Find the missing value so that the line passing through the points has the given slope.

(7,1) and (x,4); m = 3/4
​

The equation of the tangent line is [tex]y = \frac{b^{2} x_{0}x }{a^{2} y_{0} } - \frac{b^{2} x_{0}^{2} }{a^{2} y_{0} } + y_{0}[/tex]

To find the tangent to the hyperbola [tex]\frac{x^{2} }{a^{2} } - \frac{y^{2} }{b^{2} }[/tex] at (x₀, y₀), we differentiate the equation implicitly to find the equation of the tangent at (x₀, y₀).

So, [tex]\frac{d}{dx} (\frac{x^{2} }{a^{2} } - \frac{y^{2} }{b^{2} }) = \frac{d0}{dx}\\\frac{d}{dx} \frac{x^{2} }{a^{2} } - \frac{d}{dx}\frac{y^{2} }{b^{2} }= 0\\\frac{2x }{a^{2} } - \frac{dy}{dx}\frac{2y }{b^{2} } = 0\\\frac{2x }{a^{2} } = \frac{dy}{dx}\frac{2y }{b^{2} } \\\frac{dy}{dx} = \frac{b^{2}x }{a^{2}y }[/tex]

So, at (x₀, y₀)

[tex]\frac{dy}{dx} = \frac{b^{2} x_{0} }{a^{2} y_{0} }[/tex]

So, the equation of the tangent line is gotten from the standard equation of a line in point-slope form

So, [tex]\frac{y - y_{0} }{x - x_{0} } = \frac{b^{2} x_{0} }{a^{2} y_{0} } \\y - y_{0} = \frac{b^{2} x_{0} }{a^{2} y_{0} }(x - x_{0}) \\y = \frac{b^{2} x_{0} }{a^{2} y_{0} }(x - x_{0}) + y_{0} \\y = \frac{b^{2} x_{0}x }{a^{2} y_{0} } - \frac{b^{2} x_{0}^{2} }{a^{2} y_{0} } + y_{0}[/tex]

So, the equation of the tangent line is [tex]y = \frac{b^{2} x_{0}x }{a^{2} y_{0} } - \frac{b^{2} x_{0}^{2} }{a^{2} y_{0} } + y_{0}[/tex]

Learn more about equation of tangent line here:

https://brainly.com/question/12561220

Step-by-step explanation:

volume of a rectangular pan = length of the pan × width of the pan × height of the pan

V=l.b.h

234=9.13.h

h=234/9×13

h= 2in.

hope this helps you.

Answer:

2 inches

Step-by-step explanation:

V= 234, L=9, W=13, H=?

V= LxBxH

234= 9x13xH

234= 117H

divide through by 117

234/117 = 117H/117

H= 2inches

Answer:

130 will be correct answer

Step-by-step explanation:

The three angles are

34° 70° and 126°

we have to find fourth angle

let us consider fourth angle as X

The sum of quadrilateral is 360°.

So

34°+70°+126°+ x = 360°

130+X =360°

X = 360°-130°

X = 230°

Here we got the fourth angle

Answer:

The answer should be C!

Step-by-step explanation:

When you multiply the y value 0.04 and 5 it comes out as 0.02.

9514 1404 393

Answer:

  one solution: (x, y) = (-8, -7)

Step-by-step explanation:

We can add 6 times the first equation to the second equation in order to eliminate y.

  6(x -y) +(4x +6y) = 6(-1) +(-74)

  10x = -80

  x = -8

  y = x+1 = -7 . . . . . solve the first equation for y; substitute x

The one solution is (x, y) = (-8, -7).

Answer:

4x2-6x+6

Step-by-step explanation:

(9x2-2x) +(3x-5)+(m) =13x2-5x+1

(13x2-5x+1)-(9x2+x-5)=m

Answer:

24.15

Step-by-step explanation:

10.35 x 2 = 20.7 But you still need 1 bag 1/3 of 10.35 =  3.45 Add all of them up = 24.15

Answer:

từ khoảng 70 đến 90 phần trăm

Answer:

Step-by-step explanation:

The smallest integer is 2x - 2

The middle integer = 2x

The largest integer = 2x + 2

2x - 2 + 2x + 2x + 2 = 2x  + 2 + 50      Combine

6x = 52 + 2x                                         Subtract 2x from both sides

6x-2x = 52                                            Combine

4x = 52                                                  Divide both sides by 4

4x/4 = 52/4

x = 13

The three integers are

2x - 2 = 24

2x =    26

2x + 2 = 28

Answer:i have no Step-by-step explanation:

a

Answer:

Part A:  A) [tex]\frac{4y^{10}}{3w}[/tex]

Part B:

C) Quotient Rule of Powers (explained in Part A of this post).

D) Zero Exponent Rule (explained in Part A of this post, in solving for base z).

Step-by-step explanation:

[tex]\frac{28y^{15}w^{3} z^{7}}{21y^{5}w^{4} z^{7}}[/tex]

Use the Quotient Rule of Exponents:

[tex]\frac{a^{m}}{a^{n}} = a^{m-n}[/tex]

The 28 and 21 can be reduced by dividing both of them by 7.  For the exponential expressions with the same base, you could subtract their exponents.  I'll do each base separately so it doesn't get confusing.

[tex]\frac{28y^{15}w^{3} z^{7}}{21y^{5}w^{4} z^{7}}[/tex]

[tex]y^{15-5}[/tex] = [tex]y^{10}[/tex] (in the numerator).

[tex]w^{4-3}[/tex] = w (in the denominator. The "w" in the numerator cancels out).

[tex]z^{7-7}[/tex] = [tex]z^{0} = 1[/tex]  We used the Zero Exponent Rule here, were it states: [tex]a^{0} = 1[/tex]. (unnecessary to include in the final answer).

Altogether, you'll have:

Option A: [tex]\frac{4y^{10}}{3w}[/tex]

C) Quotient Rule of Powers (explained in Part A of this post).

D) Zero Exponent Rule (explained in Part A of this post, in solving for base z).

Answer:

J=15t+50

Step-by-step explanation:

The equation to represent this situation will be in the form J=mt+b where b is the starting value of love units, m represents the "love units" that are multiplied by the number of week, t is the number of weeks, and J represents Jack's love at that specific week.

The equation becomes: J=15t+50

To check, the equation should equal 50 when t=0, 65 when t=1, and 80 when t=2.

Checking t=0:

J=15(0)+50=0+50=50

Checking t=1:

J=15(1)+50=15+50=65

Checking t=2:

J=15(2)+50=30+50=80

The equation J=15t+50 does model the behavior of Jack's love at any week t based on the given data. Note that the equation used was based on slope intercept form (y=mx+b) due to the given data having a linear relationship.

Answer:

there is no line parallel to y = -3x + 8 that goes through (5, -7). this point falls on this line

Step-by-step explanation:

[tex]y = - 3x + 8[/tex]

[tex] - 7 = - 3(5) + b \\ - 7 = - 15 + b \\ b = 8[/tex]

The answer is

[tex]y = - 3x + 8[/tex]

Answer:

d{0 less than or equal to x less than or equal to 20, xer}

r{0 less than or equal to y less than or equal to -6,yer}

Step-by-step explanation:

The Domain and Range of the graph given is -

Domain ↔  [1, -6]

Range ↔ [- 21, 20]

We have a graph as shown in the figure.

We have to determine its domain and range.

For any function y = f(x), Domain is the set of all possible values of y that exists for different values of x. Range is the set of all values of x for which y exists.

According to question, we have -

From the graph it is clear that -

The values of y belong to the set - [1, -6]

and

The values of x belong to the set -  [- 21, 20]

Therefore, according to the definition of domain and range -

Domain ↔  [1, -6]

Range ↔ [- 21, 20]

Hence, the Domain and Range of the graph given is -

Domain ↔  [1, -6]

Range ↔ [- 21, 20]

To solve more questions on finding the domain and range of functions, visit the link below -

brainly.com/question/1632425

#SPJ2

Answer:

c

Step-by-step explanation:

Answer:

46.84

Step-by-step explanation:

Add the decimals first to get .84 then add the real numbers to get 46.

Answer?: I believe its C

No Explanation Because No

Answer: C is the answer

Step-by-step explanation:

Answer: -2

Step-by-step explanation:

Answer:

The distance is the absolute value of the difference. aka c

Step-by-step explanation:

Answer:

73,if you need explanation then let me know, always happy to help anyone! btw if you could give me brainliest then that would be great, i also undestand if not because im not the first to answer so dont be shy and hit theirs with brainliest if you want! :))

Step-by-step explanation:

Answer:

B. 60°

Step-by-step explanation:

1. The measure of all angles in a triangle sum up to 180°. This means that y + y + 60 = 120.

2. (Solving)

Step 1: Simplify both sides of the equation.

Step 2: Subtract 60 from both sides.

Step 3: Divide both sides by 2.

Step 4: Check if solution is correct.

Therefore, the answer is B. 60°.

Answer: 15

Step-by-step explanation: 20% → .20

.20 x 75 = 15

Answer:

=2x+4

Step-by-step explanation:

Let's simplify step-by-step.

5x+4−3x

=5x+4+−3x

Combine Like Terms:

=5x+4+−3x

=(5x+−3x)+(4)

=2x+4

Answer:

2x+4

Step-by-step explanation:

Hope fully it is correct

Answer:

568 to the negative power of 8

so. -8

568

1. 75

2. 105

3. 105

4. 75

6. 105

7. 105

8. 75

Answer:

The correct answer should be D.

Step-by-step explanation: