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ziro4ka [17]
3 years ago
9

What is the converse of the statement? If a point lies in Quadrant III, then its coordinates are both negative. If the coordinat

es of a point are both negative, then the point is in Quadrant III. If the coordinates of a point are both negative, then the point is not in Quadrant I. If a point is in Quadrant I, then its coordinates are both positive. If the coordinates of a point are both negative positive, then the point is not in Quadrant II.
Mathematics
2 answers:
Vladimir [108]3 years ago
6 0
<h2>Answer:</h2>

The converse statement is:

  • If the coordinates of a point are both negative, then the point is in Quadrant III.
<h2>Step-by-step explanation:</h2>

We know that for any conditional statement of the type:

          If p then q i.e. p → q

where p is the hypothesis and q is the conclusion.

The converse of the statement is given by:

       If q then p i.e. q → p.

We are given a statement as:

If a point lies in Quadrant III, then its coordinates are both negative.

i.e. Here p=Point lie in Quadrant III

and q= Coordinates are both negative.

Hence, the converse statement will be:

If the coordinates of a point are both negative, then the point is in Quadrant III.

Dovator [93]3 years ago
5 0
<span>If the coordinates of a point are both negative, then the point is in Quadrant III.

</span>
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Answer:

Option c, A square matrix

Step-by-step explanation:

Given system of linear equations are

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Now to find the type of matrix can be formed by using this system

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A matrix can be written by

A=co-efficient of x of 1st linear equation    co-efficient of y of 1st linear equation   constant of 1st terms linear equation

co-efficient of x of 2st linear equation   co-efficient of y of 2st linear equation  constant of 2st terms linear equation

co-efficient of x of 3st linear equation   co-efficient of y of 3st linear equation    constant of 3st terms linear equation           3\times 3

which is a 3\times 3 matrix.

Therefore A can be written as

A= \left[\begin{array}{lll}3&-2&-2\\7&3&26\\-1&-11&46\end{array}\right] 3\times 3

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3 years ago
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Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular area and then divide it into four
Alina [70]

Answer:

Step-by-step explanation:

(a)

Suppose we came up with an ideology whereby we pick a value for the length including the length dividing the inside into 4 parts(5 parallel sides), then we can get the value for breath by using the following process.

Let assume the length of the rectangle is 50;

Then, the breath can be calculated as follows:

= 50 × 5 = 250   ( since the breath is divided into 5 parallel sides)

The fencing is said to be 950 ft

So, 950 - 250 = 700

Then divided by 2, we get:

= 700/2

= 350

So for the first diagram; the length = 50 and the breath = 350

The area = 50 × 350 = 17500 ft²

Now, let's go up a little bit.

If the length increase to 100;

Then 100 × 5 = 500

⇒ 950 - 500 = 450

⇒ 450/2 = 225

The area = 225 × 100 = 22500 ft²

Suppose the length increases to 150

Then 150 × 5 = 750

⇒ 950 - 750 = 200

⇒ 200/2 = 100

The area = 150 × 100 = 15000 ft²

The diagrams for each of the outline above can be seen in the image attached below.

(b) The diagram illustrating the general solution can be seen in the second image provided below.

(c) The expression for  the total area A in terms of both x and y is:

Area A = x×y

(d) Recall that:

The fencing is said to be 950 ft.

And the length is divided inside into 5 parallel sides;

Then:

5x + 2y = 950  (from the illustration in the second image below)

2y  = 950 - 5x

y = \dfrac{950}{2} - \dfrac{5}{2}x

y = 475- \dfrac{5}{2}x

(e)

From (c); replace the value of y in (d) into (c)

Then:

Area A = x×y

f(x)= x\times ( 475 -\dfrac{5}{2}x)

Open brackets

f(x)= ( 475 x-\dfrac{5}{2}x^2)

(f)

By differentiating what we have in (e)

f(x)= ( 475 x-\dfrac{5}{2}x^2)

f'(x)= ( 475 (1)-\dfrac{5}{2}(2x))

f'(x)= 475 -5x

\implies  475 = 5x

x = 475/5

x = 95

From (d):

y = 475- \dfrac{5}{2}x

y = 475- \dfrac{5}{2}(95)

y =237.5

∴

Area A = x × y

Area A = 95 × 237.5

Area A = 22562.5 ft²

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3 years ago
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