Solve: 3x - 2x + 4 = 5x - 4x - 8
2 answers:
The equation has
.
Further explanation:
Given:
The equation is .
Calculation:
The above equation involves only one variable.
To solve a one variable linear equation, arrange all the terms that contain variable on one side and the terms that are free from variable on the other side.
Write the given equation by taking terms that contains variable on left side and the terms which are free from variables on right side.
Subtract from both the sides of the given equation.
Subtract from both the sides of the above equation,
The above equation shows that the value of is equal to
.
The statement “0 is equal to -12” is a false statement.
Therefore, the equation has no solution.
No solution means there exists no value of that satisfies the given equation.
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Linear equation
Keywords: Equation, variable, 3x - 2x + 4 = 5x - 4x – 8, constant, linear equation, no solution, solve, addition, subtraction, isolate, plug, substitute.
Answer:
No solution for the given algebraic expression.
Step-by-step explanation:
To solve the algebraic equation we must isolating the variable or rewriting the equation so that the one expression is only the variable with the coefficient 1.
Solve:
Now put every terms that contains variables on one side of the equation and those terms on the other side which does not contains the variable.
Combine like terms:
which is not true.
therefore, the given expression have NO SOLUTION.
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Answer: About 72 feet
The more accurate value is roughly 71.7260397 feet (however, this value isn't fully exact either).
======================================================
Explanation:
Check out the diagram below. It's effectively the same diagram your teacher provided, but I've added points M and N. I've left out any unnecessary lines.
- M = center of the circle
- N = location where the cable is anchored to the ground
We're told that "(the length of cable from) E to the ground is 35 feet", so this is the red portion of cable that I've marked this as NE = 35, ie segment NE is 35 feet long. We're also told that NF = 40 feet, which is also shown in red.
The blue portions are chords of the circle. We're given one chord as LE = 80 ft, while the other chord JF is what we want to find out.
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What we need to find is the radius of this circle. Right away, it's not clear what the radius is; however, we can use the chord LE = 80 to help find it.
It turns out that the chord length c is connected to the radius r and central angle theta like so:
c = 2*r*sin(0.5*theta)
where theta must be in radian mode. The central angle subtends the arc that forms the chord in question.
If we started at point L, and counted the number of spaces to get to E while going clockwise, then we can see that there are 5 spaces
Those five spaces could be written as
- The jump from L to A
- The jump from A to B
- The jump from B to C
- The jump from C to D
- The jump from D to E
Or you could mark it as such on the diagram for a visual reference. Overall, the circle has been cut into 12 equal slices. So going from L to E, going clockwise, will have us take up 5/12 of the full circle.
There are 2pi radians in a full circle, meaning the central angle LME is (5/12)*2pi = 5pi/6 radians.
-----------------
Plug theta = 5pi/6 and c = 80 into the formula mentioned. Isolate the radius.
c = 2*r*sin(0.5*theta)
80 = 2*r*sin(0.5*5pi/6)
80 = 2*r*sin(5pi/12)
80 = 2*r*0.9659258
80 = 2*0.9659258*r
80 = 1.9318516r
1.9318516r = 80
r = 80/1.931 8516
r = 41.4110483
The radius is approximate. The radius is in feet. Make sure your calculator is in radian mode.
-----------------
Now that we know the radius, we can determine how long chord JF is.
The central angle for chord JF is angle JMF
If we start at J and go to F, along the shorter path, then we've gone 4 spaces. This is 4/12 = 1/3 of the full circle. So the radian measure of angle JMF is (1/3)*2pi = 2pi/3 radians.
So,
c = 2*r*sin(0.5*theta)
c = 2*41.4110483*sin(0.5*2pi/3)
c = 71.7260397
Chord JF is roughly 71.7260397 feet long.
When rounding to the nearest foot, that's about 72 feet.
