Simplify the following:
2^3 (4×36/12 + 1/4)
4×36/12 = (4×36)/12:
2^3 ((4×36)/12 + 1/4)
2^3 = 2×2^2:
2×2^2 ((4×36)/12 + 1/4)
2^2 = 4:
2×4 ((4×36)/12 + 1/4)
2×4 = 8:
8 ((4×36)/12 + 1/4)
36/12 = (12×3)/12 = 3:
8 (4×3 + 1/4)
4×3 = 12:
8 (12 + 1/4)
Put 1/4 + 12 over the common denominator 4. 1/4 + 12 = 1/4 + (4×12)/4:
8 1/4 + (4×12)/4
4×12 = 48:
8 (1/4 + 48/4)
1/4 + 48/4 = (1 + 48)/4:
8 (1 + 48)/4
1 + 48 = 49:
8×49/4
8×49/4 = (8×49)/4:
(8×49)/4
8/4 = (4×2)/4 = 2:
2×49
2×49 = 98:
Answer: 98
Answer:
A. (–8, 2)
Step-by-step explanation:
(1) y = ½x + 6
(2) y = -¾x – 4 Set (1) = (2)
½x + 6 = -¾x – 4 Multiply each side by 4
2x + 24 = -3x – 16 Add 16 to each side
2x + 40 = -3x Subtract 2x from each side
40 = -5x Divide each side by -5
(3) x = -8 Substitute (2) into (1)
y = ½(-8) +6
= -4 + 6
= 2
The solution to the system of equations is (-8 ,2).
You can see the graphs of the two functions in the figure below. The two lines intersect at (-8, 2).
Check:
2 = ½(-8) + 6 2 = -¾(-8) - 4
2 = -4 +6 2 = 6 - 4
2 = 2 2 = 2
Answer:
True
False
True
Step-by-step explanation:
Answer:
The answer is
<h2>
</h2>
Step-by-step explanation:
The distance between two points can be found by using the formula
where
(x1 , y1) and (x2 , y2) are the points
From the question
The points are D(2, 0) and E(8, 6
The distance between them is
We have the final answer as
Hope this helps you
Answer:
Segment BF = 16
Step-by-step explanation:
The given theorem states that a line parallel to one side of a triangle divides the other two sides proportionately
The given theorem is the Triangle Proportionality Theorem
According to the theorem, given that segment DE is parallel to segment BC, we have;
Therefore;
Which gives;
Similarly, given that EF is parallel to AB, we get;
Therefore;
Which gives;
Therefore, the statement that can be proved using the given theorem is segment BF = 16.