Kiran is solving 2x-3/x-1=2/x(x-1) for x, and he uses these steps.He checks his answer and finds that it isn’t a solution to the original equation, so he writes “no solutions.” Unfortunately, Kiran made a mistake while solving. Find his error and calculate the actual solution(s).
Answers
Solution:
Given:
[tex]\begin{gathered} To\text{ solve,} \\ \frac{2x-3}{x-1}=\frac{2}{x(x-1)} \end{gathered}[/tex]Kiran multiplied the left-hand side of the equation by (x-1) and multiplied the right-hand side of the equation by x(x-1).
That was where he made the mistake. He ought to have multiplied both sides with the same quantity (Lowest Common Denominator) so as not to change the actual value of the question.
Multiplying both sides by the same quantity does not change the real magnitude of the question.
The actual solution goes thus,
[tex]\begin{gathered} \frac{2x-3}{x-1}=\frac{2}{x(x-1)} \\ \text{Multiplying both sides of the equation by the LCD,} \\ \text{The LCD is x(x-1)} \\ x(x-1)(\frac{2x-3}{x-1})=x(x-1)(\frac{2}{x(x-1)}) \\ x(2x-3)=2 \\ \text{Expanding the bracket,} \\ 2x^2-3x=2 \\ \text{Collecting all the terms to one side to make it a quadratic equation,} \\ 2x^2-3x-2=0 \end{gathered}[/tex]Solving the quadratic equation;
[tex]\begin{gathered} 2x^2-3x-2=0 \\ 2x^2-4x+x-2=0 \\ \text{Factorizing the equation,} \\ 2x(x-2)+1(x-2)=0 \\ (2x+1)(x-2)=0 \\ 2x+1=0 \\ 2x=0-1 \\ 2x=-1 \\ \text{Dividing both sides by 2,} \\ x=-\frac{1}{2} \\ \\ \\ OR \\ x-2=0 \\ x=0+2 \\ x=2 \end{gathered}[/tex]Therefore, the actual solutions to the expression are;
[tex]\begin{gathered} x=-\frac{1}{2} \\ \\ OR \\ \\ x=2 \end{gathered}[/tex]Related Questions
White the standard form of the equation of the line through the given point with the given slope.
Answers
The standard form equation of a line is expressed as
Ax + By = C
where
A, B and C are real numbers and A and B are not both zero. From the information given,
the line passes through(- 2, 5) and slope = - 4
We would find the y intercept of the line, c by substituting slope, m = - 4, x = - 2 and y = 5 into the slope intercept equation which is expressed as
y = mx + c
Thus, we have
5 = - 4 * - 2 + c
5 = 8 + c
c = 5 - 8 = - 3
Thus, the equation of the line in the slope intercept form is
y = - 4x - 3
We would convert it to standard form. Thus, we have
y + 4x = - 3
4x + y = - 3
Thus, the equation in standard form is
4x + y = - 3
Sonia has $725,000 she wants to save. If the FDIC insurance limit per depositor, per bank, is $250,000, which of these ways of distributing her money between three banks will guarantee that all her money is insured?
$220,000 in Bank A, $230,000 in Bank B, $275,000 in Bank C
$220,000 in Bank A, $250,000 in Bank B, $255,000 in Bank C
$240,000 in Bank A, $230,000 in Bank B, $255,000 in Bank C
$240,000 in Bank A,, $245,000 in Bank B 245,000 in Bank c
Answers
As per the dividing method, there are 3 ways of distributing her money between three banks.
Dividing method:
Division is the process of repeated subtraction.
This method, we start from the number called dividend in the number line and keep subtracting the number called divisor till we reach at 0 that is called remainder, and the number of steps we go on backward counting is the quotient or result of division.
Given,
Sonia has $725,000 she wants to save.
FDIC insurance limit per depositor, per bank, is $250,000
So, here we need to find the ways of distributing her money between three banks will guarantee that all her money is insured.
We know that, he limit is $250,000.
So, we have to divide the total amount within these limit across three bank.
Therefore, the possible ways of dividing the amount is given below:
Way 1:
if $250,000 deposited in bank A,
$250,000 deposited in bank B and
remaining money $175,000 will be deposited in bank C.
Way 2:
if $200,000 deposited in bank A,
$250,000 deposited in bank B,
$225,000 deposited in bank C.
Way 3:
If $225,000 deposited in bank A,
$225,000 deposited in bank B,
and $ 225,000 in bank C.
To know more about Dividing method here.
https://brainly.com/question/27961007
#SPJ1
Use synthetic division to find the quotient and remainder when2x^3+ 9x^2- 8x+ 4 is divided by x - 2
Answers
Solution:
Given;
[tex]\frac{2x^3+9x^2-8x+4}{x-2}[/tex]Using Synthetic division;
Thus, the solution is;
[tex]\frac{2x^{3}+9x^{2}-8x+4}{x-2}=2x^2+13x+18+\frac{40}{x-2}[/tex]The quotient is;
[tex]2x^2+13x+18[/tex]The remainder is;
[tex]18[/tex]–8.38 as a mixed number.
Answers
Answer:
4 3/4
Step-by-step explanation:
What is the area of this trapezoid? Enter your answer in the box. ft2
Answers
Given the figure, we can deduce the following information:
Upper base = 15 ft
Lower base = 37 ft
Height = 18 ft
To determine the area of a trapezoid, we use the formula:
[tex]A=\frac{a+b}{2}h[/tex]where:
A=Area
a=upper base
b=lower base
h=height
We plug in what we know:
[tex]\begin{gathered} A=\frac{a+b}{2}h \\ =\frac{15+37}{2}(18) \\ \text{Simplify} \\ A=\frac{52}{2}(18) \\ =\frac{936}{2} \\ A=468ft^2 \end{gathered}[/tex]Therefore, the area of the trapezoid is 468 ft^2.
How do the coordinates of the blue point relate to the solution of the equation 3x = x + 4
Answers
we have the following:
They are related in the way taht if we replace, in both equations it gives the same result:
[tex]\begin{gathered} 3x=2\cdot3=6 \\ x+4=2+4=6 \end{gathered}[/tex]Jamal is comparingprices of several different brandsof peanuts. Which brand is thebest buy? Explain.
Answers
So we need to figure out which is the best buy. In order to do this we must look at a particular variable: the price per ounce of peanuts. This price is given by dividing the total price of a certain amount of peanuts divided by its weight in ounces. So for the Barrel brand we get:
[tex]\frac{3.39}{10}=0.339[/tex]So the Barrel peanuts cost $0.339 per ounce. For the Mr. Nut peanuts we get:
[tex]\frac{4.54}{14}=0.324[/tex]Then the Mr. Nut peanuts cost $0.324 per ounce. Finally, the price per ounce of the Chip's peanuts is:
[tex]\frac{6.26}{18}=0.348[/tex]Then, the cheapest peanuts are those of the brand Mr. Nut and that is the best buy.
Greg is ordering tile for a floor he is installing. The owner picks out tile that is 16in by 16in including the grout . The floor is 350 sq ft . (part 1) How many tile must Greg order for the floor ( assume no waste)(part 2) Each tile cost $ 1.75 plus 8% sales tax . How will the tile cost ?
Answers
ANSWER
(part 1) 196 tiles
(part 2) $ 1.89
EXPLANATION
(part 1)
First we have to find the area of each tile, that is the product of the dimensions because it is a rectangle,
[tex]A_{\text{tile}}=16in\cdot16in=256in^2[/tex]To compare it to the floor's area, we have to transform it into square feet. Knowing that 1 ft² = 144 in²,
[tex]256in^2\cdot\frac{1ft^2}{144in^2}=\frac{16}{9}ft^2[/tex]This is a partial result, so it is best if we leave it as a fraction so we don't miss any decimals.
Now, the area of the floor is 350 ft². To find how many tiles Greg has to order, we have to divide the area of the floor by the area of each tile,
[tex]\#tiles=\frac{A_{\text{floor}}}{A_{\text{tile}}}=\frac{350ft^2}{\frac{16}{9}ft^2}=196.875[/tex]But the number of tiles has to be an integer. If Greg buys 197 tiles they will have to cut some (waste). If he buys 196 there will be some of the floor not covered. However we were asked to assume no waste, so Greg will have to order 196 tiles.
(part 2)
To answer this question we have to add 8% to the cost of the tile. The 8% of 1.75 is,
[tex]1.75\cdot\frac{8}{100}=0.14[/tex]So the cost of each tile is,
[tex]1.75+0.14=1.89[/tex]Garvin earned $ 948.35 in net pay for working 24 hours. He paid $ 348.26 in federal and state taxes, and $ 145.06 in FICA taxes. What is Garrett's hourly wage? Round your answer to two decimal places. If answer doesn't have two decimal places include zeros to make two decimal places. For the units, use a word not a symbol. Be sure to attach your work to this question in order to receive credit for your answer.Your Answer:units:
Answers
ANSWER:
18.96 dollars per hour
STEP-BY-STEP EXPLANATION:
The 24-hour salary is calculated with the earnings and we subtract the taxes, as follows:
[tex]\begin{gathered} s=948.35-348.26-145.06 \\ s=455.03 \end{gathered}[/tex]Now, we divide by 24 to find out Garvin's hourly wage:
[tex]\begin{gathered} h=\frac{455.03}{24} \\ h=18.96 \end{gathered}[/tex]Therefore, the hourly wage is $18.96.
Are the answers to question six part a b c and d correct?
Answers
How do i dilate a scale factor by 2?
Answers
The dilated figure is larger than the original figure if the dilation factor is greater than 1 and the dilated figure becomes smaller than the origial figure if the dilation factor is less than 1.
Since, the dilation factor is 2, the dilated image is larger than the original figure two times.
For the coordinate (x,y) in original figure, the coordiante in the dilated figure will be (2x,2y).
- 32 + 2Determine for each 2-value whether it is in the domain of f or not.In domainNot in domain203
Answers
f(x) = x-3 / x+2
To be in the domain, we have to avoid 0 on the bottom of the fraction.
So, the bottom of the fraction is x+2.
x=-2
(-2)+2= 0
-2 is not in the domain
x= 0
(0)+2= 2
0 is in the domain
x=2
(2)+2=4
Consider the equation below. 4(x - 4) + 6x = 14 Part A: Enter the value for x that makes the equation true. X = Part B: Explain the algebraic steps you took to get the solution. thea Part C: Explain how you know your solution in Part A is correct.
Answers
Part A) To find out the value for x that makes it an identity, (true), we need to solve it.
4(x-4) +6x=14 Distiribute
4x -16 +6x = 14 Combine like terms
2x -16 = 14 Add 16 to both sides
2x = 30 Divide both sides by 2
x =15
Part B) Above explained.
Part C) We can know it by plugging it into the original equation:
4(15 -4) +6(15) = 14
4(11) +90 = 14
44
WILL MARK BEST ANSWER BRAINLIEST
The system of conics has two solutions.
(x−1)2+(y+4)2=25(x−1)225+(y+4)2100=1
What are the solutions to this system of conics?
Enter your answer by filling in the boxes.
Answers
Answer:
(2,0) and (-2,0)
Step-by-step explanation:
pls mark me Brainliest
Answer: (-4,-4) (6,-4)
Step-by-step explanation:
I took the test and it said these were the corrects answers.
8. Kayla finds the multiplication
facts for 12
by doubling the multiplication facts for 6.
Does Kayla's strategy work?
Use words, numbers, or pictures to explain.
Answers
A strategy is a way to manipulate numbers, use connections and interactions between numbers to solve an issue. For each procedure, there are a few key tactics. The first thing you do with the statistics is frequently used to categorize, characterize, or label a technique.
What is a doubling strategy?By doubling the multiplication facts for 6, Kayla discovers the 12 multiplication facts.The participant does as instructed, multiplying the number twice or three times. Lily, for instance, rolls "4" and "DDD." She believes that double 4 is equal to 8, double 8 to 16, and double 16 to 32. Four times eight equals 32.A number is simply doubled when multiplied by two, according to the two times table. Any number plus itself is the same as any number multiplied by two.The card below depicts the mental image of two groups of six, or double six, that we want pupils to have. (Students who have been using ten-frames may interpret the amount as ten plus two extra.)To Learn more about strategy refer to:
https://brainly.com/question/27747591
#SPJ1
what is the slope of (12 -18) (-15 -18)
Answers
Answer:
m = 0
Step-by-step explanation:
[tex]m=\frac{-18-(-18)}{-15-12)} \\m=\frac{0}{-27} \\m= 0/-27 = 0\\m=0[/tex]
can i get some help please?
Answers
Describe the translation:A) 4 units right and 6 units downB) 4 units left and 6 units upC) 6 units left and 4 units upD) 6 units right and 4 units down
Answers
To describe the transfer we will review what the points of the blue and red triangle are.
Blue triangle
I = (-2, 8)
I' = (4, 4)
First, we will determine the x-axis translation
[tex]\begin{gathered} \Delta x=x2-x1 \\ \Delta x=4-(-2) \\ \Delta x=6 \end{gathered}[/tex]6 units right
Now let's calculate the y-axis transfer
[tex]\begin{gathered} \Delta y=y2-y1 \\ \Delta y=4-8 \\ \Delta y=-4 \end{gathered}[/tex]4 units down
The answer would be 6 units right and 4 units down
how much is 2 gallons in quarts
Answers
how much is 2 gallons in quarts
Answer:
8 quarts
convert this number into scientific notation 0.00098
Answers
We have to convert the number into scientific notation.
The number is 0.00098.
We start by expressing it as a fraction.
If we divide it by 10, we can express it as:
[tex]\frac{0.00098\cdot10}{10}=\frac{0.0098}{10}[/tex]Dividing by 10 is not enough. In the same way, we have to look a numerator that is multiple of 10 that gives us a numerator that is 9.8.
We would get:
[tex]\frac{0.00098\cdot10000}{10000}=\frac{9.8}{10000}[/tex]Now we have the numerator we need.
We now express the denominator 10,000 as a power of 10 and we get the number in scientific notation as:
[tex]\frac{9.8}{10000}=\frac{9.8}{10^5}=9.8\cdot10^{-5}[/tex]Answer: 0.00098 = 9.8 * 10^(-5)
What values of z and y make angle ABC = RPM?
Answers
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
If triangles ABC and RPM are congruent, it means that:
[tex]\begin{gathered} AB=RP \\ BC=PM \\ AC=RM \\ m\angle A=m\operatorname{\angle}R \\ m\operatorname{\angle}B=m\operatorname{\angle}P \\ m\operatorname{\angle}C=m\operatorname{\angle}M \end{gathered}[/tex]For x, we have that:
[tex]\begin{gathered} BC=PM \\ BC=43 \\ PM=3x-8 \end{gathered}[/tex]Thus, we have that:
[tex]\begin{gathered} 43=3x-8 \\ 3x=43+8=51 \\ x=\frac{51}{3} \\ x=17 \end{gathered}[/tex]For y, we have:
[tex]\begin{gathered} m\operatorname{\angle}B=m\operatorname{\angle}P \\ m\operatorname{\angle}B=12y\degree \\ m\operatorname{\angle}P=62.4\degree \end{gathered}[/tex]Thus, we have that:
[tex]\begin{gathered} 12y=62.4 \\ y=\frac{62.4}{12} \\ y=5.2 \end{gathered}[/tex]Therefore, the answers are:
[tex]x=17,y=5.2[/tex]The LAST OPTION is correct.
Solve the inequality: 3x + 4 ≤ 5
Answer in interval notation.
Answers
Answer: [tex]x\leq 1/3\\[/tex]
Step-by-step explanation:
Find a unit vector u with the same direction as v = : (-3, 8)
Answers
Given:
The vector
[tex]v=<-3,8>[/tex]Required:
To find the unit vector u with the same direction.
Explanation:
Unit formula is the vector is divided by its magnitude.
Now the magnitude of v is,
[tex]\begin{gathered} mag.v=\sqrt{(-3)^2+8^2} \\ =\sqrt{9+64} \\ =\sqrt{73} \end{gathered}[/tex]Now the unit vector is,
[tex]u=<-\frac{3}{\sqrt{73}},\frac{8}{\sqrt{73}}>[/tex]Final Answer:
[tex]u=<-\frac{3}{\sqrt{73}},\frac{8}{\sqrt{73}}>[/tex]How do you write 6 tens + 4 ones + 5 tenths + 2 hundredths + 8 thousandths
Answers
Answer:64.528 is the decimal
Step-by-step explanation:
kmarks Solve the following system of equations graphically on the set of axes below 1 y 22 - 4 y = -X – 7 Plot two lines by clicking the graph. Click a line to delete il. y 10 9 8 7 6 5 4 3 2. 1 5 6 7 8 9 10
Answers
Explanation:
For the first line :
1. Draw a line which has a slope of 1 /2
2. Adjust the line so that it has a y-intercept of -4.
For the second line:
1. Draw a line which has a slope of -1
2. Adjust this line so that it has a y-intercept of -7.
Finally, find the point where the two lines intersect.
The coordinates of the point of intersection are the solution to our system.
To get a line which has a slope 1/2, you start from (0, -4 ) and then move 2 units to the right and then 1 unit up.
The sides of an L-shaped figure meet all the right angles
Answers
ANSWER:
24 ft²
STEP-BY-STEP EXPLANATION:
To determine the area of the figure, we must divide the L-shaped figure into two rectangles just like this:
We calculate the area of each rectangle and the sum of both areas would be the area of the L-shaped figure, in the following way:
[tex]\begin{gathered} A_1=L\cdot W=6\cdot2=12\text{ ft}^2 \\ \\ A_2=L\cdot W=3\cdot4=12\text{ ft}^2 \\ \\ \text{ Therefore:} \\ \\ A_t=A_1+A_2=12+12 \\ \\ A_t=24\text{ ft}^2 \end{gathered}[/tex]The area of the L-shaped figure is equal to 24 ft².
Given f(x)=6(1-x), what is the value of:a) f(-8)_____b) f(x) = -30 _____c) f(x) = 30____d) f(30)_____
Answers
Answer:
a) f(-8) = 54
b) f(x) = -30, x = 6
c) f(x) = 30, x = -4
d) f(30) = -174
Explanation:
Given the function:
f(x) = 6(1 - x)
To find f(-8), we replace x by -8 in the equation and then solve
f(-8) = 6[1 - (-8)8]
= 6(1 + 8)
= 6(9)
= 54
For f(x) = -30, we replace f(x) by -30 and solve for x
-30 = 6(1 - x)
Divide both sides by 6
1 - x = -30/6 = -5
Subtract 1 from both sides
-x = -6
Multiply both sides by -1
x = 6
For f(x) = 30, we replace f(x) by 30 and solve for x
30 = 6(1 - x)
Divide both sides by 6
1 - x = 30/6 = 5
Subtract 1 from both sides
-x = 4
Multiply both sides by -1
x = -4
f(30) = 6(1 - 30)
= 6(-29)
= -174
For a science project, Sammy observed a chipmunk and a squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did the chumpkin hide
Answers
Let x and y be the number of holes dug by the chipmunk and the squirrel, respectively.
Therefore, the number of hidden acorns by each animal is given by the equations below
[tex]\begin{gathered} a_{chipmunk}=3x \\ a_{squirrel}=4y \end{gathered}[/tex]On the other hand, since the squirrel needed 4 fewer holes, and the number of hidden acorns is the same
[tex]\begin{gathered} y=x-4 \\ and \\ a_{chipmunk}=a_{squirrel} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \Rightarrow3x=4y \\ \Rightarrow3x=4(x-4) \\ \Rightarrow3x=4x-16 \\ \Rightarrow x=16 \end{gathered}[/tex]Hence,
[tex]\Rightarrow16*3=48[/tex]The chipmunk hid 48 acorns.[tex]( - 2 \div 5) \leqslant (x + 4) \div 3 \ \textless \ x + 5[/tex]solve the inequalities
Answers
We will solve this problem first, by solving the inequality in the left hand side and next the inequality on the right hand side.
In the left hand side, we have
[tex]-\frac{2}{5}\le\frac{x+4}{3}[/tex]If we move 3 to the left hand side, we obtain
[tex]-\frac{2}{5}\cdot3\le x+4[/tex]which is equal to
[tex]-\frac{6}{5}\le x+4[/tex]Now, if we move 4 to the left hand side as -4, we have
[tex]\begin{gathered} -\frac{6}{5}-4\le x \\ -\frac{6}{5}-\frac{20}{5}\le x \\ \frac{-6-20}{5}\le x \\ -\frac{26}{5}\le x \end{gathered}[/tex]Now, in the right hand side, we have
[tex]\frac{x+4}{3}and if we move 3 to the right hand side, we obtain[tex]x+4<3(x+5)[/tex]we must note that, since 3 is positive, it doesnt flipt the inequality sign. Then, we obtain
[tex]x+4<3x+15[/tex]Now, if we move x to the right hand side we have
[tex]\begin{gathered} 4<3x-x+15 \\ 4<2x+15 \end{gathered}[/tex]and finally, we have
[tex]\begin{gathered} 4-15<2x \\ -11<2x \\ \frac{-11}{2}In summary, we have the following conditions:[tex]-\frac{26}{5}\le x[/tex]and
[tex]\frac{-11}{2}and we must choose one of them. We can see that
[tex]\begin{gathered} -\frac{11}{2}<-\frac{26}{5} \\ \text{because} \\ -5.5<-5.2 \end{gathered}[/tex]Therefore, the answer which fulfil both conditions is
[tex]-\frac{26}{5}\le x[/tex]This is matching:#1 If solving a problem with population growth compounding CONTINUOUSLY, which of the following formulas would you use?#2 If solving a problem with population growth compounding ANNUALLY, which of the following formulas would you use?#3 If solving a problem with population growth compounding QUARTERLY, which of the following formulas would you use?#4 If solving a problem with continuously compounding interest, which of the following formulas would you use?A: A(t)=P(1+r÷n)^ntB: A(t)=Pe^rtC: P(t)=P0(1+r)^tD: P(t)=P0^e^rt
Answers
#1
The formula for continuous compounding is:
[tex]A(t)=P_{}e^{r\cdot t}[/tex]#2
Since the population grows compounding annually, we have that:
[tex]P(t)=P_0(1+r)^t[/tex]#3
For a problem with population growth compounding quarterly, we have to divide the rate between n=4, therefore:
[tex]A(t)=P(1+\frac{r}{n})^{n\cdot t^{}}[/tex]#4
Finally, for continuously compounded interest we have the formula:
[tex]P(t)=P_0e^{r\cdot t}[/tex]