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3 years ago

How to Prove that the base angles of an isosceles triangle are congruent?.

Mathematics

1 answer:

Schach [20]3 years ago

5 0

The base angles theorem- if two sides of a triangle are congruent, then the angles opposite of them are congruent. Hope this helps :)

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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

Angles L and M are supplementary. What is the sum of their measures? The sum of the measures of angles L and M is

Reil [10]

Supplementary angles will always add up to 180. If you had a straight line, and you drew another line across that line, the two angles on either side of that line would add up to 180 because a flat line is equal to 180 degrees.

3 0

3 years ago

Read 2 more answers

Can I please get help? Find M1 and M2

marishachu [46]

Answer:

m∠1 = 110° and m∠2 = 70°

Step-by-step explanation:

m∠1 = 110° since vertical angles

To find m∠2, m∠1 and m∠2 must add to 180°

m∠1 + m∠2 = 180°

110° + m∠2 = 180°

m∠2 = 70°

8 0

2 years ago

I will give brainiest to whoever answers correctly !! There are two parts to this question A and B

laila [671]

Answer:

Step-by-step explanation:

5 1/2%=0.024

3500 x 0.025 = 87.5

She paid 87.5$ dollars for the use of money

due date is after 6 months so

3500 times 6 = 21000

21000 times 0.025 = 525

She paid 525$ dollars on the due date

4 0

3 years ago

If Fernando paid $450 for a netbook that was 75% of the original price, what was the original price?

Sav [38]

Answer:

$600

Step-by-step explanation:

75*100/450

7500/450

600

<em>Thank me later :)</em>

(<em>Or just give brainliest)</em>

4 0

3 years ago

Read 2 more answers