h(2) + j(−7) = −7(1 + j)
Suppose that f(x) = h^−1(x) and that both j and h are defined for all values of x. Let h(11) = 2 and f(12) = −7. We need to evaluate the following. h(2) + j(−7)For finding the value of h(2), we can use f(x) = h^−1(x) where x = h(2)f(h(2)) = 2h(2) = f^−1(2)We need to find h(2). Therefore, we need to find f^−1(2). We know f(12) = −7f(h(2)) = 2⟹ h(2) = −7Substitute h(2) = −7 in h(11) = 2h(11) = h(2 + 9) = h(2) + 9 = 2 + 9 = 11Therefore, h(2) = −7 and h(11) = 2.h(2) + j(−7) = −7 + j(−7) = −7(1 + j)Therefore, h(2) + j(−7) = −7(1 + j).
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A mobile phone company offers a data-only plan for a monthly charge of $15, plus an additional $10 for each gigabyte of data used. Which of the following equations can be used to calculate the total monthly cost, c, in dollars based on the number of gigabytes, g, of data used?
C(g) = 10 + 15g
C'(g) = 80
The monthly charges of Company C for using 2 Gigabyte of data usage.
Step-by-step explanation:
The cell phone plan from Company C costs $10 per month, plus $15 per gigabyte for data used. The plan from Company D costs $80 per month, with unlimited data.
Now, the monthly cost in Company C for using g gigabyte of data will be
C(g) = 10 + 15g ........ (1)
Again, the monthly cost in Company D for using g gigabyte of data will be
C'(g) = 80 ......... (2)
Now, from equation (1), the statement C(2) = 10 + 15 × 2 = 40, means that monthly charges of Company C for using 2 Gigabyte of data usage. (Answer)
simplify 3 c -9 d+7 c+5 d
4.
[2020/Canberra Sec]
The numbers 1450 and 2400, written as a product of its prime factors are
2x5²x29 and 25×3×52 respectively. Find
(a) the largest integer which is a factor of both 1450 and 2400,
Therefore, 150 is the largest integer that is a factor of both 1450 and 2400.
What is prime factorization?Prime factorization is the process of breaking down a positive integer into its prime factors, which are prime numbers that can divide the integer without a remainder. Every positive integer can be written as a product of prime numbers in a unique way, called its prime factorization. Prime factorization is important in many mathematical applications, such as finding the greatest common divisor and least common multiple of two or more integers, simplifying fractions, and solving problems related to divisibility, prime numbers, and modular arithmetic.
Here,
To find the largest integer that is a factor of both 1450 and 2400, we need to first express both numbers in terms of their common prime factors and then find the product of the common prime factors raised to their lowest exponent.
The prime factorization of 1450 is 2 × 5² × 29.
The prime factorization of 2400 is 2⁴ × 3 × 5².
To find the common factors of these two numbers, we need to look for the prime factors that appear in both factorizations. These common prime factors are 2, 5², and 3.
To find the largest integer that is a factor of both 1450 and 2400, we need to multiply these common prime factors raised to their lowest exponent:
2 × 5² × 3 = 150
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To promote his new business, Claudio made 300300300 tamales to give to pedestrians. The expression above describes the number of tamales remaining after passing out samples to ppp pedestrians. If Claudio passed out samples to 160160160 pedestrians, how many tamales would remain?
As a result, 140140140 tamales would be left as Claudio began with 300300300 and distributed samples to 160160160 passersby.
what is expression ?An expression in mathematics is made up of different numbers, variables, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation. Expressions can be simple or complicated and can express a wide range of mathematical connections and concepts. Expressions can be evaluated to get a numerical result or to be simplified using mathematical principles and rules. For instance, the equation "2 + 3" can be evaluated to get the value "5", whereas the expression "2x + 3y - 4z" can be made easier by fusing comparable terms to produce a more straightforward expression, such as "2x - z + 3y."
given
The quantity of tamales left if Claudio began with 300300300 and distributed samples to 160160160 passersby would be:
300300300 - 160160160 = 140140140
As a result, 140140140 tamales would be left as Claudio began with 300300300 and distributed samples to 160160160 passersby.
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Suppose you bought a house for $349,634 and the value has increased by 63%. What is the new value of the house in dollars? Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
If the value of the house has increased by 63%, it is still worth 100% of the $349,634 it was originally, but now we are adding 63% to that 100% to find the new value. Thus, 349634(1.63) = $569,903.42. The 1.63 is 163% as a decimal, just in case.
I don’t know how can I do this please help meeeee
Answer:
x = 8
Step-by-step explanation:
You want to know the value of x in this similar triangle geometry.
Similar trianglesWhen a segment is drawn in a triangle parallel to the base, it divides the sides proportionally. Every segment on the left has the same ratio to the corresponding segment on the right:
x/6 = 4/3
This equation is solved in the usual way. Multiply by the inverse of the coefficient of x:
6(x/6) = 6(4/3)
x = 8
__
Additional comment
Every proportion can be written several ways. Another way to write this one is ...
x/4 = 6/3
x = 4(2) = 8 . . . . . multiply by 4
If you need to, you can prove the triangles are similar by considering corresponding angles. ∠A≅∠A, ∠APW≅∠AVZ, so the triangles are similar by the AA postulate. (Corresponding angles where a transversal crosses parallel lines are congruent.)
Perhaps not so obvious is the relationship between segments of the long side and segments of the short side. The similarity relation tells us ...
AV/AP = AZ/AW
(4+x)/x = (3+6)/6
4/x +1 = 3/6 +1 . . . . . do the division
4/x = 3/6 . . . . . . . . subtract 1
x/4 = 6/3 . . . . . . invert both sides . . . compare to above
Answer the question with an explanation!!
Answer: 212.5
Step-by-step explanation: you find a base to multiply it with the height so like this 17X25=425 now you have to divided it into a half because it's a triangle 425 divided by 2 = 212.5
For the function below, complete the following.
f(x) = x^3 - 2x^2 - 25x + 50
a. List all possible zeroes
b. Use synthetic division to test te possible rational zeroes and find an actual zero.
c. Use the quotient from part (b) to find the remaining zeros of the polynomial function
a. The possible zeros of the polynomial function are ±1, ±2, ±5, ±10, ±25, ±50
b. x = -1 is a zero of f(x)
c. The remaining zeros of the polynomial function is -1, (3 + i√103) / 2, (3 - i√103) / 2
What are all the possible zeros of the functionTo find all possible zeros of the polynomial function f(x), we can use the Rational Root Theorem, which states that if a polynomial function with integer coefficients has a rational zero of the form p/q, where p and q are integers and q ≠ 0, then p must be a factor of the constant term and q must be a factor of the leading coefficient.
The constant term of f(x) is 50, which has the factors ±1, ±2, ±5, ±10, ±25, ±50. The leading coefficient of f(x) is 1, which has the factors ±1. So the possible rational zeros of f(x) are:
±1, ±2, ±5, ±10, ±25, ±50
b. We can use synthetic division to test each of the possible rational zeros and find an actual zero. Let's start by testing x = 1:
| 1 -2 -25 50
1 | 1 -1 -26 24
|______________
1 -1 -26 24
The remainder is 24, which means that x = 1 is not a zero of f(x).
Let's try x = -1:
| 1 -2 -25 50
-1 | 1 -3 28 -78
|______________
1 -3 28 -78
The remainder is -78, which means that x = -1 is a zero of f(x).
c. We can use the quotient from part (b), which is x^2 - 3x + 28, to find the remaining zeros of the polynomial function f(x). To do this, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
where a = 1, b = -3, and c = 28. Plugging in these values, we get:
x = (3 ± √(-103)) / 2
Since the discriminant is negative, there are no real solutions. However, there are two complex solutions:
x = (3 ± i√103) / 2
So the zeros of f(x) are:
x = -1, (3 + i√103) / 2, (3 - i√103) / 2
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What is the slope of the line represented by the following formula?
y = 2 + 6(x-3)
6
12
-3
-6
3
Answer:
slope = 6
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
given
y = 2 + 6(x - 3 ( subtract 2 from both sides )
y - 2 = 6(x - 3) ← in point- slope form
with slope m = 6
the two line segments below each have the same length l. if you were to calculate the integral the contour integer of the dot product of vector b with respect to vector s for each path, which one would yield b times l?
In response to the given question, we can state that To compute the function contour integral and establish the value of b times l for each path, the precise path of the line segments must be specified.
what is function?Mathematicians examine numbers and complex variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "functioning" signifies the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and results in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used this to denote functions (x). The symbol for admission is an x. The four primary types of usable functions are on operations, one-to-one capabilities, so multiple functionality, in capabilities, and then on functions.
It is impossible to predict which path would provide a contour integral of b times l for the dot product of vector b with respect to vector s without knowing the precise trajectories of the line segments.
The contour integral of a vector field F's dot product with respect to a curve C is given by:
∫C F · ds
To compute the contour integral and establish the value of b times l for each path, the precise path of the line segments must be specified.
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A number, n, is multiplied by -5/8 . The product is - 0.4. What is the value of n?
The value οf n is -0.64.
What is equation?
An equatiοn is a mathematical statement that prοves the equality οf twο mathematical expressiοns, accοrding tο the definitiοn οf an equatiοn in algebra. Fοr instance, the twο equatiοns 3x + 5 and 14 are cοmbined tο fοrm the equatiοn 3x + 5 = 14, which is denοted by the equal sign.
The prοduct is -0.4 in this case when the given statement, n, is multiplied by -5/8.
Putting expressiοn intο practise nοw
=> [tex]n\times\frac{-5}{8}=0.4[/tex]
=> n = 0.4 × 8/-5
=> n = -0.64
Hence the value of n is -0.64.
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4.02 Lesson Check Arithmetic Sequences (1)
The first four terms of the sequence a(n) = 3n + 2 when evaluated are 5, 8, 11 and 14
How to determine the value of the first four terms?A sequence can be arithmetic or geometric or neither
The definition of the function is given as
a(n) = 3n + 2
The above definitions imply that we simply add 2 to the previous term to get the current term
So, we have
a(1) = 3 * 1 + 2
a(1) = 5
Next. we have
a(2) = 3 * 2 + 2
a(2) = 8
Also, we have
a(3) = 3 * 3 + 2
a(3) = 11
Lastly, we have
a(4) = 3 * 4 + 2
Evaluate the equation
a(4) = 14
Hence, the first four terms are 5, 8, 11 and 14
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How can I solve this?
In conclusion, we need to identify the set of values of x for which either f(x)=-1/4 or f(-x)=-1/4 in order to solve to the equation f(|x|)=-1/4.
How is a function solved?The expression f(|x|)=-1/4 indicates that the absolute value of x's function f is equal to 1/4. Any x values that satisfy this equation are what we are trying to find. We can rewrite the equation as f(x)=-1/4 when x is positive and f(-x)=-1/4 when x is negative because the absolute value of x is always positive.
We must search for values of x such that f(x)=-1/4 or f(-x)=-1/4 in order to identify the answers. Without knowing more about the function, f may be anything, hence we cannot know the precise solutions.
Therefore, we can state that x or -x is a solution to the equation if there is a value of x such that f(x)=-1/4 or f(-x)=-1/4.
As a result, we must identify the range of x values for which either f(x) or f(-x) = 1/4.
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
Plot the point on 1
Step-by-step explanation:
Answer: 1
Step-by-step explanation: There are 10 space on the number line between the two pts. Since we are finding a 1:4 ratio we will need to divide these 10 space by 5.
[tex]10/5=2[/tex]
Which means that the point is two spaces away from T. Which is point 1 on the number line.
a straight line joins the points A (2,1) and B (8,10) The point (6,y) lies on the line AB Find the y coordinate of c
(35 points!)
Which is CLOSEST to the curve of best fit for the data shown?
(a). y = -10x^2 - 0.5x + 8
(b). y = -2x^2 + 0.2x +23
(c). y = -8x^2 - 0.5x + 9
(d). y = -5x^2 - 18x + 66
The CLOSEST to the curve of best fit for the data shown is:
(c). y = -8x^2 - 0.5x + 9
How to interpret the line of best fit?The line of best fit is defined as a straight line that is drawn to pass through a set of plotted data points that produces the best and most approximate relationship between such given data points.
From the given graph, we see that:
at x = 1, y = 0
Thus:
a) -10x² - 0.5x + 8
Plugging x = 1:
-10(1)² - 0.5(1) + 8
= -10 - 0.5 + 8 = -2.5
b) y = -2x² + 0.2x + 23
At x = 1:
y = -2(1)² + 0.2(1) + 23
y = 21.2
c) y = -8x² - 0.5x + 9
At x = 1:
y = -8(1)² - 0.5(1) + 9
y = -8 - 0.5 + 9
y = 0.5
d) y = -5x² - 18x + 66
At x = 1:
y = -5(1)² - 18(1) + 66
y = 43
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Pls awnser all they easy (brainlist)
The given expressiοn is equivalent tο -19.5b - 6.9.
What is an expressiοn?A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expressiοn οr mathematical expressiοn. Unknοwn variables, integers, and arithmetic οperatοrs are the cοmpοnents οf an algebraic expressiοn.
Here, we have
Given: 3(-4.5b-2.1)-(6b+0.6)
We have tο find the expressiοn that is equivalent tο the given expressiοn.
= 3(-4.5b-2.1)-(6b+0.6)
= -13.5b - 6.3 - 6b - 0.6
= -19.5b - 6.9
Hence, the given expressiοn is equivalent tο -19.5b - 6.9.
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giving brainly
Which equation would you use to find the distance between the two points? A. |2 - 4| B. |2 - (-4)| C. |-5 - 5| D. |2 + (-4)|
The equatiοn we wοuld use tο find the distance between the twο pοints is d = √((x₂ - x₁)² + (y₂ - y₁)² ) = √((2 - (-4))² + (y₂ - y₁)² ) = √(6² + (y₂ - y₁)² ) = √36 + (y₂ - y₁)² )
Tο find the distance between twο pοints οn a number line οr in a cοοrdinate plane, we use the distance fοrmula. The distance fοrmula is given by:
d = √((x2 - x1)² + (y2 - y1)² )
where (x1, y1) and (x2, y2) are the cοοrdinates οf the twο pοints.
Nοne οf the οptiοns prοvided represents the distance fοrmula in its entirety. Hοwever, we can use οptiοn B as the first part οf the distance fοrmula, since it represents the absοlute value οf the difference between the x-cοοrdinates οf the twο pοints:
|2 - (-4)|
Simplifying this expressiοn gives:
|2 + 4|
|6|
Therefοre, the equatiοn we wοuld use tο find the distance between the twο pοints is:
d = √((x2 - x1)² + (y2 - y1)²) = √((2 - (-4))² + (y2 - y1)²) = √(6² + (y2 - y1)²) = √36 + (y2 - y1)²)
We still need tο determine the y-cοοrdinates οf the twο pοintstοο cοmplete the distance fοrmula.
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A, B & C form the vertices of a triangle. ∠
CAB = 90°,
∠
ABC = 57° and AC = 9. 2. Calculate the length of AB rounded to 3 SF
As per the given triangle, the length of AB rounded to 3 significant figures is 10.7 units.
We are given a triangle ABC with a right angle at A, i.e., CAB = 90°. Let AC be the side opposite to the right angle, and let AB be the hypotenuse. We are also given that ABC = 57° and AC = 9.2.
Using the trigonometric function, we can relate the angles and sides of a right-angled triangle. In particular, we can use the sine function to relate the angle opposite to a side and the hypotenuse. Thus, we have:
sin(ABC) = AC/AB
Substituting the given values, we get:
sin(57°) = 9.2/AB
Now, we can solve for AB by multiplying both sides by AB and dividing by sin(57°):
AB = 9.2/sin(57°)
Using a calculator, we get:
AB ≈ 10.692
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Pricing Math Quiz
QUESTION 4 of 10: You make a corn dip appetizer that feeds four. The key ingredients and prices are: corn $0.77, sour cream $0.96, cheese
$1.11, seasoning $0.44. What is the total food cost?
Answer:
13 dollars and 12 cents
Step-by-step explanation:
I added all of the ingredient prices in parenthesis then multiplies it by 4. :)
Mr. Moore has a rectangular prism shaped planter box to grow herbs inside his house. The dimensions of the planter box are 4. 5 feet long, 2 feet wide, and 1. 5 feet tall. How any cubic feet of soil does Mr. Moore need in order to fill the planter box
Mr. Moore needs 13.5 cubic feet of soil to fill the planter box.
To calculate the volume of the rectangular prism planter box, we need to multiply the length, width, and height of the box.
Volume = length x width x height
V = 4.5 ft x 2 ft x 1.5 ft
V = 13.5 cubic feet
Therefore, Mr. Moore needs 13.5 cubic feet of soil to fill the planter box.
It is important to note that the volume of the box represents the amount of space inside the box and does not take into account any obstructions or irregularities that may be present inside the box.
Thus, the actual amount of soil required may be slightly different from the calculated value. Additionally, it is always a good idea to add some extra soil to account for settling and to ensure that the planter box is completely filled.
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can yall help me with this this is due on Saturday pls help me!!!
Therefore , the solution of the given problem of fraction comes out to be Y is therefore equivalent to 26/5.
A fraction is what?Any combination of like-sized pieces or portions can represent a whole. Standard English defines "quantity" as "a portion" of a particular measure. 8, 3/4. Wholes also include fractions. In mathematics, numerals are expressed by the ratio of quotient to ratio. Every one of these fractions of integers are simple fractions. The fraction contains a fraction, but the fraction's remainder is a challenging fraction. because the values, 4.91, and numerators of real fractions can vary.
Here,
We can begin by isolating the variable with one side of the solution in order to solve for y. The reciprocal of fraction on the left side of the equation can be used to add both sides of the equation to achieve this:
=> 2/5 = (y - 4)/3
=> 3 * 2/5 = y - 4 [add 3 to both ends]
=> 6/5 = y - 4 [simplify]
=> y = 6/5 + 4 [Adjust both ends by 4]
=> y = 6/5 + 20/5 Using the denominator 5 as the corresponding fraction, write 4.
=> y = 26/5
Y is therefore equivalent to 26/5.
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For each ordered pair (x, y), determine whether it is a solution to the inequality y > 0.
(x,y)
(6, 38)
(-4, - 13)
(-1, 8)
(3, 26)
The ordered pairs (6, 38), (-1, 8), and (3, 26) are solutions to the inequality y > 0, while (-4, -13) is not a solution.
Define in short the solution to the inequality?An inequality is a mathematical statement that compares two values and shows the relationship between them using symbols like "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).
For the given ordered pairs:
(6, 38): The y-coordinate (38) is greater than 0, this ordered pair is a solution to the inequality y > 0.
(-4, -13): The y-coordinate (-13) is not greater than 0, this ordered pair is not a solution to the inequality y > 0.
(-1, 8): The y-coordinate (8) is greater than 0, this ordered pair is a solution to the inequality y > 0.
(3, 26): The y-coordinate (26) is greater than 0, this ordered pair is a solution to the inequality y > 0.
Therefore, the ordered pairs (6, 38), (-1, 8), and (3, 26) are solutions to the inequality y > 0, while (-4, -13) is not a solution.
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Factoring expressions completely 3cd^2+12cd+12c
Answer:
3c(d^2+4d+4)
Step-by-step explanation:
common factor is 3 and c
If a pair of opposite angles of a parallelogram are (3x+10)⁰and (4x_10)⁰,find the internal angles
Answer: In a parallelogram, opposite angles are equal, so we can set up the following equation:
3x + 10 = 180 - (4x + 10)
Simplifying and solving for x, we get:
3x + 10 = 170 - 4x
7x = 160
x = 20
Now we can substitute x = 20 into the expressions for the angles to find their values:
3x + 10 = 70 degrees
4x + 10 = 90 degrees
Since opposite angles in a parallelogram are equal, the other two angles must also be equal to these values. Therefore, the internal angles of the parallelogram are:
70 degrees, 70 degrees, 110 degrees, 110 degrees
Step-by-step explanation:
how do you delete your account?
Answer: go to your profile and you'll see the account or profile I
think, and you go to settings and it it will probably say something like delete the account or give you the choice to.
Step-by-step explanation:
Answer:
I think that you click on your profile picture, then go to your settings from there, and then you eventually find the cancel account or delete account choice.
Step-by-step explanation:
you do the above
The image shows a cone that has a base with area 36π square centimeters. The cone has been dilated using the top vertex as a center. The area of the dilated cone's base is 729π square centimeters.
What was the scale factor of the dilation?
The scale factor of the dilation of the vertices of the cone when dilated is 4.5
What was the scale factor of the dilation?The area of a circle is proportional to the square of its radius. Since the base of the cone is a circle
The ratio of the areas of the base of the dilated cone to the original cone is equal to the square of the scale factor.
Let the scale factor be k. Then, we have:
(area of dilated cone's base) / (area of original cone's base) = k²
(729π) / (36π) = k²
k² = 20.25
Taking the positive square root of both sides we get:
k = 4.5
Therefore, the scale factor of the dilation is 4.5.
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The insured value of a car is ¢10,500. Mr. Cudjo paid 8% of the insured value as premium in the first year. For the subsequent years
The answer of the given question based on the interest rate the answer is the premium paid for each subsequent year would be ¢840
What is Premium rate?A premium rate is price per unit of insurance coverage for specific risk that an insurer charges its policyholders. It is typically expressed as percentage of total insured value of policy.
To calculate the premium paid for subsequent years, we need to know what the premium rate is for those years. The premium rate may change from year to year depending on various factors such as the age of the car, the driver's record, etc.
Assuming the premium rate remains constant at 8% of the insured value for all subsequent years, we can calculate the premium paid for each year as follows:
First year: 8% of ¢10,500 = ¢840
Second year: 8% of ¢10,500 = ¢840
Third year: 8% of ¢10,500 = ¢840
And so on...
So the premium paid for each subsequent year would be ¢840 if the premium rate remains constant at 8% of the insured value.
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HELP PLEASE
NUMBER 18
Answer is (1,1)
i. The points of intesection of the common chords of the curve x² + y² = 4 and y² = 3x are
(1, √3) and (1,-√3)ii. The points of intesection of the common chords of the curve x² + y² = 4 and x² - 4y + 1 = 0 are
(√3, 1) and (-√3, 1)What are common chords of a circle?The common chords of circles are the chords that pass through the points of intersection of the curves.
i. Given the curve x² + y² = 4 and y² = 3x. We desire to find their points of intesection of the common chords. We proceeds as follows.
Since x² + y² = 4 and y² = 3x. Substituting the second equation into the first, we have
x² + y² = 4 and y² = 3x.
x² + 3x = 4
Re-arranging, we have
x² + 3x - 4 = 0
Factorizing the quadratic equation, we have
x² - x + 4x - 4 = 0
x(x - 1) + 4(x - 1) = 0
(x + 4)(x - 1) = 0
⇒ x + 4 = 0 and x - 1 = 0
⇒ x = - 4 and x = 1
Now, y² = 3x.
⇒ y = ±√3x
So.substituting x = -4 into the equation, we have
y = ±√3x
y = ±√(3 × -4)
= ±√(-12)
Since the square root is negative, this answer is invalid.
Substituting x = 1 into y, we have
y = ±√3x
y = ±√3(1)
y = ±√3
So, the points of intersection are (1, √3) and (1,-√3)
ii. Given the curve x² + y² = 4 and x² - 4y + 1 = 0. We desire to find their points of intesection of the common chords. We proceeds as follows.
Since x² + y² = 4 and x² - 4y + 1 = 0. From the second equation, we have
x² = 4y - 1
Substituting this equation into the first, we have
x² + y² = 4 and x² = 4y - 1
y² + 4y - 1 = 4
Re-arranging, we have
y² + 4y - 1 - 4 = 0
y² + 4y - 5 = 0
Factorizing the quadratic equation, we have
y² - y + 5x - 5 = 0
y(y - 1) + 5(y - 1) = 0
(y + 5)(y - 1) = 0
⇒ y + 5 = 0 and y - 1 = 0
⇒ y = - 5 and y = 1
Now, x² = 4y - 1
⇒ x = ±√(4y - 1)
So, substituting y = -5 into the equation, we have
x = ±√(4y - 1)
x = ±√[(4 × -5) - 1)]
= ±√(- 20 - 1)
= ±√-21
Since the square root is negative, this answer is invalid.
Substituting y = 1 into x, we have
x = ±√(4y - 1)
x = ±√(4(1) - 1)
x = ±√(4 - 1)
x = ±√3
So, the points of intersection are (√3, 1) and (-√3, 1)
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exercise 3.2.5: facts about power sets - true or false. help outline let x be a finite set. for each statement, indicate whether the statement is true or false, or whether more information about x is required to determine if the statement is true.
The given facts about power sets: Statement 1: False, Statement 2: True, Statement 3: True.
Statement 1: The power set of X is a subset of X. False. The power set of X, denoted by P(X), is a set containing all subsets of X. However, X is not a subset of P(X).
Statement 2: The cardinality of P(X) is greater than the cardinality of X. True. Since the power set of X contains all subsets of X, it has a higher cardinality than X. This can be proven with the equation |P(X)| = 2^|X|.
Statement 3: The cardinality of the power set of the empty set is 1. True. The empty set, denoted by Ø, has no elements, and therefore the power set of the empty set, P(Ø), has one element, which is the empty set itself. Therefore, |P(Ø)| = 1.
In conclusion, each statement is either true or false depending on the given information.
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