We need to solve for the height of the tree given two angles and distance between the two observers. See attached drawing for a better understanding of the problem.
We derive to equations using SOH CAH TOA such as below:
sin30 = h / x
sin 45 = h / (100-x)
sin 45 (100-x) = xsin30
70.71 - 0.71x = 0.5x
70.71 = 1.21 x
x = 58.44
Solving for h, we have:
h = xsin30
h = 58.44 sin30
h = 29.22
The height of the tree is 29.22 feet.
Based on the ratio, 6 students play musical instruments.
The mentioned problem can be solved using the concept of ratio and proportion. We will equate the two ratio. Let us assume the number of students who play musical instruments be x.
Forming the equation -
3 : 20 = x : 40
Rewriting the equation with respect to x
x = (40 × 3) ÷ 20
Performing multiplication and division on Right Hand Side of the equation
x = 120 ÷ 20
Performing division on Right Hand Side of the equation
x = 6
Therefore, 6 students play musical instruments.
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Answer:
x intercept are points passing through x axis having y=0
Step-by-step explanation:
slope=
slope
Answer:
Simplifying
5x + 12 = -13
Reorder the terms:
12 + 5x = -13
Solving
12 + 5x = -13
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-12' to each side of the equation.
12 + -12 + 5x = -13 + -12
Combine like terms: 12 + -12 = 0
0 + 5x = -13 + -12
5x = -13 + -12
Combine like terms: -13 + -12 = -25
5x = -25
Divide each side by '5'.
x = -5
Simplifying
x = -5
Step-by-step explanation:
Answer:
1) Slope: 3; y-intercept: -7
2) Slope: 2/3; y-intercept: 1
Step-by-step explanation:
y = mx + b; m is slope and b is y-intercept
1. y = 3x - 7
The equation is already in slope-intercept form, so you can find the slope and intercept.
Slope: 3
y-intercept: -7
2. y - 1 = 2/3x
For this one, you have to convert this into slope-intercept form (solving for y)
y - 1 = 2/3x
Add 1 to both sides
y - 1 + 1 = 2/3x + 1
y = 2/3x + 1
Now that the equation is in slope-intercept form, you can get the slope and y-intercept.
Slope: 2/3
y-intercept: 1