x = 14000
y = 28000
z = 12000 units of each product were sold.
Solving this with the help of equation.
What is an equation?The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.
Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.
Let, x, y and z are the three types of products.
In one year, the total revenue for the three products was $1,100,000, which corresponded to the sale of 54,000 units.
Thus, 30x + 20y + 10z = 1,100,000 ............ (i)
x + y + z = 54000 ............... (ii)
The company sold half as many units of the $30 product as units of the $20 product, so, x = y/2
putting this in equation (i)
thus, 30x + 20 (2x) + 10z = 1,100,000
70x + 10z = 1100000 ......... (iii)
next putting the value of y = 2x in equation (ii) we get -
3x + z = 54000......... (iv)
Solve this two equation we get -
40x = 560000
or, x = 14000
now, y = 2x = 28000
z = 54000 - 3(14000)
z = 12000
Now, x = 14000
y = 28000
z = 12000 units of each product were sold.
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The units of each three types of product sold are 14000, 28000, and 12000 using equations.
What is an equation?Algebraic equations simply state the equivalence of two mathematical terms in a mathematical statement. For instance, the equation 6x + 5 = 11 has the two expressions 6x + 5 and 11 separated by the 'equal' sign.
The two forms of equations are identity equations and conditional equations. For just any value of both variables, equality remains true.
Let, x, y and z are the three types of products.
The three items generated a combined $1,100,000 in revenue in a calendar year, which is equal to the sale of 54,000 units.
30x + 20y + 10z = 1,100,000 ............ (i)
x + y + z = 54000 ............... (ii)
The company sold half as many units of the $30 product as units of the $20 product, so, x = y/2
Putting this in equation (i)
Thus, 30x + 20 (2x) + 10z = 1,100,000
70x + 10z = 1100000 ......... (iii)
Next putting the value of y = 2x in equation (ii) we get -
3x + z = 54000......... (iv)
Solve these two equation we get -
40x = 560000
Or, x = 14000
Now, y = 2x
= 28000
z = 54000 - 3(14000)
z = 12000
Now, x = 14000
y = 28000
z = 12000
These units of each product were sold.
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De que numero es 41 el 18% menos
Para calcular el 18% menos de un número, se puede utilizar la fórmula: número original x (1 - porcentaje en decimal). En este caso, para calcular el 18% menos de 41, se puede utilizar la fórmula: 41 x (1 - 0.18) = 41 x 0.82 = 33.62. Entonces, el 18% menos de 41 es 33.62.
Espero que esto ayude :)
Answer:
El número es:
50
Step-by-step explanation:
Porcentaje significa "por cada cien"
18% = 18/100 = 0.18
El número buscado corresponde al 100%
Si es el 18% menos quiere decir que corresponde a:
100 - 18 = 82%
Entonces:
Por regla de tres:
41 es a 82%
A es a 100%
A = 41 * 100 / 82
A = 4100 / 82
A = 50
Comoprobación:
50 - (50*0.18) = 50 - 9 = 41
Is it possible to construct a triangle with sides 9 cm 6 cm and 17cm if not why?
It is not possible to construct a triangle with 6cm, 9cm, and 17cm.
The sides measure 6 cm, 9 cm, and 17 cm in length.
Only when the third side is greater than the sum of any two sides can a triangle be drawn. This the condition.
Let's verify the rule now.
6 + 9 > 17 Not true
6 + 17 > 9 True
9 + 17 > 6 True
As 6 + 9 > 17 does not satisfy the condition.
Hence, it is not possible to construct a triangle having 6cm, 9cm, and 17cm in length.
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She simulated 505050 classes of 303030 students where each student selected had a 0.140.140, point, 14 probability of being left-handed. Casey counted how many left-handed students were in each simulated class. Here are her results:
The empirical probability that there are more than 5 left-handed students in a class of 30 is 0.06.
Empirical probability is a sort of experimental probability that is based on historical data. Empirical probability is, then, an illustration of the likelihood of an occurrence occurring based on prior data.
The formula of the empirical probability is:
Experimental probability = number of times an event occurs / total number of outcomes.
In the problem, total number of classes = 50
From the graph, we can read that:
- number of classes with 6 left-handed students = 2
- number of classes with 7 left-handed students = 1
Hence, the empirical probability that there are more 5 left-handed students in a class of 30 is:
Empirical probability = 3/50 = 0.06
Your question is incomplete. Most likely it was:
Casey read a report that said the probability that a randomly selected America is left handed is 14%. she was curious how many left handed students to expect in a class of 30 seconds. she simulated 50 classes of 30 students where each student had a 0.14 probability of being left handed. Casey counted how many left handed students were in each simulated class. here are her results: use her results to estimate the probability that there are more than 5 left handed students in a class of 30 students. (The graph is attached)
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what theorem can be used to find segment lengths in a triangle with a segment drawn parallel to a side of the triangle?
The midsegment linking the cartesian coordinates of two of a triangle's sides is parallel to the fourth aspect of the triangle, and its length is half that of the third side, according to the midsegment theorem.
Whence came the triangle?The assertions that the Greek mathematician Pythagoras discovered the properties of right-angled triangles in the fifth century BC just did not match up, according to many. Some people think following commentary shows it was a joint effort among his disciples, the Pythagoreans.
Which four primary triangles are there?Equilateral: equal angles and all three sides. Acute isosceles: two identical sides and angles, both of which are only about 90 degrees. Acute scalene has irregular sides and angles, all of which are under 90 degrees. Obtuse isosceles: two identical sides and angles, one of which is more than 90 degrees.
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find the value of x
(need answered fast)
Answer:
The measure of the third angle of the triangle is 45°.
Step-by-step explanation:
What is a triangle?
A triangle is a polygon with 3 sides.
Given that, the measures of the two angles of a triangle are 50° and 85°.
Let the measure of the third angle be x.
Since the sum of the interior of a triangle is 180°, it follows,
50°+85°+x=180°
135° +x = 180°
x = 180° - 135°
x = 45°
Hence, the measure of the third angle of the triangle is 45°.
the 25 students in the psychology class take a 20-point quiz. five of the students each obtained a score of 10 on the quiz, ten students each obtained a score of 15, and ten students each obtained a perfect scores of 20. what would be the mean of these scores? question 25 options: a) 14 b) 18 c) 12 d) 16
The mean of these scores is 16.
The mean is a measure of central tendency that indicates the average value of a set of data. It is calculated by adding up all of the individual values in a dataset and dividing that sum by the number of values in the dataset. In mathematical terms, the mean is represented by the symbol "µ" (mu) and is calculated as:
µ = (sum of all observations) / (number of observations)
To find the mean of these scores, you would add up all of the individual scores and divide by the total number of scores.
First, we find the total score of the 5 students who scored 10: 5 students * 10 points/student = 50 points
Then, we find the total score of the 10 students who scored 15: 10 students * 15 points/student = 150 points
Then, we find the total score of the 10 students who scored 20: 10 students * 20 points/student = 200 points
Now we add all the total scores of students: 50+150+200 = 400 points
Finally, to find the mean score, we divide the total score by the number of students: 400 points / 25 students = 16 points/student.
Therefore, the mean of these scores is 16.
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mai lee bought a computer for her home office and depreciated it over 5 years using the straight line method. if its initial value was $2350, what is its value 3 years later
In this scenario, if a computer was bought for $2350 and is being depreciated over 5 years, the annual depreciation is $470, and its value 3 years later would be $1410.
The straight-line method of depreciation is a method of calculating the decline in value of an asset over time. Using this method, an asset's value is spread evenly over its useful life.
In this scenario, if the computer was bought for $2350 and is being depreciated over 5 years, the annual depreciation is ($2350 / 5) = $470.
Three years later, the computer's value would be $2350 - ($470 x 3) = $1410. This is because the value of the computer is decreasing by $470 per year, and after three years, the total amount of depreciation would be $470 x 3 = $1410.
It's important to note that the straight-line method of depreciation is a simple method and it does not reflect the real-world scenario in which assets may have a higher value of depreciation in the initial years and less in the later years. But it's easy to calculate and use.
In conclusion, if an asset is depreciated using the straight-line method, its value decreases evenly over its useful life. It's important for businesses to understand the various methods of depreciation and choose the one that best suits their needs.
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The base of the triangle, b,is three inches greater than the height. What is the area of the triangle?
Answer:
Step-by-step explanation:
Let the height be h units
then the base is h+3 units
Area = (1/2)(base)(height)
= (1/2)(h)(h+3) or (1/2)(h^2 + 3h)
Round this number to the
nearest thousandth.
1.2983
Satan said that by eating of the forbidden tree Adam and Eve could become as wise as he was.
True or false
Answer:
Step-by-step explanation:
true
Can anyone help me with this please
The turning point of the function is x = 1 and it is a local minima.
What is maxima and Minima ?The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.
Extrema is the result of maxima and minima combined. The graph in the graphic below shows several peaks and falls. We obtain the function's maximum and lowest values at x = a and 0 respectively, and at x = b and c respectively. The valleys are the minima and all the peaks are the maximum.
In a function, maxima and minima can be of two different types:
Local Maxima and Minima
Global or Absolute Maxima and Minima
The function is
y = [tex](x-1)^{2}[/tex] for -3 ≤ x ≤ 3
differentiating both side with respect to x we get
[tex]\frac{dy}{dx} = 2(x-1)[/tex]
for maxima and minima [tex]\frac{dy}{dx} = 0[/tex]
or, 2(x-1) = 0
or x = 1
Now, for x > 1 [tex]\frac{dy}{dx} > 0[/tex]
So, the function's turning point is a minima.
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Find the average rate of change of h (x) = -2x²-3x from x=2 to x = 4. Simplify your answer as much as possible.
Lebron's foul shooting average is 55%. If he shot 75 foul shot 75 foul shots, how many would he make ?
Lebron would make 41 foul shots.
The formula used to calculate the number of made foul shots is Number of Made Foul Shots = Foul Shooting Average * Number of Shots Attempted.
Therefore, the number of made foul shots for Lebron is 55% * 75 = 41.25. Since this is a decimal number, we can round it down to 41 made foul shots.
In calculation way, Lebron would make 41 foul shots. This can be calculated by multiplying his foul shooting average 55% with the number of shots attempted, which is 75. 55% can also be written as 0.55, so the equation can be written as 0.55 * 75 = 41.25 which rounds down to 41.
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Which angle is the biggest based on sides of the triangles below? explain your reasoning.
Angle C is the biggest.
The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle.
Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 5 s. The maximum rate of air flow into the lungs is about 0.3 L/s. This explains, in part, why the function f(t) = (3/10)(sin(2πt/5)) has often been used to model the rate of air flow into the lungs. Use this model to find the volume of inhaled air in the lungs at time t.
So, (3/10) ∫(0 to t) sin(2πt/5) dt would find the volume of inhaled air in the lungs at time t.
The function f(t) = (3/10)(sin(2πt/5)) is often used to model the rate of air flow into the lungs because it is cyclic, with a period of 5 seconds, and has a maximum value of 0.3 L/s. This function represents the rate of air flow into the lungs at any given time t.
To find the volume of inhaled air in the lungs at time t, we can integrate the function f(t) with respect to time. The volume of air inhaled at time t is the definite integral of f(t) from the start of inhalation (t = 0) to time t.
∫(0 to t) f(t) dt = (3/10) ∫(0 to t) sin(2πt/5) dt
The definite integral can be solved with proper limits, but the result is not in a closed form that can be expressed in terms of elementary functions.
In order to get the volume of inhaled air in the lungs at time t, we need to know the specific values of t and solve the definite integral with proper limits.
It's worth noting that this model is a simplified one and many other factors like breathing rate, lung capacity, and lung compliance could affect the actual volume of inhaled air in the lungs.
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In the stock market, changes in value used to be indicated by fractions, which represented portions of $1. A stock had a value of $11.50.
Write and then evaluate an addition expression to find how much the stock is worth after an increase of 1/4.
Enter the correct numbers in the boxes.
The value of the stock after the increase of 1/4(fraction) using the addition expression is equal to $11.75.
In Mathematics, a fraction is defined as the portion/part of the whole thing. A fraction consists of two parts, numerator and denominator. The number on the top is known as the numerator, and the number on the bottom is known as the denominator.
Given,
The initial value of stock = $11.50
Increase in stock ( in fraction) = 1/4
We know that earlier in the stock market the changes in values were indicated by fractions which represent portions of $1
Therefore,
Increase in value of stock = 1/4 * $1
= $0.25
Hence,
Value of stock after increase = $11.50 + $0.25
= $11.75
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The brick will be gold-plated (dipped in gold). Which measure would be used to find the amount of gold needed
To find the amount of gold needed for gold plating a brick, total surface area of the brick would be needed to be calculated, assuming the brick is cuboid or cube shaped.
While dealing with cubes and cuboids, we should know how to find the surface areas and volumes of the two objects. When we either fill these or talk about all the three dimensions of an object, we talk about the volume of the said object. And, when we paint or talk about just the exterior or interior walls of an object, we talk about the surface area of the said object.
When all the six faces of a cube or a cuboid are used, we calculate surface area for all the faces and this is called the total surface area.
Let us look at the different formulas to calculate volume and total surface area of a cube and a cuboid,
Total surface area of a cube (side [tex]a[/tex]) = 6 × (area of each face)
= 6 × [tex]a^{2}[/tex]
Volume of a cube (side [tex]a[/tex]) = [tex]a^{3}[/tex]
Total surface area of a cuboid (length [tex]l[/tex], breadth [tex]b[/tex], height [tex]h[/tex]) = [tex]2 ( lb + lh + bh)\\[/tex]
Volume of a cuboid (length [tex]l[/tex], breadth [tex]b[/tex], height [tex]h[/tex]) = [tex]lbh[/tex]
For plating the brick with anything, gold for instance, total surface area of the brick would be calculated to determine the amount of gold needed as all the walls or faces of the brick would be plated but not the interior volume.
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Can 1 right and 2 acute form a triangle?
Answer:
no
Step-by-step explanation:
a triangle can never only have acute sides. The other sides will either be: obtuse or a right angle.
what is the probability that a randomly selected three-digit number has the property that one digit is equal to the product of the other two? express your answer as a common fraction.
The probability of selecting a three-digit number with the property that one digit is equal to the product of the other two is 1/90.
1/90
The probability of selecting a three-digit number with the property that one digit is equal to the product of the other two is 1/90. This is because there are only 9 possible digits (1, 2, 3, 4, 5, 6, 7, 8, 9) to choose from, and each of these digits can be multiplied by itself twice to give 9 possible combinations. Therefore, there are 9 three-digit numbers that satisfy the given condition, and these 9 numbers can be chosen from a total of 900 three-digit numbers (10 x 10 x 10 = 1000, minus the 100 numbers beginning with 0). Thus, the probability of selecting a three-digit number with the property that one digit is equal to the product of the other two is 9/900, which can be simplified to 1/90.
The probability of selecting a three-digit number with the property that one digit is equal to the product of the other two is 1/90.
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A scale drawing of a rectangular park had a scale of 1 cm = 90m. What is the actual perimeter of the park in meters?
The actual perimeter is 2934. The perimeter of a rectangle is calculated as P = length + breadth + length + breadth. Alternatively, P = 2(length + breadth).
What is the actual perimeter of the park in meters?Perimeter=2(l + b)
=2[6.3cm +10cm) = 2x16.3 cm 32.6cm
Scale 1 cm = Actual 90m.
32.6cm 32.6x90m
= 2934 m
We sum the lengths of all four sides to determine the perimeter of a rectangle. Because opposing sides of a rectangle are always equal, we must obtain the length and breadth measurements to calculate the perimeter of a rectangle. The perimeter of a rectangle is equal to double the sum of its length and breadth.
To calculate the perimeter, or distance around the rectangle, sum all four side lengths. This may be done quickly by adding the length and breadth and then multiplying the total by two because each side length has two lengths. The perimeter formula is perimeter = (length + width)2.
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A company sells widgets. The amount of profit, y, made by the company, is related to
the selling price of each widget, x, by the given equation. Using this equation, find out
what price the widgets should be sold for, to the nearest cent, for the company to
make the maximum profit.
y=
-3x² +239x-2268
The price of the widgets for which it should be sold to make the maximum profit is $25.4 .
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We know that the quadratic equation ax² + bx + c ,
If a < 0; then the maximum value of the quadratic equation will be at x = -b/2a .
Given;
a company is selling a widget;
the selling price of each widget is = x
the profit made by the company = y
the equation of profit is given as y = −3x² + 152x − 1150 ,
here a = -3 , b = 152 and c = -1150
In the given quadratic equation we can see that;
a < 0 , so , the maximum will be at;
x = -b/2a
x = -152/2(-3)
x = 152/6
x = 25.333
x ≈ 25.4
Hence, the price of the widget will be $25.4
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Fill in the missing amounts.
Receipt of May is 835
Net cash flow of April is 210
Cumulative balance of March is 240
Explanation
Net cash flow = Receipt - Expense
Receipts amount = Expenses+Net cash flow
Cumulative balance amount =Cumulative amount for April-Net cash flow for April
Tv is a medsegment of UWX
if WX=3s+77 and TV=2s+42, what is TV
For the figure shown in the image having TV as the midsegment, the length of TV is 40
What are similar triangles?When the comparable triangles' angles are congruent and their respective sides are proportionate, this is referred to as similar triangles in geometry.
In light of this, if the triangle's corresponding angles are congruent, then the side should be proportionate.
For the given figure, the proportionate sides are
UV and TV, UW and WX
Calculating for s
UV / TV = UW / WX
1 / (-2s + 42) = 2 / (3s + 77)
cross multiplying
3s + 77= 2(-2s + 42)
3s + 77= -4s + 84
collecting like terms
3s + 4s = 84 - 77
7s = 7
s = 1
solving for TV
= -2s + 42
= -2 * 1 + 42
= 40
the value of TV is 40
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What is ratio short answer?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other
What is an equivalent ratios?
A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.
Given ratios are 2:1 and 3:1
we can write it as 2/1 and 3/1.
The lcm of 2 and 3 is 6.
Multiply denominator of both ratio with 6, we get
2/6 and 3/6 And we can see both the ratios are not equal.
Hence, there are not equivalent ratios.
4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2
11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)
3:1 and 9:3 are equivalent ratios ------> is true
because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3
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Find x (5x-37)=(3x+1)
Answer:
x = 19
Step-by-step explanation:
5x - 37 = 3x + 1 (move over the 3x by subtracting)
2x - 37 = 1 (move over the 37 by adding)
2x = 38 (divide both sides by 2)
x = 19
x=19
Step-by-step explanation:
(5x-37) = (3x+1)
5x - 3x = 1 + 37
5x - 3x = 38
2x = 38
x = 19
It took Jada's aunt 34 hour to put a puzzle together. It took Jada 213 times as long as her aunt to put the puzzle together.
How long did it take Jada to put the puzzle together?
Enter your answer as a mixed number in simplest form by filling in the boxes.
$$
hours
[tex]1\frac{3}{4}[/tex] hours Jada took to put the puzzle together.
What is Fraction?A fraction represents a part of a whole.
Given that Jada's aunt took 3/4 hour to put a puzzle together.
Jada took [tex]2\frac{1}{3}[/tex] times as long as her aunt to put the puzzle together.
Convert the mixed fraction [tex]2\frac{1}{3}[/tex] to improper fraction
[tex]2\frac{1}{3}[/tex] =7/3
As there is given Jada took [tex]2\frac{1}{3}[/tex] times as long as her aunt to put the puzzle together we have to multiply 7/3 with 3/4
7/3×3/4
7/4
This can be written as mixed fraction
[tex]1\frac{3}{4}[/tex]
Hence, [tex]1\frac{3}{4}[/tex] hours Jada took to put the puzzle together.
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A student draws portraits for customers. When the price of a picture is $180, the demand is 8 portraits. When the price of a picture is $100, the market is 24 portraits. Which graph best models the demand as a function of the cost? (Please show the steps on the graph)
Answer:
Q = 216 - 0.5P
Step-by-step explanation:
One approach to modeling the demand as a function of the cost is to use a linear demand equation of the form:
Q = a - bP
where Q is the quantity demanded, P is the price, and a and b are constants. To find these constants, we can use the two points given:
When P = $180, Q = 8 portraits, so 8 = a - b * 180
When P = $100, Q = 24 portraits, so 24 = a - b * 100
Solving the system of equations gives us:
a = 216
b = 0.5
So, the demand equation is:
Q = 216 - 0.5P
This represents the demand for portraits as a function of the price, where the demand decreases linearly as the price increases.
Line q passes through points (10, 9) and (4, 2). Line r passes through points (8, 8) and (2, 1). Are line q and liner parallel or perpendicular?
Answer: Parallel
Step-by-step explanation:
To solve this question, we need to find the slopes of both lines q and r.
First, let's find the slope of line q.
Δx/Δy=-7/-6 = 7/6
Next, the slope of line r.
Δx/Δy=-7/-6 = 7/6
Both lines have the same slope.
Therefore, they are parallel.
6x-2y=26 -y+3=x Solve the system by substitution
Step-by-step explanation:
6x-2y = 26 ---(1)
x+y = 3 -------(2)
so, (y = 3-x)
put in equation 1st.,
6x-2(3-x) = 26
6x-6+2x = 26
8x = 32
(x = 4)
so, put x value in equation 2nd,
4+y = 3
(y = -1 ) Answer
Answer:
x = 4
y = -1
Step-by-step explanation:
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Given:
6x-2y=26
-y+3=x
Flip the equation around:
x = 3 - y
6(3-y) - 2y = 26 << Distribute property
18 -6y -2y = 26 << Add liked term
18 -8y = 26
-8y/-8 = 8/-8 << Divide both sides by -8
y = -1
Now, substitute y into the equation also known as -1.
6x - 2(-1) = 26
6x + 2 = 26 << Subtract 2 from 2 and 26 from 2
6x = 24
6x/6 = 24/6 << Divide both sides by 6.
x = 4
Hence, x = 4 and y = -1.
RevyBreeze
what is the gcf of 81 and 72
Answer: 9
Step-by-step explanation: It's 9 because both can be divided by 9, as the largest time without going over. As you can see, 81 divided by 9 is 9, and 72 divided by 9 is 8. 8 and 9 are the closest they can be without going over 81 and 72, so it's 9. I hope this helps!
The GCF of the numbers 81 and 72 is 3², which equals 9.
To find the greatest common factor (GCF) of 81 and 72, we can use several methods.
One common approach is to factorize both numbers and identify the common factors.
The prime factorization of 81 is 3⁴, and the prime factorization of 72 is 2³×3².
To find the GCF, we look for the highest power of common prime factors in both numbers.
The highest power of the common prime factor (3) is 3², since it appears as a factor in both numbers.
Therefore, the GCF of 81 and 72 is 3², which equals 9.
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