Answer: x = 184°
Step-by-step explanation: As we can see in the figure below, angles 2 and 4 are <u>Vertical</u> <u>Angles</u>, i.e., they are angles opposite each other when two lines cross. Vertical angles are always congruent.
Then,
m∠2 = m∠4
Value of x is
x = 184
The value of x is 184°.
For Q3, you can subsitute x = 2 and y = 5 into the systems
-5(2) + 5 = -5
so it's a solution for the first system
-4(2)+2(5) = 2
it's also a solution for the second system
Answer:
Average rate of change = 3
Step-by-step explanation:
- We know that the average rate of change is basically a measure of the slope of the secant line in the closed interval [a, b].
here a = -3 and b = 4
⇒ Average rate of change = f(b) - f(a) / b - a
= (27 - 6) / (4 - (-3))
= 21 / 7
= 3
Therefore, Average rate of change = 3
Answer:
8 days
Step-by-step explanation:
On day 8, Isabella will save 256 nickels, bringing her total to 510.
_____
The number of nickels saved on day n is 2^n. The total is 2^(n+1)-2.
_____
The above can be written down from your knowledge of binary sequences. If you want a more formal development, read on.
__
The number of nickels saved on day n is a geometric sequence with first term 2 and common ratio 2. The n-th term of the sequence is ...
an = a1·r^(n-1) = 2·2^(n-1) = 2^n
The sum of n terms of the sequence is ...
S = a1(r^n -1)/(r -1) = 2(2^n -1)/(2-1)
S = 2^(n+1) -2
__
We want S > 500, so ...
500 < 2^(n+1) -2
502 < 2^(n+1)
251 < 2^n
log(251) < n·log(2)
n > log(251)/log(2)
n > 7.97 . . . . . . . . 8 days or more to save more than 500 nickels
Step-by-step explanation:
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