Answer:
Hope this helps
Step-by-step explanation:
a) x^2 + 3x = x(x+3)
b) 2x^2 - 8x = 2x(x - 4)
c) 6x + 9x^3 = 3x(2 + 3x^2)
d) 12x^3 - 4x^2 = 4x^2(3x - 1)
<h3>
Answer: 20 cm, 35 cm, and 50 cm</h3>
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Explanation:
The sides are in the ratio 4:7:10
This scales up to 4x:7x:10x showing that the sides are 4x, 7x and 10x. The variable x is some positive real number.
Add up the sides and set this equal to the given perimeter 105. Solve for x.
4x+7x+10x = 105
21x = 105
x = 105/21
x = 5
This value is then plugged into each side
- 4x = 4*5 = 20
- 7x = 7*5 = 35
- 10x = 10*5 = 50
The triangle has sides of 20 cm, 35 cm, and 50 cm.
Note how the ratio 20:35:50 reduces to 4:7:10 after dividing all three parts by the GCF 5. Also, we can see that 20+35+50 = 105 to fully confirm our answer.
<h3>
Answer: C) 12</h3>
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Explanation:
There are 3 colors of sweaters {red, green, purple} and 2 colors of skirts {tan, black}
So far there are 3*2 = 6 different outfit combinations. Imagine a table with 3 rows representing the sweater colors and 2 columns representing the skirt colors. There would be 6 cells in the table representing each possible combination. One cell would have (red sweater, tan skirt) for instance.
For each of those 6 combinations, we also have 2 shoe colors. So overall we have 6*2 = 12 outfit combinations
The tree diagram is shown below. Note how there are 3*2*2 = 12 different paths to follow.