A basketball team wants to paint half of a free-throw circle grey. If the circumference of the free-throw circle is 30.77 feet, what is the area that will be painted grey? Use 3.14 for π, and round to the nearest square foot

Answer:

Rectangle.

Step-by-step explanation:

The 2 dimensional section would be a rectangle.

Answer:

rectangle

Step-by-step explanation:

Answer:

a rational number

Step-by-step explanation:

a rational number + a rational number will always be a rational number.

Answer:

⅑

Step-by-step explanation:

Let m represents number of males, and f represents number of females taking the maths course.

Given that number of males (m) taking the maths course is 8 times as much as number of females (f), total number of students taking the maths course (T).

Thus we can represent the information above with the following:

m = no. of males

f = no. of females

T = Total

m = 8f

T = m + f

Thus,

Total = 8f + f = 9f

==>The fraction of the course that are females = No. of females (f) ÷ Total no. of students (T)

= f/9f

Fraction of females in simplified form would be ⅑

Answer:

14

Step-by-step explanation:

5x-7=3x+21

2x=28

x=14

Answer:

14

Step-by-step explanation:

Subtracting 3x and adding 7 to both sides we get 2x = 28. Dividing the equation by 2 gets us x = 14.

Step-by-step explanation:

Overtime rate= r+50%= 1.5r

Regular hours= 800/r

Overtime hours= 240/1.5r

Total hours worked

[tex]AB=8.391[/tex]

[tex]AC=13.05407[/tex]

Answer:

AB =8.4

AC = 13.1

Step-by-step explanation:

Use SOH CAH TOA, which means Sin= Opposite/Hypotenuse, Cosine= Adjacent/Hypotenuse, and Tangent= Opposite/Hypotenuse.

AB is the opposite compared to the angle, BC is the adjacent compared to the angle, and AC is the hypotenuse.

Write down what you know in the formulas:

theta = 40 degrees

BC = adjacent = 10

Plug them in to solve what you need:

AB is opposite, so use the tangent equation:

tangent (40 degrees) = AB / 10

AB =8.4

AC is the hypotenuse, so use the cosine equation:

cosine (40 degrees) = 10 / AC

AC = 13.1

Answer: $8859

Step-by-step explanation:

Let value after 10 years be y

y = 45000 (0.85)^10

y = 45000 (0.2)

y = 8859

Answer:

u^2 +7u -8=0  where u = 3x+2

Step-by-step explanation:

(3x+2)^2 + 7(3x+2) - 8=0

Let 3x+2 = u

u^2 +7u -8=0

Answer:

its a on edge

Step-by-step explanation:

Answer:

19) x=-3, 20) a=1, 21) b=3, 22) x=8

Step-by-step explanation:

hope that helps, those are the answeres to each question. :)))

Answer:

Step-by-step explanation:

Answer:

The slope of the line is: [tex]\frac{-1}{6}[/tex]

The midpoint is located in (1, 8.5)

The distance between the points is 2.236

Step-by-step explanation:

The slope of the line can be calculated by:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8-9}{4+2} = \frac{-1}{6}[/tex]

The midpoint can be calculated by:

[tex]midpoint = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})\\midpoint = (\frac{-2 + 4}{2}, \frac{9 + 8}{2})\\midpoint = (1, 8.5)[/tex]

The distance between two points is:

[tex]distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\distance = \sqrt{(-4+2)^2 + (8 - 9)^2}\\distance = \sqrt{(-2)^2 + (-1)^2}\\distance = \sqrt{4 + 1} = \sqrt{5} = 2.236[/tex]

Answer:

L= 12170  ft

Step-by-step explanation:

The runaway at the airport has the shape of a rectangle and the area of 2,312,300 ft².  The rectangular runaway is 190 ft wide . The length is what we are asked to find.

area of a rectangle = LW

Where

L = length

W = width

area of a rectangle = LW

area of the rectangular runaway = 2,312,300 ft²

W = 190 ft

L = ?

2,312,300 = L × 190

2,312,300 = 190L

divide both sides by 190

L = 2,312,300/190

L= 12170  ft

Answer:x=7/5 or 1 2/5

Step-by-step explanation:

x + 3/5=2

Step 1: Subtract 3/5 from both sides.

X+3/5-3/5=2-3/5

X=7/5

Answer:

7/5 or 1 2/5

Step-by-step explanation:

[tex]x+\dfrac{3}{5}=2 \\\\\\x=2-\dfrac{3}{5} \\\\\\x=\dfrac{10}{5}-\dfrac{3}{5} \\\\\\x=\dfrac{7}{5}= 1\dfrac{2}{5}[/tex]

Hope this helps!

Answer:

53 cupcakes

Step-by-step explanation:

Take the amount of frosting and divide by the amount needed per cupcake

431/8

53.875

We round down since we cannot frost part of a cupcake

53 cupcakes

Answer:

53 cupcakes

Step-by-step explanation:

He has a total of 431 ounces and each cupcake needs 8 ounces of frosting. Therefore can divide the total amount of frosting (431 ounces) by the amount per cupcake (8 ounces)

total amount/ amount per cupcake

431 ounces/8 ounces

431/8

53.875

0.875, or a fraction/part of a cupcake can’t be frosted, so we should round down to the nearest whole number.

53

He can frost 53 cupcakes.

Answer:

[tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.

Step-by-step explanation:

We are given that in 1995, the USPS approximated that they handled  [tex]1.8 \times 10^{11}[/tex] pieces of mail and in 2010, the USPS reported that they handled [tex]1.7 \times 10^{11}[/tex]  pieces.

To find how many more pieces of mail were handled in 1995 than in 2010, we do subtraction of the pieces of mail that were handled in both the years.

Pieces of mail handled in 1995 = [tex]1.8 \times 10^{11}[/tex]

Pieces of mail handled in 2010 = [tex]1.7 \times 10^{11}[/tex]  

As it is clear that more pieces of mail were handled in 1995.

So, Pieces of mail handled in 1995 - Pieces of mail handled in 2010 = [tex](1.8 \times 10^{11}) -(1.7 \times 10^{11})[/tex]

=  [tex]10^{11} \times (1.8 -1.7)[/tex]

=  [tex]10^{11} \times 0.1[/tex] = [tex]1 \times 10^{10}[/tex]

Hence, [tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.

The correct pairs of equivalent expressions are given below.

We have given that,

(5 + 2b)+(2b + 3/2)

(-14 + 3/2b)-(1 + 8/2b)

(-10 + b)+(7b -5)

(7/2b - 3)-(8 + 6b)

We have to determine the equivalent expression

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

(5 + 2b)+(2b + 3/2) <--> 4b + 13/2

(-10 + b)+(7b - 5) <---> 8b - 15

(-14 + 3/2b)-(1 + 8/2b) <----> -15 - 5/2b

(7/2b - 3)-(8 + 6b) <-----> -5/2b - 11

To learn more about the expression visit:

https://brainly.com/question/723406

#SPJ2

Answer:

it's answer is

125+25+5+1

Answer:

Z=+6

Step-by-step explanation:

Z^5=-7776i

Let's note that i I mathematics means negative one i.e

i = -1

So the equation is equal to

Z^5=-*-(7776)

Z^5 = 7776

Z= 5√7776

Since it's a divisible by 6

It's giving us a clue that 6 it's the answer.

Ok let's check the 5th root of 7776 in our calculator.

Z=+6

+6 is the solution to the equation

Z^5=-7776i

Answer:

1. 22x+33

2.24-16x

Step-by-step explanation:

Use the distributive property to multiply the variables

(2x times 11)plus (three times 11)

(8 times 3)plus(eight times -2x)

Answer:

  a) h(t) = -16t^2 +41t +37

  b) see attached (3.270 seconds)

  c) (41+√4049)/32 seconds

  d) 1.28125 seconds; 63.265625 feet

  e) [1.5, 2]: -15; [2, 2.5]: -31; [2.5, 3]: -47

Step-by-step explanation:

a) The formula and initial values are given. Putting those values into the formula, we get ...

  h(t) = -16t^2 +41t +37

__

b) The graph is attached. It shows the t-intercept to be about 3.270 seconds.

__

c) Using the quadratic formula, we can find the landing time as ...

  [tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-41\pm\sqrt{41^2-4(-16)(37)}}{2(-16)}\\\\=\dfrac{41\pm\sqrt{4049}}{32}\qquad\text{only $t>0$ is useful}[/tex]

The exact landing time is (41+√4049)/32 seconds.

__

d) The highest point is at t=-b/(2a) = -41/(2(-16)) = 41/32 seconds.

The value of the function at that point is ...

  h(41/32) = (-16(41/32) +41)(41/32) +37 = 41^2/64 +37 = 4049/64

The maximum height is 4049/64 = 63.265625 feet.

__

e) For a quadratic function, that average rate of change on an interval is the derivative at the midpoint of the interval. Here, the derivative is ...

  h'(t) = -32t +41 . . . in feet per second

Then the average rates of change are ...

  arc[1.5, 2] = h'(1.75) = -32·1.75 +41 = -15 ft/s

  arc[2, 2.5] = h'(2.25) = -32(2.25) +41 = -31 ft/s

  arc[2.5, 3] = h'(2.75) = -32(2.75) +41 = -47 ft/s

These are the average velocity of the water balloon over the given interval(s) in ft/s. Negative indicates downward.

Answer:

(a) h(t) = -16t² + 41t + 37

(b) About 3.3 s

[tex]\large \boxed{\text{(c) }\dfrac{41+ \sqrt{4049}}{32}\text{ s}}[/tex]

(d) -15 ft/s; -31 ft/s; -47 ft/s

Step-by-step explanation:

(a) The function

h(t) = -16t² + v₀t + s₀

 v₀ = 41 ft·s⁻¹

 s₀ = 37 ft

The function is

h(t) = -16t² + 41t + 37

(b) The graph

See Fig. 1.

It looks like the water balloon lands after about 3.3 s.

(c) Time of landing

h = -16t² + 41t + 37

a = -16; b = 41; c = 37

We can use the quadratic formula to solve the equation:

[tex]h = \dfrac{-b\pm\sqrt{b^2 - 4ac}}{2a} = \dfrac{-b\pm\sqrt{D}}{2a}[/tex]

(i) Evaluate the discriminant D

D = b² - 4ac = 41² - 4(-16) × 37 = 1681 + 2368  = 4049

(ii) Solve for t

[tex]\begin{array}{rcl}h& = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-41\pm\sqrt{4049}}{2(-16)}\\\\ & = & \dfrac{41\pm\sqrt{4049}}{32}\\\\t = \dfrac{41- \sqrt{4049}}{32}&\qquad& t = \dfrac{41+ \sqrt{4049}}{32}\\\\\end{array}\\[/tex]

[tex]\text{The water balloon will land after $\large \boxed{\mathbf{\dfrac{41+ \sqrt{4049}}{32}}\textbf{ s}} $}[/tex]

(d) Time and maximum height

(i) Time

The axis of symmetry (time of maximum height) is at t = -b/(2a)

[tex]t = \dfrac{-41}{2(-16)} = \dfrac{41}{32} = \textbf{1.281 s}[/tex]

(ii) Maximum height

The vertex is at y = h(1.281) = h(t) = -16(1.281)² + 41(1.281) + 37  = 63.27 ft

(e) Average rate of change

(i) Arc{1.5,2}

h(1.5) = 62.5

  h(2) = 55

m = (h₂ - h₁)/(t₂ - t₁) = (55 - 62.5)/(2 - 1.5) = -7.5/0.5 = -15 ft/s

The water balloon has started to fall after it has reached peak height, so it is not going very fast

(ii) Arc{2,2.5}

h(2.5) =39.5

m = (39.5 - 55)/(2 - 1.5) = -15.5/0.5 = -31 ft/s

The balloon is in mid-fall, so gravity has caused it to speed up.

(iii) Arc{2.5,3}

h(3) = 16

m = (16 - 39.5)/(2 - 1.5) = -23.5/0.5 = -47 ft/s

The balloon is about to hit the ground, so it is falling at almost its maximum velocity.

Fig. 2 shows the height of the balloon at the above times.

Answer:

  Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive

Step-by-step explanation:

There are an even number of negative factors, so the product is positive:

  Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive

Answer:

11 is the answer

Step-by-step explanation: i hope so cuz my calculations gives this answer

Answer:

a = -3

Step-by-step explanation:

5^a = 1/125

The fraction 1/125 can be written as a power with base 5.

5^a = 5^(-3)

Cancel the same bases on both sides.

a = -3

Answer:

a = -3.

Step-by-step explanation:

5^a = 1/125

1/125 = 1 / 5^3

= 5^-3

5^a = 5^-3

so a = -3.

Answer:

  y = -1/3x +3

Step-by-step explanation:

When given a point and slope, it is convenient to start with a point-slope form of the equation of a line.

  y = m(x -h) +k . . . . . line with slope m through point (h, k)

  y = (-1/3)(x -3) +2 . . . line with slope -1/3 through point (3, 2)

  y = -1/3x +3 . . . . . . . simplified to slope-intercept form

Answer:

7

Step-by-step explanation:

We want to evaluate the fraction below for x = 3. We will put the value of x to be 3:

[tex]\dfrac{7^2}{x^2-2}\\\\= \dfrac{7^2}{3^2-2}\\\\= \dfrac{49}{9-2}\\\\= \dfrac{49}{7} = 7[/tex]

The answer is 7.

Answer:

Step-by-step explanation:

goodluck khan academy users

Answer:

x= 42

Step-by-step explanation:

(2x +1)°= 85° (vert. opp. ∠s)

2x +1= 85

2x= 85 -1 (bring constant to 1 side)

2x= 84 (simplify)

x= 84 ÷2

x= 42

Answer:

5 × [5(-7)]

= 5 × (-35)   ---- 5 × (-7) = -35

= -175

Answer:

C

Step-by-step explanation:

Got 100% on edge.

secx=1/cosx

1. To solve this problem you must apply the following proccedure:

2. You have to verify if secx sinx=tanx, so, you have:

3. You know that secx=1/cosx, and tanx=sinx/cosx, therefore:

(secx)(sinx)

(1/cosx)(sinx)

sinx/cosx

tanx

Answer:

The answer is B. on edge

Step-by-step explanation: