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Write the equation of the line perpendicular to 2x+3y=9 that passes through (-2,5). Write your answer in slope-intercept form. S

Harman [31]

ANSWER

$y = \frac{3}{2} x + 8$

EXPLANATION

The line given to us has equation,

$2x + 3y = 9$

We need to write this equation in the slope intercept form to obtain,

$3y = - 2x + 9$

$\Rightarrow \: y = - \frac{2}{3}x + 3$

The slope of this line is

$m_1 = - \frac{2}{3}$
Let the slope of the perpendicular line be

$m_2$

Then
$m_1 \times m_2 = - 1$

$- \frac{2}{3} m_2= - 1$

This implies that,

$m_2 = - 1 \times - \frac{3}{2}$

$m_2 = \frac{3}{2}$

Let the equation of the perpendicular line be,

$y = mx + b$

We substitute the slope to get,

$y = \frac{3}{2} x + b$

Since this line passes through
$(-2,5)$
it must satisfy its equation.

This means that,

$5= \frac{3}{2} ( - 2)+ b$

$5 = - 3 + b$

$5 + 3 = b$

$b = 8$

Wherefore the slope-intercept form is

$y = \frac{3}{2} x + 8$

6 0

3 years ago

A sum amount <br>to rupees 34476 in two and a half years at 4% CI. the sum is

Kruka [31]

Given:

Amount = Rs. 34476

Rate of compound interest = 4%

Time = $2\dfrac{1}{2}=2.5$ years

To find:

The principal value.

Solution:

Formula for amount is

$A=P\left(1+\dfrac{r}{100}\right)^t$

Where, P is principal value, r is rate of interest and t is time in years.

Putting the given values, we get

$34476=P\left(1+\dfrac{4}{100}\right)^{2.5}$

$34476=P\left(1+0.04\right)^{2.5}$

$34476=P\left(1.04\right)^{2.5}$

$\dfrac{34476}{\left(1.04\right)^{2.5}}=P$

Now,

$P=31256.0090$

$P\approx 31256$

Therefore, the value of sum or principal value is Rs.31256.

6 0

2 years ago

Which statement is true about the equations -3x + 4y = 12 and 1/4x-1/3y= 1?

Contact [7]

Answer:

the third selection is corret

Step-by-step explanation:

Ax + by + c = 0, k = - a/b.

so The slope of the first line = $\frac{4}{3}$ ,

the slope of the second line = $\frac{4}{3}$ ;

So these two lines are parallel and they don't intersect

4 0

2 years ago

6 feet<br> 12 feet<br> What is the area of the given composite shape?

Reika [66]

Answer:

choice A; 128.52 square feet

Step-by-step explanation:

This shape is made up of a semi-circle and a rectangle. The area of the rectangle will be 12*6 = 72 sq ft.

The formula for area of a circle is $\pi$ * $r^{2}$ . also r=radius. We are given the diameter, 12 feet. The radius is diameter/2, so the radius of the circle will be 6 feet.

Since pi is infinite we round it to 3.14.

Plug in the values and our expression will be (3.14* $6^{2}$ )/2 because it is a semi-circle. Simplify that to (3.14*36)/2 = 113.04/2 = 56.52 sq ft.

Remember to add the area of the rectangle and semi-circle. 72 + 56.52 = 128.52 sq ft.

3 0

2 years ago

Simply the expression given below (3x^3+4x^2+4x-12)+(-5x^3+9x^2-9x+20)

Svet_ta [14]

Answer:

1. Simplify: (4x2 - 2x) - (-5x2 - 8x).

Solution:

(4x2 - 2x) - (-5x2 - 8x)

= 4x2 - 2x + 5x2 + 8x.

= 4x2 + 5x2 - 2x + 8x.

= 9x2 + 6x.

= 3x(3x + 2).

Answer: 3x(3x + 2)

Step-by-step explanation:

6 0

3 years ago