The real or imaginary solutions of 2x² + 3 = 4x by factoring is x1 = (2 - √2) / 2 and x2 = (2 + √2) / 2
Equation
2x² + 3 = 4x
Rearrange to form a quadratic equation2x² + 3 - 4x = 0
2x² - 4x + 3 = 0
Factoring to find real or imaginary solution∆ = (-4)² - (4 × 2 × 3)
= 16 - 24
∆ = 8
√∆ = √8
= 2√2
x1 = -(-4) - 2√2 / (2 × 2)
or
x2 = -(-4) + 2√2 / (2 × 2)
x1 = 4 - 2√2 / 4
or
x2 = 4 + 2√2 / 4
x1 = (2 - √2) / 2
or
x2 = (2 + √2) / 2
Therefore, the real or imaginary solutions of 2x² + 3 = 4x by factoring is x1 = (2 - √2) / 2 and x2 = (2 + √2) / 2
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Eric rented a truck for one day. There was a base fee of 19.95 and there was an additional charge of 97 cents for each mile driven. Eric had to pay 190.67 when he returned to the truck. For how many miles did he drive the truck?
Answer: 176 miles
Step-by-step explanation:
m=mile.
97 cents=
97/100 dollars=$0.97
190.67=19.95+0.97m
170.72=0.97m
m=176 miles
Find the amount in jay's account after 6 years when the principal deposit was $285 and is compounded annually with a rate of 1.9%.
The amount in Jay's account after 6 years is $357.20.
Given that, the principal=$285, time period=6 years and rate of interest =1.9%.
We need to find the amount in Jay's account after 6 years.
How to calculate the compound interest?Compound interest, or 'interest on interest', is calculated using the compound interest formula. The formula for compound interest is [tex]A=P(1+\frac{r}{100} )^{nt}[/tex], where P is the principal balance, r is the interest rate, n is the number of times interest is compounded per time period and t is the number of time periods.
Now, [tex]A=285(1+\frac{1.9}{100} )^{6}=285(1.019)^{6}[/tex]
=285×1.1195=$357.20
Therefore, the amount in Jay's account after 6 years is $357.20.
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The answer to 5√12 × √7, given in its simplest form, is t√√u, where t and u are integers.
Calculate the values of t and u.
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Exact Form: 10√21 where t = 10 and u =21
E. -2(a-8)how do you do this question?
Answer: -2a + 16
Step-by-step explanation:
You must do the distributive property. Since "a-8" is in the parenthesis and -2 is outside the parenthesis, you must multiply -2 by (a-8). -2 multiplied by a will equal 2a since you don't know what variable a equals. Next, you multiply -2 and -8 which would equal positive 16. The reason why it is positive is because 2 negative numbers multiplied or divided would equal a positive number. Thus, the answer is -2a + 16.
14
Starting with the number 0 and counting left
to right,
0
35
5
40
10
45
Date:
15 20 25 30
50
55
60
65
write the first number
write the fourth number
write the ninth number
Answer:
first number: 0
fourth number: 15
ninth number: 40
Help!!!
6 divided by 2(1+2)
Answer:
9
Step-by-step explanation:
6 / 2(1+2)
6 / 2 (3)
6 / 2 * 3
3 * 3
9
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What is the solution to this equation?
5x+15+ 2x = 24 + 4x
O A. x = 13
OB. x = 3
O C. x=39/11
O D. x =9/11
Answer:
X=3
Step-by-step explanation:
Remember to get all your variables on one side by doing the "Reverse function" etc...
Once youve got your variables on one side (and only 1 is remaining) you should get rid of whats BESIDE the variable by dividing it by *whatever it is thats beside the variable!* AND REMEMBER TO DO THIS ON BOTH SIDES OF THE EQUATION SO THAT THEYRE EQUAL!!
Arrange the students in order from shortest to tallest. kim 56.03 alexa 56.3 roy 56.14 tom 57.1
Arrangement of students from shortest to tallest is
Kim 56.03 < Roy 56.14 < Alexa 56.3 < Tom 57.1.
As given in the question,
Number of students = 4
Height of the students
Kim = 56.03 units
Alexa = 56.3 units
Roy = 56.14 units
Tom = 57.1 units
Arrange the students from shortest to tallest
56.03 < 56.14 < 56.3 < 57.1
Kim < Roy < Alexa < Tom
Therefore, arrangement of students from shortest to tallest is
Kim 56.03 < Roy 56.14 < Alexa 56.3 < Tom 57.1.
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How many significant digits are in the number 1.00460? select one: a. 6 b. 3 c. 5 d. 4
There are 6 significant digits in the number 1.00460.
What are digits?In mathematics, digits are the single symbols used to represent numbers. For example, in the number 89, the digits 8 and 9 are both two digits. As a result, numerals such as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 are forms of digits that are used to represent a combination of numbers and perform arithmetic operations in our daily lives.We use ten digits to create all numerals. A numeral is a written number. These are the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.Therefore, there are 6 significant digits in the number 1.00460.
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How many gallons are in a 2 liter bottle of soda?
Answer:
1/2 gallon.
Step-by-step explanation:
1 liter = 1/4 gallon
Basing the measurement off of this info, we can determine that 2 liters is equal to a half-gallon because it is 2 quarters, which simplifies to one-half.
write 26/50 as a decimal fraction
Answer:
13/25
Step-by-step explanation:
hope this helps :)
In consecutive odd integers, three times the largest integer is fifteen less than two-thirds the smallest integer. find both integers. someone help please
Value of both the integers as three times the largest consecutive integer is 15 less than 2/3 the smallest one is -7, -9.
As given,
Let x, x +2 be two consecutive odd integers
Three times largest integer=3( x+2)
15 less than 2/3 smallest integer=(2/3)x -15
Equation :
3(x+2)=(2/ 3)x -15
⇒ 3x +6=(2x -45)/3
⇒ 9x-2x= -18 -45
⇒ 7x=-63
⇒ x =-9
and x+2 =-7
Therefore, value of both the integers as three times the largest consecutive integer is 15 less than the 2/3 the smallest one is -7, -9.
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A hospital stores one type of medicine in 222-decagram containers. Based on the information given in the box above, how many 111-milligram doses are there in one 222-decagram container?
Answer:
2,220,000 mlg
Step-by-step explanation:
This question can be solved by a simple conversion calculation. Thankfully we're converting between two units of measurement with the same base!
So First, let's convert 222 decagrams to grams, and then convert grams to milligrams.
The conversion rates we need are:
1 decagram = 10 grams
1 gram = 1000 milligrams
Now for the math!
[tex]222 dg *\frac{10g}{1dg} =2220g\\then...2220g * \frac{1000mlg}/1g\\\\\\=2,220,000 mlg[/tex]
a=(3,-4), b=(8,-1) y c=(-2,5)
V=3a-2b+c
Answer:
5729627829263#wyyeiwyuwityeioe
If one wanted to find the probability of ten customer arrivals in an hour at a service station, one would generally use the _____ probability distribution.
If one wanted to find the probability of ten customer arrivals in an hour at a service station, one would generally use the Poisson probability distribution.
How do you find the probability of success for each trial?
Each trial has a head (success) and a tail (failure) outcome (failure). Each trial's chances of success are p = 1/2 and its chances of failure are q = 1 1/2 = 1/2. The variable X, which counts the number of successes across 12 trials, is the one that interests us. This is an illustration of a 12-trial Bernoulli experiment.What is the probability formula?
Probability is equal to the number of favorable outcomes (Total number of outcomes) P = n (E) / n (S) E is the event, P is the probability, and S is the sample area.
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a²-7a²b² + b² factor
Verify the identity.
secx-secxsin^2x= cos x
The identity is verified, yes. secx-secxsin^2x=cos x
What is an identity?
An identity in mathematics is an equality connecting two mathematical expressions, A and B, such that both expressions provide the same result for any value of the variables falling within a given range of validity.
An identity is an equation that, regardless of the values used, is always true. 2 x + 3 x = 5 x is an identity because, according to the preceding equation, 2 x + 3 x will always equal 1 regardless of the value;
According to given information;
secx = 1/cosx
cos²x+sin²x= 1
**sin²x = 1-cos²x
by (*) :
secx - secx sin²x=(1/cosx) -(1/cosx) sin²x
= (1/cosx) (1- sin²x)....factory :(1/cosx)
by(**)
sec x-sec x sin²x = (1/cos x)cos²x
sec x-sec x sin²x = cos x
( simplify by : cos x)
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Use the diagram showing points P and Q. P(-2, 1) Q(2, 1)
Determine which point is the remaining vertex of a triangle with an area of 4 square units.
R(2, 0)
S(-2,-1)
T(-1, 0)
U(2,-2)
please help !! include explanation
A car travels 100 meters in 5 seconds. What is the speed of the car?
speed = distance over time; 1 mile = 1609 meters
Answer:
20 m/s
Step-by-step explanation:
speed = 100m /5s = 20 m/s
= 72 km/hr
= 72 km / hr * 1 mile / 1.609 km = 44.7 mph
Diego worked the SAME number of hours for FIVE days at his job at the cheese factory plus an extra 7 hours on Saturday. He worked a total 52-hours last week.
Using H as a variable for the number of hours he worked each normal day, model (create an equation) for Diego’s work week.
How many hours did he work each day for his normal work week?
The total hours worked on each day of his normal work week is 7.5 hours.
How many hours did Diego work on each normal day ?The total hours worked is a function of the total hours worked during the week and the hours worked on Saturday.
The equation that represents the total hours that Diego worked is:
Total hours = total hours worked during the five days + hours worked on Saturday
52 = (5 X H) + 7 + H
52 = 5H + 7 + H
In order to determine the value of H, take the following steps:
Combine similar terms together: 52 - 7 = 5H + H
Add similar terms together: 45 = 6h
Divide both sides of the equation by 6 : H = 45 /6
H = 7.5 hours
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About 70% of people are right-handed. Of 352students in a school. Which is a reasonable number of right-handed students ?
Answer: 246 right-handed students
Step-by-step explanation:
70%=
70/100=0.7
352*0.7=246.4
246.4=246 right-handed students ==> I rounded the answer since you can have 246 students and an additional 0.4 students. You can't have part of a student.
A model train is on a track 100 cm from its starting point. turning a switch displaces the train either forward or backward 25 cm along the track depending on which way the switch is turned. which equation models the position of the train along the track after you turn the switch?
The equation which models the position of the train along the track can be given as |x − 100| = 25.
One-variable linear equation is defined as the equation which can be written in the form of ax+b = 0, where a and b are two integers, and x is a variable. One-variable linear equation has only one solution. For example, the linear equation 4x+2=14 only has one variable and only one solution.
The location of the train is given by the value of x. Therefore, if x was equal to the value 85, it would be at the position 85 on the number line.
The distance between x and distance of track that is 100 is given as |x-100|. The distance can never be negative, so we take the absolute value. Because the switch is switched after the train has traveled 25 cm in one direction, we need this distance to be 25 cm.
Therefore, the equation which models the position of the train along the track is represented by |x − 100| = 25.
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use the diagram to find bc. (help please!!)
Answer:6
Step-by-step explanation:
The length of ac is 20 and the length of ab is 14 so all you have to do is 20-14=6
Which driver's race times were the most variable if Driver A has a mean of 4.01 seconds and a standard deviation of 0.05 seconds and Driver B has a mean of 3.96 seconds and a standard deviation of 0.12 seconds and Driver C has a mean of 3.99 seconds and a standard deviation of 0.19 seconds?
The driver B has the fastest typical race time.
It is required to find which driver's race times were the most variable.
What is a statement?A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.
Given:
From the options presented, driver B has the fastest typical race time because he recorded the smallest time taken to complete an individual race.
Also from the standard deviation given 3.96 seconds for driver B, it shows that the individual time spread from the standard deviation is minimal and that the driver maintained a fairly consistent time of race throughout the racing period.
Therefore, the driver B has the fastest typical race time.
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1. 60 high school seniors taking AP classes (advanced classes for college credit) were polled (asked a question) to see if they were taking European History or US History. A total Of 29 students said they were taking AP European History and a total of 50 students sald they were taking AP US History. How many students take both AP European History and AP US History? (Hint: Draw a venn diagram.)
The number of students take both AP European History and AP US History is 19 students
A Venn diagram is an illustration of the relationships between and among sets, groups of objects that share something in common.
Let the students take both AP European History and AP US History be x such that;
n(U) = 29 - x + 50 - x
If 60 high school seniors taking AP classes, then n(U) = 60. Substitute to have:
60 = 29 - x + x + 50 - x
60 = 79 - x
-x = 60 - 79
-x =-19
x = 19
Therefore the number of students take both AP European History and AP US History is 19 students
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simplify: 12.9 - 2.8 - 7.2 + 9.1
A. 17.6
B. -6.2
C. 26.4
D. 12
Step by step answer pls
Answer:
D
Step-by-step explanation:
the simplification of 12.9 - 2.8 - 7.2 + 9.1 is 12
Open the file to answer the question
What is a first step to solve the equation 0.3n - 15 = 0.2n - 5?
Answer:
100
Step-by-step explanation:
0.3n - 15 = 0.2n - 5
0.3n - 0.2n = - 5 + 15
0.1n = 10
10/0.1 = n
n = 100
Jolene works at Food Lion and she makes $13.25. She works 4 hours a day Monday through Friday and 8 hours a day on the weekend. How much would she make during a 7-day week?
She would make $477 during a 7-day week
How much would she make during a 7-day week?The given parameters are
Hourly rate = $13.25Weekdays = 4 hours dailyWeekends = 8 hours dailyThere are 5 days in a weekday and 2 in a weekend
So, the total earning is
Total = Rate * [Weekday hours * 5 + Weekend hours * 2]
This gives
Total = $13.25 * [4 * 5 + 8 * 2]
Evaluate
Total = $477
Hence, she would make $477 during a 7-day week
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Approximately, when did all the continents combine into the pangaean supercontinent?
a) 110ma
b) 420ma
c) 240ma
d) 650ma
Answer:
C) 240ma
Step-by-step explanation:
