[tex]\boxed{\sf x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}}[/tex]
Explanation:
Given expression: (ab)x^2 + (b^2 - ac)x + (-bc) = 0
Here given:
a = abb = b² - acc = -bcApply quadratic formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \ ax^2 + bx + c = 0[/tex]
Insert values:
[tex]\sf x = \dfrac{-(b^2 - ac) \pm \sqrt{(b^2 -ac)^2-4(ab)(-bc)} }{2(ab)}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2-ac\right)^2+4abbc} }{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{b^4+2b^2ac+a^2c^2} }{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2+ac\right)^2} }{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac \pm( b^2+ac )}{2ab}[/tex]
[tex]\sf x = \dfrac{-b^2 + ac +( b^2+ac )}{2ab} \quad or \quad \dfrac{-b^2 + ac -( b^2+ac )}{2ab}[/tex]
[tex]\sf x = \dfrac{2ac}{2ab} \quad or \quad \dfrac{-2b^2}{2ab}[/tex]
[tex]\sf x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}[/tex]
Apply quadratic formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-(b^2 - ac) \pm \sqrt{(b^2 -ac)^2-4(ab)(-bc)} }{2(ab)}[/tex]
[tex]\\ \sf\Rrightarrow x= \dfrac{-b^2 + ac \pm \sqrt{\left(b^2-ac\right)^2+4abbc} }{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm \sqrt{b^4+2b^2ac+a^2c^2} }{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2+ac\right)^2} }{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm( b^2+ac )}{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac +( b^2+ac )}{2ab} \quad or \quad \dfrac{-b^2 + ac -( b^2+ac )}{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{2ac}{2ab} \quad or \quad \dfrac{-2b^2}{2ab}[/tex]
[tex]\\ \sf\Rrightarrow x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}[/tex]
each day you read 15 pages in your textbook. use the drop-down menu to choose the correct equation that represents the total number of pages you have read after any number of days.
Answer:
15x
Step-by-step explanation:
assum 1 day you read 15 pages then after X day you reads 15*X=15X
A B Find the solution to this equation. 32x = 8(4x + 2) - 16 All real numbers No solution 22 International Academy of Science. All Rights Reserved. A B Find the solution to this equation . 32x = 8 ( 4x + 2 ) - 16 All real numbers No solution
Answer: The answer for this problem is all real numbers or R.
Step-by-step explanation: In order to solve first you must deal with what's inside the parenthesis.
[tex]8(4x+2)=8*4x + 8*2= 32x +16[/tex]
Now that the parenthesis is out of the picture, now proceed to subtract the 16 that was outside of the parenthesis.
[tex]32x+16-16=32x[/tex]
You should then have an equation set up like so.
32x = 32x
Now you need to move one of the 32x's to the other side of the equation.
[tex]32x-32x=0[/tex]
Your final equation should be.
0 = 0
So, all real numbers (R) will work for this equation.
The time series pattern that reflects a gradual shift or movement to a relatively higher or lower level over a longer time period is called the _____.
Answer:
Trend pattern
At work, Brett must check and record the internal temperature of the freezer on an hourly basis. When working
properly, the temperature should remain constant over time. What word describes the slope of a line showing the
temperature of the freezer as a function of time in hours when the freezer is working properly?
positive
zero
negative
undefined
Explanation:
A slope of zero means there isn't any change in the y value. The graph isn't going upward, and it's not going downward either. We have a flat horizontal line. All horizontal lines have a slope of zero.
You can think of it like this
slope = rise/run = 0/1 = 0
rise = 0 means the y value isn't changing.
last Saturday, 1750 people attended an event at fairway gardens. the admission fee was $3.50 for children and $8.00 for adults. if the total money collected at the event was $9,860, how many children and how many adults attended the event?
Step-by-step explanation:
I don't know on my mommy that Is the answer
Answer:
There were 920 children and 830 adults.
Step-by-step explanation:
Let C be the number of children and A be the number of adults. Set up equations. Using the attendance of 1750 people, we can write:
c+a=1750
Using the total money collected of 9860, we can write:
3.50c+8.00a = 9860
Solve by substitution. Using (1), we solve for a to obtain (3): a=1750—c
Substutute (3) to (2) and solve for c:
3.50c + 8.00(1750 — c) = 9860
3.50e+ 14000 — 8.00c = 9860
—4.50e= —4140
c=920
Solve for a using (3):
a=1750 — 920
a=830
So, there were 920 children and 830 adults. (They better have been 6 ft apart)
Suppose you did a survey of male shoes size and the mean of that survey was size 10 with a standard deviation of 1.5. What is the Z-score of a size 8.5?
Answer:
-1
Step-by-step explanation:
From 10 to 8.5 is - 1.5
this is -1 S.D. below the mean
(8.5 - 10)/1.5 = -1
A. The two spinners shown below are being used in a probability experiment.
During each trial of the experiment, the arrows on the spinners are spun once, and the outcome is recorded. For example, an outcome of (2, 1) means that the arrow pointed to 2 on the first spinner and pointed to 1 on the second spinner.
B. What is the theoretical probability that, during each trial of the experiment, the result has at least one 4 on the spinners? Show your work or explain your answer.
Explain why the experimental probability from the results does not agree with the theoretical probability you found in part B.
The theoretical probability of at least one 4 on the spinners is 0.4375
(a) The number of different outcomesThe sections on the spinners are:
Spinner 1 = 4
Spinner 2 = 4
So, the number of different outcomes is:
Outcomes = 4 * 4
Outcomes = 16
Hence, the number of different outcomes is 16
(b) The theoretical probability of at least one 4 on the spinnersThe spin results that have at least one 4 are:
Results = {(4,1), (4,2), (4,3), (4,4), (1,4), (2,4), (3,4)}
The count of these results is 7.
So, the theoretical probability of at least one 4 on the spinners is:
P = 7/16
P = 0.4375
Hence, the theoretical probability of at least one 4 on the spinners is 0.4375
(c) Why the theoretical probability and the experimental probability are different?The theoretical probability and the experimental probability are different because:
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representations are - 6x + 15 < 10 - 5x , An open circle is at 5 and a bold line starts at 5 and is pointing to the right , Option C and E are the right answers.
What is Inequality ?Inequality are the mathematical statements where algebraic expressions are equated by another algebraic expression or a constant using an Inequality Operator.
The given statement is
–3(2x – 5) < 5(2 – x)
On simplifying can be written as
- 6x + 15 < 10 - 5x
- 6x + 15 < 10 - 5x
- 6x < -5 - 5x
- x < - 5
x > 5
An open circle is at 5 and a bold line starts at 5 and is pointing to the right .
Therefore Option C and E are the right answers.
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Emma is designing a playground for her neighborhood
park. Her drawing has a scale of 1 cm: 3 feet. The length
of her drawing is 15 cm. What will be the actual lenght of
the playground in feet?
Answer:
45 feet
Step-by-step explanation:
if 1 cm = 3 ft, we can scale up the drawing from there.
We are multiplying each cm by 3, and considering that length to be 3 feet.
If we had 2 cm, (multiply both by 3) we would have 6 feet.
So, if we had 15 cm, we also need to convert this scale length into actual length. We do this by multiplying
15 × 3 = 45
So, we know that the actual length of the playground in feet is 45 feet.
can someone please help and explain its due in a littleee
The slope of the given equation of the straight line is - 5/4.
We know that the direction of a line is defined by its slope. The slope is calculated by dividing the difference between the y-coordinates of two points on a line by the difference between their x-coordinates.
Here the equation of the line is
y = - (5/4)x - 1.
At x = 0, y = -(5/4) × 0 - 1 = -1
and at x = 4, y = -(5/4) × 4 - 1 = - 5 - 1 = -6
Now the slope = (-6 - (-1))/(4 - 0) = (-6 + 1)/4 = - 5/4
Therefore the slope of the given equation of the straight line is - 5/4.
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A container is an open cylinder whose height and radius are of equal length. The total surface area of the container is 300 cm³. Find the radius of the container.
Answer:
The radius of the container is approximately 4.89 cm
Step-by-step explanation:
GivenA container with:
r = hS = 300 cm²To findThe radius of the containerSolutionUse the equation for total surface area of cylinder:
S = 2πr² + 2πrh or S = 2πr(r + h)Since we have r = h and the value of S is known, let's solve this equation:
2πr(r + h) = 3002πr(r + r) = 3002πr(2r) = 3004πr² = 300πr² = 753.14r² = 75r² = 75/3.14r² = 23.89 (rounded)r = √23.89r = 4.89 cm (rounded)Solve this question, and I'll be extremely thankful (:
Thanks to whoever can do this for me!
-
Problem:
Using Scratch (or whatever programming language you are comfortable with), create code that would allow a user to input the legs of a right triangle and the output would be the length of the hypotenuse.
Create a program that finds the leg of a triangle given the hypotenuse and another leg and add an error message if the leg is longer than the hypotenuse.
Send a screenshot when you're done.
Answer:
it is in java and it is also can be done in BlueJ
Step-by-step explanation:
please mark me brainlist
Helpppppp pleaseeee shoe your work
2p-4p ≤ -2
-2p ≤ 2
[tex]\frac{-2p}{-2} \leq \frac{-2}{-2}[/tex] (Sign flips as both sides it is getting divided by NEGATIVE 2)
p≥1
Interval notation: [1, infinity)
Hope it helps!
Using two six-sided number cubes, each labeled with the numbers 1 through 6, event A is defined by rolling a sum greater than 8. Which of the following shows the
sample space of event A?
The sample space of event A would be {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}
What is a sample space for a random experiment?An experimenter does some random experiments which have a fixed set of outputs. That set of all possible outputs of that experiment is called sample space.
Using two six-sided number cubes, each labeled with the numbers 1 through 6.
Event A is defined by rolling a sum greater than 8.
Then the sample space of event A would be;
{(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}
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Answer:
{(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}
proof in pic
HELP WITH MY GHGGHH THAKSSS
Therefore, [tex]\frac{8}{7}= 1.14[/tex] cannot represent the probability of an event. So, option C is correct.
We need to identify which of the given option cannot represent the probability of an event.
What is probability?The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.
By simply dividing the favourable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favourable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
Now, [tex]\frac{1}{14} =0.0714, \frac{8}{7}= 1.14[/tex] and [tex]\frac{20}{21}=0.952[/tex].
Therefore, [tex]\frac{8}{7}= 1.14[/tex] cannot represent the probability of an event. So, option C is correct.
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HELP 100 POINTS!
Step 1- Select three sites to review:
Tombs of Buganda Kings, Aksum, &
Step 2- Create your public service announcement.
Site # 1- Name of Site, and Picture
Paragraph that includes how it relates to the African city or kingdom, and why the site is worth preserving.
Site # 2- Name of Site, and Picture
Paragraph that includes how it relates to the African city or kingdom, and why the site is worth preserving.
Site # 3- Name of Site, and Picture
Paragraph that includes how it relates to the African city or kingdom, and why the site is worth preserving.
The tomb are worth preserving as they are important to the legacy of the people.
What is a tomb?It should be noted that a tomb simply means a repository of the remains of the dead. The Tombs of Buganda Kings can be found in Uganda.
It's a royal tomb and represents the heart of the Baganda people.
In this case, the tomb are worth preserving as they are important to the legacy of the people.
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Is in between 2 number on the number line
Answer:
D
Step-by-step explanation:
Answer:
between 3 and 4
Step-by-step explanation:
3 squared is 9 and 4 squared is 16 so something in between 3 and 4 can be squared to equal 10 (since a square root is the opposite of squaring)
the average height of 10 pupils is 140cm if a new pupil joined the group the average height of 11 pupils become 148
cm find the height of new pupils
Answer:
228 cm
Step-by-step explanation:
the average is calculated as
average = [tex]\frac{sum}{count}[/tex] , then
[tex]\frac{sum}{10}[/tex] = 140 ( multiply both sides by 10 to clear the fraction )
sum = 1400
let the height of new pupil be x , then
[tex]\frac{sum+x}{11}[/tex] = 148 ( multiply both sides by 11 )
sum + x = 1628 , that is
1400 + x = 1628 ( subtract 1400 from both sides )
x = 228
height of new pupil is 228 cm
PLEASE HELP ME WITH THIS MATH PROBLEM!!
Step-by-step explanation:
in general we would need a probabilty table or a probability calculator service on the internet.
but in this case we know.
the man value is 64. and the standard deviation is 6.
so, one standard deviation +/- interval from the mean value is 70 and 58.
and the interval of 2 standard deviations from the mean value is 76 and 52.
and 64 and 76 are exactly the limits we are asked for.
so, remember the normal distribution rule :
68% are within 1 standard deviation.
95% are within 2 standard deviations.
99.7% are within 3 standard deviations.
and 50% are below (and also above) the mean value.
so, we know, 50% of the 350 (= 175) students scored below 64.
95% of the students scored between 76 and 52. as there are 5% left, half of these 5% (= 2.5%) scored even below 52).
so, 95% + 2.5% = 97.5% of the 350 (= 341.25) students scored below 76.
therefore, the number of students that scored between 64 and 76 is
341.25 - 175 = 166.25 ≈ 166
Find the area of a cylinder of radius 4 cm and height 5 cm
Answer:
226.19cm^2
Step-by-step explanation:
Total surface area of cylinder = 2πr(r + h).
Indira makes a box-and-whisker plot of her data. she finds that the distance from the minimum value to the first quartile is greater than the distance between the third quartile and the maximum value. which is most likely true?
The statement that is most likely true is , The mean is less than the median because the data is skewed to the left.
Option E is the correct answer.
What is a Box and Whisker Plot ?The method of representing the variation in a data set is called a Box and Whisker Plot .
A data distribution in which the data is skewed to the left
the mean is less than the median.
A data distribution in which the data is skewed to the right
the mean of the data is greater than the median.
It is given in the question that
The distance from the minimum value to the first quartile is greater than the distance between the third quartile and the maximum value.
this means data is skewed to the left,
Therefore, the statement that is most likely true is , The mean is less than the median because the data is skewed to the left.
Option E is the correct answer.
The complete question is
Indira makes a box-and-whisker plot of her data. She finds that the distance from the minimum value to the first
quartile is greater than the distance between the third quartile and the maximum value. Which is most likely true?
The mean is greater than the median because the data is skewed to the right.
The mean is greater than the median because the data is skewed to the left.
The mean is less than the median because the data is skewed to the right
The mean is less than the median because the data is skewed to the left.
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In one class, homework is worth 10% of the final grade, each of 3 projects is worth 20%, and a final exam is worth 30%.
(a) If a student has an 81 homework average and a 95 on the first project, what is the student's grade at this point?
(b) If the same student from part (a) gets a 72 on the second project and a 71 on the third project, what is the lowest grade the student can get on the final exam to get an 80 overall in the course?
(a) The grade at this point is_____
(Simplify your answer. Round to the nearest tenth as needed.)
(b) The lowest possible grade is____
(Simplify your answer. Round to the nearest integer as needed.)
a) At this point, the grade is 27.1
b) The lowest possible grade is 81
How to get the grades of the student?
a) At this point the student has 81 in homework and 95 on the first project.
Remember that the homework is worth 10% of the final grade, and each project is worth 20%, then at this point the final grade is:
F = 0.10*81 + 0.20*95 = 27.1
b) The student gets 72 on the second project and 71 on the third project, at this point the final grade is:
F = 27.1 + 0.20*72 + 0.20*71 = 55.7
Now the student wants to get a final grade of 80, then if we define x as the grade on the final exam (which is worth 30%) we must have that:
55.7 + 0.30*x = 80
Now we can solve this for x:
x = (80 - 55.7)/0.30 = 81
The lowest possible grade that he must get is 81.
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Use the scatter plot to answer the question. The points in the scatter plot generally increase upward to the right. © 2018 StrongMind. Created using GeoGebra.
Which type of linear correlation is present in the scatter plot?
positive
neutral
negative
strong
The positive linear correlation is present in the scatter plot option first “positive” is correct.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\[/tex]
[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have given a scatter plot in the picture.
As we can see in the scatter plot the dots are not so close that the correlation between x and y will be weak.
If we draw a line of best fit the slope of the line will be positive, the correlation will be positive.
Thus, the positive linear correlation is present in the scatter plot option first “positive” is correct.
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The function y
f(x) is graphed below. What is the average rate of change of the
function f(x) on the interval -3 ≤ x ≤-1?
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
-3/4m - 1/2 = 2 + 1/4m
2
3
4
5
Help i need it What is the product?
Answer:
[tex]12x^9+15x^8 -8x^6-10x^5[/tex]
Step-by-step explanation:
[tex]~~(x^4)(3x^3 -2)(4x^2 +5x)\\\\=(3x^7-2x^4)(4x^2 +5x)\\\\=12x^9+15x^8 -8x^6-10x^5[/tex]
Solve a^5=?
Please thank and thank you
Answer:
341.8801
Step-by-step explanation:
6,000+50+5 standard form
The expression 6000 + 50 + 5 in standard form is 6.055 * 10^3
How to express in standard form?The expression is given as:
6000 + 50 + 5
Evaluate the sum
6055
A number in standard form is represented as
a * 10^b
Where:
0 < a < 1
b is an integer
So, we have:
6055
Multiply by 1
6055 * 1
Express 1 as 1000/1000
6055 * 1000/1000
This gives
6.055 * 1000
Express 1000 as 10^3
6.055 * 10^3
Hence, 6000 + 50 + 5 in standard form is 6.055 * 10^3
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Is LMN OPQ If so name the congruence postulate that applies
The triangle is congruent by SSS congruency because the corresponding two sides of two triangles are of the same measurement Hence, Option D is correct.
What is SSS congruency?If the corresponding two sides of two triangles are of the same measurement, then the considered pair of triangles are congruent.
We have given two triangles that are congruent to each other;
LMN is congruent to OPQ
Given;
LM = OP
MN = PQ
LN = OQ
Thus, the triangle is congruent by SSS congruency because the corresponding two sides of two triangles are of the same measurement
Hence, Option D is correct.
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can someone please help mee
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:Domain = [-3, 1)[/tex]
[tex]\qquad \tt \rightarrow \:Range = [-5 , 4][/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Domain = All possible values of x for which f(x) is defined
[ generally the extension of function in x - direction ]
Range = All possible values of f(x)
[ generally the extension of function in y - direction ]
[tex] \large\textsf{For the given graph : } [/tex]
[tex]\qquad \tt \rightarrow \: domain = [ -3, 1)[/tex]
[tex]\qquad \tt \rightarrow \: range= [ -5,4][/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
