The domain and scope of the identity function are the same. Equation for the identity function is f(x) = x, or y = x.
What is function?An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.
identity function are the same.
Equation for the identity function is
f(x) = x, or y = x.
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On solving the provided question, we can say that by unitary method Irene spend on gas = $ 33.82
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
by unitary method
Irene must pay back the money she used for gas.
Irene filled up her tank with gas for $33.82.
One gallon of gasoline costs $3.80.
There are 6.1 gallons of the petrol Irene purchased in the tank.
amount required = 15 -6.1 = 8.9 gallons
1 gallon = 3.8 dollars
8.9 gallons = $ 33.82
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Pressure =
force/area
A force of 70 newtons acts on an area of 20 cm?
berabils HBO
The force is increased by 10 newtons,
The area is increased by 10 cm?
Helen says,
"The pressure decreases by less than 20%"
Is Helen correct?
You must show how you get your answer.
Helen is not correct. The pressure decreases by 23.8% and not less than 20%.
Pressure = force/area
The initial pressure is 70 N / 0.2 m^2 = 350 Pa (Pascals). If the force is increased by 10 N and the area is increased by 10 cm^2, the new pressure is 80 N / 0.3 m^2 = 266.67 Pa
The difference in pressure between the initial and final states is 83.33 Pa (350 Pa - 266.67 Pa)To calculate the percentage change in pressure, we divide the change in pressure by the initial pressure and multiply by 100:
(83.33 Pa / 350 Pa) * 100% = 23.8%So Helen is not correct. The pressure decreases by 23.8% and not less than 20%.
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What is the slope of 5x 2y =- 3?
The slope of 5x 2y =- 3 is -5/2.
To find the slope of the equation 5x 2y =- 3, we need to rearrange it into the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).
We start by rearranging the equation 5x 2y = -3 so that all the terms with y are on one side and all the terms with x are on the other side.
5x -2y = -3
Now, we divide both sides by -2 to isolate y.
-5x/2 = y + 3/2
Finally, we subtract 3/2 from both sides to get the equation in the slope-intercept form.
-5x/2 = y - 3/2
Therefore, the slope of the equation 5x 2y = -3 is -5/2.
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Big orange trucking is designing an information system for use in "in-cab" communications. It must summarize data from eight sites throughout a region to describe typical conditions. Compute an appropriate measure of central location for the variables wind direction, temperature, and pavement
Wind direction [Mode] is South west
The [Mean] temperature is
The [Bimodal] pavement is Dry Wet
From the question the first question is to determine the wind direction
Generally from the wind direction would be the data with the highest frequency on the wind column i.e the mode of the data, this because this variable(wind direction ) is a nominal level type of level of measurement where the value assigned to the variable are for classification of the data (i.e telling what the data is all about )
So
The mode is Southwest
This means that the wind direction is Southwest
From the question second question is to determine the temperature
Generally given that their are are no outlier that will skew the data we can obtain the temperature by calculating the mean for the temperature column
This is mathematically represented as
T = 89+86+....+93+93/8
T = 91
From the question, the first question is to determine the pavement
Generally from the pavement would be the data with the highest frequency on the pavement i.e the mode of the data, this because this variable(pavement ) is a nominal level type of level of measurement where the value assigned to the variable are for classification of the data (i.e telling what the data is all about )
From the table we see that the pavement that the pavement column is bimodal
So the mode is Dry Wet
This mean that the pavement is Dry Wet
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The table below shows the number of animals at a local petting zoo.
Animal
Goats
Number
3
Ponies
3
Rabbits
8
Sheep
6
0/1
Write the ratio of ponies and goats to rabbits and
sheep.
You may write the ratio in ANY of the three forms. Remember to REDUCE the ratio, if
possible.
Answer:
3/7
Step-by-step explanation:
3 ponies + 3 goats = 6 total
8 rabbit + 6 sheep = 14 total
6/14 simplified is 3/7.
96 - y = 161 solve for y
Answer: -65
Step-by-step explanation:
96 - y = 161
-y = 161 - 96
-y = 65
y = -65
What is the mole of H2?
One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.
What is mole?A mole is a unit of measurement in chemistry that expresses the amount of a substance. It is defined as the number of entities (such as atoms, ions, or molecules) in a sample of the substance. The number of entities in one mole of a substance is known as Avogadro's number.
What is Avogadro's number?Avogadro's number is a fundamental constant of physics and chemistry, defined as the number of atoms, ions or molecules in one mole of substance. It is approximately 6.022 x 10^23 and is used in many calculations in chemistry and physics, such as the number of atoms in a sample of an element, the number of ions in a salt, or the number of molecules in a gas sample. The constant is named after Amedeo Avogadro, an Italian scientist who first proposed the concept in 1811.
One mole of a substance is equal to Avogadro's number, which is approximately 6.022 x 10^23.
The mole of H2 (hydrogen gas) is the number of H2 molecules in a sample of hydrogen gas. One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.
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What is the equation of the parabola opening upward with a focus at (9,27) and a directrix of y =11
A. F(x) = 1/16(x-9)^2 + 19
B. F(x) = 1/16(x+9)^2 -19
C. F(x) = 1/32(x+9)^2 -19
D. F(x) = 1/32(x-9)^2 + 19
The condition of the parabola opening upward with a center at and a directrix will be f(x) = 1/32(x - 9)^2 + 19. so alternative D option correct.
What is the equation of the parabola?
The equation can be written as
f(x) = 1/(4p)(x -h)^2 +(k-p)
where (h, k) is the focus, and p is half the distance between focus and directrix.
Here, We have the upward parabola;
Focus at (9,27)
P/2 = 27-19 = 8 Nature of focus
P = 16
so (x-9)^2 = 2py = 32y
y = 1/32(x-9)^2 + 19
The condition of the parabola opening upward with a center at and a directrix will be f(x) = 1/32(x - 9)^2 + 19. so alternative D option correct.
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15) 3x2 - x - 10 When this trinomial is factored completely, one of its factors is A) x 2 B) x - 5 C) 3x 5 D) 3x - 2
When the trinomial 3x² - x - 10 is factored completely, one of its factors is 3x+5.
Solving the given trinomial 3x² - x - 10.
=>3x² - 6x+5x - 10
=>3x(x-2)+5(x-2)
=>(3x+5)(x-2)
The two factors of the given trinomial 3x² - x - 10 is (3x+5) and (x-2), but according to the given options, the correct answer is option C - 3x+5.
Thus, When the trinomial 3x² - x - 10 is factored completely, one of its factors is 3x+5.
Complete question: 3x² - x - 10
When this trinomial is factored completely, one of its factors is
A) x + 2
B) x - 5
C) 3x + 5
D) 3x - 2
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The table shows information about the masses of some dogs.
a) Work out the minimum number of dogs that could have a mass of more than
27 kg
b) Work out the maximum number of dogs that could have a mass of more than
27 kg
a) The minimum number of dogs that could have a mass of more than 27 kg is 6.
b) The maximum number of dogs that could have a mass of more than 27 kg is 18.
We have a table which shows information about the masses of some dogs.
Now , we need to determine the minimum number of dogs could have a mass more than 27 kg . Let us see dogs with mass of more than 27 kg present in the following intervals , 20≤x<30 and 30≤x<40 with 12 and 6 respectively.
But we wants minimum of 12 and 6 is 6 .
so, the minimum number of dogs with mass more than 27 kg is 6.
b) We need to determine maximum number of dogs with mass more than 27 kg ,so Maximum is equals to sum of number of dogs present in interval 20≤x<30 and in interval 30≤x<40 = 12+6 = 18. So, required maximum number of dogs are 18.
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Complete question:
The above table shows information about the masses of some dogs.
a) Work out the minimum number of dogs that could have a mass of more than 27 kg
b) Work out the maximum number of dogs that could have a mass of more than 27 kg
two families with four people in each family go to a movie theater. in how many ways can they be seated
According to probability, if both families want to sit together, they can be seated in a row a maximum of two times.
What seating configuration?The direction that each person is facing is crucial when arranging the people.
In order to determine how many ways they can be seated in a row if both families want to sit together, imagine that two families with four members each attend a movie theatre.
Given that the arrangement is important, we will apply the permutation rule. We'll divide the remaining four into two groups of four each.
There are two different ways to arrange the groups so they can sit together.
2! = 2 * 1
2! = 2ways
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What is an example of an absolute value equation?
The absolute value of a given number is said to be the positive version of that number. For example, the absolute value of -5 is + 5, which can be written as: − I5 | = 5. Other examples of absolute values of numbers: |−9| = 9, |0| = 0, − |−12| = −12, etc.
Absolute Value Equation:
An absolute value function is an algebraic function whose variables lie within the absolute value bar. This function is also called the modulus function, and the most commonly used form of the absolute value function is f(x) = |x|, where x is a real number. In general, the absolute value function can be expressed as f(x) = a |x - h| + k, where a represents how much the graph stretches vertically, h represents the horizontal shift, and k represents the vertical shift of the graph for f(x) = |x|. represents If the value of 'a' is negative, the chart opens downwards, if positive, the chart opens upwards.
Now that we understand the meaning of the absolute value function, we understand the meaning of the absolute value equation f(x) = a |x - h|. + k and how the values of a, h, and k affect the value of the function.
'a' value determines how the graph of f(x) is stretched vertically.'h' value specifies horizontal displacement'k' value specifies the vertical displacementThe vertex (x) = a |x - h| + k of the absolute expression f is given by (h, k). You can also use the vertices of f(x) = a |x - h| Find + k using the formula (x - h) = 0 . When determining the value of x, substitute that value into the formula to find the value of k.
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find the value of 15/4 divided 5/8.show you reasong
[tex]\dfrac{15}{4} \div\dfrac{5}{8}[/tex]
In order to divide two fractions, you will need to use the KCF method.
Keep
Change
Flip
This means that we will keep the first fraction, change the division to multiplication, and flip the second fraction(reciprocal).
[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]
Multiply:
[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]
[tex]\dfrac{15\times8}{4\times5}[/tex]
[tex]=\dfrac{120}{20}[/tex]
Simplify:
[tex]120\div20[/tex]
[tex]=\fbox{6}[/tex]
Answer: 6
Step-by-step explanation:
1. 15/4 divided by 5/8 = 120/20
15/4 / 5/8 = 15/4 times 8/5 = 15 time 8 over 4 time 5 = 120/20
2. 120/6 = 6
HELP THIS IS MY LAST PROBLEM
The percentage markup the store made before selling those speakers
are 136.33%.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, A store bought a set of speakers for $82.86 and sold them for
$195.82.
So, The amount of profit is $(195.82 - 82.86).
= $112.96.
Now, The markup percentage can be obtained by the concept of the percentage change.
Now to obtain percentage change we'll divide the net amount change by the original amount and multiply it by 100% which is,
= (112.96/82.86)×100%.
= 136.33%.
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Choose two statements that are true for this expression.
6x3 -8x^2- 40/y+21
Observing the given equation, The answer is The degree of polynomial is 3 and the equation has variables 'x' and 'y'.
What do you mean by equation?An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two expressions separated by an equals sign (=), for example, 2 + 2 = 4. Equations can be used to express relationships between different quantities and can be used to solve problems in many areas of mathematics and science. Equations can also be represented graphically, and they can be manipulated or transformed to make solving them easier.
What is degree of polynomials?A polynomial is a mathematical expression that is made up of a sum of powers in one or more variables. The degree of a polynomial is the highest power of the variable(s) present in the polynomial. For example, in the polynomial expression 3x^2 + 2x - 5, the highest power of x is 2, so the degree of the polynomial is 2. A degree 0 polynomial is a constant polynomial, which is just a number. The degree 1 polynomial is a linear equation, and degree 2 polynomial is a quadratic equation. In general, the degree of a polynomial can give an idea about the behavior of the polynomial function. As the degree of a polynomial increase, the shape of the function become more complex.
[tex]6x^3 - 8x^2 -\frac {40}{y} +21[/tex]
The degree of polynomial is 3.
The equation has variable 'x' and 'y' .
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Kayden has 50 m of railing.
How much more railing does Kayden need
so that he can put railing all the way around
the roof garden?
12 m
3 m
7m
10 m
20 m
10 m
Not drawn accurately
Answer: Kayden needs 12 more meters of railing.
Step-by-step explanation:
To find the perimeter of the roof garden I added up all the numbers you listed (12m+3m+7m+10m+20m+10m) to get a total perimeter of 62 meters.
Since Kayden already has 50 meters of railing we can subtract that from the total he needs to get the remaining amount needed.
62m - 50m = 12 meters of railing remaining.
I really need an answer for this FAST so if anybody can answer id really appreciate it :)
both Square and Rectangle
because all squares are rectangles, but not all rectangles are squares. Hope this helps. :)
Solve the equation 2^x=1/32•x=
Answer:
2^x=1
x=0
32•x=0
32.0=0
maybe
3x + 2y = 5
x = 2y + 7
Answer:
I hope this helps you...
please mark me as brainliest..
Susan has a rectangle and a right triangle.
• The length of the rectangle is 4 more than its width, w.
.
• The length of the shorter leg of the triangle is equal to the rectangle's
width.
• The length of the longer leg of the triangle is twice the length of the
rectangle.
Answer:
A. 2w² + 8w
Step-by-step explanation:
rectangle: A = w(w+4) = w² + 4w
triangle: A = 1/2(2(w+4)(w)) = 1/2(2w+8)(w) = 1/2(2w²+8w) = w² + 4w
Total Area = w² + 4w + w² + 4w = 2w² + 8w
What is the third side of a triangle calculator?
The third side of a triangle can be calculated using the Pythagorean Theorem.
This theorem states that in a right triangle, the sum of the squares of the two sides is equal to the square of the hypotenuse. The hypotenuse is the longest side of the triangle and is opposite the right angle.
Formula:
[tex]a^2 + b^2 = c^2[/tex]
Determine the two side lengths of the triangle
Calculate the sum of the squares of the two side lengths.
Calculate the square root of the sum of the squares of the two side lengths. This is the length of the third side (the hypotenuse).
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Circles centered at $A$ and $B$ each have radius 2, as shown. Point $O$ is the midpoint of $\overline{AB}$, and $OA
The distance between the two circles is 5.
The distance between two circles is the difference between the sum of their radii and the distance between their centers. In the given diagram, the radius of the circles centered at $A$ and $B$ is 2, and the distance between their centers is the length of $\overline{AB}$, which is 5. Therefore, the distance between the two circles is 5 - (2 + 2) = 5.
The distance between the two circles is 5.
The distance between two circles is the difference between the sum of their radii and the distance between their centers.
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which of the following phrases translate to the expression y+7 ?
The required phrase to translate the expression x + 7 is, A number increases by 7 or an Addition of number and 7.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Given expression x + 7,
The expression can be translated as a number increase by 7 or the Addition of the number and 7.
Thus. the required phrase to translate the expression x + 7 is, A number increases by 7 or an Addition of number and 7.
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Please help I have a learning disability and need help with this.
Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why.
( 3 6) 9 and 3 (6 9)
yes, it uses the Associative Property
yes, it uses the Commutative Property
yes, it uses the Identity Property
no they are not equivalent
Answer:
No, they are not equivalent.
Step-by-step explanation:
The first expression, (3 6) 9, is equal to 9, while the second expression, 3 (6 9), is equal to 3. The two expressions are not equivalent because they do not produce the same result when the operations are carried out. The properties of associativity, commutativity, and identity do not apply to these expressions.
Answer:
no they are not equivalent
Step-by-step explanation:
The two expressions are not equivalent. This is because the distributive property does not apply in this case, as the parentheses on the left side of the expression have precedence over the parentheses on the right side. Therefore, the expression on the left side would be evaluated first, resulting in a different answer than the expression on the right side.
A bacteria population has been doubling each day for the last 5 days. It is currently 100,000. What was the bacterial population 5 days ago?
It becomes apparent that the initial population (or the population 5 days ago) is 3125 bacteria.
Logarithms arise in problems of exponential growth
and decay because they are inverses of exponential functions. Because of the Laws of Logarithms, they also turn out to be useful in the measurement of the loudness of sounds, the intensity of earthquakes, and other processes that occur in nature
We can write an exponential function to represent the situation.
We know that the current population is 100,000.
The population doubles each day.
The standard exponential function is given by P(t) = A (2)^t
Since our current population is 100,000, a = 100000.
Since our rate is doubling, r = 2.
So
P(t) = 100000 (2)^t
We want to find the population five days ago.
So, we can say that t = -5. The negative represent the number of days that has passed.
Therefore
P(-5) = 100000 (2)^-5 =100000*(1/32) =3125
However, we dealing within this context, we really can't have negative days. Although it works in this case, it can cause some confusion. So, let's write a function based on the original population.
We know that the bacterial population had been doubling for 5 days. Let A represent the initial population. So, our function is:
P(t) = A (2)^t
After 5 days, we reach the 100,000 population. So, when t = 5, P(t) = 100000:
100000 =A[tex]2^5[/tex]
And solving for A, we acquire :[tex]\frac{100000}{2^5}[/tex]
=3125
So, our function in terms of the original day is:
P(t) = 3125 (2)^t
So, it becomes apparent that the initial population (or the population 5 days ago) is 3125 bacteria.
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What is 2(−2x+1)−5x+2= -23
Answer:
Step-by-step explanation:
To solve this equation, you will need to manipulate the equation in order to isolate the variable x on one side of the equation. Here is one way you could solve this equation:
Begin by distributing the 2 on the left side of the equation: 2(-2x+1) = -46 + 2x.
Next, distribute the -5 on the right side of the equation: 2(-2x+1) = -23 - 5x.
Combine like terms on the right side of the equation: 2(-2x+1) = -5x - 23.
Combine like terms on the left side of the equation: -4x + 2 = -5x - 23.
Add 4x to both sides of the equation to isolate the variable on one side: 2 = -x - 23.
Add 23 to both sides of the equation: 25 = -x.
Finally, divide both sides of the equation by -1 to solve for x: x = -25.
Therefore, the solution to the equation is x = -25.
Answer:
x=3
Step-by-step explanation:
2(−2x+1)−5x+2= -23
Distribute
-4x+2-5x+2=-23
Combine like terms
-9x+4=-23
Subtract both sides by 4
-9x=-27
Divide both sides by -9
x=3
Hope this helps :)
A car's value is $9,800.A sales person receives 5% commission if he
sells the car. How much would he obtain in commission from the sale of
that car.
The commission the salesperson would receive is $490.
What is a commission?
A commission is a payment made to an individual, such as a salesperson or agent, for services rendered or a good sold. The commission is typically a percentage of the sale or revenue generated. This percentage is known as the commission rate.
To find the commission a salesperson would receive from selling a car, we need to multiply the commission rate (5%) by the car's value ($9,800).
The commission rate is given as a percentage, so we need to convert it to a decimal to do the calculation. We can do this by dividing the percentage by 100.
So 5% = 5/100 = 0.05
Then to find the commission the salesperson would receive we multiply:
Commission = 0.05 * $9,800
Commission = $490
Hence, the commission the salesperson would receive is $490.
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Analyze and Persevere
Javi is building
a birdhouse. Each of the four walls of the
birdhouse needs to be 5.5 inches long.
Javi has a piece of board that is 24.5 inches
long. Is the board long enough to be
cut into the four walls of the birdhouse?
Estimate using compatible numbers.
Answer:
yes, the board is long enough
Step-by-step explanation:
5.5 in x 4 walls = 22 inches
The board is 24.5 in, so there is enough.
24.5 > 22, there is an extra 2.5 in left over.
the graph shows the total weight of abox of cereal, y, as a function of the amount of cereal in the box, x. what is the weight of the box when it is empty?
Answer:
3
Step-by-step explanation:
Central Park in New York City is rectangular with a length of 2.5 miles and a width of 0.5 mile. During an afternoon, its population density is about 15 people per acre. Find the number of people in the park that afternoon. One acre is equal to 1640 square mile.
On solving the provided question, we can say that Surface Area of central park = 2.5 × 0.5 = 1.25 square mile
what is surface area ?An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).
Surface Area of central park = 2.5 × 0.5 = 1.25 square mile
1 acre = 1/640 square mile
1.25 square mile = 1.25 ÷ 1/640 = 800 acre
Number of people in the park = 800 ÷ 15 = 53.3 ≈ 53 people
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how many integer between 20 and 40 divisable by 3
Answer:
4 prime numbers all divisible by 3
Step-by-step explanation:
there are 4 prime numbers between 20 and 40 23, 29, 31, 37 all divisible by 3
Answer:
7 integers
Step-by-step explanation:
We can find how many integers between 20 and 40 are divisible by 3 by looking at the multiples of 3 that lie between 20 and 40.
1: 3 * 7 = 21
2: 3 * 8 =24
3: 3 * 9 = 27
4: 3 * 10 = 30
5: 3 * 11 = 33
6: 3 * 12 = 36
7: 3 * 13 = 39