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3 years ago

HELP I have this on my page for 100 points but no one is looking at it help pls

Mathematics

1 answer:

Vikentia [17]3 years ago

6 0

3 + 4x > -5 = x > -2

First, subtract 3 from both sides of the equation.

3 - 3 + 4x > -5 - 3

= 4x > -8

Now, divide 4 from both sides of the equation.

= x > -2

5(2 - b) > -3(b - 3) = b < 1/2

First multiply the coefficient by the numbers/variables in the parentheses.

10 - 5b > -3b + 9

Now, add 3b to both sides and subtract 10 from both sides of the equation.

-2b > -1

Now divide -1 by -2, but in an inequality, when you divide by a negative number, the sign gets flipped. So, > will turn into <.

b < 1/2

-1.5a + 8 ≥ 17 = a ≤ 6

First, subtract 8 from both sides of the equation.

-1.5a ≥ 9

Now divide 9 by -1.5, but, again, because the number is negative, the sign gets flipped.

a ≤ 6

5w/3 ≥ 6w/4 + 11/2 = w ≥ 22

First, you need to find a common denominator or LCD. In this case, the LCD is 12. So multiply all the fractions by 12 and eliminate factors of 12.

12(5w/3) ≥ 12(6w/4) + 12(11/2)

4(5w) ≥ 3(6w) + 6(11)

20w ≥ 18w + 66

2w ≥ 66

w ≥ 22

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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

Simplify the expression. Write the answer using scientific notation.

erik [133]

The answer is 5.88 x 10^22 because when you move your decimal point (which should be placed in between 5 and 8) to the right it turns 58800000000000 into 5.88. Then you count the numbers after the decimal which gives you 12.
( I’m pretty sure I made no sense, but hopefully it helped !! )

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3 years ago

In each box is a step in the process of solving a max/min problem like the one in Question 8. Number these steps in order (1-8)

Dmitriy789 [7]

Answer:

The steps are numbered below

Step-by-step explanation:

To solve a maximum/minimum problem, the steps are as follows.

1. Make a drawing.

2. Assign variables to quantities that change.

3. Identify and write down a formula for the quantity that is being optimized.

4. Identify the endpoints, that is, the domain of the function being optimized.

5. Identify the constraint equation.

6. Use the constraint equation to write a new formula for the quantity being optimized that is a function of one variable.

7. Find the derivative and then the critical points of the function being optimized.

8. Evaluate the y-values of the critical points and endpoints by plugging them into the function being optimized. The largest y- value is the global maximum, and the smallest y-value is the global minimum.

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3 years ago

Can you help me figure out the slope of this line?<br> please and thx<br> ASAP.

KonstantinChe [14]

The rise is the vertical distance between the two points, which is the difference between their y-coordinates. That makes the rise y2 − y1. The run between these two points is the difference in the x-coordinates, or x2 − x1.

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3 years ago

3 more than 6 times a number

Snowcat [4.5K]

Answer:

assuming you're looking for an expression, it would be written as "6x+3".

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3 years ago

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