All categories

1 year ago

5. Find the value(s) of x so that the line containing the points (2x + 3, x + 2) and (0, 2) is

Mathematics

1 answer:

Dvinal [7]1 year ago

4 0

Answer:

x = -2 or -9

Step-by-step explanation:

You want the values of x such that the line defined by the two points (2x+3, x+2) and (0, 2) is perpendicular to the line defined by the two points (x+2, -3-3x) and (8, -1).

<h3>Slope</h3>

The slope of a line is given by the slope formula:

m = (y2 -y1)/(x2 -x1)

Using the formula, the slopes of the two lines are ...

m1 = (2 -(x+2))/(0 -(2x+3)) = (-x)/(-2x-3) = x/(2x +3)

and

m2 = (-1 -(-3-3x))/(8 -(x+2)) = (2+3x)/(6 -x)

<h3>Perpendicular lines</h3>

The slopes of perpendicular lines have product of -1:

$\dfrac{x}{2x+3}\cdot\dfrac{2+3x}{6-x}=-1\\\\x(3x+2)=(2x+3)(x-6)\qquad\text{multiply by $(2x+3)(6-x)$}\\\\3x^2+2x=2x^2-9x-18\qquad\text{eliminate parentheses}\\\\x^2+11x+18=0\qquad\text{put in standard form}\\\\(x+2)(x+9)=0\qquad\text{factor}$

<h3>Solutions</h3>

The values of x that satisfy this equation are x = -2 and x = -9. The attached graphs show the lines for each of these cases.

You might be interested in

Find the derivative of the inverse function of the original function f(x)=(x+1)^3-5

____ [38]

Answer:

Step-by-step explanation:

let f(x)=y

$y=(x+1)^{3} -5\\flip ~x~and~y\\x=(y+1)^{3}-5\\(y+1)^{3}=x+5\\y=(x+5)^{\frac{1}{3} } -1\\or~f^{-1}(x)=(x+5)^{\frac{1}{3} } -1\\(f^{-1})'(x)=\frac{1}{3} (x+5)^{\frac{-2}{3} }$

4 0

3 years ago

Can some please answer this

Sonbull [250]

9514 1404 393

Answer:

B (2 violet)

Step-by-step explanation:

Let the colors be represented by their first letter. Then the balances give rise to two equation:

o +y +b +v = r +g +b

o +y +v = g +v

Subtracting the second equation from the first gives ...

(o +y +b +v) -(o +y +v) = (r +g +b) -(g +v)

b = r +b -v

Adding v-b to both sides, we have ...

b +(v -b) = r +b -v +(v -b)

v = r

Multiplying this result by 2, we can match the final balance:

2r = 2v . . . . . . . choice B

7 0

3 years ago

Read 2 more answers

Polly surveyed 850 teenagers to find out their favorite type of music. She found that 32% of the teenagers surveyed like hard ro

frosja888 [35]

Answer:

In explanation

Step-by-step explanation:

272 for part A because say you took a test out of 850 and you got a total of 272 of them right then you would of gotten a 32%

200 for 2 because if 75% of them liked pop music and 150 teenagers what the number of teenagers surveyed then that means 200 of them were surveyed because 150 out of 200 is 75%

I don't know the last one because if you had anything there only could get a 100%(im sorry for this one it's a little confusing.

Hope this helps have a great afternoon:)

7 0

2 years ago

(Worth 30 points) What are the explicit equation and domain for an arithmetic sequence with a first term of 5 and a second term

kolbaska11 [484]

Answer:

$a_n=5-2(n-1)$ , all integers where n≥1