What is the slope of the line passing through the points (1, -5) and (4, 1)?
O-2
O 2
O-


Help please

By "limit definition", I assume you mean the derivative. We have

[tex]f'(c) = \displaystyle\lim_{x\to c}\frac{f(x)-f(c)}{x-c}[/tex]

For [tex]f(x)=\frac1{x-1}[/tex] and c = 2, we have

[tex]f'(2)=\displaystyle\lim_{x\to2}\frac{\frac1{x-1}-1}{x-2}[/tex]

[tex]f'(2)=\displaystyle\lim_{x\to2}\frac{\frac{1-(x-1)}{x-1}}{x-2}[/tex]

[tex]f'(2)=\displaystyle\lim_{x\to2}\frac{2-x}{(x-1)(x-2)}[/tex]

[tex]f'(2)=\displaystyle\lim_{x\to2}\frac1{1-x}=-1[/tex]

The tangent line to (2, 1) has slope -1. Using the point-slope formula, it has equation

y - 1 = - (x - 2)

y = - x + 3

Answer:

f(x) is always 5.

Step-by-step explanation:

The formula has a fixed value. Y is the f(x) in the function, and since there is no X, then Y is as said: 5. For example, when X is -7, the f(x), or Y, is still 5, and so on.

Answer:

The coordinate of the point 3/10 of the way from A to B = (0.5, -4.4)

Step-by-step explanation:

to calculate the point 3/10 of the way from A to B, let us first find the difference in the coordinates of the point

Change in x coordinate: x₁ = -3,  x₂ = 11

= x₂ - x₁ = 11 - (-4) = 11 + 4 = 15

3/10 of 15 = 0.3 × 15 = 4.5

This means that the point on the x axis is 4.5 points away from x₁

= -4 + 4.5 = 0.5

Change y coordinate: y₁ = -8,   y₂ = 4

= y₂ - y₁ = 4 - (-8) = 4 + 8 = 12

3/10 of 12 = 0.3 × 12 = 3.6

This means that the point on the y axis is 3.6 points away from y₁

= -8 + 3.6 = -4.4

Therefore the coordinate of the point 3/10 of the way from A to B = (0.5, -4.4)

Answer:

3x+3

Step-by-step explanation:

The given expression is "The first integer plus the next consecutive integer plus the next consecutive integer."

Let the first integer is x.

Next consecutive integer of x = x+1

Other next consecutive integer of x+1 = x+1+1=x+2

ATQ,

The expression is :

=x+x+1+x+1+1

=3x+3

Answer:

32

Step-by-step explanation:

to get the area of a parallelogram you just do base times height

Answer:

Step-by-step explanation: the first time you get 0.75 and the second time you get 0.125 hope this helped

<A + <B + <C = 180 degrees

<A + 72 + x    = 180 degrees

<A + x =  180 - 72

<A = 108 degrees.

x = 180 - 108

x = 72

Answer:

Option A. is correct

Step-by-step explanation:

Like terms are those terms that have same variables of same powers. Terms that are not like terms are said to be unlike terms.

For example [tex]2x^3,7x^3[/tex] are like terms and [tex]5x^2,9x^5[/tex] are unlike terms.

Given polynomial is [tex]3x^3+x^2-8x^5+2x^3-4x[/tex]

Like terms need to be combined to write the polynomial in standard form

Here, like terms are [tex]3x^3,2x^3[/tex]

Option A. is correct.

Answer:

The next three terms are 55,89 and 144

Step-by-step explanation:

We want to predict the next three numbers in the pattern

3, 5, 8 , 13 , 21 , 34

The difference between two successive terms is written between them.

Thus, we have

3 2 5 3 8 5 13 8 21 13 34

So the rule here is to add the next term to the previous so as to get the next coming term

Thus, we have;

34 + 21 = 55

55 + 34 = 89

89 + 55 = 144

Answer:

The surface area of the log including the ends and the inside is 80424.8 cm²

Step-by-step explanation:

To determine the surface area of the log with hollow center including the ends and the inside, we will find the surface area of the outer part of the log, surface area of the inner part of the log and the surface area of the two ends; and then sum everything up.

From the question,

Diameter of log = 60 cm

Length of log = 3 m = 300 cm

Diameter of hollow center = 20 cm

For the surface area of the outer part,

Area of the outer part = Circumference of the outer part × length

Circumference = 2πr = πd

∴ Area of the outer part = πd × l

(NOTE: d here is the diameter of the log)

d = 60 cm and l = 300 cm

Area of the outer part = 60π × 300 = 18000π cm²

For the surface area of the inner part,

Area of the inner part = Circumference of the inner part × length = πd × l

(NOTE: d here is the diameter of the hollow center)

d = 20 cm and l = 300 cm

Area of the inner part = 20π × 300 = 6000π cm²

For the surface area of one end

This is the difference between the area of the outer end and the area of the inner end

Here, we can determine the area by using

Area = πr², where r is the radius

Radius = Diameter / 2

Radius of outer end (R) = Diameter of log / 2 = 60cm / 2 = 30cm

Radius of inner end (r) = Diameter of hollow center / 2 = 20cm / 2 = 10 cm

∴ Surface area of one end = πR² - πr² = π(R²-r²)

= π (30²-10²)

= π (900 - 100)

= 800π cm²

This is the area of one end

For the two ends,

Area of the two ends = 2 × 800π cm² = 1600π cm²

Hence, the surface area of the log is 18000π cm² + 6000π cm² + 1600π cm²

Surface area of the log = 25600π cm²

Putting the value of π (π = 3.141592654)

Surface area of the log = 25600 × 3.141592654 cm²

Surface area of the log = 80424.77193 cm²

Surface area of the log = 80424.8 cm²

Hence, the surface area of the log including the ends and the inside is 80424.8 cm² (to one decimal place)

Answer:

The answer is below

Step-by-step explanation:

The electrical resistance R of a wire varies inversely with the square of its diameter d:

R ∝ 1 / d

Let k represent the constant of proportionality, hence we can represent the statement as an equation:

[tex]R=\frac{k}{d^2}\\ \\when\ R=0.5 \Omega,d=2\ mm\\\\0.5=\frac{k}{2^2} \\\\k=2\\\\The\ equation\ becomes :\\\\R=\frac{2}{d^2}\\ \\When\ d=3, we\ find\ R\\\\R=\frac{2}{3^2} \\\\R=0.22\ \Omega[/tex]

Answer:

Step-by-step explanation:

Thank you ☺️☺️☺️

Answer:

4.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the question attached.

Given the zero of the polynomial 5+3i and 0, this means that (x-0) and (x-(5+3i)) are factors

Multiplying the factors together we have;

= x((x-(5+3i))

= x(x-5-3i)

= x²-5x-3xi

Hence the polynomial expression of the zeros is x²-5x-3xi

Answer:

The answer is 8

Step-by-step explanation:

Because 4x12 is 48 and so is 6x8

Answer:

C. 8

Step-by-step explanation:

4 ⋅ 12 = 6n (6 ⋅ n is the same as 6n)

Multiply 4 ⋅ 12.

48 = 6n

Divide both sides by 6

n = 8

Hope I helped :)

Please consider Brainliest :)

Answer:

5x-y +42=0

Step-by-step explanation:

Using m=Y2- Y1

X2- X1

the slope of the line is found .

Put your answer in Y - Y1 = m( X - X1)

to get the equation

Answer:

$18234

Step-by-step explanation:

Answer:

i think it's the second one

Step-by-step explanation:

i am not sure if it is correct or not. i hope it helps!

Answer:

Y=2x+5

Step-by-step explanation:

Hope this helps

Answer:

(7.13 × 10^-3) x 40 = 285.2 x 10^-3 = 2.9 x 10^-1

Step-by-step explanation:

I  think this is the answer i hope if it right or not but aleast I try on it .

Answer:

1. d

2. b

3. a

Step-by-step explanation:

1. d => "my graph is non-proportional with a negative y-intercept."

Rationale: it is non-proportional because it does not pass through the point of origin, (0, 0). And also, the line intercepts the y-axis at a point where the value of y is below the point of origin, 0. That gives us a negative y-intercept value.

2. b => "My graph is proportional with a negative slope."

Rationale: it is proportional because the straight line cuts through the point of origin, (0, 0). And also, the line slants downward from left to the right, thus, such downward slope gives us a negative slope value.

3. a => "My graph is non-proportional with a positive slope".

Rationale: it is does not cut across the point of origin, and also the slope slants upward from left to the right. Therefore, it is a non-proportional graph with a positive slope.

Answer:

A) You climbed 15 feet up a tree before coming back down 15 feet

Answer:

Step-by-step explanation:

sea level means negative so it have to be C -0.5 foot

problem solved

Answer:

3^7

Step-by-step explanation:

27 = 3^3

81 = 3^4

3+4 = 7

Answer:

D. 58

Step-by-step explanation:

pretty easy clap

bisecting is midpoint which makes the two angles congruent

Answer:

D. 37/2 divided by 17/4

Step-by-step explanation:

Answer:

D) 37/2 / 17/4

Step-by-step explanation:

Change 18 1/2 and 4 1/4 into improper fractions.

18 1/2 = 37/2

4 1/4 = 17/4

So the answer is 37/2 / 17/4.

Please correct me if I am wrong, have a great day! :)

Answer:

the answer is a line segment :)