We have two explicit functions of x for y:
[tex]y = -1/2 + \sqrt{(x^2 - x + 1/4)} \\or\\y = -1/2 - \sqrt{(x^2 - x + 1/4)}[/tex]
To define y as an explicit function of x, we need to solve for y in terms of x in the given equation:
[tex]x + y + y^2 = x^2[/tex]
First, let's simplify the equation by moving all the terms to one side:
[tex]y^2 + y + (x - x^2) = 0[/tex]
Now, we can use the quadratic formula to solve for y:
[tex]y = (-b + \sqrt{(b^2 - 4ac)} ) / 2a[/tex]
where a = 1, b = 1, and [tex]c = x - x^2.[/tex]Substituting these values, we get:
[tex]y = (-1 + \sqrt{(1 - 4(x - x^2)} )) / 2[/tex]
Simplifying further:
[tex]y = (-1 + \sqrt{(1 - 4x + 4x^2)} ) / 2\\y = (-1 + \sqrt{(4x^2 - 4x + 1)} ) / 2\\y = (-1 + 2\sqrt{(x^2 - x + 1/4)} ) / 2\\y = -1/2 + \sqrt{(x^2 - x + 1/4)}[/tex]
Therefore, we have two explicit functions of x for y:
[tex]y = -1/2 + \sqrt{(x^2 - x + 1/4)} \\or\\y = -1/2 - \sqrt{(x^2 - x + 1/4)}[/tex]
Either of these expressions represents y as an explicit function of x.
for such more question on explicit functions
https://brainly.com/question/15683939
#SPJ11
Which sign makes the following statement true? 2/5 _____ 6/15
Answer:
2/5=6/15
Step-by-step explanation:
2/5
3x2=6
3x5=15
compare they are same
give me brainliest pls
The equal sign completes the give incomplete mathematical statement.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.The given incomplete expression is -
2/5 _____ 6/15
The given expression is -
2/5 ____ 6/15
2/5 ____ 2/5
0.4 ____ 0.4
0.4 = 0.4
Therefore, the equal sign completes the give incomplete mathematical statement.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ2
Math question, can you guys answer this? 25 points.
Answer:
5. 1/29
Step-by-step explanation:
1/. and the bottom numbers says 30-1 which is 29 soooo 1/29
To test the effectiveness of an exercise program in reducing high blood pressure, 15 participants had their blood pressures recorded before beginning the program and again after completing the program. The difference (after minus before) in blood pressure was recorded for each participant, and the sample mean difference was calculated. A hypothesis test will be conducted to investigate whether there is convincing statistical evidence for a reduction in blood pressure for all who complete the program. Which of the following is the correct set of hypotheses?
A. H0 : bar xD = 0
Ha : bar xD is not equal to 0
B. H0 : bar xD = 0
Ha : bar xD > 0
C. H0 : mu D = 0
Ha : mu D is not equal to 0
D. H0 : mu D = 0
Ha : mu D > 0
E. H0 : mu D = 0
Ha : mu d < 0
Answer:
E.
H0 : mu D = 0
Ha : mu d < 0
Step-by-step explanation:
The hypothesis is to test if there is a reduction in blood pressure for those who complete the program, this means if the mean difference in blood pressure (that is after - before) is less than 0. Here, the hypothesis is the alternative side while the opposite, that is, there is no difference in blood pressure before and after is the null.
This means :
H0 : μD = 0
Ha : μD < 0
You can use the definitions for null and alternate hypotheses
The correct set of hypothesis is given by:
Option E. [tex]H_0: \mu_D = 0[/tex]
[tex]H_a: \mu_D < 0[/tex]
How to form the hypotheses?There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.
Null hypothesis is the one which researchers try to disprove.
How to find the correct set of hypothesis for the given situation?Since the test is to test the effectiveness of the exercise program, thus the wish of the tester is to get the result that effectiveness is there. This will be the alternate hypothesis and the null hypothesis will be that there is no difference in the blood pressure before and after the exercise. Thus, we will test against the null hypothesis.
Since the evidence is to be found for all of the people who completed the program, thus it is hypothesis about population perimeter. The average blood pressure difference of the population is denoted by [tex]\mu_D[/tex] and that of the sample is denoted by [tex]\overline{x}_D[/tex]
Thus, we have:
Null hypothesis = the difference in average blood pressure before and after the program of the population is not changed(thus 0 is the difference) = [tex]H_0: \mu_D = 0[/tex]
Alternate hypothesis = the difference in average blood pressure is reduced(since the test is for seeing if the blood pressure is reduced or not) = [tex]H_a: \mu_D < 0[/tex]
Thus,
The correct set of hypothesis is given by:
Option E. [tex]H_0: \mu_D = 0[/tex]
[tex]H_a: \mu_D < 0[/tex]
Learn more about null and alternative hypothesis here:
https://brainly.com/question/18831983
b. 3.3 x 0.8 =
3 3
х
8
Answer: the answer is 2.64 or 264
Explanation: if you multiply 3.3 × 0.8=264 but if you mulyiply 33×8=264
What is the area of a circle with a radius of 4 inches? Use 3.14 for π. Enter your answer as a decimal in the box.
enter your answer
in²
Answer:
A≈ 50.27in^2
Step-by-step explanation:
A= πr^2=
π·4^2≈ 50.26548
5% of a number is 23
1% percent of the same
number is 6.4
Work out 16% of the number
Answer:
73.6Step-by-step explanation:
Let the number be mso, 5% × m = 23 5 m = 23100m = 23 × 100 5m = 46016% of that number 16 × 460 = 73.610016% of the number is 73.6Is this a proportion? 1.44/8 = 1.7/10
Answer:
No
Step-by-step explanation:
Because the equation needs to have a variable
If the sum of two numbers is 4 and the sum of their spuares minus three times their product is 76, find the numbers
Answer:
[tex]Suppose~that~two~numbers~are~x~and~y.\\From~the~first~condition,\\x+y=4.........(1)\\or, y=4-x.......(2)\\From~the~second~condition,\\x^2+y^2-3xy=76\\or, (x+y)^2-2xy-3xy=76\\or, 4^2-5xy=76\\or, -5xy = 76-16\\or, -5xy = 60\\or, xy = -12\\From~eq^n~(2),\\x(4-x)=-12\\or, 4x-x^2=-12\\or, x^2-4x-12=0\\or, x^2 +2x-6x-12=0\\or, x(x+2)-6(x+2) = 0\\or,(x+2)(x-6) = 0\\i.e. x = -2 ~or ~6\\When~ x=-2, y=4-(-2) = 4+2 =6\\When~x=6, y=4-6 = 4-6 = -2\\So,~the~two~numbers~are~-2~and~6.[/tex]
Answer:
-2 and 6
Step-by-step explanation:
Mark the first number as x
and the second number as y
Since x + y = 4
y = 4 - x
// substitute the given value of y into the equation
[tex]x^{2} + y^{2}[/tex] - 3xy = 76
[tex]x^{2}[/tex] + [tex](4-x)^{2}[/tex] - 3 * x * (4 - x) = 76
[tex]x^{2}[/tex] + 16 - 8x + [tex]x^{2}[/tex] - 12x + 3[tex]x^{2}[/tex] = 76
[tex]x^{2}[/tex] + [tex]x^{2}[/tex] + 3[tex]x^{2}[/tex] - 20x = 76 - 16
5[tex]x^{2}[/tex] - 20x = 60
5[tex]x^{2}[/tex] - 20x - 60 = 0
// divide both sides by 5
[tex]x^{2}[/tex] - 4x - 12 = 0
// write -4 x as a difference, this way it is faster than calculating discriminant
[tex]x^{2}[/tex] + 2x - 6x - 12 = 0
// factor out x and -6 from the expression
x (x +2) - 6 (x +2) = 0
(x - 6) * (x + 2) = 0
// there are two possible cases
1) x - 6 = 0
2) x + 2 = 0
1) x = -2
2) x = 6
// substitute the given value of x into the equation
1) y = 4 - x = 4 - (-2) = 6
2) y = 4 - x = 4 - 6 = -2
Now we get two pairs (-2; 6) and (6; -2), which are the solutions to the system
Since their sequence as the question suggests is irrelevant, the numbers are -2 and 6
Dave divided 3/5 of a gallon of plant fertilizer evenly among 6 smaller bottles. How many gallons did he put in each bottle?
Whoever answers first gets brainliest please help
Answer:
Brothers Sorry I don't
Step-by-step explanation:
Please give thanks to all my answers and please mark as brilliant and please follow me
5 - x/3 for x = -3
Evaluate the expression
Find the absolute value.
What is the absolute value of four
Answer:
whats the graph???
Step-by-step explanation:
Answer: 4
Step-by-step explanation:
When it’s an absolute value no matter what it’s inside the braces ( “ | # | “ ) it’s a positive. While the signs outsides can stay the same
Bir otobüste bulunan 45 yolcudan
Buna göre bu otobüsteki yolcuların
18'i çocuktur.
yüzde kaçı çocuktur?
Step-by-step explanation:
bence 27 cunkku yuzd sordugu icin kolaylıklar dilerim iyi günler
Select the correct option from the menu.
Raj determined that the equation 3 (x+3) = 8x - 5x +7 is equivalent to 9 = 7. This means that this equation has:
no solutions
One solution
Two solutions
Infinity many solutions
Your warehouse had 51 cases of Happy Cola at the start of your shift. A truck arrived this morning with another 25 cases of Happy Cola. How many cases of Happy Cola do you have now?
Answer:
76 cases
Step-by-step explanation:
original 51 plus the 21 new is equal to 76 total
how would i solve this?
i+i^2+i^3+i^4+i^5+i^6+i^7+i^8+i^9+i^10
please do a step by step process
Step-by-step explanation:
step 1. I assume i is imaginary
step 2. i^2 = -1, i^3 = -i, i^4 = 1, i^5 = I. . . . and so on
step 3. i - 1 - i + 1 + i - 1 - i + 1 + i - 1
step 4. the result is i - 1.
A marine biologist wants to estimate the average weight of a population of dolphins living in a certain region of the ocean. The biologist will collect a random sample of dolphins and use the sample weights to create the estimate Which of the following is an appropriate method for the biologist to use for inference to the population?
A A one-sample t-interval for a population mean
B A one-sample t-interval for a sample mean
C A one-sample 2-interval for a population proportion
D A matched-pairs t-interval for a mean difference
E A two-sample t-interval for a difference between means
Answer:
A A one-sample t-interval for a population mean
Step-by-step explanation:
The biologist will collect a random sample of dolphins and use the sample weights to create the estimate.
In a confidence interval, we take the data from the sample and want to estimate it for the entire population, so the interval is for a population mean.
The standard deviation will be taken from the sample, which means that the t-interval is used.
We want for one population, so it is a one sample for the population mean, and the correct answer is given by option A.
Solve for x in equation x^2-10x25=35
Answer: b
Step-by-step explanation:
x= 5+√35 and 5-√35
Find AB.
MN=22
DC=29
Answer:
AB=15
Step-by-step explanation:
Since DM =MA and CN=NB, then DC || MN || AB
29-22=7
22-7=15
AB=15
Find the selling price of a $30 item after a 40% markup.
what is estimate the product of 19.8 and 5 by grounding each factor to nearest whole number
Given:
The two numbers are 19.8 and 5.
To find:
The estimated product of given numbers by rounding each factor to nearest whole number.
Solution:
Two number are 19.8 and 5.
On rounding the given numbers to the nearest whole number, we get 20 and 5.
Now, the estimated product is
[tex]20\times 5=100[/tex]
Therefore, the estimated product of given numbers is 100.
If a well is dug at -60 feet per day. How many days did it take to dig -5400 feet?
(Answer numerically ex: 30 Days answer = 30)
Answer:
90 days
Step-by-step explanation:
This one is just simple division, so you divide the goal number which is -5400 by -60 but in this situation you can just make them positives.
An iPhone that is marked $500 is marked up 250%.
What is the new price of the iPhone?
$750
$1750
$1250
$1000
Answer:
1250Step-by-step explanation:
This would be 500 x 250/100 = 125000/100 = 1250
1. X+4x+6x need help ASAP 10 minutes remaining
Answer:
10x^2 or 10x because you are adding x
The equation of a line XY is (y-3)=3/2(x-4) what is the slope of the line perpendicular to XY?
Answer:
It must be 3/2.........
Answer: -2/3
Step-by-step explanation:
I wrote the equation y-3=3/2(x-4) in slope-intercept form. It's y=3/2x-5, so the slope is 3/2.
To find the perpendicular slope, I found the opposite reciprocal. The reciprocal of 3/2 is 2/3 and the opposite of 2/3 is -2/3
Kaitlin has four and two-thirds berry pies. She is going to share it equally among 12 people. How much pies will each person get?
Answer:
7/18
Step-by-step explanation:
4 2/3=14/3
(14/3)/12=14/36
reduces to
7/18
An equation is shown below:
8(2x − 14) + 13 = 4x − 27
Part A: Write the steps you will use to solve the equation, and explain each step. (6 points)
Part B: What value of x makes the equation true? (4 points)
Amd please show the work.
Step-by-step explanation:
first distribute the first equation
8(2x) - 8(14) +13 = 4x -27
16x - 112 +13 = 4x -27
then combine like terms
16x - 99 = 4x -27
subtract 4x from both sides
12x - 99 = -27
add 99 to both sides
12x = 72
divide both sides 12 to isolate the x
x = 72/12 = 6
Write an equation for the line in slope-intercept
form.
(Use integers or fractions for any numbers in the
equation.)
Answer:
y = 3x + 5Step-by-step explanation:
Slope-intercept form:
y = mx + b, where m is the slope, b is the y-interceptTake two points from the graph:
(-2, -1) and (0, 5)Find the slope:
m = (5 - (-1))/(0 - (-2)) = 6/2 = 3The y-intercept is b = 5
The line is:
y = 3x + 5First to answer correctly gets brainliest
The table shows the results of a survey of 100 people selected at random
at an airport. Find the experimental probability that a person selected at
random is going to City C.
The experimetal probability that a person selected at random is going to city C is
Answer:
[tex]\frac{4}{25}[/tex]
Step-by-step explanation:
22/200 simpilfy is 4/25
The experimental probability that a person selected at random is going to city C is P ( C ) = 4/25 = 0.16
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the experimental probability that a person selected at random is going to city C is P ( C )
Now , the total number of people in the city = 100
The number of people going to city C = 16
So , P ( C ) = number of people going to city C / total number of people in the city
On simplifying , we get
P ( C ) = 16 / 100
P ( C ) = 4/25
P ( C ) = 0.16
Hence , the probability is 0.16
To learn more about probability click :
https://brainly.com/question/17089724
#SPJ2
What is the least common denominator of the rational expressions below?
1/x^2 - 4/3x^2+15x
Answer:
The LCD is 3x²
The other two denominators can be factors of 3x²
Step-by-step explanation:
To get the equivalent fractions, divide the original denominator into the LCD, then multiply the original numerator by the quotient.
For the first term: 1/x²
3x² ÷ x² = 3 3×1=3 The equivalent is 3/3x²
Second term: Leave it as it is.
For the third term: 15x
The implied denominator is 1
3x² ÷ 1 = 3x² 3x² × 15 = 135x²
The equivalent is 135x²/3x²
To check the validity, substitute a value for x and calculate the numbers.
For example let x = 3
The original expression becomes
1/3² + 4/3(3²) - 15(3)
1/9 + 4/27 - 45
With the LCD it is
3/27 + 4/27 - 1215/27
Answer:
3x^2(x+5)
Step-by-step explanation:
hope this helps