Answer:
D) 20°
Step-by-step explanation:
Using the triangle sum theorem, you know that every triangle's interior angles add up to 180°. Therefore the bottom triangle's missing angle can be found by giving it the variable x.
57° + 30° + x = 180°
Simplify: 87° + x =180°
x=93°
By the vertical angles theorem, the vertical angle directly across this angle is congruent to this one. Meaning that the top triangle's angle are 67°, 93°, and unknown, which we can assign y. We can use the same method from above here.
67° + 93° + y = 180°
Simplify: 160° + y = 180°
y=20°
Answer:
23rd term of the arithmetic sequence is 118.
Step-by-step explanation:
In this question we have been given first term a1 = 8 and 9th term a9 = 48
we have to find the 23rd term of this arithmetic sequence.
Since in an arithmetic sequence
here a = first term
n = number of term
d = common difference
since 9th term a9 = 48
48 = 8 + (9-1)d
8d = 48 - 8 = 40
d = 40/8 = 5
Now 
= 8 + (23 -1)5 = 8 + 22×5 = 8 + 110 = 118
Therefore 23rd term of the sequence is 118.
The answer is 800.
To find this, multiply 10 times 8 to find the number you are dividing. (80) now, multiply 80 by 10. (800)
1/10 of 800 is 80, which is ten times as much as 8.
Since you know the triangles are congruent/equal, you know that:
m∠A and m∠X are congruent and have the same angle, and so does:
m∠B and m∠Y
m∠C and m∠Z
A triangle is 180°. (the 3 angles have to add up to 180) To find m∠B, you can do this:
m∠A + m∠B + m∠C = 180°
21° + m∠B + 35° = 180° Subtract 21 and 35 on both sides
m∠B = 124° your answer is C
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.
