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3 years ago

What is the slope of 2x + y = 5

Mathematics

2 answers:

vitfil [10]3 years ago

8 0

2. the slope is 2 because

Andrei [34K]3 years ago

7 0

The slope of this equation will be 2,

so m = 2.

To solve for the slope, all you need to do is convert this equation into slope-intercept form which is y = -2x + 5.

From there, you can tell the slope will be -2 since it's in place of the m (the slope).

Hope this helps and have a great day!

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Simplify (x + 2/ x^2 + 2x -3) / (x + 2/x^2 - x)

rjkz [21]

Answer:

The simplest form is x/(x + 3)

Step-by-step explanation:

* To simplify the rational Expression lets revise the factorization

of the quadratic expression

* To factor a quadratic in the form x² ± bx ± c:

- First look at the c term

# If the c term is a positive number, and its factors are r and s they

will have the same sign and their sum is b.

# If the c term is a negative number, then either r or s will be negative

but not both and their difference is b.

- Second look at the b term.

# If the c term is positive and the b term is positive, then both r and

s are positive.

Ex: x² + 5x + 6 = (x + 3)(x + 2)

# If the c term is positive and the b term is negative, then both r and s

are negative.

Ex: x² - 5x + 6 = (x -3)(x - 2)

# If the c term is negative and the b term is positive, then the factor

that is positive will have the greater absolute value. That is, if

|r| > |s|, then r is positive and s is negative.

Ex: x² + 5x - 6 = (x + 6)(x - 1)

# If the c term is negative and the b term is negative, then the factor

that is negative will have the greater absolute value. That is, if

|r| > |s|, then r is negative and s is positive.

Ex: x² - 5x - 6 = (x - 6)(x + 1)

* Now lets solve the problem

- We have two fractions over each other

- Lets simplify the numerator

∵ The numerator is $\frac{x+2}{x^{2}+2x-3}$

- Factorize its denominator

∵ The denominator = x² + 2x - 3

- The last term is negative then the two brackets have different signs

∵ 3 = 3 × 1

∵ 3 - 1 = 2

∵ The middle term is +ve

∴ -3 = 3 × -1 ⇒ the greatest is +ve

∴ x² + 2x - 3 = (x + 3)(x - 1)

∴ The numerator = $\frac{(x+2)}{(x+3)(x-2)}$

- Lets simplify the denominator

∵ The denominator is $\frac{x+2}{x^{2}-x}$

- Factorize its denominator

∵ The denominator = x² - 2x

- Take x as a common factor and divide each term by x

∵ x² ÷ x = x

∵ -x ÷ x = -1

∴ x² - 2x = x(x - 1)

∴ The denominator = $\frac{(x+2)}{x(x-1)}$

* Now lets write the fraction as a division

∴ The fraction = $\frac{x+2}{(x+3)(x-1)}$ ÷ $\frac{x+2}{x(x-1)}$

- Change the sign of division and reverse the fraction after it

∴ The fraction = $\frac{(x+2)}{(x+3)(x-1)}*\frac{x(x-1)}{(x+2)}$

* Now we can cancel the bracket (x + 2) up with same bracket down

and cancel bracket (x - 1) up with same bracket down

∴ The simplest form = $\frac{x}{x+3}$

5 0

3 years ago

Read 2 more answers

The length of a rectangle is 4 m less than the diagonal and the width is 5 m less than the diagonal. If the area is 82 m^2, how

nikklg [1K]

I hate rounding.

Let's call the diagonal x. It's the hypotenuse of the right triangle whose legs are the rectangle sides.

According to the problem we have a length x-4 and a width x-5 and an area

82 = (x-4)(x-5)

82 = x^2 - 9x + 20

0 = x^2 - 9x - 62

That one doesn't seem to factor so we go to the quadratic formula

$x = \frac 1 2(9 \pm \sqrt{9^2-4(62)}) = \frac 1 2(9 \pm \sqrt{329})$

Only the positive value makes any sense for this problem, so we conclude

$x = \frac 1 2(9 \pm \sqrt{329})$

That's the exact answer. Did I mention I hate rounding? That's about

x = 13.6 meters

Answer: 13.6

----------

It's not clear to me this problem is consistent. By the Pythagorean Theorem the diagonal satisfies

$x^2 = (x-4)^2 + (x-5)^2$

which works out to

$x=9 \pm 2\sqrt{10}$

That's not consistent with the first answer; this problem really has no solution. Tell your teacher to get better material.

5 0

3 years ago

40% of the groups budget was spent on activities. If $64,000 was spent on the activities, what was the full budget? solve with t

Andre45 [30]

Answer:

The full budget has a total value of $160,000

Step-by-step explanation:

This is a simple ratio problem and can be solved using the Rule of Three property. The Rule of Three is used to compare two ratios and find the missing part. In this case the ratios would be the following.

$\frac{64,000}{40 percent} = \frac{x}{100 percent}$

$\frac{64,000 * 100 percent}{40 percent} = \frac{x}$

$\frac{6,400,000}{40 percent} = \frac{x}$

$160,000= \frac{x}$

So now we know that 100% (The full budget) has a total value of $160,000.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

7 0

3 years ago

I need help really fast

antoniya [11.8K]

well 1+1=2 and 2+2=4 and 4+4=8 and 8+8=16 then..............................................ummm.....................................uhhhhhhhh...........................wow this is hard.......................................................................I have no clue sorry thats all i know

4 0

3 years ago

Work out the length of CD <br> Answer to 3 significant figures

vladimir1956 [14]

Answer:

Step-by-step explanation:

I can be wrong but i most likely sure it is correct because a triangle is 180 degrees you have to add 102 with 52 take that total and subtract it with 180 to find that angle is what you need to find the length. Again i am not sure but might be right.

5 0

3 years ago

Read 2 more answers

What is the slope of 2x + y = 5​

What is the slope of 2x + y = 5