Answers
The solutions for the system of equations " 3x²-2y²+5=0 and 2x²-y²+2=0" are :
First Solution : x = 1, y = 2
Second Solution : x = 1, y = -2
Third Solution : x = -1, y = 2
Fourth Solution : x = -1 , y = 2.
In order to solve the system of equations 3x²-2y²+5=0 and 2x²-y²+2=0, we use substitution method;
From the second equation, we solve for y² in terms of x²:
The second equation is : 2x² - y² + 2 = 0;
We get, y² = 2x² + 2
Substitute this expression for y² into the first equation:
We get,
3x² - 2(2x² + 2) + 5 = 0
3x² - 4x² - 4 + 5 = 0
-x² + 1 = 0
x² = 1
We get, x = ±1
Substitute these values of x into the equation for y²:
y² = 2x² + 2
For x = 1, y² = 4,
Which means the solution set is (1,2) and (1,-2),
For x = -1, y² = 4
the solution set is (-1,2) and (-1,-2).
Therefore, the solutions to the system of equations are (1, 2), (1,-2), (-1,2) and (-1, 2).
Learn more about Equations here
https://brainly.com/question/29499995
#SPJ1
Related Questions
Graph the equation y = − x² + 8 x − 12 on the accompanying set of axes. You must plot 5 points including the roots and the vertex. Using the graph, determine the roots of the equation − x² + 8 x − 12 = 0
Answers
A graph that represent the quadratic equation y = -x² + 8x - 12 is shown in the image attached below.
The roots of the equation are (2, 0) and (6, 0).
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).
Since the leading coefficient (value of a) in the given quadratic function y = -x² + 8x - 12 is negative 1, we can logically deduce that the parabola would open downward and the x-intercept (roots) is given by the ordered pair (2, 0) and (6, 0).
In conclusion, the turning point and vertex is given by the ordered pair (4, 4).
Read more on quadratic functions here: brainly.com/question/29499209
#SPJ1
HELP MEEEEE PLEASEEE SOMEONEEEE :(
Answers
The function is not defined for x > 5, as a result ƒ(7) does not exist.
How did we arrive at this assertion?The given piece-wise function is:
f(x) = {x - 2}²- 1
1
-x+1
x < 2
x = 2
2 < x ≤ 5
Step 2
f(x) = (x-2)² - 1
1
-x+1
x < 2
x = 2
2 < x ≤ 5
Note that the function is not defined for x > 5.
Step 3
Since the function is not defined for > 5, therefore ƒ(7) does not exist.
The function is not defined for x > 5, therefore ƒ(7) does not exist.
learn more about function: https://brainly.com/question/11624077
#SPJ1
Solve for k and graph the solution. 0≥ k+14 3 > – 2
Answers
The graph of the solution set for the inequality -14 ≥ k > -20 is on the image at the end.
How to solve the inequality for k?To do this we just need to isolate the variable k in the middle.
We start with:
0 ≥ (k+14)/3 > – 2
We can multiply both sides by 3:
3*0 ≥ (k+14) > – 2*3
0 ≥ (k+14) > - 6
Now subtract 14 in both sides:
-14 ≥ k > -6 - 14
-14 ≥ k > -20
Then we need to draw an open circle at k = -20 and a closed circle at k = -14, and connect them with a line, like in the image below.
Learn more about inequalities at:
https://brainly.com/question/24372553
#SPJ1
find the statement that is incorrect. Then, correct and rewrite the statement in the space provided. Show any necessary work.
Answers
The incorrect statement is
The transformation can be represented by (7/3x, 7/3y)What is Dilation in Transformation?In mathematics, dilation can be defined as a transformation which alters the size of an object, though its shape remains unchanged. It is described as a specific similarity transformation where all dimensions associated with the given object (i.e. height, width and length) are increased or decreased uniformly by a particular scale factor.
A dilation thus produces an alteration in size, with the figure being either magnified or diminished while keeping its unique shape intact.
The scale factor used in the dilation is 9/7 instead of 7/3.
Learn more about transformation at
https://brainly.com/question/4289712
#SPJ1
George went to the store to buy notebooks.
- He had $36 to spend.
- He purchased 4 notebooks.
- After buying the notebooks, George had less than $12 left.
-What is the solution set for x, the cost of each notebook?
Answers
Thus, the solution set for the cost of each notebook that can be bought by George is: (0 ≤ x ≤ 6).
Explain about the one variable linear equation:A linear equation is a one-variable equation of the a straight line. The variable only has one power, which is 1. Simple algebraic operations are used to solve linear equations in one variable, which can have the form ax+b=0.
Given that:
Total amount George has = $36.Number of books = 4Left amount = $12Let the cost of each notebook 'x'.So, the linear equation follows
Amount for 4 notebooks + Left amount = total amount
4*x + 12 ≤ 36
4x ≤ 36 - 12
4x ≤ 24
x ≤ 24/4
x ≤ 6
So, (0 ≤ x ≤ 6)
Thus, the solution set for the cost of each notebook that can be bought by George is: (0 ≤ x ≤ 6).
Know more about the variable linear equation
https://brainly.com/question/2030026
#SPJ1
(6x-2)(8x+4)° Intercepted arc
Answers
Answer:
[tex](6x-2)(8x+4)° \\ = 6x(8x + 4) - 2(8x + 4) \\ = 48x {}^{2} + 24x - 16x - 8 \\ = 48x {}^{2} + 8x - 8 \\ [/tex]
hope it helps
write 68.19 to one significant figure
Answers
Answer:
70...............................
Reason:
The left-most digit is the most significant when it comes to rounding. We bump the 6 up to 7 since 68 is closer to 70 (compared to 60). The other digits turn to 0 and become insignificant.
Do not write any of the following:
70.70.070.00because that would mean we would have 2, 3, and 4 sig figs respectively. We simply write 70 without a decimal point.
Level E: The repair department of the bicycle shop repairs three things: flat tires, bent handle bars and ripped seats. Today in the repair department, 25% of the bikes had flat tires only, 5% had bent handlebars only, and 10% had ripped seats only. Just 1/12th of the bikes had all three repairs to do: flat tires, bent handlebars and ripped seats. No bikes were completely fixed and there are a total of 101 repairs to be made. How many bikes are in the repair department? How many bikes need two repairs? If less than half of all the bikes have a ripped seat, what is the range of bikes that need both the tires and handlebars repaired without needing to fix the seat?
Answers
Out of 60 bikes in the repair department, 25 need two repairs and the range of bikes that need both tire and handlebar repairs without needing to fix the seat is 25 out of 60 bikes.
Let's use F, H, and S to represent the events that a bike has a flat tire, bent handlebars, and ripped seat, respectively. Then, we are given:
P(F) = 0.25
P(H) = 0.05
P(S) = 0.10
P(F ∩ H ∩ S) = 1/12
We want to find the number of bikes in the repair department and the number of bikes that need two repairs.
Let N be the total number of bikes in the repair department. Then, the number of repairs needed for each category is:
Flat tires: 0.25N
Bent handlebars: 0.05N
Ripped seats: 0.10N
The number of bikes that need all three repairs is:
P(F ∩ H ∩ S)N = (1/12)N
The number of repairs needed for these bikes is:
3P(F ∩ H ∩ S)N = (1/4)N
The number of repairs needed for bikes that need only two repairs is:
2[P(F ∩ H) + P(F ∩ S) + P(H ∩ S)]N = (5/12)N
The number of repairs needed for bikes that need only one repair is:
[P(F) + P(H) + P(S)]N = 0.4N
The total number of repairs needed is given as 101, so we have:
(1/4)N + (5/12)N + 0.4N = 101
Simplifying this equation gives:
N = 60
Therefore, there are 60 bikes in the repair department.
The number of bikes that need two repairs is:
(5/12)N = 25
Next, we need to find the range of bikes that need both the tires and handlebars repaired without needing to fix the seat. Let's use T and H to represent the events that a bike needs tire and handlebar repairs, respectively. We want to find P(T ∩ H ∩ not S).
We know that P(T ∩ H ∩ S) = P(F ∩ H ∩ S) = 1/12. Also, P(S) = 0.10, so P(not S) = 0.90. Therefore:
P(T ∩ H ∩ not S) = P(T ∩ H) - P(T ∩ H ∩ S)
= 2[P(F ∩ H) + P(F ∩ H ∩ S) + P(H ∩ S)] - P(F ∩ H ∩ S)
= 2(5/12) - 1/12
= 5/12
So, less than half of all the bikes have a ripped seat, and the range of bikes that need both the tires and handlebars repaired without needing to fix the seat is 5/12 of all the bikes, or 25 out of 60 bikes.
To learn more about Range from given link.
https://brainly.com/question/30389189
#SPJ1
Ashley bought 2 CDs that were each the same price. Including sales tax, she paid a total of $31.40 . Each CD had a tax of $0.80. What was the price of each CD before tax?
Answers
Answer:
Each CD cost $14.90 before tax.
Step-by-step explanation:
Let's call the price of each CD before tax "x".
We know that Ashley bought 2 CDs, so the total cost before tax would be 2x.
We also know that the sales tax on each CD was $0.80, so the total sales tax for both CDs would be 2(0.80) = $1.60.
So the total cost including tax would be:
2x + 1.60 = 31.40
To solve for x, we can start by subtracting 1.60 from both sides:
2x = 29.80
Then, we can divide both sides by 2 to solve for x:
x = 14.90
Find to value of a if you knew the perimeter was 250 inches long
Answers
Answer:
To find the value of "a" when you know the perimeter of a shape, you need to know the specific shape you're referring to. Please provide more information about the shape in question, such as whether it's a rectangle, triangle, or another geometric figure. Additionally, if you have any specific measurements or relationships between the sides of the shape, please provide them as well.
Use the Law of Cosines. Find x to the nearest tenth.
2
B
15
ro
30
16
C
Answers
The value of x for the triangle is,
x = 58.67 degree
We have to given that;
By Use the Law of Cosines. Find x to the nearest tenth.
And, A triangle ABC is shown in figure.
Hence, We can formulate;
c = √a² + b² - 2ab cos x
16 = √15² + 30² - 2 × 15 × 30 cos x
16 = √225 + 900 - 900 cos x
256 = 725 - 900 cos x
900 cos x = 725 - 256
900 cos x = 469
cos x = 469 / 900
cos x = 0.52
x = 58.67 degree
Thus, The value of x for the triangle is,
x = 58.67 degree
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ1
math
imaginelearning.com/lesson player/essons/1129/
Two wading pools are being filled at the same time.
The orange pool contains 4 gallons when it starts willing at a rate of 4 galtons a minute.
The blue pool fills at a rate of 5 gallons a minute.
How should the axis be labeled?
The z-axis should be labeled
How should the y-axis be labeled?
The yaxis should be labeled
What does the slope of each line represent?
The slope of each line represents the
What should the x axis be labeled
What is the y axis labeled
What does the slope line of each represent
What does the y intercept of each line represent
Answers
What does the slope line of each represent?
The slope line represents the constant change in value.
What does the y intercept of each line represent
The y-intercept indicates the y-value when the x-value is 0.
Two points on the path of a planet are A and B. The points A and B have coordinates (1, 4, 2) and (2, –1, 3) respectively.
The line l has equation r= (2i-j+3k)+µ(i-j+k)
(a) Calculate the distance between the points A and B .
(b) The line AB makes an acute angle θ with l. Calculate θ.
(c) The point P on the line l is where λ = p.
(i) for the vector AP how that :
AP. (i-j+k)=7+3p
(ii) Hence find the coordinates of the foot of the perpendicular from the point
A to the line l.
(c) Determine the cartesian equation of line l.
(d) Determine the cartesian equation of line A
Answers
Answer:
Step-by-step explanation:
(a) The distance between two points A(x1, y1, z1) and B(x2, y2, z2) is given by the formula: AB = √((x2-x1)² + (y2-y1)² + (z2-z1)²). Substituting the coordinates of points A and B into this formula gives: AB = √((2-1)² + (-1-4)² + (3-2)²) = √(14).
(b) The direction vector of line l is given by the vector (i-j+k). The direction vector of line AB is given by the vector AB = (2-1)i + (-1-4)j + (3-2)k = i - 5j + k. The cosine of the angle between two vectors is given by the dot product of the vectors divided by the product of their magnitudes. Therefore, cos(θ) = (AB.(i-j+k)) / (|AB|.|i-j+k|) = ((i - 5j + k).(i-j+k)) / (√14.√3) = -3/√42. Hence θ = cos⁻¹(-3/√42).
©(i) Let P be the point on line l where λ = p. Then P has position vector r = (2i-j+3k)+p(i-j+k) = (2+p)i + (-1-p)j + (3+p)k. The vector AP is given by AP = r - a = ((2+p)i + (-1-p)j + (3+p)k) - (i+4j+2k) = pi - (5+p)j + pk. Taking the dot product of AP with (i-j+k), we get AP.(i-j+k)=7+3p.
©(ii) The foot of the perpendicular from point A to line l is the point on line l that is closest to point A. This point is obtained when AP is perpendicular to the direction vector of line l, which is (i-j+k). Therefore, AP.(i-j+k)=0. Substituting the expression for AP.(i-j+k), we get 7+3p=0, so p=-7/3. Substituting this value of p into the expression for r, we get r = (2-7/3)i - 8/3j + 2k. Hence, the coordinates of the foot of the perpendicular from point A to line l are (1/3,-8/3,2).
(d) The cartesian equation of a line with direction vector d and passing through a point with position vector a is given by r=a+λd. For line l, d=(i-j+k), a=(2i-j+3k), so its cartesian equation is r=(2i-j+3k)+λ(i-j+k).
A company knows that 32% of their customers order their product in Black and 26% in White and 22% in Grey.
2 orders are made, Find the probability that at least 1 is Grey.
Answers
The probability that neither order is Grey is equal to the probability that both orders are not Grey. We can calculate this probability by multiplying the probabilities of both orders not being Grey:
P(both not Grey) = (1 - 0.22) x (1 - 0.22) = 0.64
Therefore, the probability that at least 1 order is Grey is:
P(at least 1 Grey) = 1 - P(both not Grey) = 1 - 0.64 = 0.36
So the probability that at least 1 order is Grey is 0.36, or 36%.
Use the unit circle to find the exact value of the trig function
Cos(45°)
Answers
Answer: √2/2
Step-by-step explanation: Starting from the positive x-axis (angle 0), we rotate the ray counterclockwise by 45 degrees, or π/4 radians. Since the point on the unit circle corresponding to 45 degrees lies on the line y = x, its coordinates are (cos(45), sin(45)) = (√2/2, √2/2).
pls help if u can tyyysm im struggling will gvie brainly
Answers
Answer:
Would buy Would not
again buy again Total
Aalora 77 16 93
Mederac 48 23 71
Total 125 39 164
71/164 = 43.3% of the customers purchased Mederac.
So the group that accounts for about 43% of the respondents is the percentage of the customers who purchased Mederac.
According to the graph, what is the value of the constant in the equation
below?
A. 1
B. 2
C. 0.5
D. 4
Answers
A local radio station is running a contest were 35 people have qualified. From these qualifiers, 3 will be randomly selected to win a trip to the Bahamas. How many different possibilities are there for the outcome of this contest?
Answers
Answer:
39270
Step-by-step explanation:
When the first person is picked, there is a 1 in 35 chance that it will be Person 1. If they are selected, that leaves 34 people left in the pool. After Person 2 is selected, there are 33 people left in the pool for Person 3.
35*34*33=39270
The table below shows the number of concert tickets bought by people of different age groups. Ages Number of tickets, 14 and under are (17tickets), 15 - 18 (25) ,19 - 22 (38), 23 - 30 (26 ) ,31 - 40 (18), 40 and older (6) When making a histogram of these data, what height would you make the bar for the 15 -18 age range?
Answers
We would make the bar for the 15-18 age range with a height of 25 on the y-axis of the histogram.
What is a histogram?A histogram is a type of chart used to represent the distribution of a set of continuous numerical data. It is a graphical representation that consists of a series of vertical bars, where the height of each bar represents the frequency or count of observations falling within a specific interval or "bin" of values.
To make a histogram, we need to plot the age groups on the x-axis and the corresponding number of tickets on the y-axis. The bars in the histogram should represent the frequency of each age group.
From the given data, the number of tickets bought by people of age 15-18 is 25. Therefore, we would make the bar for the 15-18 age range with a height of 25 on the y-axis of the histogram.
Learn more about histogram here: https://brainly.com/question/28164315
#SPJ1
El área del hexágono regular cuyo lado mide 1 cm es?
Answers
Answer:
Respuesta: 2,25 cm cuadrados
Explicación paso a paso:
PERIMETRO: 6
APOTEMA: 0,75
AREA DEL HEXAGONO REGULAR: 6 X 0,75 / 2 = 2,25 CM CUADRADOS
Step-by-step explanation:
The table shows the finishing times for each of the four swimmers on the men’s 100 meter freestyle relay US Olympic team in 2008. The team’s average time is 47 seconds. Estimate the team’s finishing time, in seconds, using cluster estimation.
Answers
Using cluster estimation, the team's finishing time is 188 seconds.
How to get the team's finishing time?We are given that the Team's average time is 47 seconds which means all players finishes in 47 seconds.
The Cluster Estimation means a method used to estimate sum & product when the numbers that we are adding or multiplying cluster near to a same number .
Here, all given time cluster near to the average time i.e., 47 seconds.
So, the team's finishing time will be:
= 47 + 47 + 47 + 47
= 4 × 47
= 188 seconds
Therefore, the team's finishing time is 188 seconds.
Read more about finishing time
brainly.com/question/12144239
#SPJ1
PLS HELP
The number of hours a student spent studying each week for 9 weeks is shown.
9, 4.5, 8, 6, 9.5, 5, 6.5, 14, 4
What is the value of the range for this set of data?
Answers
Range is the difference between the smallest and largest values. In this data set, 4 is the minimum number of hours and 14 is the maximum number of hours someone spent studying. 14 - 4 = 10 hours.
Here is the data in order from least to greatest: 4, 4.5, 5, 6, 6.5, 8, 9, 9.5, 14
Help Please The sum of two even numbers is even. The sum of 6 and another number is even. What conjecture can you make about the other number?
A) The other number is odd.
B) The number is even.
C) Not enough information.
D) The number is 8.
Answers
The conjecture that can be made about the other number is option A: the other number is odd.
Let's assume that the two even numbers are x and y. Then, we can write their sum as x + y = 2a, where a is some even number.
Now, let's consider the sum of 6 and another number, which we can represent as 6 + z, where z is some unknown number. If this sum is even, then we can write it as 2b, where b is some even number.
So, we have the equations:
x + y = 2a (since the sum of two even numbers is even)
6 + z = 2b (since the sum of 6 and another number is even)
We can subtract 6 from both sides of the second equation to get:
z = 2b - 6
Now, we can substitute this expression for z into the first equation:
x + y = 2a
And we get:
x + y + z - 2z = 2a
x + (y + z) - 2z = 2a
x + (2b - 6) - 2z = 2a
x + 2b - 2z - 6 = 2a
This equation tells us that x + 2b - 2z - 6 is an even number (since 2a is even). Since x and 2b are even, the expression -2z - 6 must also be even. Therefore, -2z must be even. This means that z is odd (since an even number minus an even number is even, and -6 is even).
So, we can conclude that the other number (z) is odd. Option A is the correct answer.
To learn more about conjecture click on,
https://brainly.com/question/5616153
#SPJ1
A rectangle has length (3x-8) and width (2x-7) cm as shown below... Write down and simplify an expression for the perimeter of the rectangle. (3x-8) (2x-7)
Answers
The simplified expression for the perimeter of the rectangle is 10x-30
What is perimeter of a rectangle?The perimeter of a shape is the addition of all the sides of the shape. If l is the length and w is the width, then the perimeter of a rectangle can be expressed as ;
p = 2(l+w)
The length is 3x-8 and the breadth is 2x-7
therefore the perimeter = 2( l+w)
= 2( 3x-8+2x-7)
= 2( 5x-15)
= 10x-30
therefore, the simplified expression for the perimeter of the rectangle is 10x-30
learn more about perimeter of a rectangle from
https://brainly.com/question/19819849
#SPJ1
Help me please I got an exam tomorrow
Answers
Answer:
Domain(-infinity,infinity) Range(-infinity,infinity) Zeros(0,0), (-4,0), (8,0) and (4,0) y-intercept at 0, even, y-axis, 2, -4
Step-by-step explanation:
qwtq4rg
for question 6 is wax and yau are verticle or not
Answers
In the given diagram, angle WAX and angle YAU are vertical angles
What are vertically opposite angles?From the question, we are to determine if angles WAX and YAU are vertical angles or not
Vertically opposite angles are pairs of angles that are opposite each other and formed by the intersection of two straight lines.
When two straight lines intersect, they form four angles at the point of intersection. Vertically opposite angles are the angles that are opposite each other, that is, they are located on opposite sides of the intersection point and are formed by the pair of opposite rays.
Vertically opposite angles are congruent, which means that they have the same angle measure. This property holds true for any pair of vertically opposite angles, regardless of the angle size or the orientation of the lines.
Hence, angle WAX and angle YAU are vertical angles
Learn more on Vertically opposite angles here: https://brainly.com/question/28293784
#SPJ1
please help for this question
Answers
The single transformation that maps shape P onto shape Q is given as follows:
Reflection over the line y = 1.
What are transformations on the graph of a function?Examples of transformations are given as follows:
Translation: Lateral or vertical movements.Reflections: A reflection is either over one of the axis on the graph or over a line.Rotations: A rotation is over a degree measure, either clockwise or counterclockwise.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor, which can either enlarge or reduce the figure.The orientation of the figure changed, hence it underwent a reflection.
The intercepts are given as follows:
y = 4 and y = -2.
The line of reflection is the mean of the coordinates of the intercepts, hence:
(4 - 2)/2 -> y = 1.
More can be learned about transformations in a figure at https://brainly.com/question/28687396
#SPJ1
Find the slope and y-intercept of the line: 10 + 5y = 2x.
Answers
Y-intercept: -2
Slope intercept form: y=mx+b.
Your m is your slope, and your b is your y-intercept.
The volume of a cube that is 2.9 x 5 x 4
Answers
The volume of the cuboid is 58 cubic units.
What is a cuboid?A cuboid is a 3 dimensional figure that has six rectangular faces. So that the volume of a cuboid can be determined by;
volume of cuboid = length x width x height
From the given question, we have;
the volume of a cuboid that is 2.9 x 5 x 4 can be determined as follows;
volume of cuboid = length x width x height
= 2.9 x 5 x 4
= 58
The volume of the cuboid with the given dimension is 58 cubic units.
Learn more about volume of a cuboid at https://brainly.com/question/46030
#SPJ1
I need help please
here is the picture is about Row Ops
Answers
Solving the given matrix operation gives us the solution as: y = -1.4
How to solve simultaneous equations with matrix?From the matrix expression given, we can say that the simultaneous equations it represents are:
x - 4y = 8
3x - 2y = 10
We are told to Multiply eq 1 by -3 and add to row 2 and this means we have:
eq 3: -3x + 12y = -24
Adding to row 2 gives us:
10y = -14
y = -1.4
Read more about Matrix at: https://brainly.com/question/94574
#SPJ1