Determine the height of the lift, in metres, above the gym floor. show all your work algebraically. round to the nearest cm, if necessary.
Answers
Height of lift = x + x = 2x
We can find x using triangle ABC by the cosine rule
[tex]\begin{gathered} x^2=5.6^2+5.6^2-2(5.6)(5.6)\cos40^0 \\ x^2=62.72-48.04352 \\ x^2=14.67648 \\ x=\sqrt{14.67648} \\ x=3.831m \end{gathered}[/tex]Height of lift = 2 X 3.831m = 7.662m
This will be converted to cm by multiplying by 100
Height of lift = 7.662 X 100 cm
= 766.2 cm
= 766cm ( nearest cm )
Hence the answer is 766cm
Related Questions
you are 5 feet and 4 inches tall and cast a shadow 6 feet long. At the same time , a nearby tree cast a shadow 40 feet 6 inches long. Find the heigh of the tree.
Answers
The height of the tree is such that it cast a shadow 40 feet 6 inches long and maintains the given ratio will be 36 feet.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
As per the given question,
The height of a person is 5 feet and 4 inches.
Since 1 feet = 12 inches so 4 inches = 1/3 feet
Therefore,height of a person = 5 + 1/3 = 16/3 feet
Its shadow length = 6 feet
The ratio of the height to shadow length = (16/3)/6
Now, the shadow of the tree = 40 feet and 6 inches so 40.5 feet
Let's say its length was x feet.
Then x/40.5 = (16/3)/6
x = 36 feet
Hence "The height of the tree is such that it cast a shadow 40 feet 6 inches long and maintains the given ratio will be 36 feet".
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Find the average rate of change of f(x)=x^2-4x+1 from x=2 to x=6
Answers
Answer:
The answer is 4
Select the correct answer..What is the value of i^ if the remainder of 4 is 2?OA. -i'OB.-1Ос. іOD. 1ResetNext
Answers
1) Considering that for that complex number we have the following pattern:
[tex]\begin{gathered} i^1=i \\ i^2=-1 \\ i^3=-1\cdot i=-i \\ i^4=-1\cdot-1=1 \end{gathered}[/tex]2) And that, the question asks us about the what number must be that exponent so that the remainder is 2, we can write out:
[tex]\frac{n}{4}=4d+2[/tex]which d is the divisor, so if the remainder is 2 then we can state:
[tex]i^n=i^2=-1[/tex]Hello! I need some help with this homework question, please? The question is posted in the image below. Q15
Answers
ANSWER:
A.
[tex]x=-1,-3,11[/tex][tex]f(x)=(x+3)(x-11)(x+1)[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)=x^3-7x^2-41x-33[/tex]To find the zeros of the function we must set the function equal to 0 in the following way:
[tex]x^3-7x^2-41x-33=0[/tex]We reorganize the equation in order to be able to factor and calculate the zeros of the function, like this:
[tex]\begin{gathered} x^3-7x^2-41x-33=0 \\ -7x^2=-8x^2+x^2 \\ -41x=-33x-8x \\ \text{ Therefore:} \\ x^3-8x^2+x^2-33x-8x-33=0 \\ x^3-8x^2-33x=-x^2+8x+33 \\ x(x^2-8x-33)=-(x^2-8x-33) \\ x^2-8x-33 \\ -8x=3x-11x \\ x^2+3x-11x-33 \\ x(x+3)-11(x+3) \\ (x+3)(x-11) \\ \text{ we replacing} \\ x(x+3)(x-11)=-1 \\ x(x+3)(x-11)+(x+3)(x-11)=0 \\ (x+3)(x-11)(x+1)=0 \\ x+3=0\rightarrow x=-3 \\ x-11=0\rightarrow x=11 \\ x+1=0\rightarrow x=-1 \end{gathered}[/tex]Therefore, the zeros are:
[tex]x=-1,-3,11[/tex]And in its factored form the expression would be:
[tex]f(x)=(x+3)(x-11)(x+1)[/tex]What is the value of the expression 2c( a + b) when a = 2, b = 5, and c = 4
Answers
The given expression is
2c(a + b)
From the information given,
a = 2
b = 5
c = 4
By substituting these values into the expression, it becomes
2 * 4(2 + 5)
= 8(7)
= 56
The value of the expression is 56
Line g passes through the points (-2.6,1) and (-1.4.2.5), as shown. Find theequation of the line that passes through (0,-b) and (c,0).
Answers
The blue line passes through the points
(-2.6, 1) and (-1.4, 2.5)
I will label the coordinates as follows for reference:
[tex]x_1=-2.6,y_1=1,x_2=-1.4,y_2=2.5[/tex]Step 1: Find the slope of the blue line
The slope between two points is calculated with the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We substitute the values and we get that the slope of the blue line is:
[tex]m=\frac{2.5-1}{-1.4-(-2.6)}=\frac{1.5}{1.2}=1.25[/tex]The slope m of the blue line is 1.25.
step 2: With that slope, calculate b (the intercept of the blue line with the y axis).
For this we use the point - slope equation:
[tex]y=m(x-x_1)+y_1[/tex]Where we will use the sane x1 and x2 as in the previous step, so we get
[tex]\begin{gathered} y=1.25(x-(-2.6))+1 \\ y=1.25(x+2.6)+1 \\ y=1.25x+3.25+1 \\ y=1.25x+4.25 \end{gathered}[/tex]We compare this with the slope-intercept equation
[tex]y=mx+b[/tex]And we can see that the incercept b is 4.25
[tex]b=4.25[/tex]step 3: Find the value of c.
to find the value of c, we need to know at which point the blue line crosses the x axis.
Since we already have the equation of the blue line y=1.25x+4.25, and the line crosses the x axis at y=0, we substitute this to find the x value that is equal to c:
[tex]\begin{gathered} 0=1.25x+4.25 \\ -4.25=1.25x \\ \frac{-4.25}{1.25}=x \\ -3.4=x \end{gathered}[/tex]The blue line crosses the x axis at (-3.4,0), thus we can conclude that
[tex]c=-3.4[/tex]Step 4: Define the two point where the orange line passes through.
We know from the picture that the orange line passes through (c,0) and (0,-b)
Since we have the values of c = -3.4 and b=4.25, we can say that the orange line passes through (-3.4, 0) and (0, -4.25)
Step 5: Calculate the slope of the orange line.
the orange line passes through (-3.4, 0) and (0, -4.25), so we define:
[tex]undefined[/tex]PLS HELP Rewrite the following equation in slope-intercept form.
y + 8 = –3(x + 7)
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Step by step
An equation in the slope-intercept form is written as. y=mx+b.
m is the slope of the line and b is the y-intercept.
y +8 = -3x -21
Subtract 8 from both sides to isolate y
y + 8 - 8 = -3x -21 -8
y = -3x -29
Answer:
[tex] \sf \: y = -3x - 29[/tex]
Step-by-step explanation:
Given equation,
→ y + 8 = -3(x + 7)
The slope-intercept form is,
→ y = mx + b
Let's rewrite the equation,
→ y + 8 = -3(x + 7)
→ y + 8 = -3x - 21
→ y = -3x - 21 - 8
→ [ y = -3x - 29 ]
Thus, answer is y = -3x - 29.
Subtracting algorithm
Answers
Using subtracting algorithm, we have 69,000 - 42,547 = 26,453 and 152,681 - 34,820 = 117,861.
According to the question,
We have the following expressions:
_ _ , 0 0 0
-4 2, _ _ _
_________
2 6 , 4 5 3
Now, we will first solve this.
The spaces has to be filed with the digits from 0 to 9 and in both the questions, no digit has to be repeated.
Now, we will solve it from the right hand side.
(Note that we will solve each row that is we will solve vertically.)
0 is given, then we have blank, and in result we have 3.
It is clear that no number can be subtracted from 0. So, we have to regroup it from other digits. So, it will be 10.
Now, 10-3 = 7
So, this blank will be 7.
Now, come to next one.
We have 0 and a blank and then 5 in the result.
Now, it should be 9 because 1 was taken away from it.
So, 9-5 = 4
This blank has to be filled with 4.
Now, we will solve next one.
We have 0, a blank and then 4 in the result.
Now, this 0 will make 9.
9-4 = 5
This blank has to be filled with 5.
Now, we have a blank, 2 and 6 in the result.
1 has been carried from this digit.
So, we have:
6+2+1 = 9
This blank has to be filled with 9.
Next, we have a blank, 4 and 2 in the result.
4+2 = 6
This has to be filled with 6.
Now, we will solve the second question like this.
_ 5 2, 6 8 1
- _ 4, _ _ _
__________
1 1 7, 8 6 1
Now, moving from right to left vertically:
We have 1, a blank and 1 in the result.
1-1 = 0
Blank = 0
We have 8, a blank and 6 in the result.
8-6 = 2
Blank = 2
We have 6, a blank and 8 in the result.
Now, 8 can not be subtracted from 6. So, it has to be 16.
16-8 = 8
Blank = 8
Now, next one is complete.
So, we have next one.
We have 5, a blank and 1 in the result.
We will subtract 1 from 4 because 1 was carried away from 5.
4-1 = 3
Blank = 3
Now, we have a blank and 1 in the result.
Blank = 1
Hence, the answers would be 69,000 - 42,547 = 26,453 and 152,681 - 34,820 = 117,861.
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help me pleaseeeeeeeee
Answers
Answer:
A. 200
B. 500
Step-by-step explanation:
1000x²
R(x) = --------------
x² + 4
x = years
A. the first year = 1
1000(1)²
R(1) = --------------
(1)² + 4
1000
R(1) = --------------
1 + 4
1000
R(1) = --------------
5
R(1) = 200
B. years = 2
1000(2)²
R(2) = --------------
(2)² + 4
1000(4)
R(2) = --------------
4 + 4
4000
R(2) = --------------
8
R(2) = 500
I hope this helps!
How do I solve it and what would be the answer
Answers
The quotient is x² + 4x + 3
Yes, (x - 2) is a factor of x³ + 2x² - 5x - 6
Explanation:[tex](x^3+2x^2\text{ - 5x - 6) }\div\text{ (x - 2)}[/tex][tex]\begin{gathered} x\text{ - 2 = 0} \\ x\text{ = 2} \\ \\ \text{coefficient of }x^3+2x^2\text{ - 5x - 6:} \\ 1\text{ 2 -5 -6} \\ \\ We\text{ will divide the coefficients by 2} \end{gathered}[/tex]Using synthetic division:
[tex]\begin{gathered} (x^3+2x^2\text{ - 5x - 6) }\div\text{ (x - 2) = }\frac{(x^3+2x^2\text{ - 5x - 6)}}{\text{(x - 2)}} \\ \frac{(x^3+2x^2\text{ - 5x - 6)}}{\text{(x - 2)}}\text{ = quotient + }\frac{remai\text{ nder}}{\text{divisor}} \\ \\ The\text{ coefficient of the quotient = 1 4 3} \\ \text{The last number is zero, so the remainder = 0} \end{gathered}[/tex][tex]\begin{gathered} \frac{(x^3+2x^2\text{ - 5x - 6)}}{\text{(x - 2)}}=1x^2\text{ + 4x + 3 + }\frac{0}{x\text{ - 2}} \\ \text{quotient }=\text{ }x^2\text{ + 4x + 3} \end{gathered}[/tex]For a (x - 2) to be a factor of x³ + 2x² - 5x - 6, it will not have a remainder when it is divided.
Since remainder = 0
Yes, (x - 2) is a factor of x³ + 2x² - 5x - 6
The vertices of a rectangle are located at A(4, -1), B(-4, -1), C(-4, 6), and D(4, 6). What is the distance between the side AB and BC respectively?
Answers
The coordinates of the vertices of a rectangle are:
[tex]\begin{gathered} A\left(4,-1\right) \\ B\left(-4,-1\right) \\ C\left(-4,6\right) \\ D\left(4,6\right) \end{gathered}[/tex]Plotting these points:
The figure shows two right triangles, each with its longest side on the same line. Z 3 X T y 2 R. S 1. Explain how you know the two triangles are similar 2. How long is XY? 3. For each triangle, calculate (vertical side) = (horizontal side). 4. What is the slope of the line? Explain how you know.
Answers
The triangle are similar because the ratio between 2 sides is the same as the ratio between another 2 sides.
The included angle(angle S and Y) are equal( 90 degree)
if you're lonely then be lonely with me but I need your help
Answers
Let's use distributive property to simplify:
[tex]-35-5x+2\frac{5}{6}x=0[/tex]Now we add up the x's and take number to another side:
[tex]\begin{gathered} -5x+2\frac{5}{6}x=35 \\ -2\frac{1}{6}x=35 \end{gathered}[/tex]We make 2 and one-sixth into improper fraction and divide to get x:
[tex]\begin{gathered} -\frac{13}{6}x=35 \\ x=\frac{35}{-\frac{13}{6}} \\ x=35\cdot-\frac{6}{13}=-\frac{210}{13} \end{gathered}[/tex]x is "minus 210 over thirteen"
Write an inequality:Carlos was going to sell all of his stamp collection to buy a video game. After selling half of them he changed his mind. He then bought twelve more. How many did he start with if he now has at least 29?
Answers
Answer:
He started with at least 34 stamp collection
Explanation:
Let x represent Carlos' initial stamp collection.
From the question, we're told that he sold half of them, bought twelve more, and currently has at least 29, we can go ahead and set up an inequality as shown below;
[tex]\frac{x}{2}+12\ge29[/tex]We can go ahead and solve for x following the below steps;
Step 1: Subtract 12 from both sides of the equation;
[tex]\begin{gathered} \frac{x}{2}+12-12\ge29-12 \\ \frac{x}{2}\ge17 \end{gathered}[/tex]Step 2: Multiply both sides by 2;
[tex]\begin{gathered} \frac{x}{2}\times2\ge17\times2 \\ x\ge34 \end{gathered}[/tex]From the above, we can say that Carlos started with at least 34 stamp collection
A company plans a major investment and theamount of profit is uncertain, but researchersgive the following estimate for the distribution.1.5210Profit(inmillions)Probability0.10.20.40.20.1What is the expected value of the profit?[?] million dollars
Answers
The expected value is the return you expect from some kind of investment/action.
When we are presented with probabilty of an action, we can take the expected value of the whole table [investment] by taking the sum of the products of probability and the action.
Here, we want products of "probability" and "profit". Then we sum it. Shown below:
[tex]\begin{gathered} E=(0.1)(1)+(0.2)(1.5)+(0.4)(2)+(0.2)(4)+(0.1)(10) \\ E=3 \end{gathered}[/tex]Expected value of profit = 3 million dollarsGiven the median QR and trapezoid MNOP, what is the value of X?M3.8033Rکد 73PA. 6B. 19(C. 2D, 5E 7F. Cannot be determined
Answers
SOLUTION
Consider the diagram below
Applying the rule in the diagram above, we have
[tex]|QR|=\frac{1}{2}(|ON|+|PM|)[/tex]Recall from the questions
[tex]\begin{gathered} |QR|=33 \\ |ON|=3x-8 \\ |PM|=7x+4 \end{gathered}[/tex]Then we substitute the parameters above into the expression above
[tex]\begin{gathered} 33=\frac{1}{2}(3x-8+7x+4) \\ \text{ Multiply both sides by 2} \\ 66=3x-8+7x+4 \\ \text{rerrange the terms and simplify } \\ 66=10x-4 \\ \text{collect like terms } \\ 66+4=10x \end{gathered}[/tex]simplify further
[tex]\begin{gathered} 70=10x \\ \text{divide both sides by 10} \\ x=\frac{70}{10} \\ \text{then} \\ x=7 \end{gathered}[/tex]Therefore the value of x is 7
Therefore the right option is E
The schedule for summer classes is available and Calculus and Introduction to Psychology are scheduled at the same time, so it is impossible for a student to schedule for both courses. The probability a student registers for Calculus is 0.05 and the probability a student registers for psychology is 0.62. What is the probability a student registers for Calculus or psychology?
Answers
Explanation
The given is that the probability a student registers for Calculus is 0.05 and the probability a student registers for psychology is 0.62. Since it impossible for a student to schedule for both courses, we will have
[tex]\begin{gathered} Pr(Psychology\text{ or calculus\rparen=Pr\lparen P\rparen+Pr\lparen C\rparen-Pr\lparen P}\cap C) \\ =0.05+0.62-0 \\ =0.67 \end{gathered}[/tex]Answer: 0.67
PLEASE ANSWER ASAP1. The length of a bookshelf is 5 ft. The length of a model of this bookshelf is 3 ft. Find the scale of the model to the bookshelf. Enter your answer in the box.2. A rectangular garden has a length of 8 ft and a width of 4 ft. A smaller garden was made, using a scale of 3:4 . Find the dimensions of the smaller garden. Enter your answers in the boxes.
Answers
1.
The scale factor would be:
[tex]3\colon5[/tex]2.
Divide each original dimension by 4 and then multiply by 3, as following:
[tex]\begin{gathered} \frac{8ft}{4}\cdot3=6ft \\ \\ \frac{4ft}{4}\cdot3=3ft \end{gathered}[/tex]The smaller garden has a length of 6 ft and a widht of 3 ft
What is the procedure for 31/4-17/8= I'm getting 25/8
Answers
Evaluate the value of the expression:
[tex]3\frac{1}{4}-1\frac{7}{8}[/tex]Step 1: The mixed fraction will be converted to improper fraction
[tex]\begin{gathered} 3\frac{1}{4}-1\frac{7}{8} \\ =\frac{3\times4+1}{4}-\frac{1\times8+7}{8} \\ =\frac{12+1}{4}-\frac{8+7}{8} \\ =\frac{13}{4}-\frac{15}{8} \end{gathered}[/tex]Step 2: The denominator of 8 will be used as the L.C.M, since it's the greatest of the two
[tex]\begin{gathered} \frac{13}{4}-\frac{15}{8} \\ =\frac{26-15}{8} \\ =\frac{11}{8} \\ =1\frac{3}{8} \end{gathered}[/tex]Hence the correct answer = 1 3/8
[tex]1\frac{3}{8}[/tex]ive tried to do this question multiple times but i just cant seem to understand it
Answers
The domain of the function which is the entire x values during the strike is
[tex]0\leq x\leq230[/tex]Using the origin as the center of dilation and a scale factor of k=1/2 find the coordinates of the vertices of the image of the polygon below
Answers
Given
Using the scale of 1/2
This means we divide each coordinate by 2
[tex]\begin{gathered} (0,3)=(0,1.5) \\ (-4,0)=(-2,0) \\ (2,0)=(1,0) \\ (0,-3)=(0,-1.5)_{} \end{gathered}[/tex]The science class is taking a trip to the science center. there are 20 students and an unknown number of adult chaperones going. the bus holds at most 35 people.what is the greatest number of adults who can chaperone? I know the answer is 15. however, what they want us to do is create an equation using inequalities (<, >, etc..) That's what I don't know how to do with this problem. I'm trying to explain it to my daughter but I don't know how to do it myself.
Answers
We are given that there are 20 students and an unknown number of adult chaperones.
Let x denotes the unknown number of adult chaperones.
The bus holds at most 35 people
We know that 20 students plus x number of adult chaperones should be at most 35
at most 35 means equal or less than 35
So we can write
[tex]20+x\le35[/tex]Now we can easily solve for x
[tex]\begin{gathered} 20+x\le35 \\ x\le35-20 \\ x\le15 \end{gathered}[/tex]Multiplying Polynomials 5y[tex] ({5y}^{2} + y + 3)(x - 2)[/tex]
Answers
Let's distribute those factors, and expand this:
[tex]\begin{gathered} (5y^2+y+3)\mleft(x-2\mright) \\ 5xy^2-10y^2+xy-2y+3x-6 \\ \end{gathered}[/tex]There's no further way beyond that. Either we pick the factored form or the expanded version of that polynomial. As this is not an equation we stop it here.
Martin Brothers Moving rents moving vans by the hour. The company charges a flat fee of $17.99, plus an additional $19.99 per hour. One customer pays $57.97 for her rental. How long was her rental?
Answers
Let h be the number of hours that the customer rented the van, then we can set the following equation:
[tex]19.99h+17.99=57.97.[/tex]Subtracting 17.99 from the above equation we get:
[tex]\begin{gathered} 19.99h+17.99-17.99=57.97-17.99, \\ 19.99h=39.98. \end{gathered}[/tex]Dividing by 19.99 we get:
[tex]\begin{gathered} \frac{19.99h}{19.99}=\frac{39.98}{19.99}, \\ h=2. \end{gathered}[/tex]Answer: 2 hours.
Question 10
Answer:
Not yet answered Marked out of 2.00
A tyre made of rubber (density 1.2 g/cm³) has a mass of 3.6 kg.
Find its volume.
(Use ^sign from the computer's keyboard to express the power of the units for the volume
Question 11
Not yet answered Marked out of 1.00
Flag question
What percentage of the grid is shaded?
PFlag question
Answers
1.volume = mass*density
v = 1.2 * 3.6 = 4.32 cm3
The density of a substance quantifies how tightly its molecules are packed, which affects how heavy or light it is.
Density is calculated as follows: density=mass/volume. Most often, mass is measured in grams or kilograms. Most often, volume is measured in cubic centimeters (cm3), cubic meters (m3), or millileters (mL).
How can you find mass from density?
multiply the volume by the density.
Mass per unit volume is the definition of density.
ρ = m V
This can be rearranged to yield the mass expression.
m = ρ × V
Example:
What mass of the liquid is present if 500 mL of it has a density of 1.11 g/mL
m = ρ × V = 500 mL × 1.11 g
1 mL = 555 g
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Question #3 3) The digits of a 2-digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, we get 99. Find the original number.
Answers
ones number = x
Tens number = y
y>x
Number at the tens place y = (x+5)
original number = 10 (x+5)+x
Interchange digits:= 10x+(x+5)
original number + new number = 99
¨[10(x+5)+x]+ [10x+ (x+5)] =99
Solving for x:
(10x+50+x )+( 10x+x+5) = 99
Combine like terms
(11x+50) + (11x+5) = 99
11x+11x+50+5 =99
22x+55 =99
subtract 55 from both sides
22x +55-55= 99-55
22x = 44
Divide both sides by 22
22x/22= 44/22
x = 2
unit place: 2
tens place = x+5 = 2+5 = 7
original number = 72
What is the probability that a random selected yard will have fewer than 6 trees
Answers
Based on the given histogram on yards and the number of trees they have, the probability that a random selected yard will have fewer than 6 trees is 60%
How to find the probability?The probability that in a random yard, the number of trees would be less than 6 trees can be found by the formula:
= Proportion of yards with 0 - 2 trees + Proportion of yards with 2 - 4 trees + Proportion of yards with 4 - 6 trees
The probability that a random yard would have fewer than six trees is therefore:
= 0.35 + 0.20 + 0.05
= 0.60
= 60%
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Permutation/combination In how many ways can five people line up to get on a bus? (Hint: all 5 people are lining up)
Answers
We have to calculate in how many ways can five people line up to get on a bus.
This is a permutation of 5 in 5 without repetition, so it can be calculated as:
[tex]P(5,5)=5!=120[/tex]Answer: in 120 ways.
triangle OPQ is similar to triangle RST. Find the measure of side RS. Round your answer to the nearest tent if necessary
Answers
To answer this question, we have that, if two triangles are similar, they maintain the same proportion on their corresponding sides.
We have that the corresponding sides are QP and TS, OP and RS, and QO and TR, so we can write:
[tex]\frac{TS}{QP}=\frac{RS}{OP}=\frac{TR}{QO}[/tex]Then, since we have the values for QP, TS, and OP, we can find RS using the above proportion:
[tex]\frac{TS}{QP}=\frac{RS}{OP}\Rightarrow\frac{41.4}{11}=\frac{RS}{8}\Rightarrow RS=\frac{41.4\cdot8}{11}=\frac{331.2}{11}\Rightarrow RS=30.109090\ldots[/tex]Then, we have that we can round this value to 30.11 units, and if we round the answer to the nearest tenth, we finally have that RS = 30.1 units.
Answer:
x = 30.1 (round 30)
Step-by-step explanation:
being similar we can solve with a simple equation
11 : 8 = 41.4 : x
x = 8 × 41.4 : 11
x = 331,2 : 11
x = 30.1 (round 30)
5. Noah is solving an equation and one of his moves is unacceptable. Hereare the moves he made. Which answer best explains why the "divide eachside by x step is unacceptable? *2(3+6) - 4= 8 + 6321 + 12 - 4= 8 + 612.1 + 8 = 8 + 6.120 = 602 = 6original equationapply the distributive propertycombine like termssubtract 8 from both sidesdivide each side by IO When you divide both sides of 2x = 6x by x you get 2x^2 = 6x^2.When you divide both sides of 2x = 6x by x it could lead us to think that there is nosolution while in fact the solution is x = 0..aWhen you divide both sides of 2x = 6x by x you get 2 = 6x.aOWhen you divide both sides of 2x = 6x by x it could lead us to think that there is nosolution while in fact the solution is x = 3..
Answers
SOLUTION
Write out the original equation
[tex]2(x+6)-4=8+6x[/tex]Then, Apply the distributive property on the left hand side of the equation
[tex]\begin{gathered} 2x+12-4=8+6x \\ 2x+8=8+6x \end{gathered}[/tex]Then combine trhe like terms subtracting 6x from both side
[tex]\begin{gathered} 2x+8-6x=8+6x-6x \\ 2x-6x+8=8 \end{gathered}[/tex]Subtract 8 from both sides of the last equation
[tex]\begin{gathered} 2x-6x+8-8=8-8 \\ 2x-6x=0 \\ -4x=0 \\ \end{gathered}[/tex]hence
Divide both sides by -4, we have
[tex]\begin{gathered} -\frac{4x}{-4}=\frac{0}{-4} \\ \text{Then} \\ x=0 \end{gathered}[/tex]Therefore, the solution is x=0
Hence
When we divide both sides of the equation by x, we have
[tex]\begin{gathered} \frac{2x}{x}=\frac{6x}{x} \\ 2=6 \\ \text{which implies thier is no solution} \end{gathered}[/tex]While the solution is x=0
Therefore
When we divide the equation by 2x=6x by x it could lead us to think that there is no solution while the solution is x=0
Answer; The second option is right
