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3 years ago

7

Here is a easy one for 10 points

2 answers:

kramer3 years ago

8 0

Answer:

x=30

Step-by-step explanation:

The sum of interior angles in a triangle will always equal 180 degrees. Knowing this, we can set the following equation:

2x+x+90=180

3x+90=180

Subtract both sides by 90

3x+90-90=180-90

3x=90

Divide both sides by 3

3x/3=90/3

x=30

I hope this helps!

vampirchik [111]3 years ago

3 0

Answer:

3x=90

x=30

Step-by-step explanation:

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Geometric Sequence S = 1.0011892 + ... + 1.0012 + 1.001 + 1

leva [86]

Answer:

<em /> $S_{1893} =5632.98$ <em />

<em />

Step-by-step explanation:

The correct form of the question is:

$S = 1.001^{1892} + ... + 1.001^2 + 1.001 + 1$

Required

Solve for Sum of the sequence

The above sequence represents sum of Geometric Sequence and will be solved using:

$S_n = \frac{a(1 - r^n)}{1 - r}$

But first, we need to get the number of terms in the sequence using:

$T_n = ar^{n-1}$

Where

$a = First\ Term$

$a = 1.001^{1892}$

$r = common\ ratio$

$r = \frac{1}{1.001}$

$T_n = Last\ Term$

$T_n = 1$

So, we have:

$T_n = ar^{n-1}$

$1 = 1.001^{1892} * (\frac{1}{1.001})^{n-1}$

Apply law of indices:

$1 = 1.001^{1892} * (1.001^{-1})^{n-1}$

$1 = 1.001^{1892} * (1.001)^{-n+1}$

Apply law of indices:

$1 = 1.001^{1892-n+1}$

$1 = 1.001^{1892+1-n}$

$1 = 1.001^{1893-n}$

Represent 1 as $1.001^0$

$1.001^0 = 1.001^{1893-n}$

They have the same base:

So, we have

$0 = 1893-n$

Solve for n

$n = 1893$

So, there are 1893 terms in the sequence given.

Solving further:

$S_n = \frac{a(1 - r^n)}{1 - r}$

Where

$a = 1.001^{1892}$

$r = \frac{1}{1.001}$

$n = 1893$

So, we have:

$S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{1 -\frac{1}{1.001} }$

$S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{\frac{1.001 -1}{1.001} }$

$S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{\frac{0.001}{1.001} }$

$S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001^{1893}})}{\frac{0.001}{1.001} }$

Simplify the numerator

$S_{1893} =\frac{1.001^{1892} -\frac{1.001^{1892}}{1.001^{1893}}}{\frac{0.001}{1.001} }$

$S_{1893} =\frac{1.001^{1892} -1.001^{1892-1893}}{\frac{0.001}{1.001} }$

$S_{1893} =\frac{1.001^{1892} -1.001^{-1}}{\frac{0.001}{1.001} }$

$S_{1893} =(1.001^{1892} -1.001^{-1})/({\frac{0.001}{1.001} })$

$S_{1893} =(1.001^{1892} -1.001^{-1})*{\frac{1.001}{0.001}}$

$S_{1893} =\frac{(1.001^{1892} -1.001^{-1}) * 1.001}{0.001}$

Open Bracket

$S_{1893} =\frac{1.001^{1892}* 1.001 -1.001^{-1}* 1.001 }{0.001}$

$S_{1893} =\frac{1.001^{1892+1} -1.001^{-1+1}}{0.001}$

$S_{1893} =\frac{1.001^{1893} -1.001^{0}}{0.001}$

$S_{1893} =\frac{1.001^{1893} -1}{0.001}$

$S_{1893} =5632.97970294$

Hence, the sum of the sequence is:

<em /> $S_{1893} =5632.98$ <em> ----- approximated</em>

4 0

3 years ago

63 is 75% of what number?

Simora [160]

It is 84.
x=100%
63=75%

(63*100)/75=84

8 0

3 years ago

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Answer to 2ab(3a+4ab)

EleoNora [17]

Answer:

$8{a}^{2}{b}^{2} + 6{a}^{2}b$

Step-by-step explanation:

Use the Distributive Property to get the above answer.

* All you need to know is that according to the Product-to-Power Exponential Rule, whenever you multiply similar bases, you keep the base and add the exponents.

I am joyous to assist you anytime.

6 0

3 years ago

What is 3x+2x+6=-18

maksim [4K]

Answer:

x = -4.8

Step-by-step explanation:

combine like terms

3x + 2x + 6 = -18

5x + 6 = -18

isolate the terms with the x variable

5x + 6 - 6 = -18 - 6

5x = -24

isolate x

5x/5 = -24/5

x = -4.8

6 0

3 years ago

Read 2 more answers

Solve -r/4 < 8 <br>A.r<-32<br> B. r. >-32<br> C.r < -2<br><br>D.r>-2

Gnom [1K]

$\frac{-r}{4}$

$Ans.\ B$

4 0

4 years ago