At which root does the graph of f(x) = (x – 5)3(x + 2)2 touch the x axis?

The answer is 2.37 miles. The possible explanation for this is I can illustrate 3.65 using 3 squares for ones, 6 lines for tenths, and 5 circles for hundredths. I would now then reform 1 tenth as 10 hundredths. Then, I would subtract 8 hundredths from 15 hundredths. Then, I would take away 2 tenths from 5 tenths. Last, I would deduct 1 from 3.

The given graph is scaled form of trigonometric function graph.

The formula for the graph function f(x) is given by:

[tex]f(x) = -2sin(\dfrac{x}{4})[/tex]

Note down the properties one by one.

Firstly its a periodic function.

Secondly, the maximum value of the function is 2 and minimum value is -2

Thirdly the function assumes maximum or minimum value when it reaches to [tex]2 \pi n; n \in \mathbb Z[/tex]

Fourthly, the graph from the center to right side goes down then up then down then up and so on.

If you've seen graph of sine function, then you'd know that the graph is periodic(repeating same values after some interval), the maximum and minimum values being 1 and -1 and maximum or minimum values are achieved when input is [tex]\dfrac{n\pi}{2}; \: n \in \mathbb{Z}[/tex]

Plus, the graph from center to right goes up then down then up then down and so on.

First we need down then up instead of up and down. Since down is negative output in its graph and up is positive, thus we will negate the value of sine function.

[tex]-sin(x)[/tex]  will have flipped mountains and valley's in comparison to that of sin(x).

Now since the maximum  and minimum values are needed to be 2 and -2 instead of 1 and -1, thus we will scale the output with factor of 2.

[tex]-2sin(x)[/tex]  will have maximum and minimum as 2 and -2 respectively.

We need the graph to be maximum or minimum at x = [tex]2 \pi n; n \in \mathbb Z[/tex] and not at x =  [tex]\dfrac{n\pi}{2}; \: n \in \mathbb{Z}[/tex]. Thus, we will scale down the input of -2sin(x) so that it treats  [tex]2 \pi n; n \in \mathbb Z[/tex] as if it was given  [tex]\dfrac{n\pi}{2}; \: n \in \mathbb{Z}[/tex].

The scaling needs to be by 1/4 since [tex]\dfrac{1}{4} \times 2\pi n = \dfrac{n\pi}{2}[/tex]

Thus, the resultant function is [tex]-2sin(\dfrac{x}{4})[/tex]

The below plotted graph shows graph of sin(x) (in red) and that of  [tex]-2sin(\dfrac{x}{4})[/tex] (in blue).

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if they have two quantities that are equal to the same things, then they would be equal to each others.

Answer:

B. [tex](0,-10)[/tex]

Step-by-step explanation:

We have been given an image of a line segment on coordinate plane. We are asked to find the y-intercept of line, is the line segment is extended to cross both the axes.

We will find the equation of line in slope-intercept form: [tex]y=mx+b[/tex], where,

m = Slope of line,

b = The y-intercept.

We will find slope of our given line using the coordinates of our given points (6,2) and (8,6).

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{6-2}{8-6}[/tex]

[tex]m=\frac{4}{2}[/tex]

[tex]m=2[/tex]

Now, we will substitute [tex]m=2[/tex] and coordinates of point (8,6) in slope-intercept form of equation.

[tex]6=2*8+b[/tex]

[tex]6=16+b[/tex]

[tex]6-16=16-16+b[/tex]

[tex]-10=b[/tex]

Since y-intercept of our given line is [tex]-10[/tex], which is at [tex]x=0[/tex], therefore, option B is the correct choice.

we know that

If two lines are parallel, then their slopes are the same

Step 1

Find the slope of the given line

we know that

the formula to calculate the slope between two points is equal to

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

in this problem we have

[tex](x1,y1)=(-5,-4)\\(x2,y2)=(0,-3)[/tex]

substitute in the formula

[tex]m=\frac{(-3+4)}{(0+5)}[/tex]

[tex]m=\frac{(1)}{(5)}[/tex]

[tex]m=\frac{1}{5}[/tex]

Step 2

Find the equation of the line

we know that

the equation of the line into point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{1}{5}[/tex]

[tex](x1,y1)=(-2,2)[/tex]

substitute

[tex]y-2=\frac{1}{5}(x+2)[/tex]

[tex]y=\frac{1}{5}x+\frac{2}{5}+2[/tex]

[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]

therefore

the answer is

[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]

Answer:

$9828.44

Step-by-step explanation:

The semi annual payment is such that the future value of the annuity due is equal to the desired amount when he retires.

The formula to calculate future value of an annuity due periodic payment of M  for time period T for given periodic return r,

A=[tex]\frac{M(1+r)^{T+1}-(1+r)}{r}[/tex]

in this question there are 30*2= 60 payments and the semi annual rate= 4.5/2= 2.25%

putting values we get

1250675= [tex]\frac{M(1+2.25%)^{60+1}-(1+2.25%)}{2.25%}[/tex]

on solving we get M= $9828.44

Alex needs to invest $9828.44 semiannually in his IRA

Answer:

Step-by-step explanation:

Thank you

A unit of measure is the actual unit in which the associated values are measured.  If a flower is 6.5 cm wide, its width expressed in millimeters is 65 mm,

A Unit of measure is the actual unit in which the associated values are measured.

Unit of Measurement is used as a standard for measurement of the same kind of quantity. The weight is measured in kilograms, grams. The kilogram is unit of mass. litres is the unit of measuring liquids and length is measured in different units, feet, inches, meters, kilometers, centimeters.

We know that 1 centimeter = 10 milli meters.

So if a flower is 6.5 cm wide, its width expressed in millimeters is x mm

We need to find the value of x.

6.5 cm = 6.5×10

=65

So 6.5 cm in millimeters is 65 mm.

Hence if a flower is 6.5 cm wide, its width expressed in millimeters is 65mm.

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we know that

The formula to convert K to C  is equal to

[tex]\° C =\°K - 273.15\°[/tex] --------> equation [tex]1[/tex]

and

The formula to convert C to K  is equal to

[tex]\° K =\°C +273.15\°[/tex] --------> equation [tex]2[/tex]

case a) [tex]100\° K[/tex]

convert to C

substitute in the equation [tex]1[/tex]

[tex]\° C =100\°- 273.15\°=-173.15\°[/tex]

therefore

the answer Part a) is

[tex]\° C =-173.15\°[/tex]

case b) [tex]273\° K[/tex]

convert to C

substitute in the equation [tex]1[/tex]

[tex]\° C =273\°- 273.15\°=-0.15\°[/tex]

therefore

the answer Part b) is

[tex]\° C =-0.15\°[/tex]

case c) [tex]6\° K[/tex]

convert to C

substitute in the equation [tex]1[/tex]

[tex]\° C =6\°- 273.15\°=-267.15\°[/tex]

therefore

the answer Part c) is

[tex]\° C =-267.15\°[/tex]

case d) [tex]143\° C[/tex]

convert to K

substitute in the equation [tex]2[/tex]

[tex]\° K =143\°+ 273.15\°=416.15\°[/tex]

therefore

the answer Part d) is

[tex]\° K =416.15\°[/tex]

case e) [tex]573\° C[/tex]

convert to K

substitute in the equation [tex]2[/tex]

[tex]\° K =573\°+ 273.15\°=846.15\°[/tex]

therefore

the answer Part e) is

[tex]\° K =846.15\°[/tex]

Answer:

Step-by-step explanation: The student divided the number of wins by the number of losses.

The student should have divided the number of wins by the total number of games.

The student should have first added 20 and 10 to find that there were a total of 30 games.

Answer:

SAMPLE RESPONSE: The student divided the number of wins by the number of losses, instead of dividing the number of wins by the total number of games. The student should have divided 20 by 30.

Step-by-step explanation:

other answer: The student divided the number of wins by the number of losses.

The student should have divided the number of wins by the total number of games.

The student should have first added 20 and 10 to find that there were a total of 30 games.

Answer:

260 %

Step-by-step explanation:

1) Since, the percentage formula is,

[tex]\text{Percent Increase}=\frac{\text{Amount of Increase}}{\text{Original Amount}}[/tex]

2) Given,

Original amount = 250,

New amount = 900

So, the amount of increase = New amount - Original amount = 900 - 250 = 650

By substituting the values,

[tex]\text{Percentage increase}=\frac{650}{250}[/tex]

3) Now, for expressing the ratio into percentage we need to multiply by 100,

[tex]\frac{650}{250}\times 100=\frac{65000}{250}= 260\%[/tex]

Answer:

The answer would be option 1) 12

Answer:

The circumference is [tex]C=12\sqrt{\pi }\:in[/tex].

Step-by-step explanation:

The area of a circle when we know the circumference is

[tex]A=\frac{C^2}{4\pi }[/tex]

We know the area [tex]A=36 \:{in^2}[/tex], we plug this value into the above equation and we solve for C the circumference.

[tex]36=\frac{C^2}{4\pi }\\\frac{C^2}{4\pi }=36\\\frac{C^2\cdot \:4\pi }{4\pi }=36\cdot \:4\pi \\\\C^2=144\pi \\C=\sqrt{144\pi }\\C=12\sqrt{\pi }[/tex]

The circumference is [tex]C=12\sqrt{\pi }\:in[/tex].

Answer:  (0,-10)

Step-by-step explanation:

The equation of a line (a,b) and (c,d) is given by :-

[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]

From the given graph , the line is passing through (6,2) and (8,6) is given by :_

[tex](y-6)=\dfrac{6-2}{8-6}(x-8)\\\\\Rightarrow\ y-6=\dfrca{4}{2}(x-8)\\\\\Rightarrow\ y-6=2(x-8)\\\\\Rightarrow\ y=2(x-8)+6[/tex]

To find the y intercept put x =0 , we get

[tex]y=2(0-8)+6=-16+6=-10[/tex]

Hence, the y-intercept of the graph : (0,-10)

Answer:  We compare today's soup to the usual recipe by using "Unitary Method".

Step-by-step explanation:

Since we have given that

The Soup Shack makes tomato soup with 9 tomatoes for every 12 cups of soup.

For every 12 cups of soup , 9 tomatoes is needed

For every 1 cup of soup , the number of tomato is needed is given by

[tex]\frac{9}{12}=\frac{3}{4}[/tex]

Today, they made 8 cups of soup with 6 tomatoes ,

For 8 cups, 6 tomatoes are used .

For 1 cup, number of tomato is used is given by

[tex]\frac{6}{8}=\frac{3}{4}[/tex]

So, we can see that both the soup has same quantity .

∴ We compare today's soup to the usual recipe by using "Unitary Method".

The probability of having exactly [tex]6[/tex] girls in [tex]8[/tex] birth is [tex]\boxed{\bf 0.10937}[/tex].

Further explanation:

Concept used:

The probability of an event [tex]E[/tex] is calculated as follows:

[tex]\boxed{P(E)=\dfrac{n(E)}{n(S)}}[/tex]  

Here, [tex]n(E)[/tex] is the number of favorable outcomes in an event [tex]E[/tex] and [tex]n(S)[/tex] is the number of element in sample space [tex]S[/tex].

The probability of exactly [tex]r[/tex] success in [tex]n[/tex] trial is expressed as follows:

[tex]\boxed{P(F)=^{n}C_{r}p^{r}q^{n-r}}[/tex]

Here, [tex]r[/tex] is the probability of success in an event and [tex]q[/tex] is the probability of failure.

Calculation:

Consider [tex]A[/tex] as an event of having a girl in first birth and [tex]P(A)[/tex] as the probability of event [tex]A[/tex].

The probability of having a girl is [tex]P(A)=\frac{1}{2}[/tex].

Assume that [tex]A'[/tex] is the complement event of an event [tex]A[/tex] and [tex]P(A')[/tex] is the probability of complementary event [tex]A'[/tex].

The event is the event of not having a girl in the first birth.

The probability of event [tex]A'[/tex] is calculated as follows:

[tex]\boxed{P(A')=1-P(A)}[/tex]   …… (1)

Substitute [tex]P(A)=\frac{1}{2}[/tex] in the equation (1) to obtain the probability of event [tex]A'[/tex].

[tex]\begin{aligned}P(A')&=1-\dfrac{1}{2}\\&=\dfrac{1}{2}\end{aligned}[/tex]

The probability of having exactly [tex]6[/tex] girls in [tex]8[/tex] birth is calculated as follows:

[tex]\begin{aligned}P(F&)=^{8}C_{6}\left(\dfrac{1}{2}\right)^{6}\left(\dfrac{1}{2}\right)^{8-6}\\&=\dfrac{8!}{6!\cdot 2!}\cdot (0.5)^{6}\cdot (0.5)^{2}\\&=28(0.5)^{8}\\&=0.10937\end{aligned}[/tex]  

Thus, the probability of having exactly [tex]6[/tex] girls in [tex]8[/tex] birth is [tex]\boxed{\bf 0.10937}[/tex].

Learn more:

1. Learn more about problem on numbers: https://brainly.com/question/1852063

2. Learn more about problem on function https://brainly.com/question/3225044

Answer details:

Grade: Senior school

Subject: Mathematics

Chapter: Probability

Keywords: Probability, exact event, sample space, number of element, complement event, success, failure, favorable, trial, P(E)=n(E)/n(S), P(A')=1-P(A).

Final answer:

To find the probability of getting exactly 6 girls in 8 births, we use the binomial probability formula. In this case, the probability is approximately 0.01.

Explanation:

To find the probability of getting exactly 6 girls in 8 births, we can use the binomial probability formula:

P(x = 6) = C(n, x) * pˣ * (1-p)(n-x)

Where:

In this particular case, P(x = 6) = C(8, 6) * (0.5)⁶ * (0.5)(8-6) = 28 * 0.015625 * 0.015625 = 0.009765625, or approximately 0.01.

The exponential equation, 2ˣ = 1/2, has a value of -1.

Exponential equations are equations in which variables occur as exponents.

Given is an exponential equation, 2ˣ = 1/2, we need to solve it,

2ˣ = 1/2

Taking ㏒ both the side,

㏒ 2ˣ = ㏒ 1/2

x ㏒ 2 = ㏒ 0.5

x = -0.301029996 / 0.301029996

x = -1

Hence, the exponential equation, 2ˣ = 1/2, has a value of -1.

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