Answer: The coordinates of point C after the dilation are (-2, 5)
Step-by-step explanation:
I guess that you want to find where the point C ends after the dilation.
Ok, if we have a point (x, y) and we do a dilation with a scale A around the point (a,b), then the dilated point will be:
(a + A*(x - a), b + A*(y - b))
In this case we have:
(a,b) = (2,1) and A = 3.
And the coordinates of point C, before being dilated, are: (1, 2)
Then the new location of the point C will be:
C' = (1 + 3*(1 - 2), 2 + 3*(2 - 1)) = (1 -3, 2 + 3) = (-2, 5)
*Hint: In order to find the coordinates, you plug in the coordinates into the rule and solve.
(x, y) → (x + 2, y - 8)
(4, -5) → (4 + 2, -5 - 8)
(6, -13)
The coordinates of B' is (6, -13).
To get the points at which the two boats meet we need to find the equations that model their movement:
Boat A:
vertex form of the equation is given by:
f(x)=a(x-h)^2+k
where:
(h,k) is the vertex, thus plugging our values we shall have:
f(x)=a(x-0)^2+5
f(x)=ax^2+5
when x=-10, y=0 thus
0=100a+5
a=-1/20
thus the equation is:
f(x)=-1/20x^2+5
Boat B
slope=(4-0)/(10+10)=4/20=1/5
thus the equation is:
1/5(x-10)=y-4
y=1/5x+2
thus the points where they met will be at:
1/5x+2=-1/20x^2+5
solving for x we get:
x=-10 or x=6
when x=-10, y=0
when x=6, y=3.2
Answer is (6,3.2)
Hey there!
Let's write this as a ratio/proportion.
The sum of this basic ratio is 4.25.
To figure out how much of each we have for 34, we divide this 34 by 4.25, our sum of the two ingredients. This will give us a factor we can multiply our two ingredient measurements by.
34/4.25=8
Now, we multiply our two ingredients by eight.
2.75(8)=22
1.5(8)=12
Note that these two add up to make 34 tablespoons.
Therefore, we have...
22 tablespoons of olive oil and 12 tablespoons of balsamic vinegar were used in the 34 tablespoons of bread dip.
I hope this helps! Have a great day! :)
