Yes, you are correct.
From the image, we can see 3 triangles, the large triangle and the two triangles that make the larger triangle.
All 3 of these triangles are similar since they're angle measurements are the same (can be proven by geometry).
We can gather the following information from the given information.
- The largest triangle (the one made up of two triangles) has a hypotenuse of 3+9=12, and a leg length of x. The hypotenuse to leg ratio is 12/x
- The second largest triangle has a hypotenuse length x and leg length 9. The hypotenuse to leg ratio is x/9
We know the hypotenuse to corresponding leg ratio must be equal since these two triangles are similar. Thus, we have the equation:
12/x = x/9
Using the cross product property gives us:
x² = 9 × 12
x² = 108
Taking the square root of both sides gives us:
x = √108
= 6 √3
Thus, your answer is correct. Great job!
Let me know if you need any clarifications, thanks!
Answer:
The Supreme Court.
Step-by-step explanation:
After the end of the Civil War and the enactment of the Thirteenth Amendment in 1865, slavery was officially abolished in the United States. Thus, the millions of African American slaves that inhabited the southern states of the country won their freedom and equality before the law against whites.
Now this situation began to dismember in 1877, when federal troops left the southern states and Reconstruction officially came to an end. From then on, Democratic governors and legislators began to sanction the Black Codes and Jim Crow Laws, aimed at curtailing the civil and political rights of African-Americans.
This situation was tested before the Supreme Court in 1896 in the case Plessy v. Ferguson. But in the ruling of said case, the Supreme Court established that racial segregation was constitutional and therefore neglected African Americans and their rights.
There are 20 gallons of 20% butterbeer solution.
Assume there are x gallons of 80% solution.
So total amount of the solution will be (x+20) gallons
The final solution is 50%.
So, we can set up the equation as:
.
Thus, there will be 20 gallons of 80% butterbeer solution that is needed to be mixed with 20 gallons of 20% butterbeer solution.
Answer:
What this is is factoring and these are both perfect squares.
(3x-5)(3x+5) is the answer.
Step-by-step explanation:
First we take the 9x^2-25 and split in in two statements
(3x-5) (3x+5)
then foil to check it
first side: 3x*3x=9x^2
outside: 3x*5=15x
inside: -5*3x=-15x
last: -5*5=-25
then put it together
9x^2+15x-15x-25
the 15x and -15x cancel each other out so you're left with 9x^2-25
You find the radius and you multiply it by 2, that is diameter because raidus is half of diameter
