-y[/tex]

We then proceed by plugging that back into the previous equation:

[tex]0.05(31-y)+0.10y=2.25[/tex]

[tex]1.55 - 0.05y +0.10y = 2.25\\[/tex] --> Distribute

[tex]1.55 +0.05y=2.25[/tex] --> add y's together

[tex]0.05y=0.7[/tex] --> subtract 1.55

[tex]y=14[/tex] --> divide by 0.05

Therefore, x must equal 17, which means you have 14 dimes and 17 nickels.

Answer:

  $104.49

Step-by-step explanation:

The future value of the account is given by the formula ...

  FV = P(1 +r)^t

The interest earned is the difference between that future value and the original amount deposited.

  I = FV -P

__

For the given investment, rate, and time, we find the interest to be ...

  I = $650((1 +0.0125)^12 -1) = $650(0.160755) = $104.49

Mr. Vance's account will have earned $104.49 in interest at the end of 12 years.

The volume of the compound shape, that is the object formed by two hemispheres and a right cylinder is 66π in³.

The volume is the space occupied by an object. The volume of the compound shape equals the sum of the individual volumes, that is, of each part, which are represented by two hemispheres and a right cylinder.

Now we proceed to determine the volume of the compound shape (V), in cubic inches, by apply the following calculation:

V = (4/3) · π · (3 in)³ + π · (3 in)² · (10 in)

V = 66π in³

The volume of the compound shape, that is the object formed by two hemispheres and a right cylinder is 66π in³. [tex]\blacksquare[/tex]

To learn more on volumes, we kindly invite to check this verified question: https://brainly.com/question/13338592

Step-by-step explanation:

a = 7

d = 14-7 = 7

s(50) = n/2*[a+(n-1)*d]

         = 50/2*[7+(50-1)*7]

         = 8750

Answer:

its easy it should be 1.25 or well that the answer I got

Answer:

X=-1

Step-by-step explanation:

As you can see the line is not intercepting at y also

Answer:

  (3 +1.5π) ft ≈ 7.71 ft

Step-by-step explanation:

We see a semicircle, not a "composite figure." The perimeter of the semicircle is the sum of the length of the arc and the length of the straight edge:

  P = (1/2)πd +d . . . where d is the diameter and πd is the full circumference

  P = d(1 +π/2)

  P ≈ (3 ft)(1 +1.57) = 7.71 ft . . . . . using 3.14 for π

The perimeter of the figure is about 7.71 feet.

__

In terms of pi, the perimeter is ...

  P = (3 +1.5π) ft

Answer:

positive

Step-by-step explanation:

if you subtract a negative number, it’s the same as adding a positive number. If you add 2 positive numbers, you get a positive number, so the expression is positive.

40.

60 - 20 = 40.

Very simple.

if its diameter is 6, then its radius is half that or 3.

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h }{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\cfrac{\pi (3)^2(4)}{3}\implies V=12\pi \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2\qquad \implies \qquad SA=\pi (3)\sqrt{3^2+4^2}+\pi (3)^2 \\\\\\ 3\pi \sqrt{25}+9\pi \implies 3\pi (5)+9\pi \implies 15\pi +9\pi \implies 24\pi[/tex]

Answer:

27

Step-by-step explanation:

a+b=7; a-b=3

Add the two equations together

a+b=7

a-b=3

----------------

2a + 0b = 10

2a = 10

Divide by 2

2a/2 = 10/2

a = 5

a+b = 7

5+b = 7

b = 7-5

b = 2

3^a / 3^b = 3^(a-b) = 3^(5-2) = 3^3 = 27

Answer:

Make 2 rectangles and find perimeter and then divide by 2.

Step-by-step explanation:

Hope that helps.

Answer:

5  1/4

Step-by-step explanation:

3 3/4  / ( 5/7) =

15/4  / ( 5/7) =

15/4  *  7/5  =

(15*7) / (4*5 )

105 / 20  =  5 1/4

Answer:

5.25

Step-by-step explanation:

Turn mixed number into a improper fraction.

Divide fraction by 20.

It doesn’t matter if 5 1/4, or 21/4 or 5.25., they all equal the same.

Answer:

a=17

c=9

Step-by-step explanation:

balls

Answer:

c=9 and a=17

Step-by-step explanation:

1. 2a+3c=61

2. 3a+5c=96

the LCM between 2 and 3 is 6 so

equation 1 *3

3.6a+9c+183

equation 2*2

4. 6a+10c=192

equation 3 - equation 4

5. -c=-9

c=9

substitute c into equation 1 or 2 to find a

3a+5(9)=96

3a+45=96

3a=51

a=17

[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)}{1-\sin(t)}[/tex]

Multiply through the second term by [tex]1+\sin(t)[/tex] :

[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)}{1-\sin(t)}\cdot\dfrac{1+\sin(t)}{1+\sin(t)}[/tex]

[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)(1+\sin(t))}{1-\sin^2(t)}[/tex]

Recall that [tex]\cos^2(x)+\sin^2(x)=1[/tex] for all x :

[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)(1+\sin(t))}{\cos^2(t)}[/tex]

If [tex]\cos(t)\neq0[/tex], we can cancel a factor of it in the second fraction.

[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{1+\sin(t)}{\cos(t)}[/tex]

and this simplifies to

[tex]\dfrac{(1+\sin(t))-(1+\sin(t))}{\cos(t)} = \boxed{0}[/tex]

Answer: 24.7 square cm

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

3/12 is 0.25

3 divided by 12 when simplified or reduced

The fraction 3/12 is equal to the exact decimal number.

Answer:

The farthest temperature from zero during the week is 5 °F because it's absolute value, 5, is the highest out of all the other numbers.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

First, we find the equivalent decimal numbers:

-1.75 = -1.75

-7/10 = -0.7

-1 5/7 = -1.7142...

-0.07 = -0.07

Descending order of the equivalent decimal numbers:

-0.07, -0.7, -1.7142..., -1.75

Now we replace the equivalent decimal numbers with the original numbers.

-0.07, -7/10, -1 5/7, - 1.75

Answer: B