A PE class has 48 students. One group of 24 students chooses to play volleyball. The teacher then divides the
remaining students into as many groups of 5 as possible to shoot baskets. After that the remaining students (not
on a volleyball or basketball team) climb the rock wall.
How many students climb the rock wall?
students

Answer:

3.75

Step-by-step explanation:

Answer:

28 degrees

Step-by-step explanation:

147 - 119 = 28

Answer:

Step-by-step explanation:

Since we already know that PQR is 147 degrees, we just need to subtract PQR to QR, and you will get, (147 - 119), PQ as 28 degrees!

Answer:

55 tickets for adults

Step-by-step explanation:

Start by setting up two equations. One equation will be the total amount of money spent and the other is the total amount of tickets sold. a is the # of adult tickets and c is the # of children tickets sold.

7a+4c=469

a+c=76

Now solve for c in the second equation. Then use that to substitute for c in the first equation.

c=76-a

7a+4(76-a)=469

7a+ 304-4a =469

7a+4a=165

3a=165

a=165/3

a=55

Answer:

y = 3/4x - 5

Step-by-step explanation:

An equation of a line can be written in slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept.

Let's plug in what we know.

The slope is 3/4.

y = 3/4x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the point (4, -2). Plug in the x and y values into the x and y of the standard equation.

-2 = 3/4(4) + b

To find b, multiply the slope and the input of x(4)

-2 = 3 + b

Now, subtract 3 from both sides to isolate b.

-5 = b

Plug this into your standard equation.

y = 3/4x - 5

This is your equation. It has a slope of 3/4, and passes through (4, -2)

Hope this helps!

Answer:

1100 Inches Squared

Step-by-step explanation:

Let the triangle on the top right be - (i)

Let the triangle on the top left be - (ii)

Let the bottom rectangle be - (iii)

1) The base of the triangle (i) = 10 + (20/2) (It is the base of the rectangle halfed + the given amount of half base of the triangle)

=> 10 + 10

=> 20 in

Base = 20 in

Height = 30 in

Area = 1/2 * 20 * 30

=> 10 * 30

=> 300 in

Triangle (i) = (ii)

So, the area of triangle (ii)

=> 300 in

Area of rectangle,

Length * Breadth

=> 20 * 30

=> 500 in

Total arrow's area = 300 + 300 + 500 (i + ii + iii)

=> 1100

Therefore the total area of the shape = 1100 in squared.

Hope it helps :)

Answer:

A , B , C

Step-by-step explanation:

1) find the slope of the given line

slope = (-a/b) = (-8/4) = -2

two parallel lines have the same slope

A : correct

B : (-a/b) = -16/8 = -2 (correct)

C : correct

D : wrong (2 is different from -2)

Answer:

1) x = 12

2) x = 23.1

3) x = 19

4) x = 16

5) x = 8

6) x = 17

Step-by-step explanation:

Comparing the sides of each triangle, we have;

1) [tex]\frac{32}{32 + x}[/tex] = [tex]\frac{24}{33}[/tex]

Cross multiply to get,

(32 + x) * 24 = 32 * 33

768 + 24x =1056

24x = 1056 - 768

24x = 288

x = 12

2) [tex]\frac{14}{34}[/tex] = [tex]\frac{x}{33 + x}[/tex]

cross multiply to have;

34x = 14 (33 + x)

34x = 462 + 14x

20x = 462

x = 23.1

3) [tex]\frac{20}{36}[/tex] = [tex]\frac{30}{x + 35}[/tex]

cross multiply to have;

36 * 30 = 20(x + 35)

1080 = 20x + 700

1080 - 700 = 20x

380 = 20x

x = 19

4) [tex]\frac{22.5}{42.5}[/tex] = [tex]\frac{2x - 5}{3x + 3}[/tex]

cross multiply to have;

42.5(2x - 5) = 22.5(3x + 3)

85x - 212.5 = 67.5x + 67.5

collect like terms

85x - 67.5x = 67.5 + 212.5

17.5x = 280

x = 16

5) [tex]\frac{2x + 4}{2x + 8}[/tex] = [tex]\frac{x + 7}{x + 10}[/tex]

cross multiply to have;

(2x + 8)(x + 7) = (2x + 4)(x + 10)

2[tex]x^{2}[/tex] + 14x + 8x + 56 = 2[tex]x^{2}[/tex] + 20x + 4x + 40

2[tex]x^{2}[/tex] + 22x + 56 = 2[tex]x^{2}[/tex] + 24x + 40

collect like terms to have;

22x - 24x = 40 - 56

-2x = -16

x = 8

6) [tex]\frac{28}{82}[/tex] = [tex]\frac{2x + 8}{7x + 4}[/tex]

cross multiply to have;

82(2x + 8) = 28(7x + 4)

164x + 656 = 196x + 112

164x - 196x = 112 - 656

-32x = -544

x = 17

The value of x in all the options can be determined by using the arithmetic operations. The calculations are given below.

1)

Given :

Two side lengths of a triangle are (x + 32) and 33.

According to the similar triangles property:

[tex]\dfrac{32+x}{32}=\dfrac{33}{24}[/tex]

SImplify the above expression in order to determine the value of 'x'.

768 + 24x = 1056

24x = 288

x = 12

2)

Given :

Two side lengths of a triangle are 34 and (x + 33).

According to the similar triangles property:

[tex]\dfrac{14}{34}=\dfrac{x}{33+x}[/tex]

SImplify the above expression in order to determine the value of 'x'.

34x = 462 + 14x

20x = 462

x = 23.1

3)

Given :

Two side lengths of a triangle are 36 and (x + 35).

According to the similar triangles property:

[tex]\dfrac{20}{36}=\dfrac{30}{35+x}[/tex]

SImplify the above expression in order to determine the value of 'x'.

1080 = 20x + 700

20x = 380

x = 19

4)

Given :

Two side lengths of a triangle are (3x + 3) and 42.5.

According to the similar triangles property:

[tex]\dfrac{22.5}{42.5}=\dfrac{2x-5}{3x+3}[/tex]

SImplify the above expression in order to determine the value of 'x'.

85x - 212.5 = 67.5x + 67.5

17.5x = 280

x = 16

5)

Given :

Two side lengths of a triangle are (2x + 8) and (x + 10).

According to the similar triangles property:

[tex]\dfrac{2x + 4}{2x+8}=\dfrac{x+7}{x+10}[/tex]

SImplify the above expression in order to determine the value of 'x'.

(2x + 8)(x + 7) = (2x + 4)(x + 10)

[tex]2x^2+22x+56=2x^2+24x+40[/tex]

16 = 2x

x = 8

6)

Given :

Two side lengths of a triangle are 82 and (7x + 4).

According to the similar triangles property:

[tex]\dfrac{28}{82}=\dfrac{2x+8}{7x+4}[/tex]

SImplify the above expression in order to determine the value of 'x'.

28(7x + 4) = (2x + 8)82

32x = 544

x = 17

For more information, refer to the link given below:

https://brainly.com/question/25277954

Answer:

Polynomial

[tex]x^4 +3x^3 -5x^2 -7x +20\\\\x^3 -2x^2 +x -12\\\\x^2 + 3x^5 -6x +12x^3[/tex]

not a polynomial

[tex]4\sqrt[3]{x} -\sqrt{x} -20\\\\x^{-3}-x}^{-2}-6x^{-1}+8\\\\\frac{5}{x^3} -\frac{1}{x^2} +\frac{8}{x} -40\\\\[/tex]

Answer:

18

Step-by-step explanation:

Answer:

?

Step-by-step explanation:

Whats the question?

The proportionality constant if, A small smoothie will be 16 fluid ounces and sell for $3.52 is 22.

When the corresponding elements of two numerical sequences, frequently experimental data, have a fixed ratio, this is referred to as the coefficient of proportionality, and the two sequences are said to be proportional or directly proportional.

Given:

A small smoothie will be 16 fluid ounces and sell for $3.52,

Convert the price of the smoothie in cents as shown below,

The price of a smoothie = 3.52  × 100   ($1 = 100 cents)

The price of a smoothie = 352 cents

Calculate the proportionality constant as shown below,

The proportional constant = Fluid / price

The proportional constant = 352 / 16

The proportional constant = 22

Thus, The proportional constant is 22.

To know more about proportionality:

https://brainly.com/question/8598338

#SPJ5

The complete question is: The owners of a smoothie shop want the price of each size smoothie to be proportional to the amount of liquid it contains. A small smoothie will be 16 fluid ounces and sell for $3.52. Find the proportionality constant.

Answer: 12

Step-by-step explanation:

Answer:

33.8

Step-by-step explanation:

a²+b²=c²

15²+b²=37²

225+b²=1369

-225     -225

b²=1144

√1144

b=33.8

The distance from the bottom of the ladder to the bottom of the building would be 33.8 foot.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

If you place a 37-foot ladder against the top of a 15-foot building.

Let BC be the distance from the bottom of the ladder to the bottom of the building.

[tex]|AC|^2 = |AB|^2 + |BC|^2 \\15^2+BC^2=37^2\\225 + BC^2=1369\\BC^2 = 1369 - 225\\\\BC^2 = 1144\\\\BC = 33.8[/tex]

Learn more about Pythagoras' theorem here:

https://brainly.com/question/12105522

#SPJ2

Answer:

[tex]d=10[/tex]

Step-by-step explanation:

Pythagorean theorem:

[tex]d^2+d^2=10\sqrt{2}^2,\\2d^2=200,\\d^2=100,\\d=\boxed{10}[/tex]

Alternative:

[tex]\cos 45^{\circ}=\frac{d}{10\sqrt{2}},\\\frac{\sqrt{2}}{2}=\frac{d}{10\sqrt{2}},\\2d=10\sqrt{2}\cdot \sqrt{2},\\2d=20,\\d=\boxed{10}[/tex]

Alternative (derived from the Pythagorean theorem):

All 45-45-90 triangles have side lengths [tex]x-x-x\sqrt{2}[/tex], where [tex]x\sqrt{2}[/tex] is the hypotenuse. Since this triangle's hypotenuse is [tex]10\sqrt{2}[/tex], its sides are [tex]10-10-10\sqrt{2}[/tex].

Answer:

56 inches squared

Step-by-step explanation:

(4x6) ÷ 2 = 12

12 x 4 = 48

4 x 4 = 16

48 + 16 = 56

Answer:

[tex]k = 1[/tex]

Step-by-step explanation:

Given

[tex]3y = 5x + k[/tex]

Opposite points: [tex](1,-2)[/tex] and [tex](-2,1)[/tex]

Required

Find k

First, calculate the midpoint of the opposite points.

[tex](x,y) = 0.5(x_1 + x_2,y_1 + y_2)[/tex]

This gives:

[tex](x,y) = 0.5(1 -2,-2 + 1)[/tex]

[tex](x,y) = 0.5(-1,-1)[/tex]

Open bracket

[tex](x,y) = (-0.5,-0.5)[/tex]

The equation [tex]3y = 5x + k[/tex] becomes:

[tex]3 * -0.5 = 5 * -0.5 + k[/tex]

[tex]-1.5 = -2.5 + k[/tex]

Solve for k

[tex]k = 2.5-1.5[/tex]

[tex]k = 1[/tex]

Answer:

184.96

Step-by-step explanation:

V = (base × height) ÷ 3

base = pi × radius^2

2 × pi × radius = circumference

2×pi×r = 29.516

÷2 ÷2

pi×r = 14.758

÷3.14 ÷3.14

r=4.7

base= 3.14 × 4.7^2

= 69.36

V = (69.36 × 8) ÷ 3 = 184.96

Answer:

$1.42

Step-by-step explanation:

Ava buys a book for $8.58

She pays with a $10 bill

Hence her change would be

= 10-8.58

= 1.42

Ava change is $1.42

Answer:

556.5 cm²

Step-by-step explanation:

Area of trapezium :

Area = 1/2 (a + b)h

a = base length 1

b = base length 2

h = height

From the information given :

Distance between MN and PQ = Height, h = 21 cm

Base MN, a = 28 cm

Base PQ, b = 25 cm

Hence,

Area = 1/2 (28 + 25) * 21

Area = 1/2 (53) * 21

Area = 556.5 cm²

Answer:

0.51 and 11.24 seconds.

Step-by-step explanation:

The height h of a rocket with an initial upward velocity of 188 feet per second after t seconds is modeled by the function:

[tex]h(t)=188t-16t^2[/tex]

And we want to find all values of t for which the rocket's height is 92.

So, we can set h(t) = 92 and solve for t:

[tex]92=188t-16t^2[/tex]

We can divide everything by four:

[tex]23=47t-4t^2[/tex]

Rearrange the equation:

[tex]4t^2-47t+23=0[/tex]

We can use the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = 4, b = -47, and c = 23. Substitute:

[tex]\displaystyle x=\frac{-(-47)\pm\sqrt{(-47)^2-4(4)(23)}}{2(4)}[/tex]

Evaluate:

[tex]\displaystyle x=\frac{47\pm\sqrt{1841}}{8}[/tex]

Hence, our two solutions are:

[tex]\displaystyle x=\frac{47+\sqrt{1841}}{8}\approx 11.24\text{ or } x=\frac{47-\sqrt{1841}}{8}\approx0.51[/tex]

So, the rocket reaches a height of 92 feet after 0.51 seconds and again after 11.24 seconds.

Answer:

778.5

Step-by-step explanation:

Area of any regular polygon = ( apothem * side length * number of sides ) divided by 2

Given information:

Apothem = 15

Side length = 17.3

Polygon Type = Hexagon ( its important to note that a hexagon has 6 sides )

* Plug in the given values into the formula *

Area = [tex]\frac{15*17.3*6}{2}[/tex]

15 * 17 = 259.5

259.5*6=1557

[tex]\frac{1557}{2} =778.5[/tex]

Hence, area = 778.5 square units

Answer:

778.5

Step-by-step explanation:

Answer:

it's area is 1/2 b×h

1/2×7×3.8

13.3

Answer:

13.3 ft^2

Step-by-step explanation:

area = base x h / 2

A = 7 x 3.8 / 2

A = 26.6 / 2

A = 13.3 ft^2

Answer:

5 / 8

Step-by-step explanation:

Given :

Average age of male = 25

Average age of female = 40

Average age of entire membership = 30

The ratio of female to male students :

Male students : Female students

25 : 40

5 : 8

5/8

Answer:

x = 14

Step-by-step explanation:

Add 10 to both sides.

x− 10 + 10 = 4 + 10

x=14

Answer:

What it is is basically when you take the area of every side of a three dimensional shape and then add it all together.

don't know if this is what you were looking for but I hope this helps.

Answer:

Here.

Step-by-step explanation:

Step-by-step explanation:

BC is tangent to the circle at point B.

Therefore, by tangent-radius theorem:

Step-by-step explanation:

BC is tangent to the circle at point B.

Therefore, by tangent-radius theorem:

Answer:

f^-1(-32)=6

Step-by-step explanation:

Find the inverse of the function f(x)=4-6x:

f(x)=4-6x

y=4-6x

x=4-6y

x-4=-6y

(x-4)/-6=y

-1/6x+2/3=y

y=-1/6x+2/3

f^-1(x)=-1/6x+2/3

Plug in f^-1(-32) for f^-1(x) and simplify:

f^-1(-32)=-1/6(-32)+2/3

f^-1(-32)=16/3+2/3

f^-1(-32)=18/3

f^-1(-32)=6

Answer:

3

Step-by-step explanation:

m

Answer:

B. 5/16

Step-by-step explanation:

Multiply each side by the reciprocal of 2/5 to solve for x

(2/5)(1/8)=x

2/16=x