What is the solution set of this system of equations?y= x^2+ 2x + 2y = x +1The solution set of a system of equations is the set of all values that satisfy all theequations.
Answers
Hello there. To solve this question, we'll have to remember some properties about system of equations.
Given the following system of equations:
\(\begin{cases}y=x^2+2x+2 \\ y=x+1\end{cases}\)In the R² plane, we have that the solutions to this system are the points of intersection of the parabola y = x² + 2x + 2 and the line y = x + 1.
In fact, there must be two points of intersection and, therefore, two solutions for this system of equation.
Let's plug the first equation into the second equation (called the method of substitution):
\(x^2+2x+2=x+1\)Subtract x + 1 on both sides of the equation
\(\begin{gathered} x^2+2x+2-(x+1)=x+1-(x+1) \\ x^2+2x+2-x-1=0 \\ x^2+x+1=0 \end{gathered}\)Now, this is a quadratic equation of the form:
\(ax^2+bx+c=0,a\ne0\)Its solutions are given by the quadratic formula:
\(x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)Plugging the coefficients a = b = c = 1, we get:
\(x=\frac{-1\pm\sqrt[]{1^2-4\cdot1\cdot1}}{2\cdot1}\)Square the number and multiply the values. Add everything inside the radical.
\(x=\frac{-1\pm\sqrt[]{1-4}_{}}{2}=\frac{-1\pm\sqrt[]{-3}_{}}{2}\)In this case, we got a negative number inside the square root. This is not defined in the real numbers, therefore we don't have solutions for this system of equations.
Graphically, and this is why I omitted it from the beginning, is that in fact the parabola and the line won't have any intersection points, as you can see in the following image:
If we were to solve this system of equations in the set of the complex numbers, then we would have solutions.
First, remember:
\(\sqrt[]{-1}=i\)Such that:
\(x=\frac{-1\pm\sqrt[]{-3}}{2}=\frac{-1\pm\sqrt[]{3}\cdot\sqrt[]{-1}}{2}=\frac{-1\pm\sqrt[]{3}i}{2}\)And the values of y can be found by plugging it in the second equation (the easier one)
\(y=\frac{-1\pm\sqrt[]{3}i}{2}+1=\frac{-1\pm\sqrt[]{3}i+2_{}}{2}=\frac{1\pm\sqrt[]{3}i}{2}\)And the ordered pairs (x, y) would have been:
\(\begin{gathered} \mleft(\dfrac{-1+\sqrt{3}i}{2},\dfrac{1+\sqrt{3}i}{2}\mright) \\ \mleft(\dfrac{-1-\sqrt{3}i}{2},\dfrac{1-\sqrt{3}i}{2}\mright) \end{gathered}\)But as we're talking about real numbers, we say that this is an impossible system of equations, that has no solutions.
Related Questions
(3x−2.4)/0.02 = (8−x)/0.1 Please Help
Answers
Answer
x = 5/4
Step-by-step explanation:
3-(-8)
\(3-(-8)\)
Answers
If u(x) = −2x² +3 and v(x)=1/x, what is the range of (uv)(x)?
Answers
Given:
\(\begin{gathered} u(x)=-2x^2+3 \\ v(x)=\frac{1}{x} \end{gathered}\)Required:
To find the range of the function (uv)(x).
Explanation:
We know that
\(\begin{gathered} (uv)(x)=u(v(x)) \\ \\ =u(\frac{1}{x}) \\ \\ =-2(\frac{1}{x^2})+3 \\ \\ =-\frac{2}{x^2}+3 \end{gathered}\)The horizontal asymptote of this function is at y=3.
So, the range of this function is from
\((-\infty,3)\)Final Answer:
The range of (uv)(x) is
\((-\infty,3)\)An image of a rhombus is shown.
a rhombus with a base of 18 centimeters and a height of 15.5 centimeters
What is the area of the rhombus?
16.75 cm2
33.5 cm2
139.5 cm2
279 cm2
Answers
The area of the rhombus with a base of 18 centimeters and a height of 15.5 centimeters is 139.5 cm² (option c).
To find the area of a rhombus, we can use the formula:
Area = (base * height) / 2.
Given that the base of the rhombus is 18 centimeters and the height is 15.5 centimeters, we can substitute these values into the formula:
Area = (18 cm * 15.5 cm) / 2.
Multiplying the base and height gives us:
Area = (279 cm²) / 2.
Dividing 279 cm² by 2 gives us the final area:
Area = 139.5 cm².
Therefore, the area of the rhombus is 139.5 cm².
Thus, the correct option is c.
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Please help me I’ll mark you brainly
Answers
On solving the provided question, we can say that - here in graph we have on solving equation \(2x^2+ 9y^2 \\\) = \(8 + 9 = 17\)
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
here,
from graph, x= 2
y = 1
\(2x^2+ 9y^2 \\\)
\(8 + 9 = 17\)
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The hypotheses relating to the discoveries of radium and Neptune may be classified as empirical hypotheses.
a) true
b) false
Answers
Answer:
a) true
Step-by-step explanation:
Empirical hypothesis is the type of hypothesis used to try and explain a phenomenon which leads to a theory been developed and put to the test, using observation and experiment.
Radium was discovered due to a discrepancy in pitchblende's radiation. It was noted by the Curies that Polonium alone could not suffice for that amount of radiation, leading to the theory that another element could be present. After further testing, Radium was discovered as the culprit element.
Also, the presence pf another planet, later discovered to be Neptune was theorized to explain the phenomenon that could cause the irregularities in the motion pattern of the planet Uranus. After much experimentation, observations and calculations, Neptune was discovered.
what is the least common denominator of 5/12 and 4/18
Answers
Answer:
36
Step-by-step explanation:
Find the measures (in degrees) of the remaining angles of trapezoid ABCD (not shown) if
AB ∥ DC
and m∠A = 52° and m∠C = 124°
Answers
Answer: D=128 degrees, B=56 degrees
Step-by-step explanation:
It is known that sum of two angles in trapezoid which are close to the side leg ( sides that are not parallel to each other)=180 degrees. Otherwise A+D=C+B=180 degrees
So A+D=180
52+D=180
D=128 degrees
124+ B=180
B=180-124= 56 degrees
i am stuck on this question. any help would be greatly appreciated
Answers
step 1
determine the slope of the given line
y=(3/5)x-17
The slope is m=3/5
Remember that
If two lines are parallel, then their slopes are equal
that means
The slope of the parallel line to the given line is m=3/5 too
step 2
Find out the equation of the line parallel to the given line
y=mx+b
we have
m=3/5
point (-5,15)
substitute and solve for b
15=(3/5)(-5)+b
15=-3+b
b=18
therefore
The equation of the line is
y=(3/5)x+18what is The greatest common factor of 42 and 96? I need it to be broken down for me to understand. thanks
Answers
Answer:
GCF is 6
Step-by-step explanation:
42 :
2 | 42
3 | 21
7 | 7
| 1
; 42 = 2 x 3 x 7
96 :
2 | 48
2 | 24
2 | 12
2 | 6
3 | 3
| 1
; 96 = 2 x 2 x 2 x 2 x 2 x 3
here, common factors are 2 x 3 = 6
Hence, the GCF of 42 and 96 is 6.
HELP ME OUT PLS!!!!
When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is equal to the area of the largest square. Which three squares are an example of this relationship?
Answers
Sum of the area of the small two
= 11 + 5 =16 cm2
Area of the largest square
= L x L = 4 x 4 = 16 cm2
It is seen from both solutions that the areas are the same
Hence D is the answer
May I please get a little help with this question? Thank you so much.
Answers
The y-intercept of the function is (0, c)
The coefficients b determine the horizontal shift of the parabola compared to the parent function
If a is negative, the parabola opens downward
The y-intercept of the function is (0, c).
This means that when x = 0, the y-value is equal to c.
The constant term c represents the y-coordinate of the point where the parabola intersects the y-axis.
The coefficient b determines the horizontal shift of the parabola compared to the parent function.
The value of b affects the position of the vertex and determines if the parabola is shifted to the left or right.
A positive value of b shifts the parabola to the left, while a negative value of b shifts it to the right.
If a is negative, the parabola opens downward.
The coefficient a determines the shape of the parabola.
If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The sign of a determines the direction in which the parabola faces.
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b) In a group of 1,100 youths, each uses smart phones, either I-phone or Samsung or both or neither, 150 of them use only I-phone, 770 of them use Samsung and 900 use only one of these two smart phones. (i) Find the number of youths who use both of these smart phones. (ii) Find the number of youths who use neither of these smart phones.
Answers
How many times does 10 go into 4 1/2
Answers
Answer: 0.45
Step-by-step explanation:
it goes into 4 1/2 in 0.45 times! Hoped this helped!
Refer to the following formula for expected payoff:
Expected payoff= (Probability Of rival matching x Loss from price cut) + (Probability Of rival not matching x Gain from price cut)
Suppose the payoff for each Of four strategic interactions is as follows:
Rival Response
Your Company Action Reduce price Don't Reduce price
Reduce Price Loss=$800 Gain= $50,000
Don't Reduce Price Loss=$6000 No loss or gain
Required:
a. If the probability of rivals matching a price reduction is 98 percent, what is the expected payoff of a price cut?
b. If the probability of rivals reducing price even though you don't is 5 percent, what is the expected payoff Of not reducing price?
b. If the probability of rivals reducing price even though you don't is 5 percent, what is the expected payoff of not reducing price?
c. Based on your answers to (a) and (b), should the firm Cut its price?
Can't determine from the information given
Yes
No
Answers
Answer:
Step-by-step explanation:
From the given information:
The price reduction = 98% = 0.98
\(Then \ the \ expected \ payoff \ = \[(probability \ of \ matching \ price \ reduction \ * \ size \ of \ loss \ from \ price \ cuts \ ) \ + \ ( \ probability \ o f \ rivals\ not \ matching \ * \ gain \ from \ price \ cuts )]\)
where;
P(rival not matching ) = (100 - 98)% = 2%
P(rival not matching ) = 0.02
The expected payoff = [(0.98 * -800) + (0.02*50000)]
The expected payoff = [( -784+ 1000)]
The expected payoff = 216
(b) Probability of rivals reducing price = 5%
= 5/100
= 0.05
∴
Probability of rivals reducing price = 1 - 0.05 = 0.95
The expected payoff = (0.05 * -6000) + (0.95 *0)
The expected payoff = -300 + 0
The expected payoff = -300
(c) Yes.
Based on answers (a) and (b), the firm should cut the price.
In the figure, AXYZ AMNL.
Find m/Y.
X
33°
Y
N
L< 124°
12
Z
8
M
Answers
The measure of angle Y, considering the similar triangles in this problem, is give as follows:
m < Y = 124º.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.N and Y are the base angles, connecting the lateral segments, hence they are congruent.
As m < N = 124º, the measure of angle Y is given as follows:
m < Y = 124º.
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jasmine
was the lead dancer for her dance troupe. She and the troupe's choreographer (also a troupe member) decided that they needed to have one more rehearsal before they performed.
Answers
The members in Jasmine's dance troupe is an illustration equivalent expressions.
The number of members in Jasmine's dance troupe is 62
Assume the number of dancers is n.
One third of the rest is:
\(\mathbf{x = \frac{1}{3}(n - 2)}\)
When she called three more, we have:
\(\mathbf{x = \frac{1}{3}(n - 2) + 3}\)
Expand
\(\mathbf{x = \frac{n}{3} - \frac{2}{3} + 3}\)
\(\mathbf{x = \frac{n}{3} + \frac{-2 + 9}{3}}\)
\(\mathbf{x = \frac{n}{3} + \frac{7}{3}}\)
The remaining dancers (r) are:
\(\mathbf{r = n- \frac{n}{3} - \frac{7}{3}}\)
\(\mathbf{r = \frac{3n - n}{3} - \frac{7}{3}}\)
\(\mathbf{r = \frac{2n}{3} - \frac{7}{3}}\)
\(\mathbf{r = \frac{2n - 7}{3}}\)
When two-fifth of the remaining dancers are added, we have:
\(\mathbf{x = \frac{n}{3} + \frac{7}{3} + \frac{2}{5}(\frac{2n - 7}{3})}\)
\(\mathbf{x = \frac{n+7}{3} + \frac{2}{5}(\frac{2n - 7}{3})}\)
\(\mathbf{x = \frac{n+7}{3} + \frac{4n - 14}{15}}\)
Take LCM
\(\mathbf{x = \frac{5n + 35 + 4n - 14}{15}}\)
\(\mathbf{x = \frac{9n + 21}{15}}\)
\(\mathbf{x = \frac{3n + 7}{5}}\)
When she called one more dancer, we have:
\(\mathbf{x = \frac{3n + 7}{5} + 1}\)
\(\mathbf{x = \frac{3n + 7+5}{5}}\)
\(\mathbf{x = \frac{3n + 12}{5}}\)
The remaining of the dancer is:
\(\mathbf{r = n - \frac{3n + 12}{5}}\)
\(\mathbf{r = \frac{5n - 3n + 12}{5}}\)
\(\mathbf{r = \frac{2n + 12}{5}}\)
When three-fourth are added, we have:
\(\mathbf{x = \frac{3n + 12}{5} +\frac{3}{4} \times \frac{2n + 12}{5}}\)
\(\mathbf{x = \frac{3n + 12}{5} + \frac{6n + 36}{20}}\)
Take LCM
\(\mathbf{x = \frac{12n + 48+6n + 36}{20}}\)
\(\mathbf{x = \frac{18n +84}{20}}\)
When the last two members are added, we have:
\(\mathbf{n = \frac{18n +84}{20} + 2}\)
\(\mathbf{n = \frac{18n +84+40}{20} }\)
\(\mathbf{n = \frac{18n +124}{20} }\)
Multiply through by 20
\(\mathbf{20n = 18n +124}\)
Collect like terms
\(\mathbf{20n - 18n =124}\)
\(\mathbf{2n =124}\\\)
Divide both sides by 2
\(\mathbf{n =62}\)
Hence, the number of members in Jasmine's dance troupe is 62
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if three letter of the alphabet are slected at random find the porbability of getting all vowels letters are relaced each time before selection
Answers
The probability of getting all vowels when three letters of the alphabet are selected at random with replacement is 1/125.
There are 5 vowels in the English alphabet (a, e, i, o, and u) and 26 letters in total. If we select three letters at random with replacement, we have 5 options for each selection.
The probability of getting a vowel on any one selection is 5/26. Since we are replacing the letter each time, the probability of getting three vowels in a row is:
(5/26) × (5/26) × (5/26) = 1/125
Therefore, the probability of getting all vowels when three letters of the alphabet are selected at random with replacement is 1/125.
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How are pairs of parallel lines and skew lines similar and different?
Answers
Answer:
Two or more lines are parallel when they lie in the same plane and never intersect. ... Skew lines are lines that are in different planes and never intersect. The difference between parallel lines and skew lines is parallel lines lie in the same plane while skew lines lie in different planes.
Step-by-step explanation:
hope it helps ^^
Please help! :( Suppose that () is the mass in grams of the garbage in a dumpster minutes before 8 am.
If () is the mass in kilograms of the garbage in the dumpster minutes before 9 am, then g(t)= _________
Answers
hmmmmmmmmmmmmmmmmejjeje
10. Spotify charges x dollars for individual songs and y dollars for entire albums. Person A pays $14.9 A to download 5 individual songs and 1 album. Person B pays $22.95 to download 3 individual songs and 2 albums. How much does Spotify charge to download a song? an entire album?
Answers
Spotify charges $0.98 for individual song and $10 for entire album
According to the question,
Spotify charges "x" dollars for individual songs and "y" for entire album
Also, Person A pays $14.9 to download 5 individual songs and 1 album
Which can be written as
=> 5x + y = 14.9 --------------(1)
Person B pays $22.95 to download 3 individual songs and 2 albums
=> 3x + 2y = 22.95 ---------(2)
Solving these two linear equations by elimination method
Multiplying equation (1) by 2
=> 10x + 2y = 29.8
Now, subtracting these equation
10x + 2y - 3x - 2y = 29.8 - 22.95
=> 7x = 6.85
=> x = 0.98
Replacing value of x in equation (1),
=> 5(0.98) + y = 14.9
=> 4.9 + y = 14.9
=> y = 10
Hence , Spotify charges $0.98 for individual song and $10 for entire album
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n is an odd number.
Which statements are true?
You must get them all correct to get any marks.
A: n²-1 is odd
E: n(n-2) is odd F: (n-2)² is odd
B: n(n-1) is odd C: (n-1)² is odd
D: n² + 2 is odci
Answers
Answer:
True:
D.
E.
F
Step-by-step explanation:
First, you should know that the square of any odd number is also odd.
The easiest way to go about this is to plug in an odd number for n. Lets use 3:
Plug 3 into A:
\(3^{2} -1=9-1=8\)
Plug 3 into B:
\(3(3-1)=9-3 = 6\)
Plug 3 into C:
\((3-2)^{2} = 2^{2} = 4\)
Plug 3 into D:
\(3^{2} +2 = 9+2=11\)
Plug 3 into E:
\(3(3-2) = 9-6 = 3\)
Plug 3 into F:
\((3-2)^{2}=1^{2} =1\)
A cyclist rides her bike at a speed of 12 miles per hour. What is this speed in kilometers per hour? How many kilometers will the cyclist travel in 5 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
PLS HELP
Answers
Answer:
answers below :)
Step-by-step explanation:
Hi there!
with a ratio of 1:1.6, we can find these answers.
1. 19.2 km, multiply 12 by 1.6
2. 96. km, multiply 12 by 6 to find the total amount of miles traveled, then
multiply 60 by 1.6 to get 96.
I hope this helps!
Complete the equation to show how to use the distributive property to express the sum of 30 + 45
with a greatest common factor
30 + 45 = ____ ( ____ + ____ )
Answers
15(2 + 3)
5(6 + 9)
75
1,350
Answers
15(5)
=75
5(6+9)
5(15)
=75
Both answers are equal to 75 so it should be either or
Find the inverse of A = 9, -2 -10, 7 , if it exists.
Answers
The inverse of matrix A, if it exists, is:
A^(-1) = [7/43, 2/43; 10/43, 9/43]
To find the inverse of a matrix A, we need to determine if the matrix is invertible by calculating its determinant. If the determinant is non-zero, then the matrix has an inverse.
Given the matrix A = [9, -2; -10, 7], we can calculate its determinant as follows:
det(A) = (9 * 7) - (-2 * -10)
= 63 - 20
= 43
Since the determinant is non-zero (43 ≠ 0), we can proceed to find the inverse of matrix A.
The formula to calculate the inverse of a 2x2 matrix is:
A^(-1) = (1/det(A)) * [d, -b; -c, a]
Plugging in the values from matrix A and the determinant, we have:
A^(-1) = (1/43) * [7, 2; 10, 9]
Simplifying further, we get:
A^(-1) = [7/43, 2/43; 10/43, 9/43].
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Find the products of the following:
1.(x+7)(2x-5)
2.(4x-3)(7x-1)
3.(x+6)(x-6)
4.(2b-4)(2b+4)
5.(3m²+n)(3m²-n)
please answer it!!! ^_^
Answers
Answer:
\(1)2 {x}^{2} +9−35\)
\(2)28 {x}^{2} −25+3\)
\(3) {x}^{2} −36\)
\(4)4 {b}^{2} −16\)
\(5)9 {m}^{2} − {n}^{2} \)
Ciana earns an hourly wage of $30 at her job. In order to purchase her sneakers she will have to take time off work, so each hour away from her job
costs her $30 in lost Income. Assume that ciana travel time is the same each way (to and from the store) and that it will take her 30 minutes once
she reaches a store to complete her shopping. Assume throughout the question that ciara incurs no additional costs other than the sneakers, such as
gas.
complete the following table by computing the opportunity cost of ciana’s time and the total cost of shopping at each location
Answers
Ciana should purchase the skirt at the store across town because the total economic cost will be lowest.
How to determine the opportunity cost?Ciana makes $30 per hour at her work, and her purchase decision includes the opportunity cost of lost wages:
Total economic cost:
Local store = $114 + [1/4 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $144
Across town = $86 + [1/2 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $131
Neighboring city = $60 + [1 hour x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $135
Ciana should buy a skirt at the store across town. Because it has the lowest total economic cost ($131).
Opportunity cost is the lost benefit or additional cost of choosing one activity or investment over another. Economic costs include both accounting costs and opportunity costs.
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The volume of a cylinder is 72 7 cm. If the radius is 3 cm, what is the height
of the cylinder?
3 cm
A. 4 cm
B. 8 cm
O C. 24 cm
D. 12 cm
Answers
Answer:
The answer is B. 8 cm
Solve each equation by completing the square.
d² - 24d + c
Answers
Answer:
d² - 24d + c = (d - 12)² - 144 + c
.
My number is below sea level.
.
If
you increase my number by 100, it is above sea level.
.
If you decrease my number by 25 it is less than -80.
• My number is divisible by 5.
• My number increased by 5 is -70.
Answers
Answer:
This is an impossible question. This is because it is less than -80 but when you add the 5 it is -70 therefore it must be -75. But it saying it is below -80 therefore this is an impossible question