A relation R is a subset of the Cartesian product. Or simply, a bunch of points (ordered pairs). In other words, the relation between the two sets is defined as the collection of the ordered pair, in which the ordered pair is formed by the object from each set.
a group of some elements of the input set which are passed to a function to obtain some elements of the output set. It is the inverse of the Image. It is denoted as;
f: X → Y.
N be the set of Natural numbers and the relation R be defined as;
R = {(a ,b) : b=a2, a ,b ∈ N}. State whether R is a relation function or not.
From the relation R = {(a ,b) : b=a2, a ,b ∈ N}, we can see for every value of natural number, their is only one image. For example, if a=1 then b =1, if a=2 then b=4 and so on.
Therefore, R is a relation function here.
f:A→B, and D⊆B, the preimage D of under f is defined as
[tex]f^-1[/tex](D)={x ∈ A∣ f(x)∈D}.(5.4.5)
Hence, [tex]f^-1[/tex](D) is the set of elements in the domain whose images are in C. The symbol [tex]f^-1[/tex](D) is also pronounced as “f inverse of D.”
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An equation was created for the line of best fit from the actual enrollment data. It was used to predict the dance studio enrollment values shown in the table below:
Analyze the data. Determine whether the equation that produced the predicted values represents a good line of best fit.
No, the equation is not a good fit because the residuals are all far from zero.
No, the equation is not a good fit because the sum of the residuals is a large number.
Yes, the equation is a good fit because the residuals are not all far from zero.
Yes, the equation is a good fit because the sum of the residuals is a small number.
No, the equation is not a good fit because the sum of the residuals is far from zero.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
An equation was created for the line of best fit from the actual enrollment data. which was used to predict the dance studio enrollment values shown in the table.
We need to check whether the equation that produced the predicted values represents a good line of best fit.
No, the equation is not a good fit because the sum of the residuals is far from zero.
A line of best fit is meant to compensate for positive and negative deviation in a matter that balances them. A large residual values' sum shows that they are not balanced.
Hence, No, the equation is not a good fit because the sum of the residuals is far from zero.
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The line of best fit is No, the equation is not a good fit because the sum of the residuals is far from zero.
What is Residual?The difference between an observed value of the response variable and the value of the response variable predicted from the regression line.
Given:
According to the given data,
A line of best fit is designed to balance positive and negative deviation by making up for it.
The residual values are not balanced when their sum is significant.
Although B is near to this answer, A is simply the better appropriate one because the residuals must be somewhat close to zero to fit with the graph and validate the result, making it not a good fit.
Hence, the equation is not a good fit because the residuals are all far from zero.
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Dana reflects point A(2,5) across line ℓ to get image point A′(6,1). What is an equation for line ℓ?
The required equation of line ℓ is y = x + 3.
The slope of the line of reflection is the negative reciprocal of the slope of the line connecting the original point and the image point.
To find the slope of the line connecting A and A', we can use the slope-intercept form of a line:
y = mx + b
where m is the slope and b is the y-intercept.
To find the slope, we can use the difference of y-coordinates over the difference of x-coordinates, or
m = (1-5)/(6-2) = -4/4 = -1
The slope of the line connecting A and A' is -1
Since the line of reflection has a negative reciprocal slope, its slope is 1
Now we can use a point on the line of reflection and the slope to find its equation.
We know that point A(2,5) is on the line of reflection
We can use the point-slope form of a line:
[tex]y - y_1 = m(x-x_1)[/tex]
y - 5 = 1(x - 2)
y = x + 3
So, the equation of line ℓ is y = x + 3.
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Help me please need asap
The difference in population of 20-24 year old between California and Montana is 148 thousand
What major reason for the population difference ?
The discovery of gold brought many prospectors into the area in the 1860s, and Montana became a territory in 1864. The rapid influx of people led to boomtowns that grew rapidly and declined just as quickly when the gold ran out.It is the fourth-largest state by area, the eighth-least populous state, and the third-least densely populated state. Its state capital is Helena, while the largest city is BillingsThe state rightfully earned its motto, "oro y plata," spanish for "gold and silver." The Treasure State is known for its abundant natural and mineral resources, including coal, copper, gold, manganese, sapphire, silver, lead, oil and zinche airport's direct flights to San Francisco, Los Angeles, and Long Beach contributed to the ease of California residents moving to the greater Bozeman area. It's no surprise why so many people want to live in Montana. “It's the access to recreation,” Bozeman real estate Broker Christy Delger said to the Chronicle.To learn more about population refers to:
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50 POINTS!!! CHECK MY GEOMETRY
Answer:
Omit step 3 and 5 and then step 6 can be used as step 5 as CPCTC
Step-by-step explanation:
The table below gives the height and shoe sizes of six randomly selected men if the man has a height of 80 what would be his shoe
#3(question
y = 2.5x + 45.9
The Height is 72.3
How to find the calculation?Height = y
Shoe size = x
y = 1 / 6 (67 + 70+ 73.5 + 75 + 78 + 66) ≈ 71.6
x = 1/6 (8.5 + 9.5 + 11 +12 + 13 + 8 ) = 10.3 ≈10.3
=(67 * 8.5 + 70 * 9.5 + 73.5 * 11 + 75 * 12 + 78 * 13 + 66 * 8/ (8.5)² + 9.5 ² + 11 ² + 12 ² + 13 ² + 8²) - 6 * 10.3²
= 4485 - 4424.88 / 660.5 - 636.54
= 60.12 / 23.96
≈2.5
= 71.6 - 45 * 10.3 = 45.85 ≈45.9
⇒ y = 25 x + 45.9
When r = 10.5
y = 25 * 10.5 + 45.9 =72.15.
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Record each of the equations in slope intercept form ( y=Mx+b)
As shown below, the equations are written in slope - intercept form.
formula for the equation slope - intercept
y + x = 3 y = -x + 3
2x + y = x + 4 y = -x + 4
x + y = -3 y = -x - 3
What is linear equation?Those functions with exponents of 1 are known as linear functions.
The slope intercept form of the relation is presented below.
y = mx + b
the meaning of a variable
output variable = y
slope = m
input variable = x
b = intercept of y
The formula for the equation is as follows: y = mx + b.
y + x = 3
placing y at the left side of the equation
y = -x + 3
2x + y = x + 4
placing y at the left side of the equation
y = -2x + x + 4
y = -x + 4
x + y = -3
placing y at the left side of the equation
y = -x - 3
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What is the formula for the area A of a triangle with base b and height h?
Hi !
[tex]A= \frac{b \times h}{2} [/tex]
Have a nice day
Name the property used in each step 13+16- 4 squared
The property used in each step of solving 13 + 16 - 4 squared are
13 + 16 - 4²
addition property
29 - 4²
exponents property
29 - 16
subtraction property
13
What is addition operation?Addition is one of the four fundamental operations in mathematics, along with subtraction, multiplication, and division.
The entire amount or sum of the two whole numbers is obtained by adding them.
In the problem face 13 and 16 are two two whole numbers added to get the sum of 29
What is exponent operation?This operation allows for acting with respect to the base and the number in the exponents
In the given problem, the base is 4 and the exponent is 2. this case is solved by
= 4 * 4
= 16
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Find the value of x, if (16)245 = (32)x.
Answer:
x = 245/2 (In exact form)
and,
x = 122.5 (In decimal form)
or,
x = 1221/2 (In mixed number form)
Step-by-step explanation:
How do you find the coordinates of two points given an equation?
To find the coordinates of two points given an equation, you can substitute different values of x into the equation and solve for y, or by using the symmetry property of the equation.
The first method to find the coordinates of two points is to substitute different values of x into the equation and solve for y. Once you have the coordinates of the two points, you can use them to graph the equation and further analyze the function.
For example, if the equation is y = 2x + 1, you can substitute x = 0 and x = 1 into the equation to find the coordinates of the two points. Substituting x = 0 gives y = 2(0) + 1 = 1, so the first point is (0,1). Substituting x = 1 gives y = 2(1) + 1 = 3, so the second point is (1,3).
Another way to find the coordinates of two points is by using the symmetry property of the equation. For example, if the equation is y = -x^2 + 4x -3, you can substitute x = -1 and x = 1 into the equation and solve for y.
In conclusion, finding the coordinates of two points given an equation involves substituting different values of x into the equation and solving for y, or by using the symmetry property of the equation.
The coordinates of the two points will be used to graph the equation and further analyze the function.
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i need help! i cant figure this one out
Step-by-step explanation:
[tex]3^5\cdot3^{-1}\\=\frac{3^5}{3}\\=\boxed{3^4}[/tex]
Hello there!
Answer:
81
Step-by-step explanation:
We can use the special formula:
[tex]a {}^{n} \times a {}^{m} = a {}^{m + n} [/tex]
where a = 3, n = 5 and m = -1.
[tex]3 {}^{5} \times 3 {}^{ - 1} = {3}^{5 - 1} = 3 {}^{4} = (3 {}^{2} ) {}^{2} = 9 {}^{2} = 81[/tex]
complete!
1.2: Fruit Fly Mutations
A scientist is trying to determine the role of specific genes by looking at traits of fruit flies.
The offspring of two fruit flies are examined to determine the color of their eyes and
whether they have curled wings or standard wings. Eighty offspring are randomly selected,
and the results are recorded in the two-way table.
curled wings standard wings
red eyes
white eyes
17
5
1. Describe what the 17 in the table represents.
Tea
45
13
2. How many selected fly offspring had white eyes? Explain or show your reasoning.
3. How many selected fly offspring had standard wings? Explain or show your
reasoning.
17 represents number of offspring curled wings and red eyes.
What is number ?
The arithmetic value of a number is one that is used to denote amount. As a result, a number is a mathematical concept used for counting, measuring, and labeling. As a result, mathematics is based on numbers.
An arithmetic value known as a number is used to represent a quantity and do calculations. Numbers are represented by written symbols, such as "3," which are referred to as numerals. A number system is a method of writing that uses logically ordered digits or symbols to represent numbers.
The intriguing characteristics between numbers are known as number ideas. We can calculate and solve problems using these concepts.
1. 17 represents number of offspring having curled wings and red eyes.
2. 5+ 13
= 18
18 offspring have white eyes out of which 5 have curled wings have 13 have standard wings.
3. 45 + 13
= 58
58 offspring have standard wings out of which 45 have red eyes and 13 have white eyes .
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Is △dbe similar to △abc? if so, which postulate or theorem proves these two triangles are similar? responses △dbe is similar to △abc by the sas similarity theorem. , triangle d b e, , is similar to , , triangle a b c, , by the , , s a s theorem, , . △dbe is similar to △abc by the ssa similarity theorem. , triangle dbe, , is similar to , , triangle a b c, , by the , , s s a similarity theorem, . △dbe is similar to △abc by the sss similarity theorem. , triangle d b e, , is similar to , , triangle a b c, , by the , , s s s similarity theorem, , . △dbe is not similar to △abc. , triangle d b e, , is not similar to , , triangle a b c, , . a triangle with vertices a, b, and c. segment d e is inside the triangle with point d on side a b and point e on side b c. a d is 15 centimeters, d b is 10 centimeters, b e is 16 centimeters, and e c is 24 centimeters.
Yes , △DBE is similar to △ABC by the SAS Similarity Theorem .
What is SAS Similarity Theorem.
The SAS similarity theorem stands for side angle side. When you've got two triangles and the ratio of two of their sides are the same, plus one of their angles are equal, you can prove that the two triangles are similar.
Have given ,
we have to tell that is the triangles are similar or if similar then by which postulate and point e on side b c. a d is 15 centimeters, d b is 10 centimeters, b e is 16 centimeters, and e c is 24 centimeters.
In ΔDBE and ΔABC,
[tex]\frac{DB}{AB} = \frac{EB}{CB}[/tex]
⇒ [tex]\frac{10}{10+15} = \frac{16}{16+40}[/tex]
⇒[tex]\frac{2}{5} =\frac{2}{5}[/tex]
And also ∠B=∠B (common) i.e the one angle congruent.
Hence , △DBE is similar to △ABC by the SAS Similarity Theorem .
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The function h(x) is a continuous quadratic function with a domain of all real numbers. The table lists some of the points on the function.
x h(x)
−6 8
−5 3
−4 0
−3 −1
−2 0
−1 3
What are the vertex and range of h(x)?
Vertex (−3, −1); Range −1 ≤ y ≤ ∞
Vertex (−3, −1); Range ∞ ≤ y ≤ −1
Vertex (−1, 3); Range 3 ≤ y ≤ ∞
Vertex (−1, 3); Range ∞ ≤ y ≤ 3
The vertex and range of h(x) is (a) Vertex (−3, −1); Range −1 ≤ y ≤ ∞
How to determine the vertex and the rangeThe table of values is given as
x h(x)
−6 8
−5 3
−4 0
−3 −1
−2 0
−1 3
In this case, the vertex is the minimum, and it is represented as
Vertex = (-3, -1)
Also, the range is the set of the output values
i.e. the h(x) values
These values as an interval are −1 ≤ y ≤ ∞
i.e. minimum of -1 and till infinity
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Answer:
the person above me is valid
Step-by-step explanation:
Craig is considering four loans. loan l has a nominal rate of 8.254%, compounded daily. loan m has a nominal rate of 8.474%, compounded weekly. loan n has a nominal rate of 8.533%, compounded monthly. loan o has a nominal rate of 8.604%, compounded yearly. which of these loans will offer craig the best effective interest rate? a. loan l b. loan m c. loan n d. loan o please select the best answer from the choices provided a b c d
The effective interest rate of the loan would be
In this case, we are given 4 options:
Loan L has a nominal rate of 8.254% compounded dailyLoan M has a nominal rate of 8.474% compounded weeklyLoan N has a nominal rate of 8.533% compounded monthlyLoan O has a nominal rate of 8.604% compounded yearlyThe formula of compounded interest rate is:
[tex]A = P (1+\frac{r}{n})^{nt}[/tex]
Where:
A = amount, P = principal amount, r = interest rate, n = number of times interest rate compounded, t = time
Let’s assume the principal amount is $100 for 1 year
Loan L =
[tex]A = 100 (1+\frac{0.08254}{356})^{356x1}[/tex]
A = $108.603
Loan M =
[tex]A = 100 (1+\frac{0.08474}{52})^{52x1}[/tex]
A = $108.834
Loan N =
[tex]A = 100 (1+\frac{0.08533}{12})^{12x1}[/tex]
A = $108.875
Loan O =
[tex]A = 100 (1+\frac{0.08604}{1})^{1x1}[/tex]
A = $108.604
Therefore, the best effective interest rate for Craig is Loan L with nominal rate of 8.254% compounded daily.
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Greg drives at 50 mph for 212 hours. how far did he drive? responsesa. 20 mi b. 75 mi c. 125 mi d. 150 mi
So, the correct answer is (d) 150 mi.
To find out how far Greg drove, you need to multiply the speed of his car (50 mph) by the amount of time he spent driving (212 hours).
Speed = Distance/Time
Distance = Speed * Time
Distance = 50 * 212
Distance = 10600 miles
So, Greg drove 10600 miles.
It's important to note that the question is asking for the answer in miles and not kilometers.
To convert meters to miles, you can use the conversion factor 1 mile = 1609.344 meters.
To convert a measurement in meters to miles, you can multiply the number of meters by the conversion factor.
For example, if you want to convert 1000 meters to miles, you would multiply 1000 by the conversion factor of 1/1609.344 which is approximately 0.000621371.
1000 meters = 0.000621371 miles
So, the correct answer is (d) 150 mi.
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What is the slope of 2 over 5?
The slope of the given expression y=2/5 is calculated by comparing them with the standard slope-intercept form. Then, the slope is 0.
A line's slope provides information about its steepness, or how much y rises as x rises. The slope is used to compare the y-axis, or vertical axis, with the x-axis, or horizontal axis. It can be determined by dividing any two y values by any two x values.
The common formula for the equation is expressed by slope-intercept form as y=mx+b. In this case, the slope in this equation is denoted by m, while the y-intercept is denoted by b. In the following step, the slope is determined by comparing the provided expression with this.
Given the expression is y=2/5=0.4. Comparing this with the slope-intercept form, we get, slope m=0, x=0, and b=0.4. Therefore, the required slope is 0.
The complete question is -
What is the slope of y=2/5?
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1. Find the GG1 of a hip of 15,000 Tonne diplacement when a weight of 55 tonne ma i removed from the tarboard ide through a ditance of 15 meter
As per the given displacement value, the value of GG1 is 0.055
The term displacement is defined as the length of shortest distance from initial position to final position of the object.
Here we have given that a hip of 15,000 Ton displacement when a weight of 55 ton mass i removed from the starboard side through a distance of 15 meter.
Here we know that the following values are given in it.
They are listed as follows:
Total displacement = 15,000 ton
Mass = 55 ton
Distance = 15 meter.
Then the value of GG1 is calculated as,
=> (15 x 55)/15,000
=> 0.055
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60d - 55 > 525
help solve this for me please
Answer:
Down below
Step-by-step explanation:
60d - 55 > 525
60d - 55 + 55 > 525 + 55
60d > 580
60d/60 > 580/60
d > 9.66666666667
Hope this helps! :)
Chase bought 19 chicken wings fir $26.60. What was the cost of wings, in dollars per wing?
$1.40 for each wings.
You have to divide $26.60 by 19
Somebody help please what’s the answer
Y-intercept is P(0, 6). Then equation of the line which is perpendicular to y=4x-5 and passing through P is : x + 4y = 28.
The equations are
⇒5x+3y−35=0
⇒2x+4y−28=0
By cross multiplication
⇒ [3×(−28)−4×(−35)]x = [−35×2−(−28)×5]y = [5×4−2×3]1
⇒ −84+140x = −70+140y = 20−61
⇒ 56x = 70y = 141
⇒ 56x = 141 ⇒14x=56⇒x=4
⇒ 70y = 141 ⇒14y=70⇒y=5
⇒x=4,y=5
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Subtract: (1282 - 95 + 15) - (- 482 - 35 + 6)
Answer:
1713
Step-by-step explanation:
Just use order of operations :)
Amari gathered a random sample of bags of potato chips from a popular company. She calculated data on different variables. For one of the variables that she collected, she constructed a bar graph.
Which of the following variables did she use?
Price of bag of potato chips
Number of chips in the bag of potato chips
Weight of bag of potato chips
Flavor of potato chips
The variables that Amari used is C. Weight of bag of potato chips
What is the variable used?In this case, Amari gathered a random sample of bags of potato chips from a popular company. She calculated data on different variables. For one of the variables that she collected, she constructed a bar graph.
A variable is a symbol used to represent a mathematical object in mathematics. Any number, vector, matrix, function, function argument, set, or set element can be represented by a variable. A characteristic that can be measured and given different values is known as a variable. Variables include things like height, age, income, province of birth, school grades, and type of housing.
In this.case, the weight is used.
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Answer:
D Flavor of potato chips
Step-by-step explanation:
I took the test and it was right!
Pleae anwer quick! im being timed!!!!!!! Polygon B i a caled copy of Polygon A. What i the cale factor from Polygon A to Polygon B? Explain your reaoning. Find the miing length of each ide marked with ? in Polygon B. Determine the meaure of each angle marked with ? in Polygon A
A- The scale factor from Polygon A to Polygon B is 2.
B- The missing length of each side marked with ? in Polygon B is 3, 5
C- The measure of each angle marked with ? in Polygon A is 53°, 82°
Given that,
A- scale factor = side A/ side B = 5 / 2.5 = 2
B- Length of each missing sides= 1.5*2 = 3 and 2.5* 2 = 5
C- Since the scale factor does not change the measure of the angles, the missing angles remain the same that is 53° and 82°
Thus,
The scale factor from Polygon A to Polygon B is 2.
The missing length of each side marked with ? in Polygon B is 3, 5
The measure of each angle marked with ? in Polygon A is 53°, 82°
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4. Give a verbal description and algebraic representation of each translation in the table below.
VERBAL DESCRIPTION
ALGEBRAIC REPRESENTATION
GRAPH A
GRAPH B
GRAPH C
The principles can be used to explain how coordinates change when a figure is translated right, left, up, and down on the coordinate plane.
What is a verbal description in algebra?Verbal Descriptions: A verbal description of a set uses an English sentence to describe a rule that enables us to identify the class of objects under consideration as well as to determine whether or not any given object is a member of the set. The spoken descriptions of the three sets in the aforementioned cases are all used.
A vocal description contains the same details as on a label, including the artist's name, country, title of the work, date, size or scale of the piece, media, and method. A general description of the topic and the structure of the work is included in verbal description, which is more significant. By stating the rule that determines the value of a second quantity and assigns it to one quantity, a function can be vocally described.
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Simplify the following expressions. Type out and label your answers for A and B.
The value of the expression [tex]7^{-8} . 7^6[/tex] is 1/7
The value of the expression [tex]3. 3^7[/tex] is [tex]3^8[/tex].
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
A)
[tex]7^{-8} . 7^6[/tex]
= [tex]7^{-8 + 6}[/tex]
= [tex]7^{-2}[/tex]
= 1/7
B)
3. [tex]3^7[/tex]
= [tex]3^1.3^7[/tex]
= [tex]3^{1 + 7}[/tex]
= [tex]3^8[/tex]
Thus,
The value of the expression is 1/7 and [tex]3^8.[/tex]
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Consider the polynomial function
f(x)=x^4-2x^3+11x^2-5x+6
Which statement correctly describes the number of possible positive zeros and the number of possible negative zeros?
The correct statement for the number of negative zeros and of positive zeros is given as follows:
The number of positive zeros is of 4, while the number of negative roots is of zero.
How to obtain the number of positive and negative roots?The number of possible positive and negative roots is obtained using Descartes' Rule.
The Descartes' Rule states that the number of positive roots is at most the number of sign changes in the sequence of polynomial's coefficients (disconsidering the zero coefficients), while the difference between these two numbers is always even.
The number of changes for this problem is given as follows:
4 changes.
The changes are given as follows:
x^4 to x^3.x^3 to x^2.x^2 to x.x to constant.As there are 4 changes, the number of positive roots is of 4, while the number of negative roots is of zero, as the polynomial is of the fourth degree.
Missing InformationThe answer was given in general terms, as the statements are not presented.
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A, B, C, or D
please don't lie
picture attached
The height that Plant A has grown taller, as regards Plant B, is D. 1 / 2 inch
How to find the height difference ?The height of Plant A is 5 / 6 inches while the height of plant B is 1 / 3 inches. To find how much taller Plant A is than Plant B, you need to subtract the height of Plant B from the height of Plant A.
As these fractions have different denominators, you need to find a common denominator of the bases. This common denominator would be the least common multiple of the denominators of 3 and 6.
This least common multiple is 6. Then divide the common denominator by the denominator of the height and multiply it by the numerator to give ;
= ( 5 - 2 ) / 6
= 3 / 6 inches difference
In the simplest form, this is:
= 3 / 6
= 1 / 2 inches
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814 exceeds 12 times a number by 70. what is the number?
The number is 62
What are the basic operations in mathematics?
The basic operations in mathematics are:
Addition: The process of combining two or more numbers to find their total value. It is represented by the "+" symbol.Subtraction: The process of finding the difference between two numbers. It is represented by the "-" symbol.Multiplication: The process of finding the product of two or more numbers. It is represented by the "x" symbol or "*" symbol.Division: The process of finding the quotient of two numbers. It is represented by the "/" symbol.We can start solving the problem by using algebra. Let's call the unknown number "x". According to the problem, we know that:
814 = 12x + 70
To find the value of x, we can subtract 70 from both sides of the equation:
814 - 70 = 12x
744 = 12x
Now, we can divide both sides of the equation by 12:
x = 744/12
x = 62
So, the number is 62.
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I need some help on this question please
Answer:
The answer is attached to this response below.