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Eva8 [605]
3 years ago
14

Graph the inequality on a number line

Mathematics
1 answer:
pantera1 [17]3 years ago
4 0
I’m in middle school
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Jawad has seven rocks ​
Neporo4naja [7]

Answer:

What’s the question?

Step-by-step explanation:

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John bought 8 watches for $56 and his friend victor bought 7 watches for $63. whose watch is expensive ?
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John=$7 each watch
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1 year ago
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Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true.
grandymaker [24]

Answer:

Lines a and b are parallel

Lines a and c are perpendicular

Lines d and c are perpendicular

Step-by-step explanation:

we know that

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

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

Part 1) Find the slope of Line a

we have the points

(-3,4) and (3,6)

substitute in the formula

m=\frac{6-4}{3+3}

m=\frac{2}{6}

simplify

m_a=\frac{1}{3}

Part 2) Find the slope of Line b

we have the points

(-10,-3) and (-8,3)

substitute in the formula

m=\frac{3+3}{-8+10}

m=\frac{6}{2}

m_b=3

Part 3) Find the slope of Line c

we have the points

(0,5) and (3,-4)

substitute in the formula

m=\frac{-4-5}{3-0}

m=\frac{-9}{3}

m_c=-3

Part 4) Find the slope of Line d

we have the points

(4,-7) and (13,-4)

substitute in the formula

m=\frac{-4+7}{13-4}

m=\frac{3}{9}

simplify

m_d=\frac{1}{3}

Part 5) Compare the slopes

Remember that

If two lines are parallel then their slopes are the same

If two lines are perpendicular then their slopes are opposite reciprocal

we have

m_a=\frac{1}{3}

m_b=3

m_c=-3

m_d=\frac{1}{3}

therefore

Lines a and b are parallel (slopes are equal)

Lines a and c are perpendicular (slopes are opposite reciprocal)

Lines d and c are perpendicular (slopes are opposite reciprocal)

6 0
3 years ago
Christopher’s backyard is shaped like a rectangle with a length of 2x + 5 feet and a width of 4x - 7 feet.
Doss [256]

Answer:

8x² + 6x - 35

Step-by-step explanation:

A = (2x + 5)(4x - 7)

Front: 2x * 4x = <em>8x²</em>

Outside: 2x * (-7) = <em>-14x</em>

Inside: 5 * 4x = <em>20x</em>

Last: 5 * -7 = <em>-35</em>

Add up: <em>8x² - 14x + 20x -35</em>

Simplify: 8x² + 6x - 35

8 0
3 years ago
Help please solve<br> <img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B6x%5E5%2B11x%5E4-11x-6%7D%7B%282x%5E2-3x%2B1
Shkiper50 [21]

Answer:

\displaystyle  -\frac{1}{2} \leq x < 1

Step-by-step explanation:

<u>Inequalities</u>

They relate one or more variables with comparison operators other than the equality.

We must find the set of values for x that make the expression stand

\displaystyle \frac{6x^5+11x^4-11x-6}{(2x^2-3x+1)^2} \leq 0

The roots of numerator can be found by trial and error. The only real roots are x=1 and x=-1/2.

The roots of the denominator are easy to find since it's a second-degree polynomial: x=1, x=1/2. Hence, the given expression can be factored as

\displaystyle \frac{(x-1)(x+\frac{1}{2})(6x^3+14x^2+10x+12)}{(x-1)^2(x-\frac{1}{2})^2} \leq 0

Simplifying by x-1 and taking x=1 out of the possible solutions:

\displaystyle \frac{(x+\frac{1}{2})(6x^3+14x^2+10x+12)}{(x-1)(x-\frac{1}{2})^2} \leq 0

We need to find the values of x that make the expression less or equal to 0, i.e. negative or zero. The expressions

(6x^3+14x^2+10x+12)

is always positive and doesn't affect the result. It can be neglected. The expression

(x-\frac{1}{2})^2

can be 0 or positive. We exclude the value x=1/2 from the solution and neglect the expression as being always positive. This leads to analyze the remaining expression

\displaystyle \frac{(x+\frac{1}{2})}{(x-1)} \leq 0

For the expression to be negative, both signs must be opposite, that is

(x+\frac{1}{2})\geq 0, (x-1)

Or

(x+\frac{1}{2})\leq 0, (x-1)>0

Note we have excluded x=1 from the solution.

The first inequality gives us the solution

\displaystyle  -\frac{1}{2} \leq x < 1

The second inequality gives no solution because it's impossible to comply with both conditions.

Thus, the solution for the given inequality is

\boxed{\displaystyle  -\frac{1}{2} \leq x < 1 }

7 0
3 years ago
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