Let X represent Karma's fathers age and Y represent Karma's age. The first term can be found using this formula:
Y = 1/3X → 5 Years ago
Y = 1/2X → 5 Years from now
From mental math, I can concur she's 15 and her father is 35. Then we plug in to check.
1/3(30) = 10 √ (Five years ago).
1/2(40) = 20 √ (Five years from current).
Their current ages are 15 and 35.
Answer:
x=28
Step-by-step explanation:
Hi there!
SSS similarity theorem is a theorem that can determine similar triangles; the criteria for SSS~ is that the corresponding sides of the triangles create proportions which is the same as the ratio of similitude (k)
First, we need to find the ratio of similitude.
We need to assume that the triangles are similar.
15 corresponds with 20 (if you turn both triangles until they're titled the same way, you will see that 15 and 20 are the measures of the same sides on the triangles)
so that means 15/20 must make the ratio of similitude
15/20 is equal to 3/4
therefore k=3/4
as the triangle is already assumed similar, that means that 21/x will also give us a ratio that is equal to 3/4 (ratio of similitude)
therefore, 21/x=k
Since both ratios are equal to k, set 3/4 and 21/x equal to each other. This is possible via a property called transitivity (if a=b and b=c, then a=c)
3/4=21/x
cross multiply
3x=84
divide both sides by 3
x=28
So that means that 28 will make the triangles similar by SSS similarity
*you double check by doing 21/28 and see that it's also equal to 3/4
Hope this helps!
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:
=> 5x + 9 = 4
Adding - 9 on both sides,
=> 5x + 9 - 9 = 4 - 9
=> 5x = - 5
Divide by 5 on both sides,
=> x = - 1
Hence the value of the variable x is - 1