For the curve [tex]x^{2} +xy+y^{2} = 27[/tex] , the line tangents to the curve at the x intercepts of the curve are parallel .
The Slope of tangent line to a function at any point is denoted by [tex]\frac{dy}{dx}[/tex] .
The Curve is given as ⇒[tex]x^{2} +xy+y^{2} = 27[/tex] ;
On differentiating both sides of the curve with respect to "x" ,
we get ;
the slope of the line as ⇒ [tex]Slope = \frac{dy}{dx} = -\frac{2x+y}{x+2y}[/tex] ;
Now for the x- intercepts , the value [tex]y = 0 ,[/tex]
On substituting [tex]y=0[/tex] in the curve [tex]x^{2} +xy+y^{2} = 27[/tex] ,
we get ;
[tex]x^{2} +x(0)+0^{2} =27[/tex]
On simplifying further ,
we get ;
[tex]x=\pm 3\sqrt{3}[/tex] ;
So , the two x intercepts of the curve are [tex](3\sqrt{3},0)[/tex] and [tex](-3\sqrt{3},0)[/tex] ;
to find the slopes , we substitute the values in the slope equation .
On substituting the values in the slope equation ,
we get ;
[tex]Slope_{(3\sqrt{3} ,0)} = -\frac{2(3\sqrt{3}) +9}{3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex] and
[tex]Slope_{(-3\sqrt{3} ,0)} = -\frac{2(-3\sqrt{3}) +9}{-3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex].
we see that the slope at both the intercepts is same ,
Therefore , the lines tangents of the curve at the x intercepts are parallel .
The given question is incomplete , the complete question is
Consider the curve defined by [tex]x^{2} +xy+y^{2} = 27[/tex] . Determine whether the lines tangent to the curve at the x - intercept of the curve are parallel .
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What is the degree of the polynomial 2x² 5x²³ 7?
The degree of the polynomial [tex]2xA^2 5xA^2A^37[/tex] is 9
A polynomial's degree is the sum of the degrees of its monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a non-negative integer.
The degree of a polynomial is the highest or largest power of a variable in a polynomial equation. The degree denotes the polynomial with the maximum exponential power (ignoring the coefficients).
Consider the following polynomial expression with two variables: [tex]x^3 + 6x^2y^4 + 3y^2+5[/tex]
The polynomial has a degree of 6.
This is because the exponent values of x and y in the second term of the algebraic formula, [tex]6x^2y^4[/tex], are 2 and 4, respectively. We get 6 when we sum the exponent values. As a result, the multivariable polynomial expression has a degree of 6.
As per question, polynomial is: [tex]2xA^2 5xA^2A^37[/tex]
The total sum of power is: 1+2+1+2+3=9
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Random students from a high school were surveyed to determine if there was enough interest to start a Ukulele Club.
Identify the population:
A. Students of high schools across the country
B. Students of the high school
C. Citizens of the city
D. Every citizen of the country
Answer:
b
Step-by-step explanation:
Answer:
B. Students of the high school
Step-by-step explanation:
It is high school because you just want to ask that area.
y<3x+12, y≥5x+7
The solution of the system of linear inequalities.
Answer: nswer ; x , we can find ; y with the first equation :.
1 answer
·
We know that y=5x−7 so we are just going to replace the y in the other equation : −3x−
Step-by-step explanation:
What is the inverse of the logarithmic function f x log9x?
The inverse of the logarithmic function f x log9x is f-1(x)=9^x.
The inverse of a logarithmic function is the exponential function. To find the inverse of the logarithmic function f x log9x, we can use the following equation: f-1(x)=9^x. This equation states that the inverse of the logarithmic function f x log9x is the exponential function f-1(x)=9^x.
The inverse of the logarithmic function f x log9x is f-1(x)=9^x, which is the exponential function.This means that for any value of x, the inverse of the logarithmic function f x log9x is equal to 9 raised to the power of x. For example, if x=2, then the inverse of the logarithmic function f x log9x is 9^2, or 81. Similarly, if x=3, then the inverse of the logarithmic function f x log9x is 9^3, or 729. In general, the inverse of the logarithmic function f x log9x is 9 raised to the power of x, for any value of x.
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Answer: f –1(x) = 9x
Step-by-step explanation:
(Car Sales) Of the cars sold during the month of July, 85 had air conditioning, 102 had automatic transmission, and 54 had power steering. 8 cars had all three of these extras. 24 cars had none of these extras. 25 cars had only air conditioning, 56 cars had only automatic transmissions, and 26 cars had only power steering. 11 cars had both automatic transmission and power steering. How many cars had exactly two of the given options
24 cars lacked power steering but did have air conditioning and an automatic gearbox.
According to the question,
No. of cars with Air conditioning = 88
No. of cars with Automatic transmission = 96
No. of cars with power steering = 76
All three = 4
None of these extras = 19
Only air conditioning = 23
Only automatic transmissions = 61
Only power steering = 28
Power steering and automatic transmission both = 11
The calculation for missing values:
11 - 4 = 7
96-61-4-7 = 24
88-24-4-23=37
It is obvious that 24 cars lacked power steering but did have air conditioning and an automatic gearbox.
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Torrin rode his bike to school at 13. 5 km/h. He returned home using the same route at 10. 5 km/h. Torrin took a total of 36 min to ride to school and back. Express your answer to the nearest hundredth. A) how many minutes did torrin take to ride to school? B)how far is it from Torrins house to school?
To ride a bike to school Torrin takes 15.75 min to ride to school and 3.54 km is the distance from his house to school.
Let v₁ = 13.5 km/h the speed to school
v₂ = 10.5 km the speed returning home
t = the time of the ride to school in minutes
36 - t = the time of the ride from school in minutes
Since, distance = speed × time
⇒v₁ × t/60 = v₂ × (36 - t)/60
⇒13.5 × t/60 = 10.5 × (36 - t)/60
⇒t = 15.75 min
Now, the distance = v₁ × t/60 = 13.5 × 15.75/60 = 3.54 km.
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Solve the following equation, and check your solution. Show all of your work.
-17+n/5=33
I’ve added my work attached :)
n = 250
What is the horizontal asymptote * 1 point?
The area of the right triangle shown is 24 square feet.
Which equations can be used to find the lengths of the legs of the triangle? Select three options.
0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x – 24 = 0
x2 + 2x – 48 = 0
x2 + (x + 2)2 = 100
The area of a right-angled triangle is represented by the expression
x(x + 2) = 24 having area 24 square feet.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the area of a right-angled triangle is (1/2)×base×height.
Given, The area of a triangle is 24 square feet whose height is 2 more than it's base.
Let, The base of the triangle be 'x', Therefore the measure of the height is (x + 2).
Therefore, The area of the triangle is,
(1/2)×x(x + 2) = 24.
x(x + 2) = 24.
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i dont know how to do it
Answer:
x = 4
y = 28
Step-by-step explanation:
1) y = 7x
2) y = 2x + 20
substitute y = 7x into equation 2:
7x = 2x + 20 now you can solve for x:
7x - 2x = 20
5x = 20
x = 20/5 = 4
Plug x = 4 into either equation 1 or 2 to solve for y:
y = 7x = 7(4) = 28
Find the Values of x and y
The values of x and y could be 25 and 113
What are parallel lines ?
parallel lines can be stated as , they both are equi distant from each other and which never intersect.
From the given figure,
y+12 = 3x + 50
as both are parallel to each other.
y-3x = 38
and 5x = y + 12
as vertically opposites are always equal .
y = 3x + 38
y = 5x - 12
hence,
5x - 12 = 3x +38
2x = 50
x = 25
put x = 25 in y = 3x + 38
y = 3 * 25 + 38
y = 113
hence the values of x and y are 25 and 113 respectively.
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Given: quadrilateral MATH; M(-5,-2), A(-3,2),
T(3,2) and H(1,-2)
Prove: MATH is a parallelogram
State the formula you will be using.
Show all work.
Answer:
MATH is not a parallelogram
Step-by-step explanation:
(sqrt means squareroot)
To prove that quadrilateral MATH is a parallelogram, we can use the following formula:
A quadrilateral is a parallelogram if and only if both pairs of opposite sides are congruent.
In other words, if the lengths of the sides opposite each other in a quadrilateral are the same, then the quadrilateral is a parallelogram.
To prove that MATH is a parallelogram, we need to show that both pairs of opposite sides are congruent.
The first pair of opposite sides consists of segment MA and segment TH. To show that these sides are congruent, we can use the Distance Formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points that define the line segment.
Substituting the coordinates of points M and A, we get:
d = sqrt((-3 - (-5))^2 + (2 - (-2))^2)
= sqrt((-3 + 5)^2 + (2 + 2)^2)
= sqrt(8^2 + 4^2)
= sqrt(64 + 16)
= sqrt(80)
= 8.944
Substituting the coordinates of points T and H, we get:
d = sqrt((1 - 3)^2 + (-2 - 2)^2)
= sqrt((-2)^2 + (-4)^2)
= sqrt(4 + 16)
= sqrt(20)
= 4.472
Since 8.944 is not equal to 4.472, we cannot conclude that MA and TH are congruent. Therefore, MATH is not a parallelogram.
what is 20% of 14000
Answer:
2800
Step-by-step explanation:
20% of 14,000 is 2800
Multiply both sides by 14,000, then divide the left side to get the result.
Answer:
2800
is what the calculator says
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Simplify the complex numbers using de Moivre's Theorem and match them with their solutions 2(3+1) 2. cos(20°) + sin(20°)] 2[ coo(4)+isin(7)]* (-1+i) -41 (1+1) -16 4+4731 Reset Next
The complex numbers are solved using De Moivre's Theorem and then are matched with their respective solutions.
What is De Moivre's Theorem?
De Moivre's formula, also known as the theorem and identity of de Moivre, says that for any real number x and integer n, holds -
(cos x + i sin x)^n=cos nx + i sin nx
where i is the imaginary unit (i^2 = 1).
Also, [r(cos x + i sin x)]^n = r^n(cos nx + i sin nx) or [r cis x]^n = [r^n cis nx].
The first complex number is (1+i)^5.
Solve using De Moivre's formula -
(1+i)^5 = [√2{(1/√2)+(i/√2)}^5]
=(√2)^5[cos(π/4)+i sin(π/4)]^5
=(√2)^5[cos(5π/4)+i sin(5π/4)]
=(√2)^5[(-1/√2)-(i/√2)]
=4(-1-i)
=-4-4i
The second complex number is (-1+i)^6.
Solve using De Moivre's formula -
(-1+i)^6=(1-i)^6
=[√2{(1/√2)-(i/√2)}^6]
=(√2)^6[cos(-π/4)+i sin(-π/4)]^6
=(√2)^6[cos(-6π/4)+i sin(-6π/4)]
=8(0+1i)
=8i
The third complex number is 2[cos(20)+i sin(20)]^3.
Solve using De Moivre's formula -
2[cos(20)+i sin(20)]^3=2^3[cos(60)+i sin(60)]
=8[(1/2)+{(√3)i/2}]
=4+4√3i
The last complex number is 2[cos(π/4)+i sin(π/4)]^4.
Solve using De Moivre's formula -
2[cos(π/4)+i sin(π/4)]^4=2^4[cos(4π/4)+i sin(4π/4)]
=16[cos(π)+i sin(π)]
=16(-1+i(0)]
=-16
Therefore, the complex numbers are solved using the theorem.
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What is the dual of a ∧ b ∨ c ∧ d?
On interchanging the logical AND operator with logical OR operator and zeroes with ones,
(B'+C).A = (B'.C) + A
Now, According to the question:
Concept:
Duality theorem states that the dual of the Boolean function is obtained by interchanging the logical AND operator with logical OR operator and zeroes with ones. For every Boolean function, there will be a corresponding Dual function.
Calculation:
On interchanging the logical AND operator with logical OR operator and zeroes with ones,
(B'+C).A = (B'.C) + A
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The complete question is this:
Calculate the dual of the Boolean expression (B' + C).A
The diagram shows two proportional right triangles.
What is the perimeter of the larger triangle?
The perimeter of the possible larger triangle with possible side lengths of 24, 32 and 40 is 96 units
What is the perimeter of a plane figure?The perimeter of a figure is the length of the boundary surrounding the figure.
Two triangles that have proportional dimensions are similar triangles
The dimensions (arranged in the order of corresponding sides) of the possible similar right triangles in the question, obtained from a related question, having two similar right triangles, posted online are;
First (larger) triangle side lengths; 24, 32, and xSecond (smaller) triangle side lengths; 9, 12, and 15The similarity of the triangles (proportional corresponding sides, indicates that we get;
[tex]\dfrac{24}{9} = \dfrac{32}{12} = \dfrac{x}{15}[/tex]
Therefore, by cross multiplication, we get;
32 × 15 = 12 × x
x = 32 × 15 ÷ 12 = 40
The perimeter of the larger triangle is; 24 + 32 + 40 = 96
The perimeter of the larger triangle is 96 units.Please find attached the possible diagram of proportional right triangles, created with MS Word, obtained from a question with regards to proportional right triangles online.
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These are the numbers and I need the ratio
to thank you!
help me please it's due tomorrow !!!!!!!!!!
help please
ill get in trouble!!!!
Answer: 1:3
Step-by-step explanation:
I'd say 1:3 but I could be wrong
Solve the system of inequalities by graphing.
y≤10x–3
y>
–
1
2
x+1
Can u please help ………….
Answer:
x = 17
Step-by-step explanation:
the midsegment of a triangle is half the length of the third side, that is
DE = [tex]\frac{1}{2}[/tex] × BC = [tex]\frac{1}{2}[/tex] × 34 = 17
so x = 17
For what value of k does the pair of linear equations 3x +5y 3 6x KY 8 do not have any solution?
The pair of linear equations 3x + 5y = 3 and 6x + ky = 8 does not have any solution for any value of k.
We can rewrite the equations as:
3x + 5y = 3
6x + ky = 8
To solve this system, we need to eliminate one of the variables. To do this, we can multiply the first equation by 2 and the second equation by -3. This will give us:
6x + 10y = 6
-18x - 3ky = -24
Now we can add the two equations together and get:
-12x - 3ky = -18
Since the coefficient of x is 0, this equation does not have any solution for any value of k.
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Two vehicles start from the same point traveling in the same direction. One vehicle travels 55.5 miles per hour (mph) and the other 45 ¼ mph. When will the two cars be 350 miles apart?
The number of hours after which the cars will be 350 miles apart is 34 hours.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
Vehicle 1.
Speed = 55.5 mph
Distance(1) = 55.5 x Time
Vehicle 2.
Speed = 45(1/4) mph
Distance(2) = 45(1/4) x Time
The difference in the distance = 350 miles.
Distance(1) - Distance(2) = 350
55.5 x Time - 45(1/4) x Time = 350
55.5 x Time - (181/4) x Time = 350
(55.5 - 181/4) x Time = 350
Time = 350 / (55.5 - 45.25)
Time = 350 / 10.25
Time = 34 hours.
Thus,
The car will be 350 miles apart after 34 hours.
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What is the coefficient of the variable in the expression 4 − 3x − 7 6 3 points?
The coefficient of the variable x in the expression 4a+3x +a is 3
Given that,
The expression is 4a+3x +a which can be simplified as 4a+3x +a
To find : The coefficient of the variable x in the expression
The coefficient of x in 4a+3x +a is 3
A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6
Coefficient is the number that is beside the variable in the equation.
As we can see that the term that is in multiplication with x is 3
Hence, the coefficient of x in the equation is 3
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I NEED HELPPPPppppppp
Check the picture below.
What is the log2 function?
The log2 function is a mathematical function that returns the logarithm of a given number to the base 2.
It is used to calculate the power to which a number must be raised to get a particular result.
For example, the log2 of 16 is 4, since 2^4 = 16. It can also be expressed as log2 16 = 4. Log2 is used in many areas of mathematics, including number theory, probability theory, and calculus.
It is also used in computer science and engineering to solve complex problems. Furthermore, it is used in cryptography to calculate the key sizes of encryption algorithms. In general, it is an essential tool for solving mathematical and scientific problems.
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A bag contain 27 ball. The ratio of red to blue to yellow ball i 6:1:2 find how many red, blue and yellow ball there are
On solving the provided question we can say that by linear equation number of, Red Balls = 6x 18; Blue Balls = 3; Yellow Balls = 6
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
A bag contains 27 balls
• The ratio of red to blue to yellow balls is 6:1:2
To Find : The number of red,blue and yellow balls present in the bag
Let us take the variable as 'x' to represent the number of balls in the bag
When we Put the values in a equation,
6X+X+2x = 27
9x = 27
x = 3
Hence the number of,
Red Balls = 6x 18
Blue Balls = 3
Yellow Balls = 6
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A B. C A3 x 3 matrix is above. It has a pattern going both horizontally across the rows and vertically down the columns. The pattern is not necessarily the same in both directions. There is one object that fits correctly in the bottom right corner of the matrix. Choose this object from the list below the matrix Select one: a. A ОБ. В Ос, с d. D e. E f.F 8.G h. H
We can conclude from answering the above question that the first two patterns of the matrix form a sequence in the third from top with the numbers 4-2-6.
what is matrix i?A matrix is a set of numbers arranged in rows and columns. learns about the elements and dimensions of matrices and introduces them for the first time. A rectangular grid of numbers in rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. Its single row and 1 n row matrix order are the reasons behind its name. A = [1 2 4 5] is a row matrix of order 1 by 4, for instance. P = [-4 -21 -17] of order 1-by-cubic is another illustration of a row matrix.
We can conclude from answering the above question that the first two patterns of the matrix form a sequence in the third from top with the numbers 4-2-6.
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Pythagorean theorem and its converse
problem 3:
leg:16
leg:x
hypo:27
problem 4:
leg:12.8
leg:5.3
hypo:x
problem 5
18 <--------->
`20
x'
The missing measures, using the Pythagorean Theorem, are given as follows:
3. Leg x = 21.75.
4. Hypotenuse x = 13.85.
What is the Pythagorean Theorem?The Pythagorean Theorem states that length of the hypotenuse squared is equals to the sum of each of the sides of the triangle squared.
For item 3, we have that the leg x is missing, while another leg and the hypotenuse are given, meaning that the relation is of:
x² + 16² = 27²
Hence:
x² = 27² - 16²
[tex]x = \sqrt{27^2 - 16^2}[/tex]
x = 21.75.
For item 4, we are given two legs and want to find the hypotenuse, hence the relation is given as follows:
x² = 12.8² + 5.3²
[tex]x = \sqrt{12.8^2 + 5.3^2}[/tex]
x = 13.85.
As for item 5, there is not enough information to answer, but the procedure should be the same.
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Part II:
13. Use the information in the table to answer the following:
A relation is Given below:
M
a) Identify the domain and the range for the given relation:
Domain:
X 0
1
- 1
0
y 0 -1 0 1
Range:
Formal Asso
Using the information in the table the domain is 4 and the range [-1,1]
Is it in the X or Y domain?The term "domain" refers to a group of potential input values, and the domain of a graph is made up of all the input values visible on the x-axis. The y-axis displays the range, which is a collection of possible output values.
How do you discover a table's domain and range?The domain is typically listed in the left column and the range is typically listed in the right column in a table like the one below. The domain and range of a relation or function, respectively, can be thought of as the input values (x) and the output values (y), respectively.
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The table shows the balances of two bank accounts for 3 months. In what month will the balance of account A be equal to the balance of account B?
As per Given data,
The month in which the balance of two bank accounts A is become equal to the balance of account B is 30thmonths,
How to find unknown values?Unknown variables are used to find the unknown values of the problem using the algebraic expressions.
Month Account A Account B
0 $ 100 $ 250
1 $ 125 $ 270
2 $ 150 $ 290
Clearly
The amount in account A is growing with $25 each month. Thus, the amount in this account in nth month is,
100+25[tex]n[/tex]
The amount in account B is just growing with $20. Thus, the amount in this account in nth month is,
250+20[tex]n[/tex]
x month
balances of two
account becomes equal,
then
100 + 25x =250 + 20x
25x - 20x = 250 - 100
5x = 150
x =30
Therefore, in 30th month balance of account A equal to balance of account B
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Q. The table shows the balances of two bank accounts for 3 months. In 30th month will the balance of account A be equal to the balance of account B?
Month Account A Account B
0 $100 $250
1 $125 $270
2 $150 $290
When a calcium atom forms an ion, it loses two electrons. what is the electrical charge of the calcium ion? responses −2 negative 2 −1 negative 1 1 1 2
When a calcium atom forms an ion, it loses two electrons. The electrical charge of the calcium ion is +2
What do you meant by electrical charge of a calcium ion?Calcium ions are net positive two charges. In calcium, when it has assumed its most stable state, the relationship between the quantity of protons (20) and the quantity of electrons (18) is represented by the +2 charge.
In the event that calcium (Z = 20) picks up two electrons, the resultant ion will have 18 electrons and 20 protons, giving it a charge of +2. (two more positive protons than negative electrons). It's a cation, this ion. Using the Ca2+ symbol, we can identify a calcium ion.
Atoms that lose electrons acquire a positive charge as there are fewer electrons left with negative charges to balance the positive charges of the protons in the nucleus. Positively charged ions are known as cations.
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