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2 years ago

Find the sum of the arithmetic series for which a_1 = 7, n = 31, and a_n = 127.

Mathematics

1 answer:

uranmaximum [27]2 years ago

8 0

Answer: 2077

There are 31 terms.

S₃₁ = 31(a₁+a₃₁)/2 = 31(7+127)/2 = 2077

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Pamela and her friend Nicole are each baking apple pies and tarts for a bake sale, using the same recipes. Pamela baked 5 apple

valentina_108 [34]

Answer:

Each apple pie requires 8 apples, and each apple tart requires 4 apples.

Step-by-step explanation:

We see that both Pamela and Nicole bake the same amount of apple pies, but different amounts of apple tarts. Because of this, we can subtract the two to try to figure out the amount of apples for each apple tart. We subtract 68 from 76, giving us 8. Nicole baked 9 apple tarts, while Pamela baked 7, and 9-7=2. So we can bake two apple tarts with 8 apples, so one apple tart requires 4 apples (we divide by 2). Now that we know the amount of apples per each apple tart, we multiply 7 apple tarts that Pamela made by 4 apples, giving us 28. We subtract that from the total amount of apples Pamela used, which was 68, giving us 40. From this we can deduct that 5 apple pies need 40 apples, and we divide by 5, giving us 1 apple pie requires 8 apples.

3 0

2 years ago

The area of a rectangular garden is 5828 m

evablogger [386]

Answer:

The length of the garden is 94 m.

Step-by-step explanation:

you do 5828 m. divided by 62m. and that is how you get your answer of 94 m.

6 0

2 years ago

Read 2 more answers

What is the median for 76,84,93,67,82,and 76

Lapatulllka [165]

First arrange the numbers from least to greatest:

67, 76, 76, 82, 84, 93

The median is the middle number. But since we have two numbers that are in the middle we have to find the average of them.

76 + 82 = 158
158/2 = 79

So your answer is 79

3 0

3 years ago

Read 2 more answers

For the polynomial function ƒ(x) = −x6 + 3x4 + 4x2, find the zeros. Then determine the multiplicity at each zero and state wheth

murzikaleks [220]

There is a multiple zero at 0 (which means that it touches there), and there are single zeros at -2 and 2 (which means that they cross). There is also 2 imaginary zeros at i and -i.

You can find this by factoring. Start by pulling out the greatest common factor, which in this case is -x^2.

-x^6 + 3x^4 + 4x^2

-x^2(x^4 - 3x^2 - 4)

Now we can factor the inside of the parenthesis. You do this by finding factors of the last number that add up to the middle number.

-x^2(x^4 - 3x^2 - 4)

-x^2(x^2 - 4)(x^2 + 1)

Now we can use the factors of two perfect squares rule to factor the middle parenthesis.

-x^2(x^2 - 4)(x^2 + 1)

-x^2(x - 2)(x + 2)(x^2 + 1)

We would also want to split the term in the front.

-x^2(x - 2)(x + 2)(x^2 + 1)

(x)(-x)(x - 2)(x + 2)(x^2 + 1)

Now we would set each portion equal to 0 and solve.

First root

x = 0 ---> no work needed

Second root

-x = 0 ---> divide by -1

x = 0

Third root

x - 2 = 0

x = 2

Forth root

x + 2 = 0

x = -2

Fifth and Sixth roots

x^2 + 1 = 0

x^2 = -1

x = +/- $\sqrt{-1}$

x = +/- i

7 0

3 years ago

Two bowls and one cup weigh 800 grams. One bowl and two cups weigh 700 grams. Find the weight of the bowl and the cup

antoniya [11.8K]

Answer:

\large \boxed{\textbf{Bowl = 300 g; cup = 200 g}}

Step-by-step explanation:

Let b = the mass of a bowl

and c = the mass of a cup

We have two conditions:

$\begin{array}{lrcl}(1) &2b + c & = & 800\\(2) & b + 2c & = & 700\\\end{array}$

Calculations:

$\begin{array}{lrcll}(3) & 4b + 2c &= & 1600&\text{ Multiplied (1) by 2}\\& 3b & = & 900&\text{Subtracted (2) from (3)}\\(4) & b & = & \mathbf{300}&\text{Divided each side by 3}\\ & 600 + c & = & 800&\text{Substituted (4) into (2}\\ & c & = & \mathbf{200}\\\end{array}\\\text{The mass of a bowl is $\large \boxed{\textbf{300 g}}$ and that of a cup is $\large \boxed{\textbf{200 g}}$}$

Check:

$\begin{array}{rlcrl}2(300) + 200& =800 & & 300 + 2(200) & = 700\\600 + 200 & = 800& & 300 + 400 & = 700\\800 & = 800& & 700 & = 700\\\end{array}$

OK.

6 0

2 years ago