A straight line is 180°. The angles of QRT (2x + 33) and TRS (5x - 21) make up the 180° angle. So you can do:
∠QRT + ∠TRS = 180°
(2x + 33) + (5x - 21) = 180°
2x + 33 + 5x - 21 = 180 Combine like terms
7x + 12 = 180 Subtract 12 on both sides
7x = 168 Divide 7 on both sides
x = 24
Now that you found x, you can find the angles of QRT and TRS.
m∠QRT = 2x + 33
= 2(24) + 33
= 48 + 33
∠QRT = 81°
m∠TRS = 5x - 21
= 5(24) - 21
= 120 - 21
∠TRS = 99°
Answer:
12
Step-by-step explanation:
These are similar triangles, so the ratio of their sides is the same for each side.
AB = 8 and BD = 10
So, the ratio is 8:10 or 4:5
Because the triangles are similar....
The ratio of AC:CE is also 4:5
12:15 = 4:5
So, 12 is the answer!
Answer:
<h2>A) 52 units</h2>
Step-by-step explanation:
The formula of a distance between two points X and Y on the number line:
d = |Y - X|
We have
P = -76, Q = -24
Substitute:
d = |-24 - (-76)| = |-24 + 76| = |52| = 52
To determine the inverse of a function, we first write the parent function in terms of y. So, in this part the x would be isolated to one side of the equation. Then, with the new form of the parent function, we switch the x into y and y to x. The new function would be the inverse function. For the given function, we do as follows:
<span> y=-4/x + 1
y - 1 = -4/x
x ( y - 1 ) = -4
x = -4 / (y -1)
Replacing x into y and y into x,
</span>y = -4 / (x -1)
<span>Therefore, the inverse is y=-a/x-b where a = 4 and b = 1.</span>
