L is the midpoint of MN¯¯¯¯¯¯¯, ML=2x+7 and LN=3x−3. Find ML, LN, and MN.
Answers
Answer:
Step-by-step explanation:
Since L is the midpoint of MN, by the definition of midpoint:
We can picture the following segment:
M----------L----------N
We know that and
. Since the two segments are equivalent, we can set them equal to each other:
Now, let's solve for x. Subtract -7 from both sides:
Subtract 3x from both sides:
Divide both sides by -1:
So, the value of x is 10.
With this, we can find the remaining lengths.
We know that ML is .
Substitute 10 for x. So, the length of ML is:
We know that LN is . So, the length of LN is:
Finally, MN will be the combined lengths of ML and LN. So:
And we're done!
The lengths of each segment are:
ML = 27, LN = 27, and MN = 54.
We have,
Let's use the information given to find the values of ML, LN, and MN.
ML = 2x + 7
LN = 3x - 3
L is the midpoint of MN, which means that ML is equal to LN:
2x + 7 = 3x - 3
Now, let's solve for x:
Move the x term to one side of the equation:
2x - 3x = -3 - 7
-x = -10
Now, multiply both sides by -1 to get rid of the negative sign:
x = 10
Now that we have the value of x, we can find the lengths ML, LN, and MN:
ML = 2x + 7
ML = 2(10) + 7
ML = 20 + 7
ML = 27
LN = 3x - 3
LN = 3(10) - 3
LN = 30 - 3
LN = 27
MN = ML + LN
MN = 27 + 27
MN = 54
Thus,
The lengths of each segment are:
ML = 27, LN = 27, and MN = 54.
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Answers
The inequality representing the statement "The quotient of the sum of 3 and a number and 6 is less than -2" is \(x < -15\), indicating that any number less than -15 satisfies the condition.
Let's translate the given statement into an inequality.
"The quotient of the sum of 3 and a number and 6 is less than -2."
Let "x" represent the unknown number.
The sum of 3 and a number is 3 + x.
The quotient of that sum and 6 is .
Now, we can write the inequality:
To solve for "x," we can multiply both sides of the inequality by 6 to get rid of the fraction:
3 + x < -12
Now, subtract 3 from both sides to isolate "x":
x < -12 - 3
x < -15
So, the inequality representing the given statement is x < -15. This means that any number lessthan -15 will make the quotient less than -2.
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Explanation:
It’s an inequality:
Quotient: division
Sum: addition
A number: the variable, n
3x-4y=27
A.7x=29
B.x=-23
C.7x=35
D.4x=29
Answers
Final answer:
By manipulating and then adding the given system of equations, we can eliminate the variable 'y', resulting in the equation 7x = 35.
Explanation:
To eliminate the variable y in the given system of equations, we need to manipulate the equations to cancel out the y term. The system of equations is:
x + y = 2
3x - 4y = 27
We can accomplish y-elimination by first multiplying the first equation by 4 to match the coefficient in front of y in the second equation. The equations now are:
4x + 4y = 8
3x - 4y = 27
Now, we can add the two equations together, effectively eliminating the y-variable:
4x + 3x = 8 + 27
7x = 35
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Answer:
C
Step-by-step explanation:
x + y = 2
Subtract x from both sides;
y = -x + 2
3x - 4y = 27
Substitute y;
3x - 4(-x + 2) = 27
Distribute;
3x + 4x - 8 = 27
7x - 8 = 27
Add 8 to both sides;
7x = 35
Divide both sides by 7;
x = 5
Answers
9×11+12×11+(2×0.5×9×12)+11×15=
=99+132+108+165=504cm²
the motorcycle travel in 3 hours?
Answers
Answer:
93
Step-by-step explanation:
62/2=31
31x3=93
Answer:
93 miles
Step-by-step explanation:
62 miles/2 hours= 31 mph
31+62= 93 miles
Answers
=LCM OF DENOMINATORS
=90
=60+75+72/90
=207/90
=2.3