How to Find he Tangent Line to a Curve at a Given Point?

P(t)=20t+3660 is the formula for the moose population.

We will consider x on the graph to be years since 1990 and y on the graph to be the number of Moose.

We have two points on the graph:(0,3560) and (5,3460)

Using the slope formula, we can find the slope of this line:

m=(y2 - y1)/(x2 - x1)  

Substituting the points in the slope formula:      

m=(3560-3460)/(5-0)

m=100/5                        

m=20                            

Now that we have the slope of the line, we can use the point-slope formula to find the equation for the line:

y - y1 = m(x - x1)                              

y - 3560=-20(x-5)                            

y-3560=20x+100                  

y =20x+3660

Since the formula that is being sought is supposed to be in terms of P and t, we get:

P(t) =20t+3660

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The answer choice which correctly represents the value of cos B as required is; Choice B; Cosine B = StartFraction 40 Over 41 EndFraction.

It follows from the task content that the ratio which represents cos B is to be identified among the given answer choices.

Recall from trigonometric ratios that the cosine of an angle is the ratio of its opposite and hypothenuse.

Hence, it can be inferred that;

cos B = 80 / 82

cos B = 40 / 41.

Ultimately, the cosine of angle B following from trigonometric ratios as requested is; cos B = 40 / 41.

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If f(x) = x³ - 2x² - 5x + 6 then the factored form is (x - 1)(x + 2) and (x - 3).

A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to find factors.

Given, f(x) = x³ - 2x² - 5x + 6

We have to find the complete factored form of f(x).

Consider (x - 1) as a factor of f(x).

Let us check (x - 1) is a factor of f(x)

f(1) = (1)³ - 2(1)2 - 5(1) + 6

simplifying the above equation, we get

= 1 - 2 - 5 + 6

= 6 - 6

= 0

f(1) = 0

Therefore, (x - 1) is a factor of f(x) = x³ - 2x² - 5x + 6.

Now, find the factor of x2 - x - 6

x² - x - 6 = 0

simplifying the above equation, we get

x² - 3x + 2x - 6 = 0

x(x - 3) + 2(x - 3) = 0

(x + 2)(x - 3) = 0

Therefore, the factored form is (x - 1)(x + 2) and (x - 3).

The complete question is:

What is the factor of  f(x) = x³ - 2x² - 5x + 6?

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The sum of a number and negative three multiplied by the number is not linear.

A series of numbers called a "linear number pattern" have constant term differences. Here are a few examples: Every phrase has a 2 difference between them. These figures are additionally known as linear numbers.

A number is then represented as x, and the total is added.

sum of a number and -3 multiplied by that number

(x+-3) (or (x-3)x

distribute

a(b+c)=ab+ac

x(x-3)=x^2-3x

if the degree (power) of the placeholder equals 1 and x2 2 is not equal to 1, the placeholder is linear else it is second degree and NOT linear.

IS NOT LINEAR

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The answer are,

x=14√2

y=9.90

z=17.15

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

from the given figure,

we get.

x=14√2

y=9.90

z=17.15

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The inequality is 13 + 39x ≤ 325 and the solution is x ≤ 8

Let's call the number of people in the group "x".

The total cost of parking and admission is no more than $325, so we can write the inequality:

13 + 39x ≤ 325

Subtracting 13 from both sides:

39x ≤ 312

Dividing both sides by 39:

x ≤ 8

So the group can have no more than 8 people if they want to stay within their budget of $325 for parking and admission.

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The compound inequality represents the inequality ly - 31 - 4 ≤-3

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The volume of the rectangular box is equivalent to → V = x³ - 2x² - 8x.

Given is that the width is of the rectangular box is two feet shorter than its height while the length is two feet longer than its height.

We can assume the height {H} of the box be {x} feet's. Then its width will be -

{H} = {x} feet's

{W} = {x - 4} feet's

{L} = {x + 2} feet's

Then, we can write the volume as -

V = L x B x H

V = {x}{x + 2}{x - 4}

V = {x² + 2x}{x - 4}

V = x²{x - 4} + 2x{x - 4}

V = x³ - 4x² + 2x² - 8x

V = x³ - 2x² - 8x

Therefore, the volume of the rectangular box is equivalent to -

V = x³ - 2x² - 8x.

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The evaluation of the straight line graph of the taxi cost for the daytime taxi, are as follows;

1. The point at which the line crosses the x-axis is (0, 250)

2. The y-intercept is; c = 250

3. The distance traveled at the y-intercept is 0

4. The y-intercept represents the initial fee for the taxi

The equation of a straight line graph in the slope-internet format is;  y = m·x + c.

The graph in the question obtained from the graph in a similar question posted online, is a straight line graph

The equation of the graph is therefore of the form; y = m·x + c

Where;

m = The slope of the graph

c = The y-intercept

The points on the possible graph of the question are;

(0, 250), (0.8, 400)

The y-intercept of the graph is therefore;

(0, 250), c = 250

The slope of the graph is therefore;

(400 - 250)/(0.8 - 0) = 187.5

The equation of the graph is therefore;

y = 187.5·x + 250

1. The point the graph crosses the y-axis is the point at which the x-value is 0. Therefore, the point the graph crosses the y-axis is the point (0, 250).

2. The y-intercept of the graph, c, is the point the graph intersects the y-axis, which is the point x = 0

3. The graph of the Cost to Distance Traveled indicates that distance traveled, x at the y-intercept, where, x = 0 is 0 miles

4. The y-intercept represents the initial fee for the daytime taxi

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The area, in square inches, of the floor in the scale drawing is, 300 inches²

Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.

For example, Two spheres look similar but could have different radii.

Given that,

The rectangular floor of a classroom is 40 feet in length

And 38 feet in width

length in scale drawing  =  20 inches

The area, in square inches = ?

Scale factor  = length in scale drawing/ length of floor

length in scale drawing = 20 inches

length of floor =  40 feet = 480 inches

Scale factor  =  20/480

                      =   1/24

Dimensions in scale drawing,

length of scale drawing =   length of floor x  Scale factor

                                       =   480 x 1/24

                                       =   20 inches

Width of scale drawing =  width of floor x  Scale factor      

                                       =   30 x 12 x 1/24

                                       =    15 inches

Area of scale drawing =  20 x 15

                                     =  300 inches²

Hence, the area is 300 inches²

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Since the natural log function, ln(x), is a logarithmic function with base e, the inverse of lnx exists since logarithmic functions are one-to-one. In actuality, an exponential function with the same base is the inverse of a logarithmic function. As a result, [tex]e^x[/tex] is the inverse of function lnx.

There aren't always inverse functions for functions. An inverse function can only exist if certain requirements are met.

1. If and only if a function is a one-to-one function, it has an inverse.

2. There exists an inverse over that confined domain if a function is not one-to-one but the domain may be restricted to an interval where the function is one-to-one.

3. Logarithmic relationships are 1:1.

4. Exponential relationships are 1:1.

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Answer: z = 133

Step-by-step explanation:  From the question

126 + z = 259

Make z the subject

z = 259 - 126

z = 133

Answer:

left 4(B)

Step-by-step explanation:

When the number is (x+4) or (×-4)

The plus one moves left.

The minus one moves right.

The rowers travelled 7.5 miles upstream.

We can define relative speed as the speed of a moving body with respect to another. When two bodies move in the same direction, their relative speed is computed by their difference. But when two bodies are moving in the opposite direction, the relative speed is calculated by adding the speed of both the bodies.

Given here: The speed of the rowers in still water as 4 mph but since they are rowing upstream their relative speed will be equal to 4-3= 3 mph and while in downstream their speed is 5 mph

Now the distance they travelled on both ends of the river is equal

let they reach the upstream end in x hours and travel downstream for 4-x hours then we have

3x=(4-x )× 5

3x+5x=20

x=20/8

x=2.5 hours

Thus the distance travelled is 2.5×3=7.5 miles

Hence, The rowers travelled 7.5 miles upstream.

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The coordinates of the centre of the circle after dilating with scale factor 2 will be (0,0).

What is scalar factor?

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x= -17

y=5

——-

I had this question on a quiz and got it right

Answer:

Step-by-step explanation:

x = 4y - 3

2x +3y = 16

First, plug the equation x = 4y - 3 into the second equation so it looks like this:

2 (4y - 3) + 3y = 16    Now we only have one variable to solve for.

8y - 6 + 3y = 16    Simplify like variables

11y - 6 = 16     try to get y by itself

11y = 16 + 6

11y = 22     divide both sides by 11

y = 2

Now you can put Y back into the first equation

x = 4y - 3

x = 4(2) - 3

x = 8 - 3

x = 5

so the answer is x = 5 and y = 2

Slope is 4 and represents the rate at which the water flows into the tank in liters per minute.

The correct option is B.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

Tank has 9 liters water already

By the table

Amount of water is 17 liters in 2 minutes

But there was 9 liters of water already

So, the tank filled in 2 minutes = 17 - 9 = 8 liters

Tank filled per minute = 8/2 = 4 liters

Amount of water in the tank can be written as

y = 4x + 9

where x is number of minutes

comparing it with slope form of equation

y = m x + c

slope m = 4

Hence, 4 is the slope that represents rate of the flow of water into the tank in liters per minute.

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There are 134596 ways to distribute 24 slices between 6 people

Since pizza slices are the same hence order doesn't matter and also people are distinct so it is a case of combination.

Combination in mathematics is a way of choosing or distributing selected items from a list of the total set with distinct values. It is used when there is no repetition and order doesn't matter. It can also be depicted as permutation/r!

combination = nCr =n!/(r!(n-r!)

where n is the total number of objects

r is the number of chosen objects from the total.

Now, 24c6=24!/6!18!

=24x23x22x21x20x19x18!/6!18!

=24x23x22x21x20x19/6x5x4x3x2x1

=134596

Therefore, There are 134596 ways to distribute 24 slices between 6 people

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Five examples of polynomial are 3x, 5x + y, 2, 7x² - 3, and 8x⁵ - 2x³ + 2.

A polynomial is a mathematical expression that involves a sum of powers in one or more variables. The general form of a polynomial in one variable x is a_nx^n + a_{n-1}x^{n-1} + ... + a_2x^2 + a_1x + a_0, where n is a non-negative integer and the coefficients a_0, a_1, ..., a_n are real or complex numbers.

Here are five more examples of polynomials in one variable x:

x^4 + 2x^3 - 5x^2 + 3x - 2

x^5 - 4x^4 + 3x^2 - 2x + 1

3x^6 + x^5 - 2x^4 - 5x^3 + 7x^2 + x - 6

5x^3 - x^2 - 2x + 4

2x^7 - 3x^5 + 4x^3 - x^2 + 6x - 7

It's worth noting that polynomials can also have multiple variables, like for example a polynomial in two variables x and y.

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Answer:

Step-by-step explanation:

Momentum = mass x velocity

Elephant Momentum = 6300 x 0.11

                                    = 693 kg m/s

Dolphin momentum = 66 x 10.5

                                 = 693 kg m/s

The momentum of the dolphin and the elephant are the same.

The function [tex]$\mathbf{y}=\mathbf{0 .} 5^{\mathbf{x}-\mathbf{5}}+\mathbf{8}$[/tex] shifts the parent function 5 units right, and 8 units up.

The simplest function that nonetheless meets the criteria for a certain type of function is referred to as a parent function.

Families can be created by categorizing and arranging functions. A parent function is a fundamental equation that applies to each of these groups. The quadratic function family serves as an illustration. They all have a second degree with the highest exponent, and this family has a parabola—a U-shaped graph—in common.

The function [tex]$y=0.5^{\mathrm{x}-5}+8$[/tex] shifts the parent function 5 units right, and 8 units up.

The parent function is given as:

[tex]$$\mathrm{y}=0.5^{\mathrm{x}}$$[/tex]

Move the function right, by 5 units

[tex]$$y=0.5^{x-5}$$[/tex]

Move the function up by 8 units

[tex]$$y=0.5^{x-5}+8$$[/tex]

Therefore,the function [tex]$\mathbf{y}=\mathbf{0 .} 5^{\mathbf{x}-\mathbf{5}}+\mathbf{8}$[/tex] shifts the parent function 5 units right, and 8 units up.

The complete question is:

Use what you know about translations of functions to analyze the graph of the function f(x) = (0.5)x−5 + 8. You may wish to graph it and its parent function, y = 0.5x, on the same axes. The parent function y = 0.5x is across its domain because its base, b, is such that . The function, f, shifts the parent function 8 units . The function, f, shifts the parent function 5 units .

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The coach can use this information to help determine the uniform size for each player based on their height. For example, if a player's height is 78 inches, they would need a Size Medium uniform. If a player's height is 82 inches, they would need a Size Large uniform. This correlation between height and uniform size will make it easier for the school to purchase the correct sizes for each player and ensure that they are comfortable and properly fitted in their uniforms.

The 45 45 90 triangle theorem states that 45 45 90 special right triangles have sides of which the lengths are in a special ratio of 1 : 1 : 2 and two 45° angles and one right angle of 90°.

When two rays intersect and form a 90˚ angle or are perpendicular to each other at the intersection, they are said to form a right angle. It is the most frequently encountered angle in our daily lives. It can be noticed in room corners, box edges, mobile phone screens, and so on.

A square's and a rectangle's sides always make a right angle with each other. It is represented in radians as /2.

The angle formed by two lines that are perpendicular to each other is called a right angle. A right angle is equal to 90° and is in the shape of the letter "L". In the following figure, ray AB and BC form a right angle ABC.

Thus, The 45 45 90 triangle theorem states that 45 45 90 special right triangles have sides of which the lengths are in a special ratio of 1 : 1 : 2 and two 45° angles and one right angle of 90°.

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Answer:

In the problem, we are told that Amelie completed 56 sit-ups, and this is 7 times the number of sit-ups that Kiki completed.

We can use this information to create an equation that models the problem.

Let k represent the number of sit-ups Kiki completed.

One equation that models this problem is:

k = 56/7

Another equation that models this problem is:

56 = 7k

Both equations represent the same information, the first one is solved for k, and the second one is solved for the number of sit-ups Amelie completed.

So either k = 56/7 or 56 = 7k is the equation that models the problem.

Answer:

k=8

Step-by-step explanation:

If Amelie completed 56 sit-ups and its 7 times more you would divide

y=kx

k=56 divided by 7

k=8

k is the constant of proportionality

Answer: B. 450

Step-by-step explanation:

Eugene can type 55 words per minute, so in 30 minutes he will type 55 * 30 = 1650 words.

Allen can type 80 words in 2 minutes, so in 30 minutes he will type 80 * 15 = 1200 words.

To find out how many more words Eugene will type than Allen, we subtract Allen's total from Eugene's total:

1650 - 1200 = 450 words

So, Eugene will type 450 more words than Allen in 30 minutes. Therefore the answer is B. 450

Answer:

B. 450

Step-by-step explanation:

We can find how many words each person types by multiplying how fast they type by how long they get to type (30 minutes).

Eugene:

[tex] \frac{55 \: words}{1 \: minute} \times 30 \: minutes \: = 1650 \: words[/tex]

Allen:

[tex]\frac{80 \: words}{2 \: minutes} \times 30 \: minutes \: = 1200 \: words[/tex]

we can find how many more words Eugene types using subtraction

[tex]1650 - 1200 = 450[/tex]

Eugene types 450 more words

The axis of symmetry for f(x) = 3x^2 + 12x - 6 is x = -2. To find the axis of symmetry for a parabola, you need to find the vertex.

To find the axis of symmetry for a parabola, you need to find the vertex. The formula for the vertex is:

Vertex = (-b/2a, f(-b/2a))

where

a = the coefficient of x^2

b = the coefficient of x

In this equation,

a = 3

b = 12

So the vertex is:

(-12/2(3), f(-12/2(3)))

(-12/6, f(-12/6))

(-2, f(-2))

Therefore, the axis of symmetry is x = -2.

The axis of symmetry for f(x) = 3x^2 + 12x - 6 is x = -2.

The axis of symmetry for f(x) = 3x^2 + 12x - 6 can be found by calculating the vertex of the parabola. The formula for the vertex is (-b/2a, f(-b/2a)), where a is the coefficient of x^2, and b is the coefficient of x. In this equation, a = 3 and b = 12, so the vertex is (-12/2(3), f(-12/2(3))), or (-2, f(-2)). Therefore, the axis of symmetry is x = -2.

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Raisins cost 0. 97. Per pound Michael for $15. 25 worth of raisins, Michael thus purchased 16 pounds of raisins.

cost of raisins = 0.97

worth of raisins per pound = $15. 25

15.25 ÷ 0.97 = 16

therefore, Michael purchased 16 ponds of raisins.

'What are raisins?'

The dried grapes known as raisins are actually grapes that have been dried in the sun or in a food dehydrator. They are the shriveled yellow, brown, or purple morsels.

Raisins are frequently used in salad dressings, oatmeal, yogurt, granola, and cereal.

You might have also eaten them after baking them into scrumptious muffins, breads, and cookies. Even though they are little, raisins are incredibly energizing and full of fiber, vitamins, and minerals.

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The dilation center is at C. The scale factor is 5/12. The value of x is 5/2.

What is dilation?

Meaning of Dilation in Math. Dilation is a transformation that allows you to resize an object. Dilation is a technique for making objects larger or smaller. This transformation yields an image that is identical to the original shape. However, there is a size difference in the shape.

Given that the length of the original rectangle is 12. The length of the new rectangle is 5.

The scale factor is the ratio of the dimension of the new rectangle to the dimension of the original rectangle = 5:12 = 5/12

The width of the new rectangle is the product of the original width by the scale factor = 5/12 × 6 = 5/2

The value of x is 5/2.

The vertex of the triangles is at C.

The dilation center is at C.

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The k is not constant, so the table data does not display a proportional relationship.

What is the proportional relationship?

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.

Here, we have

Given:

x    y

4    1

5    64.125

6    216

10   1,000

A proportional relationship defines that two or more quantities vary directly with one another.

y is proportional to x if  y=kx  for all values of y and x, and k is the constant of proportionality.

for the first value on the tale

k = 1/4  =0.25

for second value

k = 64.125/5 = 12.825

Hence, the k is not constant, so the table data does not display a proportional relationship.

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