Solve using a formula. Please don't guess, I would like professionals to take a look
Answers
Let's take this problem step by step:
What we know:
[tex]x+y=4\\xy=-2[/tex]
Before we solve, let's do one thing that will help us out greatly later down the road:
[tex]x+y=4\\(x+y)^2=4^2\\x^2+2xy+y^2=16\\x^2+2(xy)+y^2=16\\x^2+2(-2)+y^2=16\\x^2+4+y^2=16\\x^2+y^2=20[/tex]<--- useful equation
Let's rearrange the problem a little bit:
[tex]x+\frac{x^3}{y^2}+\frac{y^3}{x^2} +y=\frac{x^3}{x^2} +\frac{x^3}{y^2}+\frac{y^3}{x^2}+\frac{y^3}{y^2}[/tex]
Combine fractions of common denominators:
[tex]\frac{x^3+y^3}{x^2} +\frac{x^3+y^3}{y^2} =(x^3+y^3)*(\frac{1}{x^2}+\frac{1}{y^2} )[/tex]
Now's let factor everything apart:
[tex](x^3+y^3)=(x+y)(x^2-xy+y^2)\\\\\frac{1}{x^2}+\frac{1}{y^2} =\frac{x^2+y^2}{x^2y^2}[/tex]
Let's use what we know and our useful equation:
[tex](x+y)*(x^2-xy+y^2)*(\frac{x^2+y^2}{x^2y^2} )\\=4*(x^2+y^2-xy)*(\frac{20}{(xy)^2} )\\=4*(20-(-2))*\frac{20}{(-2)^2} \\=4*22*5\\=440[/tex]
The value is 440
Answer: 440
Hope that helps!
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Related Questions
Moscow: -5.5°C Cold Lake: -17.5°C Choose the correct inequality symbol to complete the inequality statement, -5.5°C ________ -17.5°C.
Answers
Answer:
-5.5°C > -17.5°C
Step-by-step explanation:
Since -5.5 is larger than -17.5
The correct inequality symbol to complete the inequality statement is ">" (greater than). [tex]-5.5^{\circ}C > -17.5^{\circ}C[/tex].
To understand why this symbol is used, let's compare the two temperatures.
The temperature in Moscow is -5.5C, while the temperature in Cold Lake is [tex]-17.5^{\circ}C[/tex].
Since -5.5 is greater (warmer) than -17.5, use the ">" symbol to indicate that [tex]-5.5^{\circ}C[/tex] is greater than [tex]-17.5^{\circ}C[/tex].
Here's a step-by-step explanation:
Begin by comparing the numerical values of the temperatures: -5.5 and -17.5.Since -5.5 is a higher value (closer to 0) compared to -17.5, it means that Moscow's temperature is warmer than Cold Lake's temperature.The ">" symbol is used to represent "greater than" in an inequality statement.By using the ">" symbol, we express that [tex]-5.5^{\circ}C[/tex] is greater (warmer) than [tex]-17.5^{\circ}C[/tex].In summary, when comparing the temperatures of Moscow and Cold Lake, the correct inequality statement is [tex]-5.5^{\circ}C > -17.5^{\circ}C[/tex], indicating that Moscow's temperature is higher (warmer) than Cold Lake's temperature.
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A,B, C and D are the four corners of a rectangular plot marked out on level ground. Given that the bearing of B from A is 40 and the bearing of C from A is 90, Find the bearing B frOm C
Answers
Answer:
given - a rectangle ABCD
AB = 40
AC. = 90
BC = ?
in triangle ABC
using Pythagoras theorem
(AB) ² + (BC) ² = (AC) ²
(40)² + (BC) ² = (90)²
(BC) ² = (90)²- (40)²
(BC) ² = 8100 - 1600
(BC) ² = 6500
BC =
[tex]20 \sqrt{10} [/tex]
The diagram shows a swimming course set out on a lake. Angle BCA = 90°. B 80m 145m C A Not to scale C is due north of A. Calculate the bearing of B from A.
Answers
the pronunciation of this question is wrong make it right first then I will answer
Step-by-step explanation:
please send this question again because I I think you want to write it fast and by mistake you are wright wrong
What is 2 2/3 - (-3 2/6) show your work
Answers
The value of the expression 2 2/3 - (-3 2/6) is 6
How to solve the expression?The expression is given as:
2 2/3 - (-3 2/6)
Open the bracket
2 2/3 + 3 2/6
Express as improper fractions
8/3 + 20/6
Rewrite as:
16/6 +20/6
Evaluate the sum
36/6
Evaluate the quotient
6
Hence, the value of 2 2/3 - (-3 2/6) is 6
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On. map with a scale of 1:75 000 the distance between a hotel and the airport is 3 cm
What is the actual distance I'm km?
a. 2.25
b. 2.5
c. 22.5
d. 25 km
please help
Answers
Answer:
a. 2.25 km
Step-by-step explanation:
the scale on a map means how many units in the mapp corresponds to how many units in reality.
in this case
1 cm on the map = 75000 cm in reality =
= 75000/100 m = 750 m =
= 750/1000 km = 0.75 km
3 cm = 3×1 cm = 3 × 0.75 km = 2.25 km
Work out the equation of line B. Give your answer in the form y = mx + c, where m and care integers or fractions in their simplest forms. Work out the equation of line B. Give your answer in the form y = mx + c , where m and care integers or fractions in their simplest forms .
Answers
Answer:
y = -3x + 1
Step-by-step explanation:
the line crosses the y-axis at (0,1) then c = 1
The points (0,1) and (1,-2) lie on the line then
m = slope = [(-2)-1]÷(1-0) = [-3]÷(1) = -3÷1 = -3
Therefore,
The equation of the line is : y = -3x + 1
Jeremy is reading a 60-page book. He read the first 20 pages in 30 minutes. If Jeremy continues to read a the same rate, how long will it take him to finish the book?
Answers
It will take total 90 minutes to finish the book and 60 minutes to read the left 40 pages.
What is Ratio and Proportion ?When two numbers can be written as p/q is called a Ratio , and when two ratios are equal they are said to be in proportion .
It is given that
Jeremy is reading a 60-page book.
The time taken to read 20 pages is 30 minutes
Then it can be written as 20:30 = 2:3
The rate of reading is same so To read the rest 40 pages is given by
40:x
40: x = 2:3
40*3/2 = x
x = 60 minutes
Therefore it will take total 90 minutes to finish the book and 60 minutes to read the left 40 pages.
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Solve the following inequalities and represent the solution on the number line.
d) 5x ≥ 15
e) 3(2x + 1) ≤ 15
Answers
d) 5x ≥ 15
Let's solve your inequality step-by-step.
5x≥15
Step 1: Divide both sides by 5.
[tex]\frac{5x}{5} \geq \frac{15}{5}[/tex]
[tex]x\geq 3[/tex]
(Attachment #1)
e) 3(2x + 1) ≤ 15
Let's solve your inequality step-by-step.
3(2x+1)≤15
Step 1: Simplify both sides of the inequality.
6x+3≤15
Step 2: Subtract 3 from both sides.
6x+3−3≤15−3
6x≤12
Step 3: Divide both sides by 6.
[tex]\frac{6x}{6} \leq \frac{12}{6}[/tex]
[tex]x\leq 2[/tex]
(Attachment #2)
You’re planning to place an order from an online boutique. Leggings are $12 each and shipping is a flat rate of $5. Write an expression that represents the total cost of your order (not including tax) based on the number of leggings (l) you buy.
Answers
Answer:
For the cost of each legging to be $12, and the shipping of $5, the expression is a straight line C = 12x + 5 where x is the number of leggings.
Step-by-step explanation:
It is given that each legging costs $12. This means that for x number of leggings, the cost will be $12x. Now there is an additional cost of shipping that is $5. So, total cost will be a linear equation and can be written as
C = 12x + 5
This equation represents a straight line like y = mx + c. Here y = C, m = 12 and c = 5.
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What is the intersection of line CA a and line XA?
Answers
Answer:
point A is the intersection point between XA and AC
Sara wants to find the input value that produces the same output for the functions represented by the tables.
A table headed with f(x) equals negative 0.5 x plus 2, with 2 columns and 8 rows. The first column, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2, 3. The second row, f(x), has the entries 3.5, 3, 2.5, 2, 1.5, 1, 0.5. A table headed with g(x) equals 2 x minus 3, with 2 columns and 8 rows. The first column, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2, 3. The second row, g(x), has no entries.
What is the input value that produces the same output value in both charts?
–2
–1
1
2
Answers
The input value that produces the same output value in both charts is 2. so the correct answer is option D.
What is a function?
A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
You are given two functions f (x) = -0.5X +2 and g(x) = 2x - 3
x f(x)
-3 3.5
-2 3
-1 2.5
0 2
1 1.5
2 1
3 0.5
The second table is given below:-
x g(x)
-3
-2
-1
0
1
2
3
We will put the points and will find the value of functions:-
g(-3) = 2(-3) - 3 = -6 -3 = -9
g(-2) = 2 -(-2) -3 = -7
g(-1) = 2( -1) -3 = -3
g(0) = 2 - 0 - 3 = -3
g(1) = 2.1 - 3 = -1
g(2) = 2.2 -3 = 1
g(3) = 2.3 -3 = 3
Hence the second table will be
x g(x)
-3 -9
-2 -7
-1 -5
0 -3
1 -1
2 1
3 3
The input value that produces the same output value in both charts is 2.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
The correct representations are - 6x + 15 < 10 - 5x , An open circle is at 5 and a bold line starts at 5 and is pointing to the right , Option C and E are the right answers.
What is Inequality ?Inequality are the mathematical statements where algebraic expressions are equated by another algebraic expression or a constant using an Inequality Operator.
The given statement is
–3(2x – 5) < 5(2 – x)
On simplifying can be written as
- 6x + 15 < 10 - 5x
- 6x + 15 < 10 - 5x
- 6x < -5 - 5x
- x < - 5
x > 5
An open circle is at 5 and a bold line starts at 5 and is pointing to the right .
Therefore Option C and E are the right answers.
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what is the equation (in slope-intercept form) of a line that passes through the point (3,-2) and has a slope of -2
Answers
Answer:
[tex]y = - 2x + 4[/tex]
Step-by-step explanation:
Thank you
y’all help find the area and perimeter
Answers
Answer:
área is 15 perimeter is B
Lillian went shopping for a new phone because of a sale. The price on the tag was $20, but Lillian paid $16 before tax. Find the percent discount.pls help
Answers
Answer:
20 % discount
Step-by-step explanation:
Lilian got 4 dollars off of the original price (20 - 16 = 4 )
4 / 20 * 100% = 20% off
The percentage of discount that Lillian gets because of sale is 20%.
What is percentage?Percentage is a measurement to find value of given number out of hundred.
Given that,
The price of phone on tag = $20.
Lillian paid for phone = $16.
To find the percent discount on phone,
First find amount of discount = 20 - 16 = $4.
The percentage of discount = (4 / 20) x 100 = 20 %
Lillian gets 20% discount on new mobile.
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Ten years ago Victors age WAs half of the age he will be in 10 years how old is he now?
Answers
By solving a linear equation, we will see that Victor is 30 years old.
How old is Victor now?
Let's say that Victor is x years old.
We know that 10 years ago, (x - 10), his age was half of what it will be in 10 years (x + 10).
Then we can write the linear equation:
(x - 10) = (x + 10)/2
Now we can solve that equation for x:
2*(x - 10) = x + 10
2x - 20 = x + 10
2x - x = 10 + 20
x = 30
So we conclude that Victor is 30 years old.
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Question 13 (4 points) (05.03) Which of the following statements best describes the graph of -5x + 2y = 1? (4 points)
A) It is a curve joining the points (-5, 2), (2, 3), and (4, 1).
B)It is a curve joining the points (-1, -3), (-1, -3), and (1, 5).
C)It is a straight line joining the points (1, 3), (3, 8), and (-3, -7).
D)It is a straight line joining the points (4, -3), (-1, 2), and (-4, 5).
Answers
Answer:
C) straight line through (1, 3) ... (-3, -7)
Step-by-step explanation:
The linear equation will describe a straight line. The slope and general location of the line on a graph can be estimated from its x- and y-intercepts.
__
interceptsThe x-intercept is the value of x that satisfies the equation when y=0.
-5x +2·0 = 1
x = -1/5 . . . . . . divide by the coefficient of x
The y-intercept is the value of y that satisfies the equation when x=0.
-5·0 +2y = 1
y = 1/2 . . . . . . divide by the coefficient of y
nature of the graphThe intercept values mean the line crosses the positive y-axis and the negative x-axis. It will have a positive slope. Points on the line that have integer x- and y-coordinates will have coordinates that have the same sign.
Of the offered answer choices, A and B are eliminated because the graph is not a curve. D is eliminated because the suggested points have coordinates with opposite signs. The correct choice is C:
It is a straight line joining the points (1, 3), (3, 8), and (-3, -7)
Use the information given in the diagrams to show that
Answers
Answer:
d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))
Step-by-step explanation:
The Law of Sines tells us that sides of a triangle are proportional to the sine of the opposite angle. This can be used along with a trig identity to demonstrate the required relation.
__
top triangleThe law of sines applied to the top triangle is ...
BC/sin(A) = AC/sin(θ)
Triangle ABC is isosceles, so the base angles at B and C are congruent. Then the angle at vertex A is ...
∠A = 180° -θ -θ = 180° -2θ
A trig identity tells us the sine of an angle is equal to the sine of its supplement. That means the sine of angle A is ...
sin(A) = sin(180° -2θ) = sin(2θ)
and our above Law of Sines equation tells us ...
BC = sin(A)/sin(θ)·AC = k·sin(2θ)/sin(θ)
__
bottom triangleThe law of sines applied to the bottom triangle is ...
DC/sin(B) = BC/sin(D)
d/sin(α) = BC/sin(β)
Multiplying by sin(α) we have ...
d = BC·sin(α)/sin(β)
__
Using our expression for BC gives the desired relation:
d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))
Question 11 of 20
What is the solution to the equation below? (Round your answer to two
decimal places.)
log₂ x = 5.6
Answers
Step-by-step explanation:
log2(x) = 5.6
so,
x = 2^5.6 ≈ 48.50293013... ≈ 48.50
Find the least common denominator for these
two rational expressions.
-4
-1
4y²
Enter the correct answer.
Answers
Answer:
4y^2
Step-by-step explanation:
least common denominator is 4y^2
Ramon has $80.00 saved from mowing yards and raking leaves. If half of his money came from mowing yards, how much money came from raking leaves?
Answers
Answer:
$40
Step-by-step explanation:
Ramon has $80 saved
half of it came from mowing yard
therefore 80/2 = 40
the rest from raking leaves
80-40=40
Brianna bought a total of 8 notebooks and got 16 free pens
Answers
Answer: 1:2
Step-by-step explanation:
Well, if you're asking for the ratio, it is 1:2
For every 1 notebook bought, there would be 2 free pens.
Since she bought 8 notebooks, just multiply 2 by 8 which will result in 16.
At Pine Time Summer Camp, 12 campers sign up to go swimming. Of the 12 campers, 2/3 of them are advanced swimmers. How many of these campers are advanced swimmers?
(not highschool)
Answers
The way I solved this is I used my calculator and did 2 divided by 3 and then multiplied the answer by twelve.
If you draw all hearts from a deck of 52 cards,
what is the ratio of the remaining cards to the
whole deck?
Answers
Answer:
39
Step-by-step explanation:
Okay so there are 52 cards in a deck and there are 4 of each card. 4 kings 4 Queens 4 Jacks 4 Ace 4 Twos 4 Threes 4 fours 4 fives 4 sixes 4 sevens 4 eights 4 nines 4 tens. One from each group is a heart there are 13 groups so therefore subtract 13 from 52.
A cylindrical barrel of water has a base radius of 30 cm and is 110 cm high.
a) Find it’s volume in cm³.
b) Find it’s capacity in litres
( Hint is 1 cm³= 1 ml )
c) Find the number of bottles of water that can be filled from the barrel if each bottle holds 0.73 litres.
Answers
The volume of the cylinder is in the cubic cm is 311017.67 and in litres is 311.017, and the number of bottle is 426.
What is a cylinder?In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the volume of the cylinder is given by:
[tex]\rm V = \pi r^2 h[/tex]
We have:
The radius of the cylindrical barrel r = 30 cm
Height of the cylindrical barrel h = 110 cm
Volume:
[tex]\rm V = \pi (30)^2 (110)[/tex]
V = 311017.67 cubic cm
The volume of litres:
V = 311.017 cubic ml (1 liter = 1000 cubic cm)
Number of bottles = 311.017 /0.73= 426 bottles
Thus, the volume of the cylinder is in the cubic cm is 311017.67 and in litres is 311.017, and the number of bottle is 426.
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The sides of the base of a right square pyramid are 10 feet long. The slant height is 15 feet. When the side lengths of the base and the slant height are both multiplied by a factor of 4, by what factor is the surface area multiplied?
Answers
The surface area is multiplied by a factor of 16
How to determine the factor of the surface area?The dimensions are given as:
Base = 10 feetSlant height = 15 feetFactor, k = 4The factor of the surface area is calculated as:
Surface area = Factor^2
So, we have:
Surface area = 4^2
Evaluate
Surface area = 16
Hence, the surface area is multiplied by a factor of 16
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16
Step-by-step explanation:
Which inequality describes the acceptable weights for the suitcase?
x≤ 32.5 or x ≤ 47.5
32.52x2 47.5
x≤ 32.5 or x ≥ 47.5
32.5 ≤ x ≤ 47.5
Answers
Based on the given options, the inequality for the acceptable weights of the suitcase is 32.5 ≤ x ≤ 47.5.
What is the acceptable weight for the suitcase?You didn't include the full question but this question can be answered based on the given options.
When inequalities are written, there is no inclusion of "or" which eliminates options A and C.
It is illogical to have an inequality as 32.5 ≥ x ≥ 47.5. This is because if 32.5 is larger or equal to x, then x cannot be larger than 47.5. This is mathematically impossible.
This leaves the likely answer as 32.5 ≤ x ≤ 47.5 which means that the weight of the suitcase has to be larger than or equal to 32.5 but less than or equal to 47.5.
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Answer:
32.5 ≤ x ≤ 47.5
Step-by-step explanation:
how many solutions exists for the given equation?
3x+13=3(x+6)+1
Answers
Answer:
No Solutions.
Step-by-step explanation:
original equation
3x+13 = 3(x+6)+1
distribute 3
3x+13 = 3x+18+1
simplify
3x+13 = 3x+19
since the slope is the same for both equations and the y-intercept is different the two equations are parallel meaning they will never intersect so there are no solutions.
Answer:
No solutions
Step-by-step explanation:
3x + 13 = 3 (x + 6) + 1
3x + 13 = 3x + 18 + 1
3x + 13 = 3x + 19
3x + 13 = 3x + 19 meaning no solution since they aren't equivalent to each other
Given: cot = -0.59 in QII, find sin
Answers
The value of sin x in Q II is 0.86 .
What are Trigonometry ?This the field in Maths which deals with a right angled triangle and the other angles in the triangle.
It is given that cot = -0.59
cot x = cos x / sin x
Using online trigonometric calculator
sin x in Q II is 0.86 .
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if x + 3y = 25 write y in terms of x and also find the two solutions of this equation
Answers
Answer:
y= 25/3 - x/3
Step-by-step explanation:
y= 25/3 - x/3
