<A and <J are complementary angles. Find the value of x m<A = 5x + 30 m<J = 4x +15
1 answer:
Sum of complementary angles always equal to 90°.
Given, <A and <J are complementary angles. So, we can set up an equation as following:
m<A+ M<J= 90
Next step is to plug in m<A = 5x + 30 and m<J = 4x +15 in the above equation. So we will get,
5x+30+4x+15=90
(5x+4x)+(30+15)=90 Group the like terms.
9x+45=90 Combine the like terms.
9x+45-45=90-45 Subtract 45 from each sides.
9x=45 By simplifying.
Divide each sides by 9.
x=5.
So, x=5.
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Answer:
You can look at the screenshot
Step-by-step explanation:
So one point of the line is (0, -4) and another point is (4/3, 0). Plot these points on a graph and draw a line.
0, -4 is from making x = 0, and then 4/3, 0 is from making y = 0.
Answer:
x >= -7 ................(1a)
x >= 3 ...............(2a1)
Step-by-step explanation:
f(x) = .............(0)
find the domain.
To find the (real) domain, we need to ensure that each term remains a real number.
which means the following conditions must be met
x+7 >= 0 .....................(1)
AND
x^2+2x-15 >= 0 ..........(2)
To satisfy (1), x >= -7 .....................(1a) by transposition of (1)
To satisfy (2), we need first to find the roots of (2)
factor (2)
(x+5)(x-3) >= 0
This implis
(x+5) >= 0 AND (x-3) >= 0.....................(2a)
OR
(x+5) <= 0 AND (x-3) <= 0 ...................(2b)
(2a) is satisfied with x >= 3 ...............(2a1)
(2b) is satisfied with x <= -5 ................(2b1)
Combine the conditions (1a), (2a1), and (2b1),
x >= -7 ................(1a)
AND
(
x >= 3 ...............(2a1)
OR
x <= -5 ................(2b1)
)
which expands to
(1a) and (2a1) OR (1a) and (2b1)
( x >= -7 and x >= 3 ) OR ( x >= -7 and x <= -5 )
Simplifying, we have
x >= 3 OR ( -7 <= x <= -5 )
Referring to attached figure, the domain is indicated in dark (purple), the red-brown and white regions satisfiy only one of the two conditions.
