Given :-
x² + y² = 8Product of x and y is 4 .( say )To Find :-
The value of x and y .Answer :-
Here we are given that,
[tex]\red{\longrightarrow}[/tex] x² + y² = 8 .
And ,
[tex]\red{\longrightarrow}[/tex] xy = 4
[tex]\red{\longrightarrow}[/tex] y = 4/x
So that ,
[tex]\red{\longrightarrow}[/tex] x² + (4/x)² = 8
[tex]\red{\longrightarrow}[/tex] x² +16/x² = 8
[tex]\red{\longrightarrow}[/tex] x⁴ + 16 = 8x²
[tex]\red{\longrightarrow}[/tex] x⁴ - 8x² + 16 = 0
Assume k² = x⁴ and k = x²
[tex]\red{\longrightarrow}[/tex] k² - 8k + 16 = 0
[tex]\red{\longrightarrow}[/tex] k² -4k -4k +16 = 0
[tex]\red{\longrightarrow}[/tex] k(k-4) -4(k-4) = 0
[tex]\red{\longrightarrow}[/tex] (k-4)² = 0
[tex]\red{\longrightarrow}[/tex] k = 4
So ,
[tex]\red{\longrightarrow}[/tex] k = x²
[tex]\red{\longrightarrow}[/tex] 4 = x²
[tex]\red{\longrightarrow}[/tex] x = √4
[tex]\red{\longrightarrow}[/tex] x = ±2
Hence the required answer is ±2.
The values of x and y of the given function are; x = y = ±2
Roots of a Polynomial
We are given;
x² + y² = 8 -----(1)
Product of x and y = 4;
Thus; xy = 4
Now, making y the subject we have;
y = 4/x
Putting 4/x for y in eq 1 gives us;
x² + (4/x)² = 8
x² + (16/x²) = 8
Multiply through by by x² to get;
x⁴ + 16 = 8x²
⇒ x⁴ - 8x² + 16 = 0
using online polynomial root calculator, we have x = ±2
Thus, y will also be ±2
Complete question is;
If x² + y² = 8 and the product of x and y is 4, what are x and y?
Read more about roots of a polynomial at; https://brainly.com/question/10702726
Decide whether each set of side lengths could form a valid triangle: (6,8,9), (3,8,5), (4,9,14).
This year the CDC reported that 30% of adults received their flu shot. Of those adults who received their flu shot,
20% still got the flu. Of those who did not receive the flu shot, 65% got the flu.
Use the tree diagram to determine the probability that a person with the flu is a person who received a flu shot.
Enter your answer as a decimal to the ten thousandths place.
=> 0.1165
Using conditional probability, it is found that there is a 0.1165 = 11.65% probability that a person with the flu is a person who received a flu shot.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.In this problem:
Event A: Person has the flu.Event B: Person got the flu shot.The percentages associated with getting the flu are:
20% of 30%(got the shot).65% of 70%(did not get the shot).Hence:
[tex]P(A) = 0.2(0.3) + 0.65(0.7) = 0.515[/tex]
The probability of both having the flu and getting the shot is:
[tex]P(A \cap B) = 0.2(0.3) = 0.06[/tex]
Hence, the conditional probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.515} = 0.1165[/tex]
0.1165 = 11.65% probability that a person with the flu is a person who received a flu shot.
To learn more about conditional probability, you can take a look at https://brainly.com/question/14398287
Answer:
flu shot
flu
no flu
.30
.20
Step-by-step explanation:
trust
how to find the perimeter of a triangle with vertices
Answer:
P = A + B + C
Step-by-step explanation:
Essentially, just add the length of each side. The sum is the perimeter.
Hit brainliest if this was helpful :)
add each side
hope ithelps you
the monthly income of a family is rs 2500 the ratio of the expenditure and saving is 3:2 find amount of saving.
Answer:
The amount of saving is Rs.1000.
Step-by-step explanation:
Solution :
Let the,
>> Expenditure = 3x>> Saving = 2xSo, solving for x.
[tex]{\dashrightarrow{\tt{Expenditure + Saving = 2500}}}[/tex]
[tex]{\dashrightarrow{\tt{3x + 2x = 2500}}}[/tex]
[tex]{\dashrightarrow{\tt{5x = 2500}}}[/tex]
[tex]{\dashrightarrow{\tt{x = 2500 \div 5}}}[/tex]
[tex]{\dashrightarrow{\tt{x = \dfrac{2500}{5}}}}[/tex]
[tex]{\dashrightarrow{\tt{x = \cancel{\dfrac{2500}{5}}}}}[/tex]
[tex]{\dashrightarrow{\tt{x =500}}}[/tex]
[tex]{\star{\underline{\boxed{\tt{\red{x =500}}}}}}[/tex]
Hence, the value of x is 500.
Thus,
>> Expenditure = 3 × 500 = Rs.1500>> Saving = 2 × 500 = Rs.1000[tex] \rule{300}{1.5}[/tex]
Which binomial is a factor of 100x2 – 49?
a
O 10x + 7
O 25% - 7
O 25x + 49
O 203 – 49
-
Answer:
Step-by-step explanation:
What you have here is called "the difference of two squares"
Difference means subtraction and both 100x2 and 49 are perfect squares.
The factored form of 100x2-49 is
(10x+7)(10x-7)
Because 10x times 10x is 100x2 and 7 times 7 is 49
One factor has a + and
One factor has a -
It is a pattern worth memorizing!
So 10x + 7 is the factor you're looking for.
Help again please
A stack of 400 pieces of paper is 1.800 inches tall.
A. Derion guesses that each piece of paper is 0.015 inches thick. Explain how you know that Derion’s answer is not correct.
B. Compute the thickness of each piece of paper. Show your reasoning.
On a scale drawing of a town,two landmarks are shown 6 inches apart. These two places are actually separated by 54 miles. What is the map's scale? 1 inch = ______ miles
Answer:
9
Step-by-step explanation:
[tex]54 \div 6 = 9[/tex]
what is 0.75 greater than 9
Answer: 9.75
Step-by-step explanation: i just added
Answer:
less
Step-by-step explanation:
order the numbers from least to greatest .
least to greatest
-4.5
-4
-3 1/2
-3
2.5
Answer:
-4.5, -4, -3 1/2, 2.5, 3
Step-by-step explanation:
Plz, Help Me!!!
Which graph represents the equation (x + 4)^2 + (y + 5)^2 = 36?
Answer:
d
Step-by-step explanation:
the center of the circle is at (-4. -5) with a radius of 6
Which is the graph of 2x + 3y > -3
Graph: C
Each unit in the coordinate plane corresponds to 1 mile. Find the distance from the stadium to Pine Avenue. Round your answer to the nearest tenth.
The distance is about
miles.
The distance from the stadium to Pine Avenue is [tex]13.4miles[/tex], (to the nearest tenth)
The stadium is on Hazel Street(the green line). Pine Avenue is the blue line. The distance from the stadium to Pine Avenue will be the distance on the graph (in miles) from the point representing the stadium, to the point of intersection between Hazel Street and Pine Avenue.
We know the location of the stadium, [tex]S=(-6,6)[/tex]
The point of intersection can be obtained by solving the simultaneous equations
[tex]y=-\dfrac{1}{2}x+3\\y=2x-12[/tex]
since both equations are set equal to [tex]y[/tex], set them equal to each other, to eliminate [tex]y[/tex], and solve for [tex]x[/tex]
[tex]-\dfrac{1}{2}x+3=2x-12\\\\x=6[/tex]
Substitute this value of [tex]x[/tex], into the equation for Pine avenue
[tex]y-2x-12\\=2(6)-12\\=0[/tex]
The point of intersection between Hazel Street and Pine Avenue is [tex]I=(x,y)=(6,0)[/tex]
To compute the distance between the stadium and Pine Avenue, we find the distance between the two points [tex]S[/tex] and [tex]I[/tex]. So,
[tex]d=\sqrt{(6-(-6))^2+(0-6)^2}\\\\=\sqrt{12^2+(-6)^2}\\\\=6\sqrt5\approx13.4\text{ (to the nearest tenth)}[/tex]
The distance is [tex]13.4miles[/tex]
Learn more about coordinate geometry here: https://brainly.com/question/15318780
Someone Plz help me
Using the tables to answer the question, the correct option is D.
Only table B represents a function
A relation/table will represent a function if each value of x is attached to a unique value of y.
That is, no value of x must be mapped to more than one value of y.
By considering the tables represented
Set A = {(-5, 2), (-8, 5), (-5, 8)}
As clearly shown above, when x = -5, y = 2 and 8. This means that there are more than 1 value of y for a single value of x, therefore, table A does not represent a function.
Set B = {(-5, 2), (-8, 5), (-11, 2)}
As shown above, all values of x have different values of y. Therefore, table B represents a function.
Learn more here: https://brainly.com/question/25902874
I NEED HELP ON THIS MATH PROBLEM ASAP
Answer:
y= -5x +5
Step-by-step explanation:
HELP PLZ I NEED THIS DONE ASAP
Answer:
Step-by-step explanation:
The answer would be -19
Hope you could get an idea from here.
Doubt clarification - use comment section.
simply 5(x-y)+2(x+y)
Answer:
5x-5y+2x+2y
7x-3y
That's it
Find the slope-intercept form of the line that satisfies the given conditions.
Through A(−7, 5) and B(6, 11)
Answer:
[tex]y=\frac{6}{13}x+\frac{107}{13}[/tex]
Step-by-step explanation:
(x1, y1) = (-7, 5)
(x2, y2) = (6, 11)
The firs thing to do is fine the slope. That is the distance between the y-coordinates divided by the distance between the x-coordinates:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
I marked the points above as points 1 and 2, so you can plug those numbers into the formula:
[tex]m=\frac{11-5}{6--7}\\\\m=\frac{6}{13}[/tex]
That fraction can't be simplified any further, so the slope of this line is 6/13. The next thing to do is to find the y-intercept.
[tex]y=mx+b[/tex]
Plug the slope and any point of your choice into the equation. I'll use point b:
[tex]11=(\frac{6}{13})6+b[/tex]
Now, solve for b:
[tex]11=\frac{36}{13}+b\\\\11-\frac{36}{13}=b\\\\\frac{143}{13}-\frac{36}{13}=b\\\\\frac{107}{13}=b\\\\b=\frac{107}{13}[/tex]
They're far from clean, but those are the correct slope and y-intercept. Using those, the equation for this line is:
[tex]y=\frac{6}{13}x+\frac{107}{13}[/tex]
You can confirm that this is the correct equation by checking it with one of the points. Plug in one of the known values of x and make sure it gives the correct value of y:
[tex]y=\frac{6}{13}(-7)+\frac{107}{13}\\\\y=\frac{-42}{13}+\frac{107}{13}\\\\y=\frac{65}{13}\\\\y=5[/tex]
That works out.
Please help question in pic
Answer:
O = (1,-1)
N = (1,-2)
M = (3,-2)
L = (3,-1)
Step-by-step explanation:
Apply the distributive property to create an equivalent expression.
-9x(5j+k)
PLEASE HELP THANK YOUU!!
Answer:
-45xj-9xk
Step-by-step explanation:
-9x(5j+k)
Multiply -9x with 5j
Multiply -9x with k
-9x times 5j is -45xj
-9x times k is -9xk
So the equivalent expression is
-45xj-9xk
Hope this helps!
can y’all please help me out
Step-by-step explanation:
x⁴ + 4x³ - 5x² + x - 3 ÷ x² + x - 3 = x² + 3x - 5
- x⁴ + x³ - 3x²
-------------------------
0 3x³ - 2x² + x - 3
- 3x³ + 3x² - 9x
-------------------------------
0 - 5x² + 10x - 3
- - 5x² - 5x + 15
-------------------------------------
0 15x - 18
the result is therefore
x² + 3x - 5 + (15x - 18)/(x² + x - 3)
The quotient of 45% -31. - 15) and a polynomial is (-3). What is the pokyrıcaiak
A
Ox5% -6% -30% * 944 45
0-5
O % 45
O % * 5% 46% - 30% * 944 45
Answer:
A
Step-by-step explanation:
The area of a rectangle is 65 square inches.
The length is x + 5, and the width is x – 3.
Find the value of x, and the dimensions of the rectangle.
A = lw
x=
length =
width=
Answer:
x=-10,8
length=13
width=5
Step-by-step explanation:
(x+5)(x-3)=65
x^2+2x-15-65=0
x^2+2x-80=0
(x+10)(x-8)=0
x=-10,8
x+5
(-10)+5=-5, negative length does not make sense
x+5
8+5=13
x-3
(-10)-3=-13, negative width does not make sense
x-3
(8)-3=5
Answer:
x=8
length= 13inches
width=5inches
Step by step explanation:
A=lw
65= (x+5)(x-3)
65= x²-3x+5x-15
x²+2x-80=0
x²+ 10x - 8x - 80 = 0
x(x+10) -8(x+10) = 0
(x-8)(x+10)=0
x= 8 or -10
x cannot be negative
hence x= 8
length= x+5
=8+5
=13inches
width= x-3
=8-3
=5inches
Please answer the following question
(d+m)A=2
A= ?
Answer:
A is equal to 3
please mark me as brianleast
Rewrite the equation in slope -intercept form then graph the linear equation x+4y=8
Answer:
Step-by-step explanation:
x + 4y = 8
-x -x
4y = -x + 8
divide by 4
y= -1/4x + 2
then graph
The ordered pairs (−4,−3)
, (−2,−2), (4,1), (6,2), and (8,3) represent a function. What is a rule that represents this function?
Write an inequality for the following statement:
The difference between twice a number and 6 is at least 35.
6−2n≥35
2n−6≥35
2n−6≤35
6−2n<35
The formula below represents the standard form of a quadratic equation.
ax2+bx+c=0
Solve for b.
b=−ax2−cx
x=−ax2−c
x=−ax2−cb
b=x−ax2−c
The tables below each follow a different pattern
Which table follows the input-output rule: “Each output is one less than double the input”
table 2
table 4
table 1
table 3
Which inequality accurately represents the graph shown below?
Jordan has a part-time job which pays $75 a week. He has already saved $55 toward the purchase of a $400 iPhone. Write an inequality you could use to find the minimum number of weeks Jordan must work to have enough money to buy the iPhone.
55w+75≥400
75w+55≤400
55w+75≤400
75w+55≥400
The equations and inequality expresses the relationship between the variables.
The correct responses are;
First part; The rule that represent the function is; y = 0.5·x - 1Second part; the correct option is the inequality; 2·n - 6 ≥ 35Third part; [tex]\displaystyle \underline{b = \frac{- a\cdot x^2 - c}{x}}[/tex]Fourth part; Table 4Fifth part; [tex]\displaystyle \underline{y < -\frac{1}{2} \cdot x - 4}[/tex]Sixth part; 75·w + 55 ≤ 400Reasons:
First part;
The difference between y-values following a change in 2 units of the x-value is a constant, and is equal to 1;
The rate of change of the function, m, is therefore;
[tex]\displaystyle m = \frac{2 - 1}{6 - 4} = \frac{1}{2} = 0.5[/tex]
The slope and intercept form of the equation of the function is therefore;
y - 3 = 0.5·(x - 8) = 0.5·x - 4
y = 0.5·x - 4 + 3 = 0.5·x - 1
The rule that represent the function is; y = 0.5·x - 1
Second part;
2·n represent twice the number
The difference between twice the number and 6 = 2·n - 6
At least 35 = ≥ 35
Therefore, the inequality is; 2·n - 6 ≥ 35
Third part;
The given quadratic equation is; a·x² + b·x + c = 0
Therefore;
[tex]\displaystyle \underline{b = \frac{-c - a\cdot x^2}{x}}[/tex]
Fourth part;
The best correct option is table 4, given that the table is as follows;
[tex]\begin{tabular}{|c|cc|}In&&Out\\Not clear&&\\9&&17\\10&&19\end{array}\right][/tex]
Fifth part;
The y-intercept of the graph is -0.5
The slope is -4 ÷ 8 = -0.5
Therefore, the equation is; y = -0.5·x - 4
The shaded area is the area lower than the y-values, with broken lines (indicating < relationship) which gives, the correct inequality as follows;
[tex]\displaystyle \underline{y < -\frac{1}{2} \cdot x - 4}[/tex]
Sixth part;
The amount Jordan part-time job pays = $75
The amount he has already saved = $55
The cost of the iPhone = $400
Let w represent the number of weeks Jordan works, at his part-time job to purchase the iPhone, we have;
75·w + 55 ≤ 400
Learn more about writing equations and inequalities here:
https://brainly.com/question/14321394
What is the linear function equation represented by the graph?
Answer:
y=1/3x-4
Step-by-step explanation:
The point where the line intercepts the y-axis is the y-intercept and where the digit -4 comes from
1/3 comes from how many times the line rises (1) and run (3)
Hope this helps!
Stacey is selling popcorn at a rate of $2 per bag. She is only charging a one time thing for $0.50 for tax. What is the equation of this description?
X - 5V + 17 = 0 2x+ V + 1 = 0
Answer:
x= -[tex]\frac{10}{3}[/tex], v = [tex]\frac{7}{3}[/tex]
Step-by-step explanation:
x= - 10/3, v = 7/3
jus so u want to copy so u don't have to type ur self
If 5/3 liters of water is enough to water ⅕ of your yard, 5 3 how much water is needed to water the entire yard?
Answer:
8 1/3 liters
Step-by-step explanation:
create a proportion from water : yard
let 'y' = water for entire yard
5/3 ÷ 1/5 = y ÷ 5/5
5/3 · 5/1 = y/1
25/3 = y/1
3y = 25
y = 8 1/3
Given that m||n, determine the relationship between ∠9 and ∠15.
The relationship between ∠9 and ∠15 is (c) alternate exterior angles.
There are several relationships that can be formed by angles within the transversal of parallel lines.
From the attached figure, we can see that angles ∠9 and ∠15 are exterior angles of parallel lines m and n.
Because these lines are parallel, then both angles are alternate exterior angles.
Read more about parallel lines at:
https://brainly.com/question/24607467