The equation of the circle in standard form is (x + 5)² + (y)² = 9/4.
How to write the equation of the circle in standard formThe general representation of the equation is:
(x-h)² + (y-k)²= r²
Where (h,k) is the coordinates of the center of the circle and r is the radius. And x and y are the corresponding x and y values of the point the circle passes through
Since we have the coordinate of the center as (-5,0) and the circle passes through (-5, 3/2). Therefore:
h = -5, k = 0, x = -5 and y = 3/2
Let's put these values in the formula.
(x-h)² + (y-k)²= r²
(-5 - (-5) )² + (3/2 - 0)² = r²
(-5 + 5)² + (3/2)²= r²
(0)² + (3/2)²= r²
(3/2)² = r²
r = 3/2
Putting radius, r = 3/2, h = -5 and k = 0 back into the formula wiil give:
(x + 5)² + (y - 0)²= (3/2)²
(x + 5)² + (y)² = 9/4
Therefore,the standard form of the equation of the circle is (x + 5)² + (y)² = 9/4.
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15% of x=20% of y what is x:y?
The ratio of x:y is 4:3.
What is ratio?Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categories ratios. Part to whole ratio is one, while part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.
For instance, a class has a 12:15 boy-to-girl ratio, but the part-to-whole ratio refers to the relationship between a particular group and the entire. For instance, five out of every ten people enjoy reading. As a result, the ratio of the portion to the total is 5: 10, meaning that 5 out of every 10 persons enjoy reading.
Given:
15% of x=20% of y
So,
15 / 100 × x = 20 / 100 × y
3 / 20x = 1/5y
x / y = 1/5 x 20/3
x / y = 4/3
Hence, the ratio of x:y is 4:3.
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a playground is rectangular with a length of 7/8 miles. If the area of the play ground is 8/20 miles what is the width.
Answer: Width = 8/20 ÷ 7/8 = 8/20 x 8/7 = 16/35 Therefore, the width will be 16/35 miles. Hope you do great :) !
Caitlin purchased n notebooks. They were 4 dollars each. Write an equation to represent the total cost c that Caitlin paid
The equation for the purchase of n number of notebooks by Caitlin is
4n = c , where c is representing the cost that Caitlin paid.
What is unitary method ?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Finding the value of a single unit using the unitary technique allows us to determine the value of the necessary number of units based on this value.
Calculationthe price for one notebook was = $4 each
n number of notebooks were purchased by caitlin
therefore the cost price of 4 notebooks will be = 4 * n
as per given in the question cost price = c
therefore the equation formed will be
4n = c
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each individual in a random sample of high school and college students was cross-classified with respect to both political views and marijuana usage. does the data support the hypothesis that political views and marijuana usage level are independent within the population?
Since X² (68.732) > X²₀.₀₁ (13.277), we reject the null hypothesis and conclude that There is evidence that political views and level of marijuana usage are related.
The alternative hypothesis states that political beliefs and marijuana use depend on one another within the population, contrary to the null hypothesis that asserts these two variables are independent.
H₀ : Pij = Pi · Pj ; i = 1, 2, 3 ; j = 1, 2, 3
Ha : at least one Pij ≠ Pi · Pj
We want to test whether there is a relationship between political views and marijuana usage levels. The results of a random sample of size n = 1353 are derived from the following formula;
e = (Row total) x (Column total) /Total sample size
We are told to use the 0.01 level of significance to test the null hypothesis. Thus, α = 0.01. The table has r = 3 rows and c = 3 columns. An r × c table has degrees of freedom df = (r - 1) x (c - 1). So, a 3×3 table has degrees of freedom df = (3 - 1) x (3 - 1) = 4. From formula the df = 4 and α = 0.01, χ²₀.₀₁ = 13.277. Reject the null hypothesis if X² ≥ 13.277 where
x² =Σ(a - e)²/e
Substituting the observed and expected frequencies summarized in the table above into the formula for x², we get
X² = 68.732
Rejection Region → X² ≥ 13.277
Test statistic → X² = 68.732
Since X² (68.732) > X²₀.₀₁ (13.277), we reject the null hypothesis and conclude that There is evidence that political views and level of marijuana usage are related.
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A circle has a circumference of 320 cm.
What is its radius?
A. 80 cm
B. 160 cm
C. 320 cm
D. 320 cm!
If a circle has a circumference of 320 cm, then its radius can be calculated as 50.92 cm according to the formula of circumference of a circle.
What is circumference?In geometry, the circumference can be defined as the perimeter of a circle or an ellipse. It can also be said as the linear distance present around it.
To better describe it, you can imagine that if a circle is opened out and placed as a straight line, then the total length of that straight line can be described as the circumference of the circle.
It is synonymous to perimeter, but the terminology can only be used with circled and ellipses. It is the curved length of the object. In this case, the object is mostly 2 dimensional but sometimes 3 dimensional objects can also be placed to take out their circumference with other methods.
In this particular question,
2[tex]\pi[/tex]r = 320
⇒ r = 320/2[tex]\pi[/tex]
⇒ r = 50.92
⇒ r ≈ 51 cm
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In circle Q with the measure of arc ⌢=118∘PR⌢ =118 ∘ , find m∠PQRm∠PQ
Explanation
We are given the measure of arc PR = 118°.
We are required to find m∠PQR.
We know that an arc measure is an angle the arc makes at the center of a circle. Therefore, we have:
[tex]\begin{gathered} obtuse\text{ }m\angle PQR=118\degree \\ obtuse\text{ }m\angle PQR+reflex\text{ }m\angle PQR=360\degree\text{ }\lbrace angles\text{ }at\text{ }a\text{ }point\rbrace \\ reflex\text{ }m\angle PQR=360\degree-obtuse\text{ }m\angle PQR \\ reflex\text{ }m\angle PQR=360\degree-118\degree \\ reflex\text{ }m\angle PQR=242\degree \end{gathered}[/tex]Hence, the answer is:
[tex]\begin{gathered} obtuse\text{ }m\angle PQR=118\degree \\ reflex\text{ }m\angle PQR=242\degree \end{gathered}[/tex]But since Q is the measure of the angle, then the final answer is 118°.
What is the image point of (-8, 9) after a translation right 3 units and
down 1 unit?
Answer: (-5, 8)
Step-by-step explanation:
The x-coordinate is responsible for left and right, and the y-coordinate is responsible for up and down translations. Coordinate points are written as (x, y).
(-8, 9) ➜ (-8 + 3, 9 - 1) ➜ (-5, 8)
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Canon needs to produce 1000 milliliters of 36% alcohol solution. At his disposal he has 40% alcohol solution and 20% alcohol solution. How much of each does he need in order to produce his desired solution?
x = milliliters of 40% alcohol
y = milliliters of 20% alcohol
so just alcohol alone in each quantity will just be "x" * (40/100) = 0.4x and "y" * (20/100) = 0.2y, whilst trying to get 1000 mL of 36% alcohol only.
[tex]\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{mL of }}{amount}\\ \cline{2-4}&\\ \textit{40\% solution}&x&0.4&0.4x\\ \textit{20\% solution}&y&0.2&0.2y\\ \cline{2-4}&\\ mixture&1000&0.36&360 \end{array}~\hfill \begin{cases} x+y=1000\\\\ 0.4x+0.2y=360 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=1000\implies }x=1000-y ~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.4(1000-y)+0.2y=360} \\\\\\ 400-0.4y+0.2y=360\implies 40-0.4y+0.2y=0\implies 40-0.2y=0 \\\\\\ 40=0.2y\implies \cfrac{40}{0.2}=y\implies \boxed{\stackrel{mL}{200}=y} ~\hfill \boxed{\underset{mL}{\stackrel{1000~~ - ~~200}{x=800}}}[/tex]
I need help finding the perimeter
Answer:
Perimeter (to the nearest tenth) = 24.3
Step-by-step explanation:
Using the math tool graph your points on the graph and connect them to each other. You should have something like this (look at the first image)* [note the scale of my graph is one but I skip the odd numbers] From there you can count the distance from those points. To find the distance from point R to Q and from point Q to S you can simply count the number of square from those points. For instance from point R to point Q is 9 units and from point Q to point S is 5 units (look at the second image) To find the distance from point R to point S you do the Pythagorean theorem since this triangle is a right triangle which is Leg² + Leg² = Hypothnose². Let line segments RQ and QS be the legs and let line segment RS be the hypothnose. Since the square root of the hypothnose is an irrational number we take advantage of round to the nearest tenth so 10.295... will become 10.3. (In case you're confused follow the steps of the third image)To find the perimeter of the triangle you add all of the sides together so the formula for solving for it would be P = 9 + 5 + 10.3 which is 24.3. The perimeter is 24.3. (The foruth and last image shows all the work)I need help please ! I'm struggling
The graph of the quadratic equation:
y = x^2 -8x + 16
Can be seen in the image at the end.
How to graph the functions?First, we have a quadratic function:
y = x^2 -8x + 16
To graph this we need to find some points on the parabola, to do that, we will evaluate it in some values of x.
if x = 0
y = 0^2 - 8*0 + 16 = 16
So we have the point (0, 16)
if x = 1
y = 1^2 - 8*1 + 16 = 9
So we have the point (1, 9)
if x = -1 we have:
y = (-1)^2 - 8*-1 + 16 = 23
So we have the point (-1, 23)
And so on, once you have enough points, you can graph them in a coordinate axis and then draw a parabola that connects them, the graph of the quadratic equation can be seen in the image below.
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Find the value of x in each case.
The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.
How do you find the value of x?In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown. "x is a variable in x + 2 = 7, but we can figure out its value if we try! The order in which you perform operations in arithmetic and algebra is governed by a number of laws.The Commutative, Associative, and Distributive Laws are the three that receive the most attention.People have discovered over time that the sequence of the numbers has no bearing on the results of addition or multiplication.4x+2x+5x+50= 180
= 6x+5x+50 =180
combine 6x and 5x
= 11x
11x+50= 180
subtract 50 both sides
11x = 180- 5
= 130
11x=130
x= 130/11
11.81
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x+3 is greater than or equal to 2x-6 solve
The solution for x + 3 is greater than or equal to 2x - 6 is x ≤ 9.
Given,
x + 3 is greater than or equal to 2x - 6
That is,
x + 3 ≥ 2x - 6
Solve for x in this solution.
So,
x + 3 ≥ 2x - 6
Here,
6 + 3 ≥ 2x - x
Then,
9 ≥ x
That is,
The solution for x + 3 is greater than or equal to 2x - 6 is x ≤ 9.
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An engineer is designing a parking lot for a local grocery store. The parking spaces are marked with lines where
The value of x and y in the angles are 15.6 and 10.5 respectively.
How to find the variable x and y in the angles?When parallel lines are cut by a transversal lines, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, line XD, TZ, YF and LP are parallel to each other.
WC is the transversal line.
Hence,
m∠CNL = 6x - 17.6
m∠FBH = 12y - 22
m∠THR = 3x + 29.2
Hence,
180 - (12y - 22) = 6x - 17.6(corresponding angles)
Corresponding angles are congruent
180 - 12y + 22 = 6x - 17.6
6x + 12y = 180 + 22 + 17.6
6x + 12y = 219.6
Therefore,
180 - (3x + 29.2) = 12y - 22 (alternate angles)
Alternate angles are congruent .
180 - 3x - 29.2 = 12y - 22
180 + 22 - 29.2 = 12y + 3x
172.8 = 3x + 12y
combine the equation
6x + 12y = 219.6
3x + 12y = 172.8
subtract equation(ii) from equation(i)
3x = 46.8
x = 46.8 / 3
x = 15.6
12y = 219.6 - 6(15.6)
12y = 219.6 - 93.6
12y = 126
y = 126 / 12
y = 10.5
Therefore,
x = 15.6
y = 10.5
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The diagram shows a lawn with a fence along one edge.
12 m
Fence
17 m
20 m
One can of weedkiller can cover 100 square metres.
Each can costs £19.75
Work out the total cost of the cans of weedkiller needed to cover the lawn.
You must show some working.
59.25 euros is the the total cost of the cans of weedkiller needed to cover the lawn
What is Trapezium?A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other
The figure that is formed is the following with the respective measurements, now to calculate the area we need the height, for Pythagoras we have:
17 ²= h ² + 8 ²
h ² = 289 - 64
h ² = 225
h = 15
now the figure area is as follows:
A = h × (b + a) / 2
b long side 20 m and short side 12 cm, replacing:
A = 15 × (12 + 20) / 2
A = 240 m²
We are told that each can of weed killer can cover up to 100m ^ 2
Thus:
240/100 = 2.4, so you would need 3 cans of weedkiller
each can costs 19.75, which means that the total cost is:
19.75 × 3 = 59.25 euros
Hence 59.25 euros is the the total cost of the cans of weedkiller needed to cover the lawn.
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is equivalent to /x-
20 For the function w, w(9) = -7, and w(-7)= 9. If y = w(x), what is the value of y when
X = -7?
Record your answer and fill in the bubbles on your answer document.
The value of y when x = -7 according to the function defined y = w(x) is; 9.
What is the value of y when x = -7 as required in the task content?It follows from the task content that the value of y when x = -7 is to be determined according to the given expression; y = w(x).
Since it follows from the task content that;
y = w(x)
Therefore, it follows that when; x = -7; we have;
y = w(-7).
However, recall from the function instances given that; w(-7) = 9;
Therefore, y = w(-7) = 9.
Ultimately, the value of y when x = -7 as required in the task content is; 9.
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I need help on this 3rd grade homework
Pls help
The correct option or equation that applies to the given situation is 7*6 = (4*6) + (3*6).
According to the question,
We have the following information:
Akela drew smaller arrays to find the product of a larger array.
Now, we have two figures where one has 6*3 boxes (6 horizontal boxes and 3 horizontal boxes) and in the second figure we have 6*4 boxes (6 horizontal boxes and 4 vertical boxes).
Now, to find the correct option, we will look for these two in options:
So, the option that has both of them is 7*6 = (4*6) + (3*6).
Now, we can verify whether the sides of the equation given are correct or not.
We have:
7*6 = 42
On right hand side, we have:
(4*6) + (3*6)
24+18
42
Hence, the correct option is 4th one.
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Write the equation for g(x)
The equation of the graph of g is represented by y - 6 = (x-2)²
The very first step in balancing a variable equation is to correctly identify the specific values of the variables that lead to equality.
The equation's solutions are the specific values of the unknown variables that perfectly satisfy the equality, which are often referred to as the variables for which the particular equation must be solved. Identity equations and conditional equations are the two types of equations. The variables all have the same identity for all conceivable values. A conditional equation can only be true in particular situations where the values of the variables match. The equals sign is an important symbol that is used in mathematical formulas to denote the equality of two expressions.The graph of the function is f is y = x²
Now we can see that the graph of g is translated to 2 units to the right and 6 units up.
We know from the properties of translation that when the graph moves 2 units to the right we get the equation as y = (x-2)²
Again when the graph moves 6 units up wards the graph changes by
y - 6 = (x-2)²
Therefore the equation of g is y - 6 = (x-2)²
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If the knowledge that an event a has occurred implies that a second event b cannot occur, then the events a and b are said to be.
If the knowledge that an event "a" has occurred implies that another event "b" cannot occur, then the events "a" and "b" are said to be disjoint events.
As per the question statement, the knowledge that an event "a" has occurred implies that another event "b" cannot occur.
We are required to determine the characteristic name for the above mentioned events.
Now as per the Probability Theory in Mathematics, two events are said to be "mutually exclusive" or "disjoint" if they cannot occur at the same time or simultaneously.And here, if event "a" occurs, even "b" does not, implying the fact that, events "a" and "b" cannot occur simultaneously. Hence, as per the above definition of disjoint events, the events "a" and "b" are be disjoint.
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If 4a- 3 =13, then find the value of 102 - 5a+6
Answer:
86
Step-by-step explanation:
I'll assume the expression is meant to be 10^2 - 5a +6
4a- 3 =13
4a = 16
a = 4
10^2 - 5a +6
10^2 - 5(4) +6
10^2 - 20 +6
100 - 14 = 86
Someone help quickly!
Look at the picture!
What is the standard form of y=4/9x-3
Answer: 4x-9y=27 is this equation in standard form.
Write and solve an equation to
find how much greater this year's 3-month snowfall was
than last year's
In the graph, which compares the snowfall for the same three months last year and this year, you can see that the total snowfall for last year was 36.4 inches. how much more snow fell over the course of three months this year than did so last year: 5.45
what is the explanation?
The first step is to calculate the amount of snowfall from the previous year, which are:
12.6+6+9.2
=27.8
The next stage is to calculate how much snow has fallen this year, which includes:
10+15.75+7.5
=33.25
Now let's compare the snowfall over the first three months of current year to that of last year.
33.25-27.8
=5.45
In conclusion Graph showing snowfall during the same three months last year and this year, if the total snowfall for last year was 36.4
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at a delicatessen, ham costs $2.49 per pound and swiss cheese costs $3.79 per pound. The customer has $9.50 to spend on 2 pounds of ham and some cheese. how much cheese can she purchase? write an equation and solve it.
The customer can purchase 1.19788 pounds of cheese (approximately 1.2 pounds).
How much cheese can she purchase?We are given with the cost of ham is $2.49 per pound and
Cost of swiss cheese is $3.79 per pound.
So, the cost of 2 pounds of ham will be given as-
= 2× $2.49
= $4.98
Since, the customer has a total of $9.50 to spend on 2 pounds of ham and some cheese,
∴ Let the number of pounds of cheese she can purchase be x.
Then the equation will be this:
2.49*2 + 3.79*x = 9.50
4.98 + 3.79x = 9.50
Subtracting 4.98 from each side we get-
4.98 -4.98 + 3.79x = 9.50-4.98
3.79x = 4.54
x [tex]=\frac{4.54}{3.79}[/tex]
x = 1.19788 pounds of cheese (approximately 1.2 pounds).
Hence, the customer can purchase 1.19788 pounds of cheese (approximately 1.2 pounds).
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Can someone help me solved the highlighted question please. Ill give brainliest. Check attatched photo
Applying logarithm properties, the solution of the highlighted question is given as follows:
x = 4.
What is the solution for the equation?The logarithmic equation is given as follows:
[tex]\log_{a}(x + 2) = \frac{1}{3}\log_{a}{8} + \log_{a}{3}[/tex]
First, we apply the power rule, meaning that the multiplying coefficient of the logarithm can be the power of the given term, hence:
[tex]\frac{1}{3}\log_{a}{8} = \log_{a}{8^{\frac{1}{3}}} = \log_{a}{\sqrt[3]{8}} = \log_{a}{2}[/tex]
Then the equivalent expression is:
[tex]\log_{a}(x + 2) = \log_{a}{2} + \log_{a}{3}[/tex]
Now we apply the product rule, as the sum of two logarithms of same base can be written as a single logarithm, keeping the base and multiplying the terms.
Hence the equivalent expression is:
[tex]\log_{a}(x + 2) = \log_{a}{(2 \times 3)}[/tex]
[tex]\log_{a}(x + 2) = \log_{a}{6}[/tex]
The logarithm function is one-to-one, meaning that if they have the same input, they will have the same output, hence we can solve for x as follows:
x + 2 = 6
x = 6 - 2
x = 4.
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50779 / 590 remainder
Answer:
39.
Step-by-step explanation:
50779 divided by 590 is 86, with a remainder of 39.
A company produces air-filled world globes in the shape of a sphere as shown. What is the volume of a globe with a radius of 10 centimeters? Leave your answer in terms of π.A. 40π cubic centimetersB. 133π cubic centimetersC. 750π cubic centimetersD. 1333π cubic centimeters
The formula for getting the volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]where r = radius of the sphere.
Let's plug into the formula the given radius of the sphere in the question.
[tex]V=\frac{4}{3}\pi(10cm)^3[/tex]Then solve.
Multiply 10 cm by itself three times.
[tex]V=\frac{4}{3}\pi(10cm\times10cm\times10cm)[/tex][tex]V=\frac{4}{3}\pi(1000cm^3)[/tex]Multiply 1000 by 4, then divide by 3.
[tex]V=\frac{4000}{3}\pi cm^3[/tex][tex]V=1333.33\pi cm^3[/tex]Rounding the calculated volume to the nearest whole number, the volume of the sphere is 1,333π cm³ (Option D or 4)
Answer:
The volume of the sphere is 1,333π cm³ (Option D or 4)
A. No, because one x-value corresponds to two different y-values.
B. Yes, because there are two x-values that are the same.
C. No, because two of the y-values are the same.
D. Yes, because every x-value corresponds to exactly one y-value.
Answer:
its A
Step-by-step explanation:
:)
Find x of the triangle.
Answer:
x = 130°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
x is an exterior angle of the triangle , then
x = 50° + 80° = 130°
Answer: 130
Step-by-step explanation:
180 = y + 50 + 80
y = 50
180 - y = x
x = 130
Johnny found a sick abandoned kitten in his yard. It was very malnourished and he decided to nurse it back to health. He started feeding the kitten enough food to help it gain weight. On average the kitten was gaining 4 ounces per day. After 6 days in Johnny's care, the cat weighed 73 ounces. Determine how many days until the kitten will weighs 105 ounces.
Answer:9 days
Step-by-step explanation:A lot of division is required, but because 8.75 probably isn't an answer, I rounded up to 9.
A school talent show is featuring 12 acts.
In how many ways can the first 5 acts be ordered?
By the concept of basic arithmetic solo acts are 5 minutes long and ensemble acts are 15 minutes long
What are basic arithmetic?Mathematics' fundamentals are arithmetic operations. Addition, subtraction, multiplication, and division are the main operations that make up this concept. The phrase "mathematical operations" also refers to these.
The math operation of subtracting two integers reveals the difference between them. The '-' sign is used to indicate it. In math, subtraction is the process of taking one number away from another to determine what is left over after something has been taken away. Rational number operations are equivalent to those performed on whole numbers. The main distinction is that rational numbers take the form p/q, where p and q are integers and q is not equal to 0. It is necessary to take the LCM of the numerators when adding or subtracting two rational integers.
Here we are discussing the four basic rules of arithmetic operations for all real numbers.
Addition (sum; ‘+’)Subtraction (difference; ‘-’)Multiplication (product; ‘×’ )Division (÷)12 × x + 2 × y = 90
6 × x + 2 × y = 60
To write system of equation you just need to sum all solo and ensemble acts and make it equal to how much they will last for.
B. Here we can multiply second equation with negative 1 and add it to first equation.
6x = 30
x = 5
Now we replace x in any of 2 equations to get y.
30 + 2y = 60
2y = 30
y=15
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