Write x2 − 6x + 7 = 0 in the form (x − a)2 = b, where a and b are integers. (1 point)
(x − 4)2 = 3
(x − 3)2 = 2
(x − 2)2 = 1
(x − 1)2 = 4
Answer:
B. [tex](x-3)^2=2[/tex].
Step-by-step explanation:
We have been given an equation [tex]x^2-6x+7=0[/tex]. We are asked to write our given expression in form [tex](x-a)^2=b[/tex].
First of all, we will subtract 7 from both sides of our given equation.
[tex]x^2-6x+7-7=0-7[/tex]
[tex]x^2-6x=-7[/tex]
Now, we will complete the square for left side of equation by adding the half the square of 6.
[tex](\frac{6}{2})^2=(3)^2=9[/tex]
Upon adding 9 on both sides of our equation, we will get:
[tex]x^2-6x+9=-7+9[/tex]
[tex](x-3)^2=2[/tex]
Therefore, our required equation would be [tex](x-3)^2=2[/tex] and option B is the correct choice.
Winning the jackpot in a particular lottery requires that you select the correct fourfour numbers between 1 and 6262 and, in a separate drawing, you must also select the correct single number between 1 and 1616. find the probability of winning the jackpot.
There are 2 drawings, in the 1st one we have to select correct four numbers between 1 and 62 while the 2nd one is to select the one single number between 1 and 16.
In the 1st drawing, the probability of success is 1 divided by the total number of 4 combinations that can be created from 62 numbers.
P1 = 1 / 62C4
P1 = 1 / 557,845
In the 2nd drawing, the probability of success is 1 divided by 16:
P2 = 1 / 16
Since the two drawings must be satisfied before you can win the jackpot, then multiply the two:
P = P1 * P2
P = (1 / 557,845) (1 / 16)
P = 1 / 8,925,520 = 1.12 x 10^-7 = 1.12 x 10^-5 %
Therefore the odd in winning this lottery is 1 in 8,925,520 chances.
In how many ways can we seat 6 people around a round table if Fred and Gwen insist on sitting opposite each other? (Two seatings are considered equivalent if one is a rotation of the other.)
Answer:
24
Step-by-step explanation:
If Julie invests $9,250 at a rate of 7%, compounded weekly, find the value of the investment after 5 years. $13,455.78
A chord of a circle is any line segment whose endpoints are on the circle
A.True
B.False
Answer:
True
Step-by-step explanation:
Chord: It is that line segment which connect the two points on the circle.
It is a distance between two boundary points of circle.
Or we can say that
Chord: It is a line segment which connect the two points on circle's circumference.
A chord of a circle is any line segment whose endpoints are on the circle.
Diameter of circle is a largest chord of circle.Diameter is that line segment which divides the circle into two equal halves.
Hence, we can say that given statement is true.
A random sample of 49 statistics examinations was taken. the average score, in the sample, was 84 with a variance of 12.25. the 95% confidence interval for the average examination score of the population of the examinations is
Given a random sample of 49 exams with an average score of 84 and variance of 12.25, the 95% confidence interval for the average score for the all exams is between 82.4 and 85.6.
Explanation:Based on the given problem, a random sample of 49 statistics exams was examined. The statistics from this sample recorded an average score of 84 with a variance of 12.25. Using this information, we can establish a 95% confidence interval for the average score for the entire population of statistics exams - that's our goal here.
To calculate this, we take the sample mean (84) and add and subtract the standard deviation (sqrt(12.25)=3.5) multiplied by the z value for 95% confidence level (which is about 1.96).
The confidence interval calculation should look like this: [84 - (1.96*3.5/sqrt(49)), 84 + (1.96*3.5/sqrt(49))]. Obtaining 82.4 and 85.6 as the lower and upper limits, we can see that our 95% confidence interval estimate for the population's average exam score is from 82.4 to 85.6.
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Duncan shares 20 percent of all of his sales commissions with his personal assistant. If Duncan earns x dollars in commissions and gives his assistant y dollars, which equation correctly models this situation? mc011-1.jpg
Answer:
X * (0.2)y
Step-by-step explanation:
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 - 3 sin θ
Answer:
Symmetry about y-axis
Step-by-step explanation:
We are given that
[tex]r=4-3sin\theta[/tex]
When the graph is symmetric about x- axis then the point (x,y) change in to (x,-y) and the function remain same.
The point[tex] (r,\theta,)[/tex] is replaced by [tex]( r,-\theta)[/tex]
Substitute the value then we get
[tex]r=4-3 sin(-\theta) [/tex]
[tex]r=4+3sin\theta[/tex] ([tex]sin(-\theta)=-sin\theta)[/tex]
The value of function changes .Hence , the function is not symmetric about x- axis.
When the function is symmetric about y-axis then the point [tex](r,\theta) [/tex] change into point [tex](r,\pi-\theta)[/tex] and function remain same
Substitute the value
[tex]r=4-3sin(\pi-\theta)[/tex]
[tex]r=4-3 sin\theta[/tex] ([tex]sin(\pi-\theta)=sin\theta[/tex])
The value of function does not change when point change ,Hence, the function is symmetric about y- axis.
When the graph is symmetric about origin then the point [tex](\theta,r)[/tex] change into point[tex](r,\pi+\theta)[/tex] and the value of function remain same.
Substitute the value then we get
[tex]r=4-3sin(\pi+\theta)[/tex]
[tex]r=4+3sin\theta [/tex]
[tex]r=4+3sin\theta [/tex]
Hence, the graph has symmetry about y-axis .
Identify the measure of arc PQ
Every minute, the first letter of each word is moved to the other end of the word. After how many minutes will the original sentence first reappear?
To find the time it takes for the original sentence to reappear, we need to find the least common multiple (LCM) of the cycle counts of each word. The LCM of the cycle counts gives us the number of minutes for the original sentence to reappear.
Explanation:To find the number of minutes it takes for the original sentence to reappear, we need to analyze the pattern of the letters in a word. Let's take an example sentence: 'The quick brown fox jumps over the lazy dog.' After the first minute, the sentence becomes 'ehT uickq norwb foxp smuj revo eht yzal god.' Notice that each word has its first letter moved to the end. So, each word becomes a cyclic permutation of itself, with a period equal to the number of letters in the word.
Now, let's count the number of cycles for each word in the original sentence. 'The' has one cycle, 'quick' has five cycles, 'brown' has five cycles, 'fox' has three cycles, 'jumps' has five cycles, 'over' has four cycles, 'the' has one cycle, 'lazy' has four cycles, and 'dog' has three cycles. To find the time it takes for the original sentence to reappear, we need to find the least common multiple (LCM) of these cycle counts. The LCM of 1, 5, 5, 3, 5, 4, 1, 4, and 3 is 60.
Therefore, it will take 60 minutes for the original sentence to first reappear.
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Which number can each term of the equation be multiplied by to eliminate the fractions before solving? 6 –3/4x +1/3 =1/2 x + 5
Answer:
The number is 12.
Step-by-step explanation:
Given: [tex]6-\dfrac{3}{4}x+\dfrac{1}{3}=\dfrac{1}{2}x+5[/tex]
We need to find a number multiply to each term to get rid of fraction.
We will find LCD of denominator.
First we see the numbers at denominator
Denominators are 4,3,2
Now, we will find the LCD of 2,3, and 4
Factor of 2: 2x1
Factor of 3: 3x1
Factor of 4: 2x2x1
LCD = 2x2x3 = 12
If we multiply by 12 to each term to eliminate the fraction.
Simplest equation:
[tex]12\cdot 6-12\cdot \dfrac{3}{4}x+12\cdot \dfrac{1}{3}=12\cdot \dfrac{1}{2}x+12\cdot 5[/tex]
[tex]72-9x+4=6x+60[/tex]
Hence, The number is 12.
21. Compare the numbers 5/9 and 0.5. use the symbols <, >, or =.
A) 5/9=0.5
B) 5/9>0.5
C) 5/9<0.5
Answer:
B) [tex]\frac{5}{9}>0.5[/tex]
Step-by-step explanation:
We are asked to compare the numbers 5/9 and 0.5.
Let us convert 0.5 as a fraction. We will divide and multiply 0.5 by 10 as:
[tex]0.5\times \frac{10}{10}=\frac{5}{10}=\frac{1}{2}[/tex]
Now, we will make a common denominator for both numbers as:
[tex]\frac{1*9}{2*9}=\frac{9}{18}[/tex]
[tex]\frac{5*2}{9*2}=\frac{10}{18}[/tex]
Therefore, [tex]\frac{5}{9}>0.5[/tex] and option B is the correct choice.
Given the following functions f(x) and g(x), solve (f/g)(-3) and select the correct answer below:
f(x) = 6x + 8
g(x) = x - 2
A: -2
B: -1/2
C: 1/2
D: 2
We are given the functions:
f(x) = 6x + 8
g(x) = x – 2
The first step in solving this problem is to find for the value of (f / g) (x) given the two functions above. Now finding for (f / g) (x), we can see that if we distribute x inside (f / g) we get f (x) / g(x)
therefore,
(f / g) (x) = f (x) / g (x)
= (6 x + 8) / (x – 2)
Substituting x = -3 will give us:
(f / g) (- 3) = [6 (- 3) + 8] / (- 3 -2)
(f / g) (- 3) = 2
Answer:
D: 2
A figure is translated using the vector (-2,4) What translation vector would move the image back to its original position?
A translation formation is one of the simplest transformation since all it does is just to move the position of the figure without changing the size, the angles, or any other characteristics other than the position along.
So a translation by a vector (-2, 4) means that all points of the given figure is moved by:
(x – 2, y + 4)
Meaning that the whole figure is moved to the left by 2 units and moved to top by 4 units
So to revert this back into the original figure, we simply have to move again by:
(x + 2, y – 4)
Therefore move the whole figure to the right by 2 units and to the bottom by 4 units. So the translation to use is a vector (2, -4)
Answer:
(2, -4)
Last year Jill was 5.1 feet tall she grew 8% taller in 1 year how tall is she know
3y = 2x-6
x + y =8
Solve algebraically.
How to calculate ten percent of something?
Last month, a company had receipts totaling $3,700. The company had overhead costs of $444. What is the rate of overhead? A. 11% B. 10% C. 13% D. 12
divide the overhead by total receipts
444/3700 = 0.12
0.12 = 12%
Determine the factors of x2 − 8x − 12.
a. (x − 6)(x + 2)
b. (x + 3)(x − 4)
c. Prime
d. (x + 6)(x − 2)
Answer:
The correct option is: c. Prime
Step-by-step explanation:
The given expression is: [tex]x^2 -8x-12[/tex]
First we will take each given option and simplify them using FOIL method to see if we get the original given expression. So.....
[tex]a.\ \ \ (x-6)(x+2)\\ \\ =x^2+2x-6x-12\\ \\ =x^2-4x-12\\ \\ \\ b.\ \ \ (x+3)(x-4)\\ \\ =x^2-4x+3x-12\\ \\ =x^2-x-12\\ \\ \\ d.\ \ \ (x+6)(x-2)\\ \\ =x^2-2x+6x-12\\ \\ =x^2+4x-12[/tex]
We can see that options [tex]a, b\ and\ d[/tex] doesn't give the original given expression.
So, the expression [tex]x^2 -8x-12[/tex] is Prime.
You are building a rectangular dog pen with an area of 90ft^2.you want the length of the pen to be 3ft longer than twice its width. write an equation that can be used to find the width w of the pen
What is 1 / (0! - 1!)
How would I graph these equations?
a. 2x + 3y = 12
b. x = 7
The graph of f(x) = x^2 has been shifted into the form f(x) = (x − h)^2 + k
What is the value of h?
Answer: h=2
hope this helps
math???????????.../?
Answer:
Math
Step-by-step explanation:
If one coin is flipped and then a second coin is flipped, what is the probability that both coins turn up tails? question 18 options:
When constructing a circle inscribed in a triangle, what is the purpose of constructing a perpendicular segment from the incenter to a side of the triangle?
To determine the center of the circle
To determine the radius of the circle
To connect the midpoints of each side of the triangle
To connect the arc markings from the angle bisectors
How many boys are in a class of thirty-five student if the girls outnumber boys by five
There are total 35 students in the classroom. If the number of girls is 5 more than the number of boys, then the number of boys in the class is 15.
What is fraction?An object or total number of some objects can be fractionated into two more fractions where the sum of these fractions equals to the total number. Let s be the total number of pearls in a glass. Let x be the number of white pearls and y be that of black pearls in it.
then s = x +y.
It is given that, the total number of students in the class is 35. The number of girls outnumber boys by 5. Let the number of boys be x then the number of girls will be x +5.
Now, the total number of students is the sum of number of boys and girls.
x + (x +5) = 35
2x + 5 = 35
2x = 35 - 5 = 30
x = 30/2 = 15.
Therefore, the number of boys is 15 and the number of girls is 20.
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The profit P after the first month of operation for a new departmental store is $10,605. The profit of the departmental store after x months can be determined by P = 10500(1.01)x. What will the profit of the store be after 6 months?
A) $11,145.96
B) $11,500.00
C) $10,605.67
D) $10,500.00
The profit of the store after six months, using the given growth model, can be calculated by substituting x with 6 in the given equation and calculating the result, leading us to the answer A) $11,145.96.
Explanation:The question relates to an algebraic comprehension of
exponential growth
, using a mathematical model to predict future profit. The profit after x months is given by
P = 10500(1.01)^x
, where 'x' stands for the number of months after the first month. To find the profit after six months, all we have to do is substitute 'x' with '6' in the given equation, like so:
P = 10500(1.01)^6
. When you calculate this, the result is around,
$11,145.96
, so the correct answer to the question 'What will the profit of the store be after 6 months?' is option A) $11,145.96.
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In the given formula, substitute 6 for x, which results in P = 10500(1.01)^6. Upon simplification, it gives the profit after 6 months as $11,145.96.
Explanation:To calculate the profit of the departmental store after 6 months, we need to substitute the value 6 for x in the given formula P = 10500(1.01)^x. This results in P = 10500(1.01)^6.
When we simplify this, it gives the profit as $11,145.96. Therefore, the correct answer is option A) $11,145.96.
This mathematics concept is related to exponential functions in real-world applications like finance and investment, where the principal amount grows at a consistent rate over time.
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list the sides of triangle WXY in order from smallest to largest
The sides of triangle WXY can be listed from smallest to largest as YW, WX, XY, by matching the side lengths to a set of Pythagorean triplets (5, 12, and 13 cm). This corresponds to option A of the provided choices.
To list the sides of triangle WXY in order from smallest to largest, we can use the Pythagorean theorem which 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.
According to the given information, we have two right triangles with sides 5 cm, 12 cm, and 13 cm.
Recognizing these are Pythagorean triplets, where 5 and 12 are the legs and 13 is the hypotenuse, it indicates that the side measures 13 cm is the longest side, followed by the 12 cm side, and then the 5 cm side is the shortest.
Therefore, if we match these lengths to the sides of triangle WXY, we can list the sides from smallest to largest based on their corresponding lengths, with the assumption XY matches the 13 cm side (as it is not specified and must be inferred).
The correct listing of triangle sides from smallest to largest would be: YW, WX, XY. This correlates to option A in your list.
The probable question may be:
list the sides of triangle WXY in order from smallest to largest
A. YW, WX, XY
B. XY, YW,WX
C. WX,XY,YW
D. XY, WX,YW
Which of the following is a measurement conversion that you may need to make when comparing energy and mass in nuclear reactions? (A)degrees Celsius to Kelvin (B) grams to tons (C)kilojoules to joules (D)meters per second to miles per hour
Answer:
C
Step-by-step explanation: