d. y = 3/4x + 17/4.
To write the slope-intercept form y = mx + b of a line passing through (-3, 2) and (1,5).
First, we have to calculate the slope m.
m = (y₂-y₁)/(x₂-x₁), with (x₁, y₁) = (-3, 2) and (x₂, y₂) = (1, 5)
m = (5 - 2)/(1 - (-3))
m = 3/4
Second, we have to find the y-intercept.
y = mx + b, where m is the slope and b is the y-intercept.
Using one of the two ordered pair and plug it in for x and y in the equation y = mx + b.
Taking the ordered pair (1, 5):
5 = 3/4 (1) + b
5 = 3/4 + b
Solving for b
b = 5 - 3/4
b = [5(4) - 3(1)]/4
b = (20 - 3)/4
b = 17/4
Finally, write down the slope-intercept equation of the form y = mx + b, with m = 3/4 and b = 17/4:
y = mx + b
y = 3/4x + 17/4
If a quadratic equation has solutions, the standard procedure will always work: given an equation like
The solutions (if any) are given by
In your case, you have
So the formula becomes
Anyway, this is quite a special case, because you're missing the linear term (since 
)
This means that you can solve equations like these more easily: rearrange the equation to make it look like 
. In your case, it becomes
Divide both sides by 9:
Now, you know that the square of a number equals 1/9. By definition, it means that this number is the square root of 1/9. Nevertheless, both the square root and its opposite are solutions of the equation, because the minus sign will cancel out when squaring.
So, in general, you have
which of course makes sense, if you're using real numbers, only if c/a>0.
In your case, this becomes
There were 5000 mangoes in the basket, 3750 of them were good.
% mangoes
25% ---------- 1250
75% ----------- X
25x = 1250.75
25x = 93750
X = 93750/25
X = 3750 mangoes
3750+1250 = 5000
Answer:
[8.6,oo)
Step-by-step explanation:
5 times 20 (5/5) = 100%, 4 times 20 (4/5) = 80%, 3 times 20 (3/5) = 60%, 2 times 20 (2/5) = 40%, 1 times 20 (1/5) = 20%.
