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3 years ago

Write an equation for the line parallel to the given line that contains C C(-1,7);y=5/9x-1

Mathematics

1 answer:

SSSSS [86.1K]3 years ago

7 0

Answer:

The equation of the line would be y = 5/9x + 68/9

Ste-by-step explanation:

The line starts by having a slope of 5/9 since parallel lines have the same slope. Now e can use that slope and a point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 7 = 5/9(x + 1)

y - 7 = 5/9x + 5/9

y = 5/9x + 68/9

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Recall that in the problem involving compound interest, the balance A for P dollars invested at rate r for t years compounded n

RoseWind [281]

Answer:

(a)∴A=$6753.71.

(b)∴A=$1480.24

(c) ∴P=$7424.70

(d)∴P=$49759.62

(e)∴P=$5040.99

(f) ∴P=$2496.11

Step-by-step explanation:

We use the following formula

$A=P(1+\frac rn)^{nt}$

A=amount in dollar

P=principal

r=rate of interest

(a)

P=$2,500, r=5%=0.05,t =20 years , n= 4

$A=\$2500(1+\frac{0.05}{4})^{(20\times 4)$

=$6753.71

∴A=$6753.71.

(b)

P=$1,000, r=8% =0.08,t =5 years , n= 2

$A=\$1000(1+\frac{0.08}{2})^{(5\times 2)$

=$1480.24

∴A=$1480.24

(c)

A=$10,000, r=6% =0.06,t =5 years , n= 4

$10000=P(1+\frac{0.06}{4})^{(5\times 4)}$

$\Rightarrow P=\frac{10000}{(1+0.015)^{20}}$

$\Rightarrow P=7424.70$

∴P=$7424.70

(d)

A=$100,000, r=6% =0.06,t =10 years , n= 12

$100000=P(1+\frac{0.07}{12})^{(10\times 12)}$

$\Rightarrow P=\frac{100000}{(1+\frac{0.07}{12})^{120}}$

$\Rightarrow P=49759.62$

∴P=$49759.62

(e)

A=$100,000, r=10% =0.10,t =30 years , n= 12

$100000=P(1+\frac{0.10}{12})^{(30\times 12)}$

$\Rightarrow P=\frac{100000}{(1+\frac{0.10}{12})^{360}}$

$\Rightarrow P=5040.99$

∴P=$5040.99

(f)

A=$100,000, r=7% =0.07,t =20 years , n= 4

$100000=P(1+\frac{0.07}{4})^{(20\times 4)}$

$\Rightarrow P=\frac{100000}{(1+\frac{0.07}{4})^{80}}$

$\Rightarrow P=2496.11$

∴P=$2496.11

6 0

3 years ago

find an equation of the line passing through the point (-4,-6) that is parellel to the line y=-2/9x-1

ryzh [129]

The equation of the line passing through the point (-4,-6) in slope intercept form is:

$y = \frac{-2}{9}x -\frac{62}{9}$

Solution:

Given that we have to write the equation of the line passing through the point (-4,-6) that is parallel to the line y=-2/9x-1

The equation of line in slope intercept form is given as:

y = mx + c ---------- eqn 1

Where, "m" is the slope of line and "c" is the y intercept

Given equation of line is:

$y = \frac{-2x}{9} -1$

On comparing the above equation with eqn 1,

$m = \frac{-2}{9}$

We know that slopes of parallel lines are equal

Thus slope of line parallel to given line is also $\frac{-2}{9}$

Now find the equation of line with slope $\frac{-2}{9}$ and passing through (-4, -6)

$\text{Substitute } m = \frac{-2}{9} \text{ and } (x, y) = (-4, -6) \text{ in eqn 1}\\\\-6=\frac{-2}{9} \times -4+c\\\\-6 = \frac{8}{9}+c\\\\-6 = \frac{8+9c}{9}\\\\-54 = 8+9c\\\\9c = -62\\\\c = \frac{-62}{9}$

$\text{Substitute } m = \frac{-2}{9} \text{ and } c = \frac{-62}{9} \text{ in eqn 1}\\\\y = \frac{-2}{9}x -\frac{62}{9}$

Thus the equation of line is found

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Answer:

A) Is correct

Step-by-step explanation:

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