Answer:
Part A:
The y-intercept is 3.25. This shows the point where the line intersects with the y-axis.
Part B:
The slope was found using the points (1,5) and (5,12). 5 -1 = 4, which is the run. 12- 5 = 7, which is the rise. 7 ÷ 4 = 1.75. This is the slope.
Input b and m;
y = 1.75x + 3.25
Now, input x;
y = 1.75(13) + 3.25
y = 22.75 + 3.25
y = 26
After 13 months of practice, the team can expect to win 26 matches.
It's an 11% increase. To find this, you have to subtract 85 from 94.35 and then you divide that difference by the original amount. In this case it's 85. After that, you get .11. Then you just turn it into a percent.
Answer:
Step-by-step explanation:
Angle E is one-half the measure of the difference between arc CG and arc DF. Mathematically, that looks like this:
and
44(2) = 160 - DF and
88 = 160 - DF and
-72 = -DF so
DF = 72 degrees, second choice down
Answer:
Option C. 1020
Step-by-step explanation:
From the question given above,
512 + 256 +... + 4 =?
We'll begin by calculating the number of terms in the sequence. This can be obtained as follow:
First term (a) = 512
Common ratio (r) = 2nd term / 1st term
Common ratio (r) = 256 /512
Common ratio (r) = 1/2
Last term (L) = 4
Number of term (n) =?
Tₙ = arⁿ¯¹
L = arⁿ¯¹
4 = 512 × (1/2)ⁿ¯¹
Divide both side by 512
4 / 512 = (1/2)ⁿ¯¹
1/128 = (1/2)ⁿ¯¹
Express 128 in index form with 2 as the base
1/2⁷ = (1/2)ⁿ¯¹
(1/2)⁷ = (1/2)ⁿ¯¹
Cancel 1/2 from both side
7 = n – 1
Collect like terms
7 + 1 = n
n = 8
Thus, the number of terms is 8
Finally, we shall determine the sum of the series as follow:
First term (a) = 512
Common ratio (r) = 1/2
Number of term (n) = 8
Sum of 8th term (S₈) = ?
Sₙ = a[1 – rⁿ] / 1 – r
S₈ = 512 [1 – (½)⁸] / 1 – ½
S₈ = 512 [1 – 1/256] ÷ ½
S₈ = 512 [255/256] × 2
S₈ = 2 × 255 × 2
S₈ = 1020
Thus, the sum of the series is 1020.
Answer:
90°
Step-by-step explanation:
All angles inside a triangle add up to 180 so:
180 - 10 - 80 = 90
Therefore, the 3rd angle is 90°
