Answer:(x^2+y^2)^2=(x^2+y^2)(x^2+y^2)
Step-by-step explanation:
We can rewrite left side into right side form
(x^2+y^2)^2=(x^2+y^2)(x^2+y^2)
we can expand it
(x^2+y^2)^2=x^4+x^2y^2+x^2y^2+y^4
(x^2+y^2)^2=x^4+y^4+2x^2y^2
we can add and subtract 2x^2y^2
(x^2+y^2)^2=x^4+y^4+2x^2y^2+2x^2y^2-2x^2y^2
(x^2+y^2)^2=x^4-2x^2y^2+y^4+2x^2y^2+2x^2y^2
(x^2+y^2)^2=x^4-2x^2y^2+y^4+4x^2y^2
(x^2+y^2)^2=x^4-2x^2y^2+y^4+(2xy)^2
(x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2
The Pythagorean triple generator typically involves an algebraic formula where variables m and n are used to generate the sides of a right triangle such that a^2 + b^2 = c^2, with a common formula being a = m^2 - n^2, b = 2mn, and c = m^2 + n^2 for positive integers m and n.
The form of the Pythagorean triple generator refers to a set of algebraic formulas that produce Pythagorean triples, which are sets of three positive integers (a, b, c) that satisfy the condition of the Pythagorean theorem (a^2 + b^2 = c^2) for a right triangle.
One well-known formula to generate these triples is given by:
a = m^2 - n^2b = 2mnc = m^2 + n^2where m and n are positive integers with m > n. This formula will produce a Pythagorean triple as long as m and n are coprime and not both odd. It's important to note that not all Pythagorean triples can be generated by this formula, but it is a very common method of finding such triples.
Write the equation of a line with slope m = 6 and including point (0, 1).
Answer:
y = 6x + 1
Step-by-step explanation:
linear equations (straight line) are expressed in the following general form:
y = mx + b, where m is the gradient and b is the y-ordinate of the point where the line crosses the y-axis (called the y-intercept)
Given : m = 6
we realize that point (0,1) is actually on the y-axis (i.e x=0), therefore this is coincidentally the y-intercept. Hence b = 1
Therefore the whole equation is
y = 6x + 1
The equation for a line is:
y = mx + c
Note:
y is the y coordinate
m is the slope
x is the x coordinate
c is the y -intercept (where the line crosses the y-axis.
The question tells us that the slope is 6 (so m is 6)
It also tells that the coordinates are: (0 , 1) (so x is 0 and y is 1)
Lets plug in these values into the equation and solve to get the missing value ( which is c) :
y = mx + c
1 = 6(0) + c
1 = c.
Now to get the equation of the line, we plug in the values for m and c into y= mx + c:
Equation of line: y = 6x + 1
-----------------------------------------------------------
Answer:
Equation of line with slop m = 6 and including point (0, 1) is:
y = 6x + 1
7 ft=____ inches show work
Answer:7x12= 84
Step-by-step explanation:
7x10=70
7x2=14
70+14=84
have a good day
There are 84 inches in 7 feet.
Given that we need to determine that how many feet in 84 inches.
To convert inches to feet, you need to divide the number of inches by the number of inches in a foot.
There are 12 inches in a foot.
Given that you have 84 inches, you can divide this value by 12 to find the equivalent in feet:
84 inches ÷ 12 inches/foot = 7 feet
So, 84 inches is equal to 7 feet.
Hence there are 84 inches in 7 feet.
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What type of data is best represented by a bar graph?
A. Data that are compared using bars
B. Parts of a total amount
C. Each response shown by an X or a dot
D. Change in data over time
A bar graph is most suitable for comparing data across different categories or groups, as each bar corresponds to a particular group and the height or length of the bar shows the quantity of data for that group.
Explanation:The type of data that is best represented by a bar graph is generally data that is being compared across different categories or groups, which corresponds to option A. This is because each bar in a bar graph represents a particular group or category, and the height or length of the bar corresponds to the quantity of data for that group. For example, if you conducted a survey to find out the favorite fruit of students in a class and the choices were apples, bananas, oranges, and grapes, a bar graph would be a suitable way to present this categorical data.
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Consider the expressions $\frac{4x^3+2x^2+6x+7}{2x+1}$ and $2x^2+3+\frac4{2x+1}.$
a) Show that these expressions are equal when $x=10.$
b) Explain why these expressions are not equal when $x=-\dfrac12.$
c) Show that these expressions are equal for all $x$ other than $-\dfrac12.$
In parts (a) and (c), begin by explaining what your strategy for solving will be.
Answer:
Part a) In order to solve the equation, we will simplify both of them. Once we do that, if we notice, they are the same equation, so therefore, if x=10, then we will be able to match the equation.
Part b) The reason the expressions are not equal when x=-1/2 is because if we see, that in the second expression, 2x^2, if x=-1/2, then the answer becomes -1, and we eventually end up with 1.
Part c) As we can see, the expressions are the same, so if x is any number other than -1/2, then we will be able to show that the expressions are equal.
Step-by-step explanation:
You can simplify the explanation, also if you play ROBLOX, follow me at my username: BAMUNJI, or 24KBlingYT
By the way, this question is from the Art of Problem Solving, and you should not just copy answers or copy of them.
Part (a) We shall simplify both of them in order to find the solution to the equation.
Once we've done that, we'll see that they have the same equation, so we can match the equation if x=10.Part (b) When x=-1/2, the answers to the second expression, 2x2, change to -1, and we eventually arrive in 1.
This is why the expressions are not equal at this point.Part (c) As we can see, the expressions are identical, thus we can demonstrate that they are equal if x is any number other than -1/2.
What is an expression in maths?An expression is a set of terms combined using the operations +, – , x or , for example 4 x − 3 or x 2 – x y + 17 . An equation states that two expressions are equal in value, for example 4 b − 2 = 6 . An identity is a statement that is true no matter what values are chosen, for example 4 a × a 2 = 4 a 3 .What is a math expression example?An expression is a set of numbers or variables combined using the operations +, –, × or ÷. Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.How do you find expressions?To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.
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What is (f+g)(x)
f(x)=-x^2-3
g(x)=3x
Answer:
[tex]\large\boxed{(f+g)(x)=-x^2+3x-3}[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=-x^2-3\\\\g(x)=3x\\\\\text{Substitute:}\\\\(f+g)(x)=(-x^2-3)+(3x)=-x^2+3x-3[/tex]
(2 - yi) ^2 simplest form
Answer:
[tex]-y^{2}-4yi+4[/tex]
Step-by-step explanation:
we know that
[tex](a-b)^{2}=a^{2}-2ab+b^{2}[/tex]
we have
[tex](2-yi)^{2}[/tex]
substitute
[tex](2-yi)^{2}=(2)^{2}-2(2)(yi)+(yi)^{2}[/tex]
[tex](2-yi)^{2}=4-4yi+(y^{2})(i^{2})[/tex]
Remember that
[tex]i^{2}=-1[/tex]
substitute
[tex](2-yi)^{2}=4-4yi+(y^{2})(-1)[/tex]
[tex](2-yi)^{2}=4-4yi-y^{2}[/tex]
[tex](2-yi)^{2}=-y^{2}-4yi+4[/tex]
Please help!! Find P(A/A^c)
A.1
B.0
C. 1/2
D. Unknown
Answer: b
Step-by-step explanation:
trust!!!
Hi! I need help with this problem.
Answer:
B 70
Step-by-step explanation:
7 |H| + 4 G
H = -6 and G = 7
| H| = 6
7*6 + 4*7
42+28
70
Simplify the polynomial in standard form (3x-4x2+8x3)+(-6x+2x4-5x2)
The polynomial (3x - 4x^2 + 8x^3) + (-6x + 2x^4 - 5x^2) simplifies to 2x^4 + 8x^3 - 9x^2 - 3x in standard form by combining like terms and ordering them by descending exponents.
Explanation:To simplify the polynomial (3x - 4x2 + 8x3) + (-6x + 2x4 - 5x2) and write it in standard form, we combine like terms. Standard form for polynomials is to write the terms in descending order of their exponents. Here are the steps:
First, combine like terms which are the terms with the same power of x. This means adding coefficients of x3, x2, x, and the constant terms if there are any.Combine 8x3 (as there is no other x3 term to combine with).Combine the x2 terms (-4x2 and -5x2) to get -9x2.Combine the x terms (3x and -6x) to get -3x.Add any constant terms if they exist (there are none in this polynomial).The simplified polynomial in standard form is:
2x4 + 8x3 - 9x2 - 3x
A camera manufacturer spends $1,800 each day for overhead expenses plus $9 per camera for labor and materials. The cameras sell for $18
each. a. How many cameras must the company sell in one day to equal its daily costs? b. If the manufacturer can increase production by 50
cameras per day, what would their daily profit be?
Amount of money spent per day = $1800
Cost of overhead expenses per day for labor and materials = $9
Selling price of each camera = $18
a. Let us assume the number of cameras manufactured per day = x dollars
Then
Cost of cameras sold in 1 day = 18x
So
18x = 1800 + 9x
18x - 9x = 1800
9x = 1800
x = 200
From the above deduction, we can conclude that the number cameras sold per day is 200
b. Daily selling amount of 250 cameras = 250 * 18
= 4500 dollars
Daily manufacturing price of 250 cameras = 1800 + (9 * 250)
= 4050 dollars
Then
Daily profit = 4500 - 4050
= 450 dollars
A company needs to package 2400 pencils. A box in the shape of a rectangular prism can hold 60 pencils. A cylindrical container can hold 80 pencils. Each box cost the company $0.50, while each cylindrical container $0.75
Answer: A
Step-by-step explanation:
2,400 divided by 60 will give you 40. 40 multiplied by 0.50 give you $20.00.
2,400 divide by 80 will give you 30 but 30 multiplied but 0.75 gives you $22.50.
$22.50 minus $20.00 gives you $2.50
Let’s solve to answer the question.
Divide the amount of pencils the company needs by the amount of pencils the box holds.
2,400/60=40.
Now multiply it by the price.
40*.5=$20.
Repeat.
2400/80=30
30*.75=22.5
The cylindrical containers cost less.
Hope this helps!
-5 over 4 x -5 = -35 solve for x
Answer:
x = 9/7
Step-by-step explanation:
-5/4x-5 =-35
-5 = -35 * (4x-5)
-5 = -35*4x - 5*(-35)
-5 = - 140x + 175
- 140x + 175 = -5
-140x = -5 - 175 = -180
x = -180 / -140 =18 / 14 = 9 /7
To solve the given equation, -5/4x = -35, for x, you multiply both sides by the reciprocal of -5/4 which is -4/5. This gives you x = 28 as the solution.
Explanation:The given equation in your question is -5/4x = -35. In order to solve this equation for x, you would first want to isolate x on one side of the equation. Thus, we'll need to divide both sides of the equation by -5/4.
However, dividing by a fraction is the same as multiplying by its reciprocal. So, in this case, we'll multiply both sides by -4/5, which is the reciprocal of -5/4. This gives us:
x = (-35) * (-4/5)
Doing the multiplication results in x = 28.
Therefore, the solution for x in the equation is 28.
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In 2001, a company marketed 730,000 units of its product. In 2001 its yearly volume was 50% of its volume for 2004. The 2004 volume represents how many units for each of the 365 days of 2004?
Answer:
4000 units
Step-by-step explanation:
In 2001 the total number of marketed units= 730,000
If this number represents 50% of what was marketed in 2004, then the total number of units marketed in 2004 was:
(100/50)× 730,000=1460000
To get the number for each of the 365 days in 2004 we divide the total for 2004 by 365
1460000/365= 4000 units
Answer: 4,000 units per day.
Step-by-step explanation:
You know that in 2001 its yearly volume was 50% of its volume for 2004.
Therefore, if in 2001 the company marketed 730,000 units of its product, in 2004 the volume is:
[tex]Yearly\ volume_{(2004)}=(730,000\ units)(2)=1,460,000\ units[/tex]
Let be "x" the number of units for each of the 365 days of 2004, you can find its value by dividing the 2004 volume by 365.
The result is:
[tex]units=\frac{1,460,000\ units}{365}=4,000\ units.[/tex]
A radical equation is an equation that uses a radical. True or false ?
Yes! A radical Equation does use a radical in a Equation.
False
Step-by-step explanation:
Don’t listen to the AI answers
find the gradient of the line joining (3,7) and (6,9). Hence, find the acute angle it makes with the positive x-y axis
Answer:
33.7 degrees
Step-by-step explanation:
As we go from (3,7) to (6,9), x increases by 3 and y increases by 2. Thus, the gradient (slope) of the line connecting these two points is
m = rise / run = 2/3. Using the slope-intercept formula y = mx + b, we obtain
7 = (2/3)(3) + b, or 7 = 2 + b, so we see that b = 5 and y = (2/3)x + 5. The y-intercept is (0, 5).
Next we find the x-intercept. We set y = (2/3)x + 5 = to 0 and solve for x:
(2/3)x = -5, or (3/2)(2/3)x = -5(3/2), or x = -15/2, so that the x-intercept is
(-15/2, 0). This line intersects the x-axis at (-15/2, 0).
Now look at the segment of this line connecting (-15/2, 0) and (0, 5). Here x increases by 15/2 and y increases by 5, and so the tangent of the acute angle in question is
tan Ф = 5 / (15/2) = 10 / 15 = 2/3.
Using the inverse tangent function, we get Ф = arctan 2/3, or approx.
33.7 degrees.
I believe you meant "the acute angle it makes with the positive x-axis."
Final answer:
The gradient of the line is 2/3, and the acute angle it makes with the positive x-axis is found by taking the arctan of the gradient. which is approximately 33.69 degrees.
Explanation:
The gradient of the line joining two points, (x1, y1) and (x2, y2), is calculated using the formula:
Gradient = (y2 - y1) / (x2 - x1)
Substituting the given points (3,7) and (6,9) into the formula, we get:
Gradient = (9 - 7) / (6 - 3) = 2 / 3
The gradient is 2/3. To find the acute angle θ the line makes with the positive x-axis, we use the formula:
Tan(θ) = Gradient
So, θ = arctan(Gradient)
θ = arctan(2/3)
Calculating θ will give us the acute angle. which is approximately 33.69 degrees.
Can someone help me
Answer: D
Step-by-step explanation:
W is the total number of oranges.
W/5 is the oranges being divided equally for 5 friends
Solve for x in the equation X2 - 12x+36 = 90-
x=6+3/10
O x=6+2.17
| O x= 12+3/22
x= 12+3/10
Answer:
x = 6 ± 3√10
Step-by-step explanation:
Since this is an unfactorable expression, apply the Quadratic Formula, -b ± √b² - 4ac\2a, according to the Quadratic Equation, y = Ax² + Bx + C. Applying the Quadratic Formula will give you the above answer.
NOTE: -b = OPPOSITE of b
I am joyous to assist you anytime.
Final answer:
To solve x² - 12x + 36 = 90 for x, we simplify the equation to x² - 12x - 54 = 0 and use the quadratic formula to find x = 6 + 3√10 and x = 6 - 3√10.
Explanation:
To solve the equation x² - 12x + 36 = 90, we can first simplify it by subtracting 90 from both sides to set it equal to zero:
x² - 12x + 36 - 90 = 0Now we use the quadratic formula, which states that for any quadratic equation of the form ax² + bx + c = 0, the solutions for x can be found using:
x = (-b ± √(b² - 4ac)) / (2a)Applying this to our equation with a = 1, b = -12, and c = -54, we get:
x = (12 ± √((-12)² - 4*1*(-54))) / (2*1)Thus, the solutions are x = 6 + 3√10 and x = 6 - 3√10.
I’m If Linda age is decreased by 36, the result is twice Linda’s age. how old is linda?
Answer:
x=lindas age
3 times lindas age (3 time x or 3x) is decreased by 36 (-36), the result (=) is twice lindas age (2 times x or 2x)
now we have
3x-36=2x
subtract 2x
x-36=0
add 36
x=36
age=36
Step-by-step explanation:
Using algebra to solve the problem, we create the equation L - 36 = 2L, representing Linda's age. Solving for 'L', we find that Linda is 36 years old.
Explanation:This problem can be solved by using algebra, a branch of mathematics. Let's assume that Linda's age is denoted by the variable 'L'. According to the problem, if Linda's age is decreased by 36, the result is twice Linda's age. We can write this as an equation: L - 36 = 2L.
In order to solve for 'L', we'll need to get all terms involving 'L' on one side of the equation. We would then subtract 'L' from both sides, giving us -36 = L, or, re-arranged, L = 36. Therefore, Linda is 36 years old.
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What us the slope of the line (-7,2) and (5,8)
Final answer:
The slope of the line passing through the points (-7,2) and (5,8) is calculated using the slope formula and is found to be 0.5.
Explanation:
The student asked about the slope of the line passing through two points, (-7,2) and (5,8). To find the slope, one should use the slope formula: slope (m) = (y2 - y1) / (x2 - x1). Plugging in the values from the points, we have m = (8 - 2) / (5 - (-7)) = 6 / 12 = 0.5. Therefore, the slope of the line is 0.5.
PLEASE HELP! Let x1 = 8, y1 = 12, and y2 = 4. Let y vary inversely as x. Find x2.
x2 = 6
x2 = 24
x2 = 2.67
x2 = 92
Answer:
[tex]x_{2} =24[/tex]
Step-by-step explanation:
Your welcome :)
Which figures are shown
Answer:
Point D, Segment CD, Ray CD
Step-by-step explanation:
Which relation is a function?
Mn
The top right one, because for every argument there is only one corresponding value.
what expression is equivalent to 25 X 9y3
Answer:
D
Step-by-step explanation:
Use exponents property:
[tex]\dfrac{x^a}{x^b}=x^{a-b}[/tex]
1. Note that
[tex]\dfrac{x^9}{x^6}=x^{9-6}=x^3[/tex]
and
[tex]\dfrac{y^3}{y^{11}}=y^{3-11}=y^{-8}=\dfrac{1}{y^8}[/tex]
2. Now
[tex]\sqrt{25}=5\\ \\\sqrt{64}=8\\ \\\sqrt{x^3}=x\sqrt{x}\\ \\\sqrt{\dfrac{1}{y^8}}=\dfrac{1}{y^4}[/tex]
So
[tex]\sqrt{\dfrac{25x^9y^3}{64x^6y^{11}}}=\dfrac{\sqrt{25}\sqrt{x^3}}{\sqrt{64}\sqrt{y^8}}=\dfrac{5x\sqrt{x}}{8y^4}[/tex]
because [tex]x>0,\ y>0[/tex]
Answer: Last option.
Step-by-step explanation:
You need to remember the Quotient of powers property:
[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]
Applying this property, we know that:
[tex]\sqrt{\frac{25x^9y^3}{64x^6y^{11}} }=\sqrt{\frac{25x^3}{64y^8}}[/tex]
Descompose 25 and 64 into their prime factors:
[tex]25=5*5=5^2\\64=8*8=8^2[/tex]
Since:
[tex]\sqrt[n]{a^n}=a[/tex]
And according to the Product of powers property:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
You can simplify. So, the equivalent expression is:
[tex]\sqrt{\frac{5^2x^2*x}{8^2y^8}}=\frac{5x\sqrt{x} }{8y^4}[/tex]
What is the solution for the equation (x-5)^2+3(x-5)+9=0 Use u substitution and the quadratic formula to solve?
Answer:
Here is the answer.
x= 1/2(7+3i√3) and 1/2(7-3i√3)
What is the relationship between the volume of a cone
and the volume of a cylinder? Explain.
Hello There!
The volume of a cylinder is pi * r^2 * h. It's a circle times the height.
The volume of a cone is (1/3) * pi * r^2 * h. So it is one third of the volume of a cylinder with the same dimensions.
Answer:
The volume of a cone is one-third the volume of a cylinder.
Step-by-step explanation:
1/2x = -40
What is x?
Answer:
x = -80
Explanation
-40 divided by 1/2 is -80
Hanging 3 washers on a spring stretches it a total of 4.5 cm. If 13 washers are placed on it instead how far will the spring stretch
Using Hooke's Law, the spring would stretch a total of 19.5 cm when 13 washers are placed on it.
To find out how much a spring would elongate when the number of washers is increased, we use Hooke's Law, which describes linear elasticity.
Since it is given that 3 washers cause the spring to stretch 4.5 cm, we can assume that each washer causes an equal amount of stretch under this elastic limit. Therefore, the amount of stretch per washer is 4.5 cm divided by 3, which is 1.5 cm per washer.
If you hang 13 washers on the spring, the total stretch can be calculated by multiplying the amount of stretch per washer with the total number of washers:
Stretch per washer × Number of washers = Total stretch
1.5 cm/washer × 13 washers = 19.5 cm.
So, with 13 washers, the spring would stretch a total of 19.5 cm.
Write the equation of the line that passes through the points (8, -1) and (2,-5) in standard form, giver
slope form is y+1 = (x-8)
Answer:
2x - 3y = 19Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (8, -1) and (2, -5). Substitute:
[tex]m=\dfrac{-5-(-1)}{2-8}=\dfrac{-4}{-6}=\dfrac{2}{3}[/tex]
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute:
[tex]y-(-1)=\dfrac{2}{3}(x-8)[/tex]
[tex]y+1=\dfrac{2}{3}(x-8)[/tex] → the point-slope form
Convert to the standard form: [tex]Ax+By=C[/tex]
[tex]y+1=\dfrac{2}{3}(x-8)[/tex] multiply both sides by 3
[tex]3y+3=2(x-8)[/tex] use the distributive property a(b+c) = ab+ ac
[tex]3y+3=2x-16[/tex] subtract 3 from both sides
[tex]3y=2x-19[/tex] subreact 2x from both sides
[tex]-2x+3y=-19[/tex] change the signs
[tex]2x-3y=19[/tex] → the standard form
If f(x) = 3x-2 and g(x)= x^2 +1, find (f+g)(x).
Answer:
It's choice D.
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
= 3x - 2 + x^2 + 1
= x^2 + 3x - 1.
Answer:
D. x^2+3x-1
Step-by-step explanation:
You have:
f(x) = 3x-2
g(x)= x^2 +1
Then:
(f+g)(x)=f(x)+g(x)
(f+g)(x)=(3x-2)+(x^2+1)
(f+g)(x)=3x-1+x^2 (-2+1=-1)
(f+g)(x)=x^2+3x-1 (ordering terms)
Which graph represents the function h(x) = –(x + 6)3 – 3?
Answer:
Step-by-step explanation:
Please, if you're indicating exponentiation, use the symbol " ^ " to indicate it. Thanks.
The parent function here is f(x) = x^3.
g(x) = (x + 6)^3 has the same graph as does
f(x) = x^3, except that the entire graph of x^3 is translated 6 units to the left.
h(x) = -(x + 6)^3 has the same graph as
does g(x), except that the entire graph of g(x) is reflected in the x-axis.
The graph of h(x) = h(x) = –(x + 6)3 – 3 is the same as that of h(x) except that the entire graph is translated downward by 3 units.
Answer: B
Step-by-step explanation: