Write an equation of the line that passes through the point (2,3) and is perpendicular to the line x+4y-8

Answer:

3/1

Step-by-step explanation:

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:

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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:

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.

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 next three natural numbers after 10999 are 11000,11001, and 11002.

Step-by-step explanation:

Write first natural number after 10999:

10999 + 1 = 11000

Write second natural number after 11000:

11000 + 1 = 11001

Write the third natural number after 11001:

11001 + 1 = 11002

Hence, the next three natural numbers after 10999 are 11000, 11001, and 11002.

Answer:

x < 15

Step-by-step explanation:

[tex]\frac{x}{5}[/tex] - 3 < 0 ( add 3 to both sides )

[tex]\frac{x}{5}[/tex] < 3 ( multiply both sides by 5 to clear the fraction )

x < 15

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:

2/15

Step-by-step explanation:

1/3 x 2/5

= ( 1 x 2 ) / ( 3 x 5 )

= 2/15

Answer:

2/15

Step-by-step explanation:

1/3*2/5

(1*2)/(3*5)

2/15

Answer: The rate of change of momentum of a body over time is directly proportional to the force applied and occurs in the same direction as the applied force.

We can write the law as:

Where F is a force, and P is the momentum.

Remember that the momentum is defined as the quantity of motion, such that:

P = M*V

Where M is the mass of the moving object and V is the velocity of the moving object.

Or we can write the second law as:

F = M*a

M = mass

a = acceleration

Happy To Help ;)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The two angles must add to 180

(4x-2)+(3x+14)=180

7x+12=180

7x=168

x=24

Answer:

n = 8

Step-by-step explanation:

hope this helps

According to distributive property

[tex]{{ \large{ \blue{ \rm{{➥}}}}}} \rm \large \: \: 6.7 \: (8x \: + \: 9)[/tex]

[tex]{{ \large{ \blue{ \rm{{➥}}}}}} \rm \large \: \: 53.6x \: + \: 60.3[/tex]

Hence , Option D is the correct answer.

Answer:

3/10

Step-by-step explanation:

Answer:

it is either f or h

Step-by-step explanation:

horizontal asymptote y=0

the graph is in the image above

range[-1, infinity)

domain(-infinity, infinity)

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:

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:

8% is the sales tax rate

Step-by-step explanation:

I'm not the best with math but the way I found the answer was by first using my local sales tax rate and determining how much the tax would be.

490 * 8.75% = 42.875

Knowing that this amount was higher than in the equation, I lowered the sales tax to 8% (0.08)

490 * 8% = 39.2

Hope this was somewhat helpful

LOL, i really need points.

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.

Answer:

B

Step-by-step explanation:

Answer:

The slope in this equation is 2x, so answer is 2.

Step-by-step explanation:

8x-4y-9=0

-8x -8x

-4y-9 = -8x

+9 +9

-4y = -8x+9

Divide by 4 on both side to have y by itself and you get

y = 2x - 9/4

Answer:

x = 9

Step-by-step explanation:

Step 1: Subtract 4x from both sides.

Step 2: Divide both sides by 3.

Step 3: Check if solution is correct.

Therefore, x = 9.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]k = -0.4[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]2k+9=7-3k\\\rule{150}{0.5}\\\rightarrow 2k + 9 = 7-3k\\\\\rightarrow 2k + 3k + 9 = 7 - 3k + 3k\\\\\rightarrow 5k + 9 = 7\\\\\rightarrow5k + 9 - 9 = 7 - 9\\\\\rightarrow 5k = -2\\\\\rightarrow \frac{5k=-2}{5}\\\\\rightarrow \boxed{k = -\frac{2}{5} = -0.4}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

[tex]x + 7 < 10 \\ x < 10 - 7 \\ x < 3[/tex]