Need help with number 2 and 3

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]

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Answer: 300 miles, $220

Step-by-step explanation:

Answer:

x > -7/12. This is the answer to this question.

Answer:

%41.25

Step-by-step explanation:

80 - 47 = 33

33 divided by 80

convert to percentage

Step-by-step explanation:

I think it is 44.

if wrong forgive me.

hope this helps.

Answer:

44

Step-by-step explanation:

1. To round a number to the nearest 10, look at the ones-digit. If the digit is 5 or more, round up (raise the score). If the digit is 4 or less, round down (let it rest).

2. The ones-digit in 44 is 4 or less, meaning we round down. The 4 in the ones-place becomes zero, and therefore, rounds to 40.

Therefore, the answer is 44.

Answer:

less than or equal to -11

Step-by-step explanation:

subtract 8 to both sides

k< or equal to -11

Answer:

yes

Step-by-step explanation:

The perimeter of the rectangle ABCD and WXYZ are 14 units and 28 units respectively. The perimeter of the rectangle ABCD and WXYZ are 12 units² and 48 units² respectively.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The perimeter of a rectangle = 2(L+W)

The vertices of two rectangles are A(−5,−1),B(−1,−1),C(−1,−4),D(−5,−4) and W(1,6),X(7,6),Y(7,−2),Z(1,−2).

As per the given data, the figure of two rectangles has been attached below.

According to the graph,

The perimeter of the rectangle ABCD = 2(3 + 4) = 2(7) = 14 units

The perimeter of the rectangle WXYZ = 2(6 + 8) = 2(14) = 28 units

The area of the rectangle ABCD = (3 × 4) = 12 units²

The area of the rectangle WXYZ = (6 × 8) = 48 units²

The rectangles are similar because the ratio of length to width is equivalent.

The perimeter of the rectangle ABCD and WXYZ are 14 units and 28 units respectively. The perimeter of the rectangle ABCD and WXYZ are 12 units² and 48 units² respectively.

Learn more about the Perimeter of the rectangle here:

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Answer:

A. reflection across the y-axiss

Step-by-step explanation:

Given:

The locations of the two points are (-4 , 8) and (-4 , -8).

To find:

The relation between two points.

From the given points (-4, 8) and (-4 , -8), it is clear that the y-coordinates are same but the sign of x-coordinates are opposite.

If a figure is reflected across the y-axis, then we change the sign of x-coordinate and the y-coordinates remain same, i.e.,

[tex](x,y)[/tex]→[tex](-x,y)[/tex]

For (-4,8)

[tex](-4,8)[/tex]→ [tex](-4,-8)[/tex]

So, it is reflection across the y-axis.

Therefore, the correct option is A.

Answer:

1 17/20

Step-by-step explanation:

Put 185 over 100. Then, Simplify. Divide 180 and 100 by 5. 180 ÷ 5 = 37 and 100 ÷ 5 = 20. Then, divide 37 by 20. Write down the the quotient as the whole number and the remainder as the numerator.

9514 1404 393

Answer:

  5.6 miles

Step-by-step explanation:

Let the following distances between exits be defined:

  a = exit 5 to 6

  b = exit 6 to 7

  c = exit 7 to 8

Then the given relations are ...

  a = 3.2

  b = 1.1 +a = 4.3

  (b +c) = 2.4 +(a +b)   ⇒   c = a +2.4 = 5.6

The distance between exits 7 and 8 is 5.6 miles.

Testing the hypothesis, it is found that the correct option is:

b. Not significantly greater than 55%.

At the null hypothesis, we test if the proportion is not significantly more than 55%, that is:

[tex]H_0: p \leq 0.55[/tex]

At the alternative hypothesis, we test if the proportion is significantly more than 55%, that is:

[tex]H_1: p < 0.55[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

For this problem, the parameters are:

[tex]p = 0.55, n = 100, \overline{p} = \frac{60}{100} = 0.6[/tex]

Hence, the value of the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.6 - 0.55}{\sqrt{\frac{0.55(0.45)}{100}}}[/tex]

[tex]z = 1.01[/tex]

The p-value of the test is the probability of finding a sample proportion above 0.6, which is 1 subtracted by the p-value of z = 1.01.

Looking at the z-table, z = 1.01 has a p-value of 0.8438.

1 - 0.8438 = 0.1562.

The p-value of the test is 0.1562 > 0.05, which means that the proportion is not significantly greater than 55%, and option b is correct.

A similar problem is given at https://brainly.com/question/24330815

Answer:

The inequality is false and equals -14=3

Step-by-step explanation:

You want to start by cancelling equal terms on both sides of the equation which means getting rid of both 8's. You are left with (-7)-(7)=7+(-4).

From here you want to solve both sides meaning adding -7-7 because both terms are negative they will combine, and the other side which is -7+4. They are opposite terms so you will subtract. This leaves you with -14=3 which is false.

Answer:

B

Step-by-step explanation:

The true statement about the functions f(x) and g(x) is (b) B. Both the slopes and the y-intercepts are different.

The function g(x) is given as:

g(x) = -2x - 5

A linear equation is represented as:

y = mx + b

Where m represents the slope, and b represents the y-intercept.

So, the slope of the function g(x) is -2 and the y-intercept is -5

For the function f(x), the slope is calculated using:

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

Using the points on the graph, we have:

m =(3 - 1)/(1 - 0)

Evaluate

m = 2

The line of the function f(x) cross the y-axis at (0,3);

So, its y-intercept is 3

Hence, both functions have different slopes and different y-intercepts

Read more about linear functions at:

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Answer:

128.57

Step-by-step explanation:

each angle is equal and all of them will sum 900 degrees

Answer:

128.6... degrees

Step-by-step explanation:

Because regular shapes have all equal angles, we can do this:

900/7

regular septagons/heptagons have 7 sides

900/7 = 128.571429 or about 128.6

Answer:

I guess the equation would be 1s+1w+1j+4c= 6L

Step-by-step explanation:

the question is a bit confusing, but i hope this helped

Answer:

I'm too lazy to use a calculator but I'll explain the steps to you

Step-by-step explanation:

so basically all you have to do is you know that

volume=length*with*height

we already have the length and height

so do 7.5*5 on your calculator for me

and then divide that answer by 225

and then you will get your answer

excuse me for being lazy but at least I gave you your answer it's 4 am here

Answer:

x = - 20

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] x - 5 = x ( multiply through by 4 to clear the fraction )

3x - 20 = 4x ( subtract 3x from both sides )

- 20 = x

Answer:

1.86822

Step-by-step explanation:

take the 200 miles and devide the traveling speed

Answer:

Step-by-step explanation:

complementary angles sum to 90°

Let angle 1 =  x

    angle 2 =  3x - 8

  3x - 8 + x = 90

             4x = 98

               x = 24.5°

3(24.5) - 8 = 65.5°

or

90 - 24.5 = 65.5°

Answer:

3. a,c

4. a,c

5. c

6. a

7. y=-9x

8. y=x+9

9. y=x-7,y=x+3

13. y=x+5

14. y=8x-2

15. y=5

Step-by-step explanation:

Sry for late response

Step-by-step explanation:

3. all three equations are in the form of

[tex]y = mx + b[/tex]

where m is the slope and b is the y intercept.

A and X both have a y intercept of 1 so A and C is the answer.

4. A megative slope is included by a negative sign so A and C is the answer.

5. The linear parent function is the identity function which is

[tex]y = x[/tex]

6. Since our points share the same y coordinate, our slope will be a horinzontal line which indicates a slope of zero.

7. The sleepest line has the greatest absolute value slope which is y=-9x.

8. The fattest has the smallest absolute value slope which is y=x+9.

9.The first and second one are parallel because they have the same slope

13.The second one does.

14. 8x+10 is greater slope than 5x.

15. y=5 because it has no y intercept

Answer:

4

Step-by-step explanation:

Take the number of cards and divide by the number of cards to determine the number of piles

32/8

4

There are 4 piles

Answer:

4 piles

Step-by-step explanation:

32 ÷ 8 = 4

8 cards in a pile. 8, 16, 24 ,32.

9514 1404 393

Answer:

  ±1/4, ±1/2, ±1, ±5/4, ±2, ±5/2, ±5, ±10

Step-by-step explanation:

The rational root theorem tells you possible rational roots of this equation would be ...

  ±(divisor of 10)/(divisor of 4)

The divisors of 10 are 1, 2, 5, 10. The divisors of 4 are 1, 2, 4. Then the possible rational roots are ...

  ±1/4, ±1/2, ±1, ±5/4, ±2, ±5/2, ±5, ±10

_____

This particular cubic has one irrational real root near -2.689. It has no rational roots.

Answer:

sorry I don't know you can tell answer

Answer:

I had the project and this is what I submitted. Make sure you rewrite it in your own words to avoid plagiarism and I got 100% on the assignment. Enjoy :)

Step-by-step explanation:

Had the project and all these answers are correct

Answer: 11/9

Step-by-step explanation:

First, convert two to 18/9. This is still equal to two but this makes it easier to answer the problem, because both of the terms have the same denominator. Now, since both of them have the same denominator, all you need to do is subtract the numerators, and put that over the denominator of 9. 18-7=11. So the answer is 11/9. This is an improper fraction, though you could also make it into a mixed number: 1 and 2/9.

Answer:

11/9

Step-by-step explanation:

Add a one under the 2. So that it becomes 2/1. Now you have the expression, 2/1 - 7/9. To subtract fractions, you need the denominators of the two fractions to be the same. We can put 9 as the common denominator. All you have to do in order for 2/1 to have 9 as its denominator, is to multiply 9 for both the numerator and denominator; 2/1 x 9/9 = 18/9. After that, your new expression would be 18/9 7/9. Just subtract across, 18 - 7 = 11, keep the denominator 9. The answer should be 11/9

Answer:

because 4 is a fixed value. and it is not a variable.