Answer:
Correct options,
a) ![\frac{BA}{YX}=\frac{BC}{YZ}=\frac{AC}{XZ}](https://tex.z-dn.net/?f=%5Cfrac%7BBA%7D%7BYX%7D%3D%5Cfrac%7BBC%7D%7BYZ%7D%3D%5Cfrac%7BAC%7D%7BXZ%7D)
c)
and ∠A = ∠X
Step-by-step explanation:
Given : ΔABC ≅ Δ XYZ
We have choose out of given options that correctly prove that ΔABC ≅ Δ XYZ
Two triangles are said to be similar when their corresponding sides are in same ratio and the measure of their corresponding angles are equal.
That is ![\frac{AB}{YX}=\frac{BC}{YZ}=\frac{AC}{XZ}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7BYX%7D%3D%5Cfrac%7BBC%7D%7BYZ%7D%3D%5Cfrac%7BAC%7D%7BXZ%7D)
and ∠ A = ∠X , ∠ B = ∠Y AND ∠C = ∠Z
Also ,
We have conditions for two triangle to be similar.
1) SSS : When the ratio of all the three sides of a triangle are equal.
that is ![\frac{AB}{YX}=\frac{BC}{YZ}=\frac{AC}{XZ}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7BYX%7D%3D%5Cfrac%7BBC%7D%7BYZ%7D%3D%5Cfrac%7BAC%7D%7BXZ%7D)
2) SAS: When the ratio of two corresponding sides are equal and the measure of angle between those sides are equal
and ∠ A = ∠X
Thus, Out of given options,
a) ![\frac{BA}{YX}=\frac{BC}{YZ}=\frac{AC}{XZ}](https://tex.z-dn.net/?f=%5Cfrac%7BBA%7D%7BYX%7D%3D%5Cfrac%7BBC%7D%7BYZ%7D%3D%5Cfrac%7BAC%7D%7BXZ%7D)
c)
and ∠A = ∠X
Answer:
<em><u>see</u></em><em><u> </u></em><em><u>below</u></em><em><u>:</u></em><em><u>-</u></em>
Step-by-step explanation:
Given,
![\displaystyle{5 \frac{1}{6} + 2 \frac{1}{3} - 5 \frac{11}{12} }](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%7B5%20%5Cfrac%7B1%7D%7B6%7D%20%2B%202%20%5Cfrac%7B1%7D%7B3%7D%20-%205%20%5Cfrac%7B11%7D%7B12%7D%20%7D)
- <em><u>Convert</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>mixed</u></em><em><u> </u></em><em><u>fractions</u></em><em><u> </u></em><em><u>into</u></em><em><u> </u></em><em><u>improper</u></em><em><u> </u></em><em><u>fractions.</u></em>
![\displaystyle{ \frac{31}{6} + \frac{7}{3} \ - \frac{71}{12} }](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%7B%20%5Cfrac%7B31%7D%7B6%7D%20%20%2B%20%20%5Cfrac%7B7%7D%7B3%7D%20%20%5C%20-%20%20%5Cfrac%7B71%7D%7B12%7D%20%7D)
- <em><u>Take</u></em><em><u> </u></em><em><u>LCM</u></em><em><u> </u></em><em><u>of</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>denominators</u></em><em><u>:</u></em><em><u>-</u></em>
<h3><em><u>LCM</u></em><em><u> </u></em><em><u>of</u></em><em><u> </u></em><em><u>6</u></em><em><u>,</u></em><em><u>3</u></em><em><u> </u></em><em><u>and</u></em><em><u> </u></em><em><u>1</u></em><em><u>2</u></em><em><u>=</u></em><em><u>3</u></em><em><u>×</u></em><em><u>2</u></em><em><u>×</u></em><em><u>1</u></em><em><u>×</u></em><em><u>1</u></em><em><u>×</u></em><em><u>2</u></em><em><u>=</u></em><em><u>1</u></em><em><u>2</u></em></h3>
<em><u>
</u></em>
<em><u>
</u></em>
<em><u>
</u></em>
<em><u>
</u></em>
- <em><u>Convert</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>improper</u></em><em><u> </u></em><em><u>fractions</u></em><em><u> </u></em><em><u>into</u></em><em><u> </u></em><em><u>mixed</u></em><em><u> </u></em><em><u>fraction</u></em><em><u>:</u></em><em><u>-</u></em>
<em><u>
</u></em>
I have seen some scales that convert units and some that don't
first is convert
the scale converts from smaller to bigger
?:1in
6ft/8in=0.75ft/1
scale is 0.75ft:1in
other one doesn't convert dimentions
6ft=6*12in=72in
72in:8in
9:1
that is most ilkely what teacher is looking for
scale is 9:1
72in:8in
Answer:
Principal = $1,000
Rate of interest = 14% = 0.14
Time = 3 years
![A= P(1+r)^t](https://tex.z-dn.net/?f=A%3D%20P%281%2Br%29%5Et)
A = Amount or future value
P = Principal
r = rate of interest in decimals
t = time
Substitute the values in the formula
![A= 1000(1+0.14)^3](https://tex.z-dn.net/?f=A%3D%201000%281%2B0.14%29%5E3)
![A=1481.544](https://tex.z-dn.net/?f=A%3D1481.544)
Future Value is $1481.544
Compound interest = Amount - Principal = $1481.544- $1000 = $481.544
Formula of simple interest : ![SI =\frac{P \times R \times T}{100}](https://tex.z-dn.net/?f=SI%20%3D%5Cfrac%7BP%20%5Ctimes%20R%20%5Ctimes%20T%7D%7B100%7D)
Substitute the values :
![SI =\frac{1000 \times 14 \times 3}{100}](https://tex.z-dn.net/?f=SI%20%3D%5Cfrac%7B1000%20%5Ctimes%2014%20%5Ctimes%203%7D%7B100%7D)
![SI =420](https://tex.z-dn.net/?f=SI%20%3D420)
So, Simple interest = $420
Compound interest - Simple interest
= $481.544- $420
= $61.544
So, Compound Interest is $61.544 more than simple interest.
Answer:
yes
Step-by-step explanation:
yessssssss okkkkkkkkkkkkkkkkkk