suppose I have a 30, 60, 90 right triangle. The hypotenuse is 10 units long. How long are the other sides?

a) short leg = 5; long leg = 5 √2

b) short and long leg = 5 √2

c) short leg = 5; long leg = 5 √3

d) short leg = 5; long leg =8

Answer:

Part A

The circumference of the circular pie before the slice was cut out is approximately 69.1 inches

Part B; The area of the circular pie before the slice was cut out is approximately 380 in.²

Part C

The area of the slice of pie that was cut out in approximately 40 in.²

Part D;

The length of the crust for the slice of pie is approximately 7 inches

Step-by-step explanation:

Part A

The shape of the pie = Circular shape

The radius of the pie, r = 11 inches

The circumference of a circle = 2·π·r

Therefore, we have;

The circumference of the circular pie before the slice was cut out, 'C', is given as follows;

Where;

r = 2 inches

C = 2 × π × 11 inches  = 22·π inches ≈ 69.115 inches

The initial circumference of the circular, C ≈ 69.115 inches

To the nearest tenth of an inch, we have;

The initial circumference of the circular, C ≈ 69.1 inches

Part B; The area of a circle, A = π·r²

Therefore;

For the circular pie before the slice was cut out, A = π·(11 in.)² ≈ 380.133 in.²

To the nearest square inch, we have;

The area of the circular pie before the slice was cut out, A ≈ 380 in.²

Part C

The area of the slice of the pie that was cut out, A is given by the area of a sector of a circle as follows;

[tex]The \ area \ of \ a \ sector, A = \dfrac{\theta}{360 ^{\circ}} \times \pi \cdot r^2[/tex]

The angle of the sector formed by the slice of pie that was cut out, θ = 38°

Therefore, the area of the slice of pie that was cut out, 'A', to the nearest tenth of a square inch  is given as follows;

A = 38/360 × π × (11 in.²) = 40 in.²

The area of the slice of pie that was cut out, A = 40 in.²

Part D;

The length of the crust of the slice of pie that was cut out is given by the arc length of the sector of the circular pie the slice of pie represent as follows;

[tex]Arc \ length = \dfrac{\theta}{360 ^{\circ}} \times 2\cdot \pi \cdot r[/tex]

Therefore for the slice of pie, to the nearest inch, we have;

[tex]Arc \ length = \dfrac{38 ^{\circ}}{360 ^{\circ}} \times 2\times \pi \times 11 \, in. \approx 7 \, in.[/tex]

The length of the crust for the slice of pie ≈ 7 in.

Answer:

surface area

Step-by-step explanation:

A rectangular prism is an optical element which is transparent with flat sides that can pass or reflect light. A rectangular prism is a cube where all its sides are the same.

In the context, in order to find the total square feet of plywood needed to make a prism we have to determine its surface area.

The total surface area of a rectangular prism can be found out by the formula :

A = 2 (hl + lw + wh)

where, h = height of the rectangular prism

            l = length of the rectangular prism

            w = width of the rectangular prism

Answer:

D. x + 23

Step-by-step explanation:

Start by distributing the 3 to the numbers in the parenthesis

3(x + 6) - 2x + 5

3x + 18 - 2x + 5

now just add like terms

3x + 18 - 2x + 5

x + 23

Answer:

-8 x -3 = 24.

Step-by-step explanation:

When to negatives are multiplied, they automatically become positive.  Therefore, 8 x 3 = 24.

Answer:

(8x7)\2 + x =5

Step-by-step explanation:

8x7= 56 \2 28+x= 33

Answer:

p=0.60w

Step-by-step explanation:

Let

p ----> the price of a watermelon in dollars

w ---> the weight of a watermelon in pounds

In this problem we have a proportional relationship

Remember that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form  or  

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem

p=kw

The value of the constant of proportionality k is the same that the unit rate

Find out the unit rate

Divide the total cost by the total weight

k=4.38/7.3=0.60per lb

substitute in the equation

p=0.60w

Step-by-step explanation:

brainliest?

Answer:

Degree: 3

Number of terms: 1

Step-by-step explanation:

The exponent on x is 1. The exponent on y is 2.

1 + 2 = 3

Degree: 3

Number of terms: 1

Answer:

Step 3 contains error.

Step-by-step explanation:

The given equation is :

[tex]\dfrac{1}{4}(\dfrac{1}{3}k+9)=6[/tex]

Step 1.

Cross multiplying,

[tex](\dfrac{1}{3}k+9)=24[/tex]

Step 2.

Subtract 9 from both sides

[tex]\dfrac{1}{3}k+9-9=24-9\\\\\dfrac{1}{3}k=15[/tex]

Step 3.

Cross multiplying

[tex]k=15\times 3\\\\k=45[/tex]

So, there is an error in step 3. The correct answer should be 45.

Answer:

Step-by-step explanation:

y = 3x + 4

Plugin x = 3 in the equation,

y = 3*3 + 4

 = 9 + 4

y = 13

Plugin x = 4 in equation,

y = 3*4 + 4

  = 12 + 4

y = 16

Plugin x = 5 in the equation,

y = 3*5 + 4

  = 15 + 4

y = 19

2) y =x - 7

Plugin x = 10 in the equation

y = 10 - 7

y = 3

Plugin x = 15 in the equation

y = 15 - 7

y = 8

Plugin x = 20 in the equation

y = 20 - 7

y = 13

Answer:

(13, 16)

Step-by-step explanation:

Point A has coordinates (3,2) Point b has the coordinates (27,30)

Therefore the width of the diagram = 27 - 3 = 24 units and the height of the diagram = 30 - 2 = 28 unit

The length of the square = 28 unit / 4 square = 7 unit

Also, half of the height of the diagram = 28/2 = 14 unit

Therefore the x coordinate is given by:

27 - (2 × 7) = 27 - 14 = 13 or 27 - 14 (=13) or 3 + 7 + (24 - 3 × 7) = 13

Also, the y coordinate is given by:

30 - (2 × 7) = 30 - 14 = 16 or 30 - 14 (=16) or (30 + 2)÷2 = 16

Therefore the coordinate for point C is given by (13, 16)

hope it help :)

Answer:

exterior angle is equal to the sum of two interior opposite angle

?=53+53=106°

missing exterior angle =106°

The measure of the exterior angle is 106°.

Exterior angles are angles that are parallel to the inner angles of a polygon but lie on the outside of it.

Given that, a triangle has two interior angles 53° and 53° and an exterior angle x,

Since, we know that, sum of opposite two interior angles of a triangle is equal to measure of exterior angle.

Therefore,

53° + 53° = x

x = 106°

Hence, the exterior angle is 106°

Learn more about exterior angles, click;

https://brainly.com/question/28835566

#SPJ2

Answer:

yes

Step-by-step explanation:

Answer:

[tex] \displaystyle a) \: {x}^{ \circ} = 21.8 ^{ \circ} [/tex]

Step-by-step explanation:

we are given opposite and adjacent

we want to figure out x°

remember that,

[tex] \displaystyle \: \tan( \theta) = \frac{opp}{adj} [/tex]

where our opp is 5 and adj is 12.5

let [tex]\theta[/tex] be x°

so

[tex] \displaystyle \: \tan( {x}^{ \circ} ) = \frac{5}{12.5} [/tex]

[tex] \displaystyle \: {x}^{ \circ} = \arctan \left( \frac{5}{12.5} \right)[/tex]

by using calculator

[tex] \displaystyle \: {x}^{ \circ} = 21.8[/tex]

hence,

our answer is a

Using the table, it is found that there is a 77% probability that a seventh grader chosen at random will play an instrument other than bass.

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

From the table:

Then:

[tex]p = \frac{33}{43} = 0.77[/tex]

0.77 = 77% probability that a seventh grader chosen at random will play an instrument other than bass.

A similar problem is given at https://brainly.com/question/22203443

Answer:

C) 12.5

 The length of BC = 12.5cm

Step-by-step explanation:

Step(i):-

Given that  ΔABC

Given that  AB =  15cm and ∠A =  40°

we will use trigonometric function

                     [tex]tan x = \frac{oppositeside}{adjacentside}[/tex]

                   [tex]tan 40^{0} = \frac{BC}{AB} = \frac{BC}{15}[/tex]

Step(ii):-

we know that tan40° = 0.83909

                 [tex]tan 40^{0} = \frac{BC}{15}[/tex]

                BC =  15 × tan 40°

                BC = 12.58649

                BC = 12.5cm

Final answer:-

 The length of BC = 12.5cm

this what teacher explain to us

Answer:

0

Step-by-step explanation:

The slope of a line is also known as the change in the line. it is often referred to as ([tex]\frac{rise}{run}[/tex]) and can be found using the formula, ([tex]\frac{y_2-y_1}{x_2-x_1}[/tex]). Substitute in the given points and solve for the slope,

[tex]\frac{(2)-(2)}{(3)-(-4)}[/tex]

Simplify,

[tex]\frac{0}{3+4}\\\\\frac{0}{7}[/tex]

The slope of the line is (0).

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

The weeks is the independent variable and the height is the dependent variable.

Step-by-step explanation:

This is because the number of weeks you take to care for it depends on the height it will become. Hope this makes sense!

Answer:

slope: -3/4    y-intercept: 3   equation: y=(-3/4)x+3

Answer:

3/5 mile/h

Step-by-step explanation:

velocity = distance / time

then 1/5 / 1/3 = 1/5 * 3/1 = 3/5

Step-by-step explanation:

(Steve's distance from the tip of the monument I'm assuming?)

ans: about 893.92 ft (√798,025)

a²+b²=c²

a=700

b=555

Answer:

m j ubhyb8yvtucvyrrd86rfutiy

Step-by-step explanation:

Answer:

2.389 × 10^5

Step-by-step explanation:

the coefficient must be between 1 to 10

Answer:

-12

Step-by-step explanation:

Farenheit is on the x-axis (horizontal) so you go to 10, then find the celsius which is on the y-axis (vertical) and the line is around -12. Hope this helps!

Answer:

big shaq

Step-by-step explanation:

Answer:

This is how your function looks on a graph table. Hope this helps.

Answer:

thx for the points

Step-by-step explanation:

u

Answer:

C: 4m, 3m, 4m, 4m

Step-by-step explanation:

The opposite sides of a parallelogram have to be congruent. Since one side is 3m, the quadrilateral is not a parallelogram.