Find the derivative using the first principles. ​

Answer:

just tell me when you find the answer

In this specific case, the initial term (a) is 5 and the common ratio (r) is -2

Henceforth, after determining what a and r are, we use the formula for the nth term. Which is:

[tex]a_n = a \times r^{n-1} [/tex]

Therefore, the 14th term is :

[tex]\implies 5 \times { (- 2)}^{14 - 1} \\\implies 5 \times {( - 2)}^{13} \\ =\boxed { -40,960} [/tex]

Hope it helps!

Answer:

see explanation

Step-by-step explanation:

using the rules of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex]

Then

(a)

[tex]5^{4}[/tex] × [tex]5^{5}[/tex] = [tex]5^{(4+5)}[/tex] = [tex]5^{9}[/tex]

(b)

[tex]2^{7}[/tex] × 2 = [tex]2^{(7+1)}[/tex] = [tex]2^{8}[/tex]

(c)

[tex]6^{5}[/tex] ÷ 6² = [tex]6^{(5-2)}[/tex] = 6³

(d)

[tex]9^{7}[/tex] ÷ [tex]9^{6}[/tex] = [tex]9^{(7-6)}[/tex] = [tex]9^{1}[/tex] = 9

------------------------------------------------

(a)

3² × [tex]3^{4}[/tex] = [tex]3^{(2+4)}[/tex] = [tex]3^{6}[/tex]

(b)

[tex]5^{7}[/tex] × 5³ = [tex]5^{(7+3)}[/tex] = [tex]5^{10}[/tex]

(c)

[tex]6^{7}[/tex] ÷ 6² = [tex]6^{(7-2)}[/tex] = [tex]6^{5}[/tex]

(d)

[tex]9^{4}[/tex] ÷ 9³ = [tex]9^{(4-3)}[/tex] = [tex]9^{1}[/tex] = 9

The total area of the given composite figure is; 84.8 ft²

We are given;

Area of triangle = 5.6 ft²

Thus, area of 2 triangles = 2 * 5.6 = 11.2 ft²

Area of rectangles = 2(3.6 * 2) + 2(2 * 4) + 3(4 * 3.6)

Area of rectangles = 14.4 + 16 + 43.2

Area of rectangles = 73.6 ft²

Total Area of composite figure = 73.6 ft² + 11.2 ft²

Total Area of composite figure = 84.8 ft²

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The correct numbers to get to the media or mean are 10, 33, 3, and 2.

The media is obtained by organizing the values given and selecting the one that is in the middle; while the mean is obtained by adding all values and dividing the total by the number of values.

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Answer:

300+(300 + 0.23x)

Step-by-step explanation:

I'm not sure what you are asking but this is the only equation I can get

If these two numbers F(51) and F(52) are added together. Then the number of results will be 53,316,291,173.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Two large numbers of the Fibonacci are given below.

F(51) = 20,365,011,074 and F(52) = 32,951,280,099.

The sum of the F(51) and F(52) will be

     20, 365, 011, 074

  + 32, 951, 280, 099

      53, 316, 291, 173

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Answer:

2.9 meters.

Step-by-step explanation:

First we multiply the length, 3.8, by the width, 1.5, to get the base, 5.7 (this step is not entirely necessary, but makes it much easier).  Then we divide the volume, 16.53, by the base, 5.7, to get the height, 2.9 meters.

Answer:

i think its 21.83 i may be wrong but im pretty sure its 21.83

Step-by-step explanation:

Answer:

x = 5±2√7

Step-by-step explanation:

This quadratic cannot be factorised via the factorisation method, so we use the quadratic formula :

x = [tex]\frac{-b + \sqrt{b^{2} -4ac} }{2a}[/tex] or x = [tex]\frac{-b - \sqrt{b^{2} -4ac} }{2a}[/tex]

(The reason I did 2 equations is because brainliest does not allow me to do the ± in the equation insert thing )

x = [tex]\frac{-(-10) + \sqrt{-10^{2} -4(1)(-3)} }{2(1)}[/tex] or x = [tex]\frac{-(-10) - \sqrt{-10^{2} -4(1)(-3)} }{2(1)}[/tex]

x = [tex]\frac{10 + \sqrt{100+12} }{2}[/tex] or x= [tex]\frac{10 - \sqrt{100+12} }{2}[/tex]

x = [tex]\frac{10 + {4\sqrt{7}} }{2}[/tex] or x = [tex]\frac{10 - {4\sqrt{7}} }{2}[/tex]

x = [tex]5+2\sqrt{7}[/tex] or x = [tex]5 -2\sqrt{7}[/tex]

Hope this helped and brainliest please

Answer:

8%

Step-by-step explanation:

Divide ( 32.40 / 30 ). This outputs the answer 1.08, or 108%. This means that the outcome is 108% of the original, or 8% greater.

The simple interest in which Casho invests money was 8%.

Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, p = 30, SI = (32.40 - 30) = $2.40 and t = 1.

Therefore, 2.40 = (30×r×1)/100.

240 = 30r.

r = 240/30.

r = 24/3.

r = 8.

So, The rate of simple interest is 8%.

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The expression of time in terms of r is T = 85/9r. If he walked at an average speed of 3 miles per hour. Then the time taken by nick to reach the shopping mall will be 3 hours and 60 minutes.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

Nick walked 5 miles to reach his aunt's house.

From there he traveled 8 miles to the shopping mall on a bicycle.

He traveled 80% faster on the bicycle than on foot.

Let r represent his rate of walking in miles per hour. Then the 1.8r will be the rate of cycling in miles per hour.

Then the number of hours nick took to reach the shopping mall in terms of r will be

T = t₁ + t₂

Where t₁ is the time taken to reach his aunt's house and t₂ is the time taken to reach the shopping mall from his aunt's house. Then we have

T = 5 / r + 8 / 1.8r

T = 1/r (5 + 8/1.8)

T = 85/9r

If r is 3 miles per hour, then the time taken by nick to reach the shopping mall will be

T = 85 / (9 x 3)

T = 3.15 hours

T = 3 hours and 9 minutes

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Answer:

I am sorry if you feel mad but I do not know this question I am very sorry . . . . . . . . . .

The exponential equation of the graph is y = 1.59 * 1.26^x

On the graph, we have the following points

(x,y) = (2,1) and (4,4)

An exponential function is represented as;

y = ab^x

So, we have:

ab^1 = 2 and ab^4 = 4

Divide both equations

b^3 = 2

Take the cube root of both sides

b = 1.26

Substitute b = 1.26 in ab^1 = 2

1.26a = 2

Divide both sides by 1.26

a = 1.59

So, we have:

y = ab^x

y = 1.59 * 1.26^x

Hence, the exponential equation of the graph is y = 1.59 * 1.26^x

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A quadrilateral comprises a rectangle, which is a specific kind of quadrilateral.

A conjecture is a conclusion made on the basis of speculation rather than proof.

Rectangle has four sides and is a polygon. The internal angle total is 360 degrees. The opposing sides of a rectangle are parallel and equal, and each angle is 90 degrees.

In the first place, your search for a pattern before making an educated assumption or hypothesis about it. In the introduction, you look for a pattern and then form an educated guess or conjecture about it.

A quadrilateral comprises a rectangle, which is a specific kind of quadrilateral.

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The correct answer for the Function in the diagram is: (B). [tex]\frac{1}{X}[/tex] + [tex]x^{2}[/tex] + 2x - 5

A function can be defined as  a set of outputs that its varying is dependent on the inputs.

In this case the functions given have a designated outputs.

(f+g)(x) = f(x) + g(x)  - because its held by an addition

(f+g)(x) = [tex]\frac{1}{X}[/tex] + [tex]x^{2}[/tex] + 2x - 5

In conclusion, The correct answer for the question in the diagram is: (B). [tex]\frac{1}{X}[/tex] + [tex]x^{2}[/tex] + 2x - 5

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Answer:

Step-by-step explanation:

The common difference is 8-5 = 3

The first next term is 11 + 3 = 14

The next (second) term  is 14 + 3 = 17

tn = 5 + (n - 1)*3       This is part c

t20 = 5 + (20 - 1)*3

t20 = 5 + 19*3

t20 = 5 + 57

Answer t20 = 62

The indicated side of the right triangle is [tex]44\sqrt{2} =\frac{88}{\sqrt{2} }[/tex].

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says:[tex]hypotenuse^2=(leg_1)^2+(leg_2)^2[/tex]. And the main trigonometric ratios are:

[tex]sin(\beta )= \frac{opposite\;leg}{hypotenuse} \\ \\ cos(\beta )= \frac{adjacent\;leg}{hypotenuse} \\ \\ tan(\beta )= \frac{opposite\;leg}{adjacent\;leg} \\ \\[/tex]

The question asks to find one of the legs (y). Then, you can find y applying the trigonometric ratio (sin 45°).

[tex]sin(45\°)=\frac{y}{88}[/tex]

Like sin45° is equal to [tex]\frac{\sqrt{2} }{2}[/tex], you have

[tex]\frac{\sqrt{2} }{2} =\frac{y}{88}\\ \\ 2y=88\sqrt{2} \\ \\ y=44\sqrt{2} \\ \\ Thus\\ \\ y=\frac{88}{\sqrt{2}}[/tex]

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Answer: 88[tex]\sqrt{2}[/tex]

Step-by-step explanation:

hope it helps

Answer:

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

Step-by-step explanation:

If you multiply

(x+8)(x+3),

you get x^2 + 3x + 8x + 24

This simplifies to x^2 + 11x + 24, same as the original question.

The graph of y=x² + 11x + 24 is equivalent to the y=(x+8)(x+3).

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Constants and variables are components of a polynomial.

We have Graph whose equation is

y=x² + 11x + 24

Now, factories the above equation using splitting the middle term

y=x² + 11x + 24

y=x² + 8x + 3x + 24

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

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

Thus, the factors are (x + 3)(x+8).

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Answer:

64

Step-by-step explanation:

The information can be written as:

Let Alex's number = x

Winnie's number = y

x = 1.75y

x = y + 48

Substitute 1.75y for x:

1.75y = y +48

0.75 y = 48

3/4 y = 48

y = 64

Winnie's favourite number = 64.

The amount of sugar he will use is 5.22 cups of sugar, and the number of boxes needed to pack the muffins is 13.71 boxes.

This word problem question can be solved as follows:

Amount of sugar he will use = 1  1/7 * 4 4/7 = 1.142857142857143 * 4.0.571428571428571 = 5.22 cups of sugar

Number of boxes needed to pack the muffins for the meeting = 4 4/7 * 3 = 4.0.571428571428571 * 3 = 13.71 boxes

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Answer:

Equation in Slope intercept form :

y = 5x + 4

By completing squares, we will see that the radius is 12 units and the center is (-8, 1).

The circle of center (x₁, y₁) and radius r is written as:

(x - x₁)² + (y - y₁)² = r²

Now we go to our equation:

x² + 16x + 64 + y² - 2y + 1 = 144

Now we need to complete squares:

(a + b)² = a² + 2ab + b²

Then we can rewrite:

(x² + 2*8*x + 8*8) + (y² - 2y + 1) = 12²

(x + 8)² + (y - 1)² = 12²

So the center is the point (-8, 1) and the radius is 12 units.

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Step-by-step explanation:

. In Figure 5.144, of ΔABC, where

m(∠C) = 30, m(∠ABD) = 5x,

m(∠A) = 4x. Find m(∠ABC) in

degrees.

Answer:Calvin throws 12 sheets of paper up in the air.

He randomly catches one of the sheets as they float down.

Of the 12 sheets of paper, 9 are white and 3 are red.

Probability = Number of favorable outcomes/ total number of outcomes

The probability that Calvin caught a white sheet is = or 75%.

It is likely that this event occurs as above 70% we say that the event is likely and here the probability is 75%.

The probability that Calvin caught a red sheet is = or 25%

This is unlikely to happen. Thus, we can say that it is not likely event.

Answer:

3^4

Step-by-step explanation:

when both constants have equal base then powers are added

Answer:

144 apples 72 pears

Step-by-step explanation:

Apples 120 + 20% = 144

Pears 120 - 40% = 72

Hope This Helped

Answer:

9

Step-by-step explanation:

[tex]\text{Given that}~ x = -7\\\\\dfrac{(x-2)(x+14)}{x(x+8)}\\\\\\=\dfrac{(-7-2)(-7+14)}{-7(-7+8)}\\\\\\=\dfrac{(-9)(7)}{-7(1)}\\\\\\=\dfrac{-63}{-7}\\\\\\=9[/tex]