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AURORKA [14]
3 years ago
11

Piece of rope that is 15 ft long what is the area

Mathematics
1 answer:
amm18123 years ago
8 0
The question is not exhaustive.
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What is the solution to the rational equation x over 2x plus 1 minus 1 over 4 equals 2 over 2x plus 1
aalyn [17]
We want to solve
\frac{x}{2x+1} - \frac{1}{4} = \frac{2}{2x+1}

Subtract 2/(2x+1) from each side.
\frac{x}{2x+1} - \frac{2}{2x+1y} - \frac{1}{4} = 0

Add 1/4 to each side, and simplify the left side.
\frac{x-2}{2x+1} = \frac{1}{4}

Cross multiply.
4(x - 2) = 1(2x + 1)
4x - 8 = 2x + 1

Simplify and solve for x.
4x - 2x = 1 + 8
2x = 9
x = 9/2   or x = 4 1/2.

Answer:  x =  \frac{9}{2} \,\, or \,\, x = 4 \frac{1}{2}

5 0
3 years ago
Find the equation of the lines, that is parallel to the line 9x-8y=1, and tangent to the elipses 9x^2+16y^2=52.
lara31 [8.8K]

Answer:

The equations of the lines that satisfy these conditions are

y = (9/8)x + (13/4)

And

y = (9/8)x - (13/4)

They can be written further as

8y = 9x + 26

and

8y = 9x - 26

Step-by-step explanation:

The line parallel to the line 9x - 8y = 1 has the same slope as 9x - 8y = 1

Writing the equation of the line in the (y = mx + c) form

8y = 9x - 1

y = (9/8)x - 1

So, the line(s) we are looking for has/have slope(s) of (9/8).

Its equation is then

y = (9/8)x + k

This line is then said to be tangent to the ellipses

9x² + 16y² = 52

So, since the line is a tangent to the ellipses, it will have the same coordinates as the ellipses at the point of contact.

9x² + 16y² = 52

y = (9/8)x + k

y² = (81/64)x² + (18k/8)x + k²

y² = (81/64)x² + (9k/4)x + k²

Substituting this into the ellipses equation,

9x² + 16y² = 52

9x² + 16[(81/64)x² + (9k/4)x + k²] = 52

9x² + (81/4)x² + 36kx + 16k² = 52

29.25x² + 36kx + 16k² - 52 = 0

Taking note that the two lines that will be tangent to the ellipses and parallel to the line given, to establish tangency, we make the discriminant of this equation 0. Hence, the roots of that equation will have equal roots.

So, the discriminant, b² - 4ac = 0

29.25x² + 36kx + 16k² - 52 = 0

a = 29.25

b = 36k

c = 16k² - 52

(36k)² - (4)×(29.25)×(16k² - 52) = 0

1296k² - 1872k² + 6084 = 0

576k² = 6084

k = ±(13/4)

So, the equation(s) of the line(s) required is

y = (9/8)x ± (13/4)

So, the equations include

y = (9/8)x + (13/4)

And

y = (9/8)x - (13/4)

Multiplying by 8, we obtain

8y = 9x + 26

8y = 9x - 26

Hope this Helps!!!

6 0
3 years ago
WRITE THE FOLLOWING EQUATION IN THE FORM OF Y=MZ (a) 3x+4y=7​
Shalnov [3]

Answer:

y = \frac{ - 3x}{4}   +  \frac{7}{4}

Step-by-step explanation:

First transpose 3x

you are having 3x+4y=7

by transposing you will get

4y=-3x+7

divide by 4 throughout by making y subject of the formula you will find your equation as y=mx+c.

4 0
2 years ago
Fully simplify −10x3y2(9x)
lbvjy [14]

Answer:

Step-by-step explanation:

-10*9*x^3*x*y^2 = -90x^4y^2

5 0
2 years ago
Write an equation between the two points (-3, 0) and (-3, -6)
Valentin [98]

The equation is x=-3

6 0
3 years ago
Read 2 more answers
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