1 < x < 5
Left side is 1 and right is 5
To find the slope of a line that goes through given points with known coordinates, you divide the subtraction of the y of the second point minus the y of the first point, by the subtraction of the x of the second point minus the x of the first point:
m = (yB-yA) / (xB-xA)
Let A(8,5) and B(6,7).
With yB = 7; yA = 5; xB = 6; xA = 8
m = (7-5) / (6-8)
m = 2/-2
m = -1
So the slope of the line that goes through the given points (8,5) and (6,7) is m = -1.
I've added a pic of the line with both points under the answer.
Hope this Helps! :)
Answer:
add all the sides together
a+b+c+d
First translate the English phrase "Four times the sum of a number and 15 is at least 120" into a mathematical inequality.
"Four times..." means we're multiplying something by 4.
"... the sum of a number and 15..." means we're adding an unknown and 15 and then multiplying the result by 4.
"... is at least 120" means when we substitute the unknown for a value, in order for that value to be in the solution set, it can only be less than or equal to 120.
So, the resulting inequality is 4(x + 15) ≤ 120.
Simplify the inequality.
4(x + 15) ≤ 120
4x + 60 ≤ 120 <-- Using the distributive property
4x ≤ 60 <-- Subtract both sides by 60
x ≤ 15 <-- Divide both sides by 4
Now that we have the inequality in a simplified form, we can easily see that in order to be in the solution set, the variable x can be no bigger than 15.
In interval notation it would look something like this:
[15, ∞)
In set builder notation it would look something like this:
{x | x ∈ R, x ≤ 15}
It is read as "the set of all x, such that x is a member of the real numbers and x is less than or equal to 15".
We can use the formula y2-y1/x2-x1 to find our answer. So, we have : t-16/5-2 = -3. We simplify that to t-16/3 = -3. We can then multiply both sides by 3 to get t-16 = -9. Then we can add 16 to both sides to get t = 7.
