Answer:
In set-builder notation, the set of solutions is:
Step-by-step explanation:
Let's start by isolating the absolute value expression on one side of the inequality:
8 | u - 2 | - 7 < 33
add 7 on both sides:
8 | u - 2 | < 40
divide both sides by 8:
| u - 2 | < 5
Now, in order to remove the absolute value symbols, we need to consider two different cases:
1) what is inside the absolute value symbols is larger than or equal to zero, so in such case when we remove the absolute value we get exactly what was inside:
u - 2 < 5
u < 5 + 2
u < 7
Now the other case;
2) what is inside the absolute value is smaller than zero, then when removing the symbols we get:
2 - u < 5
2 - 5 < u
-3 < u
Then the set of solutions of this inequality are the set of u values such that u is larger than -3 (to the right of -3 on the number line, and smaller than 7 (to the left of the number 7 on the number line.
In graph form this should look like a highlighted segment on the number line that starts at -3 on the left, ends at 7 on the right, and doesn't include the endpoints -3 and 7.
in set builder notation, the set of solutions is given by:
Answer:
Step-by-step explanation:
Answer:
1.25 OR 1 1/4
Step-by-step explanation:
I will teach you the procedure and make a calculation, based on a hypothetical dimension.
Call x the length of the side.
You will obtaind two equilateral triangles from a square if you cut by the diagonal.
The length of the diagonal is x√2.
If the sign is placed with the diagonal as the base and the vertex up (this is the righ angle), then the heigth is half the diagonal, i.e. (x√2) / 2.
So, if the side of the square is 100 inches, the diagonal is 100√2 and half diagonal is 50√2, which to the nearest tenth is 70,7 in.
Answer:
13
Step-by-step explanation:
Given the expression;
2 1/3 : 4 1/3 = 7 : x
Wea re to look for x;
Convert to improper fractions;
7/3 : 13/3 = 7:x
7/3 * 3/13 = 7/x
7/13 = 7/x
Cross multiply
7x = 13 * 7
7x = 91
x = 91/7
x = 13
Hence the unknown value is 13