Answers
We are given with an equation and need to find it's solution set also we are given with a condition that m ≠ {0, 1} . So , let's start ;
So we are given with :
[tex]{:\implies \quad \sf \dfrac{6}{m}+2=\dfrac{m+3}{m-1}}[/tex]
First , we will simplify the given Equation and then we will solve it . So , now taking LCM in LHS ;
[tex]{:\implies \quad \sf \dfrac{6+2m}{m}=\dfrac{m+3}{m-1}}[/tex]
Now , Cross Multiplying ;
[tex]{:\implies \quad \sf (m-1)(6+2m)=m(m+3)}[/tex]
[tex]{:\implies \quad \sf m(6+2m)-1(6+2m)=m^{2}+3m}[/tex]
[tex]{:\implies \quad \sf 6m+2m^{2}-6-2m=m^{2}+3m}[/tex]
Now , transposing whole RHS to LHS and collecting like terms ;
[tex]{:\implies \quad \sf (2m^{2}-m^{2})+(6m-2m-3m)-6=0}[/tex]
[tex]{:\implies \quad \sf m^{2}+m-6=0}[/tex]
Now , we will solve this by splitting the Middle term ;
[tex]{:\implies \quad \sf m^{2}+3m-2m-6=0}[/tex]
[tex]{:\implies \quad \sf m(m+3)-2(m+3)=0}[/tex]
[tex]{:\implies \quad \sf (m+3)(m-2)=0}[/tex]
So , now either , m+3 = 0 or m-2 = 0 . On simplification we will get , m = 2 , -3. So m = {-3, 2}
Hence Option 1) {-3, 2} is correct
Related Questions
whats wrong with my answers?
Answers
77a)
[tex]y=0.5x-2\implies y=\cfrac{x}{2}-2\implies \stackrel{x-intercept}{0=\cfrac{x}{2}-2} \\\\\\ 2=\cfrac{x}{2}\implies 4=x\qquad \qquad \boxed{(4~~,~~0)} \\\\\\ \stackrel{y-intercept}{y=0.5(0)-2}\implies y=-2\qquad \qquad \boxed{(0~~,~~-2)}[/tex]
77b)
[tex]y=-0.4x+2\implies y=-\cfrac{4x}{10}+2\implies y=\cfrac{2x}{5}+2 \implies \stackrel{x-intercept}{0=\cfrac{2x}{5}+2} \\\\\\ -2=\cfrac{2x}{5}\implies -10=2x\implies \cfrac{-10}{2}=x\implies -5=x~\hfill \boxed{(-5~~,~~0)} \\\\\\ \stackrel{y-intercept}{y=-0.4(0)+2}\implies y=2\qquad \qquad \boxed{(0~~,~~2)}[/tex]
please solve!!!!!!!!!!!!!!!!!!!!!!!
Answers
Solution:
We know that:
[tex]\bullet \ \ \tex\text{Area of triangle:} = \frac{1}{2} \times \tex\text{Base} \times \tex\text{Height}[/tex]
Let the base of the triangle be 11 yd. If we extend the base, it will allow us to find the height of the triangle, which is 8 yd.
Using the formula:
[tex]\bullet \ \ \tex\text{Area of triangle:} = \frac{1}{2} \times 11 \times 8[/tex]
Now, let's simplify.
[tex]\bullet \ \ \tex\text{Area of triangle:} = \frac{1}{2} \times 11 \times 8[/tex]
[tex]\bullet \ \ \tex\text{Area of triangle:} = 11 \times 4[/tex]
[tex]\boxed{\bold{\tex\text{Area of triangle:} = 44 \ \tex\text{yd}^{2}}}[/tex]
Find an equation of a square root curve of the form
= √ + that approximately contains the points
(3,7) and (6, 8)
Answers
Answer:
y = √(5x+34)
Step-by-step explanation:
The regression formula that matches a square root function to these points can be worked out by a suitable calculator. The attachments shows the points are matched exactly by the function ...
y = √(5x+34)
__
If you would like to work this by hand, you can put the (x, y) point values into the proposed equation and see what the coefficients need to be:
y = √(ax +b)
7 = √(3a +b) ⇒ 49 = 3a +b
8 = √(6a +b) ⇒ 64 = 6a +b
Subtracting the first equation from the second, gives ...
(64) -(49) = (6a +b) -(3a +b)
15 = 3a ⇒ a = 5
49 = 3(5) +b ⇒ b = 34
A pair of shoes usually sells for $59. If the shoes are 40% off, and sales tax is 8%, what is the total price of the shoes including tax?
A.
$41.42
B.
$38.23
C.
$38.59
D.
$40.12
Answers
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{40\% of 59}}{\left( \cfrac{40}{100} \right)59}\implies 23.6~\hfill \underset{sale~price}{\stackrel{59~~ - ~~23.6}{35.4}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{8\% of 35.4}}{\left( \cfrac{8}{100} \right)35.4}\implies 2.832~\hspace{10em}\underset{\textit{sale price plus tax}}{\stackrel{35.4~~ + ~~2.832}{\approx 38.23}}[/tex]
Estimate 26 % of 160.
Answers
Answer:
about 42 the not rounded is 41.6
Answer:
60
Step-by-step explanation:
Multiply to find that the answer is: 41.6
To estimate, simply round the numbers before multiplying. That would be thirty percent of 200. The answer is 60. This is close to 41.6 and is a reasonable estimate.
M is directionally proportional to r^3. when r=4, M=160. work out value of M if r=2
Answers
Answer:
M = 20
Step-by-step explanation:
given M is directly proportional to r³ then the equation relating them is
M = kr³ ← k is the constant of proportion
to find k use the condition when r = 4, M = 160 , then
160 = k × 4³ = 64k ( divide both sides by 64 )
[tex]\frac{160}{64}[/tex] = k , then
k = 2.5
M = 2.5r³ ← equation of proportion
when r = 2 , then
M = 2.5 × 2³ = 2.5 × 8 = 20
PLEASE HELP ME!!!! All three friends want to purchase the same gaming system so they can play games together. The list price of the gaming system is 349.99 How much will each friend pay for the gaming system?
Answers
Answer:
116.663333333 repeating
Step-by-step explanation:
do 349.99 divided by 3
Covert 6 pounds and 4 ounces into ounces
Answers
Answer:
6 pounds = 96 ounces
4 pounds = 64 ounces
4 pounds is: 64 ounces
Assume that in a local city it rains once every 7 days, on average. Also, assume that a full moon occurs once every 29 days. If we select a random date on the calendar, what is the probability that there will be rainfall and a full moon on that date.
Answers
The events of rainfall and having a full moon on a given date are illustrations of probability
The probability that there will be rainfall and a full moon on that date is 0.0049
How to determine the probabilityFrom the question, we have the following parameters
P(A) = 1/7 --- the probability that it rains
P(B) = 1/29 --- the probability of having a full moon
So, the probability that is rains and there is a full moon on a given day is:
[tex]p = \frac 17 * \frac 1{29}[/tex]
Simplify
[tex]p = 0.0049[/tex]
Hence, the probability that there will be rainfall and a full moon on that date is 0.0049
Read more about probability at:
https://brainly.com/question/25870256
PLEASE HELP, THIS IS DUE ALREADY AND I AM IN A HUGE HURRY
Answers
Solution:
Note that:
Given equation: y = 8xLet's substitute x as 2 to find out y.
y = 8x=> y = 8(2)=> y = 16Let's substitute x as 4 to find out y.
y = 8x=> y = 8(4)=> y = 32Final answer:
When x = 2, y = 16When x = 4, y = 32Option B is correct.
Solve each equation. a. 8x = 2/3 b. 1 1/2 = 2x c. 5x = 2/7 d. 1/4x = 5 e. 1/5 = 2/3x
Answers
Answer:
a. x = [tex]\frac{1}{12}[/tex]
b. [tex]\frac{1}{4}[/tex] = 1x
c. 3x = [tex]\frac{3}{3}[/tex]
d. x = [tex]\frac{1}{20}[/tex]
e. x = [tex]\frac{10}{3}[/tex]
pls help due in 5 min.
Answers
Answer:
4 containers orange juice
4 containers pinapple
2 containers cranberry
Step-by-step explanation:
1000 milliliters are in a liter
4 liters orange juice, 4*500 = 2,000
4 liters pinapple, 4*500 = 2,000
2 liters cranberry, 2*500 = 1,000
Total 5 liters
Find the value of x if mean of the given data is 4.5
5, 7, 7, 8, x, 5, 4, 3,1 and 2
Answers
Answer:
Step-by-step explanation:
First add what you have.
Sum = 5 + 7 +7+8 + x + 5 + 4 +3 + 1 +2
Sum = x + 42
Now when you divide this by the number of terms, you get
(x + 42) / 10
The answer is 4.5
(x + 42) / 10 = 4.5 Multiply by 10
x + 42 = 4.5 * 10
x + 42 = 45 Subtract 42
x = 45 - 42
x = 3
Providing Brainliest. <3
Answers
Answer:
9/4 seconds
Step-by-step explanation:
Plug 13 into the equation
13=94-16t^2
subtract 94
-81=-16t^2
divide by -1
81=16t^2
take the square root of both sides
9=4t
divide by 4
t=9/4
Please help I don’t understand graphs !
Answers
Answer:
Vertical Asymptote at: x = - 1.5
Slanted Asymptote at: y = -x 9/2
Step-by-step explanation:
See image (I HAVE NO IDEA IF YOUR SUPPOSED TO GIVE THE SLANTED ASYMPTOTE. THE PROBLEM ONLY SAYS VERTICAL AND HORIZONTAL ONLY, SO I GUESS ONLY DRAW THE GREEN LINE, NOT THE PURPLE ONE!)
So only draw the x = - 1.5 line that is green!
At 20 degrees celsius, the ice will melt in 20 minutes. How long will it take to melt in 30 degrees celsius?
Answers
Answer:
13.33
Step-by-step explanation:
Write the equation for an inverse variation
⇒ y = k/x
Where x is degrees and y is minutes
Substitute 20 and 20 for x and y
⇒ 20 = k/20
Multiply both sides by 20 to solve k
⇒ 20 × 20 = 20 × k/20
⇒ k = 400
After solving for k, write an equation for the inverse variation
⇒ y = 400/x
Substitute 30 for x
⇒ y = 400/30
⇒ y = 40/3
⇒ y = 13.3333333333
⇒ y = 13.33
[RevyBreeze]
Find the exact area. See picture for full problem. Please and thank you so very much!(:
Answers
Answer:
384sqrt3
Step-by-step explanation:
The formula for the area of a hexagon is A = 3sqrt3 times s^2 /2
Plug in s = 16 to get A = 3sqrt3 times 16^2 (256) / 2
3sqrt3 times 256 is 768sqrt3
You divide that by 2 to get 384sqrt3
Evaluate m + 7.5, when m = 86
If you can give an answer, what could it be…..?
Answers
Answer: 86 + 7.5 = 93.5
Step-by-step explanation:
A recipe calls for 2 cups of flour and 3 cups of sugar. How many cups of flour would be needed if the amount of sugar were increased to 12 cups?
Answers
Answer:
It would be 8 cups of flour.
Answer:
8 cups
Step-by-step explanation:
Deon runs each lap in 4 minutes. He will run at most 32 minutes today. What are the possible numbers of laps he will run today? Use n for the number of laps he will run today.
Write your answer as an inequality solved for n.
Answers
Answer:
4n ≤ 32
/4 /4
n ≤ 8, he could run less than 8 or just 8 laps,
so possible laps:
1, 2, 3, 4, 5, 6, 7, or 8 laps he could've ran.
I don't understand this
Answers
Answer:
Given that measure 2 is 79 degrees, we know it'll be supplementary to angle 1 meaning that that both angle measures 1 and 2 will equal 180 degrees:
79 + x = 180
-79 -79
x = 101, ∠1 = 101°
Angles 2 and 4 are vertical, so they are congruent meaning they measure the same degrees:
if ∠2 = 79, then ∠4 is also equal to 79°
Now that we found the measure of angle 1, we can determine the measure of angle 3 since they are vertical as well, (vertical angles are congruent, meaning they measure the same degrees):
if ∠1 = 101, then ∠3 is also equal to 101°
What is the effect on the graph of the function f(x)=x^2 when f(x) is changed to f(x+8)?
A. Shifted up
B. Shifted left
C. Shifted right
D. Shifted down
Answers
Answer:
B. Shifted leftStep-by-step explanation:
Initial function is
f(x) = x²Changed function is
f(x + 8)This is best explained when graphed. See below to confirm the correct option
f(x+8)
(x+8)²So
x² is changed to (x+8)²
Change in x
It will shift 8 units left
Option B
Evaluate the expression for t = –2.
|t − 7| HELP PLS IM GIVING 23 POINTS OUT TOO FOR RIGHT ANSWERS!
Answers
Answer:
T=-9
Step-by-step explanation:
write equation from 2 points. I need help with 12 and 11.
Answers
12)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{4}}}\implies \cfrac{-2}{-8}\implies \cfrac{1}{4}[/tex]
now, I used y₂ - y₁ and x₂ - x₁, is pretty much the same slope the other way.
[tex]\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}{5}=\stackrel{m}{\cfrac{1}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-5=\cfrac{1}{4}x-1\implies y=\cfrac{1}{4}x+4[/tex]
13)
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{0}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-2)}}}\implies \cfrac{-2}{-4+2}\implies \cfrac{-2}{-2}\implies 1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_2=m(x-x_2) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{1}(x-\stackrel{x_1}{(-4)}) \\\\\\ y=1(x+4)\implies y=x+4[/tex]
notice, for the point-slope form, we can use either x₁ , y₁ or x₂ , y₂ , doesn't quite matter, so long we use the corresponding coordinates.
Find the value of x.
3x -8°
2x + 1°
Answers
If the angles are equal, then, x = 9.
What is simplification?Simplification of expressions means rewriting the same algebraic expression with no like terms and in a compact manner.
Given are two angles, 3x -8° and 2x + 1°, simplifying by equating them,
3x -8° = 2x + 1°
x = 9
Hence, If the angles are equal, then, x = 9.
For more references on simplification, click;
https://brainly.com/question/2804192
#SPJ6
Jackson went to the mall and found a pair of jeans on sale at American Eagle. The original price of the jeans was $45.50, but they were on sale for 40% off. What was the amount of the discount?
Answers
Answer:
The discount is $18.20 which changes the price of the jeans to $27.30.
A graph titled Population of Ohio has years on the x-axis and population (millions) on the y-axis. Points are at (1930, 7), (1950, 8), (1970, 10.5), (1990, 10.8), (2010, 11.8).
What relationship between the population of Ohio and the number of years is displayed in the scatterplot ?
As the number of years increased, the population increased.
As the number of years increased, the population stayed the same.
As the number of years increased, the population decreased.
As the number of years decreased, the population decreased.
Answers
Answer
A.) As the number of years increased, the population increased.
The sides of a triangle measure 6, 8 and 10 cm. What is the area of the triangle?
Answers
Answer:
24 units²Step-by-step explanation:
The sides of a triangle measure 6, 8 and 10 cm. What is the area of the triangle?
from the data it is a right triangle, 10 cm is the hypotenuse
so
1/2 (6 * 8) =
1/2 * 48 =
24 units²
back again pls help
Answers
Answer:
100
Step-by-step explanation:
Angle x and the angle equaling 100 are vertical angles.
the 45 degree angle is just there to confuse you
Find the perimeter and area of a plank of size 300 cm * 30 cm
Answers
Given :
Length of the plank = 300 cm.Breadth of the plank = 30 cm.⠀
To Find :
The perimeter and area of the plank.⠀
Solution :
Perimeter of the plank :
[tex]\: {\qquad \dashrightarrow \sf 2 \times (Length + Breadth) }[/tex]
[tex]\: {\qquad \dashrightarrow \sf{{ 2 \times (300 + 30) \: cm }}}[/tex]
[tex]\: {\qquad \dashrightarrow \sf{{ 2 \times (330) \: cm }}}[/tex]
[tex]\: {\qquad \dashrightarrow \sf{{ 600 \: cm }}}[/tex]
⠀
Area of the plank :
[tex]\: {\qquad \dashrightarrow \sf (Length \times Breadth) }[/tex]
[tex]\: {\qquad \dashrightarrow \sf (330 \times 30) \: {cm}^{2} }[/tex]
[tex]\: {\qquad \dashrightarrow \sf 9 000 \: {cm}^{2} }[/tex]
⠀
Step-by-step explanation:
Given :-
Length = 300cmWidth = 30 cmTo find :-
Perimeter and area of plankSolution :-
Perimeter of rectangular plank = 2(L+W)
putting the values,
perimeter = 2(300+30)cm
⇝660 cm
Area of rectangular plank = L × W
putting the known values ,
Area = 300 × 30 cm²
⇝ 9000cm²