Answer:
Step-by-step explanation:
This is a question that uses the Pythagorean Theorem.
a = 35 feet
b = x which is the height of the tree.
c = 3*x + 1 so we are trying to find x. Substitute into a b and c
a^2 + b^2 = c^2
35^2 + x^2 = (3x + 1)^2
35^2 + x^2 = 9x^2 + 6x + 1 Subtract x^2 from both sides.
35^2 = 8x^2 + 6x + 1 Subtract 35^2 from both sides.
0 = 8x^2 + 6x + 1 - 35^2
0 = 8x^2 + 6x - 1224
Does this factor?
(x + 12.75)(x - 12)
x - 12 = 0 is the only value that works.
x = 12
The tree is 12 feet high.
Note: I used the quadratic formula to solve this.
Answer:
Step-by-step explanation:
Let the 10s digit = x
Let the units digit = y
x +y = 11 Sum of the digits = 11
10x + y + 45 = 10y + x Reversed number is 45 more than original #
10x - x + y + 45 = 10y We subtracted x from both sides.
9x + y + 45 = 10y Subtract y from both sides.
9x + 45 = 10y - y Combine the right
9x + 45 = 9y
Put x + y = 11 into the equation just found.
9x + 45 = 9(11 - x) divide through by 9
x + 45/9 = 11 - x add x to both sides
2x + 5 = 11 Subtract 5 from both sides
2x = 11 - 5
2x = 6 Divide by 2
x = 6/2
x = 3
x + y = 11
3 + y = 11
y = 11 - 3
y = 8
Now check it out.
the original number is 38
the new number is 83 which the digits are reversed.
83 - 38 = 45 just as it should.
Step-by-step explanation:
let the 2 integers be x and x + 1
2(x + 1) + 186 = x
2x + 188 = x
x = -188
therefore the 2 integers are -188 and -187
Topic: Algebraic equations
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54 yards =
4937.76 centimeters
Answer:
Step-by-step explanation:
As 360°= 2 π Radian
1 Radian =
1. Sin(-1)= Sin ( )
= Sin (-57°16'22")=-0.84147
2.
= (229°54'32")
=75.963757 Degrees
3.
= (5°43'38")
= 84.26083 Degrees
