Hello from MrBillDoesMath!
Answer: 9
Discussion
By the Pythagorean theorem, the length of the third side (the hypotenuse) in the triangle with sides 4 and 6 is sqrt ( 4^2 + 6^2) = sqrt (52)
Applying Pythagoras to the left most triangle (sides, x and 6) gives:
x^2 + 6^2 = m^2 (I am calling the unknown side "m)
Finally, in the big right triangle (the one containing the two right triangles)
(x + 4) ^2 = (sqrt(52)) ^2 + m^2
OK! Subtract the first equation from the second:
(x+4)^2 = 52 + m^2
x^2 + 36 = m^2
-----------------------------------------------------
( x+4)^2 - x^2 - 36 = 52 + (m^2 - m^2) =>
x^2 + 8x + 16 - x^2 -36 = 52 =>
x^2 - x^2 + 8x + 16 -36 = 52 =>
0 + 8x - 20 = 52 =>
8x = 72 =>
x = 9
Thank you,
MrB
Answer:
Option (2).
Step-by-step explanation:
Coordinates of points A(-2, 2), B(-1, -1), C(-1, 4) and (0, -2)
By using formula to get the length of any segment having extreme ends at
and
,
d = 
Length of segment AB = 
=
≈ 3.16
Length of segment CD = 
=
≈ 6.08
Length of CD ≈ 2(length of AB)
But length of horizontal segments are equal.
Therefore, function 'f' is vertically stretched to form 'g'.
g(x) = 2f(x)
Now 'f' is translated by 1 unit right,
g(x) = 2f(x - 1)
Option (2) will be the answer.
Answer:
x=11
Step-by-step explanation:
x=11 because, 6x+8= 74, so you do 74-8=66 and 66/6= 11. so x=11,
the measure of 2 is 7(11)-2+m=106.
so you add 2 on both sides to cancel it out, and you end up with 7(11)+m=108
now you do 7(11)= 77, and you subtract from both sides and get 31.
therefore, m=31.
hope this helps!
3x + x - 2 = -14
Add two to both sides
3x + x = -12
4x = -12
x= -3