Just simplify the given equation
y = 7.2 + 4(x-2)
y = 7.2 + 4x - 8
y = 4x - 0.8
Now they want to know the answer if X = 2
y = 4(2) - 0.8
y = 8 - 0.8
y = 7.2
First, we use the rational root theorem to determine any solutions of p(x). <span>= x3 + 4x2 + x − 6</span>
Factoring -6:
1
-1
2
-2
3
-3
6
-6
<span>x = 1 </span>
<span>p(1) = 1^3 + 4 * 1^2 + 1 - 6 = 6 - 6 = 0 </span>
<span>x = 1 is a solution. </span>
(x^3 + 4x^2 + x - 6) / (x - 1) =
x^3 / x = x^2
x^2 * (x - 1) = x^3 - x^2
x^3 + 4x^2 - x^3 + x^2 = 5x^2
5x^2 / x = 5x
5x * (x - 1) = 5x^2 - 5x
5x^2 + x - 5x^2 + 5x = 6x
6x / x = 6
6 * (x - 1) = 6x - 6
6x - 6 - 6x + 6 = 0
<span>(x - 1) * (x^2 + 5x + 6) </span>
x^2 + 5x + 6 factors to (x + 3) * (x + 2)
Factors:
<span>(x - 1) </span>
<span>(x + 2) </span>
<span>(x + 3) </span>
<span>roots: </span>
<span>x = 1 </span>
<span>x = -2 </span>
<span>x = -3</span>
Answer:
14
Step-by-step explanation:
First, find out how many she had to distribute
96 - 12 = 84
Now divide 84 by the number of students
84/6=14
4. Steps:
.......Find least common denominator
.......Add numerators
.......Simplify
1/4 + 1/2 + 2/3 .....
........12 is least common denominator
....... multiply numerator and denominator by same number
1/4 4×3=12 so multiply 1/4 × 3/3 = 3/12
1/2 2×6=12 so multiply 1/2 × 6/6 = 6/12
2/3 3×4=12 so multiply 2/3 × 4/4 = 8/12
ADD: 3/12 + 6/12 + 8/12 = 17/12
SIMPLIFY: 17/12 = 1 5/12 CUPS of sugar
5. Total cost:$12.30
..Icing Costs: 1/3 of Total
Equation (of means multiply):
1/3 × 12.30= N
12.30/3 = N
4.10= N
Icing Supplies Cost $4.10
6. Students: 25
.....1/5 of students
..... ate 1/8 of cake
..... How much cake is left?
In order to determine how much cake was eaten, you first need to know how many students ate it
1/5 × 25= 25/5 = 5
So 5 students ate 1/8 of cake each. So how much cake was eaten
5 × 1/8 = 5/8
cake had 8/8 pieces from which 5/8 was eaten. How much left?
8/8 - 5/8 = 3/8
so 3/8 of cake is left.
7. 3/4 × 3 = 9/4 = 2 1/4
8. Eggs 3/4 of dozen
...... Dropped 1/3 of 3/4 of dozen
3/4 × 12 = 36/4 = 9 eggs needed
1/3 × 9 = 9/3 = 3 eggs dropped
9-3=6 eggs left
9.
So for variables, you just substitute the number in for the variable.
177 - 5r
If r = 9,
117 - 5 × 9
117 - 45
72