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4 years ago

Find the equivalent expression using the same bases. (21 x15)9

Mathematics

1 answer:

aleksklad [387]4 years ago

7 0

Answer:

2835

Step-by-step explanation:

(21×15)9=

(315)9=

2835

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In a circle of radius 10 cm, a sector has an area of 40(pi) sq. cm. What is the degree measure of the arc of the sector?

emmasim [6.3K]

The main formula is

sector area = n / 360° x Pi r²

4 = n / 360 x r² = <span>n° / 36,

144° = n</span>

3 0

3 years ago

Read 2 more answers

Tentukan hasil dari (tanpa menghitung satu persatu)

liubo4ka [24]

a . 1 + 3 + 5 + 7 + 9 + ... + 99 = 2500

b. 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... - 100 = -50

c. -100 - 99 - 98 - .... -2 - 1 - 0 + 1 + 2 + ... + 48 + 49 + 50 = -3775

<h3>Further explanation</h3>

Let us learn about Arithmetic Progression.

Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.

$\large {\boxed {T_n = a + (n-1)d } }$

$\large {\boxed {S_n = \frac{1}{2}n ( 2a + (n-1)d ) } }$

<em>Tn = n-th term of the sequence</em>

<em>Sn = sum of the first n numbers of the sequence</em>

<em>a = the initial term of the sequence</em>

<em>d = common difference between adjacent numbers</em>

Let us now tackle the problem!

<h2>Question a :</h2>

1 + 3 + 5 + 7 + 9 + ... + 99

<em>initial term = a = 1</em>

<em>common difference = d = ( 3 - 1 ) = 2</em>

Firstly , we will find how many numbers ( n ) in this series.

$T_n = a + (n-1)d$

$99 = 1 + (n-1)2$

$99-1 = (n-1)2$

$98 = (n-1)2$

$\frac{98}{2} = (n-1)$

$49 = (n-1)$

$n = 50$

At last , we could find the sum of the numbers in the series using the above formula.

$S_n = \frac{1}{2}n ( 2a + (n-1)d )$

$S_{50} = \frac{1}{2}(50) ( 2 \times 1 + (50-1) \times 2 )$

$S_{50} = 25 ( 2 + 49 \times 2 )$

$S_{50} = 25 ( 2 + 98 )$

$S_{50} = 25 ( 100 )$

$\large { \boxed { S_{50} = 2500 } }$

<h2>Question b :</h2>

In this question let us find the series of even numbers first , such as :

2 + 4 + 6 + 8 + ... + 100

<em>initial term = a = 2</em>

<em>common difference = d = ( 4 - 2 ) = 2</em>

<em />

Firstly , we will find how many numbers ( n ) in this series.

$T_n = a + (n-1)d$

$100 = 2 + (n-1)2$

$100-2 = (n-1)2$

$98 = (n-1)2$

$\frac{98}{2} = (n-1)$

$49 = (n-1)$

$n = 50$

We could find the sum of the numbers in the series using the above formula.

$S_n = \frac{1}{2}n ( 2a + (n-1)d )$

$S_{50} = \frac{1}{2}(50) ( 2 \times 2 + (50-1) \times 2 )$

$S_{50} = 25 ( 4 + 49 \times 2 )$

$S_{50} = 25 ( 4 + 98 )$

$S_{50} = 25 ( 102 )$

$\large { \boxed { S_{50} = 2550 } }$

At last , we could find the result of the series.

1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... - 100

= ( 1 + 3 + 5 + 7 + ... + 99 ) - ( 2 + 4 + 6 + 8 + ... + 100 )

= 2500 - 2550

= -50

1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... - 100 = -50

<h2>Question c :</h2>

-100 - 99 - 98 - .... -2 - 1 - 0 + 1 + 2 + ... + 48 + 49 + 50

<em>initial term = a = -100</em>

<em>common difference = d = ( -99 - (-100) ) = 1</em>

<em />

Firstly , we will find how many numbers ( n ) in this series.

$T_n = a + (n-1)d$

$50 = -100 + (n-1)1$

$50+100 = (n-1)$

$150 = (n-1)$

$n = 151$

We could find the sum of the numbers in the series using the above formula.

$S_n = \frac{1}{2}n ( 2a + (n-1)d )$

$S_{151} = \frac{1}{2}(151) ( 2 \times (-100) + (151-1) \times 1 )$

$S_{151} = 75.5 ( -200 + 150 )$

$S_{151} = 75.5 ( -50 )$

$\large { \boxed { S_{151} = -3775 } }$

<h3>Learn more</h3>

Geometric Series : brainly.com/question/4520950
Arithmetic Progression : brainly.com/question/2966265
Geometric Sequence : brainly.com/question/2166405

<h3>Answer details</h3>

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term

3 0

3 years ago

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Karen wakes up at 6:00 a.m. It takes her 1 1/4 hours to shower,get dressed,and comb her hair. It takes her 1/2 an hour to eat br

dangina [55]

She will be ready at 7:45 am.
1 1/4 hour = 1 hour and 15 minutes ( 1 hour divided by four is 15 minutes per quarter)
adding that to the initial time of 6:00am you get the time to be 7:15am adding the 1/2 an hour which is 30 minutes. Your final answer is, she will be ready at 7:45am.

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4 years ago

Shelia rode her bike daily to get ready for a bike race.The following list shows the number of miles she rode each day of the we

AnnyKZ [126]

To find average add all the numbers then divide your answer by the number of numbers

30+27+22+32+35+18+39=203

203÷7=29miles

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3 years ago

Which ordered pair is NOT a solution to the inequality in the graph? (5,1) (4,6) (0,0) (-2,-8)

n200080 [17]

<h3>Answer: (5,1) </h3>

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

Explanation:

The red shaded region is the solution set. In other words, if the point is in the red region, then it is a solution. A point like (0,0) is in the red area, so we cross that off the list. The same applies for (4,6) and (-2,-8) as well.

In contrast, a point like (5,1) is <u>not</u> in the red shaded area, so this point is <u>not a solution</u>. Hence it's the final answer.

Note: the solid boundary line means points on the boundary are considered solutions. A dashed boundary line would be used to exclude boundary points from the solution set. Solid boundary lines always go with "or equal to".

Refer to the drawing below if you need a visual of what's going on. I've plotted the four points on the graph given.

--------------------------

Here's an algebraic approach if you don't have a graph and only have the inequality. Ignore this section if you prefer the first section above.

If we plugged (x,y) = (0,0) into the inequality, then we get...

$y \ge 2x-4\\\\0 \ge 2(0)-4\\\\0 \ge 0-4\\\\0 \ge -4\\\\$

That's a true statement because 0 is to the right of -4 on the number line, making 0 larger than -4. Since the last inequality is true, this makes the first inequality true. Furthermore, it algebraically confirms why (0,0) is a solution. You should find that (4,6) and (-2,-8) will lead to true statements as well, so they are solutions.

In contrast, (x,y) = (5,1) is not a solution because...

$y \ge 2x-4\\\\1 \ge 2(5)-4\\\\1 \ge 10-4\\\\1 \ge 6\\\\$

which is false. The value 1 is not larger than 6, nor is it equal to 6.

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3 years ago