All categories

2 years ago

What is the equation of a line with a slope of 3 and contains point (4.1)

Mathematics

2 answers:

cricket20 [7]2 years ago

5 0

Answer:

y = 3x - 11

Step-by-step explanation:

y=mx+b

1=3(4)+b

1=12+b

b=-11

Alborosie2 years ago

5 0

Answer:

y = 3x –11

or 3x – y = 11 Standard form

Explanation:

using slope-intercept form, calculate b

1 = 3(4) + b

1= 12 + b

1 –12 = b

–11 = b rewrite the equation using this value.

y = 3x –11

You might be interested in

Darrius bought 3 gallons of ice cream for $9.50 how much will it cost him if he wants 7 gallons?

Charra [1.4K]

Answer:

Its going to cost him 22.167

Step-by-step explanation:

Divide $9.50 by 3 = 3.167

multiply it by 7= 22.167

3 0

2 years ago

1. (5pts) Find the derivatives of the function using the definition of derivative.

andreyandreev [35.5K]

2.8.1

$f(x) = \dfrac4{\sqrt{3-x}}$

By definition of the derivative,

$f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h)-f(x)}{h}$

We have

$f(x+h) = \dfrac4{\sqrt{3-(x+h)}}$

and

$f(x+h)-f(x) = \dfrac4{\sqrt{3-(x+h)}} - \dfrac4{\sqrt{3-x}}$

Combine these fractions into one with a common denominator:

$f(x+h)-f(x) = \dfrac{4\sqrt{3-x} - 4\sqrt{3-(x+h)}}{\sqrt{3-x}\sqrt{3-(x+h)}}$

Rationalize the numerator by multiplying uniformly by the conjugate of the numerator, and simplify the result:

$f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x} - 4\sqrt{3-(x+h)}\right)\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x}\right)^2 - \left(4\sqrt{3-(x+h)}\right)^2}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16(3-x) - 16(3-(x+h))}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16h}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}$

Now divide this by h and take the limit as h approaches 0 :

$\dfrac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-x}\left(4\sqrt{3-x} + 4\sqrt{3-x}\right)} \\\\ \implies f'(x) = \dfrac{16}{4\left(\sqrt{3-x}\right)^3} = \boxed{\dfrac4{(3-x)^{3/2}}}$

3.1.1.

$f(x) = 4x^5 - \dfrac1{4x^2} + \sqrt[3]{x} - \pi^2 + 10e^3$

Differentiate one term at a time:

• power rule

$\left(4x^5\right)' = 4\left(x^5\right)' = 4\cdot5x^4 = 20x^4$

$\left(\dfrac1{4x^2}\right)' = \dfrac14\left(x^{-2}\right)' = \dfrac14\cdot-2x^{-3} = -\dfrac1{2x^3}$

$\left(\sqrt[3]{x}\right)' = \left(x^{1/3}\right)' = \dfrac13 x^{-2/3} = \dfrac1{3x^{2/3}}$

The last two terms are constant, so their derivatives are both zero.

So you end up with

$f'(x) = \boxed{20x^4 + \dfrac1{2x^3} + \dfrac1{3x^{2/3}}}$

8 0

1 year ago

It costs $198.00 to buy beef to make 300 meatballs. What will the cost be to make 120 meatballs?

Vika [28.1K]

Answer:$181.81

Step-by-step explanation:300/198

=1.5151515….multiple by 120

=181.818181

3 0

2 years ago

Pepsi [2]

Answer:

B. x = 2

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

check by substituting each given value of x into the function

x = 0 ⇒ y = × 0² = 0

hence (0, 0) is correct

x = 2 ⇒ y = × 4 = 3

hence (2, 4 ) is incorrect

x = 3 ⇒ y = × 9 = 6

hence (3, 6 ) is correct

x = 5 ⇒ y = × 25 = 18

hence (5, 18 ) is correct

7 0

2 years ago

Please help me with this??

Ludmilka [50]

Answer:

c, d and f are rational numbers

Step-by-step explanation:

$c) 3\sqrt{5}*2\sqrt{5}=3*2*\sqrt{5*5} = 3*2*5 = 30\\\\\\d) \dfrac{3\sqrt{5}}{2\sqrt{5}}= \dfrac{3}{2}\\\\\\f) \dfrac{2\sqrt{5}}{3\sqrt{5}}= \dfrac{2}{5}$

6 0

1 year ago