C) x = -19/10 because when solving it with substitution u get x=-19/10 & y=153/10
Answer:
1. C
2. D
Step-by-step explanation:
1.
Pattern A is adding by 2's (1 -> 3, 4 -> 6, 7 -> 9 and so on).
Pattern B is multiplying by 2's (2 -> 4, 3 -> 6, 4 -> 8 and so on).
2.
If 0.25 gallons of paint = 24 ft^2, then 1 gallon will equal?
Set up an equation:
Variable x = area of ft^2 for 1 gallon of paint
0.25/24 = 1/x
Cross multiply
0.25 × x = 24 × 1
0.25x = 24
To make calculations easier, you can convert the decimal into a fraction: 0.25 = 1/4
1/4x = 24
Multiply both sides by 4
1x = 96
x = 96 ft^2
Check your work:
0.25/24 = 1/96
0.25 × 96 = 24 × 1
24 = 24
Correct
Lets remember the property "alternative-interior angles" when we have parallels lines:
Given two paralles lines, the following is true:
In our question, we have:
We know that the angles J + P + K=180
So, the triangles have all the angles the same, so they are similar by angle-angle-angle, and they have one side congruent, AC=CD, so the triangles are congruents.
Step1: Define an odd integer.
Define the first odd integer as (2n + 1), for n = 0,1,2, ...,
Note that n is an integer that takes values 0,1,2, and so no.
Step 2: Create four consecutive odd integers.
Multiplying n by 2 guarantees that 2n will be zero or an even number.
Therefore (2n + 1) is guaranteed to be an odd number.
By adding 2 to the odd integer (2n+1), the next number (2n+3) will also be an odd integer.
Let the four consecutive odd integers be
2n+1, 2n +3, 2n +5, 2n +7
Step 3: require that the four consecutive integers sum to 160.
Because the sum of the four consecutive odd integers is 160, therefore
2n+1 + 2n+3 + 2n+5 + 2n +7 = 160
8n + 16 = 160
8n = 144
n = 18
Because 2n = 36, the four consecutive odd integers are 37, 39, 41, 43.
Answer: 37,39,41,43
This can be solved using the system of equations:
5500 = 1000c + 1500s
5 = c + s
As the first equation can have different combinations, it is the second equation that defines just how much acres or corn or strawberries(or mathematically, it defines the values of c or s in the first equation) there are. Therefore, the equation " 5 = c + s" is the constraint.
