Answer:
XZ > XY > YZ
Step-by-step explanation:
1. Approach
To solve this problem, one must find the value of (x), then the measure of every angle in the triangle. Remember, the sum of all angles in a triangle is equal to 180 degrees. Another property of a triangle is that the largest side of a triangle will be opposite the largest angle of the triangle, conversely, the smallest side of a triangle will be opposite the smallest angle in the triangle.
2. Find the value of (x)
The sum of all angles in a triangle is equal to 180 degrees. Using this theorem, one can state,
m<X + m<Y + m<Z = 180
Substitute,
(50) + (5x + 10) + (5x) = 180
Simplify,
10x + 60 = 180
Inverse operations,
10x + 60 = 180
-60 -60
10x = 120
/10 /10
x = 12
3. Find the measure of each angle
Now substitute the value of (x) into the expressions given to represent the value of each angle.
m<X = 50
m<Y = 5x + 10 = 5(12) + 10 = 60 + 10 = 70
m<Z = 5x = 5(12) = 60
4. Now apply this to find the comparative lengths of the sides
One property of a triangle is that the side opposite the largest angle in the triangle is the largest side. Moreover, the side opposite the smallest angle in a triangle is the smallest side. In this problem, it is impossible to find the exact lengths of the sides of the triangle, but one can find out which side is larger or smaller than the other side.
m<Y = 70
m<Z = 60
m< X = 50
<u>m<Y</u> > <u>m<Z</u> > <u>m<X</u>
Side XZ is opposite m<Y
Side XY is opposite m<Z
Side YZ is opposite m<X
This means,
XZ > XY > YZ
Answer:
3. y = 1
4. y = 3, x = 12
Step-by-step explanation:
Like the question says, we'll be using substitution, so for the first one, we'll be substituting the value of x into the equation
x = 5
3x- 5y = 10
3 (5) - 5y = 10
15 - 5y = 10
5y = 15 - 10
5y = 5
y = 1
For the next one, it's a similar idea, except the value of x has the variable y in it, which is fine, as there is still only one value in the equation we'll be solving:
x = 4y
x + y = 5
4y + y = 5
5y = 15 (we needed to collect like terms to simplify)
y = 15/5
y = 3
we still have to find x, to this, we substitute the value of y into any of the equations:
x = 4y
x = 4 (3)
x = 12
Hope this helps,
Cate
The displacement between t = 0 and t = 3 is 45 meters, so the correct option is d.
<h3>
How to find the displacement?</h3>
The displacement is defined as the difference between the final position and the initial position.
The initial position is what we get when we evaluate in t = 0.
s = 0^3 -18*0^2+60*0 = 0
The initial position is 0 meters.
The initial position is what we get when we evaluate in t = 3.
s = 3^3 -18*3^2+60*3 = 45
The final position is 45 meters.
Then the displacement is:
D = 45m - 0m = 45m
The correct option is d.
If you want to learn more about displacements:
brainly.com/question/4931057
#SPJ1
The correct question is
Use calculator to find √(<span>68.1) to the nearest hundredth
we know that
T</span><span>o the nearest 'hundredth' is the same as saying </span>
<span>'Round off to two decimal places
</span><span>To do this you first have to determine the answer with a calculator to at least 3 decimal place
</span>√68.1-------> 8.252
The rounding will happen at the 5. It will either stay 5 or round up to 6, depending on the next digit which is a 2.
<span>The 2 is below 5, so the answer rounds down to give 8.25
</span>
the answer is
8.25