Answers
EXPLANATION
a) State the inequality:
All the Real numbers greater than 7.
x>7
b) Express the inequality in interval notation:
In order to obtain the interval notation, we must represent with a parenthesis the 7-value because it is not included in the Domain, and then, close the infinite symbol with "]" because it is included in the Domain:
So, the Domain are all Real numbers greater than 7, excluding the 7.
(7,∞]
Related Questions
Determine the number of real solutions of -5x² + 8x = 9 The equation has how many real solution(s).
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Answer:
0 real solutions
Step-by-step explanation:
discriminant : b^2-4ac
in this case, rearrange the quadratic to get -5x^2 + 8x - 9 = 0.
the discriminant is 8^2-4(-9)(-5)=64-180=-116
negative so 0 real solutions
Which choice is equivalent to the quotient below? √64/√16a) √4/4b) √8/2c) 2d) √2
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Answer: option c
The revenue from the sale of a product is given by the function R=400x−x3. Selling how many units will give positive revenue?
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ANSWER:
Selling more than 0 and less than 20 units will give positive revenue.
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]R=\: 400x-x^3[/tex]Now, we propose the following inequality:
[tex]\begin{gathered} 400x-x^3>0 \\ \text{ solving for x:} \\ x\cdot(400-x^2)>0 \\ x\cdot(x-20)\cdot(x+20)>0 \\ \text{ therefore:} \\ x>0 \\ x-20>0\rightarrow x>20 \\ x+20>0\rightarrow x>-20 \\ \text{ in interval form:} \\ (-\infty,-20)\cup(0,20) \end{gathered}[/tex]Since negative units cannot be sold, we are then interested in the range from 0 to 20, therefore, if more than 0 and less than 20 units come in, the revenue will be positive.
Create an example of a linear system that would best be solved using the substitution method. Explain your reasoning
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An example of a linear system that would be solved using the substitution method is "A man bought 2 pens and a book that cost $3 for a total cost of $5. Find the cost of the pen.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the man bought 2 pens and a book that cost $3 for a total cost of $5.
This will be:
2p + b = 5
Substitute b = 3
2p + 3 = 5
Collect like terms
2p = 5 - 3
2p = 2
Divide
p = 2/2
p = 1
The cost of the pen is $1.
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Can you help me solve? Sarah deposited $1,400 for one year at 10% compounded semi-annually. a. How many times was interest added to Sarah's account? (The lesson is on Compound Interest)
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Given the following question:
Sarah deposited $1400 for one year
10% compounded semi-annually
Semi-annually means twice a year or it occurs twice in a year.
Since semi-annually means twice a year we know that the amount of times interest was added to Sarah's account was twice a year.
How many times was interest added to Sarah's account?
A: Two times
i need help getting the answer to this pleaseDetermine the equation of the circle graphed below
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Graph
Center = ( - 7 , 2)
Radius = 2
equation of the circle = ?
Step 02:
equation of the circle
(x - h) ² + (y - k) ² = r ²
( h , k) = ( - 7 , 2)
r = 2
( x - (-7)) ² + (y - 2)² = 2 ²
(x + 7)² + (y - 2)² = 4
The answer is:
The equation of the circle is (x + 7)² + (y - 2)² = 4
according to the data, Vannessa mean quiz ...
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Answer: x = 108
Given the below equation
x + 13 1/2 = 121 1/2
Firstly, we need to convert the mixed fraction into an improper fraction
[tex]\begin{gathered} x\text{ + 13}\frac{1}{2}\text{ = 121 }\frac{1}{2} \\ 13\frac{1}{2}\text{ = }\frac{(2\text{ x 13) + 1}}{2} \\ 13\text{ }\frac{1}{2}\text{ = }\frac{26\text{ + 1}}{2} \\ 13\frac{1}{2}\text{ = }\frac{27}{2} \\ 121\frac{1}{2}\text{ = }\frac{(2\text{ x 121) + 1}}{2} \\ 121\frac{1}{2}\text{ = }\frac{243}{2} \\ \text{Therefore, the new equation becomes} \\ x\text{ + }\frac{27}{2}\text{ = }\frac{243}{2} \\ \text{Isolate x} \\ x\text{ = }\frac{243}{2}\text{ - }\frac{27}{2} \\ \text{Common denominator = 2} \\ x=\text{ }\frac{243\text{ - 27}}{2} \\ x\text{ = }\frac{216}{2} \\ x\text{ = 108} \end{gathered}[/tex]Find the relationship between zeros and x-intercepts of the polynomial x2 + 15x + 54.They are equal to zeroThey are oppositesThey are sameThey are different
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Given:
x2 + 15x + 54.
Required:
Find the relationship between zeros and x-intercepts of the polynomia
Explanation:
Although the zeroes of
[tex]\begin{gathered} x^2+15x-9 \\ \\ are\text{ -6,-9} \\ \\ And\text{ the x-intercepts of it are -6 and -9 } \\ \\ \\ they\text{ mean different things.} \end{gathered}[/tex]Required answer:
They are different
Which of the following expressions are equivalent? Justify your reasoning.4A.1B.-1х10C.√x5 4 2X X X1 1 13 3 3D. X X X
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B and D.
B .
[tex]\frac{1}{x^{-1}\text{ }}=\text{ 1 }\times x^1=x[/tex]D. Since all terms have the same base, we can add exponents.
[tex]x^{\frac{1}{3}}\times x^{\frac{1}{3}}\times x^{\frac{1}{3}}^{}=x^{(\frac{1}{3}+\frac{1}{3}+\frac{1}{3})}=x^1=x^{}[/tex]HELP NOW!!!! use the graph of the function y = 4x to answer the following questions. The domain of the function is to because an exponent can be any real number. On a coordinate plane, an exponential function approaches the x-axis in quadrant 2 and increases exponentially in quadrant 1.
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The domain of the function is negative infinity (-∞) to positive infinity (∞) because an exponent can be any real number.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.
This ultimately implies that, a domain simply refers to the set of all possible input numerical values (x-values) to a function. Additionally, the domain of a graph consist of all the input numerical values (x-values) that are located on the x-coordinate.
By critically observing the graph of this function (see attachment), we can reasonably and logically deduce the following about its domain:
Domain = [-∞, ∞].
In conclusion, the range of this function is from zero (0) to positive infinity (∞) because 4^x is always positive.
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Complete Question:
Use the graph of the function y = 4x to answer the following questions. The domain of the function is _____ to _____ because an exponent can be any real number.
On a coordinate plane, an exponential function approaches the x-axis in quadrant 2 and increases exponentially in quadrant 1.
Solve the inequality. Write the solution in both interval notation and graphically -3x-1 ≥ 5
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Given the inequality;
[tex]-3x-1\ge5[/tex]First, we add 1 to both sides of the inequality, we have;
[tex]\begin{gathered} -3x-1+1\ge5+1 \\ -3x\ge6 \end{gathered}[/tex]Thus, we divide both sides of the inequality by -3, then changes the inequality sign. We have;
[tex]\begin{gathered} -\frac{3x}{3}\leq\frac{6}{-3} \\ x\leq-2 \end{gathered}[/tex]Then, the interval notation of the inequality is;
[tex](-\infty,-2\rbrack[/tex]The graphical representation is;
Prove if the test point (2,-3) is a solution to the system:3x+y≥ -3x+2y ≤ 4
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To solve this question, we can substitute the given point into the inequalities. That is, by substituying x=2 and y=-3 into the first inequality, we obtain
[tex]3(2)+(-3)\ge-3[/tex]and the left hand side is equal to 6-3=3. Because 3>-3, the point (2,-3) can be a solution. However, we must be the same for the remaining inequality, that is, by substituying x=2 and y=-3 into the second inequality, we have
[tex]2+2(-3)\leq4[/tex]and the left hand side is equal to 2-6=-4, then -4<4.
With both results, we can conclude that the point (2,-3) is a solution of the system.
I have to find which line is perpendicular to the line given
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Perpendicularity law
[tex]\begin{gathered} m_1m_2=-1 \\ -5m_2=-1 \\ m_2=\frac{1}{5} \\ y-y_1=m(x-x_1) \\ y-(-4)=\frac{1}{5}(x-10) \\ y+4=\frac{x}{5}-2 \\ y=\frac{1}{5}x-2-4 \\ y=\frac{1}{5}x-6 \end{gathered}[/tex]Boris will take the 10:45 AM train to San Diego. The train is estimated to arrive in San Diego In 3 hours 44 minutes. What is the estimated arrival time?
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Given:
Boris takes the train at 10:45 AM to San Diego.
The train is estimated to arrive in 3 hours 44 minutes.
The objective is to calculate the estimated arrival time.
Now, the train starts at 10:45 AM and arrives in 3 hours 44 minutes,
so first we add time time given , that is:
The train will take 3 hours 44 minutes that is 10.45+3.44=13.89
That is 1 PM and 89 minutes.
Now convert 89 minutes to hours, so
89=60+29 means 1 hour and 29 minutes,
Hence the time is 1 PM +1 hour and 29 minutes
That is,
the estimated arrival time is 2:29 PM
Please help I need an answer ASAP!!!!!!!!!!!!!!!!!!
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Answer:
{-5,-3,0}
Step-by-step explanation:
Since you need it ASAP, the domain is listed above. No explanation.
geometry_I dont know how to calculate 80/360 pie r^2
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Hello there. To solve this question, we'll have to remember some properties about circular sectors.
Given a circular sector of a circle with radius R:
Suppose the length of the arc AB is alpha (in radians).
From a well-known theorem about angles in a circle, we know that the angle generating this arc from the center has the same measure, that is:
So we want to determine the area of the sector knowing the radius and the length of the arc.
First, we know that the area of the full circle is given by:
[tex]A=\pi\cdot R^2[/tex]The sector is a fraction of this circle, that means that:
[tex]A=kA_{sector}[/tex]A is a multiple of Asector.
In fact, this proportionality constant is the ratio between the central angle and the angle alpha forming the sector, that is
[tex]k=\dfrac{2\pi}{\alpha}[/tex]It is also possible to have alpha in degrees, but we have to convert the center angle to degrees as well, so we get
[tex]k=\dfrac{2\pi\cdot\dfrac{180^{\circ}}{\pi}}{\alpha\cdot\dfrac{180^{\circ}}{\pi}}=\dfrac{360^{\circ}}{\alpha^{\circ}}[/tex]As we want to solve for the area of the sector, we have that:
[tex]A_{sector}=A\cdot\dfrac{\alpha^{\circ}}{{360^{\circ}}}=\dfrac{\alpha^{\circ}}{360^{\circ}}\cdot\pi R^2[/tex]Okay. With this, we can solve the question.
We have the following circle:
In this case, notice R = 18 yd and the length of the arc is 80º. This gives us the angle alpha:
Now, we take the ratio between the angle and the total angle applying the formula:
[tex]A_{sector}=\dfrac{80^{\circ}}{360^{\circ}}\cdot\pi\cdot18^2[/tex]Square the number
[tex]A_{sector}=\dfrac{80^{\circ}}{360^{\circ}}\cdot\pi\cdot324[/tex]Simplify the fraction by a factor of 40º
[tex]A_{sector}=\dfrac{2}{9}\cdot\pi\cdot324[/tex]Multiply the numbers and simplify the fraction
[tex]A_{sector}=\dfrac{648\pi}{9}=72\pi[/tex]This is the area of this sector.
5. Bill is making candy bags for his nieces and nephews that are visiting. He has 45 M & Ms and 75 Reese's Pieces. If he wants to put the same number of M&Ms in each bag and the same number of Reese's Pieces in each bag, what is the greatest number of candy bags that Bill can make?
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We have to take the GCF (Greatest Common Factor) of 45 and 75 to get our answer.
We prime factorize the numbers. Shown below:
45 = 3 * 3 * 5
and
75 = 3 * 5 * 5
The greatest number of time 3 is common is 1 time
The greatest number o time 5 is common is 1 time
So,
GCF(45, 75) = 3 x 5 = 15 bags
For the following sequence, state the common difference, identify which is the explicit form and which is the recursive form of the rule, and find the term listed.Sequence: 0,100,200,300,…Common difference: ?An=-100+100nexplicit or recursive?An=an-1+100A1=0Explicit or recursive?
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Solution:
Give the sequence:
[tex]0,\text{ 100, 200, 300,..}[/tex]The common difference is the difference between two consecutive terms.
Thus, the common diffrence is evaluated as
[tex]\begin{gathered} 100-0 \\ =100 \end{gathered}[/tex]Thus, from the explicit formula,
[tex]\begin{gathered} a_n=a+(n-1)d \\ where \\ a=0 \\ d=100 \end{gathered}[/tex]The explicit form is evaluated to be
[tex]\begin{gathered} a_n=0+(n-1)100 \\ \implies\text{A}_n=-100+100n \end{gathered}[/tex]The recursive form is evaluated as
[tex][/tex]A sofa is on sale for $363 which is 34% less than a regular price what is the regular price
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Given that a sofa is on sale for $363, which is 34% less than the regular price.
To determine: The regular price.
Let the regular price be Y. If the regular price is Y, then the 34%regular price would be
[tex]\begin{gathered} P_{\text{less}}=(100-34)\text{ \% of \$Y} \\ P_{\text{less}}=66\text{ \% of Y} \end{gathered}[/tex]It should be noted that the 34 % less the regular price is the price on sale. Then,
[tex]\begin{gathered} P_{\text{less}}=\text{ \$363} \\ \text{Therefore,} \\ 66\text{ \% of Y = \$363} \\ \frac{66}{100}\times Y=363 \\ \frac{66Y}{100}=363 \\ 66Y=363\times100 \\ 66Y=36300 \\ Y=\frac{36300}{66} \\ Y=550 \end{gathered}[/tex]Hence, the regular price of the sofa is $550
Given f(x)=9x and g(x)=3x2+2, find the following expressions.
(a) (f◦g)(4) (b) (g◦f)(2) (c) (f◦f)(1) (d) (g◦g)(0)
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Value of the expressions for the given functions f(x) =9x , g(x) =3x² +2 is given by:
a. (fog)(4) = 450
b. (gof)(2) =974
c. (fof)(1) = 81
d. (gog)(0) = 14
As given in the question,
Given functions are:
f(x) =9x
g(x) =3x² +2
Value of the expressions for the given functions f(x) =9x , g(x) =3x² +2 are as follow:
a. (fog)(4)
= f(g(4))
= f( 3(4²)+2)
= f(50)
= 9×50
=450
b. (gof)(2)
=g(f(2))
=g(9(2))
=g(18)
=3(18)² +2
=974
c. (fof)(1)
= f(f(1))
= f(9(1))
=f(9)
=9×9
=81
d. (gog)(0)
=g(g(0))
=g(3(0²) +2)
=g(2)
=3(2)² +2
=14
Therefore, Value of the expressions for the given functions f(x) =9x , g(x) =3x² +2 is given by:
a. (fog)(4) = 450
b. (gof)(2) =974
c. (fof)(1) = 81
d. (gog)(0) = 14
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He'll am just trying to make sure I did this right
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EXPLANATION
Number of books = 12
Bill = $112
Amount spent = $16
Cost = $12/book
The variable is the number of books--> x
In the following exercise a formula is given along with the values of all but one of the variables in the formula. Find the value of the variable that is not given S=2LW+2WH+2LH; S=108,L=3 W = 4
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Question:
In the following exercise, a formula is given along with the values of all but one of the variables in the formula. Find the value of the variable that is not given
S=2LW+2WH+2LH;
S=108,
L=3
W = 4
Solution:
Consider the following equation:
[tex]S=2LW+2WH+2LH[/tex]now, if we replace the given data, in the previous equation, we obtain:
[tex]108=2(3)(4)+2(4)H+2(3)H[/tex]this is equivalent to:
[tex]108=24+8H+6H[/tex]this is equivalent to:
[tex]108-24=14H[/tex]this is equivalent to:
[tex]14H=84[/tex]thus, solving for H, we get:
[tex]H\text{ = }\frac{84}{14}=\text{ 6}[/tex]Then, we can conclude that the value of the variable that is not given is:
[tex]H\text{ = 6}[/tex]Perform the indicated operation and express the result as a simplified complex number. (5−6i)(4+8i)
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we have the expression
[tex](5-6i)(4+8i)[/tex]Apply distributive property
[tex]\begin{gathered} (5)(4)+(5)(8i)-(6i)(4)-(6i)(8i) \\ 20+40i-24i-48i^2 \\ Reemmber\text{ that }i^2=-1 \\ 20+40i-24i-48(-1) \\ 20+40i-24i+48 \\ combine\text{ like terms} \\ (68+16i) \end{gathered}[/tex]the question is hard to write i will take a picture of it when I met you!
Answers
Answer
The score on her next test that would keep her mean and median the same would be 95. Because her mean and median are already 95, another score of this value would not alter the mean or the median.
Explanation
To answer this, we need to first obtain the current mean and median
96, 95, 98, 92, 94, 93, 97
The mean is the average of the distribution. It is obtained mathematically as the sum of variables divided by the number of variables.
Mean = (Σx)/N
x = each variable
Σx = Sum of the variables
N = number of variables
Σx = 96 + 95 + 98 + 92 + 94 + 93 + 97 = 665
N = 7
Mean = (Σx)/N
Mean = (665/7) = 95
Median
The median is the variable that falls in the middle of the distribution when all the variables are arranged either in ascending or descending order.
So, to obtain the median for this, we have to arrange all the scores in data.
96, 95, 98, 92, 94, 93, 97
92, 93, 94, 95, 96, 97, 98
We can easily see that the number in the middle is the fourth number and that number is 95
So, currently the mean and the median are already the same score, 95, so, the score that she needs to get in her next test to keep the mean and median equal is still 95.
Hope this Helps!!!
What is 72 hours to 3 days in ratio form
Answers
Answer:
3:3 / 1:1
Step-by-step explanation:
72 hours is 3 days
Someone help please
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Answer:
c = 30
b = 150
8 CHILDREN PARTICIPATE IN A IN A CONTEST. FOUR DIFFERENT PRIZES ARE AWARDED T0 THE WINNER AND THE FIRST,SECOND AND THIRD RUNNER UPS. IN HOW MANY DIFFERENT WAYS CAN THE FOUR PRIZES BE AWARDED?
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We have that there are 8 participants and 4 prizes, in this problem, it's important the order of the prizes too.
Now, for the first time, there are 8 possibilities for awarding the winner prize.
For the second moment, there are just 7 possibilities for awarding the first runner-up.
Then, we have that there are 6 possibilities for awarding the second runner-up.
And, finally, we have 5 possibilities for awarding the third runner-up.
So, we have that all the ways are represented as:
[tex]8\ast7\ast6\ast5=1680[/tex]And since the order of the 4 prizes is important to get a specific prize, we have:
[tex]\frac{1680}{4!}=70[/tex]Then the correct answer would be 70.
It takes 2 1/2 poster boards to display half of your project. how many poster boards will you need for your entire project? Please help me thank you
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Since 2 1/2 boards can display half of your project. You will need two 2 1/2 boards to display your full project. Multiply 2 1/2 by 2 and we get
[tex]2\frac{1}{2}\times2=\frac{5}{2}\times2=\frac{10}{2}=5[/tex]Therefore, you need 5 boards to display your entire project.
What is the base for each curve and where should I shift for each? I’ve been getting this wrong because I don’t know which way to shift and what the base should be for both
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Answer:
Here is the graph of the equation and its inverse.
The inverse is the purple graph.
Explanation:
• The base of the equation is 8.
,• There is no vertical shift to the graph because there's no constant added to the function f(x) = 8^x.
,• In addition, there is no horizontal shift to the graph because there's no constant added to the exponent x.
if a trend line had the equation [tex]y = - 3.7x + 0.68[/tex]what y-value would you expect to obtain when x has the following values? a. 13; b. 0; c. 5.8; d. 7.7
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Step 1: Write out the equation given in the question
[tex]y=-3.7x+0.68[/tex]Step 2: Solve for y by substituting each of the values of x given in the question
[tex]\begin{gathered} (a)\text{when x=13} \\ y=-3.7(13)+0.68 \\ y=-48.1+0.68 \\ y=-47.42 \end{gathered}[/tex][tex]\begin{gathered} (b)\text{when x=0} \\ y=-3.7(0)+0.68 \\ y=0+6.8 \\ y=0.68 \end{gathered}[/tex][tex]\begin{gathered} (c)\text{when x=5.8} \\ y=-3.7(5.8)+0.68 \\ y=-21.46+0.68 \\ y=-20.78 \end{gathered}[/tex][tex]\begin{gathered} (d)\text{ when x=7.7} \\ y=-3.7(7.7)+0.68 \\ y=-28.49+0.68 \\ y=-27.81 \end{gathered}[/tex]Hence, when x= 13, y= -47.42; x=0, y= 0.68; x=5.8, y=-20.78; x=7.7, y=-27.81