$11.75 is how much change sam should receive this is because 20+20 is 40 and 40- 28.25 = 11.75 so, that’s how much change sam should receive
Hey there!
We know that since the triangle got smaller, it had to have shrunk. The answer will be a fraction, we can eliminate choice A and C.
We can use the x-axis as reference to figure out how much it was dilated.
J went from 8 to 4.
L went from 12 to 6.
K went from 4 to 2.
We know that the dilation was centered around the origin, so, we can assume that these numbers were not influenced by anything other than the dilation.
4 is half of 8, 6 is half of 12, and 2 is half of 4.
The correct answer is 1/2.
I hope this helps!
~kaikers
Use the law of sines when you're given: (a) 2 angles, 1 side OR (b) 2 sides, non-included angle (aka an angle not created by those two sides)
Use the law of cosines when you're given: (a) 3 sides OR (b) 2 sides, included angle
Since you're given the measurements of two angles (A and C) and one side (a), you can solve the triangle using the law of sines.
Start by drawing the triangle. Remember that the uppercase letters are the angles and the lowercase letters are the length of the sides opposite the angle with the same letter (see picture - letters in blue are given, letters in green are what we're trying to find).
The law of sines says:
![\frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%7D%7Bsin%28A%29%7D%20%3D%20%20%5Cfrac%7Bb%7D%7Bsin%28B%29%7D%20%3D%20%20%5Cfrac%7Bc%7D%7Bsin%28C%29%7D)
1) You are told that angle A = 40°, angle C = 70°, and side a = 20. That means you can plug these values into
![\frac{a}{sin(A)} = \frac{c}{sin(C)}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%28A%29%7D%20%3D%20%5Cfrac%7Bc%7D%7Bsin%28C%29%7D)
(which we know is true because of the law of sines) to find the length of side c:
The length of side c is about 29.238.2) Also remember that all the angles in a triangle add up to 180°. We know two of the angles, A and C, so subtract A and C from 180 to find the measure of angle B:
The measure of angle B is 70°.3) Now you can use the law of sines to find the length of side B. You can use
![\frac{a}{sin(A)} = \frac{b}{sin(B)}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%28A%29%7D%20%3D%20%5Cfrac%7Bb%7D%7Bsin%28B%29%7D%20)
or
![\frac{c}{sin(C)} = \frac{b}{sin(B)}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7Bsin%28C%29%7D%20%3D%20%5Cfrac%7Bb%7D%7Bsin%28B%29%7D%20)
. I'll be using the first one:
The length of side b is also about 29.238. You can also say b ≈ 29.238 without doing that math because triange ABC is an isosceles triangle since two angles (C and B) are the same, which makes their corresponding sides (c and b) the same!
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Your answer: C) B = 70°, b = 29.2, c = 29.2
Answer:
6075
Step-by-step explanation:
- Given series is: 25 + 30 + 35 + ⋯ + 245.
- Here, first term (a) = 25
- Common difference (d) = 5
- Last term
![(a_n) = 245](https://tex.z-dn.net/?f=%28a_n%29%20%3D%20245)
- First we find the number of terms that this series has by the following formula:
- Plugging the values of a, d and
, we find.
- Thus, the given series contains 45 terms.
- Next, we find the sum of the given series using the formula given below.
Answer:
Step-by-step explanation:
The number of miles that he ran last week is m.
His goal this week was to run one mile more than twice the miles he ran last week. This means that his goal this week is
m + 2m = 3m
If he tripled his goal, it means that the number of miles that he ran this week would be
3 × 3m = 9m
An expression in simplest form to show how many more miles he ran this week compared to last week would be
9m - m = 8m