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Korolek [52]
3 years ago
5

Find the length of LM if L is the midpoint of NM. NL = 3x + 1, LM = 8x - 24.

Mathematics
1 answer:
SashulF [63]3 years ago
8 0

Answer:

LM = 16

Step-by-step explanation:

From the question given:

L is the midpoint of NM

NL = 3x + 1

LM = 8x - 24

LM =?

Next, we shall determine the value of x.

This can be obtained as follow:

Since L is the midpoint of NM, it means that NL and LM are equal i.e

NL = LM

Thus, we can obtain the value of x as follow:

NL = 3x + 1

LM = 8x - 24

NL = LM

3x + 1 = 8x - 24

Collect like terms

3x - 8x = - 24 - 1

-5x = - 25

Divide both side by - 5

x = -25/-5

x = 5

Finally, we shall determine the length of LM as follow:

LM = 8x - 24

x = 5

LM = 8(5) - 24

LM = 40 - 24

LM = 16

Therefore, the length of LM is 16

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Answer <u>(assuming it is allowed to be in point-slope format)</u>:

y-4 = \frac{2}{3}(x-1)

Step-by-step explanation:

1) First, determine the slope. We know it has to be perpendicular to the given equation, y = -\frac{3}{2} x-4. That equation is already in slope-intercept form, or y = mx + b format, in which m represents the slope. Since -\frac{3}{2} is in place of the m in the equation, that must be the slope of the given line.

Slopes that are perpendicular are opposite reciprocals of each other (they have different signs, and the denominators and numerators switch places). Thus, the slope of the new line must be \frac{2}{3}.  

2) Now, use the point-slope formula, y-y_1 = m (x-x_1) to write the new equation with the given information. Substitute m, x_1, and y_1 for real values.

The m represents the slope, so substitute \frac{2}{3} in its place. The x_1 and y_1 represent the x and y values of a point the line intersects. Since the point crosses (1,4), substitute 1 for x_1 and 4 for y_1. This gives the following equation and answer:

y-4 = \frac{2}{3}(x-1)

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3 years ago
What is the slope line ?
Drupady [299]

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Step-by-step explanation:

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3 years ago
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Determine where to place the decimal point in the dividend and divisor so that the quotient is between 23 and 25
timama [110]

Answer:

Place the decimal before the last digit in both number i.e. 1602.3 and 65.4

Step-by-step explanation:

We are given the numerical expression 16023÷654.

Here, we have,

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Divisor = 654

it is required that the quotient of the division to be between 23 and 25.

If we take the numbers,

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This gives us,

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Hence, placing the decimal before the last digit in both number will give the desired result.

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2 years ago
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Alex

Answer:

7x+9

Step-by-step explanation:

f(x)=7x-5

g(x)=x+2

f[g(x)]=  Substitute g(x) in for x in the function f(x)

           =7(g(x))-5

          = 7( x+2) - 5

Distribute

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Combine like terms

           =7x +9

5 0
3 years ago
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baherus [9]

Answer:

4/5

Step-by-step explanation:

Okay, I'm pretty sure about this one! I might be wrong but:

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I might have done this wrong, but I hope it helps!! Have a nice day c:

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