The total number of miles Reuben biked last year and this year is the sum of the miles he biked last year and this year.
You can represent the total number of miles he biked as:
Total miles = 496 + m
Where 496 is the number of miles biked last year and m represents the number of miles biked this year.
So the expression for the total number of miles he biked is 496 + m
Where are exponential functions used?.
In the biological sciences, exponential functions are frequently employed to simulate the evolution of a certain quantity over time, such as population number. Experimental data graphs are often created with the quantity on the y-axis and the time on the x-axis.
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth. You will find the formulas, rules, characteristics, charts, deviations, exponentially series, and examples of exponential functions in this article.
Depending on the exponential function, an exponential curve might increase or decrease. A quantity should have either exponential growth or exponential decay if it regularly increases or decreases by a predetermined percentage.
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Periodical Express is a newspaper printing company. They printed 450 copies of The Informer in just 15 seconds! They next need to print 300 copies of the Sport Report.
If they print at the same rate, how many seconds will it take to print the Sport Report?
Answer:
10 seconds
Step-by-step explanation:
create a proportion
450 copies over 15 seconds = 300 copies over 't' seconds
cross-multiply to get:
450t = 4500
t = 10
it will take 10 seconds for Periodical Express to print 300 copies of the Sports Report if they maintain the same printing rate.
What are arithmetic operations?
Arithmetic operations are basic mathematical operations that include addition, subtraction, multiplication, division, and others.
Periodical Express printed 450 copies of The Informer in 15 seconds, which means they printed 450/15 = 30 copies per second.
To find out how long it would take to print 300 copies of the Sports Report, we just need to divide the number of copies by the rate of printing.
So, the calculation is 300 / 30 = 10 seconds
Therefore, it will take 10 seconds for Periodical Express to print 300 copies of the Sports Report, if they maintain the same printing rate.
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Find the length of a rectangle whose breadth is 1.8m and area is 6.12m
a)2. 2.6 m
b)3.2 m
c)3.4 m
d)3.6 m
Answer:
C
Step-by-step explanation:
Rectangle Area = Length x Breadth
6.12 = Length x 1.8
Therefore, Length = 3.4m
What is tan formula?.
The tangent formula is thus written as follows:
tan θ = (opposite side) / (adjacent side)
where "opposite side" refers to the side that is across from angle x and "adjacent side" refers to the side that is right next to it.
The tangent (tan) function is discussed in the tangent formulas. Let's assume a right-angled triangle where x is the acute angle.
The tangent formulas are trigonometric formulas that describe the tangent function. One of the six trigonometric functions, the tangent function, also known as "tan," is the ratio of the opposite side to the adjacent side.
Numerous trigonometric identities and formulas can be used to obtain numerous tangent function-related formulas.
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Ivan tart with 150$ and ave 5 each week uma ha 45 and ave 20 each week write linear equation to repreaent ivan and uma aving
The equation that represent Ivan having is: 150+ 5x and Uma having is: 45 + 20x
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
To solve this problem, we have to state the equation using the information of the problem:
Information about the problem:
Ivan start = 150$Ivan's weekly profit= 5$Uma start = 45$Uma's weekly profit= 20$Ivan equation = ?Uma equation= ?Writing the equation according to the information gave, we have:
y(Ivan) = 150+ 5x
y(Uma) = 45 + 20x
Where:
Amount earned = yNo. weeks passed = xThe relationship between the No. weeks passed and the amount earned is: linear and direct because when the number of weeks increases (x), the amount earned (y) will decrease.
The "y" variable is the dependent variable, because it will change according to the number of weeks passed (x).
The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of weeks passed.
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what do we know about data points that are plotted below our y=x? (line of best fit)
Data points plotted below the line y=x (also known as the line of best fit) indicate that the observed value is less than the predicted value.
What exactly is a math graph?
A math graph is a visual representation of mathematical data or concepts. It typically uses Cartesian coordinates (x, y) to plot points, lines, and shapes that help to illustrate mathematical relationships. Graphs can be used to represent many types of mathematical information, including functions, equations, data sets, and geometric shapes. They are commonly used in fields such as science, engineering, economics, and statistics to analyze and understand complex information. Graphs are also an important tool for conveying mathematical ideas and results in a clear and understandable way.
This could be due to measurement errors, outliers, or other factors that are not accounted for in the model used to generate the line of best fit. It's important to note that the location of data points relative to the line of best fit can provide insight into the underlying pattern or relationship between the variables being studied, but further investigation is needed to determine the specific cause of the discrepancy.
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3. Let R be the region in the first quadrant bounded by the graph of y = x2, the x-axis, and the line x = 3. Part A: Find the area of the region R. Part B: Find the value of h such that the vertical line x = h divides the region R into two regions of equal area.Previous question
The dimensions of the region bounded by the curve, y² = x, the lines, x = 1 and x = 4, and the x-axis exists the dimensions ABCD
What is meant by angle?Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet. The word "angle" is derived from the Latin word "angulus," which means "corner," and there are numerous types of angles depending on measurement. Acute, obtuse, right, straight, reflex, and full rotation are the names of basic angles. Two rays can be joined at their termini to form the geometric shape known as an angle.Everyone has an angle, according to cynical belief, is wisdom. Having an angle refers to operating in a way that prioritises your own needs over those of others. No one can be impartial or selfless if everyone has a point of view.Thus area of ABCD = [tex]\int_1^4 \mathrm{ydx} \\[/tex]
[tex]& =\int_1^4 \sqrt{\mathrm{x}} \mathrm{dx} \\[/tex]
[tex]$& =\left[\frac{\mathrm{x}^{\frac{3}{2}}}{\frac{3}{2}}\right]_1^4 \\[/tex]
[tex]$& =\frac{2}{3}\left[(4)^{\frac{3}{2}}-(1)^{\frac{3}{2}}\right][/tex]
simplifying,
[tex]$& =\frac{2}{3}[8-1] \\[/tex]
Then we get,
[tex]$& =\frac{14}{3} \text { units }[/tex]
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The square root parent function is translated so that the endpoint is located at (-7,7). Write an equation that represents this new function
The square root function is translated so that the endpoint is located at (-7,7), [tex]g(x)= \sqrt{x+7} +7[/tex] and this can be determined by using the transformation.
The square root parent function is translated so that the endpoint is located at (-7,1).
The following steps can be used to determine the equation that represents this new function:
Write the square root parent function.[tex]f(x) =\sqrt{x}[/tex]
The graph of the above function is translated by a factor of 7 in the negative x-axis that is in the left direction.Then the graph obtained in the above step is translated by a factor of 7 in the positive y-axis in the upward direction.Write the equation of the function that obtains in step 3.[tex]g(x)= \sqrt{x+7} +7[/tex]
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−3x(4x−2),2x(6x 2 +4x−3) multiply
(2x−3)(5x+6),multipy the polynomial by the box method
2x(6x2 + 4x − 3) × (2x − 3)(5x + 6)
= (2x)2(6x2 + 4x − 3)(5x + 6)
= 12x3(5x + 6) + 8x2(5x + 6) − 6x(5x + 6)
= 60x4 + 48x3 − 45x2 − 36x
Sides of a triangle are (x^2-1), (x^2+1) and 10cm. If the area of the triangle is 120cm^2, find x
If the area of the triangle is 120 cm^2, the value of x is equal to 6.
How to calculate the area of a triangle?Mathematically, the area of a triangle can be calculated by using this mathematical expression:
Area of a triangle (A) = 1/2 × b × h
Where:
b represents the base area of a triangle.h represents the height of a triangle.According to Hero's Formula area of triangle by Heron of Alexandria, if a, b, c are the side lengths of a triangle, then, the area of a triangle can be calculated by using this mathematical expression:
Area of a triangle (A) = √[s(s − a)(s − b)(s − c)]
Where:
s = (a + b + c)/2
s = (x + x + 1 + 2x - 1)/2
s = 4x/2
s = 2x
Substituting the parameters into Hero's Formula formula, we have the following;
x√10 = √[2x(2x − x)(2x − x - 1)(2x − 2x + 1)]
x√10 = x√2(x − 1)
√10 = √2(x − 1)
Taking the square of both sides, we have:
10 = 2(x - 1)
10 = 2x - 2
2x = 12
x = 12/2
x = 6.
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During a food drive, one classroom collected 268268268 cans of food and another classroom collected 424424424 cans. They packed the cans in boxes with 242424 cans in each box.
Answer:
268268268 + 424424424 = 692692692
So there are 692692692 cans of food
692692692 - 242424 × x = 0
x = Amount of boxes used
x = 2857.36021186...
The rounded answer is 2857.
How do you teach division to Year 3?.
Chunking is a good way to introduce your child to some of the more basic concepts of division, and once they have come to terms with this they can then move onto the short method of division.
Now, According to the teaching Ideas:
Start with a clear definition of division. Reinforce Mathematical language expectations with clear definitions for dividend, divisor and quotient. Explore word problems with pictorial support.Model how to use manipulatives to represent the grouping in the word problem.We have four basic arithmetic operations i.e., addition, subtraction, multiplication, and division. Amongst these four operations, the division is one of the major operations we use in our daily activities. It is the process of splitting a large group into equal smaller groups. For example, divide 25 by 5. Division fact for this example will be, 25 ÷ 5 = 5.
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Why is a circle not 100 degrees?.
A circle not 100 degrees because 360 is a highly composite number, when a circle is drawn it completes a whole loop making it a 360 degrees.
As you surely well know, we modern people like to divide a circle into 360 wedges that resemble pies. We define the angle at the vertex of each of these wedges as being one degree in size. As you presumably well know, we can measure angles in other ways other in degrees. Angles are also measured in radians and, on a very rare occasion, in the enigmatic gradians used by the military (thus the presence of "deg rad grad" buttons on many calculators).
While the reason the 360 degree convention was chosen is unknown to us, we do know roughly when and where it all began (more on that in a moment). We at least know that it originated a very, very long time ago—around 4,000–5,000 years ago with the Babylonians, the Greeks, and possibly other much older peoples.
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In 2014, the U. S. House of Representatives approved a new farm bill establishing the Margin Protection Program (MPP) for dairy producers. Assume that the program has effectively created a price floor for milk at $0. 18 per pound. Use the following additional information to answer the following questions: Without the price floor, the equilibrium price of milk is $0. 15 per pound, and the equilibrium quantity is 200 billion pounds of milk. The supply curve intersects the price axis at $0. 05 and the demand curve intersects the price axis at $0. 25. At the price floor of $0. 18, the quantity supplied is 260 billion, and the quantity demanded is 140 billion. To support the price floor, the USDA buys up the 120 billion pounds of excess milk. In the absence of a price floor, how much consumer surplus is created? How much producer surplus? What is the total surplus (producer surplus plus consumer surplus)?
Without the price floor, the equilibrium price is $0.15, and the equilibrium quantity is 200 billion pounds of milk.
Consumer surplus is calculated as the difference between the maximum price a consumer is willing to pay for a good and the price they actually pay. With an equilibrium price of $0.15, the consumer surplus can be calculated by calculating the area between the demand curve and the price line at $0.15.
The producer surplus can be calculated using an equilibrium price of $0.15 by calculating the area between the supply curve and the price line at $0.15. The producer surplus is the triangular area between the two prices and the supply curve, which intersects the price axis at $0.05.
The sum of the consumer and producer surpluses is the total surplus. Without the price floor, the consumer and producer surpluses would be different than they are now. The total surplus would also differ, reflecting changes in consumer and producer behavior.
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[tex]4 3/8 + 2 5/12 -3 1/6[/tex]
55/24 will be the simplified form of the expression 43/8 + 25/12 -31/6.
What is Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
given an expression 43/8 + 25/12 -31/6
Simplify given data
=> 43/8 + 25/12 -31/6
=> 5 + 3/8 + 2 + 1/12 - 5 - 1/6
=> 2 + 3/8 + 1/12 - 2/12
=> 2 + 3/8 -1/12
=> 2 + 9/24 -2/24
=> 2 + 7/24
=> 55/24
therefore, The simplified form of the given equation will be 55/24.
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If point A is located at (-9, 3) on a coordinate plane, and point B is located at (-9, 10), what is the distance between the two points?
Answer: 7
Step-by-step explanation:
the -9 coordinate is the same, so to get the distance you do 10 - 3 which is 7
The distance between points A and B is 7units if point A is located at (-9,3) on a coordinate plane, and point B is located at (-9,10).
A point A is located at (-9,3) on a coordinate plane, and point B is located at (-9, 10)
The coordinate of point A is (-9, 3)
The coordinate of point B is (-9, 10)
The distance formula can be given as:
d=[tex]\sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]
d=[tex]\sqrt{((-9)+9)^2 + (10-3)^2}[/tex]
d=[tex]\sqrt{7^2}[/tex]
d=7
The distance is 8 units.
Therefore, the distance between points A and B is 7 units if point A is located at (-9,3) on a coordinate plane, and point B is located at (-9, 10).
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in birr 24000is invested at interested rate of 4% compounded you fairly then the amount of money after 10 years in birr?
Answer:
To find the amount of money after 10 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt)
Where:
A = the amount of money after 10 years
P = the initial investment (24000 birr)
r = the interest rate (4%)
n = the number of times the interest is compounded per year
t = the number of years
In this case, since the interest is compounded annually, n = 1.
So,
A = 24000(1 + 0.04)^(1*10)
A = 24000(1.04)^10
A = 24000(1.46) = 24000*1.46 =35,040 birr
So, after 10 years the total amount of money will be 35,040 birr.
50 points!!!
7. Write and solve an inequality for the value of x.
The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.
What is Triangle inequality theorem?
The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.
We are given three sides of a triangle as 8, 6 and x+20
Using Triangle inequality theorem,
⇒8+6 > x+20
⇒14 > x+20
⇒-6 > x
Also,
⇒x+20+6 > 8
⇒x+26 > 8
⇒x > -18
Also,
⇒x+20+8 > 6
⇒x+28 > 6
⇒x > -22
From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.
This means that x must lie between -18 and -6.
Hence, the value of x must be between -18 and -6.
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Moira can olve 15 math problem in 20 minute. How long will it take her to olve 21 math problem?
So it will take 945 sec to solve 21 math problem.
As per the data given in the above question are as bellow,
The details provided are as bellow,
Moria solve 15 math question in 20 minutes,
We have to determine how long will it take her to solve 21 math problem?
First taking how much time its take to solve one question ,
So, Total number of question divide the total time we get,
Substitute the value in above equation we get,
=15* 60 =900 Sec
=900/20
=45 sec
So the time taken to solve 21 question will be,
=45*21
=945 sec
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Paul received a $15 tip on a meal that cost $120. What percent of the meal cost was the tip?.
Answer:
12.5%
Step-by-step explanation:
12.5% of 120 is 15 so if you take 15 divided by 120 you would get 0.125 and turned into a percentage is the 12.5%
Julianne and Vito caught 6 flounders, which was 75% of the fish they caught. How many fish did Julianne and Vito catch altogether?
Answer:
8 FISHES
Step-by-step explanation:
There are several ways to solve this but lets use proportion cus I feel it's easier. So what you are looking for is simply 100% of the fish they caught.!
So therefore, 75% = 6
100% = (100 × 6) ÷ 75
= 600 ÷ 75
= 8 FISHES
The um of Joy' age and her brother' age i $24. Her brother' age i $3 year older than twice Joy' age. What i the difference, in year, between Joy' age and her brother' age?
To determine their ages, the substitution approach is used.
Joy's age and her brother's age are differed by 10 years.
What is linear system?
It is an system of equation where the maximum power of the variable is consistently 1. a single-dimensional object with no breadth. It consists of an endless number of dots placed side by side.
Given
The combined ages of Joy and her brother total 24.
Joy's older brother is three years older than twice his age she is.
To locate
Joy's age as compared to that of her brother.
Assume that Joy is x years old and her brother is y.
then in line with the first circumstance.
x + y = 24 ...(1)
And according to the second condition.
2x + 3 = y ...(2)
On solving equations 1 and 2. We get
x + 2x + 3 = 24
x = 7
Then
y = 2x + 3
y = 17
Then, the difference between Joy's age and her brother's age.
y - x = 17 - 7 = 10
Thus, the difference between Joy's age and her brother's age is 10.
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How do you find no solution?.
We can find no solution by the condition; if (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂), then there will be no solution.
A linear equation in two variables is a type of equation in the form ax + by + c = 0 where a, b, c ∈ R, a, and b ≠ 0. A linear equation with no solution is named an inconsistent pair of linear equations.
Suppose the pair of linear equations is in two variables, x and y.
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Where a₁, b₁, c₁, a₂, b₂, c₂ are all real numbers.
Note that, a₁² + b₁² ≠ 0, a₂² + b₂² ≠ 0
If (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂), then there will be no solution.
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The 7th grade Tigers went on a trip to Canobie. Admission was $15 per person and the bus fee was $270. The total cost for the trip was $1440. How many Tigers went on the trip?
Answer:
78 Tigers
Step-by-step explanation:
1440=270+15x
1170=15x
78=x
What are the rectangular coordinates for (4. 5, -30 degrees)?
A. (-2. 3, 3. 9)
B. (3. 9, -2. 3)
C. (3. 9, 2. 3)
D. (2. 3, -3. 9)
The rectangular coordinates for (4.5, -30 degrees) are (3.9, -2.3), which is option B.
What is rectangle ?
A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle.
To find the rectangular coordinates for a point in a plane given its polar coordinates, use the following formula:
x = r * cos(θ)
y = r * sin(θ)
Where (r, θ) are the polar coordinates and (x, y) are the rectangular coordinates.
For the point (4.5, -30 degrees), have:
r = 4.5
θ = -30 degrees = -30 * (π / 180) radians
x = r * cos(θ) = 4.5 * cos(-30 * (π / 180)) = 3.9
y = r * sin(θ) = 4.5 * sin(-30 * (π / 180)) = -2.3
So, the rectangular coordinates for (4.5, -30 degrees) are (3.9, -2.3), which is option B.
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The rectangular coordinates for (4. 5, -30 degrees) are (3.9, -2.3).
The rectangular coordinates for (4.5, -30 degrees) can be found using the following formula:
x = r * cos(θ)
y = r * sin(θ)
where r is the magnitude (or distance from the origin) and θ is the angle in radians.
In this case, r = 4.5 and θ = -30 degrees = -30 * (π/180) radians.
So:
x = 4.5 * cos(-30 * (π/180)) = 4.5 * cos(-π/6) = 4.5 * sqrt(3)/2
y = 4.5 * sin(-30 * (π/180)) = 4.5 * sin(-π/6) = -4.5 / 2
Therefore, the rectangular coordinates are (x, y) = (4.5 * sqrt(3)/2, -4.5 / 2), which is approximately (3.9, -2.3).
Option B (3.9, -2.3) is the right response as a result.
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What is the area of this triangle in the coordinate plane?
25. 0 units²
27. 5 units²
50. 0 units²
55. 0 units²
Previous
Next
The area of this triangle in the coordinate plane with coordinates A( 4,5) , B(1,2) and C( 6,2) is equals to the 15 unit². So, option (d) is correct.
The basic formula for the area of a triangle is (1/2) × base × altitude. But we have to calculate the area of a triangle in coordinate geometry. Coordinate geometry is defined as the study of geometry using coordinate points. If coordinates of the triangle are(x₁, y₁), (x₂, y₂), and (x₃, y₃) then the area of the triangle is defined as Area = 1/2[ x₁(y₂ - y₃) + x₂( y₃ - y₁) + x₃(y₁ - y₂) ]
We have a triangle ABC in coordinate plane in above figure. The coordinates of triangle are A( 4,5) , B(1,2) and C( 6,2). Here, x₁ = 4 , y₁ = 5 , x₂ = 1 , y₂ = 2 ,x₃ = 6 , y₃ = 2. So, Area of ∆ABC
= 1/2[ 4( 2 - 2)+ 1( 2 - 5) + 6(5 - 2)
= 0 + (-3) + 18 = 15
Hence, the required area is 15 unit².
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Complete question:
What is the area of this triangle in the coordinate plane? See the above figure.
a)25. 0 units²
b) 27. 5 units²
c) 50. 0 units²
d) 15. 0 units²
How do you graph an absolute value piecewise function?.
The process to graph an absolute value piecewise function is explained below .
Let us consider the Absolute value function as :
y = | x -2 | ;
this absolute function can be written in piecewise wise form as :
⇒ [tex]y =\begin{array}{cc} \{ & \begin{array}{cc} -x+2 & x < 2 \\ x-2 & x\geq 2 \end{array}\end{array}[/tex] ;
this piecewise function means that the main function divides into two pieces ,
for any input value that is less than 2 , the function"-x+2" will be used , and
for any input value greater than or equal to 2, the function "x-2" , will be used ;
for example : if x = 3 , then ⇒ y = 3 - 2 = 1 ;
and is x = 1 , then ⇒ y = -1 +2 = 1 ;
the points to be plotted are (3,1) and (1,1) .
The graph of this absolute value piecewise function is shown below .
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How to solve 2x 3y 10?.
To solve the equation 2x + 3y = 10 we need to plot the graph for the equation by calculating the intercepts for the same.
Here we see that we are given the equation
2x + 3y = 10
Since we do not have any other equation we will solve this by plotting it on a graph by the intercepts.
Intercepts of both the x and y axes are obtained by equating the other to 0.
Hence to get the x-intercept, we need to equate y to 0
Hence we get
2x = 10
or, x = 5
Hence for the y-intercept, we equate x to 0 to get
3y = 10
or, y = 10/3
By plotting these points and drawing a line through them we will get the graph for the equation.
Now to obtain a unique solution, we need to follow similar steps for the other equation and the intersecting point will give us the solution.
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Complete Question
How to solve 2x + 3y = 10?
Given m∥n, find the value of x.
The value of x is 16.2degrees
What are supplementary angles?Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
Given;
(x+14), (9x-4)
Now,
According to supplementary angles;
(x+14)+ (9x-4)=180
10x+18=180
10x= 180-18
10x= 162
x= 16.2
Therefore, in these angles the value of x will be 16.2degree
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A pet tore employee put only ilver fih and goldfih in an aquarium. The ratio of the number of goldfih to the total number of fih in the aquarium wa 6 to 11. Which number could be the number of ilver fih the employee put in the aquarium?
The number of silverfish employees put in the aquarium is 11.
The ratio is defined as a comparison of two quantities of the same unit to determine how much of one quantity is contained in the other. Ratios are divided into two sorts.
The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between two distinct entities or groupings.
Given that,
The ratio of the number of g total number of fish in the aquarium = 6: 11
Let us assume that the total number of silverfish employees put in the aquarium is x
So, The total number of fish = 6+11 = 17 out of which 11 are silverfish.
Complete question: A pet store employee put only silverfish and goldfish in an aquarium. The ratio of the number of g total number of fish in the aquarium was 6 to 11. Which number could be the number of silverfish employees put in the aquarium?
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