Find (f-g)(x) if f(x)=3x-5 and g(x)=x2-5x+4

Mathematics

1 answer:

solmaris [256]2 years ago

4 0

Answer:

Step-by-step explanation:

Hello,

$(f-g)(x)=f(x)-g(x)=3x-5-(x^2-5x+4)\\\\=3x-5-x^2+5x-4\\\\=-x^2+8x-9$

Thanks

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3 years ago

A line passes through the point (1, - 6) and has a slope of 8. Write an equation in slope-intercept form for this line.

Annette [7]

Answer:

$\boxed {\boxed {\sf y=8x-14}}$

Step-by-step explanation:

We are asked to find the equation of a line in slope-intercept form. We are given a point and a slope, so we can use the point-slope formula.

$y-y_1= m(x-x_1)$

In this formula, m is the slope and (x₁, y₁) is the point the line passes through. The slope of the line is 8 and it passes through the point (1, -6). Therefore,

m= 8
x₁= 1
y₁= -6

Substitute these values into the formula.

$y- (-6) = 8(x-1)$

Remember that 2 back to back subtraction signs are the same as an addition sign.

$y+6=8(x-1)$

The line must be in slope-intercept form or y=mx+b (m is the slope and b is the y-intercept. We must isolate the variable y on one side of the equation. First, distribute on the right side of the equation. Multiply each term inside the parentheses by 8.

$y+6 = (8*x) + (8*-1)$