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2 years ago

Treena flew home to visit her family for

Mathematics

1 answer:

devlian [24]2 years ago

7 0

x + y = 71.5

x = 47.8

y = 71.5 - 47.8

71.5 - 47.8 = 23.7

y = 23.7 pounds

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Right triangle XYZ has right angle Z. If the sin(X)=1213<br> , what is the cos(X)

AlekseyPX

Given:

Right triangle XYZ has right angle Z.

$\sin(x)=\dfrac{12}{13}$

To find:

The value of $\cos x$ .

Solution:

We know that,

$\sin^2(x)+\cos^2(x)=1$

$\cos^2(x)=1-\sin^2(x)$

$\cos(x)=\pm\sqrt{1-\sin^2x}$

For a triangle, all trigonometric ratios are positive. So,

$\cos(x)=\sqrt{1-\sin^2x}$

It is given that $\sin(x)=\dfrac{12}{13}$ . After substituting this value in the above equation, we get

$\cos(x)=\sqrt{1-(\dfrac{12}{13})^2}$

$\cos(x)=\sqrt{1-\dfrac{144}{169}}$

$\cos(x)=\sqrt{\dfrac{169-144}{169}}$

$\cos(x)=\sqrt{\dfrac{25}{169}}$

On further simplification, we get

$\cos(x)=\dfrac{\sqrt{25}}{\sqrt{169}}$

$\cos(x)=\dfrac{5}{13}$

Therefore, the required value is $\cos(x)=\dfrac{5}{13}$ .

6 0

3 years ago

Three years hence a father will four times as old as his son will be. Before two years he was seven times as old as his son was.

myrzilka [38]

Answer: The father is 37 years and the son is 7 years

Step-by-step explanation:

Let x represent the present age of the father.

Let y represent the present age of the son.

Three years hence a father will four times as old as his son will be. This means that

x + 3 = 4(y + 3)

x + 3 = 4y + 12

x - 4y = 12 - 3

x - 4y = 9- - - - - - - - - - - - - - - -1

Before two years he was seven times as old as his son was. This means that

(x - 2) = 7(y - 2)

x - 2 = 7y - 14

x - 7y = - 14 + 2

x - 7y = - 12- - - - - - - - - - - - - - -2

Subtracting equation 2 from equation 1, it becomes

3y = 21

y = 21.3 = 7

Substituting y = 7 into equation 1, it becomes

x - 4 × 7 = 9

x - 28 = 9

x = 9 + 28

x = 37

7 0

3 years ago

Read 2 more answers

Indify 5(2x-3)=8x+3<br><br><br> .........

vivado [14]

Answer:

solution,

5(2x-3) = 8x +3

or, 10x -15 = 8x+3

or, 10x -8 x= 3+15

or, 2x = 18

or, x = 18/2

or, x = 9

.:. x = 9

6 0

3 years ago

What is a mixed number for 5/2

m_a_m_a [10]

Answer: 2 1/2

Step-by-step explanation: Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction. Hope this helps!! PLZ mark me!!!

8 0

3 years ago

A 6-sided die is rolled. The sides contain the numbers 1, 2, 3, 4, 5, 6. List the sample space of rolling one die.

krek1111 [17]

Answer:

{1,2,3,4,5,6}

Step-by-step explanation:

since the die gives only these values

the sample space becomes the outcomes of the die

3 0

3 years ago