I’m assuming what you’re asking here is how to *factor* this expression. For that, let’s rearrange the expression into a more familiar form:
-c^2-4c+21
From here, we’ll factor out a -1 so that we have:
-(c^2+4c-21)
Let’s focus on the quadratic expression inside the parentheses. To find our factors (c + x)(c + y), we’ll need to find two terms x and y that multiply together to make -21 and add together to make 4. It turns out that the numbers -3 and 7 work out perfectly for that purpose (-3 x 7 = -21 and 7 + (-3) = 4), so substituting them in for x and y, we have:
(c + (-3))(c + 7)
(c - 3)(c + 7)
And adding back on the negative from a few steps earlier:
-(c - 3)(c + 7)
Answer:
Jelly beans: $6 for 1 kg
Gummy worms: $7 for 1 kg
Step-by-step explanation:
In this question, we need to find the cost of 1kg of jelly beans and gummy worms.
To do this, make equations for both scenarios and solve:
2j + 2g = 26
2j + 3g = 33
Turn the bottom equation negative, as we will first solve for gummy worms (g).
2j + 2g = 26
-2j - 3g = -33
Solve:
-g = -7
Divide both sides by -1.
g = 7
We now know that gummy worms cost $7 for 1 kg
To solve for jellybeans (j), plug in 7 to g in one of the equations and solve:
2j + 2(7) = 26
2j + 14 = 26
Subtract 14 from both sides.
2j = 12
Divide both sides by 2.
j = 6
Jellybeans cost $6 for 1 kg.
Check answer by plugging in values to one of the equations:
2(6) + 2(7) = 26
12 + 14 = 26
26 = 26
Answer: 63%
Step-by-step explanation:
First find the rate of loss that would cause the average rate of loss over the 10-year period equal to 38.0%.
Assume that rate is x.
38 = (36.2 + 29.0 + 46.2 + 37.5 + 40.9 + 40.0 + 32.6 + 40.5 + 40.1 + x) / 10
38 = (343 + x ) / 10
380 = 343 + x
x = 380 - 343
x = 37%
The survival rate is the opposite of the rate of loss which means that the survival rate is;
= 1 - rate of loss
= 1 - 37%
= 63%
30 = 100%
1 = 100/30 = 10/3 %
24 = 10/3 x 24 = 80%
Answer: 80%
