If sin α = 12/13 , and cosα = 5/13 , then tanα =?It would be great if you could add a few words of explanation

Answers

Answer 1

Answer: $sin\alpha=(12)/(13)\n\ncos\alpha=(5)/(13)\n\ntan\alpha=(sin\alpha)/(cos\alpha)\n\ntan\alpha=(12)/(13):(5)/(13)=(12)/(13)\cdot(13)/(5)=(12)/(5)=2(2)/(5)=2.4$

Answer 2

Answer: If you draw a right angles triangle you can fill in the values. So since sinx= opposite/hypotenuse then the hypotenuse of the triangle is 13. And the side opposite the angle a is 12. Since cosx= adjacent/ hypotenuse, the adjacent side is 5.
Tanx=opposite/adjacent and therefore tana= 12/5

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How do you find LCM of 5 and 35

35.4% expressed as a decimal becomes
A.35.54
B. 0.354
C. 35.0
D.354

Answers

35.4 expressed as a decimal is
B. 0.354

B is the answer because what you do is take 35.4% and divided it by 100 and that gives us our answer.

Solve each system by the addition method.-4x+7y =9
2y=-5x-22
Put the answer in (x,y) form

Answers

-4x + 7y = 9 ⇒ -4x + 7y = 9 ⇒    8x - 14y = -18
2y = -5x - 22 ⇒ -5x - 2y = 22 ⇒ -35x - 14y = 154
       43x = -172
      43    43
   x = -4
      -4x + 7y = 9
         -4(-4) + 7y = 9
      16 + 7y = 9
      - 16     - 16
      7y = -7
   7 7
      y = -1
      (x, y) = (-4, -1)

Aricela is trying to estimate the distance between her house and the park. On a map with a scale of 0.5 in. = 2 miles, the distance between her house and the park is 2.75 in. Which proportion can Aricela use to determine the distance, d, between her house and the park?A)
0.5
2.75
=
2
d
B)
d
0.5
=
2.75
2
C)
d
2
=
0.5
2.75
D)
0.5
d
=
2
2.75

Answers

If you would like to know the proportion Aricela can use to determine the distance, d, between her house and the park, you can calculate this using the following steps:

0.5 in. ... 2 miles
2.75 in. ... d miles = ?

0.5 * d = 2 * 2.75
d = 2 * 2.75 / 0.5
d = 11 miles

The correct result would be B) and D).

To determine the distance between her house and the park, Aricela can use the proportion:

0.5

2.75

. The distance on the map for 2 miles (0.5 in.) corresponds with the distance on the map between Aricela’s house and the park (2.75 inches) and the scaled distance (2 miles) corresponds to the actual distance between Aricela’s house and the park (d).

A the answer would be A.

-3/7, -8/3 and -5/2,-2 slope

Answers

so the points are (-3/7,-8/3) and (-5/2,-2)
to find the slope do
(y2-y1)/(x2-x1)
(x,y)
x1=-3/7
y1=-8/3
x2=-5/2
y2=-2

subsitute
$(-2-( (-8)/(3) ))/( (-5)/(2) - (-3)/(7) )$
simplify by finding similar denomenators
$((-6)/(3)-( (-8)/(3) ))/( (-35)/(14) - (-6)/(14) )$
$((-6)/(3)( (8)/(3) ))/( (-35)/(14) + (6)/(14) )$
add
$((2)/(3))/( (-29)/(14))$
multiply top and bottom by $\frac{-14}{29$
$((-28)/(87))/(1)$
$(-28)/(87)$
answer is
slope= $(-28)/(87)$

If x-y=9 and xy=2,find the value of (x square + y square)