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Blababa [14]
2 years ago
12

The second term of an arithmetic sequence is 13 and the fourth term is 7.

Mathematics
1 answer:
Tomtit [17]2 years ago
5 0

Answer:

<h3>                 \bold{a_{13}=52}</h3>

Step-by-step explanation:

d=a_4-a_3=a_3-a_2\\\\a_3-a_2=a_4-a_3\\\\2a_3=a_2+a_4\\\\2a_3=13+7\\\\2a_3=20\\\\a_3=10\\\\d=10-13=-3\\\\\\a_2=a_1+d\quad\implies\quad a_1=a_2-d=13-(-3)=16\\\\a_n=a_1+d(n-1)\\\\a_{13}=16+(-3)(13-1)=16+36=52

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Which number line shows the solution to the inequality -2(3x-1)&lt;8
Zigmanuir [339]

Answer:

x  > -1

Step-by-step explanation:

Given

-2(3x - 1) < 8

Required

Show on a number line

-2(3x - 1) < 8

Divide through by -2

\frac{-2(3x - 1)}{-2} < \frac{8}{-2}

3x - 1 > -4

Add 1 to both sides

3x -1 + 1 > -4 + 1

3x > -3

Divide through by 3

x  > -1

<em>See Attachment for number line</em>

6 0
3 years ago
20liters of mixture contain milk nad water in the ratio 5:3 if 4liters of the mixture are replaced by 4 liters of milk find the
Finger [1]

Answer:

the new ratio milk/water is  14:6  or 7:3

Step-by-step explanation:

milk/water=5/3

milk +water=5+3=8

ratio of milk=5/8  and ratio of water=3/8

if 4 liter removed from mixture then: 20=4= 16 liter

the amount of milk in 16 liter=16*5/8=10 liter of milk

the amount of water in 16 liter=16*3/8= 6 liter

add 4 liter of milk to the mixture: 10+4=14 liter of milk and 6 liter of water

the new ratio milk/water is  14:6  or 7:3

5 0
3 years ago
Simply 15 to the 18 power divide by 15 to the 3 power
andrew11 [14]
The property of exponents says that when you divide two exponents with the same base, you can keep the base and subtract the exponents. So you can do 18-3, which is 15, so it would be 15 to the 15th power
6 0
3 years ago
If y varies inversely as x, and y = 4 as x = 8, find y for the x-value of 2.
anyanavicka [17]
Because y varies inversely as x, instead of directly, you will need to multiply x by a fractional number (or divide x) in order to find y.
When x=8, y=4. Therefore, to find y, you need the "equation" y=(1/2)(x) or y=x/2.
So, when x=2, y=(1/2)(2) or y=2/2.
And so, y=1
Hope this helps!
5 0
3 years ago
Factor 1/3 out of 1/3p-2/3 please answer this! Easy 20 points!
Tju [1.3M]

Answer:

\frac{1}{3} (\frac{1}{p} - 2)

Step-by-step explanation:

Given the equation = \frac{1}{3p} - \frac{2}{3}

Required: To factor out 1/3;

\frac{1}{3p} - \frac{2}{3}

1/3 is common to both sides;

So, 1/3 is a common factor

\frac{1}{3} (\frac{1}{p} - 2)

To solve for the value of p;

\frac{1}{3} (\frac{1}{p} - 2) = 0

\frac{1}{p} - 2 = 0

\frac{1}{p} = 2

1 = 2p

p = \frac{1}{2}

5 0
3 years ago
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