Answer:
x = 7, arc DE = 198°
Step-by-step explanation:
Inscribed angles from the same arc are congruent.
∠ DCE and ∠ DWE are inscribed angles from the same arc DE , thus
12x + 15 = 3x + 78 ( subtract 3x from both sides )
9x + 15 = 78 ( subtract 15 from both sides )
9x = 63 ( divide both sides by 9 )
x = 7
Thus
∠ DCE = 12x + 15 = 12(7) + 15 = 84 + 15 = 99°
The inscribed angle DCE is half the measure of its intercepted arc, thus
arc DE = 2 × 99° = 198°
Answer:
x = 1, y = 10
Step-by-step explanation:
y = -5x + 15 --- Equation 1
2x + y = 12 --- Equation 2
Substitute y = -5x + 15 into Equation 2:
2x + y = 12
2x - 5x + 15 = 12
Evaluate like terms.
15 - 3x = 12
Isolate -3x.
-3x = 12 - 15
Evaluate like terms.
-3x = -3
Find x.
x = -3 ÷ -3
x = 1
Substitute x = 1 into Equation 2:
2x + y = 12
2(1) + y = 12
2 + y = 12
Isolate y.
y = 12 - 2
y = 10
Answer:
A. 4 2/3 hours
B. (i) 9 4/5 hours
(ii) 1 19/30
Step-by-step explanation:
Firstly, to find the number of hours he used in visiting old folks, what we have to do is to multiply the fraction of hours he used by the total number of hours.
Mathematically, that would be;
4/7 * 8 1/6
8 1/6 is same as 49/6
So the number of hours he spent visiting old folks would be ;
49/6 * 4/7 = 14/3 = 4 2/3 hours
B. What we do here is simply multiply the fraction now by what he spent last year.
That would be 1 1/5 * 8 1/6 hours
= 6/5 * 49/6 = 49/5 = 9 4/5 hours
ii) Now we want to know how much more time will be spent this year than last year.
What to do here simply is to subtract the time taken last year from what we have this year
That would be;
49/5 - 49/6 = 49/30 = 1 19/30
3,6,9,7
1/3 = 0.33333 forever
1/6 = 0.1666666666 forever
1/9 = 0.1111111 forever
1/7 = 0.1428----
