Hi there!
We are given the equation w² + 7w + 12 = 0, and we are told to solve it. Well, we can first take all the factors of 12 -
1 12
2 6
3 4
Now, take the sum of each factor pair -
1, 12 = 13
2, 6 = 8
3, 4 = 7
Find which factor pair adds up to 7, and we can see that 3 and 4 add up to seven, while also having a product of 12. Therefore, since the whole equation has addition signs, we can factor the equation w² + 7w + 12 into (w + 3)(w + 4) = 0. Next, using the Zero Product Property, we can set each term to zero.
w + 3 = 0
w = -3
w + 4 = 0
w = -4
Therefore, the solution to the equation w² + 7w + 12 = 0 is w = -3, -4. Hope this helped and have a great day!
Answer:
$10,000
Step-by-step explanation:
Let b represent the amount invested in bonds. Then 50,000 - b wil be the amount invested in stocks. Molly's total return is ...
0.15b + 0.18(50000-b) = 8700
-0.03b +9000 = 8700 . . . . simplify
300 = 0.03b . . . . . . . . . . . . add .03b-8700
10,000 = b . . . . . . . . . . . . . divide by 0.03
Molly invested $10,000 in bonds.
Answer:
23ft approx
Step-by-step explanation:
Given data
Distance from tree= 10ft
Length of ladder= 25ft
We can find the height of the tree by applying the Pythagoras theorem
z^2= x^2+y^2
z= The height of the ladder
x= The distance from the tree
y= The height of the tree
25^2= 10^2+ y^2
625=100+y^2
625-100=y^2
525=y^2
y= √525
y= 22.91
Hence the height of the tree is 23ft approx
Answer:

Step-by-step explanation:
Given

Required
Simplify

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So:


Answer:
See below.
Step-by-step explanation:
5/6 is a fraction. The 5 is in the numerator, and the 6 is in the denominator.
The denominator is the number of parts the unit was divided into. In this case, the denominator is 6. That means one unit, 1, was divided into 6 equal parts. Each part is one-sixth.
The numerator is the number of those parts that you use. 5 in the numerator means to use 5 of those parts, each of which is 1/6 of 1.
In other words, 5/6 means divide 1 into 6 equal parts, and take 5 of those parts.
5/6 is the same as 5 divided by 6, so as a decimal it is 0.8333...
As a percent it is 83.333...%