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3 years ago

If x varies inversely as y and x=16 when y=5, find x when y=20.

Mathematics

1 answer:

Elanso [62]3 years ago

4 0

9514 1404 393

Answer:

x = 4

Step-by-step explanation:

The inverse variation means that when y goes up by a factor of 20/5 = 4, the value of x goes down by the same factor.

x = 16/4

x = 4

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part 2. Find the value of the trig function indicated, use for that Pythagorean theorem to find the third side if you need it.

andreev551 [17]

Answer: $\bold{5)\ \cos \theta=\dfrac{\sqrt{11}}{6}\qquad 6)\ \tan \theta =\dfrac{8}{17}\qquad 7)\ \cos \theta = \dfrac{4}{3}\qquad 8)\ \cos \theta = \dfrac{\sqrt{10}}{10}}$

<u>Step-by-Step Explanation:</u>

Pythagorean Theorem is: a² + b² = c² , <em>where "c" is the hypotenuse</em>

$5)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{3\sqrt{11}}{18}\quad \rightarrow \large\boxed{\dfrac{\sqrt{11}}{6}}$

Note: (15)² + (3√11)² = hypotenuse² → hypotenuse = 18

$6)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{8}{17}\quad =\large\boxed{\dfrac{8}{17}}$

Note: 8² + 15² = hypotenuse² → hypotenuse = 17

$7)\ \tan \theta=\dfrac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{20}{15}\quad \rightarrow \large\boxed{\dfrac{4}{3}}$

Note: hypotenuse not needed for tan

$8)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{2}{2\sqrt{10}}\quad =\large\boxed{\dfrac{\sqrt{10}}{10}}$

Note: 2² + 6² = hypotenuse² → hypotenuse = 2√10

8 0

3 years ago

It's a system of equations x=-4y x+6y=18

Misha Larkins [42]

Subsitute -4y for x

-4y+6y=18
2y=18
divide both sides by 2
y=9
sub back

x=-4y
x=-4(9)
x=-36

(x,y)
(9,-36)

3 0

4 years ago

Use the coordinates of the labeled point to find a point-slope equation of the line.

DerKrebs [107]

Answer:

(-2,-5) (0,-1)

(-1+5)/(0+2)= 4/2= 2

y + 5 = 2(x + 2)

y + 5 = 2x + 4

y = 2x - 1

Step-by-step explanation:

8 0

3 years ago

Simplify (n+3)(n-9)

Katarina [22]

From multiplying the binomial expression

(n+3)(n-9)

It would be n^2 - 9n + 3n - 27 or simplified

n^2 -6n - 27.

6 0

4 years ago

Xavier climbs 9 feet up into an apple tree. What integer represents the direction and how far he will climb to get back down to

natima [27]

Answer:

-9

Step-by-step explanation:

We are told in the question that:

Xavier climbs 9 feet up into an apple tree.

The direction symbol or sign for upwards movement = Positive (+) sign

If Xavier would climb back down , he will climb back down 9 feet as well

The direction symbol or sign for downwards movement = Negative (-) sign

Since we know the distance (or how far) he has to climb by downwards is also 9 feet, therefore, the integer that represents the direction and how far he will climb to get back down to the ground is -9

7 0

3 years ago