1. Find the equation of a normal to the curve y= 2² - 2x +3 at the point (3,0)​

Answer:

-x-y=1

-x= 1+y

x= -1-y

3x+2y=0

3(-1-y) +2y=0

-3-3y+2y=0

-3-y=0

y= -3

x= -1-(-3)

x= -1+3

x= 2

Therefore, x= 2 and y= -3

The expression calculates the population x years from now will be given as y = 1024 (0.75)ˣ.

Consider the function:

y = a (1 ± r) ˣ

Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, then there is exponential growth happening by r fraction or 100r %

If there is a minus sign, then there is exponential decay happening by r fraction or 100r %

The population of sea turtles decreases by 25% per year. The population size is currently 1,024.

Let y be the population of sea turtles and x be the number of years.

Then we have

y = 1024 (1 - 0.25) ˣ

y = 1024 (0.75) ˣ

More about the exponent link is given below.

https://brainly.com/question/5497425

#SPJ1

Answer:

Whole integers

Step-by-step explanation:

0, 1, 2, 3, 4, 5... are all whole numbers, or the counting numbers. If we didn't specify "whole", then that would also include decimals, and we don't count usually with decimals.

Hope this helps!

Answer:

Step-by-step explanation:

The slope of a line is the rate of change of the line. The slope of the line is 1

The slope of a line is the rate of change of the line. The slope os calculated as:

Slope = y2-y1/x2-x1

Using the coordinate points (-1, 0) and (0, 1)

Substitute

Slope = 1-0/0-(-1)

Slope = 1/1

Slope = 1

Hence the slope of the line is 1

Learn more on slope here: https://brainly.com/question/3493733

#SPJ1

The attached graph represents the scatter plot of the points

The lists of options are not given. So, I will plot the points and upload the scatter plot as an attachment.

The points are given as:

(1,31), (2,8), (3, 38), (4, 14), (5, 22), (6, 31), (7, 27), (8, 47), (9,34), (10,3), (11, 33), (12, 35)

The above points would be plotted using the following scale:

See attachment for the scatter plot

Read more about scatter plots at:

https://brainly.com/question/6592115

#SPJ!

Answer:

10

Step-by-step explanation: The sum of 3+7 is 10

Answer:

10

Step-by-step explanation:

3+7 is 10

if you add 1 on to 7 three times, we get

8,9,10

(i know this is a troll question lol)

hope this helps!

give brainliest :)

The greatest whole possible whole number length of the unknown side is 9 inches.

Let us have:

H = biggest side of the triangle

And let we get  A and B as rest of the two sides.

Then we get:

If

[tex]A^2 + B^2 < C^2[/tex]

then the triangle is acute

Two sides of an acute triangle measure as 5 inches and 8 inches

The length of the longest side is unknown.

We have to find the length of the unknown side

WE know that the longest side of any triangle is a hypotenuse

For an acute triangle we know:

[tex]A^2 + B^2 < C^2[/tex]

Here in this sum,

a = 5 inches

b = 8 inches

c = ?

Substituting we get,

[tex]A^2 + B^2 < C^2\\\\5^2 + 8^2 < C^2\\\\25 + 64= C^2[/tex]

c < 9

Hence, The greatest whole possible whole number length of the unknown side is 9 inches.

Learn more about angles;

https://brainly.com/question/14489478

#SPJ1

Answer:

The answer is the second option

Step-by-step explanation:

Let u=x^2.

[tex]( {x}^{2} ) {}^{2} - 9( {x}^{2} ) + 8( {x}^{2} ) {}^{0} [/tex]

[tex] {u}^{2} - 9u + 8[/tex]

[tex](u - 1)(u - 8)[/tex]

[tex]u = 1[/tex]

[tex]u = 8[/tex]

Set this equal to x^2

[tex] {x}^{2} = 1[/tex]

[tex]x = 1[/tex]

or

[tex]x = - 1[/tex]

[tex] {x}^{2} = 8[/tex]

[tex]x = 2 \sqrt{2} [/tex]

or

[tex]x = - 2 \sqrt{2} [/tex]

Answer:

for a) the next three would be 36, 49 and 64

for b) the next three would be 25, 36 and 49

for c) the next three would be 13, 16, and 19

for d) the next three would be 27, 33, and 39

Step-by-step explanation:

Answers:

========================================================

Explanations:

Using translation concepts, it is found that the equation of the resulting graph is given by:

[tex]y = 2.5(\cos{(4x - 60^\circ)} - 3)[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The parent function is given by:

[tex]y = \cos{x}[/tex]

The transformations are as follows:

More can be learned about translation concepts at https://brainly.com/question/4521517

#SPJ1

The linear function which computes the total cost C (in dollars) to deliver x cubic yards of mulch is C(x) = 44x + 22

Using the slope-intercept form (y = mx +b),

The delivery charge of $22 is a constant and will represent the y-intercept.

The $44 per cubic yard of mulch will represent the slope.

Therefore,

C(x) = 44x + 22

Learn more about linear function:

https://brainly.com/question/4025726

#SPJ1

105600

Significant figures are used in scientific fields to show precision.

Multiplication

When rounding to significant figures you need to first do the operation shown. So, before we round we need to multiply 573.06 * 184.25.

This is an important step whenever you are rounding to significant figures. If you preround, you will be left with the wrong answer.

Significant Figures

Now that we have the answer before rounding, we need to know how to determine significant figures. If there is a decimal point present, then start counting significant figures at the first non-zero digit from the left.

For example:

If the decimal point is not present, then start counting significant figures from the first non-zero digit from the right.

For example:

Rounding

Finally, we can round our answer. Firstly, there are more than 4 digits before the decimal point. This means that our rounded answer will not have a decimal point, so when counting sig figs we will start from the right. Remember, even when rounding, a number should always have the same number of digits before the decimal point, even if they are not all significant.

Since we are rounding to 4 sig figs, we need to look at the 5th digit from the left, which is 8. This means we will round up.

So, write the first 4 digits of the number, but round the last one up. Then, write the remaining digits before the decimal point as 0.

Since the line is a solid line and the graph is shaded below, the required equation will be 3y-  x≤ -4

The standard equation of a line in slope intercept form is expressed as y = mx+b

Using the coordinate points (4,0) and (1, -1)

Determine the slope

Sope = -1/-3
Slope = 1/3

For the y-intercept

0 = 1/3(4) + b

b = -4/3

Substitute

y = 1/3x - 4/3

Rewrite in standard form

3y = x - 4
3y - x = -4

Since the line is a solid line and the graph is shaded below, the required equation will be 3y-  x≤ -4

Learn more on equation of a line here: https://brainly.com/question/18831322

#SPJ1

Answer:

Arrange the following number in descendig otder

Answer:

One Rectangular Pan

Step-by-step explanation:

Part C cannot be answered since the dimensions of the pool are not given.  Please check the question.

The cake pans may be compared by calculating the volume of each shape:

Rectangular pan:  Volume = Length x Width x Height

  Volume Rectangle = (13")*(9")*(2") = 234 in^3

Round pan:  Volume = [tex]\pi r^{2} h[/tex]

  Volume Round = (3.14)*(4")^2(2") = 100.5 in^3

Two round pans will hold 2*(100.5 in^3) or 201 in^3 of batter

One rectangular pan holds 234 in^3.

Go with the rectangular pan if you want more cake.

its b Answer:

Step-by-step explanation:

The cost of the apples is a function of their weight option (A) is correct because the independent variable (x) is the weight of the apples.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

The options are:

From the graph:

The y-axis is representing the cost(c) of the apples in dollars and

The x-axis is representing the weight(w) of the apples in pounds.

c = f(w)

The independent variable (w) is the weight of the apples

The dependent variable (c) is the cost of the apples

Thus, the cost of the apples is a function of their weight option (A) is correct because the independent variable (w) is the weight of the apples.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

Work Shown:

54% = 54/100 = 0.54

54% of 77 = 0.54*77 = 41.58

That rounds to 42 if your teacher wants you to round to the nearest whole minute.

Step-by-step explanation:

by using the radical and suds rule

Answer:

50cm squared

Step-by-step explanation:

Imagine the width is 'a'

Then the length will be 2a as it's twice as wide as it's long.

The formula for perimeter is 2(L+W)

If we subsitute the algebra/numbers in we get

P = 2(L+W)

30 = 2(2a+a)

30 = 2(3a)

30 = 6a

5 = a

a = 5cm

Then the area is the following

A = LW

A = 2a(a)

A = (2(5))(5)

A = 10(5)

A = 50cm squared

The angle m1 will be equal to 50°. The correct answer is option A.

The complete question is as below:-

Mr Jefferson is building a seesaw for the playground using the diagram shown. (see picture) In the diagram, the seesaw board is parallel to ground level and the triangle is an isosceles triangle.

What is m1?

A. 50º

B. 65º

C. 115º

D. 130º

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

We can find the angle using the opposite angles theorem.  When two are lines are crossed, there are four angles formed between them, and the opposite angles will be always equal.

Now, since the seesaw board is parallel to the ground, we can deduct (applying the opposite angles theorem) that both angles formed at the base of the triangle are equal to 65°.

Also, we must remember that the sum of the three interior angles of a triangle will be always equal to 180°, so:

m1 = 180 - ( 65 + 65 0

m1 = 50°

Therefore the angle m1 will be equal to 50°. The correct answer is option A.

To know more about Trigonometry follow

https://brainly.com/question/24349828

#SPJ1

Answer:

-0.33333 (3 is repeating )

Step-by-step explanation:

Answer:

  W = k·n^(-1/2)

Step-by-step explanation:

When two quantities are proportional, their relationship can be described by the linear equation y = kx, where k is the constant of proportionality.

Saying two quantities are inversely proportional is the same as saying one is proportional to the inverse of the other. Then "inversely proportional to the square root" is the same as "proportional to the inverse of the square root."

__

W is inversely proportional to the square root of n, so we have ...

  [tex]W=k\cdot\dfrac{1}{\sqrt{n}} = \dfrac{k}{n^{\frac{1}{2}}}\\\\\boxed{W=kn^{-\frac{1}{2}}}[/tex]

_____

Additional comment

The rules of exponents let us write the square root as a fractional power, and the inverse as a negative power. Thus our power function ends up with a negative fractional power.

The Power function representing the verbal statement is W = k.[tex]n^{1/2}[/tex].

A power function is in the form of f(x) = kxⁿ, where k = all real numbers and n = all real numbers. You can change the way the graph of a power function looks by changing the values of k and n.

When two quantities are proportional, their relationship can be described by the linear equation y = kx, where k is the constant of proportionality.

Now "inversely proportional to the square root" is the same as "proportional to the inverse of the square root."

According to question,

       W α 1/√n

      W = k/√n

      W = k.[tex]n^{-1/2}[/tex]

Thus, the Power function representing the verbal statement is W = k

Learn more about Power function from:

https://brainly.com/question/12431044

#SPJ1

From the image that we have here, the translation of the image would be:

In the field of mathematics, this is the type of transformation which would take points in an image and move it in similar distance and direction.

It has to do with the movement of points in an horizontal manner or in a vertical manner.

Read more on transformation of graphs  here:

brainly.com/question/4002639

#SPJ1

The equation represents a line that passes through(4, 1/3) and has a slope of 3/4 option A; y - 1/3 = 3/4 ( x - 4).

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

we know that            

The equation of the line into point-slope form is equal to                        

y-y₁ = m(x-x₁)

we have          

(x₁, y₁) = (4, 1/3)

m = 3/4

substitute the given values                

y-y₁ = m(x-x₁)

y - 1/3 = 3/4 ( x - 4)

therefore,

y minus StartFraction one-third EndFraction equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus 4 right-parenthesis.(x – 4)

Thus, option A is correct.

Learn more about slope;

https://brainly.com/question/13458632

#SPJ1

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{4}v^2\stackrel{\stackrel{b}{\downarrow }}{-16}v\stackrel{\stackrel{c}{\downarrow }}{+7}=0 \qquad \qquad v= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ v= \cfrac{ - (-16) \pm \sqrt { (-16)^2 -4(4)(7)}}{2(4)} \implies v= \cfrac{ 16 \pm \sqrt { 256 -112}}{ 8 } \\\\\\ v=\cfrac{16\pm\sqrt{144}}{8}\implies v=\cfrac{16\pm 12}{8}\implies v= \begin{cases} \frac{7}{2}\\[1em] \frac{1}{2} \end{cases}[/tex]

Answer:

Answer:

b

Step-by-step explanation:

ig becuase the line goes through 0,0 so it starts from negative