A rational function is a function whose equation contains a rational expression.A.Trueb.False

6y - x = 12 //Solve for y.

6y = x + 12

y = x/6 + 2

Slope = m = 1/6

For the second which is perpendicular to line one has a slope of -6.

NOTE: Perpendicular line has negative reciprocal slope. 1/6 negative reciprocal would be -6.

Second line:

m = -6

point = (-1,2)

y - y1 = m(x - x1) //Plug in m and point in place of (x1,y1).

y - 2 = -6(x - -1)

y - 2 = -6x -6

y = -6x -6 +2

y = -6x - 4

//Hope it helps

Answer:

Step-by-step explanation:

Divide 2/3 by 4/5

Which is done by K(eep)C(hange)F(lip)

2/3 * 5/4 = 10/12 = 5/6

N= 5/6

Here is how we do it:

First, we must simplify 4/5n to 4n/5.

Then we simplify:   [tex]2/3n[/tex] to get [tex]2n/3.[/tex]

After we multiply both sides by the number 15.

[tex]12n =  10n[/tex]

Alright, now let's move them all together.

It would be: [tex]12n - 10n = 0[/tex]

Our last step is to simplify 12n - 10n to 2n.

Then we receive: [tex]2n = 0[/tex]

After we divide both sides by 2.

Our final answer is: [tex]n = 0[/tex]

Height = SQRT(30^2 - 8^2)

Height = SQRT(900-64)

Height = SQRT(836)

Height = 28.9 feet

Answer:

w = [tex]-\frac{9}{8}[/tex]

Step-by-step explanation:

The question is  [tex]4w-4+2(5w+8)=-2(w+3)[/tex]

We can first use distributive property to simplify, the distributive property is  [tex]a(b+c)=ab+ac[/tex]

Thus we have:

[tex]4w-4+2(5w+8)=-2(w+3)\\4w-4+10w+16=-2w-6[/tex]

Now we combine like terms and simplify to get the final answer for w.

[tex]4w-4+10w+16=-2w-6\\14w+12=-2w-6\\14w+2w=-6-12\\16w=-18\\w=\frac{-18}{16}\\w=-\frac{9}{8}[/tex]

Thus, w = [tex]-\frac{9}{8}[/tex]

Answer:

1.125

Step-by-step explanation:

we first open the brackets by multiplying every term inside the brackets by 2

We get the following equation: 4w-4+10w+16=-2w-6

collecting like terms together we get 4w+10w+2w=-6-16+4

   16w=-18

dividing both sides by 16 we get w=18/16

=9/8

= 1 1/8 or  1.125

Answer: 5 km and 25 km

Answer:

18%

Step-by-step explanation:

18% is the percent increase in tuition fees.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, The tuition at a college increased from 50,000 in 2006 to 59,000 in 2007.

From the general formula of percentage change,

percentage change = change in value/original value * 100

In our case,

original value = 50,000

change in value = 59,000 - 50,000

change in value = 9,000

thus,

Percentage change = 9,000/50,000 *100

Percentage change = 18%

Therefore,  the percent increase in tuition fees is 18%.

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Answer:The answer is -3 and 3. You can do this by using a graphing calculator and plugging in the equation.

Answer:

3, -3, 6i, -6i

Step-by-step explanation:

Answer:

Step-by-step explanation:

Usain Bolt

Part A

d = 200 m

t = 19.30 seconds

r = d/t

r = 200 / 19.30

r = 10. 36

r = 10.4 m/s

Part B

d = 400 meters

t = 43.18 seconds

r = d/t

r = 400/43.18

r = 9.26 m/s

r = 9.3

Not much difference.

Michael Johnson

Though you have not given us the distance, it was 100 meters. He was the first man to eclipse 9.7 seconds for the 100 meters.

d = 100 m

t = 9.69 seconds

r = 100 meters/9.69 seconds

r = 10.32 m/s

r = 10.3

Answer:

(kj)(x)= -16x^2- 12x +10

Step-by-step explanation:

Answer:

Option A is correct

[tex](kj)(x)=-16x^2-12x+10[/tex]

Step-by-step explanation:

Given the functions are as follows:

[tex]j(x) = -4x+2[/tex]

[tex]k(x) = 5+4x[/tex]

We have to find (kj)(x).

Consider,

[tex](kj)(x) = k(x)j(x)[/tex]

Substitute the given values we have;

[tex](kj)(x) = (5+4x)(-4x+2)[/tex]

Using distributive property, [tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex]

[tex](kj)(x)=-20x+10-16x^2+8x[/tex]

Combine like terms;

[tex](kj)(x)=-12x+10-16x^2[/tex]

or

[tex](kj)(x)=-16x^2-12x+10[/tex]

Therefore, the function rule for  (kj)(x) is, [tex]-16x^2-12x+10[/tex]

The volume of Nadya's container, calculated using the formula for the volume of a cylinder and rounded to the nearest cubic centimeter, is 1414 cubic centimeters.

The volume of Nadya's container can be calculated using the formula for the volume of a cylinder, which is V = πr²h, where V represents volume, r represents the radius of the base, and h represents the height. Given that the radius of the container's base is 5 centimeters and the height of the container is 18 centimeters, substituting these values into the formula gives you V = π(5)²(18) = 1413.72 cubic centimeters. Rounded to the nearest cubic centimeter, the volume is 1414 cubic centimeters.

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This is through multiplication and division.

Remember your order of operations!

Answer: 6.3

Good luck!

-RxL

Answer:

The answer is 6.3

Step-by-step explanation:

14 x 90 divided by 200 = 14*90/200

= 7*9/10

= 6.3

Answer:

[tex]s = 21\ ft\\\\a = -6\ \frac{ft}{s^2}[/tex]

Step-by-step explanation:

To find the changes in the slope of the function s(t) we find its derivative

[tex]\frac{ds(t)}{dt} = 3t^2 - 18t +24\\[/tex]

Now we make [tex]\frac{ds(t)}{dt} = 0[/tex]

[tex]3t^2 - 18t +24 = 0[/tex]

[tex]3t^2 - 18t +24\\\\3(t^2-6t + 8)\\\\3(t-4)(t-2)\\\\t_1 =4\\t_2=2\\[/tex]

The particle changes direction for the first time at t = 2 sec

The position at t = 2 sec is:

[tex]s(t=2) = (2)^3 - 9(2)^2 + 24(2) + 1\\\\\s(2) = 21\ ft[/tex]

The acceleration after t = 2 sec is the second derivative of s(t), evaluated at t = 2:

[tex]\frac{d^2s(t)}{d^2t} = 6t -18\\\\\frac{d^2s(t)}{d^2t}(2) = 6(2) -18\\\\ a = 12-18\\\\a = -6\ \frac{ft}{s^2}[/tex]

Answer:

The position is 21 feet

The acceleration is -6 ft/sec²

Step-by-step explanation:

∵ s(t) = t³ - 9t² + 24t + 1

- where s is the displacement in feet and t is the time in second

∵ v(t) = ds/dt ⇒ velocity is the differentiation of s(t)

∵ a(t) = d²s/dt² = dv/dt ⇒ acceleration is the differentiation of v(t)

∴ v(t) = 3t² - 18t + 24

∵ When the particle reverses means v(t) = 0

∴ 3t² - 18t + 24 = 0 ⇒ ÷ 3

∴ t² - 6t + 8 = 0

∴ (t - 2)(t - 4) = 0

∴ t - 2 = 0 ⇒ t = 2 seconds

∴ t - 4 = 0 ⇒ t = 4 seconds

- That means the particle will change its direction first after 2 seconds

  and again after 4 seconds

∵ a(t) = dv/dt

∴ a(t) = 6t - 18

∵ t = 2

∴ a(2) = 6(2) - 18 = 12 - 18 = -6 ft/sec²

∵ s(t) = t³ - 9t² + 24t + 1

∴ s(2) = 2³ - 9(2)² + 24(2) + 1 = 21 feet

Answer:

(0,12)

Step-by-step explanation:

Just plug in 0 for x so (0-6)(0-2) = 12 so that's the y value.

Also, a y intercept has to be of the form (0,y) where y is some number.  The x value has to be 0, so that eliminates the last two options automatically, but if we put the x and y value we got together we get (0,12)

Answer:

(0,12)

Step-by-step explanation:

[tex]f(x) = (x - 6)(x - 2)[/tex]

To find out y intercept , plug in 0 for x and find out f(0)

y intercept are the value where the graph crosses y axis

[tex]f(x) = (x - 6)(x - 2)[/tex]

[tex]f(0)= (0-6)(0 - 2)=12[/tex]

When x is 0 the value of y is 12

Write y intercept as (0,y) that is (0,12)

Answer:

Miles

Like asking what measures distance between a lake and a city.

The range of the sample means calculated from the provided data is 2.2.

To find the range of the sample means, we first need to calculate the mean for each row and then find the range of these means.

Calculating the mean for each row:

1st row: (3 + 1 + 0 + 4 + 1) / 5 = 9 / 5 = 1.8

2nd row: (4 + 2 + 3 + 0 + 5) / 5 = 14 / 5 = 2.8

3rd row: (0 + 1 + 1 + 2 + 0) / 5 = 4 / 5 = 0.8

4th row: (4 + 1 + 4 + 4 + 2) / 5 = 15 / 5 = 3

5th row: (3 + 2 + 0 + 1 + 4) / 5 = 10 / 5 = 2

Now, let's find the range of these means:

Range = Maximum mean - Minimum mean

Range = 3 - 0.8 = 2.2

Therefore, the range of the values for the sample means is 2.2.

Answer:

5

Step-by-step explanation:

The nth term of the geometric sequence is

[tex]a_n=(-2)(5)^{n-1}[/tex]

In general the nth term of a geometric sequence is

[tex]a_n=a_1(r)^{n-1}[/tex]

By comparism;

[tex]r=5[/tex] is the common ratio of the sequence.

Or

[tex]a_1=(-2)(5)^{1-1}=-2[/tex]

[tex]a_2=(-2)(5)^{2-1}=-10[/tex]

Common ratio is

[tex]r=\frac{-10}{-2}=5[/tex]

Answer:

$4.

Step-by-step explanation:

20x20%= 4.

To record the issuance of the note payable and the first monthly payment, create a debit entry for the delivery truck and credit entry for the notes payable. Then, debit the notes payable to reduce the amount owed and credit the cash for the same amount to show the outflow of cash.

To record the issuance of the note payable and the first monthly payment, we will first create an entry to record the note payable on January 1, 2018. We will debit the Delivery Truck account for $25,000 and credit the Notes Payable account for the same amount. This represents the borrowing of the $25,000.

Next, we will record the first monthly payment on January 31, 2018. We will debit the Notes Payable account for $760.55 to reduce the amount owed, and credit the Cash account for the same amount to show the outflow of cash.

Answer:

d. [tex]x=1,4,\:or\:7[/tex]

Step-by-step explanation:

The given equation is

[tex]x^3-12x^2+39x-28=0[/tex]

To find all real solutions using the x-intercept method, we to graph the corresponding function using a graphing tool.

The corresponding function is;

[tex]f(x)=x^3-12x^2+39x-28[/tex]

The real solutions to [tex]x^3-12x^2+39x-28=0[/tex], are the x-intercepts of the graph of the corresponding function.

From the graph the x-intercepts are

(1,0),(4,0) and (7,0).

Therefore the real solutions are

[tex]x=1,4,\:or\:7[/tex]

I think the answer is 144

Answer:

3 hours

Step-by-step explanation:

39 miles/ 13 miles per hour means 3 hours. SIMPLE!

The measure of angles in a rhombus can be found understanding the properties of a rhombus (i.e., opposite angles are equal and adjacent angles are supplementary) and possibly applying trigonometry in which angles are not aligned in regular horizontal or vertical manner. Specific measurements can be obtained using a protractor.

To find the measure of the numbered angles in the rhombus, you need to understand the geometric properties of a rhombus. The opposite angles of a rhombus are equal, and the adjacent angles are supplementary, meaning they add up to 180 degrees. Further, the diagonals of a rhombus bisect its angles, and they are perpendicular to each other, forming 90-degree angles where they intersect.

Clearly, the exact measures of the angles will depend on the specific information provided about the rhombus in your diagram. Here are some steps on how you might determine these measures:

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Answer: [tex]\frac{1}{4}=2^{(-2)}[/tex]

Step-by-step explanation:

You know that an expression written is logarithmic form is:

[tex]x=log_b(y)[/tex]

And an expression equivalent to the expression above that is written in exponential form is:

[tex]y=b^x[/tex]

Therefore, keeping the information above on mind, you have that an equivalent exponential equation for [tex]log_{2}(\frac{1}{4}) =-2[/tex] , is the shown below:

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

Answer:

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

Step-by-step explanation:

We are given the following expression and we are to write an equivalent exponential equation for it:

[tex] log_2 (\frac { 1 } { 4 } ) = - 2 [/tex]

We know that the standard form of a logarithmic expression is given by:

[tex] y = log_a ( x ) [/tex]

which is equivalent to the exponential form [tex] x = a ^ y [/tex].

Therefore, for the given expression, the equivalent exponential equation will be:

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

Answer:

Kayla is correct; the center is a fixed point in the middle of the sphere.

Answer:

Kayla is correct; the center is a fixed point in the middle of the sphere

Step-by-step explanation:

To understand the solution we need to understand what a sphere is.

What is Sphere?

Sphere is a 3 dimensional solid where every point is equidistant from the center.

Center is the point in the middle

radius is the line joining any point on the surface to the center of the sphere

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Answer: Option a.

Step-by-step explanation:

- Divide both sides of the expression by 7.8:

[tex]7.8e^{\frac{x}{3}ln5}=14\\\\\frac{7.8e^{\frac{x}{3}ln5}}{7.8}=\frac{14}{7.8}\\\\e^{\frac{x}{3}ln5}=\frac{14}{7.8}[/tex]

- By definition:

[tex]e^y=x[/tex]→[tex]y=ln(x)[/tex]

Then:

[tex]\frac{x}{3}ln5=ln(\frac{14}{7.8})[/tex]

- Now, you must solve for x.

Then, you obtain:

[tex]xln5=3ln(\frac{14}{7.8})[/tex]

[tex]x=\frac{3ln(\frac{14}{7.8})}{ln5}[/tex]≈[tex]1.0903[/tex]

Answer:

180°

Step-by-step explanation:

The measures of the angles in the triangle shown are ...

81.87°, 60.26°, 37.87°

The sum of those measures is ...

81.87° + 60.26° + 37.87° = 180.00°

Answer:

Step-by-step explanation:

Use the formula of a midpoint:

[tex]\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have the points P(-2a, 0) and Q(0, 2b). Substitute:

[tex]x=\dfrac{-2a+0}{2}=\dfrac{-2a}{2}=-a\\\\y=\dfrac{0+2b}{2}=\dfrac{2b}{2}=b[/tex]

Answer:

(5, -2)

Step-by-step explanation:

x + y = 3 can become x = 3-y

we are going to use substitution

now plug x = 3-y into the other equation

2(3-y) + 3y = 4

6-2y+3y = 4

6 + y = 4

subtract 6 from both sides

y = -2

now plug in y back into one of the equations, it doesn't matter which one. I am going to use the x + y = 3 equation

x -2 = 3

x = 5

Answer:

Which of the following sampling techniques is the most likely to produce a random sample, representative sample of all students at a high school?

A. Choosing every 10th name on the student roster

B. Choosing every 10th student arriving in a 9th grade homeroom

C. Choosing the first 100 students who arrive at school

D. Asking students to call a phone number to answer survey questions

Step-by-step explanation:

A random sample is choosing the first 100 students who arrive at school.

There are five types of Sampling Techniques

Random sampling is similar to putting everyone's name into a bowl and drawing out random names. Each element has a chance of being called.

Systematic sampling is easier to do than random sampling. In systematic sampling, the list of elements is "counted off". That is, every kth element is taken.

Convenience sampling is very easy to do, but it is the least effective technique to use. In convenience sampling, data that is easily available is used.

Cluster sampling is accomplished by dividing the population into groups usually geographically. These groups are called clusters or blocks. The clusters are randomly selected, and each element in the selected clusters are used.

Stratified sampling also divides the population into groups called strata. However, this time it is by some characteristic, not geographically.

Option C , i.e. Choosing the first 100 students who arrive at school is an example of Random Sampling.

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Answer:

yes the first step is

Step-by-step explanation:

Answer: a- |x - 9.5| ≤ 1.5

b- x - 9.5 ≤ 1.5

x - 9.5 + 9.5 ≤ 1.5 + 9.5

x ≤ 11

Step-by-step explanation: