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EleoNora [17]
3 years ago
14

How can I simplify these?

Mathematics
1 answer:
Schach [20]3 years ago
4 0

Answer:

\large\boxed{343=7\sqrt7}\\\boxed{10\sqrt{96}=40\sqrt6}

Step-by-step explanation:

343=7^3=7^2\cdot7\\\\\sqrt{343}=\sqrt{7^2\cdot7}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{7^2}\cdot\sqrt7\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=7\sqrt7\\=====================\\\\96=16\cdot6\\\\10\sqrt{96}=10\sqrt{16\cdot6}=10\sqrt{16}\cdot\sqrt6=(10)(4)\sqrt6=40\sqrt6

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Use Gauss's approach to find the following sums (do not use formulas) a 1+2+3+4 998 b. 1+3+5 7+ 1001 a The sum of the sequence i
valkas [14]

Answer:

(a) 498501

(b) 251001

Step-by-step explanation:

According Gauss's approach, the sum of a series is

sum=\frac{n(a_1+a_n)}{2}         .... (1)

where, n is number of terms.

(a)

The given series is

1+2+3+4+...+998

here,

a_1=1

a_n=998

n=998

Substitute a_1=1, a_n=998 and n=998 in equation (1).

sum=\frac{998(1+998)}{2}

sum=499(999)

sum=498501

Therefore the sum of series is 498501.

(b)

The given series is

1+3+5+7+...+ 1001

The given series is the sum of dd natural numbers.

In 1001 natural numbers 500 are even numbers and 501 are odd number because alternative numbers are even.

a_1=1

a_n=1001

n=501

Substitute a_1=1, a_n=1001 and n=501 in equation (1).

sum=\frac{501(1+1001)}{2}

sum=\frac{501(1002)}{2}

sum=501(501)

sum=251001

Therefore the sum of series is 251001.

8 0
3 years ago
7+8 = 87<br>9+3 + 6 = 639<br>4+ 5+ 4+ 5 = 5454<br>2 + 3 + 1 + 2 + 3 = ?<br>mout answer here​
Bess [88]

Answer:

The answer is 32132.

(Answer - no. from right to left)

6 0
3 years ago
Read 2 more answers
Students and adults purchased tickets for a recent school play. All tickets were sold at the ticket booth (discounts of any type
joja [24]

Answer:

Adult ticket = 80

Children ticket = 120

Step-by-step explanation:

Given that :

Cost of student ticket = $8

Cost of adult ticket = $10

Number of tickets sold = 200

Total amount collected = $1760

Let number of adult ticket sold = a ; children ticket = b

a + b = 200 _-_(1)

10a + 8b = 1760 ___(2)

a = 200 - b

10(200 - b) + 8b =. 1760

2000 - 10b + 8b = 1760

- 2b = 1760 - 2000

-2b = -240

b = 120

a = 200 - b

a = 200 - 120

a = 80

3 0
3 years ago
Write a compound inequality for the graph shown below. Use x for your variable
BigorU [14]
4 is less than or equal to x < 6
8 0
3 years ago
Abdul uses 15 1/2 cups of flour to make 3 loaves of bread. At that rate, how many cups of flour would Abdul need to make 4 loave
Tamiku [17]

Answer: 10 cups of flour

Step-by-step explanation:

15 1/2 cups of flour = 7 1/2 cups

7 1/2 ÷ 3 = 2 1/2

So, it takes 2 1/2 cups of flour to make one loaf of bread

If you want to make 4 loaves of bread, you multiply 2 1/2 × 4

2 1/2 × 4 = 10

It will take 10 cups of flour to make 4 loaves of bread.

5 0
3 years ago
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