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
PLS HELP ILL MARK BRAINLIEST
TechWiz Electronics makes a profit of $35 or each MP3 player sold and $18 for each DVD player sold. Last week, TechWiz sold
combined total of 143 MP3 and
DVD players.
Let x be the number of MP3 players TechWiz sold last week. Write an expression
TechWiz made from MP3 and DVD players last week.
for the combined total profit (in dollars)
Answers
Answer:
Total profit=$35x+$18(130-x)
Total profit=$35x+$2340-$18x
Total profit=$17x+$2340
Step-by-step explanation:
3. The vertices of a rectangle are R(-5, -5), S(-1,-5), 7(-1, 1), and U(-5, 1). After translation,
R' is the point (-11, -11). Find the translation rule and coordinates of U'.
O(x, y) → (x – 6, y + 6); (-11, 7)
O(x, y) → (x – 6, y - 6); (-11, -5)
(x + 6, y-6); (1, -5)
O(x, y) → (x + 6, y + 6); (1,7)
O(x, y) ☺
Answers
U' = x - 6 , y + 6
U' = ( - 5 - 6 ) , ( 1 + 6 )
U' = ( - 11 ) , ( 7 )
U' = - 11 , 7
The local sales tax is 8% if a pair of shoes sells for $140 what is the cost after tax
Answers
Answer:
$151.2
Step-by-step explanation:
To find the price after the tax is implemented,
set a relationship x/140=8/100 (8/100) basically means 8%.
cross multiply (140)(8)=1120. Then divide it by 100x, you get $11.2.
But that's just 8 percent of the total amount. So you need to add onto the original price, 140+11.2=$151.2.
5) The solution to 7X2 + 2X – 1 = 0 can be written as:
Answers
Answer:
2/7 or -30/7
Step-by-step explanation:
Use the quadratic formula
a = 7, b = 2, c = -1
-2 + or - (sqrt (2^2 - 4 * 7 * -1) / 2 * 7
-2 + or - 32/14
-2 + or - 16/7
2/7, or -30/7
Answer:
Step-by-step explanation:
7x² + 2x - 1 = 0
x = (-2 ±[tex]\sqrt{2^2 - 4(7)(-1)}[/tex] )/ (2(7))
x = (-2 ± [tex]\sqrt{32}[/tex] ) /14
x = (-2 ± 4[tex]\sqrt{2}[/tex] ) /14
x = [tex]\frac{-1}{7}[/tex] ± [tex]\frac{2}{7}[/tex][tex]\sqrt{2}[/tex]
Can you please help me with number 15
Answers
Answer:
142.25 miles
Step-by-step explanation:
239- 96.75
142.25
Kenya uses mental math to find the sum of 235 and 23. She uses 235, 20, and one other number. What is the missing
number?
3
5
35
58
Answers
Answer:
3
Step-by-step explanation:
235 + 23
She uses 235, so 23 is left
235 + something + something = 235 + 23
235 + 20 + something = 235 + 23
subtract 235 from both sides
20 + something = 23
20 + something = 20 + 3
the missing number is 3
The missing number is 3.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
Kenya uses mental math to find the sum of 235 and 23.
She uses mental math.
That means,
she breaks the term in simple manner.
And she uses 235, 20, and one other number.
And the other number is 23 - 20 = 3
So, addition,
235 + 23
= 235 + 20 + 3
= 258
Therefore, the required number is 3.
To learn more about the addition;
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#SPJ5
You have a balance of $4,500 on your credit card. The interest rate is 12% (1% per month). The late payment fee is $40. You miss a payment. What are your fees plus interest for the month?
Answers
Answer:
multiplying 4500 by .01. This gave me $45 as in interest. Then I added the payment fee, $40. 40+45 is 85,
Step-by-step explanation:
What is the solution
Answers
Answer:
the answer is -21
Step-by-step explanation:
(4²-42)+(3²-4)
=16-42+(9-4)
=-26+5
=-21
Is the sentence Equivalent or non equivalent 12:24,50:100
Answers
Therefore, the sentence is Equivalent.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
1985 x 99 I already know the answer: 196515
Answers
Answer:
the answer is 196515
Step-by-step explanation:
If u already knew the why u put upped the question?
Can someone help me find w and X for my parallelogram ?? Will mark brainiest :)
Answers
Answer:
5x+3x=8x, 6w+2w=8w is the answer
give a pair of alternate interior angles, a pair of corresponding angles and a pair of alternate exterior angles.
Answers
corresponding: 5&7
alternate exterior: 8&1
The ratio of men to women working for a company is to 8 to 5 . If there are employees total 208 , how many women work for the company?
Answers
Answer:
130
ratio of woman to man is : 5/8
5/8×208=130
Answer:
130 women
Step-by-step explanation:
3 men to 5 women:
We can add the variable x:
3x + 5x = 208
8x = 208
x = 26
3 * 26 = 78 men,
5 * 26 = 130 women.
It takes cadence 36 hours to read 12 books. Write a unit rate that models the situation.
Answers
Answer:
three hours every 1 book
Step-by-step explanation:
36-12
6-2
3-1
help me please i'll mark as brainliest asap
Answers
Answer:
a. A(x) = 3x² - 8x + 5
b. x = ⁸/₃
Step-by-step explanation:
a.
A(x) = shaded area
A(x) = (2x - 3)² - (x - 2)²
= 4x² - 12x + 9 - (x² - 4x + 4)
= 4x² - x² - 12x + 4x + 9 - 4
= 3x² - 8x + 5
b.
ΔABF area = ⁵/₄ cm²
A(x) = 4(⁵/₄)
= 5
Substitution:
3x² - 8x + 5 = A(x) = 5
3x² - 8x + 5 = 5
3x² - 8x = 0
x(3x - 8) = 0
3x - 8 = 0
x = ⁸/₃
x = 0
Since x > 2, x = 0 is not valid;
So, x = ⁸/₃
Examine the figure. What is the measure of angle b?
Answers
B = 180-31
B = 149
Answer: 149
F(x)=2x^2+7 what is the value f(-2)
Answers
Answer:
f(x)=2(x+7/4)^2-49/8
Step-by-step explanation:
Solve the equation. Express radicals in simplest form.
-4k2 - 13 = -77
Answers
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
The Hayes family and the Rodrigues family use their sprinklers last summer. The water output rate for the Hayes family sprinkler was 15 L per hour. The water Output rate for the Rodriguez family speakers is 30 L per hour.Families used their sprinklers for a combined total of 75 hour result in a total water of output of 1725 L how long was a sprinkler used?
Answers
Answer:
Hayes family: 35 hoursRodrigues family: 40 hoursStep-by-step explanation:
Let x and y represent the usage hours by the Hayes and Rodrigues families, respectively. The problem statement gives us relations that can be used to write equations for volume of use and for total hours.
15x +30y = 1725 . . . . . total liters of use
x + y = 75 . . . . . . . . . total hours of use
The second equation lets us write an expression for y:
y = 75 -x
This can be substituted into the first equation to give ...
15x +30(75 -x) = 1725
-15x + 2250 = 1725 . . . . . . simplify
-15x = -525 . . . . . . . . . . . subtract 2250
x = 35 . . . . . . . . . . . . . . divide by -15
y = 75 -35 = 40
The Hayes family used their sprinklers for 35 hours; the Rodrigues family used theirs for 40 hours.
Can you please help me with number 16
Answers
Solve for X
5x-8
Answer is not 4.5 or 9/2
Answers
Answer:
[tex]{ \rm{5x - 8 < x + 10}} \\ \\ { \rm{5x - x < 10 + 8}} \\ \\ { \rm{4x < 18}} \\ \\ { \rm{x < 4.5}}[/tex]
Solving for x in the inequality gives us;
x < 4.5
InequalityWe are given the inequality;
5x - 8 < x + 10
The first step is to use addition property of equality to add 8 to both sides;
5x - 8 + 8 < x + 10 + 8
5x < x + 18
Use subtraction property of equality to subtract x from both sides to get;
5x - x < x + 18 - x
4x < 18
Using division property of equality, we have;
x < 18/4
x < 4.5
Read more on inequalities at; https://brainly.com/question/25275758
Find the value of y 7=6+y
Answers
Answer:
y is 1
Step-by-step explanation:
6+1=7, so 7 is = to 6+1
-3 (-3 - n) - 4 = 3n + 5
Answers
[tex]-3 (-3 - n) - 4 = 3n + 5\\\\\implies 9+3n -4 = 3n+5\\\\\implies 5 +3n = 3n+5\\\\\text{The equation is true for all values of n.}[/tex]
...............................
Answers
Step-by-step explanation:
.....................
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ooooooooooooooooooooooooo0oo00o00oo0oo0o0o0o0o0oooooooooooooooooo
Answers
Answer:
wat?
Step-by-step explanation:
merry christmas....yey!!
f(x) = 3x + 12, g(x) = 3x - 1;
=
=
Find (fºg)(x).
Answers
[tex]\text{Given that,}\\\\f(x) = 3x +12, ~ ~ g(x) = 3x -1\\\\(f \circ g)(x)\\\\=f(g(x))\\\\=f(3x-1)\\\\=3(3x-1) +12\\\\=9x - 3 +12\\\\=9x +9\\\\=9(x+1)[/tex]
el valor númerico del término n=15 de la sucesión 5 20 80... es?
Answers
Answer:
É 5x3=15
Step-by-step explanation:
Evaluate 40x40x402x2x2
Answers
Answer:
2,572,800
Step-by-step explanation:
I hope this helps!
Answer: 40 x 40 x 402 x 2 x 2 =128,640
Dev has a monthly food budget of $182. He maps the amount of money,x, he spends each month to the number of food items he buys. What are the constrains on the domain?
Answers
Using it's concept, it is found that the domain of the function is [tex]0 \leq x \leq 182[/tex], that is, the constraints are:
x is of at least $0.x is of at most $182.The domain of a function is the set that contains all possible values for the functions.
In this problem, the input of the function is how much he spends on food.
His budget is of $182, hence, considering this and the fact that he cannot spend a negative amount on food, the constraints are that x is between $0 and his budget of $182(inclusive), and the domain is [tex]0 \leq x \leq 182[/tex].To learn more about the domain of functions, you can take a look at https://brainly.com/question/25897115
The domain of a function is the set of input values the function can have.
The constraints on the domain are: the amount (x) is at least $0, and it is at most $182
From the question, Dev's budget on food is given as:
[tex]Budget = \$182[/tex]
This means that, he cannot spend more than $182.
Represent the amount with x.
So, we have:
[tex]x \le 182[/tex]
Also, he cannot spend a negative amount.
So, we have:
[tex]x \ge 0[/tex]
So, the domain is:
[tex]x \ge 0[/tex] and [tex]x \le 182[/tex]
Rewrite as:
[tex]0 \le x[/tex] and [tex]x \le 182[/tex]
Combine both inequalities
[tex]0 \le x \le 182[/tex]
Hence, the constraints on the domain are: the amount (x) is at least $0, and it is at most $182
Read more about domain at:
https://brainly.com/question/10197594