Triangle PQR is similar to triangle XYZ. What is the perimeter of triangle XYZ? Where is the picture
Answer:
We can get 27 pieces of wire 3.6 cm long and have a piece 7/9 cm left over
Step-by-step explanation:
Find the "unit length" by dividing 1 m by 3.6 cm:
1 m
-----------
3.6 cm
Recall that 1 m = 100 cm. Multiply the following by the conversion factor 100 cm / 1 m:
1 m 100 cm
----------- * ----------------- = 27,7777777...
3.6 cm 1 m
We can get 27 pieces of wire 3.6 cm long and have a piece 7/9 cm left over (verify this by dividing 7 by 9 on a calculator).
Base case: if <em>n</em> = 1, then
1² - 1 = 0
which is even.
Induction hypothesis: assume the statement is true for <em>n</em> = <em>k</em>, namely that <em>k</em> ² - <em>k</em> is even. This means that <em>k</em> ² - <em>k</em> = 2<em>m</em> for some integer <em>m</em>.
Induction step: show that the assumption implies (<em>k</em> + 1)² - (<em>k</em> + 1) is also even. We have
(<em>k</em> + 1)² - (<em>k</em> + 1) = <em>k</em> ² + 2<em>k</em> + 1 - <em>k</em> - 1
… = (<em>k</em> ² - <em>k</em>) + 2<em>k</em>
… = 2<em>m</em> + 2<em>k</em>
… = 2 (<em>m</em> + <em>k</em>)
which is clearly even. QED
To help you graph this, get y alone in both equations. If you don't have a graphing calculator, use the Desmos graphing calculator online.
So, you will end up graphing this:
y=8-x
y=(34/3)-(5/3)x
They will meet at (5,3)
Answer:
-84
Step-by-step explanation:
The formula for the nth term of a geometric progression is
Un = ar^n- 1
The sum of the first six terms of a geometric series (U6) = 21/16
Common ratio = -1/2 ,
a = First term ??
21/16 = a × (-1/2 )^6- 1
21/16 = a ×(-2^-1)^5
21/16 = a × -2^-6
Cross Multiply
16 × a × -2^-6 = 21
a = 21/16 × -2^-6
a = 21/16 ×- 1/2⁶
a = 21/16 × -1/64
a = 21 ÷(-1/4)
a = 21 × -4
a = -84
The first term = 84
