The congruent statement and the reason why the triangles are congruent is (b) ΔUVZ ≅ ΔVYX, SSS
<h3>How to determine the congruent statement and the reason?</h3>
From the question, we have the following parameters that can be used in our computation:
Triangles = UVZ and VYX
There are several theorems that make any two triangles to be congruent
One of these theorems is the SSS congruent theorem
The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent
From the question, we can see that the following corresponding sides on the triangles UVZ and VYX have the same mark
UV and VY
UZ and VX
VZ and YX
This implies that these sides are congruent sides
Hence, the congruent statement on the congruency of the triangles is (b) ΔUVZ ≅ ΔVYX and the reason is by SSS
Read more about congruent triangles at
brainly.com/question/1675117
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Answer:
The error is at step (3) .
The correct step (3) will be,
![\log_{b}(\frac {b^{x}}{b^{y}})](https://tex.z-dn.net/?f=%5Clog_%7Bb%7D%28%5Cfrac%20%7Bb%5E%7Bx%7D%7D%7Bb%5E%7By%7D%7D%29)
=
[by using the laws of indices]
All other steps are correct.
Step-by-step explanation:
The error is at the step (3) , because the student has tried to prove the quotient rule of logarithms by using the property i.e., 'The quotient rule of logarithm' itself , i.e. ,by assuming the property does hold before proving it. So, the proof is fallacious.
The correct step (3) will be,
![\log_{b}(\frac {b^{x}}{b^{y}})](https://tex.z-dn.net/?f=%5Clog_%7Bb%7D%28%5Cfrac%20%7Bb%5E%7Bx%7D%7D%7Bb%5E%7By%7D%7D%29)
=
[by using the laws of indices]
All other steps are correct.
Answer:
32760
Step-by-step explanation:
This is a permutation of 15 objects taken 4 at a time. To calculate this, we use the formula:
![_nP_r=\frac{n!}{(n-r)!}](https://tex.z-dn.net/?f=_nP_r%3D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21%7D)
In our case, n is 15 and r is 4:
![_{15}P_4=\frac{15!}{(15-4)!}=\frac{15!}{11!}=32760](https://tex.z-dn.net/?f=_%7B15%7DP_4%3D%5Cfrac%7B15%21%7D%7B%2815-4%29%21%7D%3D%5Cfrac%7B15%21%7D%7B11%21%7D%3D32760)
Answer:
Associative
Step-by-step explanation:
The associative property of addition states that you can add numbers however they are grouped inside parentheses.
It doesn't matter where you put the parentheses. You will always get the same answer.
For example,
![\begin{array}{rcl}(5 + 3) + 7 & = & 5 + (3 + 7)\\8 + 7& = & 5 + 10\\15 & = & 15\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7D%285%20%2B%203%29%20%2B%207%20%26%20%3D%20%26%205%20%2B%20%283%20%2B%207%29%5C%5C8%20%2B%207%26%20%3D%20%26%205%20%2B%2010%5C%5C15%20%26%20%3D%20%26%2015%5C%5C%5Cend%7Barray%7D)
Answer:
Scientists can tell by observing the seismic waves that are recorded all over the surface of the earth from distant earthquakes. The seismic waves are reflected (bounced off) layers of different density, and they are refracted (bent) when they enter layers of different density.