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3 years ago

Explain please. . . . . . . . . . . . .

Mathematics

2 answers:

masha68 [24]3 years ago

6 0

The answer would be <

olga nikolaevna [1]3 years ago

3 0

Since x=2, 11x is 11×2

11×2=22
22-2=20

x + 7 is 2+7

2+7=9

your answer is 20>9

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

ANYONE PLEASE HELP!!

lapo4ka [179]

Answer:

Step-by-step explanation:

Corresponding angles are angles that you can follow down the transversal and they will land in the same spot on the other parallel line. Look at angle 8. It is the bottom left angle in the group of 4 angles around it. If you slide it to the left it would land right on top of angle 4 which is also in the bottom left of its group of 4 angles.

You can do the same thing taking angle 8 down to angle 12.

4 0

2 years ago

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Rob buys a rocking chair priced at 27$. if the sales tax is 10%, what will be the total cost including tax?

seraphim [82]

Answer:

$29.7

Step-by-step explanation:

10 percent of 27 is 2.7 then you add 27 and 2.7 and you get 29.7

8 0

2 years ago

"at the end of the year Juan has $52.71 more than 4 times his balance at the beginning of the year if his ending balance was $17

Salsk061 [2.6K]

At the end of the year, Juan has 52.71 more than 4 times his balance at the beginning. Okay, let's set this up.

4x + 52.71
(4 times) (52.71 more)
His ending was 172.90, so
4x + 52.71=172.90
4x= 120.19
x= 30.05
He had $30.05 at the beginning of the year.

8 0

4 years ago

Sassy jeans are $90 a pair. If they are 40% off today, how much will they cost?

Slav-nsk [51]

They will cost $54
i know this because if youre getting 40% off, you will have to pay 60% of the total cost
so, 90 x .60 = 54
let me know if you have any further questions
:)

7 0

3 years ago

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