What are the solutions for the following system of equations?–2x^2 + y = 64x^2 + 3y = 28 (0, 6) and (1, 8) (0, 6) and (–1, 8) (–1, 4) and (1, 4) (–1, 8) and (1, 8)
Answers
Step 1
Given;
\(\begin{gathered} -2x^2+y=6---(1) \\ 4x^2+3y=28---(2) \end{gathered}\)Step 2
Make x² the subject of the formula in equation 1
\(\begin{gathered} x^2=\frac{6-y}{-2} \\ x^2=\frac{-6+y}{2} \\ Substitute\text{ for x}^2\text{ in equation 2} \\ 4(\frac{-6+y}{2})+3y=28 \end{gathered}\)\(\begin{gathered} -12+2y+3y=28 \\ 5y=28+12 \\ 5y=40 \\ y=8 \end{gathered}\)\(\begin{gathered} From\text{ equation 1} \\ x^2=\frac{-6+y}{2} \\ x^2=\frac{-6+8}{2} \\ x^2=1 \\ x=\pm1 \\ x=-1\text{ or 1} \end{gathered}\)The second value of y will be;
\(8\)Answer; in (x,y)
\((-1,8)\text{ and \lparen1,8\rparen}\)Related Questions
What point is a solution to the inequality shown in this graph? (-3,-6) & (3,2)
Answers
Answer:
(0,5)
Step-by-step explanation:
Write the fraction below as a sum or difference.
11x + 5
6
Answers
The fraction in form of sum or difference will be;
⇒ 11/6x + 5/6
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The fraction is,
⇒ (11x + 5) / 6
Now,
Since, The fraction is,
⇒ (11x + 5) / 6
It can be written as;
⇒ (11x + 5) / 6
⇒ 11x/6 + 5/6
Thus, The fraction is written as;
⇒ 11/6x + 5/6
Learn more about the fraction visit:
https://brainly.com/question/5454147
#SPJ1
List all of the subgroups of S4. Find each of the following sets. Are any of these sets subgroups of S4?(a) {σ ∈ S4 : σ(1) = 3}(b) {σ ∈ S4 : σ(2) = 2}
Answers
This set {σ ∈ S4 : σ(1) = 3} contains the following elements of S4: (13), (23), (34), (24), (14), (12)(34), (13)(24), (14)(23) and {σ ∈ S4 : σ(2) = 2} this set contains the following elements of S4: (12), (21), (13)(24), (24)(13).
What are the subgroups of S4The group S4 is the symmetric group on 4 elements and has 24 elements. We can list all of its subgroups as follows:
The trivial subgroup {e}.Three subgroups isomorphic to the cyclic group of order 2: {e, (12)}, {e, (13)}, {e, (14)}.Four subgroups isomorphic to the cyclic group of order 3: {e, (123), (132)}, {e, (124), (142)}, {e, (134), (143)}, {e, (234), (243)}.Two subgroups isomorphic to the dihedral group of order 4: {e, (1234), (13)(24), (1432)}, {e, (1234), (14)(23), (1324)}.The alternating group A4 of even permutations: {e, (123), (132), (124), (142), (134), (143), (234), (243), (12)(34), (13)(24), (14)(23), (12)(34), (13)(24), (14)(23)}.Now, let's consider the sets (a) and (b) and see if they are subgroups of S4:
(a) {σ ∈ S4 : σ(1) = 3}
This set contains the following elements of S4: (13), (23), (34), (24), (14), (12)(34), (13)(24), (14)(23). We can check that this set is not a subgroup of S4 because it is not closed under composition. For example, (13)(14) = (134) is not in the set.
(b) {σ ∈ S4 : σ(2) = 2}
This set contains the following elements of S4: (12), (21), (13)(24), (24)(13). We can check that this set is a subgroup of S4. It is closed under composition, inverses, and contains the identity element e. Therefore, it is a subgroup of S4 and is isomorphic to the cyclic group of order 2.
Learn more on sets here;
https://brainly.com/question/13458417
#SPJ1
Two alien spaceships start traveling toward each other from space stations that are 710,000 km apart. The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr. In how many hours will the two spaceships meet if the second spaceship is traveling at 90,000 km/hr?
Answers
Answer:
They will meet after 4 hours from the departure------------------------
The distance is 710000 km and the first spaceship has travelled 110000 km in the first hour.
The remainder of the distance is reducing by:
110000 + 90000 = 200000 km an hourTime to travel before they meet:
(710000 - 110000)/200000 = 600000/200000 = 3 hoursAdd the first hour to this to get total travel time of 4 hours.
PLEASE HELP ME
The function f(x) = -2(4)^x+1 +140
represents the number of tokens a child has x hours after arriving at an arcade.
What is the practical domain and range of the function?
If necessary, round to the nearest hundredth.
The practical domain of the situation is ?
The practical range of the situation is ?
PLEASE SEE PHOTO FOR FUNCTION
Answers
The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).
The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.
To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.
For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.
Therefore, the practical domain of the situation is x ≥ 0.
For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.
Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.
Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).
To summarize:
- The practical domain of the situation is x ≥ 0.
- The practical range of the situation is [140, ∞).
Know more about the domain here:
https://brainly.com/question/30096754
#SPJ8
What is the volume of the cylinder below?
Answers
Answer:
c
Step-by-step explanation:
Dominic took a 20-question online quiz. He received 5 points for every correct answer. For every question he answered
incorrectly, he lost 2 points. The quiz also had a 20-point bonus for finishing in one hour or less. Since Dominic finished
the quiz in less than one hour, his score S is determined by x, the number of questions answered correctly.
Drag and drop expressions into the function to correctly define S(a).
Answers
The function that correctly defines S(x) is S(x) = 5x - 2(20 - x) + 20
How to determine the function that correctly defines S(x)We have the following definitions in the question
Correct answers = xTotal questions = 20Points for correct answers = 5Points for incorrect answers = -2Bonus for finishing in one hour or less = 20If the total questions is 20, then
Incorrect answers = 20 - x
So, the points gained/lost are
Gained = 5 * x = 5x
Lost = -2 * (20 - x) = -2(20 - x)
Bonus = 20
Add the above points to get the function S(x)
S(x) = 5x - 2(20 - x) + 20
Hence, the definition is S(x) = 5x - 2(20 - x) + 20
Read more about functions at
https://brainly.com/question/28277110
#SPJ1
For what value of theta is the cosecant of theta undefinedThe answers are a 90° b 180° C 270° or D 315°
Answers
Okay, here we have this:
Considering the provided expression, we are going to identify for what value of theta is the cosecant of theta undefined, so we obtain the following:
Then let us remember that the cosecant is equal to 1/sine(tetha), that is to say that if the cosecant is indeterminate it will be because the sine of thetha is equal to zero, for which we will find for which values the sine of thetha is equal to zero, so, we have:
\(\begin{gathered} sin(\theta)=0 \\ \theta=sin^{-1}(0) \\ \theta=0\text{\degree}+360\text{\degree n, }\theta=180\text{\degree+360\degree n} \end{gathered}\)According to this we finally get that the correct answer is option B (180°).
Find the surface area of this rectangular prism 4ft, 8ft, 2ft
Answers
Answer:
112ft^2
Step-by-step explanation:
A = 2(wl+hl+hw)
A = 2[(4)(8)+(2)(4)+(2)(8)]
A = 2(32+8+16)
A = 2(56)
A = 112
1. A frame is 9 in wide and 6 in tall. If it is reduced to a width of 3 in then how
tall will it be?
Answers
Answer:
18 units tall
Step-by-step explanation:
As the frame is 9x6, and the width divides by 3, the height should multiply by 3. In this case, 6x3=18, so the height is 18 units. Hope it helps!
A county office gets an average of 10 calls in a 2 hour time period. What is the probability that the county office will get more than 0 calls in a 15 minute period? Round your answer to three decimal places.
Answers
Answer:
0.713 = 71.3% probability that the county office will get more than 0 calls in a 15 minute period.
Step-by-step explanation:
We have the mean during a time-period, which means that the Poisson distribution is used to solve this question.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)
In which
x is the number of sucesses
e = 2.71828 is the Euler number
\(\mu\) is the mean in the given interval.
A county office gets an average of 10 calls in a 2 hour time period.
10 calls each 120 minutes, which means that the mean for n minutes is:
\(\mu = \frac{10n}{120} = \frac{n}{12}\)
15 minute period:
This means that \(n = 15, \mu = \frac{15}{12} = 1.25\)
What is the probability that the county office will get more than 0 calls in a 15 minute period?
This is:
\(P(X > 0) = 1 - P(X = 0)\)
In which
\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)
\(P(X = 0) = \frac{e^{-1.25}*1.25^{0}}{(0)!} = 0.287\)
So
\(P(X > 0) = 1 - P(X = 0) = 1 - 0.287 = 0.713\)
0.713 = 71.3% probability that the county office will get more than 0 calls in a 15 minute period.
Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each. How much total money would Ellie have to pay for her family if she were to buy 4 snacks for everybody to share? How much would Ellie have to pay if she bought x snacks for everybody to share?
Total cost with 4 snacks:
Total cost with x snacks:
Answers
Answer:
The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.
Step-by-step explanation:
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each.
The amount of tickets is given as,
Ticket's amount = 3 x $13
Ticket's amount = $39
Then the amount spent on snacks is given as,
Snack's amount = 4 x $5
Snack's amount = $20
Then the total amount is given as,
Total amount = $39 + $20
Total amount = $59
The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.
Help me!! Thank you for the help!!
Answers
Answer:
D. 0.34
Step-by-step explanation:
0.24²+0.31²=x² then you find the square root
Answer:
the answer is 0.28, Because of SEGEMENT FH IS HALF OF FG BECAUSE ITS A RIGHT ANGLE.
If 2x-y=9 and 3x+4y=19, then y=
Answers
Answer:
x = 5
y = 1
Step-by-step explanation:
2x - y = 9
3x + 4y = 19
We multiply the first equation by 4
8x - 4y = 36
3x + 4y = 19
11x = 55
x = 5
Now we put 5 in for x and solve for y
2(5) - y = 9
10 - y = 9
-y = -1
y = 1
Let's Check the answer
2(5) - 1 = 9
10 - 1 = 9
9 = 9
So, x = 5 and y = 1 is the correct answer.
Megan's gas fireplace uses propane. The liquid propane is stored in a spherical tank. The tank has a radius of 1 foot, 6 inches. The tank contains 7,741,000 Btu of energy when it is filled to 80% of its total volume. How much energy does 1 gallon of liquid propane in the tank contain?
Hint: There are exactly 231 cubic inches in 1 gallon.
If necessary, round your answer to the nearest hundred.
Answers
Answer:
First, we need to find the total volume of the spherical tank. We can use the formula for the volume of a sphere:
V = (4/3)πr³
We are given that the radius is 1 foot, 6 inches, which is 1.5 feet.
V = (4/3)π(1.5)³
V ≈ 14.14 ft³
To find the volume of propane in the tank when it is filled to 80%, we multiply the total volume by 0.8:
V_propane = 0.8 × 14.14
V_propane ≈ 11.31 ft³
We are also given that the tank contains 7,741,000 Btu of energy. To find the energy per gallon, we need to know how many gallons are in the tank. One gallon is equal to 231 cubic inches.
1 ft³ = 12³ = 1,728 in³
11.31 ft³ = 11.31 × 1,728 in³
11.31 ft³ ≈ 19,536 in³
19,536 in³ ÷ 231 in³/gal ≈ 84.5 gallons
So, the tank contains approximately 84.5 gallons of propane. To find the energy per gallon, we divide the total energy by the number of gallons:
7,741,000 Btu ÷ 84.5 gal ≈ 91,580 Btu/gal
Therefore, 1 gallon of liquid propane in the tank contains approximately 91,580 Btu of energy.
What is 3/6 plus 1/3
Answers
Answer:
5/6
Step-by-step explanation:
3/6 + 1/3 = 3/6 + 2/6 = 5/6
Answer:
5/6
Step-by-step explanation:
3/6 + 1/3 = 3/6 + 2/6 = 5/6
A triangular pyramid is formed from three right triangles as shown below.
Use the information given in the figure to find the length AC.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.
A
41
B
85
Answers
Answer:
76 units
Step-by-step explanation:
You want the length of AC in the given triangular pyramid.
Pythagorean theoremThe Pythagorean theorem can be used to find the lengths of AD and CD.
AD² + 40² = 41²
AD² = 41² -40² = 81 . . . . . = 9²
and
CD² +40² = 85²
CD² = 85² -40² = 5625 . . . . . = 75²
It can also be used to find AC:
AD² + CD² = AC²
81 + 5625 = AC²
AC = √5706 = 3√634 ≈ 76
The length of side AC is about 76 units.
__
Additional comment
The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the legs of a right triangle.
<95141404393>
Which of the following is the correct point-slope equation for the line that
passes through the point (5, -6) and is parallel to the line given by
y = -10x + 3?
O A. Y-6 = -10(x + 5)
O B. y + 6 = -10(x - 5)
O c. y-60 = -4x-5
O D. y-60 = -10(x - 5)
Answers
If the relationship is proportional, what is the missing value from the table?
-3
-5
-7
у
9
?
21
-18
-15
O 15
O 18
Answers
Answer:
B. -15
Step-by-step explanation:
Took the test, this question was correct when you choose -15.
Answer:
b
Step-by-step explanation:
I need to know how to do this problem please
Answers
Answer: Total expenses if 3 widgets are produced is $11,018.00
Step-by-step explanation: The variable cost per unit is given by the coefficient of q in the expense function. In this case, the variable cost is $6.00 per widget. To find the variable costs to produce 2 widgets, we simply multiply the variable cost per unit by the number of units produced: Variable costs for 2 widgets = 2 x $6.00 = $12.00 Therefore, the variable costs to produce 2 widgets is $12.00. To find the variable costs to produce q widgets, we simply multiply the variable cost per unit by the number of units produced: Variable costs for q widgets = q x $6.00 = $6q Therefore, the variable costs to produce q widgets is $6q. To find the total expenses if 3 widgets are produced, we can use the expense function and substitute q = 3:E = 6.00 q + 11,000
E = 6.00 (3) + 11,000
E = 18.00 + 11,000
E = 11,018.00 Therefore, the total expenses if 3 widgets are produced is $11,018.00.
In the diagram below of triangle BCD, E is the midpoint of BD and F is the midpoint of CD. If EF = 43-4x, and BC = 32-2x, what is the measure of EF?
Answers
The measure of the length EF of the triangle is; 21
How to solve similar triangles?We are given the the triangle BCD and we are told that;
E is the midpoint of BD.
F is the midpoint of CD
Now, since we have those midpoints, it means that by the concept of similar triangles, that;
DF/DC = EF/BC
Since F is the midpoint of DC, then it means that;
2DF = DC
We are given;
EF = 43 - 4x, and BC = 32 - 2x
Thus, we now have;
DF/(2DF) = (43 - 4x)/(32 - 2x)
1/2 = (43 - 4x)/(32 - 2x)
Cross multiply to get;
32 - 2x = 43 - 4x
4x - 2x = 43 - 32
2x = 11
x = 11/2
x = 5.5
Thus;
EF = 43 - 4(5.5)
EF = 43 - 22
EF = 21
Thus, we conclude that the side length EF is 21.
Read more about similar triangles at; https://brainly.com/question/14285697
#SPJ1
PLEASE ANSWER QUICK I WILL GIVE BRAINLIEST IF ITS RIGHT
Answers
Step-by-step explanation:
try this option, all the details are in the attachment.
What is the root of 48 in simplified form
Answers
Answer:
\( \sqrt{48} = \sqrt{ {2}^{2} \times 2 {}^{2} \times 3} \)
\( = 2 \times 2 \times \sqrt{3} \)
\( = 4 \sqrt{3} \)
hope you understand ☆☆☆☆☆☆Answer:
4 √3
Step-by-step explanation:
Write an equation for a rational function with the given characteristics.
Vertical Asymptotes at x= -2 and x=4, x-intercepts at (-4,0) and (2,0), horizontal asymptote at y= -3.
Enclose numerators and denominators in parentheses. For example (a-b)/(1+n).
Include a multiplication sign between symbols. For example, a*x.
F(x) =
Answers
An equation for a rational function with the given characteristics is found as: f(X) = a(x+4)(x) / (x+2)(x-4).
Explain about the rational function?Any function that can be expressed as a polynomial divided by such a polynomial is said to be rational. The domain of either a rational function is just the set of all numbers besides the zeros of the denominator since polynomials are specified everywhere.As x = -2 and X = 4 have vertical asymptotes, the denominator will contain the equations (x+2) and (x-4)
The terms (x+4) and 1 will be in the numerator since the x intercepts are (-4,0) , respectively (x-0).
Our current formula is f(X) = a(x+4)(x) / (x+2)(x-4)
We examine the horizontal asymptote to determine the value of A.
The limit of a function as x -> infinity would be - 3 since the horizontal asymptote reflects what the function looks like as x approaches infinity.
Thus, an equation for a rational function with the given characteristics is found as: f(X) = a(x+4)(x) / (x+2)(x-4)
Know more about rational function
https://brainly.com/question/19044037
#SPJ9
Perimeter (numerical) cm
Answers
Answer:
101 cm
Step-by-step explanation:
Add all the side lengths up to get 101 cm.
log(5x-4)-log(×+1)=log4
Answers
Answer:
x = 8
Step-by-step explanation:
log(5x-4)-log(x+1)=log 4
log [ (5x - 4) / (x+ 1) ] = log 4
[ log (a/b) = loga - logb]
(5x - 4 ) / ( x + 1) = 4
(5x - 4) = 4x + 4
5x - 4x = 4 + 4
x = 8
Hope it will help :)❤
Joyce saved $220 on an item that was 75% off what was the original price
Answers
Answer:
$880
Step-by-step explanation:
Use the equation:
\(P=(1-d)x\) with d being the discount in a decimal form, and P being the price that was bought at.
220=(1-0.75)x
simplify parenthesis terms
220=0.25x
divide both sides by 0.25
880=x
So, the original price was $880.
Hope this helps! :)
Solve the inequality below for z.
8z+3>3z-17
A.z>-4
B.z<-14/5
C.z<-4
D.z>-14/5
Answers
8z+3 > 3z-17
subtract 3 from both sides
8z > 3z -20
subtract 3z from both sides
5z > -20
divide both sides by 5
z > -4
Therefore, the solved inequality is z > -4.
Hoped this helped.
\(BrainiacUser1357\)
subtraction of fractions 7 1/4 - 2 1/8 =
Answers
Answer:
Exact form: 41/8
Decimal: 5.125
Mixed Fraction: 5 1/8
Answer:
5 1/2
Step-by-step explanation:
I'm not sure if I'm right but I did 7-2
and 1/4 is 1/2 of an 8th. You might have to wait for someone who is fully sure about the question
Write an equation of a line that is perpendicular to y=-2x +4
that passes through the point(4,2)
Answers
Answer:
Step-by-step explanation:
perp. 1/2
y - 2 = 1/2(x - 4)
y - 2 = 1/2x - 2
y = 1/2x