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2 years ago

The common difference of the arithmetic sequence

Mathematics

2 answers:

oksian1 [2.3K]2 years ago

5 0

Answer:

its 1/3

Step-by-step explanation:

please mark it as brainliest!!<3

Ilya [14]2 years ago

4 0

Answer:

We conclude that the common difference of the Arithmetic sequence is: 1/3

Step-by-step explanation:

Given the Arithmetic sequence

1/2, 5/6, 7/6, 3/2, 11/6

We know that an Arithmetic sequence has a constant common difference.

Let us compute the common difference 'd' of all the adjacent terms

$\frac{5}{6}-\frac{1}{2}=\frac{1}{3},\:\quad \frac{7}{6}-\frac{5}{6}=\frac{1}{3},\:\quad \frac{3}{2}-\frac{7}{6}=\frac{1}{3},\:\quad \frac{11}{6}-\frac{3}{2}=\frac{1}{3}$

The difference between all the adjacent terms is the same and equal

Therefore,

$d=\frac{1}{3}$

Hence, we conclude that the common difference of the Arithmetic sequence is: 1/3

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Jean runs 8 mi and then rides 11 mi on her bicycle on a biathlon. She rides 9 mph faster than she runs. If the total time for he

Ipatiy [6.2K]

Let Jean's speed while running = x mph

Then Jean's speed while riding will be = x+9 mph

Distance covered by running = 8 miles

Distance covered by riding = 11 miles

Total time taken to complete the race = 1.5 hours

As, $time=\frac{distance}{speed}$

So, time for running= $\frac{8}{x}$

And time for riding= $\frac{11}{x+9}$

Equation becomes:

$\frac{8}{x}+\frac{11}{x+9}=1.5$

Now, multiply every term by 2x(x+9) to clear denominators:

$16(x+9)+22x=3x(x+9)$

Simplifying it we get

$3x^{2}-11x-144=0$

Solve the quadratic equation using formula

$x= \frac{-b+\sqrt{b^{2}-4ac }}{2a}$

putting a=3 , b= -11, c= -144

we get (x - 9)(3x + 16) = 0

where x=9 and x= $\frac{-16}{3}$

Neglect the negative answer as speed cannot be negative, so x = 9 mph

Hence, Jean's running speed is 9 mph and riding speed is x+9 = 9+9 = 18 mph

4 0

3 years ago

-2/3- (-3/4) Simplify if needed Brainliest Also, 5/6+5/12

bazaltina [42]

Answer:

$-\frac{2}{3} - (-\frac{3}{4}) = \frac{1}{12}$

$\frac{5}{6} + \frac{5}{12} = \frac{5}{3}$

Step-by-step explanation:

Given

$-\frac{2}{3} - (-\frac{3}{4})$

Required

Solve:

$-\frac{2}{3} - (-\frac{3}{4})$

Open bracket

$-\frac{2}{3} - (-\frac{3}{4}) = -\frac{2}{3} +\frac{3}{4}$

Take LCM

$-\frac{2}{3} - (-\frac{3}{4}) = \frac{-8+9}{12}$

$-\frac{2}{3} - (-\frac{3}{4}) = \frac{1}{12}$

$\frac{5}{6} + \frac{5}{12}$

Take LCM

$\frac{5}{6} + \frac{5}{12} = \frac{10+5}{12}$

$\frac{5}{6} + \frac{5}{12} = \frac{15}{12}$

Divide by 3/3

$\frac{5}{6} + \frac{5}{12} = \frac{5}{3}$

4 0

2 years ago

I dont understand it :/

photoshop1234 [79]

Step-by-step explanation:

It's telling you to plug in the numbers inside the parenthesis as x

Example: F(-1)= 2(-1)^3 -3(-1)^2 +7

4 0

3 years ago

6(-2-3x)+8=68 Find x

yawa3891 [41]

$6(-2-3x)+8=68 \\ 6(-2-3x)=60 \\ -12-18x=60 \\ -18x=72 \\ 18x=-72 \\ x= \frac{-72}{18} \\ \\ \boxed{x=-4}$

3 0

2 years ago

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What fraction is 1 yard 2 feet and 6 inches

MA_775_DIABLO [31]

Answer:

Make sure you convert these numbers into one unit. Convert everything to yard. Just convert the feet and inches in yard since it's the biggest unit, and then add them together. You should get a fraction not a whole number.

3 0

3 years ago

Read 2 more answers