Answer:
gradient m = - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the gradient and c the y- intercept )
y = - x - 3 ← is in slope- intercept form
with gradient m = - 1
For the regular sequence 1, 2, 3, ...,
, then sum is
If we multiply each number by 7 (7, 14, 21, ...), then the sum is
and if we add 1 to each number (8, 15, 22, ...) then the sum is
We have
terms, so the sum is:
Answer:
4/3
Step-by-step explanation:
12x-9y=-9
9y=12x-(-9)
9y=12x+9
y=12/9x+9/9
y=4/3x+1
y=mx+b where m=slope and b=y-intercept,
so the slope is 4/3
We have to find the values of F.
In this case. F is unlikely to be a polynomial.
But the problem is, we can’t calculate the values of F directly.
There is no real value of x for which x = x−1 x because F isn’t defined at 0 or 1. so,
substituting x = 2.
F(2) + F(1/2) = 3.
Substitute, x = 1/2
F(1/2) + F(−1) = −1/2.
We still are not getting the required value,
therefore,
Substitute x = −1
As, F(2) +F(−1) = 0.
now we have three equations in three unknowns, which we can solve.
It turns out that:
F(2) = 3/4
F(3) = 17/12
F(4) = 47/24
and
F(5) = 99/40
Setting
g(x) = 1 − 1/x
and using
2 → 1/2
to denote
g(2) = 1/2
we see that :
x → 1 - 1/x → 1/(1-x) →xso that:
g(g(g(x))) = x.
Therefore, whatever x 6= 0, 1 we start with, we will always get three equations in the three “unknowns” F(x), F(g(x)) and F(g(g(x))).
Now solve these equations to get a formula for F(x)
As,
h(x) = (1+x)/(1−x)which satisfies
h(h(h(h(x)))) = xNow, mapping x to h(x) corresponds to rotating the circle by ninety degrees.
Answer:
7 1/2 cups
Step-by-step explanation:
1 1/2 cups x cups
---------------- = ------------------
7 pancakes 35 pancakes
using cross products
1 1/2 * 35 = 7 * x
change 1 1/2 to an improper fraction (2*1+1)/2 = 3/2
3/2 * 35 = 7x
105/2 = 7x
divide each side by 7
105/2 * 1/7 = x
15/2 =x
change back to a mixed number
2 goes in to 15 7 times with 1 left over
7 1/2 cups