Answer:
81
Step-by-step explanation:
Using PEMDAS/BODMAS, we will have to do the exponent first, which is 
.
Substitute the variable z with 6, since z = 6.
.
Thus, we will get
Solve the multiplication next.
Finally, add/subtract the numbers:
Answer:
Step-by-step explanation:
Given (12^13–12^12+12^11)(11^9–11^8+11^7),
(12^13–12^12+12^11)(11^9–11^8+11^7) =
[(12^12)12 – 12^12 + 12^11][(11^8)11 – 11^8 + 11^7)
[(12^12)(12 – 1) + 12^11][(11^8)(11 – 1) + 11^7] =
(12^12(11) + 12^11)(11^8(10) + 11^7) =
(12^11(12x11) + 12^11)(11^7(11x10) + 11^7) =
[(12^11)(12x11 + 1)][(11^7)(11x10 + 1)] =
[(12^11)x(11^7)](12x11 + 1)(11x10 + 1) =
[(12^11)x(11^7)](133 x 111) =
[(12^11)x(11^7)](133 x 111) =
[(12^11)x(11^7)](14763) =
[(12^11)x(11^7)](3x7x19x37)
From here, it is clear that the given number is divisible by 3, 7, 19 and 37.
This problem can be readily solved if we are familiar with the point-slope form of straight lines:
y-y0=m(x-x0) ...................................(1)
where
m=slope of line
(x0,y0) is a point through which the line passes.
We know that the line passes through A(3,-6), B(1,2)
All options have a slope of -4, so that should not be a problem. In fact, if we check the slope=(yb-ya)/(xb-xa), we do find that the slope m=-4.
So we can check which line passes through which point:
a. y+6=-4(x-3)
Rearrange to the form of equation (1) above,
y-(-6)=-4(x-3) means that line passes through A(3,-6) => ok
b. y-1=-4(x-2) means line passes through (2,1), which is neither A nor B
****** this equation is not the line passing through A & B *****
c. y=-4x+6 subtract 2 from both sides (to make the y-coordinate 2)
y-2 = -4x+4, rearrange
y-2 = -4(x-1)
which means that it passes through B(1,2), so ok
d. y-2=-4(x-1)
this is the same as the previous equation, so it passes through B(1,2),
this equation is ok.
Answer: the equation y-1=-4(x-2) does NOT pass through both A and B.
Answer:
B
Step-by-step explanation:
90+45+45=180
All triangles equal 180.
Its B because if one angle is 90° then the other angles will equal each other. It cant be 60° and 30° because they dont equal, so your final answer is B.
Hope this Helps!!! :)
Answer:
Step-by-step explanation:
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