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3 years ago

Simplify. (8) = 81 DONE

Mathematics

1 answer:

pickupchik [31]3 years ago

4 0

Answer:

What are we supposed to simplify? 8/81?

Step-by-step explanation:

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The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep

Alchen [17]

Ooh, fun

geometric sequences can be represented as
$a_n=a(r)^{n-1}$
so the first 3 terms are
$a_1=a$
$a_2=a(r)$
$a_2=a(r)^2$

the sum is -7/10
$\frac{-7}{10}=a+ar+ar^2$
and their product is -1/125
$\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3$

from the 2nd equation we can take the cube root of both sides to get
$\frac{-1}{5}=ar$
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
$\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r$
subsituting -1/5 for ar
$\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r$
which simplifies to
$\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}$
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for $ax^2+bx+c=0$
$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$
so
for 2r²-5r+2=0
a=2
b=-5
c=2

$r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}$
$r=\frac{5 \pm \sqrt{25-16}}{4}$
$r=\frac{5 \pm \sqrt{9}}{4}$
$r=\frac{5 \pm 3}{4}$
so
$r=\frac{5+3}{4}=\frac{8}{4}=2$ or $r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}$

use them to solve for the value of a
$\frac{-1}{5}=ar$
$\frac{-1}{5r}=a$
try for r=2 and 1/2
$a=\frac{-1}{10}$ or $a=\frac{-2}{5}$

test each
for a=-1/10 and r=2
a+ar+ar²= $\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}$
it works

for a=-2/5 and r=1/2
a+ar+ar²= $\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}$
it works

both have the same terms but one is simplified

the 3 numbers are $\frac{-2}{5}$ , $\frac{-1}{5}$ , and $\frac{-1}{10}$

6 0

3 years ago

Based only on the given information, it is guaranteed that AB L CDGiven AABCAD BDBCCDs CDA. True

serious [3.7K]

Hello,

any point equidistant from the ends of a segment belongs to the perpendicular bisector of the segment.
|AD|=|BD| and |AC|=|BC|

7 0

3 years ago

Read 2 more answers

P plus (negative 9)= thirty three

Cloud [144]

Answer:

Step-by-step explanation:

33+9=42

42-9=33

5 0

3 years ago

HELP PLEASE!! THANK YOU!

dmitriy555 [2]

Answer: choice B, 40.5 degrees

The triangle is isosceles based on the fact that AC = BC (the tick marks are the same). The angles opposite the congruent sides are also congruent

angle A = angle B = x for some unknown number x

The three angles A,B,C add to 180, so,

A+B+C = 180

x+x+99 = 180

2x+99 = 180

2x = 180-99

2x = 81

x = 81/2

x = 40.5

So angle A and angle B are both 40.5 degrees

Check:

A+B+C = 180

40.5+40.5+99 = 180

180 = 180 answer is confirmed

==============================

Edit

The sides with the two tick marks are the same length, so 7x-4 is the same as length as 31

7x-4 = 31

7x = 31+4

7x = 35

x = 35/7

x = 5

Answer is choice B) 5

3 0

4 years ago

Katrina wants to build a fence around her square garden. Her garden has an area of 121 square feet. How much fencing will Katrin

Luba_88 [7]

$121 \div 2 = 11$
each side equals 11
$11 \times 4 = 44$
katrina needs 44 ft of fence

4 0

3 years ago

Read 2 more answers