Answers
GIVEN:
We are given the function below;
[tex]f(x)=9x^3+2x-12[/tex]Required;
To find the domain of the cubic function.
Step-by-step solution/explanation;
The domain of a function is the set of all input values (that is, x values) for which the function is defined.
For the function given, there is no constraint, which means the function is always true for any value of x.
Therefore,
ANSWER:
[tex]Domain=(-\infty,+\infty)[/tex]The domain is the set of all real numbers.
Option B
Related Questions
A spinner with 5 equally sized slices has 2 red slices, 2 yellow slices, and 1 blue slice. Keiko spun the dial 1000 times and got the following results. From Keiko's results, compute the experimental probability of landing on yellow
Answers
Probability is expressed as
number of favorable outcomes/number of total outcomes
But probability can also be classified as theoretical probability and experimental probability. The theoretical probability is the normal probability of each outcome while the expreimental probability is the probability of an outcome given that trials have been made.
In this scenario,
total number of trials = 400 + 195 + 405 = 1000
favorable outcomes = number of times that we landed on yellow = 405
the experimental probability of landing on yellow is
405/1000 = 0.405
Solve for x. 6 244 - 21.A. 0.53B. 0.45 C. 0.06 D. 0.24
Answers
ANSWER:
B. 0.45
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]6\cdot2^{4x}^{}=21[/tex]We solve for x:
[tex]\begin{gathered} 2^{4x}=\frac{21}{6} \\ \ln \: \mleft(2^{4x}\mright)=\ln \: \mleft(\frac{7}{2}\mright) \\ 4x\cdot\ln (2)=\ln \: \mleft(\frac{7}{2}\mright) \\ x=\frac{\ln \: \mleft(\frac{7}{2}\mright)}{4\cdot\ln (2)} \\ x=0.45 \end{gathered}[/tex]The value of x is 0.45
represents holly records
Answers
The holly records a temperature at 15 below zero
This implies that the temperature i
It takes Anastasia 50 minutes to walk 3 1/2 miles to the park. At this rate, about how many minutes should it take her to walk 5 miles?
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Answer:
about 71minutes
Explanation:
If it takes Anastasia 50 minutes to walk 3 1/2 miles to the park, then;
50 minutes = 3.5 miles
To get the time taken for her to walk 5miles;
x = 5miles
Divide both expressions
50/x = 3.5/5
Cross multiply
3.5x = 50*5
3.5x = 250
x = 250/3.5
x = 71.42miles
Hence it will take her about 71minutes to walk 5miles
if the area of a rectangle is 6 m, then the dimension would be 2 meters by 3 meters?True or False
Answers
To be able to verify the statement, let's first recall the formula in getting the area of a rectangle:
Can you help me find the answer to my homework questions thankyouuuu
Answers
In this problem, we have an exponential decay function of the form
[tex]y=a(1-r)^x[/tex]where
y is the area in km2
x is the number of years
a=3,800 km2 (initial value)
r=6.25%=6.25/100=0.0625
substitute given values
[tex]\begin{gathered} y=3,800(1-0.0625)^x \\ y=3,800(0.9375)^x \end{gathered}[/tex]For x=12 years
substitute
[tex]\begin{gathered} y=3,800(0.9375)^{12} \\ y=1,752\text{ km}^2 \end{gathered}[/tex]therefore
The answer is 1,752 square kilometersfind the height of a cone with a diameter of 12m whose volume is 264m ^3 . use 3.14 for π and round your answer to the nearest meter . A. 42m B. 6m C. 7mD. 2m
Answers
find the height of a cone with a diameter of 12m whose volume is 264m ^3 . use 3.14 for π and round your answer to the nearest meter .
A. 42m
B. 6m
C. 7m
D. 2m
we have that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]we have
V=264 m3
pi=3.14
r=12/2=6 m ------> the radius is half the diameter
substitute
[tex]264=\frac{1}{3}\cdot3.14\cdot6^2\cdot h[/tex]solve for h
[tex]\begin{gathered} h=\frac{264\cdot3}{3.14\cdot36} \\ \\ h=7\text{ m} \end{gathered}[/tex]answer is option C
Here’s math questions see below:Find and simplify the difference quotient f(x+h)-f(x) ___ hfor the given function: f(x)=2x-5
Answers
The given function is:
[tex]\begin{gathered} f(x)=2x-5 \\ f(x+h)=2(x+h)-5=2x+2h-5 \end{gathered}[/tex]So the expression is evaluated as follows:
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{2x+2h-5-(2x-5)}{h} \\ =\frac{2x+2h-5-2x+5}{h} \\ =\frac{2h}{h} \\ =2 \end{gathered}[/tex]So the value of the expression is 2.
Directions - Graph the following slope intercept equation:y=-1/3x+4
Answers
Answer:
See below for graph
Explanation:
Given the slope-intercept equation:
[tex]y=-\frac{1}{3}x+4[/tex]To graph it, first, we find the x and y-intercepts.
When x=0
[tex]\begin{gathered} y=-\frac{1}{3}(0)+4 \\ y=4 \end{gathered}[/tex]We have the point (0,4).
When y=0
[tex]\begin{gathered} 0=-\frac{1}{3}x+4 \\ \frac{1}{3}x=4 \\ x=12 \end{gathered}[/tex]We have the point (12,0).
We then draw a line joining points (0,4) and (12,0).
B. When are the y-values the same? When are theydifferent?
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B. When are the y-values the same? When are they
different?
Since there are absolute values, and the y =|x| and y =x will be the same when the values of x are positive and they're going to be different when the values for x are negative ones.
Like this:
y =x | y = |x|
3 y =3
-3 3
Solve the compound inequality.2u+6<18
Answers
Given:
An inequality 2u+6<18
To find:
We have to solve the given inequality.
Solution:
Subtract 6 from both sides to get:
[tex]\begin{gathered} 2u+6-6<18-6 \\ 2u<12 \end{gathered}[/tex]Divide by 2 both sides:
[tex]\begin{gathered} \frac{2u}{2}<\frac{12}{2} \\ u<6 \end{gathered}[/tex]Thus, the solution to the inequality is u < 6.
Which type of association does the scatter plot show? ту 00:00 Weak positive 00:00 Strong negative Strong positive Nonlinear
Answers
SOLUTION
From the diagram, we can see that Scatter Plot is NON- LINEAR.
1. m = -2; b=5
Write an equation in slope-intercept form
Answers
Answer:
y=-2x+5
Step-by-step explanation:
Slope-intercept form is y=mx+b
8 increased by 3 times a number t in expression
Answers
It rained 3.5 inches in the month of April. It rained 45 less in the month of May. How much did it rain in May?
Answers
It rained 1.925 inch in the month of may as the question said "It rained 3.5 inches in the month of April. It rained 45% less in the month of May".
What is inch?In both the British imperial and American customary systems of measurement, the inch serves as a unit of length. It is equivalent to 1/12 of a foot or 1/36 of a yard. The definition of an inch during King Edward II's reign was "three dry, round grains of barley placed end to end lengthwise." The lengths of 12 poppyseeds combined have also been used at various times to define an inch. Since 1959, 2.54 cm has been the official definition of an inch. One inch is exactly equal to 2.54 cm in the metric system, according to the relationship between the two units. The prefix "in" can be used to denote inches. For instance, five feet ten inches could be written as five ft ten in or five feet ten inches.
Here,
45% of 3.5 inch=1.575 inch
Since it rained 45% less than 3.5 inch so,
3.5-1.575=1.975 inch
it rained 1.925 inch in the month of may.
According to the question, it rained 1.925 inches in the month of May "In April, there was 3.5 inches of rain. May saw a 45% decrease in rainfall ".
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Question 21 and 22 list all 6 zeros, write in factored form
Answers
the zeros are
x=-1.5 -----> multiplicity 1
x=0
x=2 ----> multiplicity 2
possible function
y=-x(x+1.5)(x+2)^2 -----> leading coefficient must be negative
Evaluate the first operation 6^2?options: 12, 36, 6-1, 62
Answers
The operation
[tex]6^2[/tex]means that
[tex]6^2=6\times6[/tex]since 6 times 6 is equal to 36, the answer is option 2.
Find u · v.u = 6i − 4jv = i − j
Answers
I need some help please out
Answers
Question:
Solution:
Let the following equation:
[tex]\sqrt[]{12-x}=\text{ x}[/tex]this is equivalent to:
[tex](\sqrt[]{12-x})^2=x^2[/tex]this is equivalent to:
[tex]12-x=x^2[/tex]this is equivalent to:
[tex]x^2+x-12=\text{ 0}[/tex]thus, we can conclude that
x= 3.
A kid is selling cupcakes, each cupcake sold for $1.25 and cookies for $1.75, Jason sold 92.50 worth of cake and cookies if he sold both combined how many cakes were sold and how many cookies
Answers
Set x and y to be the number of cupcakes and cookies, respectively.
Therefore, according to the question,
[tex]Cost=1.25x+1.75y[/tex][tex]\Rightarrow1.25x+1.75y=92.50[/tex]There is only one provided equation; therefore, we cannot determine x and y but just x in terms of y or vice versa. To determine x and y, more information is needed.Solving for x,
[tex]x=\frac{92.50-1.75y}{1.25}[/tex]Use the information in the table to complete the remaining information. Note: The section to the right of the table states "Rewrite the information from the table as a list of ordered pairs in the form of (height, shoe size).
Answers
Given:
A table represents the height and the shoe size of seven students
We will rewrite the information from the table as a list of ordered pairs in the form of (height, shoes size).
So, the order pairs will be as follows:
[tex]\lbrace(5^{\prime}6^{\prime}^{\prime},8),(5^{\prime}7^{\prime}^{\prime},9),(5^{\prime}8^{\prime}^{\prime},9),(5^{\prime}10^{\prime}^{\prime},10),(6^{\prime}6^{\prime}^{\prime},13),(5^{\prime}10^{\prime}^{\prime},12),(5^{\prime}8^{\prime}^{\prime},11)\rbrace[/tex]A mapping diagram:
The table could be represented by the relationship as shown in the following figure:
A company produces standard size American flags with a measurement of 3’ x 5’. Another company produces mega American flags that are similar to this size. If the shorter side of the mega flag is 48',. What is the length of the longer side?
Answers
Solution:
Given:
[tex]\text{Standard size American flag of 3' x 5'}[/tex]Let L be the longer side of the mega flag.
Another company produces a similar flag of 48' x L
Since both flags are similar, then the ratio of the corresponding sides is equal.
Hence,
[tex]\begin{gathered} \frac{3}{5}=\frac{48}{L} \\ \\ \text{Cross multiplying the equation,} \\ 3\times L=5\times48 \\ 3L=240 \\ \\ \text{Dividing both sides by 3,} \\ L=\frac{240}{3} \\ L=80^{\prime} \end{gathered}[/tex]Therefore, the length of the longer side of the mega flag is 80'
Don't understand how to find this answer. Can't find my notes for it.
Answers
Given that
The two sides of the triangle are 6x and 3x+9 and the two angles are 65 degrees each.
Explanation -
According to the property of the triangle " If the two angles of the triangle are equal then the sides opposite to them will be equal."
Then, we have
AB = BC -------------because angle A = angle B = 65
Substituting their values
6x = 3x + 9
6x - 3x = 9
3x = 9
x = 9/3 = 3
x = 3
So side AB will be,
AB = 6(3) = 18 units.
So opption D is correct.
Hence the final answer is 18.Find the y-intercept of a line that passes through (-2,6) and has a slope of -5
Answers
First find the equation of the line whose slope is -5 and passes through (-2, 6).
[tex]\begin{gathered} y-6=-5(x-(-2)) \\ y-6=-5(x+2) \\ y-6=-5x-10 \\ y=-5x-4 \end{gathered}[/tex]For y-intercept, substitute x = 0.
[tex]\begin{gathered} y=-5(0)-4 \\ y=-4 \end{gathered}[/tex]Thus, the y-intercept is -4.
A coin is flipped 3 times. What is the probability that it lands on tails exactly 3 times? Write your answer as a reduced fraction (numerator /denominator).
Answers
Note the probabilty of getting a tail when a coins is flipped 1 time is 1/2
Now for the probability when flipping a coin 3 times, the probability if the a single flipped is multiplied by itself 3 times..
Therefore, the probability of getting a tail for 3 times is :
[tex]\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8}[/tex]The answer is 1/8
Another solution is to list down the possible outcomes :
HHH
THH
HTH
HHT
TTH
THT
HTT
TTT
There are a total of 8 outcomes.
and getting the probability of TTT over 8 outcomes is 1/8
write the slope intercept form:through: (-2, 3), perp. to x=0
Answers
write the slope intercept form:
through: (-2, 3), perp. to x=0
we know that
If the line is perpendicular to x=0 (y-axis), then we have a horizontal line
and the equation of a horizontal line (slope is equal to zero) is
y=3For the function f(x)= 8/9+4xfind f-1(x)
Answers
The inverse of the function is f⁻¹(x) = x/4 - 2/9
The given function is :
f(x)= 8/9+4x
This can be written in the form of an equation such as
y = 8/9+4x
Now we have to find the value of x in terms of y
4x = y - 8 / 9
or, x = y/4 - 2/9
When a code is formed, the domain and its codomain are sometimes not clearly given, and without doing a calculation, one may just be aware that such a domain is a part of a bigger set.
A function from X to Y" often refers to an action that may accept a sufficient subset of X as its domain in mathematical analysis. A "function as from reals here to reals" might be used to explain the function of a valid real variable, for example.
Instead of the entire set of real numbers, a "function out from reals to the reals" refers to a group of real numbers with a non-empty open interval. This kind of job is
Hence the inverse of the function is given by f⁻¹(x) = x/4 - 2/9
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What is the x-intercept of the following graph?a. (0,2)b. (2,0)C. (0, -4)d. (-4,0)
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The x-intercept is the point where the curve (line) cuts the x-axis.
Looking at the graph, the x-intercept is at x = 2.
In coordinates, it is
(2,0)
Correct Answer is B
caluculate the length of AC to 1 decimal place in the trapezium below.
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Check the picture below.
usign the pythagorean theorem let's find the side CD, then let's get the side AC using the same pythagorean threorem.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{16}\\ a=\stackrel{adjacent}{CD}\\ b=\stackrel{opposite}{7}\\ \end{cases} \\\\\\ \sqrt{16^2 - 7^2}=CD\implies \sqrt{207}=CD \\\\[-0.35em] ~\dotfill[/tex]
[tex]c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{AC}\\ a=\stackrel{adjacent}{CD}\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ AC=\sqrt{(\sqrt{207})^2~~ + ~~11^2}\implies AC=\sqrt{207 + 121}\implies \boxed{AC\approx 18.1}[/tex]
BD bisects ZABC such that mZABD =(4x – 5) and mZDBC =(3x + 2)Find the value of ..17
Answers
Solution
For this case we know that
m m < DBC = 3x+2
So then we can do the following:
4x -5 = 3x+2
4x-3x = 5+2= 7
x = 7