<h3>
Answer: D) The triangles are <u>
not</u>
similar</h3>
============================================================
Explanation:
We can immediately rule out choice C because we don't have info about all three pairs of sides. So that's why we can't use the SSS rule.
We may be able to use SAS however. This rule says that if we know a pair of sides are proportional, and if the angles between them are congruent, then we have similar triangles.
However, note the jump from XZ = 2 to XW = 8 is "times 4" while the jump from XY = 3 to XV = 9 is "times 3". The two multipliers don't match up. We would need them to be the same for the sides to be proportional.
Put another way, the equation
8/2 = 9/3
is a false equation
If we tried the equation
8/3 = 9/2
then that's also false. No matter what combos we try, the sides aren't proportional.
So ultimately, we can't use SAS either. This eliminates choice B.
Consequently, it means that we know the triangles aren't similar. If they were similar, then we'd be able to use SAS to prove them to be so.
Therefore, we do have enough information to conclude that the triangles are not similar.
This is why choice D is the final answer.
Answer: Choice C) Multiplication property of inequalityThe rule basically says that if you start with a < b and you multiply both sides by some positive number c, then a*c < b*c. The sign doesn't flip if you multiply both sides by a positive number.
The sign will flip if c is negative. So we'll go from a < b to a*c > b*c if c is negative.
Example 1:
1 < 5
-2 > -10 ... multiplied both sides by -2; sign flips
Example 2:
3 < 7
9 < 21 ... multiplied both sides by 3; sign does not flip
Similar rules apply to a > b,
![a \le b](https://tex.z-dn.net/?f=a%20%5Cle%20b)
and
Answer:
X= - 1 /14
Step-by-step explanation:
combine like terms
7x+=2x + 2 - 9x
7x + 3 = -7x + 2
Subtract 3 from both sides
7x + 3 = - 7x + 2
7 x + 3 - 3 = - 7x + 2 - 3
Simplify
7x + 3- 3 = - 7x + 2 - 3
7x = - 7x + 2- 3
7x = - 7x - 1
Add 7x to both sides
7x = - 7x - 1
7x + 7x = - 7x - 1 + 7x
Simplify
14x = - 7x - 1 + 7x
14x = - 1
Divide both sides by the same factor
14x = - 1
14x = - 1
___ ____
14 14
Simplify
Cancel terms that are in both the numerator and denominator
14x = - 1
___ ___
14 14
Answer:
[293.21;372.28]
Step-by-step explanation:
Hello!
You are asked to construct a 90% Confidence Interval for the mean duration of the foreclosure process in Boston.
The Study variable is X: duration of foreclosure in Boston. X≈N(μ;σ²)
Sample n=8
To study the population sample you can use either a Z or a t-statistic. Since the sample is less than 10, I'll choose a Student t-statistic, because it is more potent with small samples than the Z, but either one is a good choice.
X[bar]= 332.75
S= 59.01
![X[bar] ± t_{n-1; 1-\alpha /2}*\frac{S}{\sqrt{n} }](https://tex.z-dn.net/?f=X%5Bbar%5D%20%C2%B1%20t_%7Bn-1%3B%201-%5Calpha%20%2F2%7D%2A%5Cfrac%7BS%7D%7B%5Csqrt%7Bn%7D%20%7D)
![332.75 ± 1.895*\frac{59,01}{\sqrt{8} }](https://tex.z-dn.net/?f=332.75%20%C2%B1%201.895%2A%5Cfrac%7B59%2C01%7D%7B%5Csqrt%7B8%7D%20%7D)
[293.21;372.28]
With a confidence level of 90% you'd expect the interval [293.21;372.28] to contain the population mean of the duration of the foreclosure process in Boston.
I hope you have a SUPER day!
Answer:
<u>x</u><u> </u><u>is</u><u> </u><u>2</u>
Step-by-step explanation:
![3x(12x - 4) - 9x(4x - 3) = 30](https://tex.z-dn.net/?f=3x%2812x%20-%204%29%20-%209x%284x%20-%203%29%20%3D%2030)
• First open brackets [ by distributive property ]
![( {36x}^{2} - 12x) - ( {36x}^{2} - 27x) = 30 \\ \\ - 12x + 27x = 30 \\ \\ 15x = 30 \\ \\ x = 2](https://tex.z-dn.net/?f=%28%20%7B36x%7D%5E%7B2%7D%20%20-%2012x%29%20-%20%28%20%7B36x%7D%5E%7B2%7D%20%20%20-%20%2027x%29%20%3D%2030%20%5C%5C%20%20%5C%5C%20%20-%2012x%20%2B%2027x%20%3D%2030%20%5C%5C%20%20%5C%5C%2015x%20%3D%2030%20%5C%5C%20%20%5C%5C%20x%20%3D%202)