Answer:
B is the better detergent
Step-by-step explanation:
If A has a lower number on the 1-10 scale, that means on average it was closer to the lower end, or the least clean end. This means that A cleans worse than B., and B is better.
F(x)=(x-10)^2
Right is negative
Left is positive
Remember that - those become handy later on. Try to become really good at transformations!
Good luck!
Answer:
b) i) Curve A
ii) - 1.75
iii) x = 1 - √5 or x = 1 + √5
Step-by-step explanation:
b) i) We are given a function y = x² - 2x - 3 and the graph of this function is also shown in the side diagram.
The equation can be rearranged to y = (x - 1)² - 4
⇒ (x - 1)² = y + 4
Therefore, this is an equation of a parabola having the vertex at (1,-4) point and its axis is parallel to the positive y-axis.
So, the curve A represents the equation given. (Answer)
ii) Now, at x = 2.5, f(x) = 2.5² - 2 × 2.5 - 3 = - 1.75 (Answer)
iii) When y = 1, then x² -2x - 3 = 1
⇒ x² - 2x - 4 = 0
⇒ (x - 1)² - 5 = 0
⇒ (x - 1)² - (√5)² = 0
⇒ (x - 1 + √5)(x - 1 - √5) = 0
⇒ x = 1 - √5 or x = 1 + √5 (Answer)
Answer:
a=35 given
b=40
c=110
I couldn't complete see c. Please look at the picture to see what I assumed it to be.
Step-by-step explanation:
Hmmm... I guess a and b are not vertical.
We are given b=180-4a and a=35 so b=180-4(35)=180-140=40.
So b=40.
Isosceles triangles always have congruent base angles. So let's call both of the base angles in the bottom triangle x.
That means x+x+40=180.
We need to solve this for x.
Combine like terms:
2x+40=180
Subtract 40 on both sides:
2x=140
Divide both sides by 2:
x=140/2
Simplify:
x=70
So I'm assuming that c and it's adjacent angle are sitting on a straightedge together which means 70+c=180.
70+c=180
Subtract 70 on both sides:
c=180-70
Simplify:
c=110
Answer:
y = 1x - 5
Step-by-step explanation:
We will use the slope equation for this: y = mx + b
y is our output/answer
m is our slope, or the rate of change
x is our x coordinate. For example, in (3,2) x would be 3.
b is our y intercept, or where the line passes through the y axis.
Knowing this, we can fill out the blanks.
when we look at one point on the grid, and then find the next closest number from the point we chose, we can see that the slope is 1 so we now have: y = 1x + b
to find b, we find where the line passes over the y axis which on our grid is -5. Normally we would write: y = 1x + 5 Since we have a negative 5 or -5, we will change the + to a -
This means we write y = 1x -5.
I hope this helps you and have a great day :D
