Ask question

Ask question

All categories

4 years ago

10

What is the point slope form of the line with slope -1/4 that passes through the point ( -2,9 )

1 answer:

morpeh [17]4 years ago

8 0

$\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{9})~\hspace{10em} \stackrel{slope}{m}\implies -\cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{-\cfrac{1}{4}}[x-\stackrel{x_1}{(-2)}]\implies y-9=-\cfrac{1}{4}(x+2)$

You might be interested in

What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 27 − x^2? show your

LUCKY_DIMON [66]

Answer:

Option B.

Step-by-step explanation:

The given curve is

$y=27-x^2$

We need to find the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve $y=27-x^2$ .

Let the vertex in quadrant I be (x,y), then the vertex in quadrant II is (-x,y) .

Length of the rectangle = 2x

Width of the rectangle = y

Area of a rectangle is

$Area=Length\times width$

$Area=2x\times y$

Substitute the value of y from the given equation.

$Area=2x(27-x^2)$

$A=54x-2x^3$ .... (1)

Differentiate with respect to x.

$\frac{dA}{dx}=54-6x^2$

Equate $\frac{dA}{dx}=0$ , to find the critical points.

$0=54-6x^2$

$6x^2=54$

Divide both sides by 6.

$x^2=9$

$x=\pm 3$

The value of x can not be negative because side length can not be negative.

Substitute x=3 in equation (1).

$A=54(3)-2(3)^3$

$A=162-54$

$A=108$

The area of the largest rectangle is 108 square units.

Therefore, the correct option is B.

7 0

3 years ago

The linear combination method gives a solution of (–4, 2) for which of these systems of linear equations?

Andrew [12]

Answer:

$3x + 13y = 14$

$6x + 11y = -2$

Step-by-step explanation:

<em>See Attachment for complete question</em>

To determine which of the options has (-4,2) as its solution; we have to test each linear combination until we arrive at an answer;

Given that

$(x,y) = (-4,2)$

Testing Option A

$3x + 13y = 14$

$6x + 11y = -2$

Substitute $x = -4$ and $y = 2$ in $3x + 13y = 14$

$3(-4) + 13(2) = 14$

Open Brackets

$-12 + 26 = 14$

$14 = 14$

Substitute $x = -4$ and $y = 2$ in $6x + 11y = -2$

$6(-4) + 11(2) = -2$

Open Brackets

$-24 + 22 = 2$

$2 = 2$

<em>In both cases, the expression on the right hand side equates to that on the left hand side; </em>

<em>Hence, there's no need to check for other options. </em>

8 0

4 years ago

Estimate a 15% tip on a dinner bill of $32.58 by first rounding the bill amount to the nearest ten dollars.

Katen [24]

Answer:

9

Step-by-step explanation:

rounding the cost and the percent gratuity to the nearest ten.

hope it helps

6 0

3 years ago

5*198 in distributive property

Mandarinka [93]

5 * 198 = 5(100 + 98) = (5 * 100) + (5 * 98) = 500 + 490 = 990

7 0

3 years ago

Which of the following options also describes a square?

Vlad1618 [11]

Answer:

A and C quadrilateral and parallelogram

Explanation:

A square is a quadrilateral, meaning it has four sides. Therefore a square is a quadrilateral.

have a nice day! Also could you mark me brainliest I'm trying to rank up! :D

3 0

3 years ago

Read 2 more answers