First make the graph of the functions, then if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.
Symmetric
A figure or shape that can be divided into two equal parts by a line is called symmetric figures.
Inverse Functions
The inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.
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A copy machine makes 32 coples per minute. How many copies does it make in 4 minutes and 15 seconds?
Answer:
136
Step-by-step explanation:
because 32 times 4 is 128 and 32 divided by 4 is 8 that together is 136 its dived by four because 15 is 1/4 of 60 which is an hour
Answer: 136 copies in 4 minutes and 15 seconds
Step-by-step explanation:
First, we need to find how many copies the machine makes per second
a minute has 60 seconds. Divide the number of copies made per minute by 60
32/60
simplify
8/15
It can make 8/15 copies per second.
It takes a minute to print 32 copies, so multiply the number of copies per minute by 4 minutes
32*4=128
128 copies in 4 minutes
now 8/15 * 15 =120/15 = 8
128+8=136
What is the integer between 1 to 100?
The number of intergers between 1 to 100 (i.e two integers) is equals to ninty-eight in count.
The integers are collection of all positive and negative whole numbers. The positive integers are represented by adding (+) symbol in front of number and negative integers by adding (-) sign.
To calculate the number of integers between two integer using the following concept , Subtract the integers of interest i.e, if we have to calculate integer between a to b and then( b-a) and then subtract one .
As a proof of concept, calculate the number of integers that fall between 5 and 10 on a number line. We know there are 4 (6, 7, 8, 9), 10−5−1=4.
We have, to calculate the integers between 1 to 100. Using the above concept, total number of intergers between 1 to 100 are 100 - 1 -1 = 98
Hence, the number of required integers are 98.
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eight identical machines produce the same parts at the same rate. the 8 machines complete the required number of parts in 6.5 hours. how many hours does is take 12 machines to produce the same number of parts?
It becomes
[tex]$$\begin{aligned}5: 8: & 6.5: x \\5 \times x & =8 \times 6.5 \\x & =\frac{8 \times 6.5}{5} \\x & =\frac{52}{5} \\x & =10.4\end{aligned}$$[/tex]
Therefore,
5 machines will take $10.4$ hour to produce the same number of parts.
What is equal rate?Equivalent interest rates are interest rates that produce the same future value after one year. For example, 10% compounded quarterly and 10.125% compounded semiannually are equivalent nominal interest rates. If you calculate the future value of $100 invested at either rate for one year, you will obtain $110.38.
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What is the quotient of x³ 3x² 3x 2 X² x 1 )?
To simplify the denominator, we can subtract the common terms - x² and x - leaving us with just x. We can then combine our simplifications to form the final answer of x + 2, then the quotient is x³ + 3x² + 3x + 2 / x² + x = x + 2
x³ + 3x² + 3x + 2
x² + x
Simplifying the numerator:
x³ + 2x² + 3x + 2 - x² - x = x² + 2x + 2
Simplifying the denominator:
x² + x - x = x
Final Answer:
x + 2
The expression x³ 3x² 3x 2 X² x 1 is a fraction, with the numerator being x³ 3x² 3x 2 and the denominator being X² x 1. To solve this expression, we need to simplify both the numerator and the denominator. To simplify the numerator, we can subtract the common terms - x² and x - leaving us with x² + 2x + 2. To simplify the denominator, we can subtract the common terms - x² and x - leaving us with just x. We can then combine our simplifications to form the final answer of x + 2.
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These are two separate questions
Answer:
Hi,
The first one is the second one, the one on the top right. This is because you add two branches every step.
I'm not so sure about the second question. sorry ! hope it helps tho
What is the value of the polynomial 4x² 7x 5 when x 3?
When X=3 a polynomial has a value of 61 and when X=3 a value of 143.
Given that,
Let p(x)=3x²−4x²+7x−5 is our polynomial.
Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.
Substitute x=3 in above expression,
∴p(3)=3(3) 3−4(3) 2 +7(3)−5
=3(27)−4(9)+21−5
=81−36+21−5
=61
Now,
p(−3)=3(−3)
3 −4(−3) 2 +7(−3)−5
=3(−27)−4(9)−21−5
=−81−36−21−5
=−143
So, value of polynomial when X=3 is 61 and when x=−3 is −143
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Plot the graph of y = x³ - 2x for -2 ≤ x ≤2 on the axes below.
y =
-2
3
-1
0
1
2
The value of y are when x = -2, -1, 0, 1, 2 are -4, 1, 0, -1, 4. The graph of the function attached.
What is coordinate plane?
A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.
Given function is y = x³ - 2x
Putting x = -2 in the equation y = x³ - 2x:
y = (-2)³ - 2×(-2)
y = -4
Putting x = -1 in the equation y = x³ - 2x:
y = (-1)³ - 2×(-1)
y = 1
Putting x = 0 in the equation y = x³ - 2x:
y = (0)³ - 2×(0)
y = 0
Putting x = 1 in the equation y = x³ - 2x:
y = (1)³ - 2×(1)
y = -1
Putting x = 2 in the equation y = x³ - 2x:
y = (2)³ - 2×(2)
y = 4
The points on the equations are (-2,-4), (-1, 1), (0,0), (1,-1), (-2,4).
Plot the points and joint them by curve.
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How does performing a rigid motion transformation help you prove congruence?
Only if two figures can be precisely mapped to one another using transformations are two figures said to be congruent.
What is congruence?
A "matching" figure is one that can be placed perfectly on another. The bread has the same size and form when it is stacked. Match refers to objects that are precisely the same size and form. If one of two geometric figures can be consistently overlaid on the other, they are said to be congruent or to be in a congruent relationship.
Only if two figures can be precisely mapped to one another using transformations are two figures said to be congruent. Due to the stiff transformations' preservation of the distance and angle scales, all related sides and angles are congruent.
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Which equation represents the same relationship
Answer:
The linear function which is passing through the points (-20, -268) and (-1, -40) is y + 268 = 12(x + 20). Then the correct option is C.
What is the linear system?
A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
The table represents some points on the graph of a linear function.
Let the linear relationship is given below.
Is 12 a prime number yes or no?
Answer:
12 is not a prime number.
Step-by-step explanation:
⭐What is a prime number?
A prime number is a real number that is only divisible by 1 and itself12 is not a prime number because it is divisible by numbers other than 1 and itself, such as...
2346What is the surface area of a 4 in cube?
On solving the provided question, we can say that, A 4 cm Cube has a 96 cm2 total surface area.
what is total surface area of cube ?Total surface area is the total area, which includes the curved portion and any bases. It refers to the entire surface area of the thing. The total area will be the sum of the two areas if the shape has a curved base and surface.
The cube's surface area is calculated as six times the square of its side lengths. 6a2, where an is the cube's side length, serves as its representation. Basically, it refers to the overall surface area.
total surface area of a cube of 4 cm is 96 cm2
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What is the equation of the line that passes through the point (-6, 3) and has a slope of 4
Are all equilateral triangles isosceles as well?
Find the value of x or y so that the line passing through the two points has the given slope
16. (-3, y), (-9, -2); m = 1
Answer:
(-3, -2)
Step-by-step explanation:
To find the value of y so that the line passing through the two given points has a slope of 1, we can use the formula for the slope of a line, which is given by:
m = (y2 - y1) / (x2 - x1)
In this case, we know that the slope of the line is 1, so we can set up the equation:
1 = (y - (-2)) / (-9 - (-3))
Solving for y, we get:
1 = (y + 2) / 6
Therefore, y = 1 * 6 - 2 = 4, so the value of y that we are looking for is 4.
Alternatively, we can use the two given points to write the equation of the line in slope-intercept form, which is given by:
y = mx + b
In this case, we know that the slope of the line is 1, so we can write the equation as:
y = x + b
We also know the coordinates of one of the points on the line, (-3, y), so we can substitute these values into the equation to solve for b:
y = (-3) + b
Substituting the value of y that we found earlier, 4, we get:
4 = (-3) + b
Solving for b, we get:
b = 4 + 3 = 7
Therefore, the equation of the line that passes through the two given points and has a slope of 1 is y = x + 7. This equation is in slope-intercept form, so it shows us the value of y when x is 0, which is 7. Since the y-coordinate of one of the given points is -2, we know that this point must be (-3, -2), and we can verify that this point satisfies the equation y = x + 7.
Does (3, 1) make the equation y = x true?
Answer:
no
Step-by-step explanation:
x=3, y=1
3≠1
therefore x≠y
How many times can you claim SSS sickness benefit?
In a given year, a member may get illness benefits for a maximum of 120 days. The total number of permitted compensable days for the next year cannot be increased by any unused fraction being carried forward. For the same condition, the sickness benefit cannot be awarded for more than 240 days.
A daily cash payment is made for each day a member is unable to work as a result of illness or accident.
Qualification Requirements
If a member meets the following criteria, they may be eligible to receive this benefit: Is unable to work due to illness or injury and is confined to a hospital or their home for a minimum of four (4) days;
Has duly notified the SSS directly of the fact of sickness or injury;
Has paid at least three (3) months' worth of payments within the 12-month period immediately preceding the semester of illness or injury.
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Natalie works in a toy shop and earns $43 per day. She earns an extra $3 for each toy she sells. If Natalie wants to earn at least $70 per day, which inequality shows the minimum number of toys, n, that she should sell?
43 + 3n ≥ 70, so n ≥ 9
43 + 3n ≤ 70, so n ≤ 9
43 + 3n ≥ 70, so n ≥ 24
43 + 3n ≤ 70, so n ≤ 24
Answer:
Hello! Natalie earns a fixed amount of $43 per day. She earns $3 more every toy she sells. Basically, you can set up this equation as 43 + 3n >= 70. This is because she wants to make a least $70 and earns $3 each for "n" toys that she sells. When you solve the inequality, the answer is 9. Subtract 43 from both sides to get 3n >= 37 and divide by 3 to get n >= 9. The answer is A.
Step-by-step explanation:
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How many solutions does the pair of equations 3x 2y 5 2x 3y 7 have?
The pair of linear equations 3x+2y= 5 and 2x-3y= 7 have one unique solution.
The number of solutions for a pair of equations can be determined by looking at the coefficients of the variables in the equations. In particular, the number of solutions will depend on whether the coefficients of the variables are the same or different.
In this case, the pair of equations 3x+2y= 5 and 2x-3y= 7 have different coefficients for the variables x and y. Specifically, the coefficient of x is 3 in the first equation and 2 in the second equation, and the coefficient of y is 2 in the first equation and -3 in the second equation.
When the coefficients of the variables are different, there is exactly ONE solution to the system of equations. This is because the two equations will intersect at a single point in the x-y plane, which is the solution to the system of equations.
Therefore, based on the coefficients of the variables in the equations 3x+2y= 5 and 2x-3y= 7, we can conclude that there is only ONE solution to this system of equations.
--The question is incomplete, answering to the question below--
"How many solutions does the pair of equations 3x+2y= 5 and 2x-3y= 7 have?"
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If 5 and (7+ square root 2) are roots of a polynomial with integer coefficients, what must be another root?
Answer:
x = 7 - [tex]\sqrt{2}[/tex]
Step-by-step explanation:
note that roots of the form x = a + b[tex]\sqrt{c}[/tex] occur in conjugate pairs, that is
x = a - b[tex]\sqrt{c}[/tex]
given x = 7 + [tex]\sqrt{2}[/tex] is a root then x = 7 - [tex]\sqrt{2}[/tex] is the other root
Letr = (7, 1) and s= (-12, -3). What is r-s?
Answer: (19,4)
Step-by-step explanation:
Subtract the x axis with the x axis and y with y.
So,
7-(-12)= 19
1-(-3)= 4
What is the measure of angle LMN?
According to the given figure, we can conclude that ∠LMN is 90° in the given triangle LMN.
What is a right triangle?A right triangle is a triangle having one right angle or two perpendicular sides.
It is also referred to as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or originally rectangle triangle.
The relationship between the sides and various angles of the right triangle serves as the basis for trigonometry.
The hypotenuse of a right triangle is its longest side; its "opposite" side is the one that faces the angle in question, and its "adjacent" side is the one that faces it.
We use special terminology to define the sides of right triangles.
The hypotenuse of a right triangle is always the side across from the right angle.
Therefore, according to the given figure, we can conclude that ∠LMN is 90° in the given triangle LMN.
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5* Le terrain de M. Campo mesure 1250 m².
C'est 450 m² de plus que celui de M. Vergne.
Quelle est la superficie du terrain de
M. Vergne ?
Answer:
800 m^2
Step-by-step explanation:
= 1250 - 450
= 800 m^2 est la superficie de la terre de M. Vergne
j'espère que ma réponse t'aidera.
Suppose you invested $1200 for four years. You earned $312 in simple
interest. What is the interest rate?
Answer: 6.5%
Step-by-step explanation: 312/4 = 78
78/1200 = 0.065
0.065 x 100 = 6.5%
Justine just ran her first race. Her distance from the finish line decreased as she ran.
This situation can be modeled as a linear relationship.
What does the y-intercept of the line tell you about the situation?
A. justine finished the race in 40 minutes
B. when justine started the race she was 10 kilometers from the finish line
C. after running for 20 minutes justine was 6 kilometers from the finish line
D. justine ran 4 kilometers every 20 minutes
Choices B and C are both correct statements.
Choices A and D are both false.
The y-intercept of the line tells us about the situation when Justine started the race she was 10 kilometers from the finish line.
What are y-intercept and x-intercept?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
Given, a line whose y-intercept is at y = 10 which is represented by the distance remaining in kilometers. Since x shows the time spent running that means at x = 0 she started running.
Therefore, The y-intercept of the line reveals that Justine was 10 kilometers from the finish line when she started the race.
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PLS HELP WHO EVER ANSWERD FIRST WILL GET THE BRAINLIEST PLS
Leo is a salesperson. Let y represent her total pay (in dollars). Let x represent the number of items she sells. Suppose that x and y are related by the equation y=32x+1900.
What is Leo's total pay if she doesn’t sell any items?
A. $19
B. $3,200
C. $32
D. $1,900
Explain your work pls
By using Linear equation, it can be calculated that
Leo's total pay if she doesn’t sell any items = $1900
Option D is correct.
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Let y represent Leo's total pay (in dollars).
Let x represent the number of items she sells
x and y are related by the equation y=32x+1900.
If Leo does not sell any item, x = 0
y = 32 [tex]\times[/tex] 0 +1900
y = $1900
Leo's total pay if she doesn’t sell any items = $1900
Option D is correct.
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A tank containing 100 gallons of brine made by dissolving 6 pounds of salt in water. Salt water containing one (1) pound of salt per gallon runs in at the rate of 2 gallons per minute. A well stirred mixture runs out at the rate of 2 gallons per minute. Find the amount of salt in the tank at the end of one hour.
The amount of salt in the tank at the end of one hour is 103 lbs .
Given
Initially there are 100 gal in the tank. There are 6 lbs of salt. The concentration of salt in the tank is 6/100 or 0.06 lbs per gal.
Water flowing in has concentration of 1 lb/gal.
Water flowing out has unknown concentration because mixture is constantly changing.
Tank is losing 1 gal per minute. ( 2 - 2 = 0 )
V ( t ) = 100 - t
s ( t ) = 6 + 2t − 3t ∗ C( t )
C ( t ) = s ( t ) / V ( t )
= 100 - t / 2t − 2t ∗ C( t )
= 6 + 2t / 100 + 2t
After 60 minutes
C ( t ) = 6 + 2 * 60 / 100 + 2 * 60
= 6 + 120 / 100 + 120
= 126 / 220
= 63 / 110
Salt content s( t ) = 6 + 2 * 60 - 3 * 60 * 63 / 110
= 126 - 180 * 63 / 110
= 126 - 103
= 103 lbs
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How to find x+y?
(Explain pls, thank you!
The correct option is A)289
What is a polynomial?A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division. For example 3x+2x-5
Given here, x²+74x+2021=y²
x²+2×37x + 37² = y²-652
(x+37)²= y²-652
(x+37)²- y² = -652
(x+y+37) (x-y+37) = 289 × -2
thus, x+y+37 = 289 . . . .(1)
x-y+37 = -2 . , . . . . .(2)
Solving the two equations we get x = 125 & y=164
Thus x+y = 125+164
= 289
Hence option A) is the correct answer
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the volume of the cone in 270 pi
Answer:
[tex] \displaystyle{\frac{2810}{3}} \pi \: \: \text{cm} ^{3} [/tex]
Step-by-step explanation:
The solid shape is composed of a cone and a hemisphere.
Let's work out the radius of the cone since the hemisphere and the cone share the same radius.
Let the radius be r cm.
Volume of cone= [tex] \displaystyle{\frac{1}{3} \pi {r}^{2} h}[/tex]
Substituting the volume and height of the cone:
[tex]270\pi = \displaystyle{\frac{1}{3} (\pi)( {r}^{2} )(10)}[/tex]
Simplify:
[tex] \frac{10}{3} {r}^{2} = 270[/tex]
[tex]81 = {r}^{2} [/tex]
Square root both sides:
[tex]r = \sqrt{81} [/tex]
r= 9
The volume of a hemisphere is half the volume of a sphere.
Volume of hemisphere
[tex] = \displaystyle{ \frac{1}{2}( \frac{4}{3} )(\pi )( {r}^{3}) }[/tex]
[tex] = \displaystyle{ \frac{2}{3}\pi {r}^{3} }[/tex]
Substituting the value of r:
Volume of hemisphere
[tex] = \displaystyle{ \frac{2}{3} (\pi)(10^{3} )}[/tex]
[tex] = \displaystyle{ \frac{2}{3}(1000)(\pi) }[/tex]
[tex] = \displaystyle{\frac{2000}{3} \pi}[/tex]
Volume of the shape
= volume of cone + volume of hemisphere
[tex] = \displaystyle{(270 + \frac{2000}{3} })\pi[/tex]
[tex] = \displaystyle{ \frac{2810}{3} \pi} \: \: \text{{cm}}^{3} [/tex]
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Which of the following is the value of the discriminant for 2x² 5x 7 0?
The value of the discriminant for 2x² + 5x + 7 = 0 is -31.
The discriminant of a quadratic equation is the part of the equation used to determine the number and type of solutions. It is calculated by subtracting 4 times the coefficient of the squared term, a, from the coefficient of the linear term, b, squared. This is then divided by four times the coefficient of the squared term, a.
In this case, the equation is 2x² + 5x + 7 = 0.
The discriminant for this equation is calculated as follows:
Discriminant = b² - 4ac
Discriminant = (5)² - 4(2)(7)
Discriminant = 25 - 56
Discriminant = -31
Therefore, the value of the discriminant for 2x² + 5x + 7 = 0 is -31.
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Is zero a real number in math?
Answer:
Zero is a real number in math
Step-by-step explanation:
Zero is considered to be both a real and an imaginary number.