Given f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity, which of the following is true
Answers
The correct answer is option D which is f(x) is decreasing for all the values of x < 3.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
The value of the function [tex]f(x) = \dfrac{x+6}{x^2-9x+18}[/tex] is represented on the graph in the graph we can see that at x>6 the value of the function is decreasing and at x<3 the value of the function is increasing.
Therefore the correct answer is option D which is f(x) is decreasing for all the values of x < 3.
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Related Questions
A candle on Pauline’s dresser is 4 inches tall and burns at a rate of 0.6 inches per hour. How many hours will it take for the candle to burn down to a height of 1.3 inches?
Answers
The time taken for the candle to burn down to a height of 1.3 inches is 4.5 hours
What is a Linear Function ?A linear function is what can be written in the form of
y =mx+c
The rate at which the candle is burning is 0.6 inches/ hour
The initial height is 4 inches at t=0
The straight line equation can be written for this as
y =mx +c
as m = -0.6
at x = 0 , y = 4 therefore c =4
y = -0.6x +4
The time at which y = 1.3 inches is
1.3 = -0.6x +4
-2.7 = -0.6 x
x =4.5
4.5 hours is the time taken for the candle to burn down to a height of 1.3 inches.
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Question 2 On the line that passes through point C, mark a point D that is distinct from point C. Use the slope formula along with coordinates of points to find the slopes of and . Show your work.
Answers
The slope formula along with coordinates of points ( p,q) and (x,y) [tex]m = \dfrac{y-q}{x-p}[/tex].
What is the slope of a straight line?A slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When the slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
This is because the more the height of the line to the amount we walk or run on the horizontal axis, the more the slope is.
The slope of a line that passes through points ( p,q) and (x,y)
Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
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The following diagram shows a 4-step process that begins with Operation 1 and ends with Operation 4.
Answers
Based on the operations and their times, the capacity of this process is 10 per hour and the action that would yield the greatest increase would be 2. increase operation 2 by 14%.
What is the capacity of the process?The capacity of the process is the least operation time in the process which is 10/ hr.
How can we get the greatest increase in process capacity?Check all the alternatives given. The alternative with the lowest capacity is best.
Increase operation 1 by 12%:
= 11 x (1 + 12%)
= 12.32 per hour
Increase operation 2 by 14%:
= 10 x (1 + 14%)
= 11.4 per hour
Increase operation 3 by 10%:
= 12 x (1 + 10%)
= 13.2 per hour
The best alternative is therefore to increase operation 2 by 14%.
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where do banks get the money to lend to consumers
Answers
Answer:
Depositors
Step-by-step explanation:
Answer:
Banks get the money from the people that deposit their money at the bank for a low interest rate and lend to the customers with a high interest rate.
follow the steps to construct a diagram:
1:create points A, B, and C in order on a horizontal line with a distance of four units between successive points.
2:draw Circle with center that passes through b, and two tangents to the circle passing through C.
3:locate the points of intersection of the tangents with the circle, and labeled them D and E.
4: draw the radii AD and AE to create central angel EAD.
Take a screenshot of your construction, and paste it below.
Answers
Answer:
a=3=8
Step-by-step explanation:
there is none
The construction forms a diagram consisting of a circle, two tangents, and a central angle EAD as shown in the attached figure.
Construction is a topic that requires drawing a required shape, line, and figure with constructing tools. The appropriate steps should be taken so as to complete the required figure.
In the given question, the circumference of the required circle passes through points A and C. And the radius of the circle with center B is 4 units so its diameter is 8 units. Then joining the points D and E to A, creates a central angle EAD.
Following the appropriate steps, the required diagram for the construction is as given in the attachment to this question.
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To best show a possible linear trend in a scatter plot, draw a _________________.
A. regressive line
B. line of best fit
C. vertical line
D. horizontal line\
Answers
Answer:
b. line of best fit
Which of the following numbers is shown plotted on the number line ?
Answers
Write the prime factorization of 10
Answers
Answer:
2|10
5|5
1
Prime factors of 10 are 2*5
EASY POINTS
Which of the following exponential functions represents the graph below?
Answers
Answer: It's B.
Step-by-step explanation: It can't be A or D. The y-intercept is 2, not 4 so it is B.
Which one of these functions is a quadratic function?
OA Rx) = x-3x+1
OB. f(x)=3*
OC. f(x)=x²³
OD. f(x) = log(x+7)
Answers
Answer:
x^2 -3x+1
it is your answer
The function x² - 3x + 1 represents a quadratic function.
A quadratic function is a function of the form f(x) = ax² + bx + c, where a, b, and c are constants.
In option A, we have f(x) = x² - 3x + 1, which fits the form of a quadratic function with coefficients a = 1, b = -3, and c = 1.
In option B, the function is Exponential.
In option C, the function is Exponential.
In option D, the function is logarithm.
Therefore, x² - 3x + 1 represents a quadratic function.
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Solve the inequality |a + 3| > 14
Answers
Answer:
a∈(-∝;-17)∩(11;+∝).
Step-by-step explanation:
|a+3|>14; ⇔ 14<a+3<-14; ⇔ 11<a<-17;
Test Scores Find the percentile rank for each test score in the data set. Round to the nearest whole percentile.
10, 15, 19, 23, 30
Part 1 of 6
The percentile rank for the value 10 is
Answers
The percentile rank for 10 will be 10th.
What is percentile rank?The percentile rank of a particular score in statistics refers to the percentage of scores in the frequency distribution that are smaller than that score.
Percentile rank = [(Number of values below x) + 0.5]/ total number of values * 100
For 10,
Percentile rank = {[0 + 0.5]/5} x 100 = 10th
For 15,
Percentile rank = ([1 + 0.5]/5) x 100 = 30st
For 19,
Percentile rank = [2 + 0.5]/5 x 100 = 50th
For 23,
Percentile rank = [3 + 0.5]/5 x 100 = 70th
For 30,
Percentile rank = [4 + 0.5]/ 5 x 100 = 90th
The percentile rank for 10 will be 10th.
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3t-2/4 - 2t-3/3 = 2/3 - t
Answers
The value of the variable t will be 13 / 12.
What is Algebra?The analysis of mathematical representation is algebra, and the handling of those symbols is logic.
The equation is given below.
3t - 2/4 - 2t - 3/3 = 2/3 - t
Then the value of t will be
t - 3/2 = 2/3 - t
2t = 2/3 + 3/2
2t = 13 / 6
t = 13/12
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what is two significant digit for 59.3506494?
Answers
Answer:
59
Step-by-step explanation:
Round 59.3506494 to the first 2 sig figs which is 59 since the number next to the decimal isnt over or 5, so it stays as 59 instead of 60.
Elaina Kicks A Soccer Ball With An Initial Velocity Of
Answers
By using the motion equations, we conclude that she will make the goal.
Will she make the goal?
First, we know that the goal is 20ft away, and the position in x is given by:
[tex]x = 28*cos(58)*t[/tex]
Let's find the time in which the ball will travel these 20 ft.
[tex]20 = 28*cos(58)*t[/tex]
[tex](20)/(28*cos(58)) = t = 1.35[/tex]
So the horizontal distance is covered in 1.35 seconds, now let's see which is the height of the ball at that time.
The height equation is:
[tex]y = -16*t^2 +28*sin(58)*t[/tex]
Evaluating in t = 1.35 we get:
[tex]y = -16*(1.35)^2 +28*sin(58)*1.35\\\\y = 2.9[/tex]
And the goal is 5ft tall, so we can conclude that she will make the goal.
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help pleseeeeeeeeeeeeeeeeeeeeeeee
Complete the information as requested:
1.- Indicated dose: 300 mg of Ceftriaxone ampoules IV every 6 hours for 10 days.
Available: 1.2 g of Ceftriaxone vial. Reconstitute with 5ml of Sterile Water
a) Dose volume … Calculations
b) Number of doses per day to comply with the indication.
c) Number of ampoules needed for the entire treatment
2.- The patient has indicated:
Indicated quantity: 250 mg Tobramycin ampoule every 12 hours
Available Tobramycin 100 mg /ml vial
a) Dose volume for administration according to indication.
b) Number of ampoules needed for one day of treatment.
c) Amount of Tobramycin received per day - mg
3.- A doctor indicates 0.5 g PO c6h x 5 days
The drug available is 125 mg / 5 mL
a) What is the amount of drug administered per dose? in ml
b) how many total doses for the 5 days are required
c) how many 100 ml bottles do I need to deliver
Answers
Let f(x)=20/5+6e^−0.1x What is (5)? Round your answer to 4 decimal places.
Answers
We can conclude that the function evaluated in x = 5 is equal to 2.3150
How to evaluate the function?Here we have the function:
[tex]f(x) = \frac{20}{5 + 6e^{-0.1x}}[/tex]
And we want to evaluate in x = 5, this just means to replace the x by a 5 in the given function:
We can evaluate this with a calculator (as doing it by hand is kinda hard), we will get:
[tex]f(5) = \frac{20}{5 + 6e^{-0.1*5}} = 2.3150[/tex]
So we can conclude that the function evaluated in x = 5 is equal to 2.3150.
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Una camioneta transportaba 3/4 de tonelada de arena para entregar a diferentes clientes. Si al primer cliente le dejo 1/3 de la carga que fracción de toneladas quedo en la camioneta
Answers
IK
rying the Distributive Property
Try it
Which statement is an example of the distributive property?
O3+ (2)(15)= 3(2) + 3(15)
O3(2+15) = 3 + 2(3) + 15
O3(2+15)= 3(2) + 3(15)
O 3(2+15)= 3(2) + 15
Answers
The statement that is an example of the distributive property is (c) 3(2+15)= 3(2) + 3(15)
How to determine the example?The distributive property states that:
a(b + c) = a(b) + a(c)
Using the above property, we have:
3(2+15)= 3(2) + 3(15)
Hence, the statement that is an example of the distributive property is (c) 3(2+15)= 3(2) + 3(15)
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After sales tax, a $600 antique clock costs $642. What is the sales tax percentage?
Answers
well, clearly the tax is the added 42 bucks, so hmmm if we take 600 to be the 100%, how much is 42 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 600 & 100\\ 42& x \end{array} \implies \cfrac{600}{42}=\cfrac{100}{x}\implies \cfrac{100}{7}=\cfrac{100}{x} \\\\\\ 100x=700\implies x=\cfrac{700}{100}\implies x=7[/tex]
Answer:
Answer is 7% sales Tax
Step-by-step explanation:
I first like to take one percent of the original value, in this case 1% of 600 is 6 dollars. I then multiply 6 by the number needed to get to 642, which is 107- you will always then subtract 100 from this number and you get 7%. This should work for other problems as well. This is probably not the best explanation btw
Mary throws a plastic disc to her friend. Her friend
catches the disc six seconds after Mary throws it. The
table shows the height of the disc at one-second
intervals.
Time (seconds)
Height (feet)
0
3
1
A
2
6
3
7
6
4
B
4
5
6
Mark this and return
Assuming that the throw represents projectile motion,
what are the missing values in the table?
O A = 5, B = 3
O A=4, B=0
O A=4, B = 3
O A = 5, B = 0
Submit
Next
Answers
By assuming that the motion of the plastic disc thrown by Mary is a projectile motion, the missing values are 4 and 3 respectively.
How to determine the missing height?Since we're assuming that the motion of the plastic disc thrown by Mary is a projectile motion, it simply means that the motion can be represented by a quadratic function (parabolic).
For a projectile motion, the height of the disc at the time when it's at the top would be the same (equal). Thus, we can logically deduce that:
Height at time (t = 1 seconds) = Height at time (t = 5 seconds)
4 = A.
Similarly, Height at time (t = 0 seconds) = Height at time (t = 6 seconds)
3 = B.
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If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be ______ that when the population is not highly skewed a. different from b. the same as c. larger than d. smaller than
Answers
Answer:
2
Step-by-step explanation:
the same as...
(2) is the answer
If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.
What is the central limit theorem?The central limit theorem states in probability theory that, in many instances, when independent random variables are added together, their correctly normalized sum tends toward a normal distribution, even if the original variables are not normally distributed.
If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.
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A freight elevator has a weight limit of 2 tons. Each crate that is loaded weighs 80 pounds. What is the greatest number of crates that can be loaded onto the elevator
Answers
Use the commutative property of addition to write an expression equivalent to the following.
5a + b
The answer is
Answers
Explanation:
The commutative property of addition is where we can add two numbers in any order.
The general equation is x+y = y+x
A more concrete example would be something like 2+3 = 3+2 since both sides simplify to 5.
For 5a+b, it is the same as b+5a. We swap the two terms.
If 0 lies in the quadrant IV. What can be the value of cos 0 ?
Answers
Answer:
the value of cos 0 is 7
Step-by-step explanation:
because you have to times it twice
Answer:
Between 0 and 1
Step-by-step explanation:
Cos Θ is the x coordinate of the unit circle. The points of that circle in quadrant IV have an x coordinate of 0≤x≤1.
Find the value of x of the given right triangle.
Answers
Answer:
In the right triangle, the side a=[tex]4[/tex] and the hypotenuse c=[tex]7[/tex].
To find: the value of x
We have,
[tex]a=6[/tex] and [tex]c=7[/tex]
Now,by the pythagorean theorem,
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
Substitute the values,
[tex] {6}^{2} + {x}^{2} = {7}^{2} [/tex]
[tex]36 + {x}^{2} = 49[/tex]
Subtract 36 from each sides,
[tex] {x}^{2} = 13[/tex]
Take square root from each sides,
[tex]x = \sqrt{13} [/tex]
Hence, the value of x is [tex]\sqrt{13}[/tex].
In which triangle is the value of x equal to cos−1(StartFraction 4.3 Over 6.7 EndFraction)?
(Images may not be drawn to scale.)
A right triangle is shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
A right triangle is shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle opposite to side with length 4.3 is x.
A right triangle is shown. The length of the hypotenuse is 4.3 and the length of another side is 6.7. The angle between 2 sides is x.
A right triangle is shown. The length of the 2 sides are 6.7 and 4.3. The angle opposite to side with length 4.3 is x.
Answers
The correct answer is option A. which is the right triangle shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
The complete figure is attached with the answer below.
What is trigonometry?
The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
In the given figure of option A, we can see that the hypotenuse is 6.7 and the base is 4.3 and the angle between both the sides is x. Now we will calculate the angle of cosine x.
Cos(x)= Base / Hypotenuse
Cos(x) = ( 4.3 / 6.7 )
(x) = Cos⁻¹ ( 4.3 / 6.7)
Therefore the correct answer is option A. which is the right triangle shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
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Answer:
The answer is A
Step-by-step explanation:
Just took the test
if x+7y=16 and 3x-7y=4 what is the value of x
Answers
Answer:
[tex]x=5\\[/tex]
Step-by-step explanation:
First, put your equations into a system.
[tex]\left \{ {{x+7y=16} \atop {3x-7y=4}} \right.[/tex]
Next, use the method of elimination to solve the system. Elimination is when either x or y has an opposite coefficient (so in this case y has a coefficient of 7 or -7 depending on the equation). You can then add the equations, and y is eliminated as a variable. Now you can solve for x.
[tex]4x=20[/tex]
Lastly, divide by 4 on both sides to get x by itself.
[tex]x=5\\[/tex]
If a 6-foot-tall baby giraffe casts a 4- foot-long shadow, then how tall is an adult giraffe that casts a 10-foot shadow?
Answers
Answer:
8- foot shadow? i am not sure
Answer:
i believe its 12 feet!
Step-by-step explanation:
assuming that the difference from the 6 foot giraffe with a four foot shadow is two feet, the 10 foot shadow would be two feet less then the giraffes height.
You can buy a car for $5995.67 cash or pay $759.00 as a down payment and $129.95 a month for 4 years.
How much more does the installment plan cost than paying cash?
A. $1000.93
B. $241.93
C. $507.43
D. $2475.27
E. $99.27
Answers
well, if you had the cash right now, you can put it down cold for 5995.67 bucks
OR
put as a downpayment now 759 and then over 48 months pay 129.95 each month, well, 129.95 48 times is 129.95 * 48 = 6237.6, now let's add the 759 down and that's 6237.6 + 759 = 6996.6.
well, heck if you had the cash it'd be 5995.67, if you don't is 6996.6, their difference is 6996.6 - 5995.67 = 1000.93.