The following pair of linear equations 5x - 15y = 8 and 3x - 9y = 24/5 has infinitely many solutions.
To find the number of solutions that a pair of linear equations will have, we can use the concept of the ratio of coefficients.
For the pair of linear equations:
5x - 15y = 8
3x - 9y = 24/5
We can find the ratio of the coefficients of x in both equations and check if it's the same or not.
In the first equation, the coefficient of x is 5 and in the second equation, the coefficient of x is 3. The ratio of these coefficients is 5/3.
We can also find the ratio of the coefficients of y in both equations. In the first equation, the coefficient of y is -15 and in the second equation, the coefficient of y is -9. The ratio of these coefficients is -15/-9, which is equal to 5/3.
Since the ratio of the coefficients of x and y in both equations are same, check ratio of constants,
8/(24/5) = 5/3
As all ratios are same, the system has infinitely many solutions.
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Question: Each group represents the 5 shots taken by the other team. To win the game, the Ice blades cannot let the other team score any goals.
For a group to be a success, how many of the 5 shots does the goalie need to save?
1. A goal scored represents as 73 to 99.
2. All the 5 shots does the goalie need to save.
In the given question,
The goalie on the Ice blades hockey team saves the opponent's shots = 73%
The other team takes 5 shots in the final 10 minutes.
1. We have to find which digits represent a goal scored.
As given the paired digits 00 to 99 represent 100 shots.
Let 00 to 72 = a shot that is saved. So a goal scored represents as 73 to 99.
2. For a group to be a success, we have to find how many of the 5 shots does the goalie need to save.
A saved shot is represented by the numbers 00 to 72, and a goal is represented by the numbers 73 to 99. Thus, in the groups, it is necessary to save all five shots.
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The complete question is:
The goalie on the Ice blades hockey team saves (blocks) 73% of the opponent's shots. With 10 minutes to go, the Ice blades are ahead by one goal, and they will win if the other team does not score.
The other team takes 5 shots in the final 10 minutes. The Ice blades do not score any more goals. The table shows pairs of random digits. The pairs in each group simulate the 5 shots taken by the opponent.
1. The paired digits 00 to 99 represent 100 shots.
Let 00 to 72 = a shot that is saved. Which digits represent a goal scored? Explain.
2. Each group represents the 5 shots taken by the other team. To win the game, the Ice blades cannot let the other team score any goals.
For a group to be a success, how many of the 5 shots does the goalie need to save?
when was robbie knievel diagnosed with pancreatic cancer ?
Robbie Knievel, a daredevil stuntman, passed away on Friday morning, 13 january 2023 at the age of 60.
He was battling pancreatic cancer, which, according to the American Cancer Society, accounts for around 3% of all cancers but about 7% of all cancer fatalities in the U.S. He was in a hospice in Reno, Nevada. Because the pancreas is hidden deep inside your abdomen, where it cannot be seen in selfies, the diagnosis of pancreatic cancer is frequently delayed. Therefore, the tragic news of Knievel's departure presents a chance to spread greater awareness of this terrible sickness, which will likely claim the lives of over 50,000 individuals once more in 2023.
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Is +B the y-intercept?
y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept.
Now, According to the question:
y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept. x and y represent the distance of the line from the x-axis and y-axis, respectively. The value of b is equal to y when x = 0, and m shows how steep the line is.
The equation of a straight line with slope m passing through the origin (0,0) is given by:
y = mx
Hence, the y-intercept at the origin is zero
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Solve 34≤12+n . Graph the solution.
Answer:
22 ≤ n
Step-by-step explanation:
34≤12+n
22 ≤ n
Find the quotient of each expression.
1. (36a^4 - 24a^4 - 18a²) ÷ (-6a²)
-6a² + 4a² + 3 is the quotient of the given expression: (36a⁴- 24a⁴ - 18a²) ÷ (-6a²).
What is quotient?It is known as the quotient to divide two integers. The dividend is the quantity being divided, and the divisor is the quantity being divided. The quotient is the outcome of the division.
The sum is the result of multiplying two or more numbers together. The difference is determined by the result of subtracting the two values. The result of multiplying two or more integers is what is known as the product. The quotient is what remains after dividing two numbers.
Given that,
= (36a⁴- 24a⁴ - 18a²) ÷ (-6a²)
= - 6a² + 4a² + 3
thus, -6a² + 4a² + 3 is the quotient of the above expression.
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What is the derivative of inverse tangent of 4x?
The derivative of inverse tangent of 4x is
[tex](tan^{-1}x)' = \frac{1}{(1 + x^2)}[/tex] is the formula for tan inverse x's derivative. Finding tan inverse x's derivative with regard to x is the process of differentiation of tan inverse x. The derivative of tan inverse x can alternatively be thought of as the rate of change of tan inverse x, which is represented by the expression [tex]\frac{1}{(1 + x^2)}[/tex].
The derivative of inverse tangent of 4x is [tex]\frac{4}{(16x^2+1)}[/tex]
The derivative of [tex]tan^{-1}(4x)[/tex] can be represented using the derivative of formula.
[tex]tan^{-1}(x)=\frca{1}{(1+x^2)}[/tex]
[tex]\frac{d}{dx} tan^{-1}(4x)=\frac{1}{16x^2+1}\times\frac{d}{dx}(4x)[/tex]
[tex]\frac{d}{dx} tan^{-1}(4x)=\frac{1}{(16x^2+1)}\times4\times\frac{d}{dx}(x)[/tex]
as we know that [tex]\frac{d}{dx}x=1[/tex]
[tex]\frac{d}{dx} tan^{-1}(4x)=\frac{4}{(16x^2+1)}[/tex]
The derivative of inverse tangent of 4x is [tex]\frac{4}{(16x^2+1)}[/tex].
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The first term in a geometric series is 555 and the common ratio is 222. Find the sum of the first 101010 terms in the series.
The first 10 terms sum in the geometric series is 5115.
The first term of geometric series = 5
Common ratio = 2
First, let us discuss how to calculate the sum of n terms of GP. Assume the sum of the first n terms of a GP with first term a and common ratio r. Then the first 'n' terms of GP are of form a, ar, ar², ... ar^(n-1). Let S be the sum of the GP of n terms. Then:
Sₙ = a + ar + ar² + ... + ar^(n-1) ... (1)
Multiply both sides by r:
rSₙ = ar + ar² + ... + arⁿ ... (2)
Subtracting equation (1) from equation (2):
rSₙ - Sₙ = (ar + ar² + ... + arⁿ) - [a + ar + ar² + ... + ar^(n-1)]
Sₙ (r - 1) = arⁿ - a
Sₙ (r - 1) = a(rⁿ - 1)
Sₙ = a(rⁿ - 1)/(r - 1)
Note that, here, r ≠ 1.
Sₙ = -a(1 - rⁿ)/(-(1 - r)) = a(1 - rⁿ)/(1 - r).
Sₙ = a[1-rⁿ]/[1-r]
S₁₀ = 5[1-2¹⁰]/[1-2]
S₁₀ = 5[1023]
S₁₀ = 5,115
--The given question is incorrect, the correct question is
"The first term in a geometric series is 5 and the common ratio is 2. Find the sum of the first 10 terms in the series."--
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A solid object is made with the combination of a cylinder and a cone having same radii. The height of the cylinder is 30 cm and the slant height of the cone is 25 cm. If the total cost of painting the total surface of the solid object at the rate of Rs. 150 per 100 sq. cm is Rs. 3036, find the height of the cone.
Answer:
height of the cone is 25 cm.
Step-by-step explanation:
by using the formulas for the surface area of a cylinder and a cone to find the total surface area of the solid object.
The formula for the surface area of a cylinder is 2πr(r+h) where r is the radius and h is the height.
The formula for the surface area of a cone is πr(r+l) where r is the radius and l is the slant height.
Let's assume that the radius of the cylinder and cone is 'r'.
Now we know that :
2πr(r+30) + πr(r+l) = Total surface area
We are given that the cost of painting the total surface area is Rs. 3036 at the rate of Rs. 150 per 100 sq cm. So we can use this information to find the total surface area.
3036*100/150 = 2022 sq cm
Now we can substitute this value of total surface area in the above equation.
2πr(r+30) + πr(r+l) = 2022
Now we can solve for 'l' (slant height of the cone)
we know that the slant height of the cone is 25 cm so we can substitute this value in the above equation.
2πr(r+30) + πr(r+25) = 2022
Solving this equation, we get the height of the cone = 25 cm.
So the height of the cone is 25 cm.
The table shows total number of cars rented everyday for a
week from Golden State Rentals, What is the estimated
average increase in car rentals per day for Tuesday through
Friday?
The estimated average increase in the car rentals per day for Tuesday through Friday is equal to 51.
As given in the question,
Given table represents the total number of cars every day.
Day : M Tu W Th F Sa Sun
Total cars : 41 109 158 199 262 313 352
To calculate estimated average for Tuesday through Friday is given by :
Estimated number = xₙ - xₙ₋₁
Day : : Wed -Tue Thurs - Wed Friday - Thurs
Estimated cars : 158 - 109 =49 199 - 158 = 41 262 - 199 = 63
Estimated average increase in cars rental is given by
= ( 49 + 41 + 63 ) / 3
= 153 /3
= 51
Therefore, the estimated average increase in the car rentals per day for Tuesday through Friday is equal to 51.
The above question is incomplete, the complete question is:
The table shows total number of cars rented everyday for a week from Golden State Rentals, What is the estimated average increase in car rentals per day for Tuesday through Friday?
Golden State Car Rentals
Day : M Tu W Th F Sa Sun
Total cars : 41 109 158 199 262 313 352
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HELP PLEASE.
tbh ixl sucks
Answer: [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
We can use this formula to solve.
We will substitute the known points and simplify. I will use the points (0, -5) and (-3, -4)
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{-5--4}{0-3} =\frac{-5+4}{-3} =\frac{-1}{-3}= \frac{1}{3}[/tex]
How do you find the domain and range of a log graph?
To find the domain and range of a log graph, identify the x- and y-intercepts, determine the asymptotes, if any, and identify the intervals between the asymptotes and intercepts. The domain and range of the graph are the union of all of these intervals.
To find the domain and range of a log graph, identify the x- and y-intercepts, determine the asymptotes, if any, and identify the intervals between the asymptotes and intercepts. The domain and range of the graph are the union of all of these intervals.The domain of a log graph is the set of all possible x-values and the range is the set of all possible y-values. To find the domain and range of a log graph, first identify the x- and y-intercepts. Then, determine the asymptotes of the graph, if any. Finally, determine the intervals of the graph, which are the areas of the graph between the asymptotes and the intercepts. The domain and range of the graph are then the union of all of these intervals.
To find the domain and range of a log graph, identify the x- and y-intercepts, determine the asymptotes, if any, and identify the intervals between the asymptotes and intercepts. The domain and range of the graph are the union of all of these intervals.
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A triangle has two sides of length 7 and 3. What is the largest possible whole-number length for the third side?
Answer: The triangle inequality states that each side of a triangle must be shorter than the sum of 2 other sides.
Step-by-step explanation: Please make me Brainliest.
A couple gets financing for 80% of the $150,000 purchase price of a house at the rate of 6% on the monthly unpaid balance. Use the table provided to find the total amount paid to the finance company if the loan is repaid in 40 years
The total paid amount to the finance company if the loan is repaid in 40 years is $198,076.910617.
A loan is a source of funding in the form of debt that is taken out by the lender who charges interest as the price of the loan. The borrower is expected to make payments to the lender on a regular basis, usually monthly. This payment settles the interest charged on the outstanding balance and partially reduces the principal balance of the loan.
We have, A couple gets financing for 80% of the $150,000 purchase price of a house.
Price of house = 150,000
Loan = 80% × 150,000 =120,000
rate of interest = 6%
For monthly compounding, rate
= 0.06/12=0.005
time period , n = 40 years
For adjusted for monthly payment = 40 × 12 = 480 months
Now, calculate the monthly payment,
[tex]Payment = \frac{loan \times r}{1 - {(1 - r)}^{ - n} } [/tex]
[tex] = \frac{120,000 \times 0.005}{1 - {(1 + 0.005)}^{ - 480} } [/tex]
[tex] = \frac{600}{0.908737} = 660.25[/tex]
Total payment = Monthly payment × number of months
Total payment= 660.25× 300 = 198,076.910617
Hence, total amount paid to finance company is $198,076.910617.
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Solve using Synthetic substitution
f(x)=x6 +4x5-2*4+6x3_2x2 +3
f(4) =
f(-1)=
If you want to divide a polynomial by a linear expression and use synthetic division, the first number or leading coefficient should be a 1. Alternatively known as Ruffini's rule, this division by linear denominator (paper-and-pencil computation).
How to Perform a Synthetic Division?The following is a list of the prerequisites for using the synthetic process method:The polynomial presented should have a divisor of degree 1 as its denominator. Accordingly, the exponent of the specified variable should be 1. A linear factor is thought to be a divisor of this type.It is also necessary for the coefficient of the divisor variable, let's say x, to be 1.If the leading coefficient is divided by something other than one, the synthetic division process will become distorted.When using the synthetic division approach, be careful to answer the problem if the divisor's leading coefficient is something other than 1.To carry out the synthetic division process, the fundamental mantra is"Bring down; multiply and add; multiply and add; multiply and add;.You cannot divide a polynomial of two degrees by x2 + 3 or x2 - x + 7 using the synthetic division method, for instance. However, you may divide it by x + an or x - a.The leading coefficient must be divided by itself if it is not 1, which will make the leading coefficient 1. Examples include 4x - 1 becoming x - 14 and 4x + 9 becoming x + 9/4. Consequently, if the synthetic division is not functioning.To Learn more About synthetic division, refer To:
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I need help with this
Answer:
-357
Step-by-step explanation:
Multiply 17 and -21 on your calculator
Answer:
-357
Step-by-step explanation:
• means multiplication
17 • —21?
17 × (-21)
= -357
Find the product of (3a²bc³ )(5a³b4c²)
Need help Ivan starts with $150 and saves $5 each week. Uma has $45 and saves $20 each week. At what week will they both have the same amount of money? How much money will they each have? Write your answer as an ordered pair.
The two equations are 150 + 5w and 45 + 20w.
In 7 weeks they will have the same amount of $225 and in terms of ordered pairs, it is (7, 225).
What are the three types of solutions for a system of linear equations?If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.
There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.
Let, the number of weeks be 'w'.
Therefore, From the given information the two equations can be formed as,
150 + 5w and 45 + 20w.
Now, The number of weeks required when they'll have the same amount of money can be obtained if we equate these two equations.
150 + 5w = 45 + 20w.
5w - 20w = 45 - 150.
- 15w = - 105.
w = 105/15.
w = 7 weeks.
They will have 150 + 5×15 = 150 + 75 = 225 each in terms of ordered pairs (7, 225).
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seven times the quantity of three plus one
The answer of seven times the quantity of three plus one is 24.
What is expression?
A finite combination of symbols that are well-formed in accordance with context-dependent rules is referred to as an expression or mathematical expression in mathematics.
A mathematical expression is a phrase that contains a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.
Consider, the given expression
"Seven times the quantity of three plus one."
"Three" means ' 3 '
"one" means ' 1 '
"the quantity three plus one" means ' (3 + 1) '
"Seven times the quantity ..." means ' 7(3 + 1)'
That's the expression.
One of the rules for handling these things is that you should always
take care of anything inside parentheses first. So do that.
(3 + 1) = 4
Now you can can write the expression like this: ' 7(4) ' .
That's just 24.
Hence, the answer of seven times the quantity of three plus one is 24.
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Why are absolute value graphs V shaped?
Each absolute value graph will take the form of a "V." A negative slope and a positive slope make up its two sections.
Each absolute value graph will take the form of a "V." A negative slope and a positive slope make up its two sections. They meet at the vertex, which is where they do. An absolute value graph can be folded in half along its symmetry axis.The parent function, or most fundamental function, of absolute value functions is y = |x|.
Let's now plot the answers to the equations y = |x-1| and its parent function.
You'll see that the function is nothing more than the parent function moved over. One unit has been added to the right of the vertex. This is due to the fact that |x - 1| Equals 0 when x = 1, since |1 -1| = 0. Wherever the absolute value inside the value is zero, that is the vertex.
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mathew lucy and finley sold a total of 56 games at a car boot sale the ratio of games that they each sold is 2:5:1 how many more games did lucy sell than finley
The number of more games that Lucy sells than Finley will be 28 games.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Mathew, Lucy, and Finley sold a total of 56 games at a car boot sale. The ratio of games that they each sold is 2:5:1.
Let 'x' be the common factor. Then the equation is given as,
2x + 5x + 1x = 56
8x = 56
x = 7
Then the number of more games that Lucy sells than Finley will be given as,
⇒ 5 × 7 - 1 × 7
⇒ 35 - 7
⇒ 28
The number of more games that Lucy sells than Finley will be 28 games.
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What is the place value of the 2 in the number 234.58937?
Answer:
Hundreds place!
Step-by-step explanation:
Hope it helps! =D
For Rashmi good service and cost are also important factors. She would not like to spend more
than Rs 24000 for purchasing the AC. Given that the comparative rates of the models are:
AC MODEL
Cost
Special Offers (if any)
Alpha
Rs 22785
Additional Rs 3500 as Annual maintenance charges
Vidyut
Rs 24425
5% discount
Samurai
Rs. 23590
Rs 500 extra for installation
Zenith
Rs. 24725
5% discount
Versa
Rs. 29900
No installation charges
Choose the AC model which Rashmi will prefer to purchase in this case?
a. Samurai
b. Vidyut
c. Zenith
d. Versa
The AC model which Rashmi will prefer to purchase in this case:
Vidyut
The correct option is (b)
Now, According to the question:
The given information is:
Rashmi does not like to spend more than Rs 24,000 for purchasing the AC. So we need to find among the given AC Model that is suitable for Rashmi to purchase.
So the cost of AC Model Vidyut can be considered.
So the amount is Rs 24,425
Discount provided is 5%
So 5% of 24425
= 5/100 x 24,425
= 1221.25
So 24,425 – 1221.25
Rs 23203.75 will be the cost after discount.
Hence, The AC model which Rashmi will prefer to purchase in this case:
Vidyut.
The correct option is (b).
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Please please please help.
The graph of y=1-2/x^2 cuts the positive x axis at A.
B is the point (0,-2)
The equation of the line is y = √2x - 2. And the coordinate of point A will be (√2, 0).
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
y = 1 - 2 / x²
The x-intercept is given as,
y = 0
1 - 2 / x² = 0
x² = 2
x = √2
The equation of the line that passes through points A (√2, 0) and B (0, -2) will be given as,
(y + 2) = [(0 + 2) / (√2 - 0)](x - 0)
y = √2x - 2
The equation of the line is y = √2x - 2. And the coordinate of point A will be (√2, 0).
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20 points*please help
The sum of angles in the images result in -
First image - Neither (neither complementary nor supplementary angle)
Second image - Neither (neither complementary nor supplementary angle)
Third image - Complementary (sum of angles resulting in 90°)
What are complementary and supplementary angles?
When two angles are added together, complementary and supplementary angles are defined. Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees. When two angles add up to 90 degrees, however, they are said to be complementary angles and together they make a right angle.
In the first image it can be seen that the two angles measure 90° and 89° respectively.
On adding the two angles the sum is obtained as -
90° + 89° = 179°
Therefore, this is neither a complementary angle nor a supplementary angle.
In the second image it can be seen that the two angles measure 63° and 47° respectively.
On adding the two angles the sum is obtained as -
63° + 47° = 110°
Therefore, this is neither a complementary angle nor a supplementary angle.
In the third image it can be seen that the two angles measure 61° and 29° respectively.
On adding the two angles the sum is obtained as -
61° + 29° = 90°
Therefore, this is a complementary angle as the sum of the two angles equals 90°.
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elsa is choosing a 2 letter password from the letters a, b, c, d, e, and f. the password cannot have the same letter repeated in it. how many such passwords are possible?
30 such passwords are possible.
6 choices for the 1st, then 5 choices for the 2nd,
The first two are alphanumeric, and the latter three are numbers.
There are 26 letters.
Ten digits are present.
There are no repetitions among the two available letters. However, it is irrelevant which sequence they are in. He can choose from 2x4x3, or 24 distinct passwords. so: 6*5=30
or nPk=n!/(n-k)! with n=6 and k=2
Consequently, the total number of passwords that can be created while still adhering to the limitations set
so: 6*5=30
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- j(x) = −5√x + 3 +2
Contradictions, also referred to as No Solution Equations, are the final category of equations.
What mathematical problem has no answer?Contradictions, also referred to as No Solution Equations, are the final category of equations. No matter what we substitute for the variable, this kind of equation is never true. Take the equation 3x + 5 = 3x - 5 as an illustration. There is no answer to this problem.|-x - 3| = 5, |2x - 1| = 0, |5 - 3x| = -8, |-x + 9| = 0. Any equation must always have a positive absolute value. There are therefore no answers to the equation.Contradictions, also referred to as No Solution Equations, are the final category of equations.|-x - 3| = 5, |2x - 1| = 0, |5 - 3x| = -8, |-x + 9| = 0. Any equation must always have a positive absolute value. There are therefore no answers to the equation.To learn more about equations refer to:
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If 1 mine equals 1760 yards then how many miles are in 12144 yards?
Answer: 6.9 miles
Step-by-step explanation:
Just divide 12,144 by 1,760 it's pretty simple
Cheers
-RsmBro
Answer: 6.9 miles
Step-by-step explanation:
12144yd / 1760
= 6.9mi
How do you find the B in Y MX B with two points and slope?
To find the B in Y = MX + B with two points and slope, choose either the point (X₁, Y₁) and slope M, then B is given by an expression Y₁ - MX₁
The slope-intercept form of equation of line is y = mx + b
where m is the slope of the line and b is the y-intercept of the line.
We need to find the value of b i.e., y-intercept when the slope and a point is given.
We know that the equation of line with slope m and passing through point (x₁, y₁) is given by the formula
(y - y₁) = m(x - x₁)
If we have been given two points (lets say (x₁, y₁) and (x₂, y₂)) and a slope, then we use above point-slope form of equation of line by choising one of the point from (x₁, y₁) and (x₂, y₂)
For point (x₁, y₁) and slope m, we simplify equation.
(y - y₁) = m(x - x₁)
y - y₁ = mx - mx₁
y = mx + (y₁ - mx₁)
Comparing above equation with slope-intercept form we get the y-intercept ,
b = y₁ - mx₁
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How do you translate a horizontal graph?
To translate a horizontal graph, you need to adjust the x-axis. This can be done by shifting the graph to the left or right. Additionally, you can stretch or shrink the graph by adjusting the scale of the x-axis.
A horizontal graph is a type of graph that is used to represent data in a two-dimensional space. To translate a horizontal graph, you must adjust the x-axis. This can be done by shifting the graph to the left or right. Additionally, you can stretch or shrink the graph by adjusting the scale of the x-axis. This can be done by changing the number of points on the x-axis, or by making the intervals between points larger or smaller. When translating a graph, it is important to make sure that the y-axis remains unchanged as this will ensure that the data is accurately represented. Translating a horizontal graph is a useful way to compare and analyze data. It allows you to see how changes in one variable affect the other variables in the data set. It is also an essential skill for data analysis and is used in many different fields, such as finance and economics.
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PLEASE HELP URGENT
the cost of 128 tablespoons of shampoo cost 20$. how much does 6 tablespoons of shampoo cost?
PLEASE SHOW WORK
Answer:
94 pence
Step-by-step explanation:
128=20
divide both by 128, so
1 = 0.15625
now times both by 6
6 = 0.9375
£0.94 (rounded)