Answers
If the function be [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex] then the domain of the function exists
[tex]$\left[\begin{array}{ccc}\text { Solution: } & x < \frac{5}{8} & \text { or } \quad x > \frac{5}{8} \\ \text { Interval Notation: } & \left(-\infty, \frac{5}{8}\right) \cup\left(\frac{5}{8}, \infty\right)\end{array}\right]$[/tex]
What is meant by domain of a function?The collection of all potential inputs for a function is its domain.
Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
Let the function be [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex]
Domain of [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex] :
[tex]$\left[\begin{array}{ccc}\text { Solution: } & x < \frac{5}{8} & \text { or } \quad x > \frac{5}{8} \\ \text { Interval Notation: } & \left(-\infty, \frac{5}{8}\right) \cup\left(\frac{5}{8}, \infty\right)\end{array}\right]$[/tex]
Range of [tex]$\frac{x^3-3 x+1}{8 x-5}:\left[\begin{array}{cc}\text { Solution: } & -\infty < f(x) < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]
Axis interception points of [tex]$\frac{x^3-3 x+1}{8 x-5}[/tex]
X Intercepts: [tex]$(0.34729 \ldots, 0),(1.53208 \ldots, 0)$[/tex], [tex]$(-1.87938 \ldots, 0)$[/tex],
Y Intercepts: [tex]$\left(0,-\frac{1}{5}\right)$[/tex]
Asymptotes of [tex]$\frac{x^3-3 x+1}{8 x-5}: \quad$[/tex]
Vertical: [tex]$x=\frac{5}{8}$[/tex]
Extreme Points of [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex]
Minimum [tex]$(-0.54351 \ldots,-0.26422 \ldots)$[/tex]
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Related Questions
Find the reference angle for the given angles 745 degree.
Answers
Maisa,. let's recall the formula for calculating the reference angle when the angle is > 360 degrees:
Reference angle = Given angle - 360
Reference angle = 745 - 360
Reference angle = 385
It's still higher value than 360, therefore we subtract 360 again.
Reference angle = 385 - 360
Reference angle = 25 degrees
(2, -3) (4, -2)
Slope intercept
Answers
The slope of the given coordinates is m = 1/2.
What is the slope?A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the point where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.So, the slope of (2, -3) (4, -2):
The slope formula: m = y₂ - y₁/x₂ - x₁Now, solve for slope by putting the values as follows:
m = y₂ - y₁/x₂ - x₁m = -2 - (-3)/4 - 2m = -2 + 3/2m = 1/2Therefore, the slope of the given coordinates is m = 1/2.
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The correct question is shown below:
Find the slope using the coordinates (2, -3) (4, -2).
Solve each system of the equation by elimination. y=-4x+14y=10x-28
Answers
Explanation:
The elimination method consists in substracting one equation from the other, so you eliminate one of the variables and you have only one equation to solve for one variable.
In this case, y has the same coefficient in both equations, so this is the variable we will eliminate.
Substract the first equation from the second:
[tex]\begin{gathered} y=10x-28 \\ - \\ y=-4x+14 \\ \text{ ---------------------} \\ y-y=10x+4x-28-14 \\ 0=14x-42 \end{gathered}[/tex]And solve for x:
[tex]\begin{gathered} 14x=42 \\ x=\frac{42}{14} \\ x=3 \end{gathered}[/tex]Now, we replace x = 3 into one of the equations and solve for y:
[tex]y=-4\cdot3+14=-12+14=2[/tex]Answer:
• x = 3
,• y = 2
2000.5 - 351.748 +62.1
Answers
Given the expression :
[tex]2000.5-351.748+62.1[/tex]At first make all the decimal digits equally for all terms
The maximum decimal is 3 so, add 00 to the first and the last terms
So,
[tex]\begin{gathered} 2000.5-351.748+62.1 \\ =2000.500-351.748+62.100 \\ =1710.852 \end{gathered}[/tex]So, the answer is : 1,710.852
Find all solutions of the equation in the interval [0,2pi). csc =7/4 If there is more than one solution, separate them with commas.Do not round any intermediate computations. Give your answer(s) in radians, and round your answer(s) to the nearest hundredth
Answers
Since the cosecant is the inverse of the sine, we can write the following:
[tex]\begin{gathered} \csc (\theta)=\frac{7}{4} \\ \sin (\theta)=\frac{1}{\csc(\theta)}=\frac{1}{\frac{7}{4}}=\frac{4}{7} \end{gathered}[/tex]Then, using a calculator, we can calculate the angle that has a sine of 4/7:
[tex]\begin{gathered} \theta=\sin ^{-1}(\frac{4}{7})_{} \\ \theta=34.85\degree \end{gathered}[/tex]There is one more angle between 0 and 2π that has the same value of 4/7 for the sine, and it's the supplementary angle to the one we found:
[tex]\theta_2=180-\theta_1=180-34.85=145.15\degree[/tex]Therefore the answers are 34.85° and 145.15°.
Converting to radians, we have:
[tex]\begin{gathered} 34.85\cdot\frac{\pi}{180}=0.61 \\ 145.15\cdot\frac{\pi}{180}=2.53 \end{gathered}[/tex]So the final answer is 0.61 and 2.53.
Write an equation of the line passing through the point (8,-3) that is parallel to the line y= -x -1. An equation of the line is
Answers
The equation of the line, in slope-intercept form, that is parallel to the line y = -x - 1 is: y = -x + 5.
How to Write the Equation of Parallel Lines?Parallel lines have equal slope value, "m". In slope-intercept form, the equation y = mx + b represents a line, where the slope is "m" and the y-intercept is "b".
The slope of y= -x -1 is -1. This means the line that is parallel to y= -x -1 will also have a slope that is equal to -1.
Substitute m = -1 and (x, y) = (8, -3) into y = mx + b to find the value of b:
-3 = -1(8) + b
-3 = -8 + b
-3 + 8 = b
5 = b
b = 5
Substitute b = 5 and m = -1 into y = mx + b to wrote the equation of the line that is parallel y = -x -1:
y = -x + 5
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4(x - 3) - (x - 5) = 0
Answers
4(x - 3) - (x - 5) = 0
Solving for x:
4(x - 3) - (x - 5) = 0
4x - 12 - x + 5 = 0
4x - x = 12 - 5
3x = 7
x = 7/3
Answer:
x = 7/3 = 2.33
I attached the questions as images. The first image is actually the second.You can send in the work on paper like the graphing part.The questions can be typed on the solution tab or messages whichever is easier for you.Thanks again for the help :)
Answers
SOLUTION
Consider the image below,
The lenght of the compass is the radius, using a lenght of 5 unit, we have circle below as the sphere .
Where
[tex]\begin{gathered} r=\text{ radius, O= origin } \\ And \\ r=5\text{unit } \end{gathered}[/tex]Using the formula, we have
[tex]\begin{gathered} \text{Volume of sphere} \\ =\frac{4}{3}\pi r^3 \\ \text{where} \\ \pi=3.14,\text{ r=}5 \end{gathered}[/tex]Substitute into the formula, we have
[tex]\begin{gathered} \text{Volume of the sphere is } \\ =\frac{4}{3}\times3.14\times5^3 \\ \text{Hence } \\ 523.33\text{ cubic unit} \end{gathered}[/tex]Therefore
The volume of the sphere is 523.33 cubic unit
The function f (x) = x+4/3 is in a system with its inverse f-1(x). What is the solution to the system?
Answers
Find the x- and y-intercepts for the following equation. Then use the intercepts to graph the equation.
4x + 2y = 8
Answers
Answer:
Step-by-step explanation:
x int=2
y int=4
graph 2,0 and 0,4 as two points
Khloe is going to invest $7,100 and leave it in an account for 9 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for Khloe to end up with $12,600?
Answers
Solution
For this case we can use the following formula:
[tex]A=Pe^{rt}^{}[/tex]and for this case we have the following:
P= 12600
A= 7100
t = 9 years
And r is the value that we need to find, so we can do the following:
[tex]12600=7100e^{9r}[/tex]We can do the following:
[tex]\ln (\frac{12600}{7100})=9r[/tex]And we got for r:
[tex]r=\frac{\ln (\frac{12600}{7100})}{9}=0.0637[/tex]And then the rate would be:
6.37%
what is the image of -3 -7 after a reflection over the x-axis
Answers
Given the point (-3, -7)
We need to find the image after a reflection over the x-axis
The rule of reflection over the x-axis is:
[tex](x,y)\rightarrow(x,-y)[/tex]So, the image of the given point will be:
[tex](-3,-7)\rightarrow(-3,7)[/tex]so, the answer is option D. (-3, 7)
Use the quadratic function fly)=-22 +53411 to answer the following questions,a) Use the vertex formula to determine the vertes.The verteris(Type an ordered pair Simplify your answer.)
Answers
The vertex of a quadratic function can be found by using the following expression:
[tex]x=\frac{-b}{2a}[/tex]Where "a" is the number multiplying x² and b is the number multiplying x. For this function a = -2 and b = 5. Applying these on the problem we have:
[tex]x=\frac{-5}{2\cdot(-2)}=\frac{-5}{-4}=\frac{5}{4}=1.25[/tex]To find the y coordinate of the vertex we need to use the value for x that we found above. We have:
[tex]\begin{gathered} f(x)=-2x^2+5x+11 \\ f(\frac{5}{4})=-2\cdot(\frac{5}{4})^2+5\cdot(\frac{5}{4})+11 \\ f(\frac{5}{4})=-2\frac{25}{16}+\frac{25}{4}+11 \\ f(\frac{5}{4})=\frac{-50}{16}+\frac{25}{4}+11 \\ f(\frac{5}{4})=-3.125+6.25+11=14.125 \end{gathered}[/tex]The ordered pair for this function's vertex is (1.25, 14.125)
How do I find x I know you separate the shapes but I got it wrong…
Answers
Let's find this length first
6√2 is the hypotenuse, then
[tex]\begin{gathered} (6\sqrt{2})^2=6^2+y^2 \\ \\ y^2=(6\sqrt{2})^2-6^2 \\ \\ y^2=36\cdot2-36 \\ \\ y^2=36 \\ \\ y=\sqrt{36}=6 \end{gathered}[/tex]Then we can find x because
[tex]\begin{gathered} x^2=y^2+12^2 \\ \\ x^2=6^2+12^2 \\ \\ x^2=36+144 \\ \\ x^2=180 \\ \\ x=\sqrt{180} \\ \\ x=6\sqrt{5} \end{gathered}[/tex]The length of x is
[tex]x=6\sqrt{5}[/tex]1c. Clue 1The number has three digits.Clue 2 The number is less than 140.Clue 3 The number has 7 as a factor.Clue 4 The number is even.Clue 5 The sum of the digits of the number is less than 9.
Answers
We have an even 3 digits number whose sum lie is less than 9, has got 3 digits and less than 140.
We will establish the inequalities that satisfies the conditions given and then figure out the number.
[tex]\begin{gathered} 100x+10y+z<140 \\ x+y+z<9 \\ 100x+10y+z=14a\text{ where a lies between 8 and 9} \end{gathered}[/tex]From our last inequality, we can easily see that the number in question is 14 x 8 or 14 x 9. Any multiple of 7 that is even is also a multiple of 14.
[tex]\begin{gathered} 14\times8=112\text{ AND} \\ 14\times9=126 \end{gathered}[/tex]From the above, it can be easily seen that 112 satisfies the conditions listed.
The number is 112
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
Answer:
perimeter: add p + m + n
area: use (p × m)/2
find missing side: use p^2 + m^2 = n^2
Jerome rolls two six-sided number cubes. What is the probability that he rolls doubles, given the sum of the numbers is 8?
Answers
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
hope you get it thats the last pen that works in my house
Answer: There are five possible outcomes with a sum of 8:
2 and 6,
3 and 5,
4 and 4,
5 and 3,
6 and 2.
There is only one outcome, 4 and 4, that is doubles. Therefore, the probability is 1/5.
Step-by-step explanation: Got it right on Edmentum
The ordered pairs represent a function. (0,-1), (1,0), (2,3), (3,8) and (4,15). Answer the questions in the picture.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
ordered pairs:
(0,-1), (1,0), (2,3), (3,8) and (4,15)
Step 02:
functions:
graph:
The function is nonlinear
x ==> increases by 1
y ==> increases by 2
y = x² - 1E-14x - 1
That is the full solution.
What is the mean and median of the data set
Answers
The mean of a data set is the sum of the data divided by the total number of data.
The median of a data set is the middle number in the set (after the numbers have been arranged from least to greatest, or, if there is an even number of data, the median is the average of the two middle numbers.
You have the next data set:
[tex]\begin{gathered} \lbrace11,11,11,11,12,12,12,13,13,13,13,13,13,14,15,15,15,15,15, \\ 15,16,16,16,16,16,17,17,17\rbrace \end{gathered}[/tex]A total of 28 data.
The mean is equal to the sum of the 28 numbers and then divided into 28:
[tex]undefined[/tex]5 ptsIn Ms. Johnson's class a student will get 3 points forhaving their name on their paper and 4 points for eachquestion that is correct. In Mr. Gallegos class, a studentwill get 7 points for having their name on their paper and2 points for each question correct. Which inequalitycould be used to determine x, the number of questionsthat would give you a higher grade in Ms. Johnson'sclass?
Answers
In Ms. Johnson's class a student will get 3 points for
having their name on their paper and 4 points for each
question that is correct. In Mr. Gallegos class, a student
will get 7 points for having their name on their paper and
2 points for each question correct. Which inequality
could be used to determine x, the number of questions
that would give you a higher grade in Ms. Johnson's
class?
we have
Ms. Johnson's class
3+4x
Mr. Gallegos class
7+2x
so
the inequality is given by
3+4x > 7+2x
solve for x
4x-2x > 7-3
2x>4
x> 2
the number of question must be greater than 2
Find 8 3/4 ÷ 1 2/7. Write the answer in simplest form.
Answers
Problem: Find 8 3/4 ÷ 1 2/7. Write the answer in the simplest form.
Solution:
[tex](8+\frac{3}{4}\text{ )}\div(1\text{ + }\frac{2}{3})[/tex]this is equivalent to:
[tex](\frac{32+3}{4}\text{ )}\div(\text{ }\frac{3+2}{3})\text{ = }(\frac{35}{4}\text{ )}\div(\text{ }\frac{5}{3})\text{ }[/tex]Now, we do cross multiplication:
[tex]=(\frac{35}{4}\text{ )}\div(\text{ }\frac{5}{3})=\frac{35\text{ x 3}}{5\text{ x 4}}\text{ =}\frac{105}{20}[/tex]then, the correct answer would be:
[tex]=\frac{105}{20}[/tex]Two lines are shown on the grid below.Read the statements below about the graph of the two lines.Which statements are true about the two lines on the graph?A.I,II, and IV onlyB.II,III, and IV onlyC.II and III only D.I,II,III,and IV
Answers
Answer:
B. II, III, and IV only
Explanation:
Vertical lines have an undefined slope and the equation of these lines is x = c, where c is a constant value
Horizontal lines have a slope equal to 0 and the equation of these lines is y = c, where c is a constant value.
Therefore, the statements that are true about the graph are:
The equation of line b is y = -5
Line b has a slope of 0
The equation of line a is x = 3
Is the graph of the distance a person has driven over time an example of a continuous or discrete graph?
Answers
Let us first understand what are discrete and continuous variables.
Discrete variable:
A discrete variable is countable in a finite amount of time.
For example:
The number of coins in your pocket
The number of trees in the garden
It is not possible to have 2.5 coins or 7.3 trees
Continuous variable:
A continuous variable can take any numeric value.
For example:
The height of the tree
The room temperature
These values can be in decimal like 7.3, 0.23 etc
Now let us come to the question, the distance a person has driven can take any value
for example, it can be 50 miles or 23.4 miles or 120.5 miles
So, decimal values are possible
This means that it must be a continuous graph
The distance a person has driven over time an example of a continuous graph.
Lines that are perpendicular have slopes that arethe same or opposite and reciprocal.
Answers
When lines are perpendicular the slopes of both are opposite and reciprocal, that is:
[tex]m\text{ and - }\frac{1}{m}[/tex]In words, if we have a line with slope = m, the perpendicular line to that line will have a slope = - 1/m ( opposite and reciprocal).
Use a trig equation to solve for x. Round to the nearest tenth.
Answers
Given a right angle triangle
We need to find the measure of the angle x
The opposite side to the angle x = 19
the adjacent side to the angle x = 15
We will find x using the tan function as follows:
[tex]\begin{gathered} \tan x=\frac{opposite}{adjacent} \\ \\ \tan x=\frac{19}{15} \\ \\ x=\tan ^{-1}\frac{19}{15}\approx51.7098^{} \end{gathered}[/tex]Round the answer to the nearest tenth
so, the answer will be x = 51.7
The director of a film festival received 9 submissions, 7 of which were sci-fi films. If the director randomly chose to play 6 of the submissions on the first day of the festival, what is the probability that all of them are sci-fi films? Write your answer as a decimal rounded to four decimal places .
Answers
Given data:
9 submissions out of which 7 were sci-fi
If the director randomly chose to play 6 of the submissions on the first day of the festival
Then, the probability that all of them are sci-fi films will be obtained as follows
At the first selection, it will be: 7/9
At the second selection, it will be: 6/8
At the third selection, it will be: 5/7
At the fourth selection, it will be: 4/6
At the fifth selection, it will be: 3/5
At the sixth selection, it will be: 2/4
Thus, the probability will be
[tex]\frac{7}{9}\times\frac{6}{8}\times\frac{5}{7}\times\frac{4}{6}\times\frac{3}{5}\times\frac{2}{4}=\frac{5040}{60480}[/tex]=>
[tex]\frac{5040}{60480}=\frac{1}{12}[/tex]=>
[tex]\frac{1}{12}=0.0833[/tex]Answer = 0.0833
If np ≥5 and nq≥5, estimate P(at least 6) with n=13 and p = 0.5 by using the normal distribution as an approximation to the binomial distribution; if np < 5 or nq < 5, then state that the
normal approximation is not suitable.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. P(at least 6) =
(Round to three decimal places as needed.)
O B. The normal distribution cannot be used
Answers
Using normal distribution we know that the value is P(at least 6) = 0.866.
What is Normal Distribution?A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or a Gaussian distribution.The mean is 8.4 according to the formula:
q = 1 - p = 1 - 0.5 = 0.5Np = (13)(0.5) = 6.5 > 5Nq = (13)(0.5) = 6.5 > 5Consequently, the normal distribution will indeed resemble the binomial.
sqrt(Npq) = sqrt(13*0.5*0.5) = 1.802 is the standard deviation.Since it's ≥ and not > and to the right, we use 6-0.5 = 5.5Because going right from 5.5 includes 6.
P(x > 5.5) with μ = 6.5 and σ = 1.802Either find the z-score and use the table or use technology to find
Hence, Answer = 0.866Therefore, using normal distribution we know that the value is P(at least 6) = 0.866.
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Use the drawing tools to the graph the solution to this system of inequalities on the coordinate plane.
y> 2x + 4
x+y≤6
Answers
The solution to the system of inequalities y> 2x + 4 , x+y≤6 on the coordinate plane is shown below .
in the question ,
the system of inequality is given
y> 2x + 4
x+y≤6
to plot these inequalities on the coordinate plane ,we need to find the intercepts of both.
y>2x+4
put x = 0 we get y as 4 , (0,4)
put y = 0 we get x as -2 ,(-2,0)
x+y≤6
put x = 0 , we get y as 6 , (0,6)
put y = 0 , we get x as 6 , (6,0)
the solution of both the inequality is shown below .
Therefore , the solution to the system of inequalities y> 2x + 4 , x+y≤6 on the coordinate plane is shown below .
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Solve by factoring. Be sure to look for a GCF first in case there is one-2x²-4x+70=0
Answers
ANSWER
x = 5 and x = -7
EXPLANATION
We want to solve the equation by factoring.
The equation is:
[tex]-2x^2\text{ - 4x + 70 = 0}[/tex]First, there is a greatest common factor that we can use to simplify the equation. That is -2, so, first we divide through by -2.
It becomes:
[tex]x^2\text{ + 2x - 35 = 0}[/tex]Now, factorise:
[tex]\begin{gathered} x^2\text{ + 2x - 35 = 0} \\ x^2\text{ + 7x - 5x - 35 = 0} \\ x(x\text{ + 7) - 5(x + 7) = 0} \\ (x\text{ - 5)(x + 7) = 0} \\ x\text{ = 5 and x = -7} \end{gathered}[/tex]Write the following equation in standard form: x + x4 + 6x +1
Answers
To answer this question, we need to know that the standard form of an equation of this type is written as follows:
[tex]ax^5+bx^4+cx^3\ldots[/tex]We have that the polynomial given is:
[tex]\frac{8}{7}x^3+x^4+6x+1[/tex]In the standard form, we need to write it as follows:
[tex]x^4+\frac{8}{7}x^3+0x^2+6x+1=x^4+\frac{8}{7}x^3+6x+1[/tex]Therefore, the correct answer is option C. This is the standard form for this fourth-degree polynomial.