The function rule for the line that passes through the origin and (-6,-12) is y = 2x.
In mathematics, a function is a rule that assigns to each element in a set a unique output value.
To find a function rule for the line that passes through the origin (0,0) and the point (-6,-12), we first need to determine the slope of the line. The slope of a line represents the rate of change between the x and y coordinates. We can find the slope using the formula:
slope = (y₂ - y₁)/(x₂ - x₁)
where (x₁, y₁) represents the coordinates of the first point, and (x₂, y₂) represents the coordinates of the second point.
Using the given points, we can substitute in the values:
slope = (-12 - 0)/(-6 - 0)
slope = -12/-6
slope = 2
Now that we have the slope, we can use the point-slope form of a linear equation to find the function rule:
y - y₁ = m(x - x₁)
where m is the slope, and (x₁, y₁) represents the coordinates of a point on the line.
Substituting in the values we have so far, we get:
y - 0 = 2(x - 0)
y = 2x
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(1 point) The expression 4^65536g³y² √√/65536g³y² equals kg³y³
where r, the exponent of g, is:
and s, the exponent of y, is:
and k, the leading coefficient is:
The 4 is the square root
The exponent of g, r, is -65536.
The exponent of y, s, is 1.
The leading coefficient, k, is 4.
Note: The expression 4^65536g³y² √√/65536g³y² is not equal to kg³y³, but instead represents the value of 4 raised to the power of 65536 times g raised to the power of -65536, divided by the square root of 65536 times g raised to the power of -65536 times y squared. The square root symbol is used twice, which is equivalent to taking the square root of the square root, or the fourth root.
Calculate x in the following ratio: x : 4 = 54 : 3
Answer:
x = 72
Step-by-step explanation:
x : 4 = 54 : 3
express the ratios in fractional form
[tex]\frac{x}{4}[/tex] = [tex]\frac{54}{3}[/tex] = 18 ( multiply both sides by 4 to clear the fraction )
x = 4 × 18 = 72
PLEASE HELP A WHOPPING 100 POINTS!!! AND BRAINLY NO LINKS
Enter your answer and show all the steps that you use to solve this problem in the space provided. Use the 30°-60°-90° Triangle Theorem to find the answer.
Find the value of x. If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
Answer: 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
The 30-60-90 triangle rule states that the hypotenuse is twice the length of the shortest leg (which would be 5) and the longer leg is [tex]\sqrt{3}[/tex] times the length of the shorter leg.
Since we are trying to find x we would use the rule for the longer leg
so 5 * [tex]\sqrt{3}[/tex] would just be 5[tex]\sqrt{3}[/tex]
The value of the x is 5√3 after we successfully do the application of the 30°-60°-90° Triangle theorem.
What is Triangle theorem?The 30°-60°-90° Triangle Theorem states that in such a triangle, the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is the product of the length of the hypotenuse and the square root of 3 divided by 2.
here, we have,
Using this theorem, we can write:
y = hypotenuse
Opposite of 30° angle = 5 = hypotenuse/2
Opposite of 60° angle = x = hypotenuse × (√(3)/2)
Solving for the hypotenuse in terms of y from the first equation, we get:
hypotenuse = 5×2 = 10
Substituting this value into the third equation, we get:
x = 10 × (√(3)/2) = 5 × √(3)
Hence, The value of the x is 5√3 after we successfully do the application of the 30°-60°-90° Triangle theorem.
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Assume you owe $16,783 to a credit card company and interest is at 19% compounded monthly, at the end of the month, how much do you owe in interest?
This equals a total of $281.55 in interest owed at the end of the month. This means that the total balance owed to the credit card company would be 16,783 + 281.55 = 17,064.55.
The interest rate in this situation is 19% compounded monthly. This means that each month, the interest rate is applied to the total balance. The formula to calculate the amount of interest owed is:Interest Owed = Balance x (Interest Rate/12) .In this case, the formula would be:Interest Owed = 16,783 x (0.19/12).This equals a total of $281.55 in interest owed at the end of the month. This means that the total balance owed to the credit card company would be 16,783 + 281.55 = 17,064.55.
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A pet store has 80
geckos and anole lizards altogether.
The ratio of geckos to anole lizards is 1:3
.
How many geckos does the pet store have?
Answer:
About 54 geckos
Factor the following expressions.
(a-7)-y(a-7)
8a(x+y)-(x+y)
Answer:
(x+y)(8a - 1)
Step-by-step explanation:
For the first expression:
(a-7) - y(a-7)
We can factor out (a-7) from both terms:
(a-7)(1 - y)
So, the factored expression is:
(a-7)(1 - y)
For the second expression:
8a(x+y) - (x+y)
We can factor out (x+y) from both terms:
(x+y)(8a - 1)
So, the factored expression is:
(x+y)(8a - 1)
Answer: (1-y)(a-7) and (8a-1)(x+y)
Step-by-step explanation:
When the values in the parentheses are the same twice, they reappear only once after grouping. In the first problem, the coefficients are 1 and -y, therefore, the answer becomes (1-y)(a-7).
Hope this helps
MM
In the right triangle ABC below, DE is parallel to AC, and DE is perpendicular *
to CB at E. The length of AB is 26 units, the length of DE is 5 units, and the
length of BE is 12 units. What is the length, in units, of AC?
The length of AC from the given triangle ABC is 10 units.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
Given that, in the right triangle ABC below, DE is parallel to AC, and DE is perpendicular to CB at E.
The length of AB is 26 units, the length of DE is 5 units, and the length of BE is 12 units.
Consider ΔABC and ΔBDE
∠BDE=∠BAC=90°
∠ABC=∠DBE (Reflexive property)
By AA similarity, ΔABC is similar to ΔBDE.
By midpoint line segment theorem,
AC=2DE
AC=2×5
AC=10 units
Therefore, the length of AC is 10 units.
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12. (A.10.B) A sidewalk was built around a rectangular garden. Find the area of the sidewalk in terms of x
x
3x
2x-1
X+2
The area of the sidewalk in terms of x would be 3 x ² + x + 2
How to find the area of the sidewalk ?The area of the sidewalk would be :
= Area of rectangular area - Area of rectangular garden
Area of rectangular area = 2 x ( 2x + 1 )
Area of rectangular garden = x ( x + 1 )
The area of the sidewalk in terms of x is therefore :
= ( 2 x ( 2x + 1 ) ) - ( x ( x + 1 ) )
= ( 4 x ² + 2 ) - ( x ² + x )
= 4 x ² + 2 - x ² + x
= 4 x ² - x ² + x + 2
= 3 x ² + x + 2
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how many significant figures do each of the following measurements contain? type a number (i.e., 1, 2, 3, etc) for each of your responses, not the written word for the number.
Each of the following measurements contain a) 1, b) 4,c) 3,d) 1,e) 2,f) 4,g) 2 significant figures.
Significant digit -Precision refers to the number of digits to which a value can be assigned. Therefore, numbers that can have a value of digits are called significant digits.
Below are the key figures for each value reported.
(a) 2- 1significant digits
(b) 81.640 - 4 significant digits;
(c) 7.03 - 3 Significant Figures
(d) 0.003 - 1significant digits
(e) 0.0086 to 2 significant digits
(f) 3236 - 4 significant digits
(g) 8700 - 2 significant digits
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explain what is meant by statistical inference. give an example of statisticalinference from everyday life, say, a political poll
It's important to use sound statistical methods and careful analysis to ensure that the inferences drawn are as accurate as possible.
Statistical inference is the process of drawing conclusions or making predictions about a population based on data from a sample of that population. In other words, statistical inference involves using the principles of probability and statistics to make generalizations about a larger group based on information collected from a smaller group.
For example, a political survey may be conducted to gather opinions from a sample of voters about a particular issue or candidate. The data collected from this sample can be used to make inferences about the opinions of the larger population of voters. Statistical inference allows us to estimate the opinions of the larger population based on the information gathered from the smaller sample.
To illustrate this, suppose a survey is conducted on a random sample of 1000 voters in a city, and 600 of them indicate that they support a particular candidate. Based on this sample, the surveyors can use statistical inference to estimate the proportion of voters in the entire city who support that candidate. A confidence interval could be constructed to provide a range of values within which the true proportion of voters who support the candidate is likely to lie. This estimate can be used to inform political strategy and decision-making.
However, it's important to note that statistical inference is subject to certain assumptions and limitations, and there is always a degree of uncertainty associated with making predictions or generalizations based on a sample. Therefore, it's important to use sound statistical methods and careful analysis to ensure that the inferences drawn are as accurate as possible.
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suppose you believe that stress causes headaches. what is the hypothesis? explain why we would use an experiment study to test this hypothesis. identify the independent and dependent variables. explain the treatments for the experimental and control groups. make sure all parts of your potential experiment are defined and labeled
If the presented hypothesis is confirmed, it can be assumed that individuals in the experimental group suffer from headaches more frequently than those in the control group.
The study examines how stress affects headaches. The theory can be stated as follows: People who encounter stress episodes more than twice per day would feel headaches more frequently than people who do not experience stress. This question concerns a cause and effect analysis, which can be done with reliable results when using an experimental investigation. Therefore, it is advised to use an experimental design for dealing with headaches brought on by stress. Stress events are the only unchanging factor in our study, however they do cause changes in the frequency of headaches. The degree of headaches, which fluctuates when the independent variable is changed, can be thought of as the dependent variable. Here, the technique can be applied as follows: Informed consent is obtained from a sample of 400 persons, all of whom fall within the age range of 25 to 40 (to lessen the impact of any auxiliary variables on the results). The volunteers are divided into two groups at random, one of which is the experimental group and the other the control group (double-blind design to avoid any potential biases). Three times a day, participants in the experimental group are exposed to a show that is heavy on the negative feelings that can lead to stress; in contrast, individuals in the control group are not exposed to any of the shows mentioned above. Then, the presence of headaches is assessed in both groups' members.
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Because averages are less variable than individual outcomes, what is true about the standard deviation of the sampling distribution of x bar?
The standard deviation of the sampling distribution of x bar (the mean of a sample) is always less than the standard deviation of the population from which it is sampled.
Central Limit Theorem states that as the sample size increases, the sampling distribution of x bar approaches a normal distribution with a mean equal to the population's mean and a standard deviation equal to the population's standard deviation divided by the square root of the sample size.
Standard deviation of the sampling distribution of x = σ / √N,
where:
σ = standard deviation of the population
N = sample size
As a result, the standard deviation of the sampling distribution of x bar is also less variable than the standard deviation of the population.
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Solve for x show proofs
The value of x in the triangle is 6√5
How to determine the value of xfrom the question, we have the following parameters that can be used in our computation:
The triangle
Using the above as a guide, we have the following:
x/20 = 9/x
Cross multiply the equation
so, we have the following representation
x^2 = 180
TAke the square root of hoth sides
This gives
x = 6√5
Hence, the solution of x is 6√5
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OAB is a triangle. OA = 4a + 7b
OB = 5a - b
Write AB in terms of a and b. Fully simplify your answer.
Answer:
AB = a - 8b
Step-by-step explanation:
AB = AO + OB
= - OA + OB
= - (4a + 7b ) + (5a - b )
= - 4a - 7b + 5a - b ← collect like terms
= a - 8b
5 Dans chaque cas, calculet une valeur approchée
au dixième près de la longueur, en cm, de chaque
cercle.
2.8 cm
18 m
J’ai besoin d’une réponse au plus vite possible
Robin and 2 friends each were able to jump rope for 4/5 minute. How long did they jump rope for altogether?
Answer:
[tex]p(3and7)andq(1and9)[/tex]
Kelly is reading a 456- page book. During the past 7 days she has read 168 pages. If she continues reading at the same rate, how many more days will it take her to complete the book?
Answer:
12 Days
What is a ratio?A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
To find the ratio of the problem (days: pages) we can use this equation:
pages read ÷ days it took = pages read each day
Fitting the numbers into the equation:
168 ÷ 7 = 24
So, everyday Kelly reads 24 pages.
To find out how many more days Kelly needs to read, if she reads at the same rate, we can use this equation:
(456 - 168) ÷ 24 = days left
We can use this to check our work:
168 + (24 ×?) = 456
Solving for the first equation:
(456 - 168) ÷ 24 = days left
288 ÷ 24 = 12
Now, we can check our work.
168 + (24 ×?) = 456
Inserting 12 into the equation:
168 + (24 × 12) = 456
168 + 288 = 456
Therefore, to complete the book it will take Kelly 12 more days.
allintext:if we have four variables, then how many equations will we have in our system of linear equations?
If we have four variables, then four equations will we have in our system of linear equations.
A linear equation is a mathematical equation that represents a straight line on a graph. It is an equation that can be written in the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. The slope represents how steep the line is, and the y-intercept is the point where the line intersects the y-axis.
Linear equations can be used to model a wide range of real-world phenomena, from simple physics problems such as calculating the speed of a moving object, to economic models that describe the relationship between price and demand. They are also widely used in fields such as engineering, finance, and statistics.
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1^4 x 1^? = 1^12 Find '?'
un cuerpo describe un M.A.S de a cuerdo con lo especificado.
x= 2 cos (π/2 T+π) r
Hallar sus elementos en:
T= 2
T= 2/3 seg
K= f/x
The M.A.S motion for two different time periods {T} = 2s and
{T} = 2/3s is calculated above.
What is the general equation of a wave motion?The general equation is -
y{t} = A sin(ωt + Ф)
Given is a body describes an M.A.S according to the function -
{x} = 2 cos{(π/2)T+ π)r
Now -
For {T} = 2, we can write -
{x} = 2 cos{(π/2) x 2+ π)r
{x} = 2 cos{2π}r
{x} = 2 x 1 x r
{x} = 2r
For {T} = 2/3, we can write -
{x} = 2 cos{(π/2) x 2/3+ π)r
{x} = 2 cos{π/3}r
{x} = 2 x -0.33 x r
{x} = - 0.66r
Therefore, the M.A.S motion for two different time periods {T} = 2s and
{T} = 2/3s is calculated above.
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{Question in english -
a body describes an M.A.S according to what is specified.
x= 2 cos (π/2 T+π) r
Find its elements in:
T= 2
T= 2/3 sec
K=f/x}
Boat
Boat A
Boat B
Cost
$2400
$2800
< Previous
Miles Per Gallon
(MPG)
15
18
Estimated Repairs
$600
$250
Stephanie wants to compare the total cost of buying and using these boats on her local lake.
Stephanie estimates she will drive the boat at least 40 miles per month.
The average cost of gasoline per gallon in her city is $3.89.
• Stephanie plans on owning the boat for 3 years.
Which boat will cost Stephanie the least to buy and use? How much will the difference in cost be?
Boat A will cost less for Stephanie. The difference in cost will be $400.
Boat B will cost less for Stephanie. The difference in cost will be $12.24
Boat A will cost less for Stephanie. The difference in cost will be $12.24.
O Boat B will cost less for Stephanie. The difference in cost will be $400.
The boat that will cost Stephanie less to buy and use is boat B, and the difference between the cost is $11.7.
How much will each boat cost?Let's calculate first the cost of each boat:
Boat A
cost + repairs + gasoline for 3 years= total cost
2400 + 600 + gasoline cost
gasoline cost = 40 / 15 = 2.66 gallons per month x 36 = 95.76 X 3.89 = 372.5
2400 + 600 + 372.5 = 3,372.5
Boat B
cost + repairs + gasoline for 3 years= total cost
2800 + 250 + gasoline cost
gasoline cost = 40 / 18 = 2.22 gallons per month x 36 = 79.92 X 3.89 = 310.88
2800 + 250 + 310.88 = 3,360.88
Difference: 3,372.5 - 3, 360.88 = 11.7
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Your friend is on a weight-loss program and
wants to reach a final goal weight of 160
pounds. His starting weight was 180 pounds. If
he has lost 8% of his body weight so far, how
many pounds does he still have to lose to reach
his final goal.
Answer:
5.6lbs
Step-by-step explanation:
multiply 180 by .08
8%=14.4
14.4-180=165.6
165.6-160= 5.6
ver the next 14 months you have to read at least 42 books. You have to read x books per month. The inequality 14x242 represents this situation. Solve the inequality to
nd the number of books you have to read per month.
ou have to read at leastbooks per month.
The number of books to read per month is 3 or more.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
14x ≥ 42
Solve for x.
14x ≥ 42
Divide both sides by 14.
x ≥ 42/14
x ≥ 3
This means,
The number of books to read per month is 3 or more.
Thus,
The number of books to read per month is 3 or more.
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For each Diagram, write an unsimplified and simplified equation that represents the relationship between x and y.
I need the unsimplified equations on the left side of the chart from what I know it should be equal to the simplified equation across from it.
For diagram A, the unsimplified equation represents the relationship between x and y is y = x + x/3.
For diagram B, the unsimplified equation represents the relationship between x and y is y = x + 2x/3.
For diagram C, the unsimplified equation represents the relationship between x and y is y = x - x/3.
For diagram D, the unsimplified equation represents the relationship between x and y is y = x - 2x/3.
What is an unsimplified equation?Performing mathematical operations reduces an unsimplified equation to a simplified equation. A simplified equation is used for convenience.
Diagram A:
The value of x contains 3 congruent colored rectangles. The noncolored rectangle is 1. So, the value of the noncolored rectangle will be x/3.
Clearly, y will be the sum of x and x/3, that is, y = x + x/3.
Therefore, the obtained answer is y = x + x/3.
Diagram B:
The value of x contains 3 congruent colored rectangles. The noncolored congruent rectangles are 2. So, the value of the noncolored rectangles will be 2x/3.
Clearly, y will be the sum of x and 2x/3, that is, y = x + 2x/3.
Therefore, the obtained answer is y = x + 2x/3.
Diagram C:
The value of x contains 3 congruent colored rectangles. So, the value of 1 rectangle will be x/3.
Clearly, y will be the difference between x and x/3, that is, y = x - x/3.
Therefore, the obtained answer is y = x - x/3.
Diagram D:
The value of x contains 3 congruent colored rectangles. So, the value of 2 congruent rectangles will be 2x/3.
Clearly, y will be the difference between x and 2x/3, that is, y = x - 2x/3.
Therefore, the obtained answer is y = x - 2x/3.
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While shopping for clothes, Tracy spent $38 less than 3 times what Daniel spent. Write and solve an equation to find how much Daniel spent. Let x represent how much Daniel spent.
This is 7th grade math lol and i have no idea how to do it
On solving the provided question, we can say that equation for getting amount spent by Daniel is y + 38 / 3 = x
What is equation?A mathematical equatiοn is a formula that joins two statements and uses the equal symbοl (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is knοwn as an equatiοn in algebra.
For instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relatiοnship between the twο sentences οn either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which alsο serves as the symbol. for instance, 2x – 4 = 2.
equatiοn for getting amοunt spent by Daniel -
x = y+38 / 3
Tracy then spent (in dοllars) accοrding to the provided descriptiοn (we don't write symbols like $ when writing equations because it is clear from the cοntext what the quantity stands fοr).
y = 3x - 38
y + 3x8 = 3x
y + 38 / 3 = x
equation for getting amοunt spent by Daniel is
y + 38 / 3 = x
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I need help, Find the volume of this object. Use 3 for Pi.
The volume of the given 3 - D figure is 156.36 cubic inches.
What is volume?A volume is a collection of a three dimensional coordinate points enclosed by a two dimensional coordinate points.
Given is the 3 - D figure as shown in the image.
We can write the volume as -
V = πr²h/3 + lbh
V = (3.14 x 3 x 3 x 8)/3 + (9 x 9 x 1)
V = 156.36 cubic inches
Therefore, the volume of the given 3 - D figure is 156.36 cubic inches.
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Which list of numbers is ordered from greatest to least?
Responses
52%, 0.45, 3.1×101, 1011
52%, 0.45, 3.1×101, 1011
3.1×101, 52%, 0.45, 1011
3.1×101, 52%, 0.45, 1011
52%, 3.1×101, 1011, 0.45
52%, 3.1×101, 1011, 0.45
3.1×101, 1011, 52%, 0.45
PLEASE HELP!! 100 points!
The set representing the ordered numbers is given as follows:
0.45, 52%, 10/11, 31.
How to order the numbers?The numbers for this problem are given as follows:
52% = 0.52 -> conversion of percentage to decimal.0.45.3.1 x 10¹ = 31 -> scientific notation to decimal.10/11 = 0.909. -> fraction to decimal.For the three numbers with an integer part of zero, we order them according to the decimal part, hence:
0.45, 52%, 10/11.
31 has an integer part of 31 and is greater than the other numbers, hence the ordered data-set is given as follows:
0.45, 52%, 10/11, 31.
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Rewrite x(t)=(1.45)^t/2 in the form y=a(1+r)^t or y=a(1-r)^t to determine whether it represents exponential growth or exponential decay. Round a and r to the nearest hundredth if necessary.
The given function represents exponential growth, the value of a is 1 and the value of r is 0.45.
What is the exponential growth?The quantity increases slowly after which the rate of change and the rate of growth increases over a period of time rapidly. This increase in growth is calculated by using the exponential growth formula.
The exponential growth formula is [tex]Amount = Initial value(1+\frac{r}{100} )^{\frac{t}{n}}[/tex].
The given exponential function is [tex]x(t)=(1.45)^{\frac{t}{2} }[/tex].
Now, [tex]x(t)=(1+0.45)^{\frac{t}{2} }[/tex]
Compare, [tex]x(t)=(1+0.45)^{\frac{t}{2} }[/tex] with [tex]y=a(1+r)^t[/tex], we get
a=1 and r=0.45
Therefore, the value of a is 1 and the value of r is 0.45.
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Which step is NOT performed in the process of solving n²
A
B
C
D
Add 10 to each side
Add 36 to each side
Factor ² 12n 100
Take the square root of each side
12n 100 by completing the square?
A step that is not performed in the process of solving n² - 12n - 10 = 0 by completing the square is: C. Factor n² - 12n - 10 = 0.
How to solve the quadratic equation?In order to solve the given quadratic equation, we would use the completing the square method as follows;
n² - 12n - 10 = 0
By keeping x terms on the left-hand side of the quadratic equation, we would move the constant term to the right-hand side of the quadratic equation by adding 10 on both sides as follows;
n² - 12n - 10 + 10 = 0 + 10
n² - 12n = 10
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
n² - 12n + (12/2)² = 10 + (12/2)²
n² - 12n + 36 = 10 + 36
n² - 12n + 36 = 46
(n - 6)² = 46
By taking the square root of each side, we have:
n - 6 = ±46
n = 6 ±46
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Complete Question:
Which step is NOT performed in the process of solving n² - 12n - 10 = 0 by completing the square?
Add 10 to each side
Add 36 to each side
Factor n² - 12n - 10 = 0
Take the square root of each side
if each coded item in a catalog begins with 4 distinct letters followed by 4 distinct nonzero digits, find the probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even.
The probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is 5/52
probability is an occurence of a particular events. This particular problem can be solved using permutations and combinations.
Given that, if each coded item in a catalog begins with 4 distinct letters followed by 4 distinct nonzero digits
Like the 4 distinct letters be A,B,C,D
4 distinct nonzero digits are 2,3,4,5
The probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is approximately equals to the 10/104 = 5/52
Here the probability is an occurence of a particular events. This particular problem can be solved using permutations and combinations and the probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is approximately equals to 5/52
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