Differentiate the function with respect to x.

a ) The expression for the radius of the circle = r = 2x + 3

b ) The least possible value of radius is - 1.5

Given : Area of the circle = 4πx² + 12πx + 9π

a) The expression for the radius of the circle = r = 2x + 3

we can find this out by middle term split

we can write the area of the circle as

4πx² + 12πx + 9π

4πx² + 6πx + 6πx + 9π

this implies 2πx ( 2x + 3 ) + 3π ( 2x + 3 )

π( 2x + 3 ) ( 2x + 3 )

thus the radius expression is 2x + 3

b ) The least possible value of radius is 2x + 3 = 0

this implies 2x = - 3

x = - 1.5

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Answer:

The answer to your question is,

MEAN = 43.6

MEDIAN = 43

MODE = 43

RANGE = 5

Step-by-step explanation:

BC  I know math :)

Answer:

How do I show you the graph because I have it

Step-by-step explanation:

An equation that shows how the total number of diplomas signed depends on the number of seconds the principal spends signing them is y = 37 + 0.5x.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, let x be number of seconds the principal spends signing them. The principal already signed 37 diplomas. Th equation to illustrate this is 37 + 0.5x.

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The 6th term of this sequence is 360

From the question, we have the following parameters that can be used in our computation:

Sequence representation = 2n² × 5

This means that

nth term = 2n² × 5

So, we have

f(n) =  2n² × 5

For the 6th term, the value of n is 6

i.e. n = 6

Substitute the known values in the above equation, so, we have the following representation

f(6) =  2(6)² × 5

Evaluate

f(6) =  360

Hence, the 6th term s 360

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The required angles of x and y are x = 65° and y = 25°

Given is a triangle which is right angled

Thus the sum of the right angled triangle is 180 degrees

So we will write

y° + x + 90 = 180 [ angle sum property of the triangle ]

90 + x + y = 180

let the above equation be considered as equation 1

Since two sides are equal

thus the other angle will also be x°

Also the angle adjacent to 40° can be found out by linear angle property

thus according to this :

x + x + ( 90 - 40 ) = 180 °

2x + 50 = 180

thus subtracting 50 on both sides we get

2x = 130

x = 65°

Thus by equation 1

we can rewrite it as

y + x + 90 = 180

65 + 90 + y = 180

155 + y = 180

this implies y = 180 - 155

y = 25°

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Step-by-step explanation:

1.) The first shape is a parallelogram like prism, So we use Area of prism= Area of base shape*height

that is, Area of base shape= rectangle,L*B

35*14=490*height

490*24=11760 cm3

2.)A rectangle base prism,

Area of prism= Area of base shape*height

Area of Base shape=27*14

378cm2*21

7938cm3

3.)Square based prism,

Area of prism= Area of base shape*height

=21*21*21 (since all sides are the same)

=9261cm3

Answer:

[tex]\frac{7}{4}[/tex] or 1 [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

I am not sure if you meant 6x or 6+x at the end of the equation. I went with what was written.

5x -3(x-3) = -5 +4x +6x  Distribute the -3

5x -3x + 9 = -5 + 4x + 6x  Combine like terms

2x + 9 = -5 + 10x  Subtract 2x from both sides

9 = -5 + 8x  Add 5 to both sides

14 = 8x  Divide both sides by 5

[tex]\frac{14}{8}[/tex] = x

[tex]\frac{7}{4}[/tex] o r 1 [tex]\frac{3}{4}[/tex]

The equation of line parallel to 2x +3y = 9 and passing through the point (6,4) is 3y + 2x = 24

Gradient or slope is the ratio of the change in y to the change in x between two points in a line.

Gradient tells how steep a line is. A perfectly vertical or horizontal line has no slope.

2x + 3y = 9

making y the subject,

3y = 9 - 2x

y = 9/3 -2x/3

Comparing the above equation, with equation of a straight line, y = mx + c

m, which is slope = -2/3

The new line will also have a slope of -2/3 because they are parallel.

Equation for new line,

y-[tex]y_{1}[/tex] / x - [tex]x_{1}[/tex] = slope

The new point is (6,4)

y - 4 / x -6 = -2/3

By cross multiplying

3(y-4) = -2(x - 6)

3y - 12 = -2x + 12

3y + 2x = 24

In conclusion, the equation o the new line is 3y + 2x = 24

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x = 3

Step-by-step explanation:

[tex]{ \blue{ \sf{n(x) = 4x + 4}}}[/tex]

[tex]{ \blue{ \sf{16 = 4x + 4}}}[/tex]

[tex]{ \blue{ \sf{16 - 4 = 4x}}}[/tex]

[tex]{ \blue{ \sf{12 = 4x}}}[/tex]

Divide both the sides with 4

[tex]{ \blue{ \sf{ \frac{12}{4} = \frac{4}{4}x}}}[/tex]

[tex]{ \green{ \boxed{ \red{ \sf{x = 3}}}}}[/tex]

Weight of cat when 13 grams food is fed is 151.11 ounces.

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign.  LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity.

Given, the formula for weight,

W = 0.86[tex]g^{2}[/tex] - 0.01g + 5.9

    = 0.86[tex](13^{2} )[/tex] - 0.01*13 + 5.9

    = 0.86*169 - 0.13 + 5.9

    = 145.34 - 0.13 + 5.9

    = 151.11 ounces

Therefore, the weight of the cat will be 151.11 ounces.

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Answer:

value of x are 2 and 3 which make the inequality true

Answer:Qadrant 4

Step-by-step explanation:

Answer:

Mark did 12 pull ups

Step-by-step explanation:

48 / 4 = 12

a) The penalty Lorna must pay for the late payment of her real estate tax is $26.50.

b) The total amount Lorna must pay on February 27 is $2,037.38.

The penalty for unpaid taxes is computed by determining the number of days the taxes remained unpaid.

Then the penalty rate is applied to the unpaid taxes multiplied by the number of days taxes were outstanding, divided by 365 days.

The product of the above multiplication and division operations is the penalty.

Outstanding real estate tax = $2,010.88

Due date for the tax = December 14, 2017

Payment date for the tax = February 27, 2018

Number of days, tax outstanding = 74 days

Penalty rate for late payment = 6.5%

Penalty = $26.50 ($2,010.88 x 6.5% x 74/365)

Total payment on February 27 = $2,037.38 ($2,010.88 + $26.50)

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The explicit form of the arithmetic sequence is

5, 13, 21, 29, .....

What is arithmetic sequence?

A sequence of numbers is said to be in arithmetic progression if the difference between the consecutive terms of the series are same

If the first term is a, common difference is d, then nth term of the sequence is given by

[tex]a_n = a + (n-1)d[/tex]

The recursive form of the given arithmetic series is

[tex]a_n = a_{n-1} + 8[/tex]

First term [tex]a_1 = 5[/tex]

[tex]a_2 = a_1 + 8\\a_2 = 5 + 8\\a_2 = 13[/tex]

[tex]a_3 = a_2 + 8\\a_3 = 13 + 8\\a_3 = 21[/tex]

[tex]a_4 = a_3 + 8\\a_4 = 21+8\\a_4 = 29[/tex]

So the explicit form of the arithmetic sequence is

5, 13, 21, 29, .....

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The graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.

Polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). For example -

y = 4x⁴ + 3x³ + 2x² + 6x + 7

We have the following polynomial -

y = 2x⁴ - 5x³ + x² - 2x + 4

Now -

at x = 0, y = 4

at x = 1, y = 0

at x = 2, y = 32 - 40 + 4 - 4 + 4 = - 4

Refer to the graph attached. The points (0, 4), (1, 0) and (2, - 4) are plotted.

Therefore, the graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.

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Answer:

49

Step-by-step explanation:

35+14=49

mark me on brainliest please follow me to

Answer:_______________________________

We can conclude that (C) Gibbons will live in a building that is similar to the Chimpanzee's rectangular house.

So, observe the given shapes on the graph:

Therefore, we can conclude that (C) Gibbons will live in a building that is similar to the Chimpanzee's rectangular house.

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Answer:

The answer would be A. (Not sure if its A B C or D question but I will have picture below)

Step-by-step explanation:

Hope this helps you! :))

Answer:

.

Step-by-step explanation:

If [tex]n=25[/tex] and [tex]p=0.04[/tex], then the probability of [tex]P(X=4)[/tex] is found to be 0.001374.

What is Binomial Distribution?

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability, [tex]p[/tex]) or failure (with probability, [tex]q=1-p[/tex]).

How to Find the Probability of a Binomial Distribution?

From the given question, we have, [tex]n=25[/tex] and [tex]p=0.04[/tex]

Here, have to find the probability of [tex]P(X=4)[/tex], so [tex]k=4[/tex]

The binomial distribution formula is, [tex]P(X=k)={n \choose k}p^{k}(1-p)^{n-k}[/tex]

Substituting the given values in the above equation, we get

[tex]P(X=4)={25 \choose 4}0.04^{4}(1-0.04)^{25-4}[/tex]

[tex]\implies P(X=4)=12650 \times0.00000256\times0.4243\\\implies P(X=4)=0.001374[/tex]

Therefore, the value of [tex]P(X=4)=0.001374[/tex]

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Answer: 17/5 or 3.4

Step-by-step explanation:

Substitute  p for 3/5 so it would be 2/3(3/5)+3

2/3(3/5)= 2/5

2/5+3=17/5 or 3.4

Hope this helps :)

Answer:

Step-by-step explanation:

Substitute  p for 3/5 so it would be 2/3(3/5)+32/3(3/5)= 2/52/5+3=17/5 or 3.4

Reflection across the y-axis is H(-1,-3), Z(-1,2) W(-4,1).

When point M (h,k) is reflected along the y-axis, the image M' with coordinates of forms in the second quadrant (-h, k).

Thus, we get the conclusion that when a point is mirrored along the y-axis, the y-coordinate stays constant but the x-coordinate changes to the negative.

H(1,-3) → H(-1,-3)

Z(1,2) → Z(-1,2)

W(4,1) → W(-4,1)

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Answer:

82.96-22% = 67.83

Step-by-step explanation:

82.96-22% = 67.83

Answer:

No

Step-by-step explanation:

It does not make sense becuse 6x9=54

And 4x9(2)=72 so it would make no sense