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4 years ago

Which equation is satisfied by all of the plotted points?

Mathematics

1 answer:

Brums [2.3K]4 years ago

3 0

The equation that is satisfied by all of the plotted points would be F. 3x because the y-intercept is at 0 so there wouldn't be one and the graph has a ratio of 3/1 so for every 3 numbers the line moves up it moves 1 space to the right, also indicating that it is positive.

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Find the sum of the positive integers less than 200 which are not multiples of 4 and 7

taurus [48]

Answer:

$12942$ is the sum of positive integers between $1$ (inclusive) and $199$ (inclusive) that are not multiples of $4$ and not multiples $7$ .

Step-by-step explanation:

For an arithmetic series with:

$a_1$ as the first term,
$a_n$ as the last term, and
$d$ as the common difference,

there would be $\displaystyle \left(\frac{a_n - a_1}{d} + 1\right)$ terms, where as the sum would be $\displaystyle \frac{1}{2}\, \displaystyle \underbrace{\left(\frac{a_n - a_1}{d} + 1\right)}_\text{number of terms}\, (a_1 + a_n)$ .

Positive integers between $1$ (inclusive) and $199$ (inclusive) include:

$1,\, 2,\, \dots,\, 199$ .

The common difference of this arithmetic series is $1$ . There would be $(199 - 1) + 1 = 199$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times ((199 - 1) + 1) \times (1 + 199) = 19900 \end{aligned}$ .

Similarly, positive integers between $1$ (inclusive) and $199$ (inclusive) that are multiples of $4$ include:

$4,\, 8,\, \dots,\, 196$ .

The common difference of this arithmetic series is $4$ . There would be $(196 - 4) / 4 + 1 = 49$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times 49 \times (4 + 196) = 4900 \end{aligned}$

Positive integers between $1$ (inclusive) and $199$ (inclusive) that are multiples of $7$ include:

$7,\, 14,\, \dots,\, 196$ .

The common difference of this arithmetic series is $7$ . There would be $(196 - 7) / 7 + 1 = 28$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times 28 \times (7 + 196) = 2842 \end{aligned}$

Positive integers between $1$ (inclusive) and $199$ (inclusive) that are multiples of $28$ (integers that are both multiples of $4$ and multiples of $7$ ) include:

$28,\, 56,\, \dots,\, 196$ .

The common difference of this arithmetic series is $28$ . There would be $(196 - 28) / 28 + 1 = 7$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times 7 \times (28 + 196) = 784 \end{aligned}$ .

The requested sum will be equal to:

the sum of all integers from $1$ to $199$ ,
minus the sum of all integer multiples of $4$ between $1\!$ and $199\!$ , and the sum integer multiples of $7$ between $1$ and $199$ ,
plus the sum of all integer multiples of $28$ between $1$ and $199$ - these numbers were subtracted twice in the previous step and should be added back to the sum once.

That is:

$19900 - 4900 - 2842 + 784 = 12942$ .

8 0

3 years ago

Cylinder has a height of 15 centimeters and a radius of 10 centimeters. What is its volume? Use ≈ 3.14 and round your answer t

tatuchka [14]

Answer: 4712.39 centimeters

Step-by-step explanation: Using the volume of a cylinder calculator, I got the answer of 4712.3889803847 centimeters, but rounded it to the nearest hundreth. Hope this helps!

3 0

3 years ago

Find the slope please help!

Sidana [21]

Answer:

4.5 is the answer 9/2=4.5

Step-by-step explanation:

4 0

3 years ago

Tema: Operadores Matemáticos<br><br><br>a*b=4a+5b

zhenek [66]

Yes it does bdffgjkhhh BGC. Bc. G. G. G. Y. Y. Y

4 0

3 years ago

On the function machine shown below, the function rule is given as a variable expression. When the output is 99, what is the inp

beks73 [17]

Answer: option d.

Step-by-step explanation:

We have the function:

y = f(x) = x^2 - 1

The output is 99 when y = 99, and the input is x.

Then we need to solve:

y = 99 = x^2 - 1

for x.

99 = x^2 - 1

99 + 1 =x^2

100 = x^2

√100 = x

10 = x

The correct option is d, input equals 10.

7 0

3 years ago