You can use factors to solve. Determine all the factor pairs of 24, find the two that are two numbers apart.
1, 24 X
2, 12 X
3, 8 X
4, 6 YES!
Algebraic way to solve using Quadratics:
l = 2 + w
A = lw
A = (2 + w)w Substitute (2 + w) for l
24 = (2 + w)w Substitute 24 in for the area
24 = 2w + w^2 Distribute
w^2 + 2w - 24 = 0 Set equal to 0 (put in standard form)
(w + 6) (w - 4) = 0 Factor
w + 6 = 0 and w - 4 = 0 Set each factor equal to 0.
So w= -6 or w = 4 ... -6 makes no sense for a length! So the width must be 4 and the length will be 4 + 2, which is 6.
Answer:
b = 1, c = -1 and d = 4
Step-by-step explanation:
To solve this question the rule of multiplicity of a polynomial is to be followed.
If the multiplicity of a polynomial is even at a point, graph of the polynomial will touch the x-axis.
If the multiplicity of the polynomial is odd, graph will cross the x-axis at that point.
From the graph of function 'f',
f(x) = (x - b)(x - c)²(x - d)³
Since, graph of the function 'f' crosses x-axis at x = 1 and x = 4, multiplicity will be odd and touches the x-axis at x = -1 multiplicity will be even.
So the function will be,
f(x) = (x - 1)[x - (-1)]²(x - 4)³
Therefore, b = 1, c = -1 and d = 4 will be the answer.
Answer:
16
Step-by-step explanation:
Let's denote:
a: number of students wearing sneakers
b: number of students wearing boots
We have:
a + b = 36
a/b = 4/5 (multiply both sides by b => a = 4b/5)
Substitute a = 4b/5 into a + b = 36
=> 4b/5 + b = 36
=> 4b/5 + 5b/5 = 36
=> 9b/5 = 36
=> b/5 = 4
=> b = 20
=> a = 4b/5 = 4(20)/5 = 16
Know that dividing by 3 is the same as multiplying by 1/3.
Thus, 8/5 * 1/3 = 8/15
