What is the solution of the equation (x – 5)2 + 3(x – 5) + 9 = 0? Use u substitution and the quadratic formula to solve.
Answers
x² - 10x + 25 + 3x - 15 + 9 = 0
x² - 7x - 16 = 0
[tex]x = \frac{7 + \sqrt{(-7)^2-4(1)(-16)} }{2} [/tex] or [tex]x = \frac{7 - \sqrt{(-7)^2-4(1)(-16)} }{2} [/tex]
[tex] x = \frac{7 + 3i \sqrt{3} }{2} [/tex] or [tex] x = \frac{7 - 3i \sqrt{3} }{2} [/tex]
(Answer B)
Answer: [tex]x=\frac{7\pm 3i\sqrt{3}}{2}[/tex]
Explanation:
Since, given quadratic function, [tex](x-5)^2 + 3(x-5) + 9 = 0[/tex] -----(1)
let us consider,[tex]x-5=p[/tex] -----(2)
Put this value in equation (1),
We get, [tex]p^2+3 p+9=0[/tex], which is also a quadratic equation.
Since, quadratic formula for finding the root of quadratic equation of type [tex]ax^2+bx+c=0[/tex] is, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}} {2a}[/tex]
Here, a=1, b=3 and c=9, so, [tex]p=\frac{-3\pm\sqrt{3^2-4\times1 \times9}} {2\times1}[/tex]
Thus, [tex]p=\frac{-3\pm3\sqrt{-3}} {2}[/tex] ⇒ [tex]p=\frac{-3\pm3i\sqrt{3}} {2}[/tex] (because √-1=i)
Now, from equation(2) [tex]x-5=\frac{-3\pm3i\sqrt{3}} {2}[/tex]
⇒[tex]x=\frac{-3\pm3i\sqrt{3}} {2}+5=\frac{7\pm 3i\sqrt{3}}{2}[/tex]
⇒[tex]x=\frac{7\pm 3i\sqrt{3}}{2}[/tex]
Related Questions
Algebra 2 help?
5. A construction explosion has an intensity I of 1.25 x 10–4 W/m2. Find the loudness of the sound in decibels if W/m2. Round to the nearest tenth. (1 point)
81 decibels
161 decibels
82.2 decibels
12.5 decibels
The example question in the textbook is totally different so I'm not sure how to do this. I tried to make the equation and then got confused. An explanation would be great! Thanks
Answers
To solve this, we will use the formula : dB = 10 x log (Isig/Iref)
terms will be:dB= decibels,
Isig = signal's intensity
Iref= softest sound's intensity which is 10^-12.
So the solutions is,dB = 10 x log (1.25 x 10–4 / 10^-12 )
= 80.97 decibels
=81 decibels
Answer:
1. B) logb(q^2t^8)
2. D) None of these (it is actually log (x^4/(x+2)^6) :D)
3. B) log5(7)+5log5(a)
4. C) 6.209
5. A) 81 decibels
Step-by-step explanation:
trust me bro
The hypotenuse of a 45°-45°-90° triangle measures 7√2 units.
What is the length of one leg of the triangle?
A. 7 units
B. 7√2 units
C. 14 units
D. 14√2 units
Answers
Answer:
Option A is correct.
Step-by-step explanation:
Given:
Angle of the right angles triangle are 45° , 45°, 90°
Length of the Hypotenuse = 7√2 units.
To find: Length of the one leg of the triangle.
Since two angles of the triangles are equal.
⇒ Opposite sides to equal angles are also equal.
We have Isosceles right angled triangle.
⇒ both legs are equal.
Let x be the length of the leg
using Pythagoras theorem,
(7√2)² = x² + x²
2x² = 49 × 2
x² = 49
x = ±7
Length cannot be negative so, x = 7
Therefore, Option A is correct.
which of the following expressions is equal to the height, h, of this triangle?
Answers
[tex]25 \cos(56) [/tex]
The Thrill amusement park charges an entry fee of $40 and an additional $5 per ride, x. The Splash water park charges an entry fee of $60 and an additional $3 per ride, x. Based on this information, which system of equations could be used to determine the solution where the cost per ride of the two amusement parks, y, is the same?
Answers
The costs per ride for Thrill and Splash amusement parks can be represented by the equations y = 40 + 5x and y = 60 + 3x respectively. Equating these will give us the number of rides where the costs at both parks will be the same.
Explanation:The cost of visiting each park can be represented as a linear equation. For Thrill amusement park it can be written as y = 40 + 5x, where y is the total cost, 40 is the entry fee and 5x represents the cumulative cost of the rides, with x being the number of rides. For Splash Water Park, the equation is y = 60 + 3x, where 60 is the entry fee and 3x is the cost of the individual rides. To find out when the costs per ride at the two parks will be the same, we solve the system of equations by setting the two equations equal to each other: 40 + 5x = 60 + 3x.
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You read that the median equals 12 on a test, what percentage of the participants had scores higher than 12
Answers
The median cuts the data into two halves, since the median is the center-most value. The scores higher than 12 make up half (50%) of the data while scores less than 12 make up the other 50%
Clare's teacher has a box of 180 stickers for a group of students to share equally. Does each student get more stickers if there are 6 students or if there are 9 students
Answers
what transformation changes the graph of y= x^3-x-6 into the graph of y=x^3-x?
Answers
Determine if the graph of r = 4cos 5θ is symmetric about the x-axis, the y-axis, or the origin.
Answers
Answer:
y-axisStep-by-step explanation:
The function graph is symmetric about
- the y-axis when it is an even function
- the origin when it is an odd function.
A symmetrical graph about the x-axis is not a function graph.
f(x) is an even if and only if f(-x) = f(x).
f(x) is an odd if and only if f(-x) = -f(x).
We have the function r(θ) = 4cos(5θ)
(olny symmetry about the y-axis or about the origin)
Check r(-θ):
r(-θ) = 4cos(5(-θ)) = 4cos(-5θ) = 4cos(5θ)
used cos(-x) = cos x
We have r(-θ) = r(θ). Therefore the graph of r(θ) is symmetric about the y-axis.
Answer:
x-axis
Step-by-step explanation:
if r%28theta%29+=+r%28-theta%29.
Since 4cos%285%2Atheta%29+=+4cos%28-5%2Atheta%29, the graph is symmetric wrt the x-axis.
The graph is symmetric wrt the y-axis if r%28theta%29+=+r%28pi-theta%29.
Since 4cos%285%2Atheta%29+%3C%3E+4cos%285%2A%28pi+-+theta%29%29+=+-4cos%285%2Atheta%29+, the graph is not symmetric wrt the y-axis.
The graph is symmetric wrt the y-axis if r%28theta%29+=+r%28pi%2Btheta%29.
Since 4cos%285%2Atheta%29+%3C%3E+4cos%285%2A%28pi+%2B+theta%29%29+=+-4cos%285%2Atheta%29+, the graph is not symmetric wrt the origin.
Factor the polynomial completely. 4x3 – 12x2 + 7x – 21 4x2(x – 3) + 7(x – 3) Which is the completely factored polynomial? 4x2(x + 4) 3x2(x – 3) (4x2 – 7)(x + 3) (4x2 + 7)(x – 3)
Answers
factor: 4x²(x-3)+7(x-3)
factor again: (x-3)(4x²+7)
The correct answer for this problem would be D. (4x^2 + 7)(x – 3) .
Hope this helps and clears up any confusion!
The Hamden board of education wants to know how the community feels about building a new media center for the middle school. They called every tenth person on the registration list of 7,300 voters until they had called a total of 40 voters. Which of the following are true of the sample of 40 voters? Check all that apply.
The sample is not randomly chosen.
The sample should be larger to give more reliable information.
The sample size is too large to make inferences.
The sample size is too small to represent the population.
The sample size is too small and will show larger variation.
The sample is invalid because it randomly chooses voters.
The sample size is too small and can lead to false inferences.
Answers
The sample is not randomly chosen (FALSE)
Given that the statement doesn't tell us anything about the way they choose the sample, it is reasonable to conclude that this is a randomly chosen. They called every tenth person on the registration list until the number of people was 40.
The sample should be larger to give more reliable information (TRUE)
You did not have to use mathematics to determine that you would need more information to get a conclusion. You must increase the sample, that is, the sample must be larger to give a reliable information.
The sample size is too large to make inferences (False)
This is explained in the previous item. If the sample should be lager is because the size is not too large.
The sample size is too small to represent the population (TRUE
This is true because 40 voters represent barely 0.5% of the entire list. This list has 7300 voters, so getting the conclusion from this sample doesn't provide with a strong conclusion.
The sample size is too small and will show larger variation. (FALSE)
Although the sample size is too small, the sample size not necessarily will show variation. In fact, it is possible that it does not show any variation and most of the people feel well about building a new media center for the middle school but it doesn't mean that the whole community does.
The sample is invalid because it randomly chooses voters. (FALSE)
It is false because in probability studies the sample is chosen randomly, so you get conclusions about the whole population always taking samples that represent the population as a whole.
The sample size is too small and can lead to false inferences (TRUE)
You can get false conclusions given that the sample size is too small. It's important to note that the sample size supports the conclusion of the study, so the sample must increase to have a reliable study.
The sampling method used by the Hamden board of education was systematic, not random, and the sample size of 40 voters out of a population of 7,300 is too small to produce reliable conclusions regarding the community's opinion about building a new media center.
Explanation:The quality of conclusions drawn from opinion polls largely depends on the methods used to choose a sample and the sample size. When the Hamden board of education sampled every tenth person from the registration list of 7,300 voters to reach 40 voters, they applied a systematic sampling method, as opposed to a truly random sample. While systematic sampling can be used as an approximation of random sampling, this method still poses a risk of introducing bias if there are hidden patterns in the voter registration list.
The sample size is indeed critical for the reliability of the poll. In this case, surveying only 40 voters out of 7,300 is too small to capture the diverse opinions of the entire voter population, which may lead to false inferences and less confidence in the results. For public opinion polls, especially on matters like building a new media center, a larger sample would provide more reliable information and reduce the potential variation that can arise from a smaller sample. Industry standards suggest varying sizes that can balance the accuracy and cost-effectiveness, often ranging from 500 to 2,500 respondents or more depending on the desired level of accuracy.
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A small fishing boat's outboard motor requires a mixture of gasoline and oil for fuel. The mixture called for in the owner's manual is 1 gallon of oil for every 50 gallons of gas. If the boat's gas tank holds approximately 6 gallons of gas, approximately how much oil must be added to the gasoline?
3 ounces
9 ounces
15 ounces
24 ounces
Answers
Determine, for vectors u = i + 2j − k, v = −i + j + k, w = i + k (a) a unit vector in the direction u + 2v − 3w
Answers
v=-i+j+k
w=i+k
thus:
u+2v-3w
i+2j-k+2(-i+j+k)-3(i+k)
=i+2j-k-2i+2j+2k-3i-3k
=i-2i-3i+2j+2j-k+2k-3k
=-4i+4j-2k
The quality control manager of a peanut butter manufacturing plant want to ensure the quality of the peanut butter in the jars coming down the assembly line.describe a representative sampling method she could use?
Answers
Final answer:
The quality control manager can use a representative sampling method to test jars of peanut butter for quality, with tests such as total plate count and adherence to quality control protocols and good measurement practices for reliable results.
Explanation:
A quality control manager at a peanut butter manufacturing plant can ensure the quality of peanut butter jars using a representative sampling method. This involves selecting jars at regular intervals from the assembly line, and then conducting tests such as total plate count to measure potential bacterial contamination. For accurate quality control, the process should follow good measurement practices and a standardized quality control protocol that includes recording and analyzing the data and evaluating any deviations from set specifications.
The personnel responsible can reject any sample or batch that does not meet the required standards. For continuous quality assurance, statistical process control methods like mean, standard deviation, and coefficient of variation can be utilized to monitor ongoing production. Furthermore, post-production specifications will determine whether to release or reject the final product. Appropriate documentation and adherence to standard operations procedures (SOPs) are crucial throughout the process, maintaining a systematic approach to product quality.
help please asap! BRAINLIESTTTTT
2 QUESTIONS!
Answers
2nd one Is the vertex is the highest point and would the the max amount of larvae produced. SO this answer is B
In the xy-plane, if (-1, 0) is a solution to the system of inequalities y < x + c and y < -x - d, which of the following must be true about c and d? (10 POINTS + BRAINLIEST ANSWER!!)
A. c = d
B. c = -d
C. c < d
D. d < c
Answers
Final answer:
By substituting the point (-1, 0) into the inequalities, we find that c must be greater than 1, and d must be less than 1, which means the correct answer is D. d < c.
Explanation:
We are given a point (-1, 0) which is a solution to both inequalities y < x + c and y < -x - d. To find the relationship between c and d, let's plug in the x and y values of the point into each inequality.
For y < x + c, with x = -1 and y = 0, we get:
0 < -1 + c
c > 1. (1)
For y < -x - d, with x = -1 and y = 0, we get:
0 < 1 - d
d < 1. (2)
Comparing (1) and (2), we see that c must be greater than 1 and d must be less than 1. Thus, the correct answer is D. d < c.
EASY 5POINT MATH QUESTION PLEASE SOLVE
use the relationship between the angles in the figure to answer the question
which equation can be used by find the value of x?
drag and drop the equation into the box
Answers
Answer: x = 180 - (31 + 40)
Hope this helps!
~VERNEX
Graph the function f(x)= square root over x. Which table of values contains points that lie on the graph of the function?
Answers
Answer:
see attached
Step-by-step explanation:
The square root of a negative number is undefined, so the applicable table is the one shown below.
Answer:
Table 3 represents the correct points that lie on the graph of the function.
Step-by-step explanation:
We are given the function:
[tex]f(x) = \sqrt{x}[/tex]
We have to plot the given function.
The attached image shows the graph for the given function.
Putting values for x in the function we get:
[tex]f(x) = \sqrt{x}\\f(-1) = \sqrt{-1}[/tex]
which is undefined.
[tex]f(0) = \sqrt{0} = 0\\f(1) = \sqrt{1} = 1[/tex]
Table 3 represents the correct points that lie on the graph of the function.
Which graph shows a line that is perpendicular to line AB?
Answers
Which rectangle if translated 12 units down and 7 units right will result in rectangle E?
A) Rectangle A
B) Rectangle B
C) Rectangle C
D) Rectangle D
Answers
If we looked at rectangle 'E' and moved it to the left by 7 units (every unit = 1 square on the grid), we would arrive at a point. From then, we can move upwards 12 units and arrive at rectangle 'D'.
Answer:
option D
Step-by-step explanation:
translated 12 units down and 7 units right
(x,y)-> (x+7, y-12)
Lets pick a point on Rectangle A and apply the translation
(-11,4) -> (-11+7, 4-12) ->(-4, -8) That is not in our Rectangle E
Lets pick a point on Rectangle B and apply the translation
(-7,1) -> (-7+7, 1-12) ->(0, -11) That is not in our Rectangle E
Lets pick a point on Rectangle C and apply the translation
(-5,5) -> (-5+7, 5-12) ->(2, -7) That is not in our Rectangle E
Lets pick a point on Rectangle D and apply the translation
(-3,1) -> (-3+7, 1-12) ->(4, -11) That is in our Rectangle E
So option D is correct
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Find the length of the hypotenuse of an isosceles right triangle whose legs are 1 unit in length.
Answers
[tex] {x}^{2} = {1}^{2} + {1}^{2} \\ {x}^{2} = 1 + 1 \\ {x}^{2} = 2 \\ x = \sqrt{2} = 1.41[/tex]
Answer:
The length of the hypotenuse of the isosceles right triangle with leg of length unit is:
√2 units.
Step-by-step explanation:
Let a and b denote the leg of a right triangle and c denote the hypotenuse of the right triangle.
Now we apply the Pythagorean Theorem as:
[tex]c^2=a^2+b^2[/tex]
Now as triangle is isosceles.
Hence, a=b=1 unit
[tex]c^2=1^2+1^2\\\\c^2=2\\\\c=\sqrt{2}[/tex]
Hence, the length of the hypotenuse is:
√2 units.
8.42 x 10^3, Between which of the following pairs of numbers does the above number lie? A. .0083 and .0084 B. .0084 and .0085 C. 8300 and 8400 D. 8400 and 8500
Answers
Use PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction)
Solve exponent first
8.42 x 10^3
8.42 x 1000
Solve the rest
8.42 x 1000
8420
8420 is between
D.) 8400 and 8500
The number 8.42 x 10³ lies in between pairs of numbers 8400 and 8500.
Option D is correct.
What is PEDMAS?The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations.
PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.
We have the number 8.42 x 10³.
Now, expanding the exponents we get
= 8.42 x 10³
= 8.42 x 1000
= 84.2 x 100
= 842 x 10
= 8420
Thus, the values lie between 8400 and 8500.
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20 POINTS!! EASY QUESTION! WILL MARK BRAINLIEST!! READ THE INFO! THEN FILL IN THE BLANKS!
The cost for a single class session for each dance class is below.
Clodagh’s Dance = $6.00
New Steps = $7.50
Stepping High = $6.50
The class hours are below.
Clodagh’s Dance = 3:00pm - 4:00pm
New Steps = 4:00pm - 5:30pm
Stepping High = 9:00am - 10:15am
How would these answers change if you were to write the unit rate in cost per hour?
Fill in the blanks!
Dance Classes | Total Hours for Each Payment | Cost Per Hour
| |
Clodagh’s Dance | $6.00 | $6.00
New Steps | $7.50 | _____
Stepping High | $6.50 | _____
Answers
rate=(Type of session)/(time taken)
the rate for:
a]
Clodagh's Dance
Payment=$6.00
Time=1 hours
rate=6/1=6 dollars/hours
b]
New steps
payment=$7.50
Time =1.5 hours
rate=7.5/1.5=5 dollars/hour
c]
Stepping high
Payment=$6.50
Time=1.25 hours
rate=6.5/1.25=5.2 dollars/ hours
For every pound a company spends on advertising, it spends £0.26 on its website. Express the amount spent on advertising to the amount spent on its website as a ratio in its simplest form.
Answers
If we use the values in the problem, we have a ratio of 1:0.26. The problem is that we have a decimal value and we should use whole numbers.
Start by multiplying each value by 100 to eliminate the decimal.
We have 100:26.
Now, each value contains a factor of 2. So divide by 2 and we get 50:13.
Answer:
50:13
Step-by-step explanation:
Evaluate the geometric series
Answers
2^(1-1) + 2^(2-1) + 2^(3-1) + 2^(4-1) + 2^(5-1) + 2^(6-1) + 2^(7-1) + 2^(8-1)
= 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255
Can you please help me with this that’ll you so much
Answers
=1/3 + 1/8 + 5/12
need a common denominator (24)
=8/24 + 3/24 + 10/24
=21/24
simplify by 3
=7/8 like basketball, football & soccer
7/8 is the total for basketball, soccer and football. If 8/8 represents the whole class, then subtract 7/8 from 8/8 to find the number who like baseball.
=8/8 - 7/8
=1/8 of the remainder likes baseball
ANSWER: 1/8 of the students like baseball
Hope this helps! :)
what is the answer to 2+2*8
Answers
multiplication is first (in this case) and then addition
2 x 8 = 16
16 + 2 = 18
18 is your answer
hope this helps
Terry just bought a used car with only 28,500 miles on it and it cost $8,200. Every year Terry expects to put another 14,000 miles on the car. Unfortunately, the car’s value will depreciate by 15% per year. How much will the car be worth when it has 100,000 miles on it? Explain your work.
Answers
.. $8200*0.43605 ≈ $3706
_____
The difference between 100k miles and 28.5k miles is 71.5k miles. It is "used up" at the rate of 14k miles per year, so the time it takes to do that is 71.5/14 ≈ 5.1 years.
Each year the car depreciates 15%. That is, its value is multiplied by 1 -15% = 0.85. In 5.1 years, the original value will be multiplied by 0.85^5.1. (Remember, exponentiation is repeated multiplication.)
How can you use factoring to solve quadratic equations in standard form?
Answers
Solve 2x^2 - 3x - 20 = 0
multiply the first and last numbers:- 2 * -20 = -40
Note that -40 = -8 * 5 and -8 + 5 = -3 ( the 'middle' number in the standard form)
so we write:-
2x^2 - 8x + 5x - 20 = 0
2x(x - 4) + 5(x - 4) = 0
(2x + 5)(x - 4) = 0
giving 2x + 5 = 0 or x - 4 = 0
giving the roots x = -2.5 and x = 4
How many ways can 6 basketball players be listed in order in a program?
Answers
How many rays intersect at point O
1. 5
2. 4
3. 6
4. 3
Answers
We have then that the lines that contain this point are:
EC
AD
BO
We note that three lines contain point O.
Therefore, three lines intersect at the same point.
Answer:
4. 3