a car's velocity is modeled by
[tex] v(t) = 0.5t {}^{2} - 10.5t + 45 \: for\leqslant t \leqslant 10.5[/tex]
Where velocity is in feet per second and time is in seconds. When does the car come to a complete stop?​

The value of J ∩ F =  ∅

The value of J ∪ F = {c, e, f, g, k, j}

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Sets J and F are defined as follows;

J = {c, e, f}

F = {g, k, j}

Now,

Since, Sets J and F are defined as follows;

J = {c, e, f}

F = {g, k, j}

Hence, The value of J ∩ F =  {c, e, f} ∩ {g, k, j}

                                         = ∅

The value of J ∪ F = {c, e, f} ∪ {g, k, j}

                            = {c, e, f, g, k, j}

Thus, The value of J ∩ F =  ∅

The value of J ∪ F = {c, e, f, g, k, j}

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Answer:

[tex] \sf{b. \frac{x}{2} <3}[/tex]

step by step explanation:

We will try one by one.

A. x + 5 < 3

Step 1. Subtitution Value of x

= 4 + 5 < 3

Step 2. Add by 4 with 5

= 9 < 5

A is wrong because 9 is bigger then 5

B. x/2 < 3

= 4/2 < 3

= 2 < 3

is true because 2 is smaller than 3

C. 9x > 36

9(4) > 36

36 > 36

is wrong, should 36 = 36

D. 18 < 8

is wrong because 18 is bigger than 8

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Assuming that your expression is:}[/tex]

[tex]\textsf{0.5x = 0}[/tex]

[tex]\huge\textbf{If so, let's solve for the given expression:}[/tex]

[tex]\textsf{0.5x = 0}[/tex]

[tex]\huge\textbf{Divide 0.5 to both of the sides you have:}[/tex]

[tex]\mathsf{\dfrac{0.5x}{0.5} = \dfrac{0}{0.5}}[/tex]

[tex]\huge\textbf{You have to simplify the equation above:}[/tex]

[tex]\mathsf{x = \dfrac{0}{0.5}}[/tex]

[tex]\mathsf{x = 0}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = }\frak{0}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

The answer to your question is C.n ≥ 7

Step-by-step explanation:

I hope this helps and have a good day!

From the table, we can deduce that The y-values increase by a factor of 7 for each x increase of 1 and is denoted as option C.

This is defined as a number which divides another without leaving a remainder afterwards.

From the table, we can deduce that the y-values are divisible by 7 thereby  making it a factor of it and confirming that it increase by a factor of 7 for each x increase of 1.

Read more about Factor here https://brainly.com/question/219464

#SPJ1

Answer: [tex]5i\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{-50}\\\\=\sqrt{-1} \sqrt{50}\\\\=5i\sqrt{2}[/tex]

Distance formula ds = v(dx² + dy²) s = ? v(1 + (dy/dx)²) dx ......... s = the arc length y = 171 - x²/45

chegg

someone solved it on this

https://youtu.be/UGjXlMVdZvc

The time taken in years for money invested to accumulate to $1500 is 18.45 years

Simple interest = Total savings - principal

= 1500 - 1000

= $500

Simple interest = principal × rate × time

500 = 1000 × 0.0271 × t

500 = 27.1 × t

500 = 27.1t

t = 18.4501845018450

Approximately,

t = 18.45 years

Learn more about simple interest:

https://brainly.com/question/20690803

#SPJ1

The value of x is 78

Given:

[tex]\frac{m}{FCD}=x+48\\\\ \frac{m}{BCD} =x+17\\\\\frac{m}{BCD} =95^0[/tex]

From the given equations, two of them are exactly equivalent

The equivalent equations are compared below

x  +  17   =  95

x  =  95  -  17

x  =  78

Learn more on equivalent equations here: https://brainly.com/question/2972832

#SPJ1

The required equation for a line passing through point A and perpendicular to BC exists 2y + 5x = 31.

First, we must obtain the slope of the line perpendicular to BC

Given the coordinates B(7,5), and C(2,3)

Get the slope BC, exists

[tex]$m_{BC} = \frac{3-5}{2-7}[/tex]

= -2/-5 = 2/5

The slope of the line perpendicular to BC will be -5/2.

The slope of the required line in point-slope form exists expressed as;

[tex]$y - y_0 = m(x - x_0)[/tex]

m = -5/2

[tex](x_0, y_0) = (3, 8)[/tex]

Substitute the values into the formula we get

y - 8 = (-5/2)(x - 3)

2(y - 8) = (-5)(x - 3)

2y - 16 = (-5x + 15)

2y + 5x = 15 + 16

2y + 5x = 31

Therefore the required equation for a line passing through point A and perpendicular to BC exists 2y + 5x = 31.

To learn more about the slope of the line refer to:

https://brainly.com/question/19466805

#SPJ9

Distributive Property :

[tex]\boxed {a(bx + c) = a(bx) + a(c)}[/tex] or

[tex]\boxed {(ax + b)(cx + d) = acx^{2} + bcx + adx + bd}[/tex]

Question 1 :

Question 2 :

Question 3 :

Question 4 :

The  NPV of this investment if the discount rate is 10 percent is: 1.58%.

Year Cash flow  PVIF 10%  Present value

0         ($11.86)     1.000           ($11.86)

1           1.90          0.909           $1.73

2          1.90          0.826           $1.57

3          1.90           0.751           $1.43

4          1.90           0.683          $1.30

5          1.90           0.621           $1.18

6          1.90           0.564          $1.07

7          1.90            0.513          $0.98

8          1.90           0.467          $0.89

9          1.90           0.424          $0.81

10         6.45          0.386         $2.49

NPV                                          $1.58

1.9+5.25-2×35%=6.45

Hence, the NPV is $1.58.

Learn more about NPV here:https://brainly.com/question/17185385

#SPJ1

The solution to the Questions are

where

u=13

n^2=0.16

[tex]\sigma=\sqrt{0.16}\\\\\sigma=0.4[/tex]

a)

Generally, the equation for is  mathematically given as

[tex]X-N(u=13,\sigma=0.4)[/tex]

p(x<14)=P(z<\frac{13-13}{0.4})

P(z<0)

P=0.5

Therefore

P(z<0)=50%

b)

In conclusion

W=(u+2\sigma)

W=(13+2*0.4)

W=13+0.8

W=18.08oz

Read more about  probability

https://brainly.com/question/795909

#SPJ1

Answer:

A

Step-by-step explanation:

Substitute a + 2 for x:

f(a + 2) = 3 [ (a + 2) + 5 ]  + 4 / (a + 2)

            = 3 [ a + 7 ] + 4 / (a + 2)

Answer:

A.

Step-by-step explanation:

Answer:

1) y > x² + 4x - 5, y > x + 5

2) Rational

Step-by-step explanation:

For a parabola, if the shade is inside the curve then the value of y will be greater or equal to:

For a line, if the shade is above it then the value of y will be greater or equal to:

Therefore, since parabola doesn't have solid curve (--- graph) then the inequality is ">"

Therefore, the inequality for parabola is y > x² + 4x - 5

For a line, it does not have solid graph so the inequality is ">"

Therefore, the inequality for line is y > x + 5

-----------

The graph of function describes the shape of rational function. It cannot be exponential as exponential only has one curve. It cannot be logarithm  for same reason as exponential. It cannot be polynomial as polynomial is continuous function but the graph is discontinuous at specific point x = 0.

That being said, all choices except rational are all continuous function by default but rational function isn't and since the graph is discontinuous then we can say that it's rational function.

Using trigonometric identities, the simplified expression, without quotients, is given as follows:

A. [tex]\cos{\beta}\cot{\beta}[/tex]

The cosecant of an angle is given by one divided by the sine of the angle, hence:

[tex]\csc{\beta} = \frac{1}{\sin{\beta}}[/tex]

The sine and the cosine of an angle are related as follows:

[tex]\sin^2{\beta} + \cos^2{\beta} = 1[/tex]

[tex]\cos^2{\beta} = 1 - \sin^2{\beta}[/tex]

The cotangent of an angle is:

[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}}[/tex]

The expression given is:

[tex]\csc{\beta} - \sin{\beta}[/tex]

Simplifying the cosecant:

[tex]\csc{\beta} - \sin{\beta} = \frac{1}{\sin{\beta}} - \sin{\beta} = \frac{1 - \sin^{2}\beta}{\sin{beta}}[/tex]

Then, applying the last two identities in the subsection above to remove the quotient, the simplified expression will be found as follows:

[tex]\frac{1 - \sin^{2}\beta}{\sin{beta}} = \frac{\cos^2{\beta}}{\sin{\beta}} = \frac{\cos{\beta}}{\sin{\beta}} \times \cos{\beta} = \cos{\beta}\cot{\beta}[/tex]

Hence option A is correct.

More can be learned about trigonometric identities at https://brainly.com/question/26676095

#SPJ1

Answer:

4/91

Step-by-step explanation:

There are a total of 15 marbles.  In the first selection there are 15 marbles and 6 are blue.  That would be 6/15.

Since we are not replacing marbles, we now have 14 marbles and we want to select one of the 5 white marbles.  That would be 5/14.

Lastly we now only have 13 marbles and of those we want to select one of the 4 red ones.  That would be 4/13.

Now we take these 3 fractions and multiply them together.

6/15(5/14)(4/13).  I am going to try to make this a little easier and see if I can find any factors that any top number shares with any bottom number.

I see 5 on the top shares a common factor with 15 on the bottom.  I will divide these numbers by 3, so now I have

6/3(1/14)(4/14).  I think that I can do better than that.  I see that 6 on the top and 3 on the bottom share a common factor of 3.  I will divide both of these numbers by 3.  Which will give me:

2/1(1/14)(4/13) I see a 4 on top and a 14 on the bottom.  Those are both divisible by 2 so, I will divided them both by 2 and that leaves me with

2/1(1/7)(2/13)  That is a lot easier, now I will just multiple the top numbers and multiply the bottom numbers to get

4/91

Answer:

1/10

Step-by-step explanation:

the probability of drawing r the first time is 2/5, if tina had gotten the r the first time, the probability of drawing r on the second time is 1/4, so the probability tina draws an r twice is 2/5 * 1/4, or 2/20, or 1/10

Answer:

Exact form: 7/143

Decimal form: /0.048951

Answer:

[tex]x=\frac{7}{143}[/tex]

Step-by-step explanation:

Simplify the right side of the equation. [tex]3x+21=432x[/tex]. Subtract 21 from both sides of the equation. [tex]3x=432x-21[/tex]. Subtract 432x from both sides of the equation, [tex]-429x=-21[/tex]. The negative signs cancel out to get [tex]429x=21[/tex]. Divide both sides but 429 to get [tex]x=\frac{21}{429}[/tex].  Reduce to get [tex]x=\frac{7}{143}[/tex].

See the graph in the attached image.

Answer:

x = 117

Step-by-step explanation:

Foremost, we know that the three angles of the triangle always add up to 180 degrees.

So, there are two sides which are 27 degrees and 36 degrees, we need to find the third one's degree.

Add 27 and 36 (27 + 36 = 63)

Two sides equal 63.

Then, subtract 180 - 63 = 117

So the third angle's measurement is 117 degrees. The answer is 117.

To check, add 117 + 27 + 36 = 180

Hope it helps.

There are 60 questions on the test

Total number of questions = 42

Percentage equivalent= 70%

Let the total number of questions in the test be represented by x

42 = 70% of x

[tex]42=\frac{70}{100} \times x[/tex]

42 = 0.7x

Divide both sides by 0.7

42/0.7  =  0.7x/0.7

x  =  60

Therefore, there are 60 questions on the test

Learn more on percentages here: https://brainly.com/question/11360390

#SPJ1

Answer:

x = 22°

Step-by-step explanation:

Between two parallel lines, the opposite inside angles will be congruent. So, x is equal to angle V. The sum of the angles of any triangle will be 180°. Therefore, you can find the value of x by setting all the angles of the triangle SRV equal to 180°.

S = 5x + 4

R = 44

V = x

S + R + V = 180                                         <----- General equation

(5x + 4) + 44 + x = 180                              <----- Insert values

5x + 48 + x = 180                                      <----- Add 4 and 44

6x + 48 = 180                                           <----- Add 5x and x

6x = 132                                                    <----- Subtract 48 from both sides

x = 22                                                      <----- Divide both sides by 6

Option A, The option that has the same potential roots according to the rational root theorem is 3x5 – 2x4 – 9x3 + x2 – 12.

We have p, this is the factors of the number 12.

The factors are ±(1, 2, 3, 4, 6, 12)

We have factors of q = 3

= ±(1, 3)

The rational roots are the roots that have the same factors that are contained in the question.

Hence the answer is A.

Read more on Rational root theorem here:

https://brainly.com/question/2072459

#SPJ1

Answer:

The Answer is A

Step-by-step explanation:

Did it on edge :)

Notice that

[tex]7^{2014} - 7^{2012} = 7^{2012} \bigg(7^2 - 1\bigg) = 7^{2012} \times 48 = 2^4 \times 3 \times 7^{2012}[/tex]

[tex]12=2^2\times3[/tex], so

[tex]\dfrac{7^{2014}-7^{2012}}{12} = 2^2 \times 7^{2012}[/tex]

Then taking the positive square root gives

[tex]\sqrt{\dfrac{7^{2014}-7^{2012}}{12}} = \sqrt{2^2 \times 7^{2012}} = 2\times7^{1006}[/tex]

so [tex]\boxed{a=2}[/tex] and [tex]\boxed{b=1006}[/tex].

Answer:

see explanation

Step-by-step explanation:

to evaluate f(a) substitute x = a into f(x)

f(a) = 5a + 4

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

2f(a) = 2(5a + 4) = 10a + 8

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

to evaluate f(2a) substitute x = 2a into f(x)

5(a + 2) + 4 = 5a + 10 + 4 = 5a + 14

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

f(a) + f(2) ← substitute x = 2 into f(x)

= 5a + 4 + 5(2) + 4 = 5a + 4 + 10 + 4  = 5a + 18

The solution of x is x = 0, x =2 and x = -5

The equation is given as:

2x^3+6x^2-20x=0​

Factor out x

x(2x^2+6x-20)=0​

Split the equation

x = 0 or 2x^2+6x - 20=0​

Solve for x in 2x^2+6x - 20=0​

Expand the equation

2x^2 + 10x - 4x - 20 = 0

Factorize the equation

(2x - 4)(x +5) = 0

Split the equation

2x - 4 = 0 and x + 5 = 0

Solve for x

x =2 and x = -5

Hence, the solution of x is x = 0, x =2 and x = -5

Read more about equations at:

https://brainly.com/question/13712241

#SPJ1

Answer:

[tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]

Step-by-step explanation:

Let's write the equation of the line in the slope-intercept form. That is, y= mx +c, where m is the slope and c is the y-intercept.

Identify 2 coordinates on the line to calculate the slope.

The 2 points are (1, 2) and (4, 4).

Slope

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

= [tex]\frac{4-2}{4-1}[/tex]

= [tex]\frac{2}{3}[/tex]

Substitute the value of the slope into m:

[tex]y=\frac{2}{3}x+c[/tex]

Substitute any point into the equation to find c:

When x= 1, y= 2,

[tex]2= \frac{2}{3}(1)+c[/tex]

Solve for c:

[tex]c= 2-\frac{2}{3}[/tex]

c= [tex]\frac{4}{3}[/tex]

Thus, the equation that represents the line is [tex]y=\frac{2}{3}x+\frac{4}{3}[/tex].

Additional:

Should you wish to learn more about slope-intercept form, do check out the following!

The diameter of the circle is 11.8 units

The circle equation is given as:

(x - 2)^2 + (y + 6)^2 = 35

A circle equation is represented as:

(x - a)^2 + (y - b)^2 = r^2

Where

Diameter = 2r

By comparing both equations, we have

r^2 = 35

Take the square root of both sides

r = 5.9

Multiply by 2

2r = 11.8

Hence, the diameter of the circle is 11.8 units

Read more about circle equation at:

https://brainly.com/question/10618691

#SPJ1