Find the slope of each of the following functions at the given points. f(x)=x²; (-3,9)​

(Please mark brainliest <3)

Correct option is D.

We have been given a complex number 3-3i we have to convert it in the polar form:

Polar form of a complex number: z=r(cosθ+isinθ)

Where, r=√x^2+ y^2

the general form of complex number is:

x+iy

•Here, x=3 and y=-3

•Hence, r=√3^2+(-3)^2}= √18

•And θ=tan −1 y/x

•θ=tan −1 -3/3

•θ=tan −1 (−1)

•θ=2π− π/4

•θ= 7π/4

•Hence, substituting all the values in polar form formula we get:

z= √18cos( 7π/4) + isin (7π/4)

The area bounded by y = x² + 5 and the x-axis from x = 3 to x = -2 is 110/3.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

y = x² + 5

The area bounded by y = x² + 5 from x = -2 to x = 3.

= [tex]\int\limits^{3}_{-2} {(x^2 + 5)} \, dx[/tex]

= [tex][x^3/3]^{3}_{-2}[/tex] + 5 [tex][x]^{3}_{-2}[/tex]

= 1/3 [tex][(3)^3 - (-2)^3][/tex] + 5 [3 + 2]

= 1/3 [27 + 8] + 5 x 5

= 1/3 x 35 + 25

= 35/3 + 25

= (35 + 75)/3

= 110/3

Thus,

The area bounded is 110/3.

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Answer:

5 :16

Step-by-step explanation:

35:112     <===== divide both by '7 ' to get   5/16

The numbers are  23,15,30 if the sum of three numbers is 68.

When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions. For instance, an equation is defined as having one or more variables in French.

Determine which values of the variables result in the equality to be true in order to solve an equation with variables. The values of the variables that must fulfill the equality to constitute the answer are known as the unknowns, together with the variables for which the equation must be solved.

Let the first number be x

The second number is 8 Less than the x is x-8

The third number is 2 times the second is 2(x-8)

Sum of the three numbers is 68

x+x-8+2(x-8)=68

4x-24=68

4x=92

X=23

Therefore, the numbers are 23,15,30

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Answer:

Step-by-step explanation:

The speed rate at which the aircraft is gaining altitude is;

dx/dt = 250 miles per hour

Since the aircraft is climbing at 30° to the horizontal. it means there will be a vertical component which will be the altitude and also a horizontal component which will be the horizontal distance covered. while the hypotenuse will be how far it has climbed.

Let us call the vertical component x and the hypotenuse component z.

Thus, from trigonometric ratios, we can say that;

sin 30 = x/z

We are looking for how fast the aircraft is gaining altitude. Thus, using Liebniz notation, we can say this rate is; dx/dt. Thus;

sin 30 = (dx/dt)/(dz/dt)

0.5 = (dx/dt)/(dz/dt)

0.5 × (dz/dt) = dx/dt

Its' speed is 500 mph. This means dz/dt = 500

Thus;

dx/dt = 0.5 × 500

dx/dt = 250 mph

Hence, the speed rate at which the aircraft is gaining altitude is;

dx/dt = 250 miles per hour

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Answer:

a) TPR

b) NM

c) x=6

Step-by-step explanation:

a) since the angle K is the middle letter on in the first triangle, the second triangle's middle letter will be P since they correspond

b) TR is congruent to NM because if you flipped TR upside down, it would match directly with NM

c) 4x-3=21

4x=24

x=6

this is because TR and NM are congruent, so 4x-3 is equal to 21

Rates, however, differ for specific customers depending on their credit score, loan term, and other factors.

In conclusion, the finance charge formula is as follows:

Finance fee = Balance that is owed. Annual Percentage Rate (APR) / 365 Days in Billing Cycle.

The average cost of an ATV is between $5,000 and $15,000, with a down payment that is often between 10% and 20%.The typical deposit for recreational vehicles is in the range of 10% to 20%. You might need between $500 and $5,000 for the down payment for a UTV that ranges in price from $5,000 to $25,000.

Conventional ATV loans are provided by banks and credit unions for set terms that are typically between three and six years long. The yearly percentage rates are also fixed. Your credit score, the loan period, the cost of the ATV, and the company funding the loan will all have an impact on the APR.

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Answer:

Step-by-step explanation:

A.) either terminates in 0's or repeats.

Some decimals repeat and some decimals don't.

If Investors buy a studio apartment for the amount of 240,000.

a. The percent of the purchase price is 25%.

b. The percent of the purchase price is 5%.

a. Percent of purchase price

Using this formula to find the percentage of purchase price

Percent of purchase price = Down payment / Selling price

Percent of purchase price = $60,000/$240,000

Percent of purchase price =  0.25 × 100

Percent of purchase price = 25%

b. Percent of purchase price

Percent of purchase price =  Down payment /Selling price

Percent of purchase price =  $12,000/$240,000

Percent of purchase price =  0.05 ×100

Percent of purchase price = 5%

Therefore the  percent of the purchase price is 25%, 5%.

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Answer:

30.6

Step-by-step explanation:

18/4 = 4.5

4.5 × 6.8 = 30.6

Placing a point at the graph's y-intercept offor the equation (0,-5).

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The correct application of the quotient rule is  f'(x) = [(3x - 2)2x - (x²+5)(3)]/[(3x - 2)]²

The derivative of a function f'(x) is the rate of change of the function with respect to a variable.

Since we have f(x) = (x²+5)/(3x-2), to find its derivative f'(x), we use the quotient rule.

Given a function f(x) = u(x)/v(x) then the derivative of f(x) which is f'(x) = [v(x)du(x)/dx - u(x)dv(x)/dx]/[v(x)]²

So, with f(x) = (x²+5)/(3x-2)

u(x) = (x²+5) and v(x) = (3x-2)

So, du(x)/dx = d(x²+5)/dx

= d(x²+5)/d(x²+5) × d(x²+5)/dx

= 2x

and

dv(x)/dx = d(3x - 2)/dx

= d3x/dx - d2dx

= 3 - 0

= 3

Since  f'(x) = [v(x)du(x)/dx - u(x)dv(x)/dx]/[v(x)]², substituting the values of the variables into the equation, we have that

f'(x) = [v(x)du(x)/dx - u(x)dv(x)/dx]/[v(x)]²

f'(x) = [(3x - 2)2x - (x²+5)(3)]/[(3x - 2)]²

So, the quotient rule is  f'(x) = [(3x - 2)2x - (x²+5)(3)]/[(3x - 2)]²

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Answer:

length is 4 units

width is 2 units

Perimeter is 12 units

Area is 8 sq units

Step-by-step explanation:

Since you have a graph of the points, you can see the shape is a rectangle. Count to find the measure of the length and width.

Perimeter is the distance all the way around the shape.

length + width + length + width

Or 2(length)+2(width)

= 2 + 4 + 2 + 4

= 12

Area is

length × width

= 4 × 2

= 8 sq units.

The rate of growth in the exponential function is 1.98%

An exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

To solve this problem, we have to model the growth in an exponential function.

Population in 1997 = 2.12 million

Population in 2006 = 2.53 million

Time = 9

Since this is an exponential growth function, we can write this as;

2.53 = 2.12(1 + r)⁹

where r = rate of growth

2.53 = 2.12(1 + r)⁹

r = 0.0198

r = 1.98%

The rate of growth is 1.98%

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The minimum number of people that would need to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year is Three (3).

To find the number of people that would need to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year, we need to consider the number of possible birthdays that exist within the given age range (18 to 24 inclusive).

There are 12 months in a year, and each month has between 28 and 31 days (depending on the month). Therefore, there are a total of 12 * 31 = 372 possible birthdays within a given year.

There are 7 possible birth years within the given age range (18 to 24 inclusive), which means there are a total of 7 * 372 = 2596 possible birthdays within the given age range.

Since we want to guarantee that at least three people share the same birthday, we need at least 3 people to be at the party.

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Complete Question:

Assume that there is a party consisting of people between the ages of 18 and 24 inclusive. How many people would have to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year? Note: assume the range of birth years include 2 leap years.

Answer:

Step-by-step explanation:

m = slope

m =  (-7 -3 ) / (4 -(-1)

m = -10 / 5

m = -2

ask, if you want to understand  how I got that.  :)

The points is a solution for this inequality is (0, -3).

What is inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Switch sides

[tex]\frac{2}{3} x+1 \geq y$$[/tex]

Move 1 to the right side

[tex]\frac{2}{3} x \geq y-1$$[/tex]

Multiply both sides by 3

[tex]3 \cdot \frac{2}{3} x \geq 3 y-3 \cdot 1$$[/tex]

Simplify

[tex]2 x \geq 3 y-3$$[/tex]

Divide both sides by 2

[tex]\frac{2 x}{2} \geq \frac{3 y}{2}-\frac{3}{2}$$[/tex]

Simplify

[tex]x \geq \frac{3 y-3}{2}$$[/tex]

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Answer:

X = -2 - 2(square root)3 or x = -2 + 2 (square root )3

Step-by-step explanation:

Answer:

5/12 phone uses less storage space

Step-by-step explanation:

Find a common denominator so you can compare the fractions easily.  Use 12.

1/2 = 6/12

5/12 < 6/12, so now you can see that the phone that uses 5/12 of storage space uses less than the one that uses 1/2

The time left before the fossil fuel reserves run out is 2000years(1significant figure)

A rate is a special ratio in which the two terms are in different units. For example, if a 14-ounce can of corn costs 69¢, the rate is 69¢ for 14 ounces. Rate can also be defined as the ratio of two unlike units.

The total metric tonnes of fossil fuel on earth is 2.1×10⁸.

The rate of usage is 1×10⁵ metric tone of fossil fuel per year

as been said rate = total metric tone of fuel/ number of years to use

1×10⁵= 2.1×10⁸/no of years

no of years = 2.1×10⁸/1×10⁵

no of years = 2.1×10³years= 2100years

to 1 significant figure = 2000years

therefore the number of years for the fossil fuel to run out is 2000years

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Answer:

Step-by-step explanation:

To graph the equation y-2=2/3(x+4), you can follow these steps:

Begin by isolating the y term on one side of the equation. To do this, you can add 2 to both sides of the equation:

y-2+2=2/3(x+4)+2

y=2/3(x+4)+2

Next, you can simplify the right side of the equation by multiplying 2/3 by (x+4):

y=2/3(x+4)+2

y=(2/3)x+(2/3)4+2

y=(2/3)x+8/3+2

y=(2/3)x+14/3

This is the standard form of the equation y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is m=2/3 and the y-intercept is b=14/3.

To graph the equation, you can use the slope and y-intercept to plot the first point on the graph. The y-intercept is the point where the graph crosses the y-axis, so you can plot the point (0,14/3) on the graph.

From this point, you can use the slope to find the next point on the graph. The slope is the change in y over the change in x, so you can use the slope to find the change in y and the change in x between two points on the graph. For example, you could choose a point that is 1 unit to the right of the y-intercept, or (1,0). The change in y between these two points is (14/3)-0=14/3 and the change in x is 1-0=1. Using the slope, you can find the y-coordinate of the next point on the graph:

y2=y1+m(x2-x1)

y2=14/3+2/3(1-0)

y2=14/3+2/3

y2=20/3

You can repeat this process to plot additional points on the graph. For example, you could choose a point that is 2 units to the right of the y-intercept

The differentiable function f with the given properties is [tex]f(x)=4x^3-3x^2+10[/tex].

What is a differentiable function:

A function with a differentiable value of one real variable is one whose domain contains a derivative. In other words, each interior point in the domain of a differentiable function's graph has a non-vertical tangent line.

The given properties for the differentiable function f are:

[tex](i) f'(x)=ax^2+bx\\ (ii) f'(1)=6, f''(1)=18\\ (iii) \int\limits^2_1 {f(x)} \, dx =18[/tex]

From (i) we can get [tex]f''(x)=2ax+b[/tex]

By substituting (ii) in (i) we will get:

a+b=6 and 2a+b=18. By solving these two equations we will get the following:

a=12, b=-6.

We will integrate (i) on both sides, we will get:

[tex]f(x)=\frac{ax^3}{3} +\frac{bx^2}{2} +c[/tex] where c is the integration constant.

In this equation, we will substitute a,b.

[tex]f(x)=\frac{12x^3}{3} +\frac{-6x^2}{2} +c\\ \\ f(x)= 4x^3-3x^2+c[/tex]...................(iv)

Now we will substitute (iv) in (iii), and we will get:

[tex]\int\limits^2_1 {( 4x^3-3x^2+c)} \, dx =18\\ \\ (2^4-2^3+2c)-(1^4-1^3+c)=18\\ \\c=10[/tex]

Therefore [tex]f(x)=4x^3-3x^2+10[/tex].

Complete question:

Let f be a differentiable function, defined for all real numbers x, with the following properties. Find f(x). Show your work.

[tex](i) f'(x)=ax^2+bx\\ (ii) f'(1)=6, f''(1)=18\\ (iii) \int\limits^2_1 {f(x)} \, dx =18[/tex]

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a. Constant speed, C =  0. 19 miles/minutes

b. The fraction representing her constant speed is  1/x miles/minutes

c. The time it takes her to drive exactly 1 mile is 5. 38 minutes

The formula for calculating constant speed is expressed as;

Constant speed = total distance covered/ total time taken

From the information given, we have that;

Now, substitute the values into the formula

Constant speed = 1. 3 / 7

Divide the values

Constant speed = 0. 19 miles/minutes

When distance 1 mile, time taken = x minutes

Constant speed = 1/x miles/minutes

If 1. 3 miles = 7 minutes

Then, 1 mile = x

cross multiply

x = 7/1. 3

x = 5. 38 minutes

Hence, the constant speed is 0. 19 miles/minutes

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Answer:

Step-by-step explanation:

since you are rotating the image it shows y k j and l so it would be 5.5

whats the question im getting off camera blind explain it to me

Graph ii shows that 150 people preferred eating ice cream from a cone, while 60 people preferred eating ice cream from a cup. There was no association between age and preferred method of eating ice cream.

Graph ii is a table that shows the distribution of responses to the survey about preferred method of eating ice cream. The table shows that out of the 210 people surveyed, 70 were adults and 140 were children. Of the 210 people surveyed, 150 indicated the cone as the preferred method of eating ice cream, while 60 indicated the cup as the preferred method. This table indicates that there is no association between age and preferred method of eating ice cream, as the responses were evenly distributed between adults and children. This information can be used to determine the preferences of customers at the ice-cream store and can help inform decisions about how to serve the ice cream. For example, the store may choose to provide more cones than cups based on the survey results. Additionally, this table can be used to compare the preferences of different demographic groups, although in this case the survey showed that there was no association between age and preferred method of eating ice cream.

Adults: 70 people surveyed, 35 preferred cone, 35 preferred cup

Children: 140 people surveyed, 115 preferred cone, 25 preferred cup

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The "winning" guess when  played this game has been around 18.

The quality of being guided by or based on reasons is referred to as rationality. In this sense, a belief is rational if it is based on strong evidence, and an individual acts rationally if they have a good reason for doing so. This quality can be applied to a skill, like reasoning in a rational animal, a psychological process, like reasoning, mental states, like beliefs and intentions, or people who have these other kinds of rationality. If something does not meet the standards of rational evaluation, it is either irrational or rational, depending on where it falls outside the realm of rational evaluation.

Given you have to choose a number between 0 and 100. the winner of the game is the person whose number is closest to 2/3 times the average of all chosen numbers,

Theoretically,  concur that the answer is 0. As stated, this is due to widespread rationality knowledge. You should guess 2/3*50=33 if everyone chose equally between 0 and 100. The average would be 50. Everyone ought to guess 33 if they are all aware of this. However, if I know that everyone correctly predicted 33, then 33 is the average, and should seek 2/3*33=22. This logic continues until everyone should correctly guess 0.

People actually don't think this way, but I disagree that you should guess between 5 and 10, which I believe is too low. depending on who you play with, as a group of game theorists might get a lower average than a group of people from the average population.) In a real-world setting, you need to consider how many iterations the others will make. You should guess 22 if you think they will only do one, which would result in everyone guessing 33. If you assume that they iterate the reasoning twice on average and guess 22, you should estimate 15 and so on.

The "winning" guess when  played this game has been around 18.

Hence the guess should be 18.

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the complete question is,

Several people choose an integer between 0 and 100. The winner is the person whose integer is closest to 2/3 of the average of the numbers reported by all seven participants. What value would you choose?

The domain and range of the function will be Real number and [0, ∞). The parent function f(x) is get shifted down by 2 units.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

If the vertex of the absolute function is at (h, k). Then the absolute function is given as

f(x) = |x - h| + k

The function is given below.

g(x) = |x + 3|

The graph of the function g(x) is given below. From the graph, the domain and range of the function will be Real number and [0, ∞).

The parent function and translated function are given below.

f(x) |x| and h(x) = |x| - 2

The parent function f(x) is get shifted down by 2 units.

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Here is the step by step x

The equivalent expression to 24x^2 +56x is : 8x(3x+7)

Given data :

= 24[tex]x^{2}[/tex] + 56

= 24 xx + 56

Rewrite 24 as 8 * 3

Rewrite 56 as 8 * 7

= 8 * 3xx + 8 * 7x

= 8x (3x+7)

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