Write an equation that represents the line.
Use exact numbers.

First point (1,2)
Second point is (4,4)

Since the common features of the polynomial function is f(x) = 2x² + 7x + 6 and exponential function g(x) = 2^x + 5 then:

Polynomial functions are known to be a kind of an expressions that is made up of a set of variables of different extent or degrees, non-zero coefficients, positive exponents (of variables), and also it is made up of constants.

Note that the equation of the functions are stated as:

f(x) = 2x² + 7x + 6

g(x) = 2^x + 5

The right and next thing to do is to plot a graph of both functions (see image attached)

From the graph, we have the fact that Both f(x) and g(x) have the same y-intercept of (0,6)

Therefore, Since the common features of the polynomial function is f(x) = 2x² + 7x + 6 and exponential function g(x) = 2^x + 5 then:

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Answer:

3/10

Step-by-step explanation:

=4/7 + 9/70 - 4/10

=l.C.M of 7 , 70 and 10 =70

=4/7 .10/10 +9/70 -4/10 .7/7

=40/70 +9/70 -28/70

=40+9-28/70

=49-28/70

=21/70

=3/10

The general expression is 130 x - 600 and total points scored by the player is 1220

A) Let the number of correctly answered questions be x.

∴ Number of incorrectly answered questions will be 20 - x.

+ 100 points is awarded for each question answered correctly while -30 points is awarded for each question answered incorrectly.

Thus, the general equation becomes

= 100x - (20 - x)(-30)

= 100x +30x - 600

= 130x - 600

Thus the general expression becomes 130 x - 600

B)  The player answers 14 questions correctly, thus x = 14

Substituting the value of x =14 in the general equation we get,

= 130(14) - 600

= 1820 - 600

= 1220.

Thus the total points scored by the player will be 1220

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The time it was when Frank left the playground is; 6:10 PM.

We are given;

Time at which Frank went to the playground; 5:20 p.m

Amount of time that frank played on the slide = 45 minutes

Amount of time that frank swings on the play ground = 5 minutes

Now, we are told that after he played on the slide and swung on the playground, that he went home.

Thus, he spent a total time of 45 + 5 = 50 minutes on the playground before going home.

Thus, time he went home = 5:20 p.m + 50 minutes = 6:10 p.m

Thus, we can conclude that the time it was when Frank left the playground is; 6:10 PM.

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Answer:

9/14.

Step-by-step explanation:

The probability is given as a fraction or percentage.

9:5 odds in favour of a horse winning  means the horse will win 9 races for every 5 it does not win.

So the probability that this horse will win is 9/(9+5)

= 9/14.

The intervals which represents those in which case the function, f(x) is reducing are as follows; [–2.5, –2], [–2, –1.5], [1.5, 2], [2, 2.5].

It follows from the complete task content that the x-intervals between which the function value of f(x) is reducing are to be identified from the graph as attached.

On this note, by observation on the graph, it follows that from between the interval; [–2.5, –2], the function f(x) is decreasing.

Also, between the interval; [–2, –1.5], the function f(x) is decreasing.

Also, between the interval; [1.5, 2], the function f(x) is decreasing.

Also, between the interval; [2, 2.5], the function f(x) is decreasing.

Remark: The answer choices are as follows; [–2.5, –2] [–2, –1.5] [–1, 1] [1.5, 2] [2, 2.5) [2.5, 3]

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Check the picture below.

to get the equation of any straight line, we simply need two points off of it, so let's use those in the picture

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{6})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{6 -1}{4 +2} \implies \cfrac{ 5 }{ 6 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{5}{6}}(x-\stackrel{x_1}{(-2)})\implies y-1=\cfrac{5}{6}(x+2) \\\\\\ y-1=\cfrac{5}{6}x+\cfrac{5}{3}\implies y=\cfrac{5}{6}x+\cfrac{5}{3}+1\implies y=\cfrac{5}{6}x+\cfrac{8}{3}[/tex]

Combining of the two cylinders gives a composite figure that has the surface area of a solid cylinder of radius 7 mm and height 6 mm, such that the surface area of the figure is approximately 571.5 mm².

Radius of the inner cylinder, r = 3 mm

Radius of the outer cylinder, R = 7 mm

Height of the cylinders, h = 6 mm

Given that the inner cylinder exactly fits into the outer cylinder, we have;

The surface area of the composite figure is the surface area of the hollow outer cylinder + The area of the top and bottom of the inner cylinder.

Which gives;

The surface area of the composite figure, A, is the surface area of a solid cylinder, using the dimensions of the hollow outer cylinder.

Which gives;

Where, π = 3.14, we have;

A = 2 × 3.14 × 7² + 2 × 3.14 × 7 × 6 ≈ 571.5

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Answer: It is an equilateral square

Step-by-step explanation: it has 4 tick marks

The computation shows that the value of b will be 91.864.

From the information given, we are told to find the value of b (b - 4.21 = 87.654). This will be:

b - 4.21 = 87.654

b = 87.654 + 4.21

b = 91.864

Also. dividing 1.86 and 8.4 will be:

= 1.86/8.4

= 0.2213

Therefore, the values are 91.864 and 0.2213.

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Answer: 2000 meters

Step-by-step explanation: A kilometer means 1,000 meters a kilo means 1000. So, 2 x1000 = 2000 meters.

Answer:

(2030)4

Step-by-step explanation:

Base 6 to decimal calculation:

(352)6 = (3 × 62) + (5 × 61) + (2 × 60) = (140)10

Decimal to base 4 calculation:

Divide by the base to get the digits from the remainders:

= (2030)4

Still have any questions?

Do hit me up or contact me

The answer is 2030.

First, convert from base 6 to base 10.

Now, convert from base 10 to base 4.

Connecting the digits, the answer is : 2030

The value of x in the angles of Quadrilateral is 52 degree.

According to the statement

we have given a four angles and we have to  find the value of x in these give angles.

From given 4 angles it is clear that the these angles are of a quadrilateral.

And we know that the

A quadrilateral is a four-sided polygon, having four edges and four corners.

And the sum of all angles of a quadrilateral is 360 degree.

so,

50° + 3X + X + (X+110) = 360 degree

50° + 4X + (X+110) = 360 degree​

50° + 5X + 110 = 360 degree

160° + 5X  = 360

5X = 360-100

5X = 260

X = 52 degree.

So, The value of x in the angles of Quadrilateral is 52 degree.

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A sky wheel is a mechanical device that has a shape of a circle divided into a given number of equal sectors. Thus, the measure of each central angle required in the question is [tex]8.6^{o}[/tex].

A sky wheel is a mechanical device that has a shape of a circle divided into a given number of equal sectors. Thus each sector has an equal central angle. Since the sum of the internal angles of a circle is [tex]360^{o}[/tex].

From the given question, it has been stated that the sky wheel has 42 glass-enclosed gondolas. This implies that the sky wheel has been divided into 42 equal sectors.

Therefore,

the measure of each central angle = [tex]\frac{360^{o} }{n}[/tex]

where n represents the number of gondolas (42).

Thus,

the measure of each central angle between gondolas cars= [tex]\frac{360}{42}[/tex]

                                        = 8.5714

The measure of each central angle between gondolas cars is approximate [tex]8.6^{o}[/tex].

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The depth of the 84 inches wide satellite dish that has the receiver located 15 inches above the vertex is 29.4 inches.

The location of the receiver = 15 inches above the vertex

Width of the dish = 84 inches

The receiver of a satellite dish is normally located at the focus (focal point).

Taking the shape of the satellite dish as a parabola, and writing the equation of the parabola as x² = 4•a•y, we have;

Coordinates of the focus = (0, a)

Where;

a = The distance of the focus above the vertex

Therefore;

a = 15 inches

The dish is horizontally spaced equally about the vertex.

The farthest point horizontally from the vertex, X, of the dish corresponds to the furthest vertically from the vertex, which is the maximum depth or height, Y.

At the maximum height, from the vertex, Y, (farthest point, vertically from the vertex), we have;

X = 84 ÷ 2 = 42

Which gives;

42² = 4 × 15 × Y

Y = 42² ÷ (4 × 15) = 29.4

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Answer:

109°

Step-by-step explanation:

The sum of angles in all triangles is equal to 180. For this given triangle, we can solve for x.

48° + 23° + x° = 180°
180° - 71° = x°
x = 109°

The equation for the line of best fit is the linear function y = - 0.4 · x + 70. (Correct choice: A).

The equation of the line is represented by a polynomial of the form y = m · x + b, where m is the slope of the line and b is the intercept of the line. The slope is equal to the change in the dependent variable (Δy) and in the independent variable (Δx) and the intercept is the vertical distance of the line with the origin when x = 0.

In accordance with the picture, we notice that the scatter plot indice that Δy < 0 and Δx > 0 and therefore, m < 0. Besides, the intercept of the equation of the line must be greater than zero. Thus, the equation for the line of best fit is the linear function y = - 0.4 · x + 70. (Correct choice: A)

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Answer:

Step-by-step explanation:

15 hope it help

Answer:

B.  -x³ - 9x².

Step-by-step explanation:

- (3x³ + x²) +2 (x³ - 4x²)

= -3x³  + 2x³  - x² - 8x²

= -x³ - 9x²

Answer: [tex]\Large\boxed{-x^3-9x^2}[/tex]

Hi there! By my calculation, I got the answer above. However, it doesn't fit any one of the answer choices. I am not sure if I am totally correct, but I have been double-checking my answers. Please let me know whether it's the answer choices mistaken or I am wrong so that I could modify my answer if necessary.

Step-by-step explanation:

Given expression

- (3x³ + x²) +2 (x³ - 4x²)

Expand parenthesis by the distributive property

= -3x³ - x² + 2x³ - 8x²

Combine like terms

= -3x³ + 2x³ - x² - 8x²

[tex]\Large\boxed{=-x^3-9x^2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Gustavo used a simulation where the data is quantitative’

The inverse of a function is given as √x - 1

To get the inverse of any function f(x) we need to ensure that it passes the horizontal line test.

Given the following function

f(x) = (x+1)^2

Let y= f(x) to have:

y = (x+1)^2

Replace y with x to have:

x = (y+1)^2

Make y the subject of the formula

√x =y + 1

Subtract 1 from both sides

√x - 1 = y

Swap

y = √x - 1

Hence the inverse of a function is given as √x - 1

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The statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.

To determine which statement is true, we need to know the conditions for continuity and differentiablity of a function.

So, since f(x) = {x² - 1 if -1 ≤ x ≤ 3 and x²/3 if 3 < x ≤ 8}

From the equality on the first condition,we see that f(x) is exists at x = 3 but is not continuous since f(x) changes to another function when x > 3. So,left hand limit of f(x) and the right hand limit of f(x) as x → 3 are not equal.

That is [tex]\lim_{x \to 3^{-} } f(x) \neq \lim_{x \to 3^{+} } f(x)[/tex] . Thus, the function is discontinuous at x = 3.

For differentiability, both conditions must be met. Since only one condition is met, it is non-differentiable.

So, the function is discontinuous and non-differentiable at x = 3.

So, the statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.

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Answer:

B

Step-by-step explanation:

Line A mostly follows the trend of the higher points, entirely neglecting the existence of the lower points. Line b acknowledges the lower points and adjusts the line accordingly to be lower.

If the price of one ticket of bus is $180 and the bus has 56 seats then the maximum revenue that it can earn is $5107.6

Given that the price of a bus ticket to Saskatoon is $180 and the bus has 56 seats.

We are required to find the maximum revenue that the bus company can earn.

Suppose x represents the number of seats, y represents the total amount.

Price=$156

Seats=56

When the bus is of half capacity the bus seats will be 28.

As price decreases th rider gains 2 more.

Revenue equation.

y=(156.5x)(28+2x)-------------1

Expanding the equation.

y=4368-140x+312-10[tex]x^{2}[/tex]

Differentiating with respect to x.

dy/dx=0-140+312-20x

=172-20x

Put dy/dx=0

172-20x=0

x=8.6

Substitute the value of variable x in the equation 1.

y=(156-5x)(28+2x)

=$5107.6

Hence the maximum revenue that the bus company can earn is $5107.6.

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The first term of the arithmetic progression exists at 10 and the common difference is 2.

let the nth term be named x, and the value of the term y, then there exists a function y = ax + b this formula exists also utilized for straight lines.

We just require a and b. we already got two data points. we can just plug the known x/y pairs into the formula

The 9th and the 12th term of an arithmetic progression exist at 50 and 65 respectively.

9th term = 50

a + 8d = 50 ...............(1)

12th term = 65

a + 11d = 65 ...............(2)

subtract them, (2) - (1), we get

3d = 15

d = 5

If a + 8d = 50 then substitute the value of d = 5, we get

a + 8 [tex]*[/tex] 5 = 50

a + 40 = 50

a = 50 - 40

a = 10.

Therefore, the first term is 10 and the common difference is 2.

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Answer:

[tex] - \frac{ \sqrt{2} }{2} [/tex]

Step-by-step explanation:

The sine of an angle is equal to the y coordinate point where the terminal side of the angle intersects the unit circle.

Assuming there are at least 12 of each kind of cupcake, number of ways can you choose 12 cupcakes is; 1399358844975 ways

We are given the quantity of each type of cupcake as follows;

Number of types of cupcakes = 5

Number of Chocolate Cupcakes = 12

Number of Vanilla Cupcakes = 12

Number of Lemon cupcakes = 12

Number of Strawberry Cupcakes = 12

Number of coffee cupcakes = 12

Thus, total number of cupcakes will be gotten by adding all the quantities given above of the different types of cupcakes and we will get; Total number of cupcakes = 12 + 12 + 12 + 12 + 12

Total number of cupcakes = 60

Now, since there is no order of selection, then the number of ways that you can choose 12 cupcakes will be gotten by using the combination formula which is; nCr = n!/(n!(n - r)!)

Thus, number of ways that you can choose 12 cupcakes =

60C12 = 60!/(12! * (60 - 12)!) = 1399358844975 ways

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