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3 years ago

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The vertex angle of an isosceles triangle measures 64 degrees. What is the measure of its base angles?

1 answer:

Dvinal [7]3 years ago

7 0

So hmmm check the picture below

in an isosceles triangle, two sides are equal, and thus the angles those twin legs make, are also twin angles

let's say the angle made is "a", so all internal angles will be 64 + a + a = 180
or 64 + 2a = 180

thus 2a = 180 - 64 => 2a = 116, thus a = 116/2

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A cone-shaped pile of sawdust has a base diameter of 38 feet, and is 14 feet tall. Find the volume of the pile

Romashka-Z-Leto [24]

Answer:

Given: Diameter of cone = 38 feet and height of cone = 14 feet.

Volume of cone V with radius r is one-third the area of the base B times the height h.

i,e $V = \frac{1}{3} B \cdot h$ = $\frac{1}{3} \pi r^2h$ ......[1]

,where B = $\pi r^2$

First find the radius(r);

Using Diameter(D) = 2r

38 =2r

Divide both side by 2 we get;

$\frac{38}{2} =\frac{2r}{2}$

Simplify:

19 = r

or r =19 feet

Now, substitute the value of r = 19 feet and h = 14 feet in [1] [ Use value of $\pi = \frac{22}{7}$ ]

then, we have:

$V = \frac{1}{3} \pi r^2h = \frac{1}{3} \cdot \frac{22}{7} \cdot (19)^2 \cdot (14)$

or

V = $=\frac{1}{3}\cdot 22 \cdot 19 \cdot 19 \cdot 2 = \frac{22 \cdot 19 \cdot 19 \cdot 2}{3}$

or

V = $\frac{15884}{3} =5,294.66667$ ≈ 5,294.67 cubic feet.

therefore, the volume of pile is; ≈ 5,294.67 cubic feet.

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3 years ago

What is the reason for each step in the solution of the equation? -3(4-6x)

Bingel [31]

Answer:

-12+18x

Step-by-step explanation:

-3(4-6x)=-12+18x

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3 years ago

Read 2 more answers

an angle measures 38 degrees more than the measure of its supplementary angle. what is the measure of each angle?

RideAnS [48]

Answer is 71 and 109 degrees
x+(x+38)=180
2x+38=180
2x=142
x=71

x+38
71+38=109

3 0

3 years ago

Determine two numbers that have a product of 40 but have a sum of 13.

Paha777 [63]

Answer:

The two numbers are 8 and 5.

Step-by-step explanation:

Let consider x and y to be these two numbers.

So;

(x) * (y) = 40 ---- (1)

x + y = 13 ----- (2)

From (2), let x = 13 - y

Then;

(13 - y) * y = 40

13y - y² = 40

13y - y² - 40 = 0

-y² + 13y - 40 = 0

Multiply through by (-)

y² - 13y + 40 = 0

By factorization;

(y - 8) (y - 5) = 0

y = 8 or y = 5

CHECK:

8 * 5 = 40

8 + 5 = 13

Therefore, the two numbers are 8 and 5.

8 0

2 years ago