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Levart [38]
3 years ago
7

Here is a easy one for 10 points

Mathematics
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:

You might be interested in
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
Read 2 more answers
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 &lt; 8         <br>A.r&lt;-32<br> B. r. &gt;-32<br> C.r &lt; -2<br><br>D.r&gt;-2
Gnom [1K]
\frac{-r}{4}

Ans.\ B


4 0
4 years ago
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