The critical points of the given function f(x) = ** + 5x/ (10x-60) are x = 6 and x = -6/5. The function is decreasing on (-∞, -6/5) and increasing on (-6/5, 6) and (6, ∞). The First Derivative Test shows that x = -6/5 is a local maximum and x = 6 is a local minimum.
To find the critical points, we need to first find the derivative of the function. Using the quotient rule, we get:
f'(x) = (10x - 60)(**)' - **(10x - 60)' / (10x - 60)²
Simplifying, we get:
f'(x) = 50 / (10x - 60)²
The critical points occur where the derivative is zero or undefined. Here, the derivative is never undefined, so we only need to find where it is zero:
50 / (10x - 60)² = 0
This occurs when x = 6 and x = -6/5.
Next, we need to determine the intervals on which the function is increasing or decreasing. To do this, we can use the first derivative test. We test a value in each interval of interest to see if the derivative is positive or negative:
For x < -6/5, we choose x = -2:
f'(-2) = 50 / (10(-2) - 60)² = -5/81 < 0
Therefore, the function is decreasing on (-∞, -6/5).
For -6/5 < x < 6, we choose x = 0:
f'(0) = 50 / (10(0) - 60)² = 5/9 > 0
Therefore, the function is increasing on (-6/5, 6).
For x > 6, we choose x = 10:
f'(10) = 50 / (10(10) - 60)² = 5/81 > 0
Therefore, the function is increasing on (6, ∞).
Finally, we can use the First Derivative Test to determine the nature of the critical points.
For x = -6/5:
f'(-6/5 - ε) < 0 and f'(-6/5 + ε) > 0, for small values of ε.
Therefore, x = -6/5 is a local maximum.
For x = 6:
f'(6 - ε) < 0 and f'(6 + ε) > 0, for small values of ε.
Therefore, x = 6 is a local minimum.
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Can someone help me I'm stuck.
Alexandria rolled a number cube 60 times and recorded her results in the table.
What is the theoretical probability of rolling a one or two? Leave as a fraction in simplest from
The theoretical probability of rolling a one or two is 3/5 or 0.6 as a decimal.
The theoretical probability of an event happening is the number of favorable outcomes divided by the total number of possible outcomes.
In this case, Alexandria rolled the number cube 60 times and recorded her results in the table.
Looking at the table, we can see that the number 1 came up 16 times and the number 2 came up 20 times.
So the number of favorable outcomes is 16 + 20 = 36.
And the total number of possible outcomes is 60.
Therefore, the theoretical probability of rolling a one or two is:
P(1 or 2) = favorable outcomes/total outcomes = 36/60
Simplifying the fraction, we get:
P(1 or 2) = 3/5
So the theoretical probability of rolling a one or two is 3/5 or 0.6 as a decimal.
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The Royal Fruit Company produces two types of fruit drinks. The first type is 30% pure fruit juice, and the second type is 55% pure fruit juice. The company is attempting to produce a fruit drink that contains 40% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 60 pints of a mixture that is 40% pure fruit juice?
Let's use the method of setting up a system of equations to solve this problem.
Let x be the number of pints of the first type of fruit drink (30% pure), and y be the number of pints of the second type of fruit drink (55% pure). We want to find the values of x and y that will produce 60 pints of a mixture that is 40% pure.
We can start by setting up two equations based on the information given:
Equation 1: x + y = 60 (since we want to produce 60 pints of the mixture)
Equation 2: 0.3x + 0.55y = 0.4(60) (since we want the mixture to be 40% pure)
Simplifying Equation 2, we get:
0.3x + 0.55y = 24
Now we have a system of two equations with two unknowns:
x + y = 60
0.3x + 0.55y = 24
We can solve this system using substitution or elimination. Here, we'll use substitution:
Solving Equation 1 for x, we get x = 60 - y. Substituting this expression for x in Equation 2, we get:
0.3(60 - y) + 0.55y = 24
Expanding and simplifying, we get:
18 - 0.3y + 0.55y = 24
Combining like terms, we get:
0.25y = 6
Dividing by 0.25, we get:
y = 24
Substituting this value of y back into x + y = 60, we get:
x + 24 = 60
Solving for x, we get:
x = 36
Therefore, we need 36 pints of the 30% pure fruit drink and 24 pints of the 55% pure fruit drink to make 60 pints of a mixture that is 40% pure.
Find the perimeter of a rectangle whose vertices are (3,2), (13,2), (13,9), and (3,9).
The perimeter of a rectangle is 34 units.
To find the perimeter of the rectangle with vertices (3,2), (13,2), (13,9), and (3,9), you need to determine the lengths of its sides.
The distance between (3,2) and (13,2) is the length of the base: 13 - 3 = 10 units.
The distance between (3,2) and (3,9) is the height: 9 - 2 = 7 units.
The perimeter of a rectangle is given by the formula P = 2*(length + width). In this case, P = 2*(10 + 7) = 2*17 = 34 units.
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π × 4 to the second power × 3 ( with steps !! )
A particle moves along the x-axis with velocity given by v(t) = 3t2 + 6t for time t ≥ 0. If the particle is at position x = 2 at time t = 0, what is the position of the particle at t = 1?
The position of the particle at time t = 1 is x = 4 units.
What is the position of a particle that moves along the x-axis with velocity v(t) = [tex]3t^2[/tex] + 6t at time t = 1 if it is at position x = 2 at time t = 0?To find the position of the particle at time t = 1, we need to integrate the given velocity function v(t) with respect to time from 0 to 1:
x(t) = ∫v(t)dt (from t = 0 to t = 1)
= ∫([tex]3t^2[/tex]+ 6t)dt (from t = 0 to t = 1)
= ([tex]t^3 + 3t^2[/tex]) (from t = 0 to t = 1)
[tex]= (1^3 + 3(1^2)) - (0^3 + 3(0^2))[/tex]
= 4
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This is part of a city map.
City map with First Street and Second Street as two lines equal distance apart that never meet. Main Street is intersecting Arch, First, Second, and Elm. Elm Street is intersecting Main and First Street.
Which streets are parallel to each other?
A.
First Street and Second Street
B.
First Street and Arch Street
C.
None of the streets are parallel to one another.
D.
Elm Street and Main Street
in a class, 12 students finished early. this represents 40% of the students. model this situation by evenly distributing the 12 students in the 4 shaded sections
Answer:Each of the shaded sections represents 25% of the total number of students in the class, and since we have evenly distributed the 12 students among them, each shaded section now represents 30% of the students (i.e., 25% + 5% = 30%).
Step-by-step explanation: To model this situation, we need to determine the total number of students in the class. We can use the given percentage to set up a proportion:
40% = 12 students / x total students
To solve for x, we can cross-multiply and simplify:
0.4x = 12
x = 12 / 0.4
x = 30
Therefore, there are 30 students in the class.
To evenly distribute the 12 students in the 4 shaded sections, we can divide 12 by 4 to get the number of students for each section:
12 students / 4 sections = 3 students per section
Six numbers are shown.
1.25 , -1.5 , -0.75 , -3/4 , 26/8 , 5/4 .
Plot each number on the number line.
According to the information, we can infer that the correct order for these number is -1.5, -0.75, -0.75, 1.25, 3.25.
How to organize the numbers in the numberline?To plot the numbers on a number line, we need to arrange them in increasing order. Here is the organized list of the numbers:
-1.5, -0.75, -0.75, 1.25, 3.25On the number line, we can mark -1.5 first and then move to the right to mark -0.75 twice (since it appears twice in the list), then 1.25, and finally 3.25 . On the number line, we can see that -1.5 is the smallest number and 3.25 is the largest number.
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21. Marla is drawing a regular polygon. She has drawn two of the sides with an interior angle of 140°, as shown below. When Marla completes the regular polygon, what should be the sum, in degrees, of the measures of the interior angles?
The sum of the measures of the interior angles is 1260 degrees
What should be the sum of the measures of the interior angles?From the question, we have the following parameters that can be used in our computation:
An interior angle = 140 degrees
The sum of interior angles of a regular polygon is:
S = (n - 2) × 180
Where n is the number of sides of a polygon
Also, we have
S = 140n
Substitute the known values in the above equation, so, we have the following representation
140n = (n - 2) × 180
Expand
140n = 180n - 360
This gives
40n = 360
Divide
n = 9
Recall that
S = (n - 2) × 180
So, we have
S = (9 - 2) × 180
Evaluate
S = 1260
Hence, the sum of the measures of the interior angles is 1260 degrees
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Nataly compra una falda, una blusa y un saco con los precios de la lista son s/78,s/65 y s/240 pero al pagar la falda se la dejan a s/69,la blusa a s/52 y el sacon a s/198.¿cuánto se ahorró nataly?
Nataly saved s/64.
Nataly compró una falda, una blusa y un saco por s/78, s/65 y s/240, respectivamente. Pero compró la falda por s/69, la blusa por s/52 y el saco por s/198. ¿Cuánto se ahorró Nataly?The original prices for the items are:
Skirt: s/78
Blouse: s/65
Jacket: s/240
The discounted prices Nataly paid are:
Skirt: s/69
Blouse: s/52
Jacket: s/198
To find out how much Nataly saved, we need to calculate the difference between the original prices and the discounted prices, and then add them up:
savings = (78 - 69) + (65 - 52) + (240 - 198)
savings = 9 + 13 + 42
savings = s/64
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70% of a class is at lunch what percentage is still studying?
Answer:
30%
Step-by-step explanation:
If there are only 2 categories:
Students at lunch and students studying, then the whole is 100%
100% - 70% = 30%
Helping in the name of Jesus.
please answer, i have 5 mins
Use each of these rules to create 4 ordered pairs using the two sequences.
The first rule is add 12, then divide by 2, starting from 4.
The second rule is multiply by 2, then subtract 2, starting from 3.
Which table shows the 4 ordered pairs created using the two sequences?
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers zero, four, six, and seven. Under column rule 2 are the numbers three, five, nine, and seventeen. Under the column labeled ordered pair are zero and three, four and five, six and nine, and seven and seventeen.
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers two, six, eight, and nine. Under column rule 2 are the numbers two, four, ten, and twenty-eight. Under the column labeled ordered pair are two and two, six and four, eight and ten, and nine and twenty-eight.
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers four, eight, ten, and eleven. Under column rule 2 are the numbers three, four, six, and ten. Under the column labeled ordered pair are four and three, eight and four, ten and six, and eleven and ten.
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers six, eight, twelve, and twenty. Under column rule 2 are the numbers one, eight, twenty-two, and fifty. Under the column labeled ordered pair are six and one, eight and eight, twelve and twenty-two, and twenty and fifty.
Ordered pairs must be placed in the following order: (6, 1), (8, 8), (12, 22). (20, 50). The right answer is D.
What is arithmetic?According to the assertions, it deals with a number of operations in mathematics.
For the first series, let the number be x, and for the second, let it be y.
The first rule is to multiply by 2, then, beginning with 6, remove 4.
The sequence can be written as 6 is the first number: = 2x - 4
next number = 2(6) - 4
= 12-4
= 8
The following phrase is thus 8. The following two terms can be written as 12 and 20.
Values of x = 6, 8, 12, 20
The second rule is to add three and then multiply by two, counting backward from one.
= (y + 3)2
First term = 1
Next term = (1 + 3)2
= 8
The next two words can be acquired in a similar manner.
y = 1, 8, 22, 50
Therefore, ordered pairs must be placed in the following order: (6, 1), (8, 8), and (12, 22). (20, 50). The right answer is D.
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Correct question:
The first rule is to multiply by 2, then subtract 4 starting from 6. The second rule is to add 3, then multiply by 2 starting from 1. What are the first four ordered pairs using the two sequences?
A. (0, 0) (6, 1), (8, 2), (12, 22)
B. (6, 1), (10, 8), (14,22), (22, 50)
C. (6, 1), (8, 8), (12, 20), (20, 45)
D. (6, 1), (8, 8), (12, 22), (20, 50)
Calculate the surface area of the rectangular prism shown. You do not need to provide units as they have been provided for you.
Surface Area = ___ yd2
rectangular prism with the base having all measurements of 7 yards and the height measuring 5 yards
Answer:
238 ft²
Step-by-step explanation:
Base area is l*w and there are two of these so 2(7*7) = 98
Then there 4 faces that have dimensions 4(7*5)=140
98+140=238
you purchase a computer for 875 plus 5% sales tax. you decide to finance it through the stores 0% program for 12 months. the terms state that you must pay
The amount of interest paid for missing the payment in the eight month would be C. $87.28
How to find the interest ?First, find the total cost of the computer including the sales price :
= 875 x ( 1 + 0. 05 )
= 875 x 1. 05
= $ 918. 75
Then, find the monthly rate of interest :
= 14. 25 / 12
= 1. 1875 %
This leads to an eight month interest rate of :
= 8 x 1. 1875 %
= 9. 5 %
The interest to be paid:
= 9. 5 % x 918. 75
= $ 87. 28
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Full question is:
You purchase a computer for $875.00 plus 5% sales tax. You decide to finance it through the store's 0% program for 12 months. The terms state that you must pay $100.00/month and that if you miss a payment, you will be assessed a late fee of $39.00 plus the interest accrued to that point at a 14.25% APR. If you miss a payment in the eighth month, how much interest will you be charged?. A. $83.13. B. $16.63. C. $87.28. D. 58.19
Apple Inc. Stock closes at $109. 99 per share. The next day the stock goes up $1. 49. What is the new price per share? (Just type the amount of money. Do not type the words "per share". )
The new price per share is $111.48.
Stock price is the current market value of a share of a publicly traded company's stock. It represents the price at which buyers and sellers agree to trade shares in the open market. Stock prices are determined by a variety of factors, including the company's financial performance, industry trends, and overall market conditions. The stock price is often used as an indicator of investor sentiment about the company and its future prospects.
To find the new price per share, follow these steps:
1. Note the initial stock price: $109.99
2. Note the increase in stock price: $1.49
3. Add the increase to the initial stock price: $109.99 + $1.49 = $111.48
The new price per share is $111.48.
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Assume base is 2.a b c
a = 5
b = 4
c= 0
Therefore, the equation for graph C is Y = a ^b + c
Y = 5 ^4 + 0
What is a graph?A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Graphs are a popular tool for graphically illuminating data relationships. A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.
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Consider the variable coefficient linear second order non-homogeneous ODE
x^2y^n - 2xy' + (x^2 +2)y =. 3x^3, for x > 0
Write down the associated homogeneous equation.
x²y' - 2xy' + (x² + 2)y = 0 is the associated homogeneous equation with non-homogeneous ODE x²yⁿ - 2xy' + (x² +2)y = 3x³.
It should be noted that the equation is same as the variable coefficient linear second order non-homogeneous ODE but just the right side zero.
The complementary solutions or homogeneous solutions to this homogeneous equation serve as the foundation for the space of all solutions to the non-homogeneous equation.
By assuming that y has the form y(x) = xr and substituting this into the homogeneous equation to create a characteristic equation, we can determine the complementary solutions. We may find the values of r that correspond to solutions of the type y(x) = xr by looking at the characteristic equation's roots.
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(a) What is the mean of this stem and leaf plot? Show your work. What is the median of the data? Show your work
The mean of the given stem and leaf plot is 24.5 and the median of the data is 25.
The stem and leaf plot represents the given data as:
| 2 | 4, 5, 6, 9
| 3 | 1, 4, 5, 5, 7, 8
| 4 | 2, 5, 7, 8, 9
To find the mean, we need to add up all the values and divide by the total number of values.
Mean = (24 + 25 + 26 + 29 + 31 + 34 + 35 + 35 + 37 + 38 + 42 + 45 + 47 + 48 + 49) / 15
= 367 / 15
= 24.5
To find the median, we need to arrange the data in order and find the middle value. As there are 15 data points, the median will be the average of the 8th and 9th data points.
Data in order: 24, 25, 25, 26, 29, 31, 34, 35, 35, 37, 38, 42, 45, 47, 48
Median = (35 + 37) / 2
= 36.
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Parallel lines EN, BH, and RK, with transversal PW are shown. m/BMV-108 and m/KVS-72.
Part A: Based on the diagram above and the given information, what is the
m/WPN?
The value of measure of angle WPN is,
⇒ m ∠WPN = 108°
We have to given that;
Parallel lines EN, BH, and RK, with transversal PW are shown.
And, m ∠ BMV = 108° and m ∠KVS = 72°
Now, We get by definition of vertically opposite angle;
m ∠ BMV = m ∠PWN = 108°
Hence, By definition of alternate angle we get;
⇒ m ∠PWN = m ∠WPN = 108°
Thus, The value of measure of angle WPN is,
⇒ m ∠WPN = 108°
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The start of an arithmetic sequence is 29, 17, 21, 25, The rule for the sequence can be written in the form xn=cn+d, where c and d are numbers. a) By first calculating the values of c and d, work out the rule for the sequence. b) What is the value of x11?
Answer:
Step-by-step explanation:
The value of 2s in 43,290 is 2,000, while the value of 2s in 32,865 is 20.
B. 200 is 1/20 the value of 2,000.
This statement is correct, as 200 is 1/10 of 2,000, and there are two 0s in the value of 2s in 43,290 compared to one 0 in the value of 2s in 32,865.
USA Today reported that Parkfield, California is dubbed the world's earthquake capital because it sits on top of the notorious San Andreas fault. Since 1857, Parkfield has had a major earthquake on an average of 2. 0 times every 22 years.
(d) Compute the probability of at least one major earthquake in the next 49 years. Round
λ
to the nearest hundredth, and use a calculator. (Use 4 decimal places. )
(e) Compute the probability of no major earthquakes in the next 49 years. Round
λ
to the nearest hundredth, and use a calculator. (Use 4 decimal places. )
(d) Probability of at least one major earthquake in the next 49 years is 0.9884, and (e) the probability of no major earthquakes in the next 49 years is 0.0116.
We will use the Poisson distribution to compute the probabilities. First, we need to find the value of λ (average number of earthquakes in a given time period).
(d) Compute the probability of at least one major earthquake in the next 49 years:
1. Calculate λ for 49 years:
(2.0 earthquakes / 22 years) * 49 years = 4.45 (rounded to the nearest hundredth)
2. Compute the probability of no major earthquakes (P(0)) in the next 49 years using Poisson distribution formula:
P(0) = (e^(-λ) * (λ^0)) / 0! = (e^(-4.45) * (4.45^0)) / 1 = 0.0116 (rounded to 4 decimal places)
3. Compute the probability of at least one major earthquake:
P(at least 1) = 1 - P(0) = 1 - 0.0116 = 0.9884
So, the probability of at least one major earthquake in the next 49 years is 0.9884 (rounded to 4 decimal places).
(e) Compute the probability of no major earthquakes in the next 49 years:
As calculated in step (d), the probability of no major earthquakes in the next 49 years is 0.0116 (rounded to 4 decimal places).
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100 POINTS IF HELP
what is the average rate of change for the function g(x) for the interval [4,9]?
SHOW ALL WORK
g(x)=4x^2+3x-2
Answer:
Step-by-step explanation:
Help me with homework
Therefore, the perimeter of the rectangle is 38 units that is option C.
What is coordinate?A coordinate is a set of numbers or values that specifies the position or location of a point or object in a space. In mathematics, coordinates are used to describe the position of a point in a plane, a space or a higher-dimensional object. Coordinates can be represented by ordered pairs or tuples, where the first value corresponds to the position on the horizontal axis, and the second value corresponds to the position on the vertical axis.
Here,
First, we need to find the distance between points A and B to determine the length of the rectangle:
Distance AB = |yB - yA|
= |8 - 2|
= 6
Next, we need to find the distance between points B and C to determine the width of the rectangle:
Distance BC = |xC - xB|
= |6 - (-7)|
= 13
Since opposite sides of a rectangle are equal in length, we know that the distance between points A and D is also 13, and the distance between points C and D is also 6.
Therefore, the perimeter of the rectangle is:
Perimeter = 2 * (length + width)
Perimeter = 2 * (13 + 6)
Perimeter = 2 * 19
Perimeter = 38
So the answer is (C) 38.
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1ST ONE TO ANSWER MY QUESTION WILL BE MARKED BRAINLIESTT! ANSWER 1 QUESTION!
2x²t + 7xy
Step-by-step explanation:To simplify, we will combine like terms.
Given:
5xy - x²t + 2xy + 3x²t
Reorder like terms:
5xy + 2xy + 3x²t - x²t
Combine like terms:
➜ 5 + 2 = 7
➜ 3 - 1 = 2
7xy + 2x²t
Reorder by degree:
2x²t + 7xy
what are the ordered pairs of y>1/2x+3
The ordered pairs of the inequality expression is (0, 4)
What are the ordered pairs of the inequality expressionFrom the question, we have the following parameters that can be used in our computation:
The inequality expression y>1/2x+3
To determine the ordered pairs of the inequality expression, we set x - 0 and then calculate the value of y
Using the above as a guide, we have the following:
y > 1/2 * 0 + 3
Evauate
y > 3
This means that the value of y is greater than 3 say y = 4
So, we have (0, 4)
Hence, the ordered pairs of the inequality expression is (0, 4)
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Leslie works for Blank Chemical Corporation. Her annual salary is $57,285. 50. She is
paid biweekly (26 weeks). Each pay period, Leslie's employer deducts $418. 63 for
federal tax withholding. City tax for Blank Chemical employees is 3. 65%. What is Leslie’s annual social security (6. 2%) deduction?
Leslie’s annual social security deduction is $3551.70.
How to determine Leslie’s annual social security deduction?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Leslie’s annual salary is $57,285. 50 and her annual social security deduction is 6.2% of the annual salary. We can say:
Annual social security deduction = 6.2/100 * 57,285. 50
Annual social security deduction = $3551.70
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Noel borrows $800
and is charged compound interest at 60%
per year. How much will he have to pay back in total after 8
years?
Answer:
Step-by-step explanation:
PLEASE HELP ASAP (BRAINLIEST) 39 POINTS
Answer:
3x + 5 = 4x - 40
x = 45
5y - 50 = y
4y = 50
y = 25/2
Question below, please help! this is part of my grade.. (30 points)
Answer:
y = 1 + 2√7 or y = 1 - 2√7
Step-by-step explanation:
To complete the square, you need to add and subtract the square of half of the coefficient of the y term.
First, you can factor out a 1 from the y^2 - 2y term:
y^2 - 2y - 27 = 0
y^2 - 2y = 27
Next, take half of the coefficient of the y term (-2/2 = -1) and square it (1):
y^2 - 2y + 1 - 1 = 27
The "+1 -1" doesn't change the value of the equation, it's just a way to add 0 to the equation so we can complete the square.
Now you can rewrite the left side as a perfect square:
(y - 1)^2 - 28 = 0
Add 28 to both sides:
(y - 1)^2 = 28
Take the square root of both sides (remembering to include both positive and negative square roots):
y - 1 = ±√28
y = 1 ± 2√7
So the solutions are:
y = 1 + 2√7
y = 1 - 2√7
Answer: y=± 2√7+1
6.29
Step-by-step explanation: Use the formula
(b/2)^2 in order to create a new term. Solve for y by using this term to complete the square.
50+30(2x+10) What is the value of x
Distribute
50+30(2x+10)
50+30×2x+30×10
50+60×+300
add the number
50+300+60×
350+60x
re arrange the term60x+350
common factors
10(6x+35)
