Answer:
8√21
Step-by-step explanation:
A rectangle has 2 congruent pairs. Those 2 pairs are ST/RU and SR/UT. If that is the case, then that means UV is 5 and SV is also 5. Now we have triangle SRU with a hypotenuse of 10 and a side of 4. Pythagorean Theorem:
4² + b² = 10²
b² = 84
b = 2√21
Segment SR is then equal to b. Now we move on to the area formula:
(2√21)(4) = 8√21
And that is your final answer.
X= 2/3
6x/x-6 - 4/x - 24 / x^2 - 6x = 0
6x^2 -4 (x-6)-24 / x(x-6) = 0
6x^2 -4x+ 24 -24/x(x-6) = 0
X(6x-4) / x(x-6)
6x-4/x-5 = 0
6x-4= 0
6x = 4 divide both sides by 6
X= 2/3
Answer:
r = √13
Step-by-step explanation:
Starting with x^2+y^2+6x-2y+3, group like terms, first x terms and then y terms: x^2 + 6x + y^2 -2y = 3. Please note that there has to be an " = " sign in this equation, and that I have taken the liberty of replacing " +3" with " = 3 ."
We need to "complete the square" of x^2 + 6x. I'll just jump in and do it: Take half of the coefficient of the x term and square it; add, and then subtract, this square from x^2 + 6x: x^2 + 6x + 3^2 - 3^2. Then do the same for y^2 - 2y: y^2 - 2y + 1^2 - 1^2.
Now re-write the perfect square x^2 + 6x + 9 by (x + 3)^2. Then we have x^2 + 6x + 9 - 9; also y^2 - 1y + 1 - 1. Making these replacements:
(x + 3)^2 - 9 + (y - 1)^2 -1 = 3. Move the constants -9 and -1 to the other side of the equation: (x + 3)^2 + (y - 1)^2 = 3 + 9 + 1 = 13
Then the original equation now looks like (x + 3)^2 + (y - 1)^2 = 13, and this 13 is the square of the radius, r: r^2 = 13, so that the radius is r = √13.
It's a probability problem to find the odds of picking a green or red
shirt out of the 10 shirts on Thursday, Friday and Saturday since you
have randomly already know you have picked a blue shirt on the other
days. Not sure if you have this as a multiple question problem as you didn't list any possible answers (A. 7/20, B. 5/47, C. 2/5, D. 4/125) to the question. A, B, C, D being like 7 chances out of 20, 5 chances out 47, 2 chances out of chances 5 or 4 chances out of 125 (example answers only).
Probability = Number favorable outcomes / total number of outcomes
-3/5x + 1/5 > 7/20
-3x + 1/5 > 7/20 join the denominators
-3x + 1 > 7/20 * 5 multiply both sides by 5
-3x + 1 > 35/20
-3x + 1 > 7/4
-3x > 7/4 - 1
-3x > 3/4
x < -3/4 ÷ 3
x < -1/4
hope that helps, God bless!
