Priya solved the following quadratic equation by completing the square. Her work is shown.
(+ 6x-11 =0
Original equation
x?+6x=11
Step 1: Isolate the variables to one side
4x +6x+6=17
Step 2: Complete the square when b = 6
(x+3)=17
Step 3: Factor and square the trinomial
x+3=‡/17
Step 4: Take the square root of both sides of the equation
x=-3‡/17
Step 5: Inverse operations to isolate the variable
What mistake did Priya make?
A
In Step 2, Priya did not correctly complete the square.
B
In Step 5, Priya did not finish simplifying her answer.
C
In Step 3, Priya should have also squared the 17.
D
In Step 1, Priya should not have changed the sign of 11
Answers
While solving the quadratic equation, in the step 2, Priya did not correctly complete the square.
A quadratic equation is of the form of ax²+bx+c=0.
Here x is the variable. a , b and c are constants.A quadratic equation has two solutions.The graph of a quadratic equation is in the form of a parabola.A quadratic equation can be solved in various ways:Graphical solutionMiddle term factorizationcompleting the square method.The given quadratic equation is of the form:
x²-6x-11=0
Now solving it by completing the square we get:
or, x²-6x=11 (take all the variable to one side)
or, x²-6x+9=11+9 (complete the square when b=3)
or, (x-3)²=20 (factor and square the polynomial)
or, x = 3 ± √20 (use inverse operations so that the variable is isolated)
Hence Priya made a mistake while completing the square of the equation.
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Related Questions
Which is the least whole number that rounds to 2000 when rounded to the nearest hundred
Answers
The required number is 2001.
To solve this problem we need to know the concept of rounding off.
Rounding off a number means making the value of number equal to the nearest tens place.
When we round off 45 we will get 50; when we round off 44 we get 40.
So, if a number has 5 at its unit place then it will be rounded off to the tens place which is ahead of 5 and if a number is less than 5 then it is rounded off to the tens place before that number.
Here it is asked to find the least whole number that rounds off to 2000 when rounded off to nearest hundred which will be 2001.
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An experiment was conducted in which two fair dice were thrown 100 times. The sum of the pips showing on the dice was
then recorded. The frequency histogram to the right gives the results. Use the histogram to complete parts (a) through (f).
a. What was the most frequent outcome of the experiment?
b. What was the least frequent?
c. How many times did we observe a 5?
d. How many more 8's were observed than 11's?
e. Determine the percentage of time a 5 was observed.
f. Describe the shape of the distribution.
Answers
The answers to the questions are:
The most frequent outcome of the distribution that we have here is 7.The least frequent outcome is 12The number of times that we observed a 5 is 10 timesThe 8ths that were observed than 11 is 16 - 4 = 12 timesA 5 was attempted at 10 percent of the timeThe shape of the distribution is the bell shaped distribution.What is a frequency histogram?This is the term that is used to refer to the graphical representation of a frequency distribution. It helps to show us the frequency that the details in the class would have to fall under.
For example, the most frequent outcome can be seen as the one that has the highest point on the graph. We can see the highest point as 7 and its frequency is 20.
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Answer:
A. 7
B. 12
C. 15
D. 16
E. 15%
F. Bell-shaped
In a salad recipe, the ratio of carrots to broccoli must remain constant. The table below shows some possible combinations of carrots and broccoli.
Salad Ingredients
Carrots
Broccoli
3
9
4
12
6
18
7
21
If only whole vegetables can be used, what is the fewest number of vegetables that can be used to make this salad?
A.1
B.3
C.4
D.12
Answers
Using a proportional relationship, the fewest number of vegetables that can be used to make this salad is:
C. 4
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
For this problem, looming at the table, we have that the number of Broccoli is triple the number of carrots, hence the proportional function is:
B = 3C.
When there is one carrot, the number of broccoli is given by:
B = 3 x 1 = 3.
Hence the fewest number of vegetables is of 4, as 1 carrot + 3 broccoli = 4 vegetables, hence option C is correct.
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If you have the function f(x) = 5^x - 5 then find the value of f(t)
Answers
The value of the function is [tex]5^t-5[/tex] .
A function is defined as a expression containing one or more variables.
A function, in technical terms, is a mechanism to connect a collection of inputs to a set of outputs.
A function of a single variable (say x) is defined mathematically as g(x).
Let us consider a function of a variable x such that it is defined as:
g(x)=x+1
Here the output are calculated for all values of x . At x=1 the value of the function is denoted as g(1)=1+1=2.
Mathematically to calculate the value of the function f(x) for any particular value of x we substitute the value of x into the value of f(x).
Now the given function is given as:
[tex]f(x)=5^x-5[/tex]
Therefore at x=t,
[tex]f(t)=5^t-5[/tex]
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Identify the errors made in finding the inverse of
y = x- + 12x.
x = y2+ 12x
y?=x-12x
y2=-11x
y=V-11x, for x 2 0
Describe the three errors.
Answers
The following mistakes were made in the solution of the inverse function:
There is an incorrect swap between the variables y and x.The ± sign should be included in the square root.The domain of the function is incorrect because the radicand can only have a real value if x is less than 0.What are inverse functions?The original value for which the function's output was provided is returned by the inverse function.F and G are inverse in terms of functions, with f(g(x)) = g(f(x)) = x.The initial value is returned by a function that is its inverse. The inverse of f is then g(y) = (y-5)/2 = x. (x).Therefore, the first error is caused by the incorrect variable swap.
The correct expression is:
x = y² + 12yThe following error is:
y = √-11xThe correct expression:
y = ± √-11xFinally, the domain is incorrect.
Because if x is 0 or positive, y = -11x has no true value.As a result, the following errors were made in the inverse function solution:
There is an incorrect swap between the variables y and x.The ± sign should be included in the square root.The domain of the function is incorrect because the radicand can only have a real value if x is less than 0.Know more about inverse functions here:
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The correct question is given below:
Identify the errors made in finding the inverse of y = x2 + 12x.
Describe the three errors.
The perimeter of any rectangle in which the length is 4 more than twice the width is P = 6 w + 8 , where w is the width. Which formula can be used to find the width given the perimeter? Multiple choice question. cross out A) w = P − 4 3 cross out B) w = 1 6 P − 8 cross out C) w = − P + 8 6 cross out D) w = P − 8 6
Answers
Answer: option D
Step-by-step explanation:
Given equation:
P = 6 w + 8 [eq1]
l=2w+4 [where l is length]
using eq1 we have:
6w=P-8
w=(P-8)/6
hence option D
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Loan payments of $4000 due 200 days ago and $6000 due 63 days ago are to be replaced
by a payment of$5000 today and the balance 92 days from today. If money is worth 8.3%
and the agreed focal date is 92 days from today, what is the size of the final payment?
Answers
The size of the final payment is $5378.08
What is the size of the final payment?P1 = One loan payment = $4000
P2 = Second loan payment = $6000
P3 = Payment = $5000
Let P4 = Second payment
n1 = 200 days
n2 = 63 days
n3 = 92 days
r = Interest rate = 8.3%
[P1 * (1+ (r * n1 /365))] + [P2 * (1+ (r * n2 /365))] = P3 + [P4 / (1+(r*n3/365)]
[$4000 * (1+(8.3%*200/365)] + [$6000 * (1+(8.3%*63/365)] = $5000 + [P4 / (1+(8.3%*92/365))]
[$4000 * 1.04547945] + [$6000 * 1.01432603] = $5000 + [P4 / 1.02092055]
$4181.9178 + $6085.95618 = $5000 + [P4/1.02092055]
P4/1.02092055 = $5267.87398
P4 = $5378.080801
Therefore, the size of the final payment is $5378.08
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Lizzy had #500, John has #50
FIFI will have #700.Who has more money amongst the three.
Answers
Answer:
John
Step-by-step explanation:
it says Lizzy had which means we don’t know how much she has now. It says Fifi will have so we don’t know how much they have right now. But it says John has so we know what he has so therefore he has the most as of right now
help i need answer to this math question???
Answers
The solution of the geometrical system is (x, y) = (2.5, 48.5).
What are the missing values associated with a geometrical system?In this question we have a picture representing two lines and a semirray that brings out two formulae for supplementary angles, these are shown below:
(x + 10) + 30 + (3 · y + 2) = 180
x + 3 · y = 148 (1)
30 + (3 · y + 2) + (5 · x - 10) = 180
5 · x + 3 · y = 158 (2)
And now we resolve the entire system of linear equations by substitution:
By (1):
x = 148 - 3 · y
(1) in (2):
5 · (148 - 3 · y) + 3 · y = 158
740 - 15 · y + 3 · y = 158
12 · y = 582
y = 48.5
By (1):
x = 148 - 3 · 48.5
x = 2.5
The solution of the geometrical system is (x, y) = (2.5, 48.5).
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help me out
Simplify the
expression: 4^2 + 8 ÷2.
a. 12
b. 20
c. 8
d. 16
Answers
PEMDAS. Exponents first then divide then add
4^2=16
8/2 = 4
16+4=20
Market research was undertaken to determine whether an ad campaign was successful for the software company. 15 men and 75 women were asked if they had seen the company’s latest TV advertisement. Altogether, 2 5 of the people said ‘yes’. 6 15 of the men said ‘yes’. What percentage of women said ‘no’ out of the total survey population?
Answers
50% of women who said ‘no’ out of the total survey population if 15 men and 75 women were asked if they had seen the company’s latest TV advertisement.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
Market research was undertaken to determine whether an ad campaign was successful for the software company.
Total number of people = 15 + 75 = 90
The number of people who said yes = (2/5)90 = 36
The number of people who said no = 90 - 36 = 54
The number of men said yes = (6/15)x15 = 6
The number of men said No = 15 - 6 = 9
The number of women who said no = 54 - 9 = 45
Percentage = (45/90)x100
The percentage of women who said ‘no’ out of the total survey population:
= 50%
Thus, 50% of women who said ‘no’ out of the total survey population if 15 men and 75 women were asked if they had seen the company’s latest TV advertisement.
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According to a recent study, the number of prisoners in a prison decreased by 312 inmates over a one-year period. If the decrease was the
same for each of the 12 months, write the monthly decrease as a quotient of integers and find the monthly decrease.
The expression to find the monthly decrease in prisoners is.
(Do not simplify.)
The number of inmates in the prison decreased by inmates per month.
(Simplify your answer.)
Answers
Over a year, a prison's population dropped by 312 inmates. We know that 1 Year = 12 Months.
Additionally, considering that each of the 12 months declined at the same rate.
the Monthly decrease in members = 312 / 12 = 26
Therefore, the expression used to calculate the monthly drop in prisoner population = Number of prisoners decreased per year / Number of months
Note: If the monthly drop rate is the same, the aforementioned equation is correct ( for all months in that year)
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I need help with math ngl
Answers
Answer:
Oldest to newest:
10^-35, 10 ^-10, 0
Step-by-step explanation:
Scientific notation
To figure out the power of 10 think "how many places do I move the decimal point?"
When the number is 10 or greater the decimal point moves to the left, and the power of 10 is positive.
When the number is smaller than 1 the decimal point moves to the right, so the power of 10 is negative.
A bowl weighs 11/40 pound.
a. Express this weight as a decimal.
b. Explain how you can find the decimal by thinking of the denominator as a 4 and using mental math.
Answers
Answer: 0.275
Step-by-step explanation:
a. To express 11/40 as a decimal, you need to divide 11 by 40. (Steps shown in image)
b. Sorry, I can't figure out the answer to this. I don't recommend making the denominator a 4 as the numerator would become 1.1.
what is? 9x-x-2=3(2x-3)+ax
Answers
What is the midpoint of the line segment from p1 to p2 is (-4,1). If P1 =(-4,5) what is p2??
Answers
Find the distance between P1 and the midpoint:
P1 - midpoint
(-4,6) - (-4, 1)
Start with the "x" coordinates. Since the "x" coordinate is the same (x = -4) for both P1 and the midpoint, we know the line is vertical. P2's
"x" coordinate will also equal -4.
Next subtract the "y" coordinates:
P1 - midpoint
6 - 1 = 5
The distance between P1 and the midpoint is 5 coordinate points.
Next subtract 5 from the midpoint's "y" coordinate to find P2.
midpoint - 5
1 - 5 = -4.
P2 = (-4, -4)
Are you confident that you can round 7.396 to the nearest hundredth
Answers
Answer:
7.4
Step-by-step explanation:
When the decimal in any place is more than 0.5, round up.
A bookcase is to have 4 shelves including the top as pictured below.
The width is to be 12 feet less than 3 times the height. Find the width and the height if the carpenter
expects to use 22 feet of lumber to make it.
Width:
feet
Height:
feet
Answers
Answer:
The width is 3 feet and the height is 6 feet.
Step-by-step explanation:
Which diagram shows two figures intersecting at exactly four points?
Answers
Answer:
The rightmost figure
Step-by-step explanation:
That is the only figure where there are 4 points of intersection. It is a rhombus inscribed in a square
Xaivier played video games for 1 hour and 45 minutes before he went to bed. If he went to bed at 9:00 pm,what time did he start playing video games
Answers
Answer:7:15 pm
Step-by-step explanation:
We know he went to bed at 9:00 PM and spent 1 hr and 45 minutes playing games. Start by subtracting one hour away, so we get 8:00 PM. subtract 45 minutes from that and he would have started playing at 7:15 PM.
Please help i dont understand
Answers
Answer :
1) If x = 6
Substitute 6 for x in the expression.
a) 5x-9
5(6)-9
30-9
21
b) 2x-7
2(6) -7
12-7
5
c) 8x+5
8(6)+5
48+5
53
d) 4(x+3)
4(6+3)
4(9)
36
e) x²-(-4)
6²-(-4)
36+4
40
f) 3x²+1
3(6²)+1
3(36) +1
108+1
109
2) Solve
a) 54 = 3x
Divide both sides by 3.
54/3 = 3x/3
x = 18
b) x-9 = -3
Add 9 to both sides.
x-9+9 = -3+9
x = 6
c) x/7 = 140
Express the 140 over 1 and cross multiply.
x/7 = 140/1
x = 140×7
x = 980
d) x/8 = 72
Express the 72 over 1 and cross multiply.
x/8 =72/1
x = 72×8
x = 576
Maureen knows the domain of f(x) is the set of positive real numbers if she graphs f(x) on the coordinate plane what must be true about the graph
Answers
The correct option is C, if f(x) has a domain only with positive values, the graph will be on the first and fourth quadrant.
What must be true about the graph?We know that the domain of f(x) is only the set of positive real numbers. Now remember that the domain of a function is the set of the inputs of that function (the inputs are on the horizontal axis).
Then the graph of f(x) will only be on the positive side of the horizontal axis. We know that the two quadrants that are on that region are the first quadrant and the fourth quadrant.
Then if f(x) has a domain only with positive values, the graph will be on the first and fourth quadrant, this means that the correct option is C.
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Three rational numbers between 1/3 and 1/5
Answers
Three rational numbers between
1/3 and 1/5 are 4/15, 3/10, and 7/30
Given:The two numbers are 1/3 and 1/5
To find:The rational number between two numbers
Solution:Now, to find the rational number, add the numbers and divide their sum by 2.
(i) First rational number between
1/3, 1/5 = 1/3+1/5=8/5
Divide 18/5 by 2------> 8/15 x 1/2= 8/30= 4/15
The series becomes, 1/3, 4/15, 1/5
(ii) Second rational number
= 4/15+1/5 = 7/15
Divide
7/15 by 2 ------> 7/15 x 1/2 = 7/30
Hope this helps!
10-0.5(12+8b)+b
pls help if you can!
Answers
Answer: 4-3b
Step-by-step explanation:
10-0.5(12+8b)+b First, distribute -0.5 into 12 and 8b
10-6-4b+b Then combine like terms
4-3b Done!
Suppose that 14 inches of wire costs 84 cents.
At the same rate, how much (in cents) will 11 inches of wire cost?
Answers
Answer:
11 inches of wire will cost 66 cents
Step-by-step explanation:
14 inches - 84 cents
find unit rate by dividing 84 by 14
84/14=6
so is is 6 cents per inch
so multiply 6 by 11
11 inches of wire will cost 66 cents
Choose the best answer.
Use the conditional statement to answer the question.
If an angle measures 43 degrees, then the angle is acute.
Choose the best answer.
The statement is false, but the inverse is true.
Both the statement and its inverse are false.
Both the statement and its inverse are true.
The statement is true, but the inverse is false.
Answers
Answer:
D
Step-by-step explanation:
Acute angle are angles less than 90°.And 43° is less than 90° and the inverse is not less than 90°.
A person's systolic blood pressure, which is measured in millimeters of mercury (mm Hg), depends on a person's age, in years. The equation
p=0.007y^2-0.003y+122
gives a person's blood pressure, p,at the age y year
A.) Find the systolic pressure, to the nearest tenth of a millimeter, for a person of age 41 years.
Answers
The systolic pressure, to the nearest tenth of a millimeter, for a person of age 41 years is; 133.6 mm Hg
How to solve problems using quadratic equations?We are given the equation that gives a person's blood pressure, p at the age y year is;
p = 0.007y² - 0.003y + 122
To find the systolic pressure for a person of age 41 years, just plug in y = 41 into the given quadratic equation to get;
p(41) = 0.007(41)² - 0.003(41) + 122
p(41) = 11.767 - 0.123 + 122
p(41) = 133.6
Thus, the systolic pressure, to the nearest tenth of a millimeter, for a person of age 41 years is; 133.6
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use addition properties and strategies to find the sum 13 + 26 + 54=
Answers
Answer:
93
Step-by-step explanation:
13 + 26 = 39
39 + 54 = 93
5 is 1/2% of what number
Answers
How do I find out the check amount before the tip when the total amount was $55 with a 10% tip
Answers
Answer:$49.50
Step-by-step explanation:
First you have to find what 10% of 55 is. So if you times 10% by 55 you come out with $5.5. So after that you must subtract 5.5 from 55 which comes out to $49.50.
