Evaluate 4*(1/4-3) + 12 324 290 268 144

Write the equation of the line that passes through the points (8,-1) and (2,-5) in standard form, given that the point-slope for

Bess [88]

The equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.

The given coordinate are (8, -1) and (2, -5).

<h3>What is the slope of an equation?</h3>

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

The slope of the equation is $m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$ .

The standard form of an equation is Ax + By = C.

The given the point-slope form is $y+1=\frac{2}{3} (x-8)$ .

Multiply each term by 3 of the equation.

$(y+1) \times3=\frac{2}{3} (x-8) \times3$

⇒3y + 3 = 2x - 16

Subtract 2x from both sides of a equation.

That is, -2x + 3y + 3 = - 16

Subtract 3 from both sides of a equation.

That is, -2x + 3y = - 19

Multiply each term by - 1 from both sides of an equation.

That is, 2x - 3y = 19

Therefore, the equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.

To learn more about the slope visit:

brainly.com/question/3605446.

#SPJ1

4 0

1 year ago

Can anybody help plzz?? 65 points

Yakvenalex [24]

Answer:

$\frac{dy}{dx} =\frac{-8}{x^2} +2$

$\frac{d^2y}{dx^2} =\frac{16}{x^3}$

Stationary Points: See below.

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Calculus

Derivative Notation dy/dx

Derivative of a Constant equals 0.

Stationary Points are where the derivative is equal to 0.

1st Derivative Test - Tells us if the function f(x) has relative max or mins. Critical Numbers occur when f'(x) = 0 or f'(x) = undef
2nd Derivative Test - Tells us the function f(x)'s concavity behavior. Possible Points of Inflection/Points of Inflection occur when f"(x) = 0 or f"(x) = undef

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Quotient Rule: $\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

Step 1: Define

$f(x)=\frac{8}{x} +2x$

Step 2: Find 1st Derivative (dy/dx)

Quotient Rule [Basic Power]: $f'(x)=\frac{0(x)-1(8)}{x^2} +2x$
Simplify: $f'(x)=\frac{-8}{x^2} +2x$
Basic Power Rule: $f'(x)=\frac{-8}{x^2} +1 \cdot 2x^{1-1}$
Simplify: $f'(x)=\frac{-8}{x^2} +2$

Step 3: 1st Derivative Test

Set 1st Derivative equal to 0: $0=\frac{-8}{x^2} +2$
Subtract 2 on both sides: $-2=\frac{-8}{x^2}$
Multiply x² on both sides: $-2x^2=-8$
Divide -2 on both sides: $x^2=4$
Square root both sides: $x= \pm 2$

Our Critical Points (stationary points for rel max/min) are -2 and 2.

Step 4: Find 2nd Derivative (d²y/dx²)

Define: $f'(x)=\frac{-8}{x^2} +2$
Quotient Rule [Basic Power]: $f''(x)=\frac{0(x^2)-2x(-8)}{(x^2)^2} +2$
Simplify: $f''(x)=\frac{16}{x^3} +2$
Basic Power Rule: $f''(x)=\frac{16}{x^3}$

Step 5: 2nd Derivative Test

Set 2nd Derivative equal to 0: $0=\frac{16}{x^3}$
Solve for x: $x = 0$

Our Possible Point of Inflection (stationary points for concavity) is 0.

Step 6: Find coordinates

Plug in the C.N and P.P.I into f(x) to find coordinate points.

x = -2

Substitute: $f(-2)=\frac{8}{-2} +2(-2)$
Divide/Multiply: $f(-2)=-4-4$
Subtract: $f(-2)=-8$

x = 2

Substitute: $f(2)=\frac{8}{2} +2(2)$
Divide/Multiply: $f(2)=4 +4$
Add: $f(2)=8$

x = 0

Substitute: $f(0)=\frac{8}{0} +2(0)$
Evaluate: $f(0)=\text{unde} \text{fined}$

Step 7: Identify Behavior

See Attachment.

Point (-2, -8) is a relative max because f'(x) changes signs from + to -.

Point (2, 8) is a relative min because f'(x) changes signs from - to +.

When x = 0, there is a concavity change because f"(x) changes signs from - to +.

3 0

2 years ago

Make Q the subject of the formula A = Q2 - 2a.

son4ous [18]

Answer:

$\huge\boxed{Q = \sqrt{A+2a}}$

Step-by-step explanation:

$A = Q^2 -2a$

Adding 2a to both sides

$Q^2 = A+2a$

Taking sqrt on both sides

$Q = \sqrt{A+2a}$

8 0

2 years ago

1/3t + 3/4 = 2/4 -t solve

olga55 [171]

Okay so I am going to summarize the work out process because its a lot to

Here we go

1/3 (t) + 3/4 - 2/4 - t = ?

1/2 (simplify )

(1/3 (T)+3/4 - 1/2 - (t) = ?

t (2) / 2

1 - 2(t) / 2 = ?

3/4 (simplify this )

1/3(t)+ 3/4 - [1 - 2(t) / 2 = ?

1/3 (this is re last one you have to simplify)

L (Denominator): 3

R (Denominator): 4

L: [L.C.M] : 4

R: [L.C.M] : 3

Basically , we just switched the dominators around

So, Therefore The of t is -3/16

T = -3/16

4 0

2 years ago

I need help ASAP , so what’s the answer

aivan3 [116]

The answer would be A.) 1

To find this answer you solve for x. Subtract 3/2 from both sides. This will give you 1/2x = 1/2^x. Then, divide by 1/2 on both sides to get x = 1.

To check this fill in x with 1. Then solve.

1/2 * 1/1 + 3/2 = 2^1
1/2 + 3/2 = 2
4/2 = 2
2 = 2

Thus making 1 the answer. Here's an image to show how I got this. I hope this helps!

6 0

2 years ago