Please help with problem and show work
1 answer:
Answer:
x = 7
Step-by-step explanation:
The image below shows the relationship between secants chords and tangents.
Imagine that the letters in the image represent the numbers in the actually problem
E would equal 9
C would equal 12
and A would equal x
We would then use the same formula C² = E * ( E + A ) to solve for x , but once again instead of using letters we use the numbers in the problem
We would have 12² = 9( 9 + x )
we now solve for x
Step 1 simplify and distribute
12²=144
9 * 9 = 81
9 * x = 9x
we would then have 144 = 81 + 9x
step 2 subtract 81 from each side
144 - 81 = 63
81 - 81 cancels out
we now have 63 = 9x
step 3 divide each side by 9
63 / 9 = 7
9x / 9 = x
we're left with x = 7
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Answer:
Part A: The length of each side is units long.
Part B: The dimensions are 5x-4 and 5x+4 units long.
Step-by-step explanation:
Part A:
-->
--> Multiply 9 times 4 to see the factors of that product
--> 9 times4 = 36
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Use the factor 6 and make it negative so -6
add another -6
Keep in mind that it is -6x
--> 9x^2-6x-6x+4
Separate the four terms into two different binomials
--> 9x^2-6x and -6x+4
Factor the binomials
With 9x^2-6x you can factor a 3x
So it will 3x(3x-2)
Do the same thing with -6x+4
You can factor out a -2
-2(3x-2)
The reason you factor out a -2 and not 2 is because it has to be same so in this case it is (3x-2)
Take the two numbers that you factored and put them to make an expression so (3x-2)
--> (3x-2)(3x-2) or (3x-2)^2
3x-2 is the length of each side so it is 3x-2 units long
Part B:
-->25x^2-16y^2
Use the difference of squares
take the square root of 25x^2
that is 5x
take the square root of 16y^2
that is 4y
write it in this way (5x+4y)(5x-4y)
These are the dimensions of the rectangle