Find the length of JN

[tex] \underline{ \orange{\huge \boxed{ \frak{Answer : }}}}[/tex]

Let ,

[tex] \sf \large \color{purple} y = 2 {x}^{3} - 3 {x}^{2} - 12x + 10 \: --( \: 1 \: )[/tex]

[tex] \: \: \: [/tex]

Now , Diff wrt ' x ' , we get :

[tex] \sf \: \frac{dy}{dx} = \frac{d}{dx} (2 {x}^{3} - 3 {x}^{2} - 12x + 10) \\ \sf \: \sf \: \frac{dy}{dx} = \frac{d}{dx} \: 2(3 {x}^{2} ) - \frac{d}{dx} 3 {x}^{2} - \frac{d}{dx} 12x + \frac{d}{dx} 10 \\ \sf \: \frac{dy}{dx} =2(3 {x}^{2} ) - 3(2x) - 12(1) + 0 \\ \sf \: \frac{dy}{dx} =6 {x}^{2} - 6x - 12 + 0 \\ \: \sf \red{\frac{dy}{dx} = 6 {x}^{2} 6x - 12 -- (2)}[/tex]

[tex] \: \: \: [/tex]

For maxima or minima \frac{dy}{dx} = 0

[tex] \: \: \: [/tex]

[tex] \sf \: 6 {x}^{2} - 6x - 12 = 0[/tex]

[tex] \: \: \: [/tex]

Divided by 6 on both side , we get.

[tex] \: \: \: [/tex]

[tex] \sf \: {x}^{2} - x - 2 = 0 \\ \sf \: {x}^{2} - 2x + x - 2 = 0 \\ \sf \: x(x - 2) + 1(x - 2) = 0 \\ \sf \: (x - 2)(x + 1) = 0 \\ \sf \: x - 2 = 0 \: \: \bold or \: \: x + 1 = 0 \\ \sf \fbox{x = 2 \: } \: \bold or \: \fbox{ x = - 1}[/tex]

[tex] \: \: \: [/tex]

Again Diff wrt ‘ x ’ , we get.

[tex] \sf \: \frac{d}{dx} =(\frac{dy}{dx} ) = 6\frac{d}{dx} - 6\frac{d}{dx}x - \frac{d}{dx}12 \\ \sf \: \frac{ {d}^{2}y }{ {dx}^{2} } = 6(2x) - 6(1) - 0 \\ \sf \: \sf \bold{ \frac{ {d}^{2}y }{ {dx}^{2} } =12x - 6}[/tex]

[tex] \: \: \: [/tex]

At x = 2

[tex] \: \: \: [/tex]

[tex]\sf \: \frac{ {d}^{2}y }{ {dx}^{2} } =12(2) - 6 \\ \: \: \: \sf \: = 24 - 6 \\ \: \: \: \: \sf \red{ = 18 > 0}[/tex]

At x = -1

[tex] \: \: \: [/tex]

[tex]\sf \: \frac{ {d}^{2}y }{ {dx}^{2} } =12( - 1) - 6 \\ \: \: \: \sf \: = - 12 - 6 \\ \: \: \: \: \sf \red{ = - 18 < 0 }[/tex]

[tex] \: \: \: [/tex]

x = 2 gives minima value of function.

[tex] \: \: \: [/tex]

x = -1 gives maxima value of function.

[tex] \: \: \: [/tex]

Now, put x = 2 in eqⁿ ( 1 )

[tex] \: \: \: [/tex]

[tex] \sf \: y \: minima \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2( {2})^{3} - 3 ({2})^{2} - 12(2) + 10 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: \: = 2(8) - 3(4) - 24 + 10 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: \: \: = 16 - 12 - 24 + 10 \\\sf \: \: \: \: \: \: \: \: \: \: = - 20 + 10 \\\sf \color{red}{\boxed{ = - 10}}[/tex]

[tex] \: \: \: [/tex]

The Point of minima is ( 2 , -10 ).

[tex] \: \: \: [/tex]

Now , put x = -1 in eqⁿ ( 1 )

[tex]\sf \: y \: maxima \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2( { - 1})^{3} - 3 ({ - 1})^{2} - 12( - 1) + 10 \\\sf \color{red}{\boxed{ = 17}}[/tex]

[tex] \: \: \: [/tex]

The point of maxima value is ( -1 , 17 ).

[tex] \: \: \: [/tex]

[tex] \: \: [/tex]

Hope Helps! :)

The missing information of the triangle is C = 63°, b ≈ 28.084 and c ≈ 25.084. (Correct choice: C)

In this question we have a triangle with a known side lengths and two known angle measures. First, we find the missing angle by Euclidean geometry:

C = 180° - 94° - 23°

C = 63°

Lastly, we determine the missing sides by law of sines:

[tex]b = 11 \times \frac{\sin 94^{\circ}}{\sin 23^{\circ}}[/tex]

b ≈ 28.084

[tex]c = 11 \times \frac{\sin 63^{\circ}}{\sin 23^{\circ}}[/tex]

c ≈ 25.084

The missing information of the triangle is C = 63°, b ≈ 28.084 and c ≈ 25.084. (Correct choice: C)

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Check the picture below.

Answer:

1025.76

Step-by-step explanation:

Formula for a right rectangular pyramid is (l*w*h)/3

The length and width are both 18.7, so we can plug that in. The height is 8.8.

It becomes:

(18.7*18.7*8.8)/3, which equals the answer above.

The points on the graph of (-4, 0), (-2.5, -12), and (0, -3), gives;

From the description of the graph, we have;

Furthest point left of the graph = (-4, 0)

The furthest point right on the graph = (0, -3) = The maximum point

The minimum point = (-2.5, -12)

F(x) < 0 at the minimum point

The minimum point is to the right of x = -4

The point the graph crosses the y-axis = (0, -3)

Therefore;

The interval of the graph where F(x) is larger than 0 is to the left of (-4, 0), is the interval (-∞, -4)

The true statement is therefore;

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The number to add to the set of data is 26

The set of data is given as:

11,14,23 and 16

Let the new number be x

So that

Mean = 18

Mean is calculated as:

Mean = Sum/Count

So, we have:

(11 + 14 + 23 + 16 + x)/5 = 18

Multiply by 5

11 + 14 + 23 + 16 + x = 90

Evaluate the like terms

x = 26

Hence, the number to add is 26

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Complete question

A set of data already has the values 11, 14, 23, and 16. What value would have to be added to the set for the mean of the five numbers to be 18?

Answer:

  (d)  f(x) = -x²

Step-by-step explanation:

For the vertex of the quadratic function to be at the origin, both the x-term and the constant must be zero. That is, the function must be of the form ...

  f(x) = a(x -h)² +k . . . . . . . . . . vertex form; vertex at (h, k)

  f(x) = a(x -0)² +0 = ax² . . . . . vertex at the origin, (h, k) = (0, 0)

Of the offered answer choices, the only one with a vertex at the origin is ...

  f(x) = -x² . . . . . a=-1

Answer:

the answer is 22

Step-by-step explanation:

12,15,22,37,49

since 22 is in the middle its the median (make sure you put the #'s from least to greatest)

Answer:

22

Step-by-step explanation:

22, 37, 49, 15, 12

First put the data set from least to greatest.

12, 15, 22, 37, 49

The median is the middle number of the data. In this case, the median is 22.

Hope this helps!

Answer:

Step-by-step explanation:

a = number of successful events

b = total number of events.

Step-by-step explanation:

as the graphic shows, there are 2 objects : 1 block and 1 triangular shaped half-block.

the block is

7cm × 6cm × 2cm

the half-block is

8cm × 7cm × 6cm

with 10cm being the length of the tilted "roof" area.

the 2 sides facing each other are not visible to the observer, so, they are not part of the surface area of the composite figure.

let's start with the block :

top and bottom 7×2

front and back 6×2

no left (fully covered by the half-block)

right 6×7

that gives us :

2 × 7×2 = 2×14 = 28 cm²

2 × 6×2 = 2×12 = 24 cm²

6×7 = 42 cm²

in total : 94 cm²

the half-block :

top 10×7

bottom 8×7

front and back (triangles) 8×6/2

no left (due to being a half-block)

no right (fully covered by the block)

that gives us :

10×7 = 70 cm²

8×7 = 56 cm²

2 × 8×6/2 = 2×24 = 48 cm²

in total : 174 cm²

so, the complete surface area of the composite figure is

94 + 174 = 268 cm²

Area of the entire rectangle is x² + 11x + 30. This can be obtained by adding area of each square.

Method 1

Area of rectangle = length × width  

Area of entire rectangle = x² + 5x + 6x + 30 = x² + 11x + 30

Method 2

Area of entire rectangle = length × width

                                   = (x+6)×(x+5)    

                                  = x² + (6+5)x + (6×5)        [∵(x+a)(x+b) =x² + (a+b)x + ab]

                                    = x² + 11x + 30

Hence area of the entire rectangle is x² + 11x + 30.

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The Surface area of the triangular prism with the net shown below is 106 cm²

An equation is an expression that shows the relationship between two or more variables and numbers.

Surface area of the triangular prism = 2(0.5 * 5 * 3) + (7 * 3) + 2(7 * 5) = 106 cm²

The Surface area of the triangular prism with the net shown below is 106 cm²

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Answer: x=11

Step-by-step explanation:

The lines are parallel, which you can tell by the two arrows. 4x-8 is a corresponding angle to 3x+3, meaning they are congruent.

4x-8 = 3x+3

x=11

Answer:

x = 11

Step-by-step explanation:

these angles are corresponding angles so they are equal to each other.

4x - 8 = 3x + 3 Subtract 2x from both sides

x - 8 = 3   Add 8 to both sides

x = 11

Plug 11 back into the equations find the angle measurements

4(11) -8 = 36 degrees

3(11) + 3 =  36degrees

Answer:

sum

Step-by-step explanation:

example

2+3=5

Answer: 3n ants

Step-by-step explanation:

         If there are n ants one month, and the ants triple every month, then next month there will be 3n ants.

         We can multiply 3 by n to show it tripling.

      To test this, 3(10,000) = 30,000 and 3(270,000) = 810,000, which corresponds to what you've filled out in the table.

Answer:

-0.4 or [tex]\frac{-2}{ 5}[/tex]

Step-by-step explanation:

[tex]tan^-^{1} ({\frac{2}{5} })=21.80\\[/tex]

tan ( 2π-21.80)

but 2π = 360

Therefore our question becomes:

tan ( 360-21.80)=tan(338.2)= -0.4

Using the probability concept, the correct statement is:

B. P(hibiscus|red) = P(hibiscus).

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For item a, the probabilities are:

Same probabilities, hence the statement that they are different is false.

For item b, the probabilities are:

Equal, hence this is the correct statement.

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The area of the plate covered by the napkin is (C) [tex]56cm^{2}[/tex].

What is an area of a triangle?

To find the area of the plate covered by the napkin:

Given :

The following steps can be used in order to determine the area of the plate covered by the napkin:

Step 1 - The formula of the perimeter of a triangle is given below:

P = a + b + c   --- (1)

where a, b, and c are the length of the sides of the triangle.

Step 2 - According to the given data, the triangle is isosceles.

Therefore, the two sides are similar and the length of the base is 8 cm.

Step 3 - Now, substitute the values of the known terms in the above formula.

38 = 2L + 8

38 - 8 = 2L

L = 15 cm

Step 4 - The area of the plate covered by the napkin is given below:

[tex]A=\frac{1}{2} * 15 * 15 *Sin30[/tex]

Step 5 - Simplify the above expression.

[tex]A=56.25cm^{2}[/tex]

Rounding off to the nearest whole number, which is [tex]56cm^{2}[/tex].

Therefore, the area of the plate covered by the napkin is (C) [tex]56cm^{2}[/tex].

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The question you are looking for is here:

A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate, as shown. The napkin has a perimeter of 38 centimeters. To the nearest square centimeter, how many square centimeters of the plate is covered by the napkin?

(A) 16 square centimeters

(B) 30 square centimeters

(C) 56 square centimeters

(D) 60 square centimeters

The equation which could be used to find the length of the hypothenuse is; 5 squared + 8 squared = c squared.

It follows from the task content that the equation which could be used to find the length of the third side be determined.

Hence, since it follows from Pythagoras theorem that the square of the hypothenuse is equivalent to the sum of the squares of the two other sides of a right triangle.

Hence, the required equation is; 5 squared + 8 squared = c squared.

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Answer:

The answer is A
5 squared + 8 squared = c squared

Step-by-step explanation:

The number of weeks it will take for the budget money to run out is; 2 weeks.

The number of weeks it would take for the budget money to decrease till it runs out as required in the task can be interpreted as the x-value which corresponds to a Y-value of zero.

Hence, by setting y=0; we have;

-2x -0 = -4

-2x = -4

Divide both sides of the equation by; -2.

x = 2

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The total amount of fencing they need = 38x + 10.

Perimeter for the rectangular fencing of the home = 160 yards

Perimeter for the square fencing of the pool = 40 yards

Perimeter of a rectangle = 2(length + width)

Perimeter of a square = 4(side length).

Perimeter for the rectangular fencing of the home = 2(3 + 10x + 2 + 5x) = 2(15x + 5) = 30x + 10

Perimeter for the square fencing of the pool = 4(2x) = 8x

The total amount of fencing they need = 30x + 10 + 8x = 38x + 10.

If x = 5, then:

Perimeter for the rectangular fencing of the home = 30x + 10 = 30(5) + 10 = 160 yards

Perimeter for the square fencing of the pool = 4(2x) = 8x = 8(5) = 40 yards.

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Answer:

38
160
40

Step-by-step explanation:

A simple main effect analysis looks at the mean difference at each level of the independent variable.

Given With a simple main effect, the analysis examines.

Simple effects are also called the main effects of design of experiments. The main effect can be defined as the effect of the explanatory variables measured on a particular criterion or response variable of the study. It's easy to say that what happens within the level of the explanatory variables is the difference. In a factorial experiment, the simple main effect is that one independent variable is at a specified level of another. The main effect of one independent variable is averaged across the levels of the other independent variable. For a simple main effect, the results are analyzed as if a separate experiment was performed at each level of the other independent variables.

Therefore, a simple main effect analysis looks at the mean difference at each level of the independent variable.

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The domain of the function g(x) = –⌊x⌋ + 3 is (a) {x| x is a real number}

The function is given as

g(x) = –⌊x⌋ + 3

The above is a step function, and the domain is the set of input values it can accept

Step functions of the given form can accept any real value of x

Hence, the domain of the function g(x) = –⌊x⌋ + 3 is (a) {x| x is a real number}

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Complete question

The graph of the step function g(x) = –⌊x⌋ + 3 is shown. What is the domain of g(x)? {x| x is a real number} {x| x is an integer} {x| –2 ≤ x < 5} {x| –1 ≤ x ≤ 5}

Answer:

A

Step-by-step explanation:

[tex]y = 9x {}^{2} - 4 \\ flip \: x \: and \: y \\ x =9 (y ) {}^{2} - 4 \\ solve \: for \: the \: inverse \: of \: y \\ x + 4 = 9(y ) {}^{2} \\ y {} {}^{2} = \frac{x + 4}{9} \\ you \: can \: split \: it \: into \: two[/tex]

[tex]y {}^{(1)} = \sqrt{ \frac{x + 4}{9} } \\ y {}^{(2)} = - \sqrt{ \frac{x + 4}{9} } [/tex]

The total cost in 5 hours is $225

Given that the charges of a supply fee of an artist is $50

The charges per hour classes is $35

The total cost is expressed by c

The number of hours expressed by h

We need to calculate the total cost in 5 hour lesson

As per the given statement ,

C= 50 +35h

Where h is the number of hours

h = 5 hours

C = 50 + 35h

C = 50 + 35(5)

C = 50 +175

C = $225

The total cost in 5 hours is $225

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Answer:

C. [tex]\frac{1}{4}[/tex]× [tex]\frac{7}{2}[/tex]

Step-by-step explanation:

When you convert a fraction division into multiplication, you convert the divisor into its reciprocal. The reciprocal of [tex]\frac{2}{7}[/tex] is [tex]\frac{7}{2}[/tex]. So you get your answer  [tex]\frac{1}{4}[/tex]× [tex]\frac{7}{2}[/tex].

Using proportions, the expected number of adults in Palm City whose main source of news is the internet or newspaper is of 19,413.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From the table, the proportion of adults in Palm City whose main source of news is the internet or newspaper is found as follows:

p = (62 + 88)/(62 + 88 + 128 +24 + 38) = 0.4412.

Hence, out of 44,000 adults, the expected number is found as follows:

0.4412 x 44000 = 19,413.

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Answer:

[tex]\textsf{1.} \quad C^{-1}(F)=\dfrac{9}{5}F+32[/tex]

2.   [-273.15, ∞)

Step-by-step explanation:

Given:

[tex]C=\dfrac{5}{9}(F-32), \quad \text{where }F \geq -459.67[/tex]

To find the inverse of the given function, make F the subject:

[tex]\begin{aligned}C & =\dfrac{5}{9}(F-32)\\\implies \dfrac{9}{5}C & =F-32\\\implies F & = \dfrac{9}{5}C+32 \end{aligned}[/tex]

[tex]\textsf{Replace the } F \textsf{ with }C^{-1}(F)\textsf{ and the }C \textsf{ with } F:[/tex] :

[tex]\implies C^{-1}(F)=\dfrac{9}{5}F+32[/tex]

Domain: set of all possible input values (x-values)

Range: set of all possible output values (y-values)

The given domain of the function C(F) is F ≥ -459.67

Therefore, the minimum value of the function is:

[tex]\implies C(-459.67)=\dffrac{5}{9}(-459.67-32)=-273.15[/tex]

This means the range of the function C(F) is C(F) ≥ -273.15

The domain of the inverse function is the range of the function.

Therefore, the domain of the inverse function in interval notation is:  [-273.15, ∞)

Answer: -273.15

Step-by-step explanation: