The top of the cake to be triangular with one side length 10cm, one side length 12cm and a 90-degree angle between these sides

Answer:

1116

Step-by-step explanation:

3*380 = 1140

1140 - 24 = 1116

Answer:

400 meters

Step-by-step explanation:

50 + 200 + 150 = 400

[tex]c+20=55\\c=55-20\\c=35[/tex]

Answer:

The distance would be [tex]\sqrt{97[/tex].

Step-by-step explanation:

The least distance between them would be to draw a straight line between them.

By calculating the distance between the y values and the x values, you can calculate the distance.

y values:

|5 - 1| = 4

x values:

|6 - -3| = 9

| | = the absolute value, meaning you change the final sign to positive.

Use the Pythagorean theorem [tex]a^2 +b^2=c^2[/tex] and substitute the numbers in.

[tex]4^2 + 9^2=c^2 \\c^2 = 97\\c=\sqrt{97[/tex]

Answer:

5575 cm³

Step-by-step explanation:

The volume of a sphere is V = (4/3)πr³.  If we substitute r = (d/2 where r is the radius and d the diameter), this formula becomes:

                                        πd³

V = (4/3)π·d³/8, or V = -------------

                                           6

and so, if d = 22 cm, the volume is:

        π(22 cm)³

V = ------------------- = 5575 cm³

              6

Answer:

i dont know im not that smart ask someone else dude

Step-by-step explanation:

Answer: C

Step-by-step explanation:

21x+9-3x = 18x + 9

If you factor out the 9, you would be left with

9 (2x+1)

Answer: A. 9(2x - 1)

Step-by-step explanation:

combine like terms

21x+9-3x

21x-3x

18x+9

Factor the expression

factor out 9 from the expression

you get 9(2x - 1)

Answer:

450m

Step-by-step explanation:

Answer:

i think 2

Step-by-step explanation:

Answer:

5.63cm

Step-by-step explanation:

to find length of side AB

12[tex]cos[/tex][62°]

=5.63cm

Answer:

0.075 inches per year

Step-by-step explanation:

The average rate of change is measured as

( difference in diameter ) ÷ ( difference in years )

= ( 251 - 248 ) ÷ ( 2005 - 1965 )

= 3 inches ÷ 40 years

= 0.075 inches per year

Answer: x = 13

angel bge and angle agf are vertical meaning they’re equivalent

77 + 90 + x = 180 (180 because all of them added together are supplementary)

167 + x = 180

x = 13

Answer:

Step-by-step explanation:

X=13

Answer:

Step-by-step explanation:

(5,3) should be your slope. Start from the bottom of the line and go up. Use the X axis slope 1st because of the x1 y1 coordinates.

Answer:

(5,-1)

(-4,0)

Step-by-step explanation:

5 is in the X axis

-1 is in the Y axis

-4 is in the Y axis

0 is in the X axis

Answer:

5

Step-by-step explanation:

The winnings are in G.P. : 1, 2, 4, ..... till 10 toss.

[tex]$a_n = 1 \times 2^{n-1}\ \ \ \forall \ n = 1,2,3,4,....,10$[/tex]

[tex]$a_n$[/tex] denotes the winnings on the [tex]$n^{th}$[/tex] toss.

The probability of earning amount [tex]$a_n$[/tex] on the [tex]$n^{th}$[/tex] toss is = [tex]$\left(\frac{1}{2}\right)^n$[/tex]

∴ [tex]$E(X) = \sum_{n=1}^{10} \ a_n \times \left(\frac{1}{2}\right)^n $[/tex]

            [tex]$=\sum_{n=1}^{10} \ 1 \times \frac{2^{n-1}}{2^n} $[/tex]

           [tex]$=\sum_{n=1}^{10} \ \frac{1}{2}$[/tex]

Sum of the 1st n terms of the A.P. is :

[tex]$=\frac{n}{2}[2a+(n-1)d] $[/tex]

[tex]$=\frac{10}{2}[2\times \frac{1}{2}+(10-1)\times 0] $[/tex]

= 5

Therefore, E(X) = 5

Hence the expected value of the game is 5

Answer:

7. -4/5

8. 1

9. 0

10. 3/4

11. undefined/nonlinear

12. -9/4

13. parallel

Answer:

360

Step-by-step explanation:

All the angles of a polygon add up to 360, thats kinda just how it is haha

Answer:

Step-by-step explanation:

Answer:

I wanna say 16 but im not sure

Step-by-step explanation:

This is an example of a reflection.

Answer:

72°

Step-by-step explanation:

From the question,

Area of the circle = πr²

A = πr²................. Equation 1

Where r = radius of the circle.

⇒ r = √(A/π)............. Equation 2

Given: A = 346.5 cm², π = 3.14

r = √(346.5/3.14)

r = √(110.35)

r = 10.5 cm.

Therefore,

circumference of the circle = 2πr = 2×3.14×10.5

circumference = 65.94 m

If the length of the arc(s) is 1/5 of its circumference.

Therefore, length of arc (s) = 13.188

⇒ length of arc/circumference = 13.188/65.94 =  1/5

s/2πr = θ/360

Where θ = angle substends at the center of the circle

1/5 = θ/360

θ = 360/5

θ = 72°

Answer:

Kristy makes 16 per hour.

Step-by-step explanation: Divded 48 by 3.

Answer:

Length = 3.84 feets (nearest hundredth)

Step-by-step explanation:

The length of section of wire can be obtyaiejd using the length of of a arc formular :

Length of arc = θ/360° * 2πr

Radius, r = 2.5 feets

Length of arc = (88/360) *2πr

Length of arc = (88/360) * 2π*2.5

Length of arc = 0.244444 * 15.707963

Length of arc = 3.8397

Length = 3.84 feets (nearest hundredth)

Answer:

Step-by-step explanation:

3.84

Answer:

(f + g)(2) = 16

(f - g)(2) = 0

(fg)(2) = 64

Step-by-step explanation:

f(2) = 8          g(2) = 8

(f + g)(2) = f(2) + g(2) = 8 + 8 = 16

(f - g)(2) = f(2) - g(2) = 8 - 8 = 0

(fg)(2) = f(2)g(2) = 8(8) = 64

Answer:

The distance the hiker must travel is approximately 5.5 miles

Step-by-step explanation:

The distance between the two cell phone towers = 22.5 miles

The distance between the hiker's phone and Tower A = 14.2 miles

The distance between the hiker's phone and Tower B = 10.9 miles

The direction of the highway along which the towers are located = East to west

The direction in which the hiker is travelling to reach the highway quickly = South

By cosine rule, we have;

a² = b² + c² - 2·b·c·cos(A)

Let 'a', 'b', and 'c', represent the sides of the triangle formed by the imaginary line between the two towers, the hiker's phone and Tower A, and the hiker's hone and tower B respectively, we have;

a = 22.5 miles

b = 14.2 miles

c = 10.9 miles

Therefore, we have;

22.5² = 14.2² + 10.9² - 2 × 14.2 × 10.9 × cos(A)

cos(A) = (22.5² - (14.2² + 10.9²))/( - 2 × 14.2 × 10.9) ≈ -0.6

∠A = arccos(-0.6) ≈ 126.9°

By sine rule, we have;

a/(sin(A)) = b/(sin(B)) = c/(sin(C))

∴ sin(B) = b × sin(A)/a

∴ sin(B) = 14.2×(sin(126.9°))/22.5

∠B = arcsine(14.2×(sin(126.9°))/22.5) ≈ 30.31°

∠C = 180° - (126.9° - 30.31°) = 22.79° See No Evil

The distance the hiker must travel, d = c × sin(B)

∴ d = 10.9 × sin(30.31°) ≈ 5.5

Therefore, the distance the hiker must travel, d ≈ 5.5 miles.