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matrenka [14]
3 years ago
15

Cw 11.1 backside v. V.

Mathematics
1 answer:
nika2105 [10]3 years ago
3 0

Answers:

10.  28.3 cm²

11. 7.3 cm²

12. P: 32 yds, A: 76.8 sq yds

13. P: 64 units, A: 220.8 units

14.  50.3 cm²

15. 132.7 cm²

16. 9.7 in

17. 5.9 cm

18.  324.08 sq inches.

19. 39 cm²

20. 36.6 cm²

Step-by-step explanation:

10. Find the area of the shaded region.

It's a circle, let's first calculate its area, with the formula A = π * r²

A = π  * 6² = 36 π  = 113.1 cm²

The shaded area has a 90 degrees angle... so it's 1/4 of the whole circle.

The area of the shaded area of this circle is then: 113.1 * 1/4 = 28.275 cm²

Rounded to the tenths, that's of course 28.3 cm²

11. Find the area of the shaded region.

Again, let's first find the area of the complete circle, with A =  π * r²

A =  π * 4² = 16π  = 50.27 cm²

Now, let's find the angle for the shaded area.

A circle has 360 degrees, and we know the angles of 2 segments... so we can easily find the missing angle:

360 - 203 - 105 = 52

The shaded area has an arc of 52 degrees, so we multiply the area of the full circle by 52/360 to get the area of that shaded area:

(50.27 * 52) / 360 = 7.26 cm², rounded to the tenths: 7.3 cm²

12. Find perimeter AND area of this regular polygon.

The figure is a regular octagon (8 sides).

To calculate its perimeter, it's simply 8 times one side, so: 8 * 4 yd = 32 yds

For the area, you can view an octagon as 8 triangles joined together.  In this case, we have a base of 4 yds and a height of 4.8 yds, so the area of each triangle is: (4 * 4.8) /2 = 9.6, the total area of the octagon is then 8 * 9.6 = 76.8 yds

13. Find perimeter AND area of this regular polygon.

The figure is a regular octagon (8 sides).

To calculate its perimeter, it's simply 8 times one side, so: 8 * 8 = 64 units

For the area, you can view an octagon as 8 triangles joined together.  In this case, we have a base of 4 yds and a height of 4.8 yds, so the area of each triangle is: (8 * 6.9) /2 = 27.6, the total area of the octagon is then 8 * 27.6 = 220.8 units

14. Find the area of a circle of <u>radius</u> = 4 cm

We have a circle with a radius of 4 cm, we need to find its area.

The area of a circle is obtained by the formula: A = π * r²

We already have the value of r, so we will input it in the formula:

So, we'll have A = π * 4² = 16 * π = 50.27 cm²

Rounded to the tenths: 50.3 cm²

15. Find the area of a circle of <u>diameter</u> 13 cm

We have a circle with a diameter of 13 cm, we need to find its area.  To use the formula for the area, we need the radius, not the diameter.  Since the diameter is 13 cm, the radius is 6.5

The area of a circle is obtained by the formula: A = π * r²

So, we'll have A = π * 6.5² = 42.25 * π = 132.73 cm²

Rounded to the tenths: 132.7 cm²

16. Find the diameter of a circle with an area of 75 in².

We just used the area formula for a circle, based on the radius.  We'll process it in reverse from the area to get the radius... which will give us the diameter, so r² = A / π

We then have:  r² = 75 / π = 23.87

So, r = 4.88 (square root of 23.87), which we double to get the diameter: 9.76 in, rounded to 9.7 in.

17. Find the radius of a circle with an area of 108 cm².

We just used the area formula for a circle, based on the radius.  We'll process it in reverse from the area to get the radius, so r² = A / π

If we input the area given in the question into the formula, we have:  r² = 108 / π = 34.38 cm

So, r = 5.86 (square root of 34.38), rounded to 5.9 cm.

18. Find the area

We have here a half-circle with a triangle.

We just used the formula for the area of a circle, and we know the radius of that half-circle: 8 inches.

A = π * 8² = 64 * π = 201.06 sq inches, for the whole circle.

But we only have half of it, so 201.06 / 2 = 100.08 sq inches.

Now the triangle.  To calculate the area of a triangle, you multiply its base by its height, then you divide by 2, so:

A = 16 x 28 = 224 sq inches.

Which we add to the half-circle area (100.08 sq inches) to get 324.08 sq inches. So 324.1 sq inches once rounded to the tenths.

19. Find the area

We have a triangle on top of a rectangle.

Area of a triangle: (base * height) / 2.

Area of a rectangle: base * height

So, for the triangle: A = (6 * 3) / 2 = 9 cm²

And for the rectangle: A = 6 * 5 = 30 cm²

Total: 9 + 30 = 39 cm²

20. Find the area

We have a rectangle and a half circle.  The radius of the half-circle is: 2 cm (half of the height of the rectangle).

Area of the rectangle: base * height, so 6 * 4 = 24 cm²

Area of the circle:  π * r² = π * 2² = 4π = 12.56 cm²

Total for the figure: 24 + 12.56 = 36.56, or 36.6 cm² once rounded.

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Step-by-step explanation:

I assume as "equation" we mean the slope-intercept form :

y = ax + b

"a" is the slope of the line (y coordinate change / x coordinate change when going from one point to another on the line). b is the y-intercept (the y value when x = 0).

we get the slope by finding the perpendicular slope of the first line.

the slope of the first line when going from (-3, -9) to (7, 8) :

x changes by + 10 (from -3 to +7).

y changes by + 17 (from -9 to +8).

so, that slope is 17/10.

the perpendicular slope is turning the original slope upside-down and flips the sign :

-10/17

so, a = -10/17

now, as we have only the slope and a point of the new line, we can use the point-slope form to stay and then transfer into the slope-intercept form.

y - y1 = a(x - x1)

where "a" is again the slope, and (x1, y1) is a point on the line

y - -6 = -10/17 × (x - -9)

y + 6 = -10/17 × (x + 9) = -10/17 × x - 90/17

y = -10/17 × x - 90/17 - 6 =

= -10/17 × x - 90/17 - 102/17 =

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7 0
1 year ago
What is the equation for this math problem? Steven spent $90 on clothes. He bought a pair of jeans that cost $34 and spent the r
dexar [7]

Answer:

The equation for the given maths problem is $ 34 + $ 8x = $ 90  

Step-by-step explanation:

According to question :

The Total amount spent on  cloths = $ 90

The cost of a pair of jeans  = $ 34

The cost of each t-shirt pair = $ 8

The amount spent on t-shirt = $ 90 - $ 34 = $ 56

Let the number of t-shirt pair = x

So, $ 34 + $ 8x = $ 90

Or,  $ 8x = $ 90 - $ 34

∴         x = \frac{ 90 -  34}{8}

Hence The equation for the given maths problem is $ 34 + $ 8x = $ 90  Answer

8 0
3 years ago
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soldi70 [24.7K]

Answer:

Last choice. d.

Step-by-step explanation:

We are given the first term and the sixth term.

The first term is a_1=-9.

The sixth them is a_6=a_1r^5=-9216.

Let's solve for the common ratio, r.

-9r^5=-9216

Divide both sides by -9:

r^5=1024

Take the fifth root of both sides:

r=1024^{\frac{1}{5}}

r=4

So the common ratio is 4.

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a_3=-9(4)^2=-144

a_4=-9(4)^3=-576

a_5=-9(4)^4=-2304

a_6=-9(4)^5=-9216

8 0
3 years ago
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