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2 years ago

13

In an arithmetic series a1= -14 and a5=30 find the sum of the first 5 terms

1 answer:

Oxana [17]2 years ago

5 0

The sum of the 5 terms in the arithmetic series is 40.

Step-by-step explanation:

Step 1; First we need to determine the three values between a1= -14 and a5=30. The difference between the first and fifth value = 30 - (-14) = 30 + 14 = 44.

Since there are 4 values after a1 we divide the difference by the number of terms, the difference between each term = 44 / 4 = 11. So the difference between each term is 11.

Step 2; To find out the terms we just add the difference to the previous number.

a1 = -14.

a2 = -14 + 11 = -3.

a3 = -3 + 11 = 8.

a4 = 8 + 11 = 19.

a5 = 19 + 11 = 30.

So a1 + a2 + a3 + a4 + a5 = -14 -3 + 8 + 19 + 30 = 40.

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Which pair of adjacent angles is complementary?

Artist 52 [7]

<h3>part d is pair of adjacent angle is supplementary </h3>

because the angle are complementary and common vertex so it is adjacent Two complementary angles with a common vertex and arm are called adjacent complementary angles

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2 years ago

Find the circumference of the circle with 1/4 Pi square centimetre square 2<br>

otez555 [7]

Answer:

The circumference of the circle is 6 cm (approximately).

Step-by-step explanation:

Given:

Area of the circle = 1/4π²

Now, to get the circumference of the circle we need the radius.

So, finding the radius by putting the formula of area:

Area = $\pi r^{2}$

$\frac{1}{4} \pi ^{2}$ = $\pi r^{2}$

dividing π by both sides:

$\frac{1}{4}\pi$ $=r^{2}$

using square root on both the sides:

$\frac{1}{2}\sqrt{\pi } = r$

So, the radius is $\frac{1}{2}\sqrt{\pi }$

Now, putting the formula of circumference:

$circumference=2\pi r$

= $2\pi\frac{1}{2} \sqrt{\pi}$

= $\pi \sqrt{\pi}$

putting the value of π =3.14

= $3.14\times\sqrt{3.14}$

= $3.14\times1.77$

= $5.56$

Circumference = 5.56 cm

Therefore, the circumference of the circle is 6 cm (approximately).

4 0

2 years ago

Tom and Becky can paint Jim's fence together in 12 hours. If all people paint at the same rate, how many hours would it take to

Delvig [45]

Answer: 8 hours

Step-by-step explanation:

Let x be the time taken by each person to paint the fence.

Given: Tom and Becky can paint Jim's fence together in 12 hours.

Since all people paint at the same rate, then we have the following equation ;-

$\dfrac{1}{x}+\dfrac{1}{x}=\dfrac{1}{12}\\\\\Rightarrow\ \dfrac{2}{x}=\dfrac{1}{12}\\\\\Rightarrow\ x=24$

Thus, the time taken by each person to paint the fence alone = 24 hours

Now, the time taken by all three paint together:-

$\dfrac{1}{t}=\dfrac{1}{24}+\dfrac{1}{24}+\dfrac{1}{24}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{3}{24}\\\\\Rightarrow\ t=\dfrac{24}{3}=8\text{ hours}$

Hence, it would take 8 hours if all three paint together.

3 0

2 years ago

Which of the following is a correct interpretation of the expression -7- (-11)?

Brilliant_brown [7]

Answer:

B. Start at -7 on the number line and move 11 to the right.

Step-by-step explanation:

<u>Given:</u>

- 7 - (-11) expression

We can add or remove only positive numbers on the number line to get it correct, so we need to open the parenthesis. When evaluated we get:

-7- (-11) = - 7 + 11 = 4

<u>Correct interpretation of of this expression is:</u>

Start at -7 and add 11, thus move 11 points to the right, to get 4 as final point.

<u>Correct choice is:</u>

B. Start at -7 on the number line and move 11 to the right.

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2 years ago

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snow_tiger [21]

Answer:

Its C it must be true

Step-by-step explanation:

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1 year ago