Answer:
Slope=2/3
Step-by-step explanation:
slope is rise over run so you do y^2-y^1/x^2-x^1 which in this case would get you 7-1/6-(-3) that gives you 6/9 which simplifies to 2/3
Answer:
14/25
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given both numbers are greater than 6
Their HCF is 6
Their LCM is 60
The product of the HCF and LCM of two numbers is the same as the product of the numbers themselves.
Let us say those number are 
and 
So, the product of those number is 
Let us factorize
It is given that number should be greater than 6
The possible pairs of number are 
But only 
has LCM as 60.
So those numbers are
<span>If a triangle does not have one angle greater than 90°, then it is not an obtuse triangle.
Remember that you create a contrapositive by inverting and swapping both terms. So if you have
if A then B
the contrapositive would be
if not-B then not-A
Since you've been given
"If a triangle is an obtuse triangle, then it has one angle with measure greater than 90°"
the contrapositive would be something like
"If a triangle has no angles with a measure greater than 90°, then it is not an obtuse triangle."
So, now look at the available choices and see what matches in intent even if it's not phrased exactly the same.
The option
"If a triangle does not have one angle greater than 90°, then it is not an obtuse triangle."
matches the intent of the contrapositive that we constructed independently and is the correct answer.</span>
Answer:
f(x) = (x + 1)*(4*x² - 3*x + 4) - 12
Step-by-step explanation:
We have:
f(x) = 4*x³ + x² + x - 8
We want to write this in:
f(x) = (x - k)*q(x) + r.
with k = -1
Then we want to write:
4*x³ + x² + x - 8 = (x - (-1))*q(x) + r
4*x³ + x² + x - 8 = (x + 1)*q(x) + r
Because f(x) is polynomial of degree 3, we know that q(x) must be a polynomial of degree 2.
then:
q(x) = a*x² + b*x + c
Then:
4*x³ + x² + x - 8 = (x + 1)*(a*x² + b*x + c) + r
4*x³ + x² + x - 8 = a*x³ + b*x² + c*x + a*x² + b*x + c + r
if we take common factors in the right side we get:
4*x³ + x² + x - 8 = a*x³ + (b + a)*x² + (c + b)*x + (c + r)
Now, we must have:
4*x³ = a*x³
then:
4 = a
We also must have:
x² = (b + a)*x²
1 = (b + 4)
1 - 4 = b
-3 = b
We also must have:
x = (c + b)*x
1 = (c + (-3))
1 + 3 = c
4 = c
And finally:
- 8 = (c + r)
-8 = 4 + r
-8 - 4 = r
-12 = r
Then:
f(x) = (x + 1)*(4*x² - 3*x + 4) - 12
