Answer:
The scale factor is not 2
Step-by-step explanation:
Given
See attachment for the dilated triangles
Triangle ABC is dilated through center point O to form triangle A'B'C'.
From the attachment, we have:
i.e. the distance from the center point to C
and
i.e. the distance from the center point to C'
The length of OC' is calculated using:
The scale factor (k) is then calculated by dividing OC' by OC
Hence, Tiffany's claim is incorrect.
There are several ways to do this.
I'll show you two methods.
1) Pick two points on the line and use the slope formula.
Look for two points that are easy to read. It is best if the points are on grid line intersections. For example, you can see points (-4, -1) and (0, -2) are easy to read.
Now we use the slope formula.
slope = m = (y2 - y1)/(x2 - x1)
Call one point (x1, y1), and call the other point (x2, y2).
Plug in the x1, x2, y1, y2 values in the formula and simplify the fraction.
Let's call point (-4, -1) point (x1, y1).
Then x1 = -4, and y1 = -1.
Let's call point (0, -2) point (x2, y2).
Then x2 = 0, and y2 = -2.
Plug in values into the formula:
m = (y2 - y1)/(x2 - x1) = (-2 - (-1))/(0 - (-4)) = (-2 + 1)/(0 + 4) = -1/4
The slope is -1/4
2) Pick two points on the graph and use rise over run.
The slope is equal to the rise divided by the run.
Run is how much you go up or down.
Rise is how much you go right or left.
Pick two easy to read points.
We can use the same points we used above, (-4, -1) and (-0, -2).
Start at point (0, -2).
How far up or down do you need to go to get to point (-4, -1)?
Answer: 1 unit up, or +1.
The rise is +1.
Now that we went up 1, how far do you go left or right top go to point (-4, -1)?
Answer: 4 units to the left. Going left is negative, so the run is -4.
Slope = rise/run = +1/-4 = -1/4
As you can see we got the same slope using both methods.
Answer:
$17.35/h
Step-by-step explanation:
In order to get the amount per hour he made, you first need to calculate the global amount of money he made.
He was paid $2,900 then he had costs of $1,200, that leaves him a net income of $1,700 ($2,900 - $1,200)
Then he worked a total of 98 hours for that money.
A salary is an amount of money expressed by a period of time. In this case, we'll use hours.
So, Jonah earned $1,700 after 98 hours of work:
S = $1,700 / 98 hours = $17.35/h
Answer: The group wants to raise $1,200.
Step-by-step explanation:
We can use a proportion to solve.
part/whole = percent/100
If we insert the values:
276/x = 23/100
We can cross multiply.
276 x 100 = 27,600
27,600 / 23 = 1,200
$1,200 is the answer.
Answer:
x=80
Step-by-step explanation:
First of all, you must find the length of the side to add with 36 to equal 100. This would give you 64. So once you do that, you can do pythagorean theorem to find the length of x. This would give you 64^2 + 48^2 = x^2. Once you have this equation, you square your terms to get; 4,096 + 2,304 = x^2. After you add them you will now have 6,400 = x^2. Once you have this, you will need to do the square root of both sides of the equation; sqrt(6400) = x. This gives you x = 80.
Hope this helps!
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