Write the equation of a line that is perpendicular to y = 3x - 2 and goes through the point (0,5)

(i) The graph of f is symmetric about the y-axis - this is another way of saying f is an even function, which means

[tex]f(x) = f(-x) \iff \dfrac{ax+b}{x^2-c} = \dfrac{-ax+b}{x^2-c}[/tex]

The denominator remains unchanged, so

ax + b = -ax + b

Solve for a :

ax = -ax

2ax = 0

a = 0

(The alternative is that x = 0, but if that were the case then there would be infinitely many choices for a.)

So

[tex]f(x) = \dfrac{b}{x^2-c}[/tex]

(ii) Since

[tex]\displaystyle \lim_{x\to2^+}f(x) = +\infty[/tex]

it follows that x - 2 must be a factor of the denominator. If that's true, then

x ² - c = (x - 2) (x - r )

for some other root r of x ² - c. Expanding the right side gives

x ² - c = x ² - (2 + r )x + 2r

so that

-(2 + r ) = 0   ===>   r = -2

2r = -c   ===>   -c = -4   ===>   c = 4

and so

[tex]f(x) = \dfrac{b}{x^2-4}[/tex]

(iii) Finally, we're given that f ' (1) = -2. Differentiating f gives

[tex]f'(x) = -\dfrac{2bx}{(x^2-4)^2}[/tex]

so that

[tex]f'(1) = -\dfrac{2b}{(1^2-4)^2} = -\dfrac{2b}{9}[/tex]

Then

-2b/9 = -2   ===>   b = 9

and we find that

[tex]f(x) = \dfrac{9}{x^2-4}[/tex]

Answer:

a answer

Step-by-step explanation:

a answer is a answer to a answer to a answer

The rule in vector notation for the translation to the right is described by the following formula:

[tex]V'(x,y) = V(x,y) + (9, -4)[/tex]

Vectorially speaking, a translation is described by the following expression:

[tex]V'(x,y) = V(x,y) + T(x,y)[/tex] (1)

Where:

By direct inspection we see that parallelogram C'D'E'F' translated to the right is moved 9 in +x direction and 4 in -y direction. Hence, the translation vector is equal to:

[tex]T(x,y) = (9, -4)[/tex]

And the rule in vector notation for the translation to the right is described by the following formula:

[tex]V'(x,y) = V(x,y) + (9, -4)[/tex]

We kindly invite to check this question on translations: https://brainly.com/question/12463306

Answer:

b

Step-by-step explanation:

Answer:

the square root of 197

Step-by-step explanation:

delta x=14

delta y=1

therefore with the Pythagorean theorem, the hypotenuse/distance is the square root of 197

Answer:

2

I hope this helps you...

Answer:

PLS MARK BRAINLIEST

Step-by-step explanation:

m= y2 - y1/ x2 - x1( slope of a line)

m = 8 -0 / 7- 0

8/7 = m

m = 1.1

since m =y - y1/ x - x1

1.1 = y - 0/ x-0

1.1 = y/x(cross multiply)

y = 1.1 x

y -1.1 x = 0

or

y - 8/7 x = 0

Divide total dollars by the conversion rate:

68/1.36 = 50

Answer: £50

Answer:

A.   $47,143

Step-by-step explanation:

Given information:

Gross income: Total income before any deductions.

If take home pay is approximately 70% of the annual gross income, to be able to maintain the current lifestyle, 70% of the annual gross income needs to be at least $33,000.

Let x = annual gross income

Therefore:

70% of x = $33,000

⇒ 0.7x = 33000

⇒ x = 33000 ÷ 0.7

⇒ x = 47142.8571...

Therefore, the annual gross income needs to be $47,143 (nearest dollar) to maintain the current lifestyle.

Annual gross income be y

Option A

Answer:

5 apples

Step-by-step explanation:

because jonny never had any taken away or added

BENJI KROL + NIC KAUFMANN FOREVER

Answer:

hope it helps .... . . ........................!

Answer:

25x

Step-by-step explanation:

6x and 19x are like terms so we can add them

6x+19x = 25x

Answer:

y=24x/13+317/13

Step-by-step explanation:

Answer:

no HAHHAAHHA

Step-by-step explanation:

WHAT IS THAT

Answer:

$29.90

Step-by-step explanation:

Just multiply gallons by price:

13 gallons x [tex]\frac{2.30 dollars}{1 gallon}[/tex] = 29.9

Answer:

m = 2/3

Step-by-step explanation:

4y = -6x + 72

y = -3/2x + 18

Negative reciprocal = 2/3

Answer: 1/3

Step-by-step explanation: 2/3 - 1/3 = 1/3

Answer:

it could be 1/8

Answer:

x = 30.

Step-by-step explanation:

8x - 3(2x - 4) = 3(x - 6)

8x - 3*2x + - 3*-4 = 3*x + 3 * -6

8x - 6x + 12 = 3x - 18

2x + 12 = 3x - 18

2x - 3x  + 12 = 3x - 3x - 18

-x + 12 = -18

-x + 12 - 12 = -18 - 12

-x = -33

-x/-1 = -30/-1

x = 30.

Answer:

[tex]x=30[/tex]

Step-by-step explanation:

[tex]8x-3\left(2x-4\right)=3\left(x-6\right)[/tex]

First, we will expand [tex]-3\left(2x-4\right)[/tex] by applying the distributive property:

[tex]-3\times \:2x-\left(-3\right)\times \:4[/tex]

** [tex]-\left(-a\right)=a[/tex]

[tex]-6x+12[/tex]

[tex]8x-6x+12=3\left(x-6\right)[/tex]

Expand, [tex]3\left(x-6\right):[/tex]

[tex]3x-3\times \:6[/tex]

[tex]3x-18[/tex]

[tex]2x+12=3x-18[/tex]

Subtract 12 from both sides:

[tex]2x+12-12=3x-18-12[/tex]

[tex]2x=3x-30[/tex]

Subtract 3x from both sides:

[tex]2x-3x=3x-30-3x[/tex]

[tex]-x=-30[/tex]

Divide both sides by -1:

[tex]\frac{-x}{-1}=\frac{-30}{-1}[/tex]

[tex]x=30[/tex]

________________________

Answer:

1 1/2 or 1.5

Step-by-step explanation:

Hope it helps sorry if it's wrong :)

Answer:

1st year

50hdnjxwmmwdbbd

djjrjeuie

Answer:

a. 738.73

Step-by-step explanation:

hope that’s righttt.

What I did was 500x0.05 and with the answer I did x0.5 again and added it to the previous year until the 8th time each was 738.73 correct me if I’m wrong

edit so it’s wrong….not sure what I did wrong

Answer:

x = 3

Step-by-step explanation:

2 + 6x = 20

6x = 18

x = 3

Hopefully this helps!

Brainliest please?

Answer:

2+6x=20

2-        -2

6x/6=18/6

=3

Step-by-step explanation:

Answer:

1.6

Step-by-step explanation:

Answer:

69 degrees

Step-by-step explanation:

m is a point, if your trying to find lkh, is 69

lkm=111, and jkl=180, so 180-111=jkm

jkm=69

angles that are diagonal from each other are the same degree

lkh=69

hope this helps, if not see me in the commnets

HOPE THIS HELPS, BRAINLIEST PLEASE

Answer:

m < LKH = 69°

Step-by-step explanation:

Given that m < LKM = 111° and that:

<LKM and <LKH are adjacent angles as they share the same vertex, point K, and same ray between them, KL:

Then we can assume that m < LKM and m < LKH are supplementary angles whose sum = 180°.

Therefore, we can establish the following equation:

m < LKM + m < LKH = 180°

111° + m <LKH = 180°

Subtract 111° from both sides to solve for m < LKH:

111° - 111° + m <LKH = 180° - 111°

m < LKH = 69°

Therefore, the measure of < LKH is 69°.

Please mark my answers as the Brainliest if you find my explanations helpful :)

Answer:

angle 4 = 56°

Step-by-step explanation:

Interior angles in the same side of the transversal are supplementary (their sum is 180°)

Angle 1 and 4 are interior angles on the same side of the transversal.

So, angle 1 + angle 4 = 180°

Angle 1 = 124° (given)

124 + angle 4 = 180°

angle 4 = 180° - 124° = 56°

Therefore, angle 4 = 56°

Hope it helps :)

Answer:

Domain: [-2, ∞)

Range: [-4, ∞)

General Formulas and Concepts:

Algebra II

Coordinate Planes

Step-by-step explanation:

According to the graph, we see that our x-value stretches from x = -2 to infinity. Since x = -2 is a closed dot, it is included in the domain:

[-2, ∞) or -2 ≤ x < ∞

According to the graph, we see that our y-value stretches from y = -4 to infinity. Since y = -4 is a closed dot, it is included in the range:

[-4, ∞) or -4 ≤ y < ∞