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3 years ago

LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5, find the value of x

2 answers:

5 0

<span>LMNO is a parallelogram
so NM = OL
x + 15 = 3x + 5
solve for x
x - 3x = 5 - 15
-2x = -10
x = 5

Answer
x = 5</span>

ziro4ka [17]3 years ago

4 0

Since LMNO is a parallelogram all the sides are equal so if you take 3x+5 and x+15 youll find that if you replace x with 5 on each side youll end up with 20 total on both sides therefore your answer is x equals 5.

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3 years ago

What are the exact solutions of x2 − 5x − 1 = 0 using x equals negative b plus or minus the square root of the quantity b square

geniusboy [140]

Answer:

$x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}$

Step-by-step explanation:

So the question here is asking you to use the quadratic formula which is expressed as: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\$

A quadratic can generally be expressed as: $y=ax^2+bx+c$

So using the equation you gave: $0=x^2-5x-1$

We can identify the following values: a=1, b=-5, c=-1

Btw the equation explicitly write "1" as the coefficient of x, but since it's not provided it's implied that it's 1.

So plugging in the known values, we get the following equation:

$x=\frac{5\pm\sqrt{(-5)^2-4(1)(-1)}}{2(1)}\\\\x=\frac{5\pm\sqrt{25+4}}{2}\\\\x=\frac{5\pm\sqrt{29}}{2}\\\\x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}$

The last step just consists of taking the + and - solution, and since it asks for exact solutions you leave the 29 under the radical, and you don't approximate. There is no further simplification that can be done here.

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1 year ago

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2 years ago

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3 years ago

The radius of a cylinder gift box is box is 3X +1 inches the height of the gift box is twice the radius what is the surface area

Genrish500 [490]

Answer:

The surface area of the gift box is = $A = \frac{1188}{7}x^{2}+ \frac{774}{7}x +\frac{132}{7}$

Step-by-step explanation:

The surface area of the cylinder can be calculated using this formula:

$A=2\pi rh+2\pi r^2$

in this case, r is not a number, but rather an expression, which is r = $3x +1$ .

The height of the gift box is twice the radius, which is h = $2(3x+1)= 6x+2$

To get our curved surface area, we carefully put the expressions for h and r into the equation.

$A = 2 \times \frac{22}{7} \times (3x+1) \times (6x+2) + 2 \times \frac{22}{7} \times (3x+1)^{2}$

$A = \frac{44}{7} (3x+1) \times (6x +2) + \frac{44}{7} (9x^{2} + 6x +1)\\A =\frac{132}{7}x + \frac{44}{7} \times (6x+2)+ \frac{396}{7}x^{2}+\frac{246}{7}x +\frac{44}{7}$

$A = \frac{792}{7}x^{2} +\frac{264}{7}x +\frac{264}{7}x + \frac{88}{7} + \frac{396}{7}x^{2} + \frac{246}{7}x + \frac{44}{7}$

$A = \frac{1188}{7}x^{2}+ \frac{774}{7}x +\frac{132}{7}$

The surface area of the gift box is = $A = \frac{1188}{7}x^{2}+ \frac{774}{7}x +\frac{132}{7}$

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3 years ago