The two variables involved in the graph are: input variable (x - value) and output variable (y- value)
We know that many types of problems require two variables at the same time. such relation can be described algebraically by a two variable function or equation.
To represent such function graphically we use two perpendicular lines called axes and their point of intersection is called as the origin. This method of representation is known as the Cartesian coordinate system. The numerical value of one variable is measured along the horizontal axis called the x axis. Whereas the numerical value of the other variable is measured along the vertical axis called the y axis.
The four sections formed due to these axex are called quadrants.
Therefore, the two variables involved in the graph are input variable which measured along x-axis and output variable which measured along y-axis.
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What is the slope of a line perpendicular to 3x?
The slope of a line perpendicular to 3x is [tex]-\frac{1}{3}[/tex] .
What is slope ?
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
What is perpendicular ?
The word perpendicular means at right angles and this is because when two lines meet, they form right angles. Perpendicular lines can face in any direction such as up and down, crossways, and side-to-side.
Have given,
Slope of the line y=3x ,
you can compare it to y=mx+c form where m is the slope of the line.
y = 3x
differentiate respect of x
[tex]\frac{dy}{dx} = 3[/tex]
Now, the slope of the line perpendicular to the line that has a slope of m is [tex]-\frac{1}{m}[/tex]
The slope of a line perpendicular to 3x is [tex]-\frac{1}{3}[/tex] .
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A deli is trying out new labels for their cylindrical-shaped wheels of cheese. The label covers the entire wheel except the circular top and bottom.
If the wheel has a radius of 30 centimeters and a height of 20 centimeters, how many square centimeters of the wheel does the label cover? (Approximate using pi equals 22 over 7)
The required area that the label would cover is given as 3771.4 cm².
As mentioned in the question,
the wheel has a radius of 30 centimeters and a height of 20 centimeters,
The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
here,
Area of the label, = 2πrh
Substitute the value in the above formula,
Area of the label = 2 × 22 / 7 × 30 × 20
Area of the label = 3771.4 cm²
Thus, the required area that the label would cover is given as 3771.4 cm².
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Answer: Then aswer the question wit your broke answer
Step-by-step explanation:
Is the system of linear equations 2x 3y 9 0 and 4x 6y 18 consistent justify your answer?
Consistency exists inside the linear equation system.
To determine whether a system of linear equations is consistent, you can try to solve the system to find the values of the variables that satisfy all of the equations. The system is consistent if it has at least one solution. If the system has no solutions, then it is inconsistent.
In this case, the system of linear equations is 2x + 3y - 9 = 0 and 4x + 6y - 18 = 0.
To solve this system, you can use algebraic methods such as substitution or elimination. Using substitution, you can solve one of the equations for one of the variables in terms of the other, and then substitute this expression into the other equation to solve for the other variable. For example, you could solve the first equation for y:
2x + 3y - 9 = 0
3y = 9 - 2x
y = (9 - 2x)/3
Then, you could substitute this expression for y into the second equation to solve for x:
4x + 6((9 - 2x)/3) - 18 = 0
4x + (54 - 12x)/3 - 18 = 0
(12x - 54)/3 + 4x - 18 = 0
(12x - 72)/3 = 0
12x - 72 = 0
12x = 72
x = 6
Substituting this value for x back into the first equation, you can solve for y:
2(6) + 3y - 9 = 0
12 + 3y - 9 = 0
3y = -3
y = -1
Therefore, the solution to this system of equations is x = 6 and y = -1. Since there is at least one solution, this system is consistent.
The complete question is:-
Is the system of linear equations 2x+3y-9=0 and 4x+6y-18=0 consistent? justify your answer.
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10x + 8 = 8
-8-8
10x = 0 10 [?]
Answer:
the answer is three
On a radar screen, a plane is located at A(-2, 4) is flying toward B(4, 3). Another plane,
located at C(-3, 1) is flying toward D(3, 0). Are the planes' paths perpendicular? Show
work AND explain.
**i saw w/ the answer but not with the explanation… PLEASE explain!!
No, paths of planes will be not be perpendicular as their slopes comes out to be equal.
What is slope ?A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.
As a result,
m = change in y/change in x = Δy/Δx
is the formula for the change in y-coordinate with respect to the change in x-coordinate. where "m" represents a line's slope.
Slope of path of plane 1 = [tex]m_{1}[/tex]
[tex]\frac{3-4}{4-(-2)}\\ =\frac{-1}{6} \\[/tex]
Slope of path of plane 2= [tex]m_{2}[/tex]
[tex]=\frac{0-1}{3-(-3)}\\ =\frac{-1}{6}[/tex]
As slope of paths of planes are equal so we can say they are moving parallel to each other in same direction.
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suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. we find the heights of 80 people. (you may need to use the standard normal distribution table. round your answers to the nearest whole number.) (a) how many would you expect to be between 165 and 175 cm tall? 55 correct: your answer is correct. people (b) how many would you expect to be taller than 166 cm?
a) 55 people expect to be between 165 and 175 cm.
b) 76 people to be taller than 166 cm.
What is Standard normal distribution?
The standard normal distribution is a special type of normal distribution where the mean is 0, and the standard deviation is 1.
a) To answer this question, we can use the standard normal distribution table to find the proportion of heights that fall within certain ranges of the mean.
The standard normal distribution table gives us the proportion of values within a certain number of standard deviations of the mean.
Since the standard deviation of the heights is 5, we can find the proportion of heights between 165 and 175 cm by looking at the range of values that are one standard deviation below and one standard deviation above the mean.
The mean of the heights is 170, so one standard deviation below the mean is 170 - 5 = 165. One standard deviation above the mean is 170 + 5 = 175. Therefore, the range of heights that are one standard deviation below and one standard deviation above the mean is 165 to 175.
If we look at the standard normal distribution table, we find that approximately 68% of the values fall within one standard deviation of the mean. Since 80 is approximately 68% of 118, we would expect approximately 55 people to have heights between 165 and 175 cm.
Hence, 55 people expect to be between 165 and 175 cm.
b) For the second part of the question, we can find the proportion of heights that are taller than 166 cm by looking at the range of values that are more than one standard deviation above the mean.
The mean of the heights is 170, so more than one standard deviation above the mean is anything greater than 175. If we look at the standard normal distribution table, we find that approximately 95% of the values fall within two standard deviations of the mean.
Since 80 is approximately 95% of 84, we would expect approximately 76 people to be taller than 166 cm.
Hence, 76 people to be taller than 166 cm.
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Answer number 3 please thank you
Answer:
3. D
Step-by-step explanation:
1/10+1/8+1/15=1/x
24/240+30/240+16/240=1/x
70/240=1/x
7/24=1/x
1/3.4=1/x
x=3.4
Work out (13.8 × 107) × (5.4 × 10-12)
Give your answer as an ordinary number.
62017.2 is the answer
A construction worker is pouring concrete stairs. The first step requires 1. 8 cubic feet of concrete, and the first 5 steps require a total of 27 cubic feet. If the steps follow an arithmetic series, how much concrete is required for the first 12 steps? 259. 2 cubic feet 43. 2 cubic feet 156 cubic feet 140. 4 cubic feet.
We can follow Arithmetic series, then the number of cubic feet concrete is required for the first 12 steps = 140.4 cubic feet.
Given that,
The first step requires 1. 8 cubic feet of concrete,
The first 5 steps require a total of 27 cubic feet.
An arithmetic series is the sum of the terms in an arithmetic sequence with a definite number of terms. Following is a simple formula for finding the sum: Formula 1: If [tex]S_{n}[/tex] represents the sum of an arithmetic sequence with terms , then. This formula requires the values of the first and last terms and the number of terms.
For an arithmetic series
[tex]a , a+d , a+2d , a+3d , .......[/tex]
where a is the first term and d is the common difference, the sum of n terms equals,
[tex]S_{n}[/tex] = [tex]a_{n} +(\frac{n(n-1)}{2} ) d[/tex] (Equation-1)
Since the first step requires 1.8 cubic feet of concrete, a = 1.8.
Now, the first 5 steps require 27 cubic feet of concrete, that is,
[tex]S_{5}[/tex] = 27
a = 1.8
n = 5
We can substitute values in equation-1,
[tex]S_{n}[/tex] = [tex]a_{n} +(\frac{n(n-1)}{2} ) d[/tex]
[tex]S_{5}[/tex] = (5) (1.8) + [tex](\frac{5(5-1)}{2} )d[/tex]
[tex]S_{5}[/tex] = (5) (1.8) + [tex](\frac{5*4}{2} )d[/tex]
[tex]S_{5}[/tex] = (5) (1.8) + [tex]\frac{20}{2} d[/tex]
[tex]S_{5}[/tex] = (5) (1.8) + 10 d
[tex]S_{5}[/tex] = 9 + 10 d
Then, [tex]S_{5}[/tex] = 27
27 = 9 + 10d
27 - 9 = 10d
18 = 10d
d = [tex]\frac{18}{10}[/tex]
d = 1.8
Find the concrete required for 12 steps.
Then, we can substitute n = 12
So,
We can write,
[tex]S_{n}[/tex] = [tex]a_{n} +(\frac{n(n-1)}{2} ) d[/tex]
[tex]S_{12}[/tex] = (12) (1.8) + [tex](\frac{12(12-1)}{2} )d[/tex]
[tex]S_{12}[/tex] = (12) (1.8) + [tex]\frac{12*11}{2} d[/tex]
[tex]S_{12}[/tex] = (12) (1.8) + [tex]\frac{132}{2} d[/tex]
[tex]S_{12}[/tex] = (12) (1.8) + 66 d
[tex]S_{12}[/tex] = 21.6 + 66 d
We can substitute d = 1.8
[tex]S_{12}[/tex] = 21.6 + 66 (1.8)
[tex]S_{12}[/tex] = 21.6 + 118.8
[tex]S_{12}[/tex] = 140.4
Therefore,
We can follow Arithmetic series, then the number of cubic feet concrete is required for the first 12 steps = 140.4 cubic feet.
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If a and b are both negative numbers and a>b, what must be true about their absolute values?.
The absolute value of a number is the non-negative distance between the number and zero on a number line, regardless of sign.
This means that the absolute value of a negative number is always positive. Therefore, if a and b both are negative numbers, their absolute values will be positive numbers. If a is greater than b, then the absolute value of a must be greater than the absolute value of b. This can be expressed mathematically as follows:
|a| > |b|
This equation states that the absolute value of a is greater than the absolute value of b. In other words, the distance between a and zero is greater than the distance between b and zero on a number line.
To illustrate this, let’s take an example of two negative numbers, a=-3 and b=-5. The absolute values of these two numbers are 3 and 5 respectively. Since 3 is greater than 5, the absolute value of a is greater than the absolute value of b. This holds true regardless of the sign of the numbers, as long as a is greater than b.
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pleaseee help. im so confused
Solving the inequality [tex]\frac{2x + 4}{2}[/tex] < 6, we get x < 4.
What is Linear Inequality?Linear Inequalities are mathematical expressions which consist of a left hand side and a right hand side connected with inequality signs like <, >, ≤, ≥ and ≠.
They are almost like linear equations when we see it, but the '=' sign in linear equations are substituted with inequality signs like those mentioned earlier.
The expression given here is,
[tex]\frac{2x + 4}{2}[/tex] < 6
Multiplying both sides with 2, we get,
2x + 4 < 6 × 2
2x + 4 < 12
Subtracting both sides with 4, we get,
2x + 4 - 4 < 12 - 4
2x < 8
Dividing both sides by 2,
2x / 2 < 8 / 2
x < 4
Hence the inequality [tex]\frac{2x + 4}{2}[/tex] < 6 results in x < 4.
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What are the 5 Steps to Finding the mean absolute deviation?
The mean absolute deviation of a set of data is the mean distance (or the average distance) between each data element and the mean of the data elements.
The steps for Finding the Mean Absolute Deviation of a Data Set are as follows:
Step 1: Find the mean of the data set.
Step 2: Find the sum of the data values, and divide the sum by the number of data values.
Step 3: Find the absolute value of the difference between each data value and the mean: |data value – mean|.
Step 4: Find the sum of the absolute values of the differences.
Step 5: Divide the sum of the absolute values of the differences by the number of data values.
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What are the factors of 2x² 7x 15 *?
The factors of [tex]2x^2 + 7x + 15[/tex] are [tex](2x + 3)[/tex] and [tex](x + 5)[/tex].
To find the factors of [tex]2x^2 + 7x + 15[/tex] , we can use the factoring method called "splitting the middle term." Here's how it works:
Write the expression as the product of two binomials: [tex](2x^2 + 7x + 15) = (2x^2 + ax + b)(cx + d)[/tex]
Find the factors of the constant term (15) that add up to the coefficient of the middle term (7). The factors of 15 are 1 and 15, 3 and 5, and 5 and 3. The only pair that adds up to 7 are 3 and 5.
Set the coefficients of the two binomials to 3 and 5, respectively. The expression becomes: [tex](2x^2 + 3x + 5)(5x + 3)[/tex]
Rewrite the binomials using the distributive property: [tex](2x^2 + 3x + 5)(5x + 3) = (2x^2 + 5x + 3x + 15) = 2x(x + 5) + 3(x + 5) = (2x + 3)(x + 5)[/tex]
So, the factors of [tex]2x^2 + 7x + 15[/tex] are [tex](2x + 3)[/tex] and[tex](x + 5)[/tex].
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Which is a list of all the roots of
x3 −x2 =4−4x?
F {−1,2,−2} H {−1,2i,−2i}
G {1,2,−2} J {1,2i,−2i}
Answer:
J
Step-by-step explanation:
[tex]x^3-x^2+4x-4=0 \\ \\ x^2(x-1)+4(x-1)=0 \\ \\ (x^2+4)(x-1)=0 \\ \\ (x-2i)(x+2i)(x-1)=0 \\ \\ x=1, 2i, -2i[/tex]
What is the inverse of +9?
The inverse of the equation "y = 3x + 9" is "y = x/3 - 3" .
The Inverse Function is defined as a function in which domain of the original function becomes the range of inverse function and range of given function becomes the domain of inverse function.
the equation is given to be : y = 3x + 9 ;
to find the inverse we need to express the above equation in term of y .
subtracting 9 from both sides ,
we get ;
y - 9 = 3x + 9 - 9 ;
y - 9 = 3x ;
3x = y - 9 ;
x = y/3 - 9/3 ;
x = y/3 - 3 ;
switching x and y ,
we get ;
y = x/3 - 3 ;
Therefore , the inverse is y = x/3 - 3 .
The given question is incomplete , the complete question is
What is the inverse of the equation y = 3x + 9 ?
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What is unique array value?
A unique array value is a value that appears only once among all the other values in the given array. Hence the name unique.
What is an array?An array is a set of items, images, or numbers arranged in rows and columns. Arrays are practical illustrations of multiplication ideas.
Why do we need arrays?Arrays are needed in cases where you need to store and manipulate large amounts of data efficiently.
Some of the benefits of using arrays include:
1. Arrays allow you to store a large number of items in a single data structure, which makes it easier to work with large datasets.
2. Arrays allow you to access and modify the items in the array quickly, using the index of the item.
A data structure called an array is used to hold a number of elements together. Each item in an array is recognized by its index, or place within the array. A value that only appears once in an array is considered to be unique array value. Think about the following array, for instance:
[1, 2, 3, 4, 5, 6]
Because each value only occurs once in this array, each value is distinct.
Contrarily, think about the following array:
[1, 2, 3, 3, 4, 5]
Since it appears twice in this array, the number 3 is not unique. Since they only exist once, each of the other values is distinct.
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The cost of holding a children’s birthday party at a roller rink is a function of n , the number of people in the party . The cost , c , can be represented with this set of rulesB . Which graph represents the function on the coordinate plane
it will cost #150 to have a party with 9 people, and it will cost #260 to have a party with 20 people
Graph is attached:
What is Piecewise function?
A piecewise function is used to relate multiple functions at different intervals
The cost for 9 people
This means that:
n=9
When n = 9, the cost function is:
C(9)=150
Hence, it will cost #150 to have a party with 9 people
The cost for 20 people
This means that:
n=20
When n = 20, the cost function is:
C(20)=260
Hence, it will cost #260 to have a party with 20 people
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The population of a city has increased by 27% since it was last measured. If the current population is 63,500 , what was the previous population?
Answer:
50000
Step-by-step explanation:
We know it increase 27% since it was last measured
100% + 27% = 127%
We have to find 1%
We take 63500 divided by 127 = 500
500 times 27 = 13500
Now we have to take 63500 and subtract by 13500 to find the previous population.
63500 - 13500 = 50000
So, the previous population is 50000
What is the mean deviation of first 10 even natural numbers A 5 B 5.5 C 10 D 10 5?
To find the mean deviation of a set of numbers, you need to first find the average (mean) of the set, and then for each number in the set, subtract the mean and take the absolute value of the result. The mean deviation is then the average of these absolute values.
For the first 10 even natural numbers (2, 4, 6, 8, 10, 12, 14, 16, 18, 20), the mean is (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20) / 10 = 60/10 = 6.
To find the mean deviation, you would subtract the mean from each number, take the absolute value of the result, and then average those values. The mean deviation of the first 10 even natural numbers is therefore (|6 - 2| + |6 - 4| + |6 - 6| + |6 - 8| + |6 - 10| + |6 - 12| + |6 - 14| + |6 - 16| + |6 - 18| + |6 - 20|) / 10 = (4 + 2 + 0 + 2 + 4 + 6 + 8 + 10 + 12 + 14) / 10 = 5.5.
So the answer is B: 5.5.
What are natural numbers in mathematics?Numbers in Nature When counting or organizing objects, the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are utilized. Absolute numbers are integers and zeros. neither a fraction nor a decimal.
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How do you find the vertical asymptotes of the following function?
The vertical asymptotes of a function can be found by setting the denominator equal to zero and solving for x. This will give the x-values that the function cannot approach as it approaches infinity.
The vertical asymptotes of a function can be found by setting the denominator equal to zero and solving for x. This will give the x-values that the function cannot approach as it approaches infinity.In other words, a vertical asymptote is a line that the graph of a function approaches but never touches. This line is the result of the denominator of a rational function becoming equal to zero. When this happens, the function is undefined at that value of x. To find the vertical asymptotes of a function, one must first factor the denominator and set each factor equal to zero. Then, solve each factor for x to get the x-values of the vertical asymptotes. It is important to note that a vertical asymptote can also appear if the numerator of a rational function is equal to zero. In this case, the vertical asymptote is the x-value at which the numerator is equal to zero. The vertical asymptotes of a function can help us to understand the behavior of the function and its graph.
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What is the inverse of a quadratic called?
Answer: Square Root Function
The inverse of a quadratic function is a square root function because
Which series of transformation would create a congruent shape?
A series of transformations that would create a congruent shape would include any combination of rotations, reflections, and translations that preserve the size and shape of the original figure.
For example, rotating a square by 90 degrees and then reflecting it across a line of symmetry would create a congruent square. Similarly, translating a triangle to a new location on the plane while preserving its orientation would also create a congruent triangle.
What is transformation, why is it important, etc.?The structures, cultures, and business models of an institution must be realigned in order to create a learning environment that produces substantial and equitable increases in outcomes and educational value. Transformation describes this procedure.
What is the transformational process?Any activity or collection of activities that takes one or more inputs, changes and adds value to them, and produces outputs for consumers or clients is referred to as a transformation process.
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How do you write numbers in Excel?
Go to the Home tab and choose Number from the drop-down menu. In addition, you have the following choices: When choosing Number, press CTRL + 1. Right-click the cell or cell range, choose Format Cells..., then choose Number.
what are numbers ?To calculate and represent a quantity, a number, an arithmetic value, is needed. Numbers are represented by mathematical inscriptions, such the letter "3." Using logical symbols or digits to represent numbers is known as a number system.
here ,
The cells you want to format should be selected.
Place your cursor over the Dialog Box Launcher next to Number on the Home tab.
Click Fraction in the Category list.
Select the desired fraction format type from the Type list by clicking it.
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You are refilling your inventory of welcome packet for new cutomer. For each packet, it take 5 minute to print, 2 minute to organize, and 5 minute to proofread. The ink in the printer will need to be changed every 5 packet, which take 3 minute. You have 3 hour to dedicate to thi tak. Aume thathe ink in the printer wa already changed before beginning and that you have to complete each packet before completing any tep for the next one. How many welcome packet will you be able to fully complete in the time allotted?
Answer:
To complete each welcome packet, it will take a total of 5 minutes to print + 2 minutes to organize + 5 minutes to proofread = 12 minutes.
If it takes 3 minutes to change the ink in the printer every 5 packets, you will need to change the ink in the printer every 5 packets * 12 minutes per packet = 60 minutes.
In total, it will take you 60 minutes to change the ink in the printer + 12 minutes per packet to complete each packet, for a total of 60 minutes + (12 minutes/packet * number of packets) = 72 minutes per packet.
In the time allotted, you have 3 hours * 60 minutes/hour = 180 minutes.
Therefore, you will be able to fully complete 180 minutes / 72 minutes per packet = 2.5 packets.
Rounded down to the nearest whole number, you will be able to fully complete 2 welcome packets in the time allotted.
Step-by-step explanation:
What is the slope-intercept form of 5x 2y 10?
The slope-intercept form of a straight line of equation 5x + 2y = 10 is y = (-5/2)x + 5.
The slope-intercept form of a line is:
y = mx + b
where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).
To put the equation 5x + 2y = 10 in slope-intercept form, we need to solve for y. We can do this by rearranging the terms and isolating y:
2y = -5x + 10
y = (-5/2)x + (10/2)
Thus, the slope-intercept form of the equation 5x + 2y = 10 is:
y = (-5/2)x + 5
This means that the slope of the line is (-5/2) and the y-intercept is (0,5).
--The question is incomplete, answering to the question below--
"What is the slope-intercept form of 5x + 2y = 10?"
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You roll a 6-sided die.
What is P(odd)?
Write your answer as a fraction or whole number.
Answer: 3/6 or 1/2
Step-by-step explanation:
In a 6-sided die, there are 3 odd numbers 1,3 and 5. So. P(odd) is 3/6 or 1/2.
Domain
1
2
3
Range
5
7
9
Does the mapping represent a function?
Answer:
bro what u doin this on a quiz u aint goin do this on time
Step-by-step explanation:
Shivani bought egg at $30 per 10 and old at rate of $46. 80 per dozen. Find gain or lo percentage
Answer:
30% gain
Step-by-step explanation:
$30 for 10 = $3 each
$46.80 for 12 = $3.9 each
percentage change = (final price- initial price)/inital price *100
3.9-3 = 0.9
0.9/3 = 0.3
0.3 x 100 = 30
so gain of 30%
Willow homework sheet is 3×19 how can you use base 10 blocks to show 3×19
Answer: 27
Step-by-step explanation:
two base ten blocks then 7
If a and b are real numbers then a+b is a real number.This law is called ?
Step-by-step explanation:
This law is called the closure property of real numbers. It states that if a and b are real numbers, then their sum, a + b, is also a real number. This is because the set of real numbers is closed under addition, which means that any operation performed on real numbers will result in another real number.
For example, if a = 3 and b = 4, then a + b = 7, which is a real number. Similarly, if a = -2 and b = 3, then a + b = 1, which is also a real number.
The closure property of real numbers holds for many other mathematical operations as well. For example, the product of two real numbers is also a real number, as is the quotient of two real numbers (assuming that the divisor is not zero). The set of real numbers is also closed under subtraction and negation.