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Marina CMI [18]
3 years ago
14

What is the greatest common factor of 12a and 9a^2

Mathematics
2 answers:
Vinvika [58]3 years ago
7 0

Answer:3a

Step-by-step explanation:trust

svetlana [45]3 years ago
5 0

Answer:

108a^3

Step-by-step explanation:

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A rain gutter is made from sheets of aluminum that are 16 inches wide by turning up the edges to form right angles. Determine th
blsea [12.9K]

Answer:

Depth of the rain gutter is 8 inches

Step-by-step explanation:

Let’s assume ‘x’ is the depth of the rain gutter

Then the width of the rain gutter can be written as 16 - 2x

Cross sectional area

A = depth x width

Substitute values

A = x*(16 - 2x)

A = 16x – 2x^2

Now according to axis of symmetry for maximum area x = -b/2a

x = -16/2*(-2)

x = 4 inches depth of rain gutter, substitute the value of x to get

Width of rain gutter 16 – 2(4) = 8 inches

Area of the rain gutter for maximum water flow

A = 4 * 8

A = 32 square inch.

8 0
3 years ago
I don’t know how to do this, what’s the area?
Anastaziya [24]

Answer:

Hello!

Step-by-step explanation:

To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.

So,you have to multiply.

Hope this helps.

6 0
3 years ago
What is the 7th term in the sequence below?
enot [183]

Answer:

C

my answer is the image above

5 0
3 years ago
9. A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?
SSSSS [86.1K]

Answer:

Part 4) r=84\ units

Part 9) sin(\theta)=-\frac{\sqrt{5}}{3}

Part 10) sin(\theta)=-\frac{9\sqrt{202}}{202}

Step-by-step explanation:

Part 4) A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

we know that

The circumference of a circle subtends a central angle of 360 degrees

The circumference is equal to

C=2\pi r

using proportion

\frac{2\pi r}{360^o}=\frac{56\pi}{120^o}

simplify

\frac{r}{180^o}=\frac{56}{120^o}

solve for r

r=\frac{56}{120^o}(180^o)

r=84\ units

Part 9) Given cos(∅)=-2/3 and ∅ lies in Quadrant III. Find the exact value of sin(∅) in simplified form

Remember the trigonometric identity

cos^2(\theta)+sin^2(\theta)=1

we have

cos(\theta)=-\frac{2}{3}

substitute the given value

(-\frac{2}{3})^2+sin^2(\theta)=1

\frac{4}{9}+sin^2(\theta)=1

sin^2(\theta)=1-\frac{4}{9}

sin^2(\theta)=\frac{5}{9}

square root both sides

sin(\theta)=\pm\frac{\sqrt{5}}{3}

we know that

If ∅ lies in Quadrant III

then

The value of sin(∅) is negative

sin(\theta)=-\frac{\sqrt{5}}{3}

Part 10) The terminal side of ∅ passes through the point (11,-9). What is the exact value of sin(∅) in simplified form?    

see the attached figure to better understand the problem

In the right triangle ABC of the figure

sin(\theta)=\frac{BC}{AC}

Find the length side AC applying the Pythagorean Theorem

AC^2=AB^2+BC^2

substitute the given values

AC^2=11^2+9^2

AC^2=202

AC=\sqrt{202}\ units

so

sin(\theta)=\frac{9}{\sqrt{202}}

simplify

sin(\theta)=\frac{9\sqrt{202}}{202}

Remember that      

The point (11,-9) lies in Quadrant IV

then      

The value of sin(∅) is negative

therefore

sin(\theta)=-\frac{9\sqrt{202}}{202}

5 0
3 years ago
The perimeter of a semicircle is 20.56 yards. What is the semicircle's radius?
Scorpion4ik [409]

Answer:

Step-by-step explanation:

Perimeter = 20.56mm

Given the perimeter, find the diameter

= 20.56

D = 20.56 ÷

D = 6.54 mm

Perimeter of the Semicircle = half the circle arc + the straight line (Diameter)

Semicircle = 0.5(20.56) + 6.54cm

Semicircle = 16.83mm

7 0
3 years ago
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