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9514 1404 393

Answer:

  6. (A, B, C) ≈ (112.4°, 29.5°, 38.0°)

  7. (a, b, C) ≈ (180.5, 238.5, 145°)

Step-by-step explanation:

My "work" is to make use of a triangle solver calculator. The results are attached. Triangle solvers are available for phone or tablet and on web sites. Many graphing calculators have triangle solvers built in.

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We suppose you're to make use of the Law of Sines and the Law of Cosines, as applicable.

6. When 3 sides are given, the Law of Cosines can be used to find the angles. For example, angle A can be found from ...

  A = arccos((b² +c² -a²)/(2bc))

  A = arccos((8² +10² -15²)/(2·8·10)) = arccos(-61/160) = 112.4°

The other angles can be found by permuting the variables appropriately.

  B = arccos((225 +100 -64)/(2·15·10) = arccos(261/300) ≈ 29.5°

The third angle can be found as the supplement to the other two.

  C = 180° -112.411° -29.541° = 38.048° ≈ 38.0°

The angles (A, B, C) are about (112.4°, 29.5°, 38.0°).

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7. When insufficient information is given for the Law of Cosines, the Law of Sines can be useful. It tells us side lengths are proportional to the sine of the opposite angle. With two angles, we can find the third, and with any side length, we can then find the other side lengths.

  C = 180° -A -B = 145°

  a = c(sin(A)/sin(C)) = 400·sin(15°)/sin(145°) ≈ 180.49

  b = c(sin(B)/sin(C)) = 400·sin(20°)/sin(145°) ≈ 238.52

The measures (a, b, C) are about (180.5, 238.5, 145°).

Answer:

Not sure but I think the answer is 129

Step-by-step explanation:

first, substitute the value of x in the expression like this

18(3*2+1)+3

after substituting, our work has made easier

18(6+1)+3

18(7)+3 or simply 18*7+3

126+3

129

Answer:

i'm going to be honest and say sorry if i its wrong but

i think its 27 - 9x  

and ageing sorry if its wrong

Step-by-step explanation:

Answer:

50% of the time (27 times) you will get an even number

Step-by-step explanation:

sorry if it wrong

Answer:

6

Step-by-step explanation:

The difference of the two complex numbers (5 + 3i) and (2 + 9i) is; 3 - 6i.

It follows from the task content that the two difference of the two complex numbers (5 + 3i) and (2 + 9i) be determined.

Since the numbers given are; (5 + 3i) and (2 + 9i).

The difference can be mathematically as follows;

( 5 + 3i ) - ( 2 + 9i )

By the Distributive property; we have;

5 + 3i - 2 - 9i

Collect like terms so that we have;

= 5 - 2 + 3i - 9i

= 3 - 6i

On this note, the difference between the two complex numbers is; 3 - 6i.

Read more on subtraction of complex numbers;

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Answer:

5 feet

Step-by-step explanation:

Divide the area by the base to get 5 feet tall

Answer:

y=3x/2-3

Step-by-step explanation:

y=mx+c

9=m(8)-3

9+3=8m

12=8m

m=12/8

m=3/2

The equation of the line is y=3x/2-3

Answer:

y's go

13, 6, 5, 4, -3

Step-by-step explanation:

well so you have the equation y = 5 - x^3

you are given the x for all of them

y = 5 - (-2)^3

5 - (-8) = 13

y = 5 - 0^3

5 - 0 = 5

y = 5 - 1^3

5 - 1 = 4

y = 5 - 2^3

5 - 8 = -3

Answer:

x=37

Step-by-step explanation:

As you can see in the image, both angles are congruent to each other. 74 degrees and 2x degrees. You have to divide 74 by 2 to find what x equals.

74/2=37

x=37

The solution of the given equation (x + 4)(x - 3) = -10 is -2.

Thus, option C is correct.

Two algebraic expressions separated by an equal symbol in between them and with the same value of the expression are called equations.

Example = 2x +4 = 12

Here, 4 and 12 are constants and x is variable

Given equation:

Multiply the brackets,

(x + 4)(x - 3) = -10

[tex]x^2-3x+4x-12 = -10[/tex]

x^2 +x -12+10 =0

x^2 +x -2=0

x(x+2)-1(x+2)=0

(x+2)(x-1)=0

x= -2, x=1

Thus, option C is correct.

Learn more about equations here :

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Answer:

81 min I think

Step-by-step explanation:

Answer:

Step-by-step explanation:

g(x) = √(32x) = √(2⁵x) = 4√(2x)

(f∘g)(x) = f(g(x))

= f(4√(2x))

= √(2 ⋅ 4√(2x))

= √(8√(2x))

= √8∜2∜x

= ∜(2⁷x)

= ∜(128x)

which doesn’t match any of the choices. There’s an error in the question.

I believe that the functions were written incorrectly and the x should not be part of the radicands (see attachment). That makes the answer A.

Answer:

No, Lin assumption is wrong

Step-by-step explanation:

Given

Population of panama = 4 x 10^6

population of thailand = 7 x 10^7.

Taking their ratios

thailand/panama = 7x 10^7/4 x 10^6

thailand/panama  = 7/4 * 10^7-6}

thailand/panama = 1.75 * 10^1

thailand/panama  = 17.5

thailand = 17.5 * panama

Hence the amount of people in thailand is not up to 20times those in panama. Hence Lin assumption is wrong

Using proportions, it is found that the ratio is of 17.5, hence Lin is not correct.

A proportion is a fraction of a total amount.

In this problem:

The ratio between the populations is given by:

r = 7 x 10^7/(4 x 10^6) = 1.75 x 10^1 = 17.5.

The ratio is of 17.5, hence Lin is not correct.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

[tex]\Huge\boxed{\frac{3}{5}}[/tex]

Step-by-step explanation:

The trigonometric ratio for sine is

sin = opposite over hypotenuse

the opposite side length of L is 6 and the hypotenuse is 10

so sin L = 6 over 10

then we simplify

6/2 = 3

10/2=5

the answer would be 3/5

Answer:

10/7

Step-by-step explanation:

Use the slope formula y2-y1/x2-x1

You can’t reduce so the final answer is 10/7

Answer:

Step-by-step explanation:

c

Answer:

item c is the answer

1/3

...............

.

...........

Answer:

1/3

Step-by-step explanation:

A rectangle has two pairs of opposite sides that are equal in length and four right angles.

To determine the number of diagonals a rectangle has, we need to consider that a diagonal connects any two non-adjacent vertices of a shape.

In a rectangle, there are four vertices. For each vertex, we can draw a diagonal to any of the other three vertices that are not adjacent. Since there are four vertices in total, we can draw a diagonal from each of the four vertices to three other vertices, resulting in a total of 4 * 3 = 12 diagonals.

However, we must keep in mind that each diagonal is counted twice since it connects two different vertices. Therefore, we need to divide the total count of diagonals by 2, giving us the final answer.

Hence, a rectangle has 12/2 = 6 diagonals.

To know more about rectangle:

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Answer:

From what I remember A is the answer but im  not sure.

Answer:b

Step-by-step explanation:t

Answer:

Step-by-step explanation:

The volume of the pyramid with height of 6:

The volume of the smaller pyramid is:

We know:

The base sides have same ratio as similar triangles.

The volume of smaller pyramid:

The difference of the volumes is the volume of the frustum:

The ratio of V₂ to V is:

Step-by-step explanation:

1/(1 - p + p²) - 1/(1 + p + p²) - 2p/(1 - p² + p⁴) =

[ (1 + p + p²)-(1 - p + p²)/(1 - p + p²)(1 + p + p²) ] - 2p/(1 - p² + p⁴) =

2p/(1 + p + p² - p - p² - p³ + p² + p³ + p⁴) - 2p/(1 - p² + p⁴) =

2p/(1 + p² + p⁴) - 2p/(1 - p² + p⁴) =

[ 2p(1 - p² + p⁴) - 2p( 1 + p² + p⁴) ]/(1 + p² + p⁴)(1 - p² + p⁴) =

(2p - 2p³ + 2p⁵ - 2p - 2p³- 2p⁵) / (1 - p² + p⁴ + p² - p⁴ + p⁶ + p⁴ - p⁶ + p⁸) =

-4p³ / (1 + p⁴ + p⁸)

Answer:

I think it’s 18

Answer:

18

Step-by-step explanation:

the larger triangle is just a bigger version of the smaller one, and the equal sides show us that it is scaled up to be doubled in size, therefore 9x2=18

Answer:

1.  14:9

2. 14 to 9

3. 14/9

Step-by-step explanation: