1) what is the equation for the line that passes through the point (-3,5) and has a slope of -3 ?
2)the formula for the perimeter of a rectangle is P = 2(l+w). If the width of a rectangle is half its length. how many times its length is its perimeter?
3)what is the GCF of -60x^3 + 120x^2 +36x ?
4)write 3,010,000 in scientific notation
i'm having trouble with these can someone assist with this..?
(1) y-Y=m(x-X) y-5=-3(x+3) y-5=-3x-9; y=-3x-9+5; y=-3x-4 (2) since w=L/2 :- p=2(l+l/2)
Sure! I'd be happy to assist you with these questions. Let's go through each one step by step:
1) To find the equation of a line that passes through a given point (-3, 5) and has a slope of -3, we can use the point-slope form of a linear equation. The formula is:
y - y1 = m(x - x1)
where (x1, y1) represents the coordinates of the given point, and m represents the slope. Plugging the values into the formula, we have:
y - 5 = -3(x - (-3))
Simplifying further:
y - 5 = -3(x + 3)
Distributing the -3:
y - 5 = -3x - 9
Now, we want to put it in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Let's isolate y:
y = -3x - 9 + 5
Simplifying:
y = -3x - 4
Therefore, the equation for the line that passes through the point (-3,5) and has a slope of -3 is y = -3x - 4.
2) The formula for the perimeter of a rectangle is P = 2(l + w), where l represents the length and w represents the width. If the width is half the length, we can substitute w with 0.5l in the formula:
P = 2(l + 0.5l)
Simplifying the expression inside the parentheses:
P = 2(1.5l)
Now, we can distribute the 2 to both terms inside the parentheses:
P = 3l
This means that the perimeter of the rectangle is simply 3 times the length.
3) To find the Greatest Common Factor (GCF) of a polynomial, we need to factor it into its prime factors. Let's factor out the common terms from the expression -60x^3 + 120x^2 + 36x:
-60x^3 + 120x^2 + 36x = 12x(-5x^2 + 10x + 3)
Now, we can factor the quadratic expression -5x^2 + 10x + 3:
-5x^2 + 10x + 3 = (x - 1)(-5x - 3)
Therefore, the GCF of -60x^3 + 120x^2 + 36x is 12x.
4) To write 3,010,000 in scientific notation, we need to express it as the product of a number between 1 and 10 and a power of 10. We count the number of decimal places needed to move the decimal point from the original number to get a value between 1 and 10.
In this case, we count 5 decimal places:
3,010,000 = 3.01 × 10^6
So, 3,010,000 in scientific notation is 3.01 × 10^6.
I hope this helps! Let me know if you need further explanation or have any other questions.