Answer:
y = x + 1
Step-by-step explanation:
y = mx + b
First, find the y-intercept. This is where the line intersects with the y-axis.
So, 1. -> y = mx + 1
Next, find the slope. For every 1/2 moving to the right, it also vertically increased by 1/2.
(1/2)/(1/2)
= 1 -> y = x + 1
Therefore, y = x + 1
A Pythagorean triple is a set of thre integer numbers, a, b and c that meet the Pythgorean theorem a^2 + b^2 = c^2
Use Euclide's formula for generating Pythagorean triples.
This formula states that given two arbitrary different integers, x and y, both greater than zero, then the following numbers a, b, c form a Pythagorean triple:
a = x^2 - y^2
b = 2xy
c = x^2 + y^2.
From a = x^2 - y^2, you need that x > y, then you can discard options A and D.
Now you have to probe the other options.
Start with option B, x = 4, y = 3
a = x^2 - y^2 = 4^2 - 3^2 = 16 -9 = 7
b = 2xy = 2(4)(3) = 24
c = x^2 9 y^2 = 4^2 + 3^2 = 16 + 9 = 25
Then we could generate the Pythagorean triple (7, 24, 25) with x = 4 and y =3.
If you want, you can check that a^2 + b^2 = c^2; i.e. 7^2 + 24^2 = 25^2
The answer is the option B. x = 4, y = 3
Coefficient of x is less than 0 then it's across the y axis
So f(x)=2^x ---> g(x) = 2^-x
Then translating it up 5 units, should be g(x) = 2^(-x) + 5
Answer is the last one
g(x) = 2^(-x) + 5
If you would like to find the value of a in the polynomial, you can do this using the following steps:
(y - 4)(y^2 + 4y + 16) = y^3 + 4y^2 + 16y - 4y^2 - 16y - 64 = y^3 + 4y^2 + ay - 4y^2 - ay - 64
a = 16
The correct result would be 16.
