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2 years ago

16+6-6x-4=-7x+3+7how to solve for x

Mathematics

2 answers:

Alla [95]2 years ago

5 0

Answer:

x = -8

Step-by-step explanation:

16+6-6x-4=-7x+3+7

Combine like terms

18 -6x = -7x+10

Add 7x to each side

18-6x+7x = -7x+7x+10

18+x = 10

Subtract 18 from each side

18+x-18 = 10-18

x = -8

Ahat [919]2 years ago

5 0

Answer:

x = -8

Step-by-step explanation:

16+6-6x-4 = -7x+3+7

18 - 6x = -7x + 10

-6x + 7x = 10 - 18

x = -8

Check:

18 - 6*-8 = -7*-8 + 10

18 + 48 = 56 + 10 = 66

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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

This probability distribution shows the typical distribution of the number of shoes in a teenager's closet. Using the distributi

mote1985 [20]

Answer:

70%

Step-by-step explanation:

Total number of teenagers surveyed

12+20+38+20+10 = 100

Find the number of teenagers with 3 or fewer pairs of shoes

12+20+38 =70

P(3 or fewer) = teenagers with 3 or fewer/ total

= 70/100

= 70%

5 0

2 years ago

Read 2 more answers

Please help on this one (fast please)

Luba_88 [7]

The correct answer is d

7 0

3 years ago

A continuous random variable may assume :

vova2212 [387]

Answer:

Option A) any numerical value in an interval or collection of intervals

Step-by-step explanation:

Continuous Random Variable:

A continuous random variable can take any value within an interval.
Thus, it can take infinite values since there are infinite numbers in an interval.
A continuous variable is a variable whose value is obtained by measuring.
Examples: height of students in class , weight of students in class, time it takes to get to school, distance traveled between classes.
Thus, the correct meaning of continuous random variable is explained by Option A)

Option A) any numerical value in an interval or collection of intervals

6 0

2 years ago

Factor completely x2 + 25

Ganezh [65]

Answer:

(x - 5i)(x + 5i)

Step-by-step explanation:

Write this as x^2 + 25. Solving for x^2, we get x^2 = -25.

Recall that the square root of a negative number is an imaginary one. √(-25) equals ±5i (there are two roots, one positive and one negative).

Then x = ±5i.

In factored form, the given expression is (x - 5i)(x + 5i).

6 0

2 years ago

16+6-6x-4=-7x+3+7how to solve for x​

16+6-6x-4=-7x+3+7how to solve for x