Answer:
11. your choices are correct
12. 132°
Step-by-step explanation:
11. The given equations can be (re)written to slope-intercept form. Only those lines with a slope of 2 will be parallel to the given line.
A: y = 2x -8 . . . . . slope = 2, an answer
B: y = -2x +1 . . . . . slope = -2, not an answer
C: y = -2x +7 . . . . .slope = -2, not an answer
D: y = 2x +2 . . . . . slope = 2, an answer
E: y = -2x -9 . . . . . slope = -2, not an answer
__
12. The marked angles are supplementary, so ...
(3x -6)° +(x +2)° = 180°
4x -4 = 180 . . . . . . . . . . . divide by °, collect terms
x -1 = 45 . . . . . . . divide by 4
x = 46 . . . . . . . . . add 1
Now, we can find the angle of interest.
∠PQR = (3x -6)° = (3·46 -6)°
∠PQR = 132°
Answer:
2
Step-by-step explanation:
Because ABCD is a rectangle, the length of CD is 12 cm.
We need to determine the length of DE. If we can do that, then the sum of the lengths of CD and DE represents the unknown: the length of CE.
To find the length of CE, we have to "solve" the upper triangle.
Here's an outline of what to do:
1. Show that BC=AD and find the length.
2. Note that angle CAD is 60 degrees. Why?
3. Note that angle EAD is 30 degrees. Why?
4. Find the length of ED
5. Add ED and DC, that is, ED + 12 cm. This is your answer.
Please ask questions if need be.
Answer:
x = 15
Step-by-step explanation:
given that y varies directly with x
mathematically we can express this as
y = k x , where k is a constant
step 1: find k
given x = 3 and y = 21
y = k x
21 = k (3)
k = 7
hence the equation becomes
y = 7 x
when y = 105,
105 = 7x
x = 105 / 7 = 15
