Answer:
You can prove this statement as follows:
Step-by-step explanation:
An odd integer is a number of the form
where
. Consider the following cases.
Case 1. If
is even we have:
.
If we denote by
we have that
.
Case 2. if
is odd we have:
.
If we denote by
we have that 
This result says that the remainder when we divide the square of any odd integer by 8 is 1.
Answer:
<h2>A. 4 in</h2>
Step-by-step explanation:
Collinear points are points that lies on the same straight line. If the points E, F and G are collinear points, then the three points lies on the same straight line.
If E is between F and G, the FE+EG = FG
EG = FG - FE
Given FE = 3 in and FG = 7 in
On substituting into the expression above to get EG;
EG = 7in - 3in
EG = 4in
Hence the length of EG is 4in
Hi!
A is <u>FALSE</u> - If you shrink a shape, it is not increased a shape, yet it is still dilating.
B is <u>TRUE</u> - When you dilate an angle, you're really just shortening or lengthening the sides, but the angle isn't changing.
C is <u>FALSE</u> - Explained above.
D is <u>FALSE</u> - Two triangles that are congruent are <em>exactly the same, </em>therefore if you dilate a triangle, you are changing the size so they are not the same.
E is <u>TRUE</u> - Similar shapes are always the same <em>except for their size. </em>When you dilate a shape, you only change the size, therefore they are equal in every other way and they are similar.
Answer:
Stefan originally spent $110.
Stefan made a profit of $44.
Step-by-step explanation:
Given that:
Stefan sold the bike and helmet for $137 and $17
Total amount = 137+17 = $154
This is 140% of the price Stefan originally paid.
Let,
x be the original price paid by Stefan
140% of x = $154

Therefore,
Stefan originally paid $110 for the bicycle and helmet.
Profit made by Stefan = 154-110 = $44
Hence,
Stefan originally spent $110.
Stefan made a profit of $44.
1. To solve this problem, it is important to know that<span> the logarithmic functions and the exponential functions are inverse. Then, you have:
</span><span>
e^a=28.37
</span><span> a=ln(28.37)
</span><span>
2. Therefore: </span><span>Which logarithmic equation is equivalent to the exponential equation e^a=28.37? A</span><span>s you can see, the answer for this question is:
</span><span>
a=ln(28.37)</span>