The probability of obtaining at least four 3's on a die is P ( A ) = 1/1296
Given data ,
The probability of rolling a 3 on a fair die is 1/6, and the probability of not rolling a 3 is 5/6.
The possible scenarios that satisfy the condition of at least four 3's are as follows:
Getting exactly four 3's and one non-3
Getting exactly five 3's
Let's calculate the probabilities for these scenarios:
Probability of getting exactly four 3's and one non-3:
P(four 3's and one non-3) = (1/6)⁴ * (5/6)¹ * (number of combinations)
The number of combinations for this scenario can be calculated as 5C4 = 5.
P(four 3's and one non-3) = (1/6)⁴ * (5/6) * 5 = 5/7776
Probability of getting exactly five 3's:
P(five 3's) = (1/6)⁵ = 1/7776
Now, to calculate the probability of obtaining at least four 3's, we add the probabilities of the two scenarios:
P(at least four 3's) = P(four 3's and one non-3) + P(five 3's)
P(at least four 3's) = 5/7776 + 1/7776
P(at least four 3's) = 6/7776
Hence , the probability of obtaining at least four 3's when rolling a fair die five times is 1/1296
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5
Mary noticed a spider web on
her patio that formed a right
triangle. She determined the
diagonal length was 15 inches and
the height measured 12 inches.
She could not reach the top to
measure. How long is the top of
the spider web?
Answer: The diagonal and the height of the right triangle form the legs of the triangle, and the unknown length is the hypotenuse. To find the length of the hypotenuse, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).
So, if the legs of the right triangle measure 12 inches and 15 inches, the hypotenuse c can be calculated as follows:
c² = a² + b²
c² = 12² + 15²
c² = 144 + 225
c² = 369
Therefore, the length of the hypotenuse c is the square root of 369.
c = √369
c = 19.1 inches
Therefore, the top of the spider web is 19.1 inches long.
Step-by-step explanation:
56 unit needed, 6 unit per cae what i the number of cae and the number of additional unit?
As per the unitary method, the number of care is 9 and the number of additional method is 2.
The term unitary in set theory is defined as the way to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.
Here we have given that the total number of units is 56.
And here we also know that the number of units in each care is 6.
Now, we have to find the total number of care, that can be obtained by dividing the total care by the units in each care,
then it can be written as,
=> 56/6
When we divide the term then we get the quotient as 9 and the remainder as 2.
Therefore, while looking into these we have identified that there are 9 cares and 2 additional units are in the group.
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what is the probability of 45 heads in 100 tosses of a coin given the probability of heads is 50%? binomial distribution
The probability of 45 heads in 100 tosses of a coin given the probability of heads is 50% is 7.1%.
Coin Toss Probability CalculationThe binomial probability formula is used to calculate the probability of getting a certain number of heads (or success) in a certain number of coin tosses (or trials) when the probability of getting a head (or success) in each individual coin toss is known. The formula is:
P(x) = (n choose x) * (pˣ) * (1-p)^(n-x)
Where,
P(x) is the probability of getting x heads (or success) in n coin tosses (or trials)
n is the number of coin tosses
x is the number of heads (or success)
p is the probability of getting a head (or success) in a single coin toss
1-p is the probability of getting a tail (or failure) in a single coin toss
(n choose x) is the binomial coefficient, which is the number of ways to choose x heads (or success) from n coin tosses (or trials)
In this case, the probability of getting 45 heads in 100 tosses of a coin with a probability of heads of 50% can be calculated using the formula: (100 choose 45) * (0.5⁴⁵) * (0.5⁵⁵) which is approximately 0.071, or 7.1%.
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What is a pair of 3 called?
A "pair of 3" is not a commonly used term.
A set of 3 numbers can be called a triplet, or a set of 3 items can be called "a set of three".
Please let me know if you want me to clarify about something else.
What is inequality give answer?
An inequality is a mathematical statement that compares two expressions and expresses the relationship between them. It is represented by a symbol such as ">", "<", "≥", or "≤" and can be thought of as a generalization of an equation.
Unlike an equation, which has one unique solution, an inequality can have multiple solutions or no solution at all. The solutions of an inequality are the values that make the inequality true.
Inequalities are used to model real-world situations where there are constraints or limitations, such as determining the range of possible values for a variable. They are also used to describe relationships between variables, such as when one variable is greater than or less than another variable.
There are different types of inequalities, such as linear inequalities, quadratic inequalities, and absolute value inequalities, each with their own set of rules and methods for solving them.
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What transformations result in similar triangles?
The transformations that result in similar triangles are dilations, rotations, reflections, and translations.
A transformation that conserves the shape, but not necessarily the size, of a figure is called a similarity transformation. Rotation, reflection, and translation are rigid motions, which means they preserve both size and shape, on the other hand, dilation only ensures that the shape is preserved. As the rigid motions are congruence transformations, all congruent figures are also similar.
A similarity transformation is a dilation or a combination of rigid motions and dilations. Two geometric figures are similar if and only if there is a similarity transformation that maps one of the figures onto the other. Similar figures have the same shape but necessarily not the same size.
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Which geometric series diverges? three-fifths + three-tenths + three-twentieths + startfraction 3 over 40 endfraction + ellipsis negative 10 + 4 minus eight-fifths + startfraction 16 over 25 endfraction minus ellipsis sigma-summation underscript n = 1 overscript infinity endscripts two-thirds (negative 4) superscript n minus 1 sigma-summation underscript n = 1 overscript infinity endscripts (negative 12) (one-fifth) superscript n minus 1.
The geometric series which diverges is shown in the option number c as the absolute value of the common ratio of this series 4 is ∑∞n=1 (2/3)(-4)ⁿ⁻¹
What are divergent geometric series?The next term in a geometric sequence is produced by multiplying the previous term by the same number across the whole series.
It can be given as,
a+ar+ar²+ar³+...
Here,
is the sequence's (a) initial term, and (r) stands for common ratio.
It should therefore be a series as geometric series diverge.
|r|>1
the first choice is,
3/5+3/10+3/20+3/40+ ...
The common ratio in this case is,
r = (3/10)/(3/5)
r= 1/2
The average ratio is below one. Option an is therefore incorrect.
second option given as,
-10+4-8/4+18/25- ...
Here, the common ratio is,
r = (4/-10)/(-2/5)
r= -2/5
The usual ratio for the second choice is (-2/5), which is below one. This alternative is also incorrect.
The common ratio in option number c is equal to -4. The common ratio's exact value is,
|r|=|-4|
|r|= 4
This common ratio has a greater absolute value than one. This is the best choice as a result.
The absolute value of this series' common ratio, or option number c, represents the geometric series that diverges.
∑∞n=1 (2/3)(-4)ⁿ⁻¹
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A computer coast $800 it loses 1/5 of its value every year after it’s purchased complete the table after how many years will the computer be worth less than $100 _____ years write an equation representing the value v of the computer t years after it was purchased
Answer: 6
Step-by-step explanation:
Each year it will lose $160. So v=160
A ring-shaped region is show below. it’s inner radius is 6 in, and it’s outer radius is 9 in. Find the area of the shaded region. Use 3.14 for pi. Do not round your answer.
The required area of the shaded region is 141.3 sq. in.
What is area of circle?A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius. The square unit, such as m^2, cm^2, etc., is the unit of area. Area of a circle is equal to r2 or d2/4, where = 22/7 or 3.14.
According to question:inner radius = 6 in, outer radius= 9 in
are of small circle = πr^2
Area = π(6)^2 = 36π sq. in
Similarly
Area of big circle = πr^2
Area = π(9)^2 = 81π sq. in
So,
Area of shaded region = 81π - 36π
Area of shaded region = 45π
Area of shaded region = 141.3 sq. in
Thus, required area is 141.3 sq. in.
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Do you multiply in dilation?
Yes, dilation is a type of transformation that involves multiplying the coordinates of a figure by a scale factor.
This scale factor can be greater than 1, which is an enlargement, or less than 1, which is a reduction. To calculate the coordinates of a dilation, the following formula is used: (x, y) → (kx, ky), where (x, y) are the coordinates of the original point and (kx, ky) are the coordinates of the transformed point. The scale factor, k, is the same for both the x and y coordinates. For example, if the scale factor is 2 and the original coordinates are (2, 4), the new coordinates would be (4, 8). This means that the point (2, 4) has been enlarged to (4, 8).
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There are 4 boxes on a shelf A, B, C and D.................
=======================================================
Explanation:
The weight of A is 2/3 that of B. This flips to saying "the weight of B is 3/2 that of A". Because 3/2 = 1.5, we can then have this equation
B = 1.5A
The statement "C is 75% the weight of D" leads to the equation
C = 0.75D
----------------------------
The sum of A and B is triple that of the sum of C and D, giving us this equation:
A+B = 3(C+D)
Plug in the previous two equations we found in the previous section. Afterward, solve for the variable "A".
A+B = 3(C+D)
A+1.5A = 3(0.75D+D)
2.5A = 3(1.75D)
A = 3(1.75D)/2.5
A = 2.1D
----------------------------
Let's revisit the first equation we set up, and then apply substitution like so:
B = 1.5A
B = 1.5*2.1D
B = 3.15D
----------------------------
There's a lot of equations to keep track of. The key equations are these:
A = 2.1D
B = 3.15D
C = 0.75D
The one common factor of all these equations is the variable "D". This will be useful when setting up the ratio A:B:C:D
We'll go from the ratio
A:B:C:D
to
2.1D:3.15D:0.75D:1D
afterward we can divide all four parts by the GCF variable D, to arrive at
2.1:3.15:0.75:1
----------------------------
This last section will focus on converting each part of that ratio into integers. This is done by multiplying all four parts by 100 (as shown in the 2nd step).
Then we divide all parts by the GCF 5 to get the final reduced ratio.
2.1:3.15:0.75:1
100*2.1:100*3.15:100*0.75:100*1
210:315:75:100
5*42:5*63:5*15:5*20
42:63:15:20
please help me with this question thank you very much
today fever is 100.7 F, today is 2.5 higher than yesterday
yesterday is 2.5 lower than today.
x = temperature of yesterday
x + 2.5 = 100.7
x = 98.2 F
Answer:
B) Let x = yesterday's body temperature
x + 2.5° = 100.7 °F
x = 98.2 °F
Step-by-step explanation:
We want to determine Dud's body temperature yesterday. Therefore, the unknown variable is:
Let x = yesterday's body temperatureIf Dud's body temperature today is 2.5° higher than yesterday's body temperature, then his body temperature today is the sum of yesterday's body temperature and the increase:
x + 2.5° = 100.7 °FTo solve the equation, subtract 2.5° from both sides of the equation:
x + 2.5° - 2.5° = 100.7 °F - 2.5°x = 98.2 °FTherefore, Dud's body temperature yesterday was 98.2 °F.
Task #3: Felicia's Drive
As Felicia gets on the freeway to drive to her cousin's house, she notices that she is a little low on gas. There is a gas station at the exit she normally takes, and she wonders if she will have to get gas before then. She normally sets her cruise control at the speed limit of 70mph and the freeway portion of the drive takes about an hour and 15 minutes. Her car gets about 30 miles per gallon on the freeway, and
gas costs $3.50 per gallon.
a. Describe an estimate that Felicia might do in her head while driving to decide how many gallons of gas she needs to make it to the gas station at the other end.
b. Assuming she makes it, how much does Felicia spend per mile on the freeway?
Therefore , the solution of the given problem of unitary method comes out to be A.$10.5 total cost and $ 0.12 .
What is a unitary method, exactly?By first multiply the value with one unit by the number of units needed, one can use the unit method to solve a problem. Simply put, the unit function is used to distinguish a single entity unit from a given many. 40 needles may be purchased for 400 rupees, or the price of one pen. There may be a standard method for figuring this out. only one nation. Everything has a unique quality. Algebra, its dialectic and inversion, and matrix logic are all analogous concepts.
Here,
Given:
A) Estimate :
70 * 1.25
80*1.25
=> 80 + 20 = 100
and
100/30 = 3.33
thus, approx 4 gallons of gas felicia needs
=> 4 * 3.5 = 14
thus, $14 total cost
Exact :
=> 70 * 1.25 = 87.5 miles
=> 87.5/30 = 2.92 gallons
thus, approx 3 gallons of gas felicia needs
=> 3*3.5 =10.5
thus, $10.5 total cost
B)
=> per cost / miles
=> 3.5 / 30 = 0.116
=>$ 0.12
Therefore , the solution of the given problem of unitary method comes out to be A.$10.5 total cost and $ 0.12 .
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HELP PLEASE
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. if
P(chocolate chip) = 0.50, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Equally likely and unlikely
Likely
Unlikely
This value is not possible to represent probability of a chance event.
Answer: likely
Step-by-step explanation:
50/50
Answer: 50/50
Step-by-step explanation: It Is equally likely because it is 50% of the total.
Given: x = 1+a/1-b
solve for a when x=12
By solving the given expression when x=12 we get a = 11-12b
what is an algebraic expression ?
Algebraic expression can be defined as the combination of constants , variables and operators.
Algebraic expressions are the concept of expressing numbers using letters or alphabets without specifying their real values. The basics of algebra taught us a way to specific an unknown value the usage of letters which includes x, y, z, and many others. those letters are called here as variables. An algebraic expression may be a combination of each variables and constants. Any value this is positioned before and increased through a variable is a coefficient.
Given,
expression ,
x = (1+a) / (1-b )
By putting x =12
we get,
12 = (1+a) / (1-b)
12 * (1-b) = 1+a
12- 12b =1+a
a = 12-12b-1
a = 11 - 12b
Hence , By solving the given expression we get a = 11-12b
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How do you solve for R?
sqrt( A / pi ) =r is the solution for r and r is called as radius in the formula A=πr^2
A large part of the field of operations research is the use of statistical equations to solve problems in business or military operations.
Music, linguistics, and philosophy all use mathematical models (for example, intensively in analytic philosophy).
A model is, for example, the method for the area of a circle, πr2.
Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'. This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius.
Α= pi r^2
Divide each side by pi
A / pi = r^2
Take the square root of each side
sqrt( A / pi ) = sqrt(r^2)
sqrt( A / pi ) =r
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what is the decimal form of this mixed fraction: 2 4/9 (four over nine)
Answer:
2.44444
but rounded to 2.4 (tens place)
Step-by-step explanation:
hope this helps!:)
The equation y 4.3x can be used to determine the total cost, y, in dollars, of z pounds
of apples. What does the number 4.3 represent in the equation?
The price of one pound of apples is represented in the equation by the number 4.3 by the price in dollars of x pounds of apples, where x is pounds.
what is equation ?A mathematical equation is a formula that connects two statements using the equal sign (=) to denote equivalence. An algebraic equation is a mathematical statement that establishes the equality of two mathematical expressions. For example, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14.
given
y = 4.3x
the price in dollars of x pounds of apples, where x is pounds.
The price of one pound of apples is represented in the equation by the number 4.3.
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Help please!!! I’ll give brainliest!!!! (3x² - 4xy + y²)(4x + 3y)
By solving the given expression we get this simplified expression 12x³ - 7x²y - 8xy² + 3y³.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
To simplify the expression (3x² - 4xy + y²)(4x + 3y), we can use the distributive property of multiplication to expand the expression as follows:
(3x² - 4xy + y²)(4x + 3y) = 3x²(4x) - 4xy(4x) + y²(4x) + 3x²(3y) - 4xy(3y) + y²(3y)
Simplifying each term, we get:
12x³ - 16x²y + 4xy² + 9x²y - 12xy² + 3y³
Combining like terms, we get:
12x³ - 7x²y - 8xy² + 3y³
Therefore, the simplified expression is 12x³ - 7x²y - 8xy² + 3y³.
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A plot of land is 24.6 acres in size. A field next to the plot of land contains 18.9 acres. A local developer buys both pieces of property to make a community center that will use 9/25 of the total property purchased. How many acres of land will the developer need to build the community center? (Please explain how you got the answer)
A. 8.86 acres
B. 6.80 acres
C. 15.66 acres
D. 7.83 acres
Acres of land needed by the developer to build a community center that will use up 9/25 of the property is 15.66 acres, option C.
How to calculate the acre?The size of land required to build a community center is calculated as follows:
First plot size = 24.6 acres
Field size = 18.9 acres
The local developer purchases both (24.6 + 18.9) acres to have a total of 43.5 acres.
The amount needed to build a community center is 9/25
Therefore 43.5 x 9/25 = 15.66 acres
9/25 of a 43.5 acres purchased by local developer will require only 15.66 acres.
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How do you solve piecewise defined functions step by step?
To solve a piecewise defined function, you should follow these steps:
1. Understand the definition of the function. A piecewise defined function is a function that is defined differently on different intervals of its domain.
2. Identify the different intervals on which the function is defined. These intervals are usually separated by vertical asymptotes, which are points where the function is undefined.
3. Determine the formula for the function on each interval. This is usually given in the problem statement, but if not, you will need to figure it out from the context.
4. Find the domain and range of each formula. The domain of a function is the set of all input values for which the function is defined, and the range is the set of all output values.
5. Determine any discontinuities in the function. These are points at which the function is defined differently on different intervals, and they will be vertical asymptotes.
6. Sketch the graph of the function by plotting points and connecting them with line segments.
7. If the function is a piecewise continuous function, Analyze it further by finding its limits, derivatives, integrals, or other properties of interest as you would with any other function.
8. Evaluate the function for a given input value, you need to determine which interval the input value belongs to and then use the appropriate formula for that interval to find the output value.
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help me ughhhhh!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! the whole question didnt fit so there are two screenshots
The solutions of x + 2 = 2ˣ + 1 are x = 0 and 1.
The answers are given in the attached image.
What are coordinates?Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.
Given:
Two functions,
f(x) = x + 2 and g(x) = 2ˣ + 1.
The graph of the functions on the same coordinate plane is given in the attached image.
The blue line represents the graph f(x) and the green represents g(x).
Then f(x) = g(x)
x + 2 = 2ˣ + 1.
The solution is the x-value of the point of intersection.
That means,
x = 0 and 1
Therefore, the solutions of the f(x) = g(x) are x = 0 and 1.
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Mike pitches a ridge tent. The tent is 16 yards wide and the slope of the tent measures 23 yards. What is the height of the tent?
I need help
If Mike pitches a ridge tent. The tent is 16 yards wide and the slope of the tent measures 23 yards, the height of the tent is 28.07 cm
How to solve for the heightThe solution for the height would be gotten with the Pythagorean theorem. The theorem states that in a right angled triangle the sum of the square on the hypotenuse is equal to the sum of the square of the two other sides of same triangle.
This is illustrated mathematically as
C² = A² + B²
where C is the height
A is the width in yards
B is the slope.
Then we have
C² = 16² + 23²
C = √785
C = 28.07 yards
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Emily is preparing a presentation about ways to prevent heart disease for her health class. Which part of her presentation would be best suited to a video?
the explanation of how heart disease progresses over time in part of her presentation would be best suited to a video.
What is heart disease?Several different heart disorders are referred to as "heart disease." Coronary artery disease (CAD), which affects the blood flow to the heart, is the most typical kind of heart disease in the United States. A heart attack may result from reduced blood flow.
here,
Chest pain or discomfort, pain in the upper back or neck, heartburn, nausea, vomiting, extreme exhaustion, pain in the upper body, dizziness, and shortness of breath are all symptoms of a heart attack.
Heart palpitations are caused by an arrhythmia (palpitations). Heart failure symptoms include shortness of breath, exhaustion, or swelling of the legs, abdomen, or neck veins.
The three main risk factors for heart disease are excessive blood pressure, high cholesterol, and smoking. Nearly half of Americans (47%) have at least one of these three risks.
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Answer:
d
Step-by-step explanation:
evaluate the expression
For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation: y = x squared minus 6 x.
Answer:
Opens up
a = 1
b = 0
c = -6
Step-by-step explanation:
y=x^2-6
This is a parabola that opens upwards (see attached graph).
I will assume the a, b, and c are the coefficients of a parabolic equation of the form:
y = ax^2 + bx + c
Since y = x^2 - 6, the values are:
a = 1
b = 0
c = -6
Joyce has a health insurance plan at work with a $20 copay for doctor’s visits and a $10 copay for generic prescription drugs. During the most recent calendar year, she made five doctor visits and filled eight prescriptions. How much did she spend in total on copayments?
She spends a total of $ 180 in copayments, $20 for medical visits and $10 for generic prescriptions.
what is unitary method ?The system process is a strategy for addressing issues that entails first figuring out the price of a single item, than multiplication that value to figure out the needed value. Simply put, the unit technique is employed to extract a single unit quantity from a multiple that is supplied. For example, 40 pens would cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and inverse are equivalent in terms of mathematics, algebra, linear algebra, mathematical, or math and science of matrices or operators.
given
$20 for copay for doctor’s visits
$10 copay for generic prescription
for 5 doctor visits = 20*5 = $100
for 8 prescriptions = 10 * 8 = $80
so total = 100+ 80 = $180
She spends a total of $ 180 in copayments, $20 for medical visits and $10 for generic prescriptions.
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A textbook store sold a combined total of 280 history and math textbooks in a week. The number of history textbooks sold was three times the number of math textbooks sold. How many textbooks of each type were sold
The number of maths books sold is 70 and the number of history books sold is 210.
Let no of maths book sold be x.
According to the question, the number of history books sold is three times the number of maths books sold.
Therefore the number of history books sold is 3x.
Given: Total books sold = 280
So, x + 3x = 280
Solving the equation, we get:
4x = 280
x = [tex]\frac{280}{4}[/tex]
x = 70 (Number of maths books sold)
3x = 3 × 70 = 210 (Number of history books sold)
Thus the number of maths books sold is 70 and the number of history books sold is 210.
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Someone help me pleaseeeee
How do you solve y =- 3x?
the solution of equation y=x+2 and y=3x-2 are x= 2 and y=4
y = x+2 ------------ equation 1
y = 3x -2 ------------ equation 2
in the first equation y = x +2
in the second equation y = 3x -2
this mean equation 1 = equation 2
then we can equate the two together to get one of the variable
remember, we have to unknown variables which are x and y, so we need to isolate y to get x
x + 2 = 3x -2
let collect the like terms
x - 3x = -2 -2
let us factorize out x on the right hand side of the equation
x(1 - 3) = -4
x(-2) = -4
-2x = -4
divide both sides by -2
-2x/-2 = -4/-2
x = 2
to find y put x in any of the above equations
let us use equation one
y = 2 + 2
y = 4
complete question
How do you solve, y=x+2 y=3x-2
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