Hello there.
First, assume the numbers [tex]x,~y[/tex] such that they satisties both affirmations:
The sum of the squares of two numbers is [tex]8[/tex].The product of the two numbers is [tex]4[/tex].With these informations, we can set the following equations:
[tex]\begin{center}\align x^2+y^2=8\\ x\cdot y=4\\\end{center}[/tex]
Multiply both sides of the second equation by a factor of [tex]2[/tex]:
[tex]2\cdot x\cdot y = 2\cdot 4\\\\\\ 2xy=8~~~~~(2)^{\ast}[/tex]
Make [tex](1)-(2)^{\ast}[/tex]
[tex]x^2+y^2-2xy=8-8\\\\\\ x^2-2xy+y^2=0[/tex]
We can rewrite the expression on the left hand side using the binomial expansion in reverse: [tex](a-b)^2=a^2-2ab+b^2[/tex], such that:
[tex](x-y)^2=0[/tex]
The square of a number is equal to [tex]0[/tex] if and only if such number is equal to [tex]0[/tex], thus:
[tex]x-y=0\\\\\\ x=y~~~~~~(3)[/tex]
Substituting that information from [tex](3)[/tex] in [tex](2)[/tex], we get:
[tex]x\cdot x = 4\\\\\\ x^2=4[/tex]
Calculate the square root on both sides of the equation:
[tex]\sqrt{x^2}=\sqrt{4}\\\\\\ |x|=2\\\\\\ x=\pm~2[/tex]
Once again with the information in [tex](3)[/tex], we have that:
[tex]y=\pm~2[/tex]
The set of solutions of that satisfies both affirmations is:
[tex]S=\{(x,~y)\in\mathbb{R}^2~|~(x,~y)=(-2,\,-2),~(2,~2)\}[/tex]
This is the set we were looking for.
Does anyone know this?
Answer:
it's a
Step-by-step explanation:
I did this quiz. your welcome
What is the surface area of a sphere with radius 4?
A. 12π units³
B. 16π units²
C. 64π units²
D. 32 units ²
Detailed explanation please.
Step-by-step explanation:
Formula for surface of sphere is 4 X pi X radius squared.
4 x 4squared = 64 pie = 201.0622498
so your answer is
64 pie or 201.0622498
(Either would work)
Hotels R Us has kept the following records concerning the number of guests in a room. Number of Guests Probability 1 0.35 2 0.50 3 0.10 4 0.05 What is the mean (or expected value) of guests in a room
Finding the sum of each outcome multiplied by it's respective probability, it is found that the expected value of guests in a room is of 1.85.
The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
In this problem, the distribution is:
[tex]P(X = 1) = 0.35[/tex]
[tex]P(X = 2) = 0.5[/tex]
[tex]P(X = 3) = 0.1[/tex]
[tex]P(X = 4) = 0.05[/tex]
Hence:
[tex]E(X) = 0.35(1) + 0.5(2) + 0.1(3) + 0.05(4) = 1.85[/tex]
The expected value of guests in a room is of 1.85.
A similar problem is given at https://brainly.com/question/24855677
Dakota paid $301.32 for a new game system, after tax, and the tax rate is 8%. What was the original price of the game system?
Answer:
327,52
Step-by-step explanation:
301,3*2100/92=327,52
help? please.........
Answer: 60°
Step-by-step explanation: A straight angle is 180°
180°- 120° = 60°
I need helpl i dont understand
Answer:
the answer is 1.3x + 2 ≥ 20
Step-by-step explanation:
the tree is already 2ft which mean it would need to be added to the rate of growth, 1.3 by the amount of year to find out the height. The question is saying however that I can be at least 20ft. so no less than 20 which is why the greater or equal to sign is used (≥)
127343895+834823= bao nhiêu
Answer: 128178718
That should be answer
7.
Which equation is represented by the graph?
A. y = −x2 + 2
B. y = 2x2 − 1
C. y = x2 + 2
D. y = −2x2 − 1
Answer:
A. y = −x^2 + 2
Step-by-step explanation:
Hcf by division method of 5445 and 9317
Answer:
badge showing an astronaut's boot touching down on the moon.
Step-by-step explanation:
Lucy received 5/6 of the 180 votes cast for class secretary. How many votes did she receive?
Answer:
150 votes
Step-by-step explanation:
If Lucy got 5/6, we can do the following.
(5/6) * 180 = 150
So, Lucy got 150 votes.
Answer:
150
Step-by-step explanation:
We can first divide 180 by 6:
180/6 = 30
Then multiply that by 5:
5 × 30 = 150
When rolling a number cube 500 times, how many times can you expect to get a number below 6?
Answer:
250
Step-by-step explanation:
because there is a chance and 1/2*100=250 which is the answer for the chance
50,002,007 in expanded form
fifty million two thousand seven.
- BRAINLIEST answerer
Please help!! Only answer if the answer is correct though.
Answer:
f(3) = -10
g(-5) = 65
Step-by-step explanation:
Hi there!
[tex]f(x)=-3x-1[/tex]
To find f(3), replace x with 3:
[tex]f(3)=-3(3)-1\\f(3)=-9-1\\f(3)=-10[/tex]
[tex]g(x)=2x^2-3x[/tex]
To find g(-5), replace x with -5:
[tex]g(-5)=2(-5)^2-3(-5)\\g(-5)=2(25)+15\\g(-5)=50+15\\g(-5)=65[/tex]
I hope this helps!
solve the equation for x 5x^2-4x=6,
Answer:
x1=2-radical 34/5 x2=2+radical 34/5
Step-by-step explanation:
5x^2-4x-6=0x=-(-4)+radical (-4)^2-4×5×(-6)/2×54+radical 16+120/104+2radical 34/104-2radical 34/10x1=2-radical 34/5x2=2+radical 34/5HELP PLSSSSSSSSS!!!!!!!!!
Answer:
my friend, I would have to go with B: -3/4n + 3/8
The diagram represents the factorization of a2+8a+12
Answer:
(a+2)(a+6)
Step-by-step explanation:
Given expression ,
=> a² + 8a + 12
=> a² + 6a + 2a + 12
=> a(a+6) + 2(a+6)
=> (a+2)(a+6)
i need this today please
Answer:
y = (-1 / 3 ) * x - 5
Step-by-step explanation:
Slope Intercept form is y = mx + b
y = y coordinate
m = slope
x = x coordinate
b = y intercept
y intercept is where line touches the y axis
here b = -5
slope m = (y2 - y1 ) / (x2 - x1) ----- (-6, -3) (6, -7)
m = (-7 - (-3) ) / (6 - (-6) )
m = (-7 + 3 ) / (6 + 6)
m = -4 / 12
m = - 1 / 3
y = (-1 / 3 )* x + (-5)
Ordering Rational Numbers
MENU
Which number is an irrational number?
A
0
ON
7
Question 5 of 8
56.071
√10
Answer:
√10
Step-by-step explanation:
Integers, fractions, and repeating decimal numbers are all rational. The square root of an integer that is not a perfect square is irrational.
√10 is irrational
Adam and Don collected a total of 16 stickers. Adam collected 9 stickers. How many stickers did Don collect?
Answer:
7
Step-by-step explanation:
16-9=7
A coach bought a box of 50 tennis balls. The mass of each tennis ball is
58 grams.
What is the mass of all 50 tennis balls in grams?
Answer:
2,900
Step-by-step explanation:
i times 50 x 58
Kaila and Nicklaus want to compare the weights of their dogs. Kaila's dog weighs 13.096 pounds. Nicklaus's dog weighs 46.38 pounds. How much heavier is Nicklaus's dog compared to Kaila's?
Answer:
Nickaul's dog is 33.284 pounds heavier than Kaila's.
Step-by-step explanation:
find the difference;
46.38 - 13.096 = 33.284
WILL GIVE BRAINLIEST
Given: v is a midpoint of WY, XZ
Statement Reason
WV ≅ ______ definition of midpoint
XV ≅ ______ definition of midpoint
Statement Reason
△VZY ≅ △____ _______
Answer:
Statement Reason
WV ≅ YV definition of midpoint
XV ≅ ZV definition of midpoint
Statement Reason
△VZY ≅ △VXW SAS (Side-Angle-Side)
Step-by-step explanation:
Examine the graphs you drew in Problems 4 and 5. How does the dotted line y = x relate to the graphs of f(x) and f-'(x)?
What is the sum of −4x+1 and 6x−5 ?
10x + 6
2x−4
−2x+6
I don't know.
Answer:
2x - 4 is the answer
Step-by-step explanation:
Combine the like terms
The sum of -4x+1 and 6x-5 is 2x -4.
What is sum?The result of "adding two or more numbers".
According to the question,
(- 4x + 1) + (6x-5)
= -4x + 1 + 6x -5
= 2x -4
Hence, the sum of - 4x+1 and 6x-5 is 2x -4.
Learn more about Sum here
https://brainly.com/question/22412096
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now find the sum.what is 2 6/30 +1 25/20
Answer:
The result is 29/12 = 2 5/12 ≅ 2.4166667 = twenty-nine twelfths (
Step-by-step explanation:
Answer:
4 9/20
Step-by-step explanation:
Cody was given two polnts (5, 1) and(ç, 4), on a line and asked to create a linear equation in standard
form. Cody's work is shown. Identify any errors and correct them.
They found the graph to the right, which shows the miles per gallon (MPG) and the annual tons of GHG produced by 8 different types of cars. If each gallon of gasoline burned created 20 pounds of GHG, and the price of gasoline was $2.454 per gallon, how much money was saved annually on gas by the car that got 40 miles per gallon when compared to the car that got 20 miles per gallon? Provide your answer to the hundredths place. Note: 1 ton = 2,000 pounds.
The possible graph of the question is a histogram with a vertical axis of Annual Tons of GHG, and MPG on the horizontal axis.
The amount saved annually on gas by the car that gets 40 miles per gallon is $1,079.76Reasons:
The given information are;
Green House Gases, GHG, produced per gallon of gasoline = 20 poundsPrice of gasoline per gallon = $2.454
GHG produced by the car that gets 20 miles per gallon = 8.8 tons
8.8 tons = 8.8 × 2,000 pounds = 17,600 pounds
GHG produced by the car that gets 20 miles per gallon = 17,600 pounds
Number of gallons of gasoline = [tex]\displaystyle \frac{17,600 \ pounds}{20 \ pounds/gallon} = 880 \, gallons[/tex]
Cost of gasoline for car A = $2.454 × 880 = $2,159.52
GHG produced by the car that gets 40 miles per gallon = 4.4 tons
8.8 tons = 4.4 × 2,000 pounds = 8,800 pounds
GHG produced by the car that gets 20 miles per gallon = 8,800 pounds
Number of gallons of gasoline = [tex]\displaystyle \frac{8,800\ pounds}{20 \ pounds/gallon} = 440 \, gallons[/tex]
Cost of gasoline for car B = $2.454 × 440 = $1,079.76
The amount saved annually on gas by the car that got 40 miles per gallon is therefore; $2,159.52 - $1,079.76 = $1,079.76Learn more here:
https://brainly.com/question/21470991
HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
It's B
Step-by-step explanation:
The original equation is y - (y intercept)= slope(x-(x intercept))
What is the order of the following numbers from LEAST to GREATEST?
Answer:
It is the first answer
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
GIVING BRAINLIEST FOR WHOEVER IS RIGHT.
