M − 56/–7 = –6 solve for m

1) Use the number line to help you answer this question.

masya89 [10]

Answer:

Step-by-step explanation:

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4 0

2 years ago

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At noon the minute and the hour hands overlap. In how man hours and minutes will it happen next?

Readme [11.4K]

It would happen again at 1 hour and 5 minutes .

That is because at noon it is 12 p.m. and for the minute and the hour hands overlap, the next time it would happen is at 1:05 which is going to overlap again

7 0

2 years ago

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On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) an

ExtremeBDS [4]

Answer:

$y\geq x-2$

$x+2y$

Step-by-step explanation:

step 1

Find the equation of the first inequality

Find the equation of the first solid line

we have the ordered pairs

(0,-2) and (2,0)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{0+2}{2-0}$

$m=\frac{2}{2}$

$m=1$

The equation in slope intercept form is equal to

$y=mx+b$

we have

$m=1$

$b=-2$ ---> the y-intercept is given

substitute

$y=x-2$

Remember that

Everything to the left of the solid line is shaded

so

The inequality is

$y\geq x-2$

step 2

Find the equation of the second inequality

Find the equation of the second dashed line

we have the ordered pairs

(0,2) and (4,0)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{0-2}{4-0}$

$m=\frac{-2}{4}$

$m=-\frac{1}{2}$

The equation in slope intercept form is equal to

$y=mx+b$

we have

$m=-\frac{1}{2}$

$b=2$ ---> the y-intercept is given

substitute

$y=-\frac{1}{2}x+2$

Remember that

Everything below and to the left of the line is shaded

so

The inequality is

$y$

Rewrite

Multiply by 2 both sides

$2y$

$x+2y$

therefore

The system of inequalities is

$y\geq x-2$

$x+2y$

see the attached figure to better understand the problem

5 0

3 years ago

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A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021

egoroff_w [7]

The sum of the given series can be found by simplification of the number

of terms in the series.

A is approximately 2020.022

Reasons:

The given sequence is presented as follows;

A = 1011 + 337 + 337/2 + 1011/10 + 337/5 + ... + 1/2021

Therefore;

$\displaystyle A = \mathbf{1011 + \frac{1011}{3} + \frac{1011}{6} + \frac{1011}{10} + \frac{1011}{15} + ...+\frac{1}{2021}}$

The n + 1 th term of the sequence, 1, 3, 6, 10, 15, ..., 2021 is given as follows;

$\displaystyle a_{n+1} = \mathbf{\frac{n^2 + 3 \cdot n + 2}{2}}$

Therefore, for the last term we have;

$\displaystyle 2043231= \frac{n^2 + 3 \cdot n + 2}{2}$

2 × 2043231 = n² + 3·n + 2

Which gives;

n² + 3·n + 2 - 2 × 2043231 = n² + 3·n - 4086460 = 0

Which gives, the number of terms, n = 2020

$\displaystyle \frac{A}{2} = \mathbf{ 1011 \cdot \left(\frac{1}{2} +\frac{1}{6} + \frac{1}{12}+...+\frac{1}{4086460} \right)}$

$\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2} +\frac{1}{2} - \frac{1}{3} + \frac{1}{3}- \frac{1}{4} +...+\frac{1}{2021}-\frac{1}{2022} \right)$