helpe3 meeeeeeeeeeeeeee please
Lines through the given points are as follow:
a. Line1 is perpendicular to line2.
b. Line1 is neither perpendicular nor parallel to line2.
c. Line1 is parallel to line2.
As given in the question,
Slopes of the lines through the given points are as follow:
Let m₁ and m₂ be the slope of line1 and line2 respectively.
a. Line1 ( 2,-3) , (-4, -6) and Line2 (-3,2) , (2,-8)
m₁=(-6+3)/ (-4-2)
=1/2
m₂=(-8-2)/ (2+3)
=-2
m₁ × m₂ = -1
Line1 and line2 are perpendicular.
b. Line1(-4, -5) , (4,1) and line2 (6,10) , (-3,-2)
m₁=(1+5)/ (4+4)
=3/4
m₂=(-2-10)/ (-3-6)
=4/3
m₁ × m₂=1
Line1 and line2 are neither perpendicular nor parallel .
c. Line1 (0,-4) , (-2,-8) and line2 (-1,5), (1,9)
m₁=(-8+4)/ (-2-0)
=2
m₂=(9-5)/ (1+1)
=2
m₁=m₂
Line1 and line2 are parallel
Therefore, lines through the given points are as follow:
a. Line1 is perpendicular to line2.
b. Line1 is neither perpendicular nor parallel to line2.
c. Line1 is parallel to line2.
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The cost (in dollars) for manufacturing a particular flashdrive is , where x is the number of flashdrives produced. Recall from the previous chapter that the average cost per flashdrive, denoted by , is found by dividing c(x) by x. Find and interpret
The most appropriate choice for cost function and average cost function will be given by -
[tex]\lim_{x \to \infty} \bar{C}(X) = 6[/tex]
The number of flashdrive is very large, the average cost will come down to as low as $6.
What is cost function and average cost function?
Cost function C(x) is a function of x (quantity) which gives the cost of producing x units of the commodity.
Average cost function is the per unit cost of production and can be obtained by dividing the cost function by the quantity of the commodity.
Here,
C(x) = 17000 + 6x
[tex]\bar{C}(x) = \frac{17000 + 6x}{x}\\[/tex]
[tex]= \frac{17000}{x}+ \frac{6x}{x}\\[/tex]
= [tex]\frac{17000}{x}+6[/tex]
[tex]\lim_{x \to \infty} \bar{C}(x)[/tex] = [tex]\lim_{x \to \infty} (\frac{17000}{x} + 6)[/tex]
= 0 + 6
= 6
This means as the number of flashdrive is very large, the average cost will come down to as low as $6
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Complete Question
The cost (in dollars) for manufacturing a particular flashdrive is 17000 + 6x , where x is the number of flashdrives produced. Recall from the previous chapter that the average cost per flashdrive, denoted by , is found by dividing c(x) by x. Find and interpret [tex]\lim_{x \to \infty} \bar{C}(X)[/tex]
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How do you write 0.133333... as a fraction
The expression of the number 0.133333 as a fraction would give us 133333/1000000.
What is a fraction?Let us recall that the term fraction is used to show that there is a top and a bottom part in the expression. The top part of the fraction is called the numerator while the bottom part of the fraction is called the denominator.
If we want to convert the fraction as we have it back to the decimal then we just have to divide the numerator by the denominator and we are back to the decimal. The decimal is marked by the presence of a decimal point.
To convert 0.133333 to fraction, we would take the decimal point as 1 and all other digits after it as zero thus we have;
133333/1000000.
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NEED NOW OFFERING 100 POINTS!!
Which of the following expressions is equal 5^8/ 5^2 to?
5 · 5 · 5
5 · 5 · 5 · 5
3
The expression 5^8/ 5^2 is equal to 5×5×5×5×5×5. Option C
What is an algebraic expression?An algebraic expression can be defined as a are mathematical expression with a minimum of two terms containing variables, factors, constants and coefficients.
What is an exponential function?An exponential function is simply defined as a function in which its value is a constant that is raised to the power of a variable or number.
It is a relation or expression that takes the form y = aˣ in mathematics, where x is a independent variable.
Given the expression as;
⇒ 5^8 / 5²
⇒ 5^8-2
⇒ 5^6
⇒ 5×5×5×5×5×5
Hence, the value is 5×5×5×5×5×5
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The complete question;
Which of the following expressions is equal 5^8/ 5^2 to?
A.5×5×5
B. 1/5×5×5×5
C. 5×5×5×5×5×5
D.3
I NEED HELP
You recently opened your checking account with ReallyAwesomeBank on August 1 using $200.00.
Complete the checkbook register using the following transactions. Then answer the questions/show your work in the space below the register.
August 1 – Opened the checking account with $200.00
August 2 – Purchased Groceries from Shaw’s for $57.91 plus 3.5% tax. (Check 101)
August 2 – Paid $12 for parking using your debit card.
August 4 – Deposited paycheck from work. (15.50/hr for 30 hours)
August 6 – Paid National Grid $47.50. (Check 102)
August 6 – Bought 3 pairs of pants at $25.98 each with a 15% coupon and 6.5% sales tax from Kohls. (Check 103)
August 7 – Bought a bike for $165.00, helmet for $35.12, and gloves for $10.99 from Bikes-R-Us. Used a 15% off coupon and there was 5% sales tax. (Check 104)
August 11 – Deposited paycheck from work, but took out $100.00 cash (15.50/hr for 25 hours)
August 11 – Opened a savings account with $250 transferred from the checking account.
August 12 – Ate lunch at Red Robin for $24.61 plus 5.5% sales tax. Used your debit card to pay for it.
Number
Date
Transaction Description
Payment Fee, Withdrawal (-)
Deposit, Credit (+)
Balance
Use the space below to explain how you completed the first FOUR transactions.
Use the space below to show your work for how you found the total you spent at Kohl’s on August 6.
Use the space below to show your work for how you found the total you spent at Bikes-R-Us on August 7.
What was your final balance on August 12?
Completing the checkbook register using the transactions done on the checking account at Really Awesome Bank shows that the ending balance was $298.12.
What is a checkbook register?A checkbook register records transactions with a bank for a checking account.
The transactions of a checking account include withdrawals or payments, deposits, and bank charges if any.
Checkbook Register:Check Date Description Payments Deposit, Balance
No. Withdrawal (-) Credit (+)
August 1 Initial deposit $200.00 $200.00
101 August 2 Groceries (Shaw’s) $59.94 140.06
August 2 Parking fee $12 128.06
August 4 Paycheck 465.00 593.06
102 August 6 Electricity $47.50 545.56
103 August 6 Pants $70.56 475.00
104 August 7 Bike, Helmet, Gloves $188.42 286.58
August 11 Paycheck $287.50 574.08
August 11 Savings account $250.00 324.08
August 12 Luch (Red Robin) $25.96 298.12
Transaction Analysis:August 2 – $59.94 ($57.91 x 1.035%)
August 4 – $465 ($15.50 x 30) (15.50/hr for 30 hours)
August 6 – $70.56 (3 x $25.98 x 85% x 1.065)
August 7 – $188.42 ($165 + $35.12 + $10.99 x 85% x 1.05)
August 11 – $287.50 (15.50 x 25 - $100)
August 12 – $25.96 (24.61 x 1.055)
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Hudson owns a food truck that sells tacos and burritos. He only has enough supplies
to make 100 tacos or burritos. He sells each taco for $3 and each burrito for $7.
Hudson must sell at least $420 worth of tacos and burritos each day. If a represents
the number of tacos sold and y represents the number of burritos sold, write and
solve a system of inequalities graphically and determine one possible solution.
One possibility for resolving the inequality is (20, 60) in which x represents the number of tacos sold, and y the number of burritos sold
How are inequalities graphed?When graphing inequalities, the dependent variable, or y, is placed on the left side of the equation, while the other variables are placed on the right side.
The parameters are as follows:
Hudson has enough ingredients to make 90 tacos.
Each taco costs $3 to purchase.
Each burrito costs $7 to purchase.
Hudson must sell $420 worth of tacos and burritos per day.
x = number of tacos sold
y = the number of burritos sold
We need to graphically represent and solve the system of inequalities, and to identify one possible solution
The inequalities in the system are as follows:
x + y ≤ 90
3·x + 7·y ≥ 420
We have the following graphs to plot the above inequalities:
y ≤ 90 - x
y ≥ 420/7 - 3·x/7
y ≥ 60 - 3·x/7
The vertices of the feasible region's triangle are as follows from the inequality graph:
(0, 90), (0, 60), and the third vertex is found as follows for accuracy;
90 - x = 60 - 3·x/7
x = 52.5
y = 90 - x
∴ y = 37.5 at the vertex
The third vertex is (52.5, 37.5)
Therefore, the feasible region's vertices are (0, 90), (0, 60), and (52.5, 37.5), and one possible solution within the feasible region is (20, 60)
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on a multiple choice test with six possible answers for each question, what is the probability of answering a question correctly if you make a random guess?
Answer:
17%
Step-by-step explanation:
Hello!
Out of the 6 options, only 1 option will be correct. This can be represented as a ratio of 1:6.
If you randomly guess, there is an equal chance of choosing any of the 6 options.
To find the percentage of guessing the correct option, simply divide 1 by 6 (1 option is correct out of 6), and multiply the outcome by 100 (for percentage).
1:6 = 1/61/6 = 0.16666..... ≈ 0.170.17 * 100 = 17%The probability of getting an answer correct would be 17%.
The probability of getting an answer wrong would be 83%, which can be found by subtracting 17% from 100%.
Work out the surface area of the solid
cuboid.
7m
6m
3m
The surface area of the solid cuboid 7m 6m and 3m. total surface area of cuboid is 162 [tex]m^{2}[/tex].
What is a cuboid?A cuboid is a six-sided solid known as a hexahedron in the geometry. Quadrilaterals make up its faces. Cuboid implies "like a cube," in the sense that a cuboid can be converted into a cube by varying the length of its edges or the angles between its faces. A cuboid is a convex polyhedron with the same polyhedral graph as a cube in mathematics.
A cube with six square faces, a rectangular prism, rectangular cuboid, or a rectangular box with six rectangle faces are special situations. In both circumstances, the faces of the cube and the rectangular prism come together at a right angle.
total surface area of cuboid
= 2(lb+bl+lh)
=2(7×6+6×3+3×7)
=2(81)
=162 [tex]m^{2}[/tex]
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The cube of the sum of a number and 3
The expression for the cube of the sum of a number and 3 is (x+3)³
What are algebraic expressions?Algebraic expressions are simply defined as arithmetic expressions made up of variables, terms, coefficients, factors and constants
They may also be known to consist of certain mathematical operations, such as;
ParenthesesAdditionSubtractionDivisionBracketMultiplication, etcBased on the information given, we have;
cube of the sum of a number and 3
Let the number be x
We have the expression to be;
x + 3
Find the cube
(x+3)³
Hence, the expression is (x+3)³
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The complete question is;
Write the expression for The cube of the sum of a number and 3
Two thirds of. The shirts in a tee shirt shop are blue three sevenths are on sale one half are size medium
The fraction of the blue T-shirts that are on sale and are size medium are 1/7.
What is fraction ?A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.
Of all the shirts in the shop , 2/3 of the t-shirts are blue.
Of the blue shirts, 3/7 are on sale.
= 2/3 x 3/7
= 2/7
Out of all the shirts, 2/7 shirts are blue and are on sale.
Of the blue shirts on sale, 1/2 are size medium.
= 2/7 x 1/2
= 1/7
The fraction of the blue T-shirts that are on sale and are size medium are 1/7.
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is 6 a significantly high number of girls in 8 births? why or why not? use 0.05 as the threshold for a significant event. a. yes, since the appropriate probability is greater than 0.05, it is a significantly high number. b. yes, since the appropriate probability is less than 0.05, it is a significantly high number. c. no, since the appropriate probability is greater than 0.05, it is not a significantly high number. d. no, since the appropriate probability is less than 0.05, it is not a significantly high number.
We can conclude that (A) "Yes since the appropriate probability is greater than 0.05, it is a significantly high numbe"r is the correct reason for the question.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The four most popular approaches to probability are classical, empirical, subjective, and axiomatic.So,
Number of Girls x
P(x)
(0)
0.003(1)
0.021(2)
0.118(3)
0.208(4)
0.300(5)
0.208(6)
0.118(7)
0.021(8)
0.003Results from groups of 8 births from 8 different parent sets are shown in the accompanying table.
The proportion of girls among the 8 children is represented by the random variable x. It is a significantly high number because the appropriate probability is higher than 0.05, so yes.Therefore, (A) "yes, since the appropriate probability is greater than 0.05, it is a significantly high number" is the correct reason for the question.
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Simplify.
9u - 4u = ?
Answer:
5u
Step-by-step explanation:
9-4=5
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{9u - 4u}\\\large\text{COMBINE the LIKE TERMS}\\\mathsf{= (9u - 4u})\\\mathsf{= 9u - 4u}\\\mathsf{= 5u}\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{\mathsf{5u}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
what is the answer to
32z-48 using factoring
The answer to 32z - 48 using factoring is 3/2.
Given,
32z - 48
We have to find the answer using factoring:
Factoring:
Finding things to multiply together to produce an expression is known as factoring. It is comparable to splitting an expression into numerous smaller expressions.
Here,
32z - 48 = 0
Add 48 to both sides
32z - 48 + 48 = 0 + 48
32z = 48
Divide 32 on both sides
32z/32 = 48/32
z = 48/32
Now, we can factorize 48/32
Take 2 as common factor
(48/2) / (32/2) = 24/16
Again, take 2 as common factor
(24/2) / (16/2) = 12/8
Now, take 4 as common factor
(12/4) / (8/4) = 3/2
Here, z = 3/2
That is, the answer for 32z - 48 using factoring is 3/2.
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Write -1.111... as a mixed number in simplest form.
Answer:
The answer is -10/9
Step-by-step explanation:
10*x=(-1.111...*10 .) second equation
10x=-11.111....
subtruct second equation from the first equation
10x=10*-11.111.
-
x=-1.1111.
9x=10
x=10/9
John put 14,000 Euros in an account at a simple interest rate of 1% per year. How much interest will he get after 12 year?
The amount of interest John will get after 12 years given his savings and interest rate is 1,680 Euros
How to find simple interest?Simple interest is a type of interest rate paid only on principal. It is called by multiplying principal by interest rate by time.
Principal, P = 14,000 EurosRate, r = 1% = 0.01Time, t = 12 yearsSimple interest = principal × rate × time
= 14,000 × 0.01 × 12
= 1,680 Euros
In conclusion, given John's savings and interest rate, he'll earn 1,680 Euros as interest after 12 years.
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there is a line that includes the point (–2, 6) and has a slope of 2 What is its equation in slope-intercept form?
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-2)}) \implies y -6= 2 (x +2) \\\\\\ y-6=2x+4\implies {\Large \begin{array}{llll} y=2x+10 \end{array}}[/tex]
PLEASE HELP
Solve one sixth times quantity x plus 18 end quantity equals negative 5.
x = −48
x = −138
x = 12
x = 18
the answer is x= -48
solve for x by simplifying bith sides of the equation then isolating the variable so the answer is x= -48 your welcome!
I took a quiz about a week ago as of posting this and I found that this question was hard for me to answer I was wondering how I could find an easier way to solve this besides doing a long equation for scale factors. I am only here to learn so any answers to this are great.
Answer:
d(-6,-9),e(3,-9),f(3,-3),g(-6,-3
Step-by-step explanation:
first you look at the location of the point and follow in the direction of which number it is on the X line, then in the direction of which number it is on the Y line and in the parentheses of the coordinates, first write the number from the X line, then from the Y line
ps: I hope I helped you a bit :)
Complete the statement to describe the expression 4.4.4.
You can write the expression as a power, using
as the exponent.
?
Rosa has $254. She pays $7 for breakfast each day and $13 for lunch each day. If Rosa
does not spend money on anything else or receive any additional money, how many
days can she continue to buy breakfast and lunch?
The number of days that Rosa can continue to buy breakfast and lunch with the money is; 12 days
How to solve algebra Word problems?We are given the following parameters;
Amount held by Rosa = $254
Amount per breakfast = $7
Amount per Lunch = $13
Thus;
Amount spent each day = $7 + $13
Amount spent each day = $20
Now, to find out how many days this money can last her if she doesn't get any more income is;
Number of days = 254/20 = 12 days with $14 left
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358 |-14| how do I do this
During an experiment, the temperature of a liquid, in degrees Celsius, is given by the function t(m) = 0.2m + 6, where m is the number of minutes since the experiment began. Which graph correctly shows this function?
The graph that correctly represent the experiment that was graphed with the function t(m) = 0.2m + 6 is the first option with points
first point (-30, 0) second point (0, 6)How to match graph to the functiongiven data
t(m) = 0.2m + 6
information deduced from the graph
intercept = 6slope = 0.2examining the graph shows that first graph have the intercept as 6
using the points to calculate slope we have
= (y2 - y1) / (x2 - x1 )
= (6 - 0) / (0 - -30)
= 6 / (0 + 30)
= 6 / 30
= 0.2
Since the points are same with the given information we can conclude that the first option has the graph of the given function
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At what rates percent compound interest will Rs2000 amount to Rs 2420 in 2 years.
The interest rates required to get a total amount of $2,420 from compound interest on a principal of $2,000 compounded 1 times per year over 2 years is 10% per year.
What is compound interest?The interest on savings that is calculated on both the initial principal and the interest accrued over time is known as compound interest.
The concept of compound interest, also known as "interest on interest," is thought to have first appeared in Italy in the 17th century. It will accelerate the growth of a sum more quickly than simple interest, which is calculated only on the principal sum.
Money is multiplied more quickly through compounding, and the more times it is compounded, the higher the compound interest will be.
Using the formula A = P(1 + r/n)^nt
Solving for rate r as a decimal
r = n[(A/P)^(1/nt) - 1]
r = 1 × [(2,420/2,000)^{1/(1)(2)} - 1]
r = 0.1
Then convert r to R as a percentage
R = r × 100
R = 0.1 × 100
R = 10%/year
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A fair die is rolled seven times. What is the probability that it comes up 2 at least once? Write your answer as a fraction or a decimal, rounded to four decimal
places.
The probability of getting 2 at least once is 1/6.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur.So, the probability of getting a 2 at least once:
The sample space will be (refer to the image attached below).Formula of probability: P = favourable events/total events
At least once, we need to get 2 and a maximum of 7.So, favorable events = 7, and the total number of events will be 6×7 = 42.Now, substitute the values in the formula as follows:
P = 7/42P = 1/6Therefore, the probability of getting 2 at least once is 1/6.
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Suppose that diastolic blood pressure readings of adult males have a bell-shaped distribution with a mean of 80 mmhg and a standard deviation of 11 mmhg. using the empirical rule, what percentage of adult males have diastolic blood pressure readings that are greater than 102 mmhg
Answer:
95% of adult males have diastolic blood pressure readings that are at least 102 mmHg
Step-by-step explanation:
The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below
68% of data falls within the first standard deviation from the mean.
95% fall within two standard deviations.
99.7% fall within three standard deviations.
From the information given, the mean is 80 mmHg and the standard deviation is 11 mmHg.
2 standard deviations = 2 × 11= 22
80+ 22= 102 mmHg
Therefore, 95% of adult males have diastolic blood pressure readings that are at least 102 mmHg.
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What are the domain and range of f(x) = 4x – 8?
domain: {x | x is a real number}; range: {y | y > –8}
domain: {x | x is a real number}; range: {y | y > 8}
domain: {x | x > 4}; range: {y | y > –8}
domain: {x | x > –4}; range: {y | y > 8}
The domain and range of this linear function f(x) = 4x – 8 is: A. domain: {x | x is a real number}; range: {y | y > –8}.
What is a linear function?A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate. This ultimately implies that, a linear function is typically used for uniquely mapping an input variable to an output variable.
What is a domain?A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain refers to the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
In conclusion, the domain of this linear function consist of all real numbers while the range comprises the set of all real numbers on the y-axis that are greater than negative eight (-8).
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Answer:
its a
Step-by-step explanation:
A grocery store clerk can scan 1 product every
1
2
of a second. At what rate can she scan products?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
The rate at which the grocery store clerk can scan products is 2 products per second.
What is the rate?Rate is the speed at which an activity can be carried out. Rate can be determined by dividing the total products that are bagged by the time it takes to bag the product.
Division is used to determine the product of two or more numbers. The sign that represent division is ÷. Division is a mathematical operations. Other mathematical operations include addition, subtraction and multiplication. Division entails grouping a number into equal groups using another number.
Rate = number of products ÷ time
1 ÷ 1/2
1 x 2 = 2 products per second
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hi can someone help me here
Answer:
see explanation
Step-by-step explanation:
[tex]\frac{x+2}{3}[/tex] - [tex]\frac{2x-4}{2}[/tex] = 0
multiply through by 6 ( the LCM of 3 and 2 ) to clear the fractions
2(x + 2) - 3(2x - 4) = 0 ← distribute parenthesis on left side and simplify
2x + 4 - 6x + 12 = 0
- 4x + 16 = 0 ( subtract 16 from both sides )
- 4x = - 16 ( divide both sides by - 4 )
x = 4
------------------------------------------------------------
[tex]\frac{5x}{2}[/tex] + [tex]\frac{x-2}{8}[/tex] = 2 ( multiply through by 8 to clear the fractions )
4(5x) + x - 2 = 16
20x + x - 2 = 16
21x - 2 = 16 ( add 2 to both sides )
21x = 18 ( divide both sides by 21 )
x = [tex]\frac{18}{21}[/tex] = [tex]\frac{6}{7}[/tex]
-----------------------------------------------------------
[tex]\frac{x-5}{4}[/tex] - [tex]\frac{3x-1}{5}[/tex] = - [tex]\frac{3}{2}[/tex]
multiply through by 20 ( the LCM of 4, 5, 2 ) to clear the fractions
5(x - 5) - 4(3x - 1) = - 30 ← distribute parenthesis on left side and simplify
5x - 25 - 12x + 4 = - 30
- 7x - 21 = - 30 ( add 21 to both sides )
- 7x = - 9 ( divide both sides by - 7 )
x = [tex]\frac{9}{7}[/tex]
-------------------------------------------------------------
[tex]\frac{1}{x-1}[/tex] + [tex]\frac{1}{x+1}[/tex] = [tex]\frac{4x+2}{x^2-1}[/tex] ← x² - 1 is a difference of squares , then
[tex]\frac{1}{x-1}[/tex] + [tex]\frac{1}{x+1}[/tex] = [tex]\frac{4x+2}{(x-1)(x+1)}[/tex]
multiply through by (x - 1)(x + 1) to clear the fractions
x + 1 + x - 1 = 4x + 2
2x = 4x + 2 ( subtract 4x from both sides )
- 2x = 2 ( divide both sides by - 2 )
x = - 1
If we substitute this value back into the original equation, we find
[tex]\frac{1}{-1-1}[/tex] + [tex]\frac{1}{-1+1}[/tex] = [tex]\frac{4(-1)+2}{(-1)^2-1}[/tex]
[tex]\frac{1}{-2}[/tex] + [tex]\frac{1}{0}[/tex] = [tex]\frac{-2}{1-1}[/tex]
[tex]\frac{1}{-2}[/tex] + [tex]\frac{1}{0}[/tex] = [tex]\frac{-2}{0}[/tex]
division by zero is undefined
thus x = - 1 is an extraneous solution
the equation has no solution
Answer:
[tex]\textsf{1.} \quad x=4[/tex]
[tex]\textsf{2.} \quad x=\dfrac{6}{7}[/tex]
[tex]\textsf{3.} \quad x=\dfrac{9}{7}[/tex]
[tex]\textsf{4.} \quad \textsf{No solution}[/tex]
Step-by-step explanation:
Question 1Given equation:
[tex]\dfrac{x+2}{3}-\dfrac{2x-4}{2}=0[/tex]
[tex]\textsf{Add \; $\dfrac{2x-4}{2}$ \; to both sides of the equation}:[/tex]
[tex]\implies \dfrac{x+2}{3}-\dfrac{2x-4}{2}+\dfrac{2x-4}{2}=0+\dfrac{2x-4}{2}[/tex]
[tex]\implies \dfrac{x+2}{3}=\dfrac{2x-4}{2}[/tex]
Cross multiply:
[tex]\implies 2(x+2)=3(2x-4)[/tex]
[tex]\implies 2x+4=6x-12[/tex]
Subtract 2x from both sides:
[tex]\implies 2x+4-2x=6x-12-2x[/tex]
[tex]\implies 4=4x-12[/tex]
Add 12 to both sides:
[tex]\implies 4+12=4x-12+12[/tex]
[tex]\implies 16=4x[/tex]
[tex]\implies 4x=16[/tex]
Divide both sides by 4:
[tex]\implies \dfrac{4x}{4}=\dfrac{16}{4}[/tex]
[tex]\implies x=4[/tex]
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Question 2Given equation:
[tex]\dfrac{5x}{2}+\dfrac{x-2}{8}=2[/tex]
Multiply the numerator and denominator of the first fraction by 4:
[tex]\implies \dfrac{5x \cdot 4}{2\cdot 4}+\dfrac{x-2}{8}=2[/tex]
[tex]\implies \dfrac{20x}{8}+\dfrac{x-2}{8}=2[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \dfrac{20x+x-2}{8}=2[/tex]
[tex]\implies \dfrac{21x-2}{8}=2[/tex]
Multiply both sides by 8:
[tex]\implies \dfrac{(21x-2) \cdot 8}{8}=2 \cdot 8[/tex]
[tex]\implies 21x-2=16[/tex]
Add 2 to both sides:
[tex]\implies 21x-2+2=16+2[/tex]
[tex]\implies 21x=18[/tex]
Divide both sides by 21:
[tex]\implies \dfrac{21x}{21}=\dfrac{18}{21}[/tex]
[tex]\implies x=\dfrac{18}{21}[/tex]
Reduce the fraction by dividing the numerator and denominator by 3:
[tex]\implies x=\dfrac{18 \div 3}{21 \div 3}[/tex]
[tex]\implies x=\dfrac{6}{7}[/tex]
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Question 3Given equation:
[tex]\dfrac{x-5}{4}-\dfrac{3x-1}{5}=-\dfrac{3}{2}[/tex]
Multiply the numerator and denominator of the first fraction by 5, and the numerator and denominator of the second fraction by 4:
[tex]\implies \dfrac{(x-5) \cdot 5}{4\cdot 5}-\dfrac{(3x-1)\cdot 4}{5\cdot 4}=-\dfrac{3}{2}[/tex]
[tex]\implies \dfrac{5x-25}{20}-\dfrac{12x-4}{20}=-\dfrac{3}{2}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]
[tex]\implies \dfrac{5x-25-(12x-4)}{20}=-\dfrac{3}{2}[/tex]
[tex]\implies \dfrac{5x-25-12x+4}{20}=-\dfrac{3}{2}[/tex]
[tex]\implies \dfrac{-7x-21}{20}=-\dfrac{3}{2}[/tex]
Cross multiply:
[tex]\implies 2(-7x-21)=-3(20)[/tex]
[tex]\implies -14x-42=-60[/tex]
Add 42 to both sides:
[tex]\implies -14x-42+42=-60+42[/tex]
[tex]\implies -14x=-18[/tex]
Divide both sides by -14:
[tex]\implies \dfrac{-14x}{-14}=\dfrac{-18}{-14}[/tex]
[tex]\implies x=\dfrac{18}{14}[/tex]
Reduce the fraction by dividing the numerator and denominator by 2:
[tex]\implies x=\dfrac{18 \div 2}{14 \div 2}[/tex]
[tex]\implies x=\dfrac{9}{7}[/tex]
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Question 4Given equation:
[tex]\dfrac{1}{x-1}+\dfrac{1}{x+1}=\dfrac{4x+2}{x^2-1}[/tex]
Factor the denominator of the fraction on the right side of the equation:
[tex]\implies \dfrac{1}{x-1}+\dfrac{1}{x+1}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]
Multiply the numerator and denominator of the first fraction by (x+1), and the numerator and denominator of the second fraction by (x-1):
[tex]\implies \dfrac{x+1}{(x+1)(x-1)}+\dfrac{x-1}{(x+1)(x-1)}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \dfrac{x+1+x-1}{(x+1)(x-1)}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]
[tex]\implies \dfrac{2x}{(x+1)(x-1)}=\dfrac{4x+2}{(x+1)(x-1)}[/tex]
Multiply both sides by (x+1)(x-1):
[tex]\implies \dfrac{2x(x+1)(x-1)}{(x+1)(x-1)}=\dfrac{(4x+2)((x+1)(x-1)}{(x+1)(x-1)}[/tex]
[tex]\implies 2x=4x+2[/tex]
Subtract 4x from both sides:
[tex]\implies 2x-4x=4x+2-4x[/tex]
[tex]\implies -2x=2[/tex]
Divide both sides by -2:
[tex]\implies \dfrac{-2x}{-2}=\dfrac{2}{-2}[/tex]
[tex]\implies x=-1[/tex]
However, if we substitute x = -1 into the original equation we get:
[tex]\implies \dfrac{1}{(-1)-1}+\dfrac{1}{(-1)+1}=\dfrac{4(-1)+2}{(-1)^2-1}[/tex]
[tex]\implies -\dfrac{1}{2}+\dfrac{1}{0}=\dfrac{-2}{0}[/tex]
A number divided by zero is undefined. Therefore, there is no solution for this equation.
5/6 of number is 30. Find the number.
Answer:
36.
Step-by-step explanation:
I get this answer as I know 30 is divisible by six, so I start to investigate by how much It is divisible by.
30 / 6 = 5
Since I now know that, I can infer that 6x6 is 36.
And since 30 would give you 5/6, I imagine the answer is 36.
I'm so confused. I can't do word problems.
Based on the population density of the area in 1980 and the area, the population in 1980 was 807,750 people
How to find the population?The population density of an area is based on the population of the area and the area. The formula is:
Population density = Population of area / Surface area
Given that the surface area is 750 square miles and the population density in 1980 was 750 square miles, the population of the area can be found by the formula:
Population in 1980 = Population density in 1980 x surface area
Population in 1980 = 1,077 x 750
= 807,750 people
Find out more on population density at https://brainly.com/question/13902749
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