In triangle ABC, the measure of ∠B is 90°, BC=16, and AC=20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is 1/3

the length of the corresponding side of triangle ABC. What is the value of sinF?

Answers

Answer 1

Answer:

Step-by-step explanation:

From.the Pythagoras theorem,

DF² = DE² + EF²; therefore, DE²= DF²-EF².since each of the side of DEF is 1/3 of sides ABC , it implies that ,1/3 of 20 = 6.7 ( DF)and 1/3 of 16 = 5.3 (EF)

DE² = 6.7²-5.3²;

DE² = 44.89 - 28.09

DE² =16.8

Therefore taking the square root is both side to get the true value of DE

√DE² = √16.8; DE = 4.098.

there the value of sin of angle F

SinF°= 4.098/6.7; = 0.6116

Therefore F° = sin-¹0.6116; 37.7°.

SinF = 0.6116, while angle F = 37.7°

Note: the purpose of using the Pythagoras theorem is to help you find the third side of triangle DEF which is DE

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How do you find the surface area of a circle?

Answers

Answer:

πr²

Step-by-step explanation:

The surface area of a circle is πr²

Pie is 22/7 or 3.14

While the radius of a circle is any line from the centre of a circle to any part of the circumference of the circle. A diameter is any line that cuts the circle into two equal halves, cutting the circle from the centre.

To get the surface area of a circle, you draw a line from the centre of the circle, and then touch any part of the circumference of the circle. Then you measure the line, that's the radius.

If for instance, the radius gives 7cm, you find the Square, And then multiply it with pie.

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22/7 X 7 X 7

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Three universities receive endowments totaling 110 million dollars. Northern U receives twice as much as wester U. Eastern Us endowments are 10 million less than the sum of those of the other two institutions.

Answers

Answer:

Western U gets 20 million

Norther U gets 40 million

Eastern U gets 50 million

Step-by-step explanation:

We need to find the amount each university gets.

Let

Northern U get n

Western U get w

Eastern U get e

We can write equations from the given word problem:

n + w + e = 110

and

n = 2w

e = n + w - 10

Putting 2nd in 3rd, we get:

e = 2w + w - 10

e = 3w - 10

Now putting this and 2nd in first, we solve for w:

n + w + e = 110

2w + w + 3w - 10 = 110

6w = 120

w = 20

AND n = 2 (20) = 40

AND e = 3(20) - 10 = 50

So,

Western U gets 20 million

Norther U gets 40 million

Eastern U gets 50 million

What is the domain of the function y=ln(12-4x/5)

Answers

Answer:

The domain of the function is $x<3$

Step-by-step explanation:

Given : Function $y=\ln ((12-4x)/(5))$

To find : What is the domain of the function ?

Solution :

Domain is defined as the set of possible values which define the function.

We know that, log negative is not defined.

So, we will get the inequality in the function.

$\ln ((12-4x)/(5))>0$

$(12-4x)/(5)>0$

$12-4x>0$

$-4x>-12$

$x<3$

Therefore, The domain of the function is $x<3$

$\ln x$ has a domain of $x>0$ , so $\ln\left(12-\frac{4x}5\right)$ has a domain of

$12-\frac{4x}5>0\implies12>\frac{4x}5\implies x<15$

43 and 962 ten thousandths in standard form?

Answers

43.962

Example:
14,494
To round off the height value to the nearest thousand we can use the expanded from to clarity the position of numbers which is:
10, 000 = ten thousand
4, 000 = thousands
400 = hundreds
90 = tens
4 = ones
Here we can notice than four thousand is the value where the nearest thousands is placed. Hence we can round off the number of 14, 494 into 14, 000. Notice 0-4 rounding off rules.

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In triangle ABC, the measure of ∠B is 90°, BC=16, and AC=20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is 1/3 the length of the corresponding side of triangle ABC. What is the value of sinF?

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