To calculate the area of a triangle, you find the product of the base and height and then divide by 2.

Answer:

1.  The volume of the cylinder is approximately 0.153 m³

2. 25 cm

3. [tex]25.\overline 6 \ cm[/tex]

4. 16 m

5. 1,785 m³

Step-by-step explanation:

The volume of a solid can be found by the product of the uniform cross-sectional area of the solid and the (continuous) length of the solid

1. The uniform cross-sectional area of the given cylinder = The area of the circle at the base or top

The dimension of the diameter of the circle at the top of the cylinder, d = 50 cm = 0.5 m

The area of the circular cross-section, A = π·d²/4

∴ A = π × 0.5²/4 = 0.0625·π

A = 0.0625·π m²

The height of the cylinder, h = The continuous length of the circular cross-section = 78 cm = 0.78 m

∴ The volume of the cylinder, V = A × h

∴ V = 0.0625·π × 0.78 = 0.04875·π ≈ 0.153

The volume of the cylinder, V ≈ 0.153 m³

2. The given volume of the trapezium, V = 8550 cm³

The length of the short and long parallel sides 'a', and 'b', are 17 cm and 21 cm respectively

The height of the trapezium from the diagram, h = 18 cm

The cross-sectional area of the trapezium, 'A', is found as follows;

A = (17 cm + 21 cm)/2 × 18 cm = 342 cm²

The volume of the trapezium, V = The cross-sectional, A × The (missing) length, 'l' of the trapezium

∴ l = V/A

By substitution, we have;

l = 8550 cm³/(342 cm²) = 25 cm

∴ The Missing Length, l = 25 cm

3. The given volume of the solid having a uniform cross-sectional area is, V = 385 cm³

The area of the (uniform) cross-section of the solid, A = 15 cm²

∴ The length of the solid, 'l', from V = A × l, is given as follows;

l = V/A

∴ l = 385 cm³/(15 cm²) = 25.[tex]\overline 6[/tex] cm

The length of the solid, l = 25.[tex]\overline 6[/tex] cm

4. From the diagram, we have;

The cross-sectional area of the solid, A = 216 m²

The length of the solid, l = 16 m

5. The cross-section of the solid can  can be assumed to be either;

1. A trapezium from which a rectangle has been removed of dimensions 8 m by 9 m.

2. A triangle located above a rectangle

For scenario one, we have;

The cross-sectional area, A = (12.5 + 9)/2 × 15 - 8 × 9 = 89.25

For scenario two, we find 'A' as follows;

A = 7 × 9 + 1/2 × 15 × 3.5 = 89.25

∴ The cross-sectional area of the solid, A = 89.25 m²

The length, 'l', of the solid, is given as l = 20 m

The volume of the solid, V = A × l

∴ V = 89.25 m² × 20 m = 1,785 m³

The volume of the solid, V = 1,785 m³.

Answer:

x²+8x+16=24

Step-by-step explanation:

x²+8x=7 (+16)

x²+8x+16=7+16=24

(x+4)²=24

The values to be entered in the boxes are 16 and 23.

Given the equation is [tex]x^2[/tex]+8x=7

To complete the square for the equation [tex]x^2[/tex] + 8x = 7, we need to add a constant term on both sides of the equation to create a perfect square trinomial on the left side.

First, take half of the coefficient of the x-term (8) and square it:

[tex](8/2)^2[/tex] = 16

Now, add 16 to both sides of the equation:

[tex]x^2[/tex] + 8x + 16 = 7 + 16

Simplifying:

[tex]x^2[/tex] + 8x + 16 = 23

Therefore, the equivalent number sentence after completing the square is [tex]x^2[/tex] + 8x + 16 = 23

The values to be entered in the boxes are 16 and 23.

Hence, [tex]x^2[/tex] + 8x + 16 = 23.

Learn more about completing the square in quadratic equations, click here:

https://brainly.com/question/12014272

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Answer:

70 - 80 foot per second

Step-by-step explanation:

Multiply the speed value by 1,467

Answer:

$2 for 1 rose bush and $2 for one shrub

Step-by-step explanation:

32=2x+14y

26=11x+2y

32=2(2)+14(2)

32=4+28

32=32

26=11(2)+2(2)

26=22+4

26=26

Since both equations come out correct the cost of 1 rose bush is 2 dollars and the cost of one shrub is 2 dollars. kinda cool

Answer:

The cost of one rose bush is $2 and the cost of one shrub is $2.

Step-by-step explanation:

Let r represent the cost of 1 rose bush and s the cost of 1 shrub.

Kali's expenditure

2r + 14s = 32

Divide each term by 2

r + 7s = 16 ------ (i)

Kim's expenditure

11r + 2s = 26 ------ (ii)

From equation (i)

r = 16 - 7s

11(16 - 7s) + 2s = 26

176 - 77s + 2s = 26

-75s = 26 - 176

-75s = -150

s = -150/-75 = 2

r = 16 - 7s = 16 - 7(2) = 16 - 14 = 2

The cost of one rose bush is $2 and the cost of one shrub is $2

Answer:

[tex]x^2+ 18x -130=0[/tex]

Step-by-step explanation:

Given

See attachment for diagram

Required

The equation to find x

First, calculate the area of the big rectangle using:

[tex]Area = Length * Width[/tex]

So:

[tex]A_1 = (x + 6) * (3x - 2)[/tex]

The smaller rectangle

[tex]A_2 = (x - 1) * (2x)[/tex]

The difference between this areas give the area of the shaded region.

So:

[tex]A_1 - A_1 = 118[/tex]

[tex](x+6)*(3x-2) - (x-1)*2x = 118[/tex]

Open brackets

[tex]3x^2 - 2x + 18x -12 -2x^2 +2x = 118[/tex]

Collect like terms

[tex]3x^2 -2x^2- 2x +2x+ 18x -12 - 118=0[/tex]

[tex]x^2+ 18x -130=0[/tex]

The above equation can be used to solve for x

35 = 4x+3

If they're vertical then they're worth the same or equal. So 4x+3 is equal to 35 and then you solve for x from there.

Answer:

The grapes are more expensive than the green grapes.

Step-by-step explanation:

GRAPES: If you divide $20.72 by 7, to get one bag of grapes instead of seven, you get $2.96/bag.

GREEN GRAPES: If you divide $8.46 by 3, to get one bag of green grapes instead of three, you get $2.82/bag.

$2.82 is less than $2.96, therefore, the grapes are more expensive than the green grapes.

Answer:

The gradient of the line segment between the two points is -1

Step-by-step explanation:

The gradient of the line segment between two points is also known as the slope,

We  can find this by using the formula; y₂ - y₁ /  x₂ - x₁

The points given to us are;(-1,2) and (-2,3).

This implies x₁ = -1  ,     y₁=2         x₂ =  -2        y₂= 3

We can now proceed to insert our values into the formula;

Gradient = y₂ - y₁ /  x₂ - x₁

               = 3 - 2  /  -2-(-1)

                = 1  /  -2 + 1

                 =1/-1

Gradient = -1

Therefore the gradient of the line segment between the two points is -1

Heyy I'm the person who helped you with the test. Anyway I disagree with the person who answered on top. The correct answer is -5/2!

Answer:

612 inches.

Step-by-step explanation:

1 yard = 36 inches.

17 * 36 =

Answer:

612 inches

Step-by-step explanation:

1 yard = 36 inches

17 yards = 36 × 17 = 612 inches

Answer:

1

Step-by-step explanation:

sike i lied this is so easy pls try pls

Answer:

210.82

Step-by-step explanation:

arc length= 2pi r (Ø/360)

= 2x 3.14 x 47(257/360)=210.82

Answer:

297 cubic inches

Step-by-step explanation:

Given: A cylinder has a volume of 99 cubic inches. A cone has the same height and radius as the cylinder.

To find: The volume of the cone in cubic inches.

Formula: The formula for the volume of a cone is V = [tex]\frac{1}{3}[/tex]hπr².

Solution: Firstly, find out the height and radius of the cylinder

... = 297 cubic inches

Answer:

A

Step-by-step explanation:

Answer:

122.5 cm²

Step-by-step explanation:

a = 21cm

b = 14cm

h = 7cm

Area of given figure(trapezium) = [tex]\frac{a+b}{2} * h[/tex]

= 21 + 14/ 2 * 7

= 35/2 * 7

= 17.5 * 7

= 122.5 cm²

Answer:

A

Step-by-step explanation:

Answer:

It depends how many points you already have

Step-by-step explanation:

how much are the essays worth? i might be able to get your final score if you tell me

Answer:

Step-by-step explanation:

Answer:

r > 7 (C)

Step-by-step explanation:

3r−7>14

Step 1: Add 7 to both sides.

3r−7+7>14+7

3r>21

Step 2: Divide both sides by 3.

3r

3

>

21

3

r>7

Hope this helps and makes sense!! Good luck and have a wonderful day! <33

Imagine this < as a alligater and itś eating the greater number!!

Answer:

C.) r ≥ 7

Step-by-step explanation:

1. Add 7 to each side to cancel it out and keep the sign the way it is to avoid confusion

3r - 7 ≥ 14

   + 7    +7

3r ≥ 21

2. Divide each side by 3 to get the variable alone

3r/3 = r

21/3 = 7

r ≥ 7

This means r is greater than or equal to 7, and it can also be written as 7 ≤ r

Answer:

first question

5 push-ups a day

second question

50 push-ups

Step-by-step explanation:

First, you must divide 35 divided by 7 because if Cesar does the exact same amount of push-ups a day, you can divide the total number of push-ups by how many days. Which gets you your first answer 5.

Then you multiply the number of days by the number of push-ups Cesar does in a day.

10 x 5 = 50

Answer:

6 inches

Step-by-step explanation:

Hi there!

[tex]V=lwh[/tex] where l is the length, w is the width and h is the height of a rectangular prism

Plug in the volume (609), length (14.5) and width (7)

[tex]609=(14.5)(7)h\\609=(101.5)h[/tex]

Divide both sides by 101.5 to isolate h

[tex]\frac{609}{101.5} =\frac{101.5h}{101.5} \\6=h[/tex]

Therefore, the height of the shoebox is 6 inches.

I hope this helps!

B 55.8)

nearest tenth associated ground elevation 10- stretched road and car = elevated protation. which is equivalent to 45 ( 0.08 added from the elevation plus the 10 = 55.8

Answer:

complement angle = 52 + 38 = 90°

supplement angle = 47 + 133 = 180°

Step-by-step explanation:

[tex]here \: is \: your \: solution \: \\ measure \: of \: one \: angle \: = 52 \\ let \: the \: other \: angle \: be = x \\ \\ x \: + 52 \: = 90 \\ x \: = \: 90 - 52 \\ x \: = 38 \\ now \: second \: question \\ x + 47 = 180 \\ x = 180 - 47 \\ x = 133 \\ hope \: it \: helps[/tex]

Answer:

A) 0.421

Step-by-step explanation:

[tex]\frac{59}{59+68+12+1} =\frac{59}{140}[/tex]

[tex]Answer:0.421[/tex]

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

hope it helps...

have a great day!!

Answer:

C

Step-by-step explanation:

53 + 44 + x = 180

97 +x = 180

x = 83