x squared+ y squared = 2 y = 2x squared – 3 Which of the following describes the system?
Answers
Answer:
[tex]x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}}[/tex] and [tex]y=-1,\frac{1}{2}[/tex]
The ordered pair solutions are [tex](-\sqrt{\frac{7}{4}},0.5)[/tex], [tex](\sqrt{\frac{7}{4}},0.5)[/tex], [tex](-1,-1)[/tex], and [tex](1,-1)[/tex].
Step-by-step explanation:
I'm assuming the system is [tex]\left \{ {x^2+y^2=2} \atop {y=2x^2-3}} \right.[/tex]:
[tex]x^2+y^2=2[/tex]
[tex]x^2+(2x^2-3)^2=2[/tex]
[tex]x^2+(4x^4-12x^2+9)=2[/tex]
[tex]x^2+4x^4-12x^2+9=2[/tex]
[tex]4x^4-11x^2+9=2[/tex]
[tex]4x^4-11x^2+7=0[/tex]
[tex]x^4-11x^2+28=0[/tex]
[tex](x^2-7)(x^2-4)=0[/tex]
[tex](4x^2-7)(x^2-1)=0[/tex]
[tex]4x^2-7=0[/tex]
[tex]4x^2=7[/tex]
[tex]x^2=\frac{7}{4}[/tex]
[tex]x=\pm\sqrt{\frac{7}{4}}[/tex]
[tex]x^2-1=0[/tex]
[tex]x^2=1[/tex]
[tex]x=\pm1[/tex]
[tex]y=2x^2-3[/tex]
[tex]y=2(\pm\sqrt{\frac{7}{4}})^2-3[/tex]
[tex]y=2({\frac{7}{4}})-3[/tex]
[tex]y=\frac{7}{2}-3[/tex]
[tex]y=\frac{1}{2}[/tex]
[tex]y=2x^2-3[/tex]
[tex]y=2(\pm1)^2-3[/tex]
[tex]y=2(1)-3[/tex]
[tex]y=2-3[/tex]
[tex]y=-1[/tex]
Therefore, [tex]x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}}[/tex] and [tex]y=-1,\frac{1}{2}[/tex]
The ordered pair solutions are [tex](-\sqrt{\frac{7}{4}},0.5)[/tex], [tex](\sqrt{\frac{7}{4}},0.5)[/tex], [tex](-1,-1)[/tex], and [tex](1,-1)[/tex].
Related Questions
Caleb’s receipt for lunch is shown below is Caleb pays with a $10 bill how much change will he receive
Answers
Answer:
Please attach the screenshot for the receipt so people can answer
Answer:
3.08
Explanation
3.79
+1.45
1.24
-----------
6.53
+ .39
-----------
6.92 Now
10.00
- 6.92
3.08
Susanna walked 2/7 of a mile in two over five of an hour what is a unit rate in miles per hour
Answers
Answer:
speed = distance/ time so:
(2/7) / (2/5) = (2/7) x (5/2) = 10/14 = 5/7 mph
5/7 = 0.71 miles per hour if you need decimal formatStep-by-step explanation:
Step-by-step explanation:
2/7 miles in 2/5 hours.
to bring this to x miles / 1 hour, we must find the factor for 2/5 to turn into 1.
2/5 × f = 1
f = 5/2
in order to keep the value of the original ratio, we now need to multiply also 2/7 by the same factor (5/2).
2/7 × 5/2 = 10/14 = 5/7
so, the unit rate is 5/7 miles / hour.
which is very slow walking.
Jesper can run 6 miles in 45 minutes. He is thinking about running in two different races, a 9-mile race and a 15-mile race. At his current rate, how many more minutes will it take Jesper to complete the 15-mile race than the 9-mile race?
Answers
Find minutes per mile by dividing time by distance:
45 minutes / 6 miles = 7.5 minutes per mile
Now multiply his speed by each distance:
7.5 x 9 = 67.5 minutes
7.5 x 15 = 112.5 minutes
Now subtract the two:
112.5 - 67.5 = 45 minutes more
It will take Jesper 45 more minutes to complete the 15-mile race than the 9-mile race at his current running speed.
Jesper's running speed is 6 miles in 45 minutes.
To find out how long it will take him to complete the races, you can use the formula:
Time = Distance / Speed
Let's calculate the times for both races:
For the 9-mile race:
Time = 9 miles / (6 miles/45 minutes)
= 9 × (45/6)
= 67.5 minutes
For the 15-mile race:
Time = 15 miles / (6 miles/45 minutes)
= 15 × (45/6)
= 112.5 minutes
The difference in time between the 15-mile race and the 9-mile race will be:
Difference = Time for 15-mile race - Time for 9-mile race
= 112.5 minutes - 67.5 minutes
= 45 minutes
So, it will take Jesper 45 more minutes to complete the 15-mile race than the 9-mile race at his current running speed.
To learn more on Speed click:
https://brainly.com/question/28224010
#SPJ3
Complete the table for this equation. y=x+6
Answers
Answer:
Step-by-step explanation:
1 22.8 ÷ 0. 92 =
2 34.08 ÷ 0.24 =
3 28.9 ÷ 0.85 =
4 7. 15 ÷ 0.05 =
5 210.21 ÷ 0.91 =
Please answer it
Answers
Answer:
1. 24.7826087
2. 142
3. 34
4. 143
5. 231
if the answer wants number 1. rounded in tenths, put 24.8
if they want it rounded in hundreths, put 24.78
hope this helps
1) 24.78
2) 142
3) 34
4) 143
5) 231
hope u liked this answer
#keep learningExpress 972 in the exponential from using prime factors
Answers
[tex]972 = 4 \times 243 = 2^2 \times 3^5[/tex]
Luis and Erin are playing a game. They each start with 0 points. At the end of the game, Luis has 250 points, and Erin has -250
Which statement about the game is true?
A. Erin and Luis have a total of 500 points.
B. Erin has lost 250 points.
C. Luis has 250 more points than Erin.
D. Erin and Luis have an equal number of points.
Answers
Answer:
B
Step-by-step explanation:
100 points will award brainliest crown
Draw the image of EFG under the dilation with scale factor 3/2 and center of dilation (0, 0). Label the image E' F' G'
Answers
Answer:
Should be 3 units away from the picture
Step-by-step explanation:
I hope this helps! ;)
The coordinates of the image of EFG under the dilation with scale factor 3/2 and center of dilation (0, 0) are E(-3,3), F'(-3,-3) and G'(3,-3).
What is the dilation of the figure?Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.
The image of EFG under the dilation with scale factor and center of dilation has to be drawn.
The value of scale factor of dilation is 3/2.The center of dilation is at (0, 0).The coordinates or the triangle are E(-2,2), F(-2,-2) and G(2,-2). The new points after the dilation are,
[tex]E'(-2\times\dfrac{3}{2},2\times\dfrac{3}{2})=E'(-3,3)\\F'(-2\times\dfrac{3}{2},-2\times\dfrac{3}{2})=F'(-3,-3)\\G'(2\times\dfrac{3}{2},-2\times\dfrac{3}{2})=G'(3,-3)[/tex]
The dilated image of triangle EFG is attached below.
Thus, the coordinates of the image of EFG under the dilation with scale factor 3/2 and center of dilation (0, 0) are E(-3,3), F'(-3,-3) and G'(3,-3).
Learn more about the dilation of the figure here;
https://brainly.com/question/3457976
#SPJ2
Little help? Ill give 5 stars and brainly (If correct)
Answers
Answer:
C
Step-by-step explanation:
Slope is rise over run. Pick two points and then count the rise and run. The rise in this case is one and the run is 2 and one over 2 is 1/2
[tex]Hiya![/tex]
Sokka is here to help!
ANSWER:[tex]C.[/tex]
Because, All you need to do is.. Find the slope of proportional graph, by y and x, Which the line is [tex]\frac{4}{2}[/tex].
[tex]And, \frac{4}{2} =\frac{1}{2} .[/tex]
Hopefully, this helps you!!
[tex]Sokka[/tex]
Write a function rule for that table.
Answers
Answer
f(x) = x - 2
Step-by-step explanation:
If you subtract 2 from each x, you get the answer in f(x)
Worth 50 points!I need help plz!
Will mark brainliest to whoever does all the work.
A basket contains:
4 red Santa hats
6 green Elf hats
5 red jackets
7 green jackets.
Determine the probability of randomly selecting a green piece of clothing or a jacket.
(A)Use the addition rule to calculate this probability and explain your answer.
Do this equation P(AorB)=P(A)+P(B)-P(A and B)
(Write your answer as a percent.)
(B) are a green piece of clothing and a jacket mutually exclusive events?
Answers
Explanation/Answer:
Total: 4 + 6 + 5 + 7 = 22
Green: 6 + 7 = 13
Probability: 13/22
Note: It Is Not Mutually Exclusive Events
Solve by completing the square 2x^2+x-4=0
Answers
Answer:
x=-1±[65]
________
8
Step-by-step explanation:
solve the equation for xby finding a,b, and come of the quadratic then applying the quadratic formula
If a constant force acts upon an object with a mass of 2 kg, the acceleration of the object is 14 m/s^2. When the same Force acts upon another object it's acceleration is 4m/s^2. What is the mass of the object?
Answers
Step-by-step explanation:
in the first object:
force = mass × acceleration = 2 × 14 = 28 N
in the second object :
force = mass × acceleration
28=mass×4
then the mass = 28/4 = 7 kg
If I is parallel to m. Find x and y
Answers
Answer: make me brainlist
Step-by-step explanation: x=104
What I 0.00005164 written as a single digit times a power of ten
Answers
Answer:
5.164×10^-5
Step-by-step explanation:
[tex]5.164 \times {10}^{ - 5} [/tex]
What is the equation of the line in slope intercept form perpendicular to the y axis and has the point (-4,5)
Answers
Answer:
y=5
Step-by-step explanation:
If it is perpendicular to the y-axis, that means it is a horizontal line so the slope m=0.
Use the equation
y-y=m(x-x)
y-5=0(x-(-4))
y-5=0
y=5
Answer:
y=5
Step-by-step explanation:
eight and one six minus 7 and three forths
Answers
Answer:
5/12
Have a good day!
Madie drove 200 miles at a speed of 50 miles per hour. Which equation will help you find the number of hours she was driving?
StartFraction 50 miles Over 1 hour EndFraction = StartFraction 200 miles Over question mark hours EndFraction
StartFraction 50 miles Over 1 hour EndFraction = StartFraction question mark hours Over 200 miles EndFraction
StartFraction 200 miles Over 1 hour EndFraction = StartFraction 50 miles Over question mark hours EndFraction
StartFraction 200 miles Over 1 hour EndFraction = StartFraction question mark hours Over 50 miles EndFraction
Answers
she drove for 4 hours
Answer:
the person above me is wrong its not an option for me ;-;
Step-by-step explanation:
Simplify
−
2
x
×
3
x
×
−
x
Answers
Answer: 6x^3
Step-by-step explanation:
find the equation of the line that is perpendicular to the given line and passes through the given point. CD; (-2,1). C cornet point is (2,13). D cornet point is (5,7).
Answers
Answer:
x -2y = -4
Step-by-step explanation:
The slope of the line between points C and D is ...
m = (y2 -y1)/(x2 -x1)
m = (7 -13)/(5 -2) = -6/3 = -2
The slope of the perpendicular line is the opposite reciprocal of this: -1/(-2) = 1/2. The point-slope equation of the desired line is ...
y -k = m(x -h) . . . . line with slope m through point (h, k)
y -1 = 1/2(x -(-2))
We can rearrange this to standard form.
2y -2 = x +2 . . . . . multiply by 2
-4 = x -2y . . . . . . . subtract 2y+2
x -2y = -4 . . . . . . standard form equation of the desired line
Select the interval where g(2) < 0.
(graphed on khan academy)
Answers
Answer:
the number 0 Originally called finding the vertical asymptote.
Choose the term from the list that best represents the item in each box:
if y’all just commenting for the points in will literally report yall.
Answers
Answer:
1. run
2. rise
3. negative slope
4. positive slope
5. constant of proportionality
6. slope of the line
Step-by-step explanation:
Find the area of this parallelogram
Answers
Answer:
260
Step-by-step explanation:
A=bh
A=13 x 20
A=260
Last oneeee helpppp pleaseeeee
Answers
[tex]13-4x = 13 -4(-8) = 13 +32 = 45[/tex]
=> 13 - 4x
=> 13 - 4(-8) ..(when x = (-8))..
=> 13 - (-32) ..( (-) , (-) = + )..
=> 13 + 32
=> 45
_ _ _ _ _ _ _ _ _ _ _☆ Final Answer ☆45_ _ _ _ _ _ _ _ _ _ _☆- PhysicsMaths - ☆
In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm. Which is the approximate measure of angle YZX?
a. 34.8°
b.39.4°
c.50.6°
d.55.2°
Answers
find the value of log9 0.24. (hint: log2=0.301 log3=0.477)
Answers
Answer: -0.65 approximately
Work Shown:
[tex]\log_{9}(0.24) = \frac{\log(0.24)}{\log(9)}\\\\\log_{9}(0.24) = \frac{\log(0.03*8)}{\log(3^2)}\\\\\log_{9}(0.24) = \frac{\log(3*10^{-2}*2^3)}{\log(3^2)}\\\\\log_{9}(0.24) = \frac{\log(3)+\log(10^{-2})+\log(2^3)}{\log(3^2)}\\\\\log_{9}(0.24) = \frac{\log(3)-2\log(10)+3\log(2)}{2\log(3)}\\\\\log_{9}(0.24) \approx \frac{0.477-2*1+3*0.301}{2*0.477}\\\\\log_{9}(0.24) \approx \frac{-0.62}{0.954}\\\\\log_{9}(0.24) \approx -0.649895\\\\\log_{9}(0.24) \approx -0.65\\\\[/tex]
I NEED HELP FOR MY FINALS PLS N TY!!!
1. Compute the length of a rectangle with a perimeter 40.2 in and width of 6.7 in.
Answers
Answer:
13.4
Step-by-step explanation:
You would take the width x 2 which is 13.4. Now you subtract the combined width from 40.2. From here you are left with 26.8. Since this is a rectangle the length would be the same on both sides. You divide 26.8 by 2 and you get 13.4.
Mr Moore has 4 types of ice cream flavors. Each flavor can make 15 individual ice creams. 70% of these ice creams are in waffle cone. How many of these ice creams are in a waffle cone?
Answers
Answer:
42 ice creams in a waffle cone
Step-by-step explanation:
First we try to find how many ice cream does Mr. Moore has:
4*15=60 ice cream
It is said it 70% of these ice creams are in waffle cones. So 60*70/100= 60*7/10=6*7=42 ice creams in a waffle cone.
Question
Which of the following angle measures are possible for a triangle to be classified as acute? Select all that apply.
Select all that apply:
45°, 34", 101°
122, 36, 22
75°, 61°, 44°
22°, 86°, 72
Answers
Answer:
45°, 75°, 61°, 44°, 22°, 86°
Step-by-step explanation:
They have to be angles less than 90°.
Answer:
(c) 75°, 61°, 44°
(d) 22°, 86°, 72
Step-by-step explanation:
The largest angle must be less than 90°, and the sum of angles must be 180°. These conditions are met by the lists of angles shown above.
please help me with the question please ☹️
Answers
Answer:
the last one
Step-by-step explanation:
because those are oppiste poles