From 1st equation
d + e = 2
d = 2 - e
From 2nd equation, subtitute d with 2 - e
d - e = 4
2 - e - e = 4
2 - 2e = 4
-2e = 2
e = -1
Find d
d = 2 - e
d = 2 - (-1)
d = 3
The solution is (3,-1)
Answer:
(a) 4
(b) 2√3
(c) 60°
(d) 120°
Step-by-step explanation:
(a) The relationship between tangents and secants is ...
CB^2 = CD·CA
Filling in the given values, we find ...
CB^2 = 2·(2+6) = 16
CB = √16 = 4
The length of BC is 4 units.
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(b) Triangle ABC is a right triangle, so the sides of it satisfy the Pythagorean theorem.
CA^2 = CB^2 +AB^2
8^2 = 16 +AB^2
AB = √48 = 4√3
The radius is half the length of AB, so the radius is 2√3.
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(c) The measure of angle C can be determined from the cosine relation:
cos(C) = CB/CA = 4/8 = 1/2
C = arccos(1/2) = 60°
The measure of angle C is 60°.
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(d) Arc AD is intercepted by angle ABD, which has the same measure as angle C. Hence the measure of arc AD is twice the measure of angle C.
The measure of arc AD is 120°.
Answer:
Yes
Step-by-step explanation:
2/5 + 3/4 = [2(4) + 3(5)]/20
= 23/20 = 1 3/20
1 3/20 = 1 9/60
1 1/6 = 1 10/60
1 1/6 > 1 3/20
So we are trying to find the numerator of 42 in relation of 6/7.
42 divided by 7= 6 So 6 x 6 from the numerator of 6/7 = 36.
So 6/7 written as a fraction with a denominator of 42 is 36/42.
Answer:
x = 2 and y = -2
Step-by-step explanation:
We must first eliminate the y-variable:
2x + 3y = -2
3x - 6y = 18
4x + 6y = -4
3x - 6y = 18
_________
7x = 14
x = 2
Since we know x=2, we plug that back into one of the original equations to find y:
2x + 3y = -2
2(2) + 3y = -2
4 + 3y = -2
3y = -6
y = -2
Therefore, x = 2 and y = -2
