Find the range of the function y=10x+7 when the domain is {-1, 0, 1}.

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

Drag the numbers to order them from least to greatest.<br><br> free 25 points

Whitepunk [10]

Answer:

All of them

Step-by-step explanation:

if you divide 24 by 8 the you would get 3 and if you divide 24 by 4 them you will get 6 and if you divide 24 by 3 you will get 8

8 0

3 years ago

Read 2 more answers

What is an example of what property ?

vodomira [7]

Answer:

Distributive Property

Step-by-step explanation:

7 equals (3+4).

Therefore, 4*7 equals 4*(3+4).

By distributive property, this will equal (4*3) + (4*4)

8 0

3 years ago

What are the factors of the equation 24x^2=9-30x?

Dennis_Churaev [7]

Answer:

3(4x - 1)(2x + 3)

Step-by-step explanation:

Rearrange the equation into standard form

Subtract 9 - 30x from both sides

24x² + 30x - 9 = 0 ← in standard form

Take out 3 as a common factor

3(8x² + 10x - 3) = 0 ← factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term

product = 8 × - 3 = - 24, sum = 10

The factors are - 2 and + 12

Use these factors to replace the x- term, that is

8x² - 2x + 12x - 3 ( factor the first/second and third/fourth terms )

2x(4x - 1) + 3(4x - 1) ← take out the common factor (4x - 1)

(4x - 1)(2x + 3)

24x² + 30x - 9 = 3(4x - 1)(2x + 3) ← in factored form

7 0

3 years ago

Question attached plz answer

Bezzdna [24]

Answer:

x = - 2.5

Step-by-step explanation:

Given that the sketch represents

y = x² + bx + c

The graph crosses the y- axis at (0 , - 14), thus c = - 14

y = x² + bx - 14

Given the graph crosses the x- axis at (2, 0), then

0 = 2² + 2b - 14

0 = 4 + 2b - 14 = 2b - 10 ( add 10 to both sides )

10 = 2b ( divide both sides by 2 )

b = 5

y = x² + 5x - 14 ← represents the graph

let y = 0 , then

x² + 5x - 14 = 0 ← in standard form

(x + 7)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x - 2 = 0 ⇒ x = 2

The x- intercepts are x = - 7 and x = 2

The vertex lies on the axis of symmetry which is midway between the x- intercepts, thus

the x- coordinate of the turning point is $\frac{-7+2}{2}$ = $\frac{-5}{2}$ = - 2.5

8 0

3 years ago