Answers
Answer:
1 ≤ x < 7/4
Step-by-step explanation:
The function f(x) is defined as increasing on the domain (-8, 4), so the ordering of the arguments is not changed by the function. We can solve the inequality as though f(x) = x, which is increasing everywhere.
Inequality solutionsf(4x -3) ≥ f(2 -x²)
4x -3 ≥ 2 -x² . . . . . . using our assumed definition of f(x)
x² +4x -5 ≥ 0 . . . . . subtract 2-x²
(x -1)(x +4) ≥ 0 . . . . factored form; zeros at -4, +1
The values of x that make this true are ones that make the factors have the same signs: x ≤ -4 or x ≥ 1.
Domain restrictionsThe domain of f(x) is -8 < x < 4, so we require the arguments of f be restricted to those values
Left side
-8 < 4x -3 < 4
-5 < 4x < 7
-5/4 < x < 7/4
Right side
-8 < 2 -x² < 4 . . . . . right side is always true
x² < 10 . . . . . . . . . . . add x² +8
|x| < √10 . . . . . . . . . . less restrictive than the the left-side restriction
SolutionWith the given domain restrictions on f(x), the inequality will be true on the interval ...
1 ≤ x < 7/4
__
Additional comment
The attached graph shows the left-side function argument (dashed blue) and the right-side function argument (dashed green) with the given domain restrictions. The red curve is the difference in function values for the function defined as above. It is only non-negative between 1 and 1.75 as we found above.
This general behavior is applicable for any f(x) that can be described as in the problem statement. For example, f(x) = √(x+8) also gives an increasing curve for the difference f(4x-3)-f(2-x²) on the interval (-5/4, 7/4) with an x-intercept of +1.
<95141404393>
Related Questions
Which phrase best describes the relationship indicated by the scatter plot? A. Constant correlation B. negative correlation C. Positive correlation D. no correlation
Answers
Susan has a collection of 44 nickels and dimes. If the number of nickels is three times the number of dimes, how many nickels and how many dimes does she have?
Answers
Answer:
33 nickels and 11 dimes
Step-by-step explanation:
11*3= 33
11 + 33 = 44
A washer and dryer cost a total of $1280. The cost of the washer is three times the cost of the dryer. Find the cost of each item. Cost of washer: $ Cost of dryer: $
Answers
Answer:
Dryer = 320
Washer = 960
Step-by-step explanation:
Washer + Dryer = 1280
Let,
Dryer = x
Washer = 3x
3x + x = 1280
4x = 1280
x = 320
Washer = 3x = 3(320)=960
960 + 320 = 1280
Thus,
Dryer = 320
Washer = 960
~lenvy~
Which expression is equivalent to the following complex fraction?
Answers
Answer:
Option B
Step-by-step explanation:
Numerator:
[tex]\dfrac{3}{x -1 }-4 =\dfrac{3}{x-1}-\dfrac{4*(x-1)}{x-1}\\\\[/tex]
[tex]=\dfrac{3- 4x -4*(-1)}{x-1}=\dfrac{3-4x+4}{x-1}\\\\\\=\dfrac{-4x+7}{x-1} \: \textbf{ [Combine like terms]}[/tex]
Denominator:
[tex]2-\dfrac{2}{x-1}=\dfrac{2*(x-1)}{x-1}-\dfrac{2}{x-1}\\[/tex]
[tex]= \bf \dfrac{2x-2-2}{x-1}\\\\\\= \dfrac{2x-4}{x-1}\\\\= \dfrac{2*(x- 2)}{x-1}[/tex]
[tex]\dfrac{\dfrac{3}{x-1}-4}{2-\dfrac{2}{x-1}}=\dfrac{\dfrac{-4x+7}{x-1}}{\dfrac{2*(x-2)}{x-1}}[/tex]
[tex]\bf = \dfrac{-4x+7}{x-1}*\dfrac{x-1}{2(x-2)} \ \ \ \textbf{ [(x-1) in the numerator and denominator will be cancelled]}\\\\\\=\dfrac{-4x+7}{2(x-2)}[/tex]
Find the solution to the system of equation by using either graphing or substitution
y=4x and y + x=5
Answers
Answer:
x=1, y=4
Step-by-step explanation:
sub y=4x into second equation
4x + x=5
5x=5
x=1
now sub x=1 into the first equation
y = 4 x 1
y=4
A group of friends go out for a meal and the meal costs £148.
They are given a discount of 25% because of a mix-up on their orders.
How much discount did the group of friends receive?
£
Answers
you would multiply by the percent off they get.
What is the mean absolute deviation of the following set
of data?
9
2
9
9
5
4.
9
1
4
10
Answers
Answer:
3
Step-by-step explanation:
You want the mean absolute deviation of the set of numbers ...
{9, 2, 9, 9, 5, 4, 9, 1, 4, 10}
MADThe mean of this 10-number set of data is 6.2. The mean absolute deviation (MAD) is found by subtracting that from the members of the dataset, taking the absolute values of the result, and finding the means of those.
The attachment shows those calculations.
The MAD of this set of data is 3.
__
Additional comment
The period (decimal point) in the column of numbers suggests this is a 6-number dataset, and the last 4 numbers are answer choices. If that is the case, none of those answer choices is correct. That is why we assumed that this problem has a 10-number dataset.
When you're calculating this by hand, you only need to consider the values for which the deviation is negative. The MAD is twice their total absolute value, divided by the number of numbers in the dataset. Here, that is 2(4.2+2.2+5.2+2.2+1.2)/10 = 3. (Numbers 2, 5, 4, 1, 4 are less than the mean of 6.2.)
<95141404393>
what is the value of n in the equation -1/2(2n+4)+6= -9+4(2n+1)
Answers
Answer:
n=1
Step-by-step explanation:
Still stuck? Get 1-on-1 help from an expert tutor now.
The graph displays a linear function.
Answers
Answer:
[tex]y = -\frac{2}{3}x +0[/tex] OR [tex]y = -\frac{2}{3}x[/tex]
Step-by-step explanation:
First, find the slope (m) using two points (0,0) and (-6, 4)
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{4-0}{-6-0} \\\\m=\frac{4}{-6}\\\\m=\frac{2}{-3}\\\\m=-\frac{2}{3}[/tex]
[tex]y=mx+b[/tex]
[tex]y = -\frac{2}{3}x +b[/tex]
Now, we find b using (-6, 4)
[tex]y = -\frac{2}{3}x +b[/tex]
[tex]4 = -\frac{2}{3}(-6) +b\\\\4 = \frac{12}{3} +b\\\\4 = 4 +b\\\\-4 -4\\\\0=b[/tex]
[tex]y = -\frac{2}{3}x +0[/tex] OR [tex]y = -\frac{2}{3}x[/tex]
Hope this helps!
Each of 7 students reported the number of movies they saw in the past year. This is what they reported.
13, 8, 6, 6, 18, 11, 4
Find the median and mean number of movies that the students saw.
If necessary, round your answers to the nearest tenth.
(a) Median:
(b) Mean:
Answers
Answer:
A is 6
B is 9.4
Step-by-step explanation:
First you put the numbers in order. then you take the middle number of the data set. This is how you find the median. For the mean you add all of the number in the data set then divide by how many numbers are there
Determine the measure of the interior angle at vertex C.
Answers
Answer:
B. 120 Degrees
Step-by-step explanation:
We know that the total interior angle of any five sided polygon is 540 Degrees.
The total interior angle of this polygon is
4x + 4x + 4x + 3x + 3x = 18x 540 = 18x
Divide by the lowest ratio 540/18 = 30
30 = x
C = 4x
4X30 = 120
C = 120 Degrees
Help help her help help
Answers
Answer:
x = 12
Step-by-step explanation:
1. Subtract 9 from both sides:
x/6 = 2
2. Multiply both sides by 6:
x = 12
Answer:
9 + x/6 = 11
Always get rid of the constants first,
-9 -9(we subtract 9 from both sides because the inverse operation of addition is subtraction)
x/6 = 2
Isolate x by multiplying by 6 on both sides (because the inverse operation of division is multiplication)
*6 *6
x = 12
express the confidence interval 0.255 plus or minus 0.045
Answers
Answer:
0.255+45=0.300
or
0.255 - 0.045 = 0.210
I need help quick please
Answers
B=53
The reason I am saying this is because you can see the 90 degree angle in A
Angle A = 137
Angle B = 93
what is a quadrialateral?
A quadrilateral is four sided polygon. squares and rectangles are more common examples of a quadrilateral. Each quadrilateral has it's unique features however generally the sum of angles of a quadrilteral is 360
Introducing angle C such that
A + C = 180 (angle on a straight line)
C + 47 + 90 = 180 (sum of angles of a trianlge)
C = 180 - 90 - 47
C = 43
hence
A + 43 = 180
A = 180 - 43
A = 137
A + B + 90 + 40 = 360 (sum of angles of a quadrilateral )
37 + B + 90 + 40 = 360
B = 360 - ( 137 + 90 + 40 )
B = 93
Read more on quadrilaterals here: https://brainly.com/question/16691874
Help? Anything can help I’m in a rush
Answers
Answer: A vertical line from (-5 , 4 ) to (5 , 4)
Step-by-step explanation: The y axis is the vertical one. Go up 4 and draw a line connecting all the points with 4 in the coordinates.
Hope that helps :)
Answer:
Step-by-step explanation:
go up 4 lines on the y-axis then draw a straight line from left to right on y=4
I don't know if you can see the picture, but I drew a line on the picture you provided...
Please 5 stars if correct!!!
I hope this helps
Use the following table to find the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in
on-campus housing. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Students on the Student Government Board
Classification
On-Campus Housing Off-Campus Housing
Freshman
1
4
Sophomore
2
0
Junior
1
2
Senior
2
0
Graduate Student
2
3
Prey
Next
Copy Data
Answer How to enter your answer opens in new window) 2 Points
Keypad
Keyboard Shortcuts
56°F
Answers
Using it's concept, it is found that there is a [tex]\frac{11}{17}[/tex] probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, a total of 1 + 4 + 2 + 0 + 1 + 2 + 2 + 0 + 2 + 3 = 17 students were sampled.
Of those, 1 + 2 + 1 + 2 + 2 = 8 live in on campus housing, and 3 live off campus but are graduate students, hence there are 11 desired outcomes and the probability is given by:
[tex]\frac{11}{17}[/tex]
More can be learned about probabilities at https://brainly.com/question/14398287
Answer choices:
y = x
y = 1/4x - 2
y = -x + 7/4
y = 7/4x - 2
Answers
Answer:
all in all it's y=x
Step-by-step explanation:
A (4,1); B (0,-2)
G=delta y
--------
delta x
1-(-2)
-------
4-0
3/4=G
3/4=y-1/x-4
4 (y-1)=3 (x-4)
4y-4=3x-12
4y=3x+4-12
y=3/4x-3
Help me please For your points! Thanks
Answers
Answer:
Step-by-step explanation:
you will read the directions 2x before solving the problem then solve the problem
Someone pls
.
A
A
A
A
A
A
S
Answers
Answer:
7
Step-by-step explanation:
Degree of a polynomial is a variable's highest exponent
In this expression the degree is 7
Answer:
7
Step-by-step explanation:
If you used
P.E.M.D.A.S
Brainly please I worked so hard for this answer
Assume you have two six-sided dice - both numbered 1 to 6 - and add the total of the dice after each roll. Leave all answers as a fraction a/b. What is the probability of rolling a 4
Answers
Find a degree 3 polynomial whose coefficient of x^3 equal to 1. The zeros of this polynomial are -5, -4i, and 4i. Simplify your answer so that it has only real numbers as coefficients.
I got an answer by solving (x^3+5x^2-16x-80) but it says thats incorrect.
Answers
Answer:
x^3+5x^2+16x+80
Step-by-step explanation:
You know that you can write your polynom this way : (x-r1)(x-r2)(x-r3) with r1,r2 and r3 the roots so you get :
(x+5)(x+4i)(x-4i)
Simplify (x+4i)(x-4i) with the formula (a-b)(a+b)=a²-b²
so you have (x^2+16)=(x+4i)(x-4i)
Your polynom looks like this :
(x^2+16)(x+5) just expand it
and you get x^3+5x^2+16x+80
Paul leaves £4000 in the bank for two years. It earns compound interest of 5% per year. Calculate the total amount Paul's has in the bank at the end of the two year.
Pls give me working out and explanation !!!!
Answers
Answer:
£4400
Step-by-step explanation:
5% of 4000 is 200
200*2=400
4000+400=4400
£4400
f(x) = x^1/2 is continuous for all x but not differentiable at x=0. is it True or False?
Answers
Answer:
it's true because the x=0 and that why it must be true FX may be the some I would say it's true
Find the volume. Use 3.14 for π where necessary. Round the answer to two decimal places.
Answers
Answer:
25.12 feet cubed ~ 25ft^3
Step-by-step explanation:
You're doing a volume for a cone.
Volume of cone formula: 1/3 π r^2 h
You have given me the diameter of 4ft
Height of 6ft.
In order to solve this, you need to divide 4ft by 2ft because we need the radius rather than the diameter.
**The radius is half of the diameter.**
Our new radius is 2ft.
Formula: 1/3π2^2(6)
Now do the exponent first, 2 to the second power or 2 squared is 4.
You need to pull out your calculator.
Steps to calculate the volume:
Do 1 divided by 3 first
Then multiply that by 3.14
Multiply 4
Finally multiply 6
Your Volume for the cone is 25.12 feet cubed
The cheeseburger in Alan's kid's meal has 300 calories. His fries have 101 and his drink has 150. How many tota calories
are in his meal?
Answers
300+150 = 450
450 + 101 = 551
Answer:
551 calories
Step-by-step explanation:
Given the number of calories in each part of his food you can add:
300 + 101 +150
to equal the total amount of calories in his food, which would be:
551 calories
In conclusion, there would be a total of 551 calories if Alan's kid's meal.
Have a great rest of your day
#TheWizzer
What is the measure of Zx?
Angles are not necessarily drawn to scale.
Answers
Answer:
17°
Step-by-step explanation:
First, see what's the angle of "AOC"
Here, it's 90° (since it shows the Box at the bottom of the angle instead of a semicircle.
Now, lets subtract 90 by 73
that will be 17
so hence, the value of X is 17°
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If you see someone without a simle, give them one of yours!
Thanks!
Have a great day!
:D
How many square meters are there in a floor that is 9 meters long by 12 meters wide?
99
108
109
117
Answers
Answer:
108
9×12
Step-by-step explanation:
please mark me as brainlest
Find the mass of an object that has a weight of 910kg
Answers
Answer:
91kg
Step-by-step explanation:
weight= mass × gravitational force
910kg = m× 10ms^-2
m= 910÷ 10
m= 91
Which is the equation of the line with slope 3 that contains point (-1,5)?
y-1 = 3(x + 5)
y - 1 = 3(x - 5)
y - 5= 3(x - 1)
y - 5= 3(x + 1)
Answers
Answer:
D
[tex]y-5=3(x+1)[/tex]
Step-by-step explanation:
We can see that the question is asking for the Point-Slope Form;
[tex]y-y_{1} =m(x-x_{1})[/tex]
The points go into the equation for [tex]y_{1}[/tex] and [tex]x_{1}[/tex]
[tex]y-5=m[x-(-1)][/tex]
M would be the slope;
[tex]y-5=3[x-(-1)][/tex]
Which basically is:
[tex]y-5=3(x+1)[/tex]
I do not understand how they got this answer. I am stuck on the exponent party- Please see attached
Answers
Looking at the question, the answer gotten is:$4316.55. The question is related to compound interest.
What is compound interest?Compound interest is known to be the interest that is earned on a principal sum in addition to the accumulated interest previously. It is as a result of reinvesting interest.
To find the compound interest, the formula used is:
A= P(1+r/n)^nt.
Where
P is the principal sum= $3500
r is the rate = 0.035
n is the compounding period = 12 months.
t is the time = 6 years.
Substituting them in the equation, we have:
A = 3500 ( 1 + 0.035/12)^12×6
Working out the one in the bracket and multiplying the exponent, we have:
A = 3500 (1.00291667)^72
Note: We got 72 by multiplying 12 by 6.
1.00291667 raised to the power of 72 = 1.23330133
A = 3500× 1.23330133 = $4,316.55
Ans: $4,316.55
Learn more about compound interest on https://brainly.com/question/24274034