<u>Answer-</u>
<em>The value of y is </em><em>6 units</em><em>.</em>
<u>Solution-</u>
Given ∆ABC ≅ ∆GEF
If two triangles are congruent, then the corresponding sides are also congruent.
So,
EF = BC, GF = AC
Putting the values,
--------------1

--------------------2
Putting the values of x in equation 1,


Therefore, the value of y is 6 units.
Hey there! :)
Line passes through (2, -4) & parallel to y = 3x+ 2
Let's start off by identifying what our slope is. In the slope-intercept form y=mx+b, we know that "m" is our slope. "M" is simply a place mat so if we look at our given line, the "m" value is 3. Therefore, our slope is 3.
We should also note that we're looking for a line that's parallel to the given one. This means that our new line has the same slope as our given line. Therefore, our slope for our new line will be 3.
Now, we use point-slope form ( y-y₁=m(x-x₁) ) to complete our task of finding a line that passes through (2, -4) with a slope of 3.
y-y₁=m(x-x₁)
Let's start by plugging in 3 for m (our slope), 2 for x1 and -4 for y1.
y - (-4) = 3(x - 2)
Simplify.
y + 4 = 3x - 6
Simplify by subtracting 4 from both sides.
y = 3x - 10
~Hope I helped!~
Answer:
d. Two-sample t-test. There is no natural pairing between the two populations.
Step-by-step explanation:
A two-sample t - test is a test performed on the data of two random samples, each independently obtained from a different given population. The purpose of the test is to determine whether the difference between these two populations is statistically significant.
Independent samples are samples that do not affect one another. The mean math scores of the samples of boys and girls do not affect each other. They are independent samples, hence the correct test procedure is two - sample t - test
I'm going to assume that is your shape.
If that is your shape, this is simple:
First, you need to solve for the angle TZU. The formula for it is:
mTZU= 0.5(arcTU+arcSR)
mTZu= 0.5(72°+100°) = 86°
Vertical angles, as you should know, are congruent. Always. mTZU is a vertical angle to mSZR. This means mSZR is also 86°
Now, the sum of all angles should be 360°. Now you need to know the remaining angles, you can do this by:
360° - 86° - 86° = 188°
Now, last step. Since mSZR is also equal to RZU because they are vertical angles, this means you need to divide 188° by 2.
188°/2 = 94°
Your answer: m∠SZT = 94°
~Hope this helps!
20.40 
When this situation is drawn out, it forms a right triangle (as shown in the attached image). The sides that are given are the two legs of the triangle. The side that is missing is the hypotenuse. The missing side can be found using the pythagorean theorem:

A = 20
B= 4
C = ?
This process is shown in the attached image. The length of the missing side (ladder) rounded to the nearest hundredth is 20.40