Answer:
Subtract xx from both sides of the equation.
−2y=4−x
Let's start with a picture.
We see RST is smaller, and BC is parallel to but in the opposite direction to its corresponding segment ST. Both have slope -1.
If we look at the difference of points (technically called vectors but we don't have to go there) we get
C-B=(-2,2)
T-S=(1,-1)
Without further calculation we can see T-S is half the length of C-B.
The problem asks for a dilation followed by a reflection. We know the dilation scale is k=1/2 because the new triangle is half the size.
After dilation we get A'B'C':
A'(3,2), B'(-1,0), C'(-2,1)
We see now we need a reflection that flips the coordinates x and y. That's the +45° line through the origin, namely y=x.
Answer: k=1/2, y=x
Answer:
There were (4x + 2) grapes in the bowl
Step-by-step explanation:
Here, we are interested in calculating the total number of grapes in the bowl.
We have 3 people sharing the total
Damien are x grapes
Jake ate 1 more than twice what Damien and that is (1 + 2x) grapes
Makayla ate 5 fewer grapes than Damien: So what Makayla ate is (x-5) grapes
And now, we have 6 grapes left.
To find the total number of grapes in the bowl, we need to add up all what they ate plus what is left.
Mathematically, that would be;
x + 1 + 2x + x -5 + 6
= 4x + 2
Answer:
<h2>There is a 9% of chances that all three selections are apples.</h2>
Step-by-step explanation:
We know that there are 6 apples, 5 oranges and 1 pear, which gives a total of 12 fruits, that's total number of possible outcomes, the denominator of the simple probability.
Now, his friend selects three fruits with three trials without replacement, that means we need to find the probability of each even and then multiply them, because they are independent events.
Notice that we calculated the total probability using the same expression. The important thing is that you need to decrease the number of events and the total number of outcomes at each selection, because after his friends picks one apple, he doesn't put it back in the bag.
Therefore, there is a 9% of chances that all three selections are apples.
(We multiplies the number by 100 to express it in percentage)
I decided to write out the answer in paint, you can see it as an attachment.
