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2 years ago

6

Solve the question and check the solution. Express numbers as integers or simplified fractions. 5(m+5)=7m+9

1 answer:

Yanka [14]2 years ago

7 0

Answer:

m = 8

Step-by-step explanation:

5(m+5)=7m+9 (distribute & evaluate parenthesis)

5(m)+5(5)=7m+9

5m + 25 = 7m + 9 (move all m-terms to one side and constants to the other)

5m - 7m = 9 - 25 (evaluate both sides)

-2m = -16 (divide both sides by -2)

m = (-16) / ( -2) = 8

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A sequence is constructed according to the following rule: its first term is 7, and each next term is one more than the sum of t

Iteru [2.4K]

Answer:

5

Step-by-step explanation:

According to the described rule, we have

$a_1=7\\ \\a_1^2=7^2=49\Rightarrow a_2=4+9+1=14\\ \\a_2^2=14^2=196\Rightarrow a_3=1+9+6+1=17\\ \\a_3^2=17^2=289\Rightarrow a_4=2+8+9+1=20\\ \\a_4^2=20^2=400\Rightarrow a_5=4+0+0+1=5\\ \\a_5^2=5^2=25\Rightarrow a_6=2+5+1=8\\ \\a_6^2=8^2=64\Rightarrow a_7=6+4+1=11\\ \\a_7^2=11^2=121\Rightarrow a_8=1+2+1+1=5\\ \\\text{and so on...}$

We can see the pattern

$a_5=a_8=a_{11}=a_{14}=...=5\\ \\a_6=a_9=a_{12}=a_{15}=...=8\\ \\a_7=a_{10}=a_{13}=a_{16}=...=11$

In other words, for all $k\ge 2$

$a_{3k-1}=5\\ \\a_{3k}=8\\ \\a_{3k+1}=11$

Now,

$a_{2018}=a_{3\cdot 673-1}=5$

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2 years ago

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Step-by-step explanation:

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2 years ago

The perimeter of the rectangle below is 65 inches.

Tems11 [23]

Answer:

A :-) Given -

perimeter = 65 inches

Side ‘a’ = 2x

Side ‘b’ = 3 1 by 4x + 1

Solution -

Perimeter = 65

= a + b = 65

= 2x + 3 1 by 4x + 1 = 65

( 3 1 by 4 = 4 x 3 + 1 = 12 + 1 by 4

= 13 by 4 )

= 2x + 13 by 4x + 1 = 65

= 2x + 13 by 4x = 65 - 1

= 2x + 13 by 4x = 64

= 15 by 4 x = 64

= x = 64 x 4 by 15

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= x = 17.06

.:. The value of x = 17.06.

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2 years ago