Solve 5x + 1 = 2x2 + 9x. Which are steps in the process of completing the square used to solve the equation?
ANSWER CHOICES
1 = 2(x2 + 2x)
1 = 2x2 + 4x
2 = 2(x2 + 2x + 1)
3 = 2(x + 1)2
2 = 2(x + 1)2
Answer:
Choices (1), (2) and (4)
Step-by-step explanation:
5x + 1 = 2x² + 9x
By subtracting 5x form both the sides of the equation.
(5x + 1) - 5x = 2x² + 9x - 5x
1 = 2x² + 4x
1 = 2(x² + 2x)
By adding 2 on both the sides
1 + 2 = 2(x² + 2x) + 2
1 + 2 = 2(x² + 2x + 1)
3 = 2(x² + 2x + 1)
3 = 2(x + 1)²
Therefore, choices (1), (2) and (4) are the steps that have been used to complete the square.
To solve the equation 5x + 1 = 2x^2 + 9x using the method of completing the square, follow these steps: move all terms to one side of the equation, combine like terms, divide all terms by the coefficient of x^2, take half of the coefficient of x, square it, and add it to both sides of the equation, factor the left side of the equation, take the square root of both sides, and solve for x.
Explanation:To solve the equation 5x + 1 = 2x2 + 9x using the method of completing the square, the following steps are used:
Move all terms to one side of the equation: 2x2 + 9x - 5x - 1 = 0Combine like terms: 2x2 + 4x - 1 = 0Divide all terms by the coefficient of x2: x2 + 2x - 1/2 = 0Take half of the coefficient of x, square it, and add it to both sides of the equation: x2 + 2x + 1 = 1/4Factor the left side of the equation: (x + 1)2 = 1/4Take the square root of both sides: x + 1 = ±1/2Solve for x: x = -1 ± 1/2PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER
A garage contains a combination of 20 bikes and tricycles. In total, there are 44 wheels. How many bikes and how many tricycles are in the garage.
The solution explains how to find the number of bikes and tricycles in a garage based on the total number of wheels and the given combination.
Explanation:The question: A garage contains a combination of 20 bikes and tricycles. There are a total of 44 wheels.
Step-by-step solution:
Let's denote the number of bikes as B and the number of tricycles as T.
Each bike has 2 wheels, so the total number of wheels contributed by the bikes is 2B.
Each tricycle has 3 wheels, so the total number of wheels contributed by the tricycles is 3T.
Given that the total number of wheels is 44, we can form the equation: 2B + 3T = 44.
Since there are 20 bikes and tricycles in total, we have the equation: B + T = 20.
Solving the system of equations, we find that there are 12 bikes and 8 tricycles in the garage.
For which of the following displays of data is it not possible to find the mean?(Expert and Ace only please)
frequency table
line plot
stem-and-leaf plot
histogram
Answer:
The histogram
Step-by-step explanation:
It is difficult to find mean of a histogram
What is Histogram ?It is a chart that help in visualize the distribution of values in a dataset.
It is difficult to find mean just by looking at the data of the histogram
Hence , d) Histogram is the answer
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Can someone please help me with this question?! (geometry)
Answer:
see below
Step-by-step explanation:
The arc length (s) can be found in terms of angle (θ) and radius (r) as ...
s = rθ
Dividing by r gives ...
s/r = θ
Since the angles are the same for the two circles, the ratios of interest are ...
[tex]\dfrac{s_1}{r_1}=\dfrac{s_2}{r_2}=\theta [/tex]
Sally has completed 1/3 of her shift; Jerry has completed 5/6 of his shift; David has finished 1/2 of his shift; Mona has 7/8 of her shift remaining. Out of the four employees, Who has completed the most work time?
Jerry completed the most work time.
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Or, A number which is expressed as a quotient is called fraction.
It can be written as the form of p : q, which is equivalent to p / q.
Given that;
Sally has completed 1/3 of her shift.
Jerry has completed 5/6 of his shift.
David has finished 1/2 of his shift.
Mona has 7/8 of her shift remaining.
Now,
Since, Mona has 7/8 of her shift remaining.
Hence, The time for Mona = 1 - 7/8
= 1/8
We make all the denominator equal by taking LCM of 3, 6, 2, 8.
Thus, LCM of [3, 6, 2, 8] = 24
Hence, Sally has completed 8/24 of her shift.
Jerry has completed 20/24 of his shift.
David has finished 12/24 of his shift.
Mona has completed 3/24 of his shift.
Clearly, Jerry completed the most work time.
Thus, Jerry completed the most work time.
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HELP PLEASE!!
Which is greater, the total volume of three spheres, each of which has a diameter 3 in., the volume of one sphere that has a diameter 8 in., or the volume of a hemisphere with a diameter of 9 in.?
a) The volume of three spheres, each with a diameter of 3 inches, is greater.
b) The volume of one sphere with a diameter of 8 inches is greater.
c) The volume of the hemisphere with a diameter of 9 in. is greater.
d) The two volumes are the same.,
Answer:
Step-by-step explanation:
Answer:
Here is my answers for the practice that I have come across. It may be the new one. I also shortened it.
1. find the SA of a grape fruit with a c of 14cm.
62 cm^2
2. a sphere has a volume of 900 ci. find SA
451
3. a solid metal cube with an edge length of 9 in is melted and reshaped into a sphere. which is SA of sphere
391.7
4. the sphere below fits snugly inside a cube with 6 in edges what is the v of the space between the sphere and the cube
102.9
5. find the v in terms of pi of a sphere with a SA of 9 pi square feet
9/2 pi ft^3
6. which of the following is the greatest the total v of 3 sphere each of which a diameter of 5 in the v of one sphere that has a diameter 8 in or the v of a hemisphere with a diameter of 10 in
the v of 1 sphere with a diameter of 8 in is greatest
7. a sphere has center 0 0 0 and a radius of 5
0 -3 4
8. find v of figure the diameter of the base is 4 cm
46/3 pi cm^3
9. a sphere with a radius of 5 cm fits inside a box every face is tangent to the sphere
6 pi
10. tennis balls are sold in packs of 3 and come packaged in a plastic cylindrical container there is no space between
69 square inches
Step-by-step explanation:
How do you determine if two lines are perpendicular?
A right angle has an acute angle that measures 42°. what are th measures of the other angles.´?
NEED HELP ASAP!!!
What is the value of x?
/Users/mikaylee/Desktop/8104613-NG_IMC_SemB_09_UT_01.png
15.5 ft + 1.25 ft + 13.5 ft=
Which graph matches this situation
The limit as h approaches 0 of (e^(2+h)-e^2)/h = ?
The answer is e^2; please explain how to get that?
The cost of removing x percent of pollutants is expressed by the function , where C is in thousands of dollars. Which conclusion can be derived from this statement?
a)The cost of removing 40 percent of the pollutants is $120,000.
b)The cost of removing 80 percent of the pollutants is $960,000.
c)The vertical asymptote lies at x = 0.
d)The vertical asymptote lies at x = 240.
Just need an answer
There are a total of 18 chairs. If the ratio of the red chairs tobrown chairs is 2 to 4, how many of them are red?
Answer:Of the 18 chairs, 6 are red
Step-by-step explanation:
Given total no of chairs =18
Ratio of red chairs to brown chairs =2:4=[tex]\frac{2}{4}[/tex]
So there are 6(2+4) parts chair out of which 2 are red and 4 are brown
∴ 6 part equals 18 chairs
1 part equals [tex]\frac{18}{6}[/tex]
=3 chairs
Now 2 part equals 2×3=6
i.e. there are 6 red chairs
x y
2, 65
4, 74
6, 81
8, 96
10, 109
@directrix
Identify the equation of the least squares regression line that most
closely matches the data set.
yˆ = 0.17x − 13.2
yˆ = 5.5x + 52
yˆ = 3.5x − 6921.2
yˆ = −2.2x + 13.8
Which operation is NOT closed for polynomials?
A) (x3 + 8x − 5) (x4 + 6x + 2)
B) (x2 + 4x − 5)(8x2 + 3x − 6)
C) (6x2 + 2x − 3) + (x2 − 5x + 4)
D) −(2x2 + 2x − 5) − (x2 + 2x + 9)
Answer:
A
Step-by-step explanation:
You had a typo with A, and I think that is the answer as well, seeing as you typed all of your other answers correct, and none of them were labeled open by the first answerer, despite the typo.
1. The table shows the height, in centimeters, that a weight bouncing from a spring would achieve if there were no friction, for a given number of seconds.
2. How many seconds are required for the pendulum to swing from its position furthest to the right to its position furthest to the left?
3. How many degrees is the painted spot turning in 0.75 s?
Enter your answer in the box.
4. What is the average daily maximum temperature in March?
Round to the nearest tenth of a degree if needed.
Use 3.14 for π .
Enter your answer in the box
5. What is the greatest temperature the substance reached during the experiment?
Round to the nearest tenth of a degree if needed.
Use 3.14 for π .
Enter your answer in the box.
The result of rounding the whole number 72,341 to the nearest hundreds place is:
72,300.
72,000.
70,000.
72,340
The bar graph shows the z-score results of four employees for two different work weeks.
Which employee had the least earnings for Week 1?
Usan
Percy
Oberto
Michael
Chen has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Chen's Jumble has 4 classical songs,3 rock songs,and 2 rap songs on it.Chen is going to listen to 360 songs.What is the best prediction for the number of classical songs that Chen will listen to?
How do I solve this
I need some help
A student answers all 48 questions on a multiple-choice test by guessing. Each question has four possible answers, only one of which is correct. Find the probability that the student gets exactly 15 correct answers. Use the normal distribution to aproximate the binomial distribution.
I used BinomCdf(48,.25,15) and get 0.0767 but that isn't one of the choices. The choices are
0.7967
0.0606
0.0823
0.8577,
The probability that the student gets exactly 15 correct answers is 0.0823
How to determine the probability?The given parameters are:
Sample size, n = 48Correct answers, x = 15Probability of right an answer, p = 0.25 i.e. 1 of 4 options is correctStart by calculating the mean
[tex]\bar x = np[/tex]
[tex]\bar x = 48 * 0.25[/tex]
[tex]\bar x = 12[/tex]
Calculate the standard deviation
[tex]\sigma = \sqrt{np(1 -p)}[/tex]
[tex]\sigma = \sqrt{12 * (1 -0.25)}[/tex]
[tex]\sigma = 3[/tex]
To get exactly 15,we make use of the range 14.5 to 15.5.
So, we calculate the z scores at these values using:
[tex]z = \frac{x - \bar x}{\sigma}[/tex]
This gives
[tex]z = \frac{14.5 - 12}{3} = 0.83[/tex]
[tex]z = \frac{15.5 - 12}{3} = 1.17[/tex]
The probability is then calculated using
P(14.5 < x < 15.5) = p(0.83 < z < 1.17)
This gives
P(14.5 < x < 15.5) = 0.082269
Approximate
P(14.5 < x < 15.5) = 0.0823
Hence, the probability that the student gets exactly 15 correct answers is 0.0823
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How to solve for the third side of an isosceles triangle?
what is the range of y=3cosx-1?
a) -4 ≤ x ≤ 4
b) -4 ≤ x ≤ 2
c) -3 ≤ x ≤ 3
d) -2 ≤ x ≤ 0
Answer: The correct option is (b) [tex]-4\leq y\leq 2.[/tex]
Step-by-step explanation: We are given to select the correct range of the following function
[tex]y=3\cos x-1.[/tex]
We know that the range of the cosine function is from - 1 to 1.
That is,
[tex]-1\leq \cos x\leq 1\\\\\Rightarrow -(1)\times 3\leq 3\times \cos x\leq 3\times 1\\\\\Rightarrow -3\leq 3\cos x\leq 3\\\\\Rightarrow -3-1\leq 3\cos x-1\leq 3-1\\\\\Rightarrow -4\leq 3\cos x-1\leq 2\\\\\Rightarrow -4\leq y\leq 2.[/tex]
Thus, the range of the given function is [tex]-4\leq y\leq 2.[/tex]
Option (b) is CORRECT.
What do you consider to be the advantages of the numerical values? What do you consider to be the advantages of the visual representations? Which do you prefer working with, and why?
your primary jobs gross income is 3468.73/month deductions are fica (7.65%) federal tax witholding (11.5%) and state tax withholding (7.8%) how much are your ficed expenses if they are 36% of your relized income
Answer:
$912.21
Step-by-step explanation:
Your primary jobs gross income = $3468.73
All deductions 7.65% (fica) + 11.5% (federal) + 7.8% (state tax) = 26.95%
Income after deductions = 3468.73 - ( 26.95% × 3468.73 )
= 3468.73 - (0.2695 × 3468.73)
= 3468.73 - 934.82
= $2,533.91
Fixed expenses on your realized income = 36%
Fixed expenses = 36% × 2,533.91
= 0.36 × 2,533.91
= $912.2076 ≈ $912.21
Fixed expenses are $912.21
Given an exponential function for compounding interest, A(x) = P(1.04)x, what is the rate of change?
A. 0.04%
B. 1.04%
C. 104%
D. 4%
The given expression is
[tex] A(x) = P(1.04)^x [/tex]
Which can also be written as
[tex] A(x) = P(1+0.04)^x [/tex]
And the formula of compound interest is
[tex] A(x) = P(1+r)^x [/tex]
On comparing, we will get rate of change equals to 0.04 or 4 %.
So the correct option is the last option .
The following polynomials can be factored using the techniques of this lesson. x^2-36
the correct answer to that question would be true
Answer:
true
Step-by-step explanation:
A P E X