Calculate the following limits

Marrrta [24]

Answer:

Since pair of opposite sides are parallel and adjacent sides meets at right angles, the quadrilateral COAT is a rectangle.

Step-by-step explanation:

The vertices of the given quadrilateral is $C(2,0),O(7,0),A(7,2),T(2,2)$

It is sufficient to show that pair of opposite sides are parallel and adjacent sides are perpendicular.

The slope of each side can be found using the formula;

$m=\frac{y_2-y_1}{x_2-x_1}$

Slope of CO,

$M_{CO}=\frac{0-0}{7-2}=\frac{0}{5} =0$

A line with a zero slope is a horizontal line.

The slope of OA,

$M_{OA}=\frac{2-0}{7-7} =\frac{2}{0}$

This slope is undefined.

A line with an undefined slope is a vertical line.

This shows that,the side CO and OA of the quadrilateral meets at right angle.

The slope of AT,

$M_{AT}=\frac{2-2}{7-0}=\frac{0}{5}=0$

This is also a horizontal line.

The slope of TC,

$M_{TC}=\frac{2-0}{2-2} =\frac{2}{0}$

This also a vertical line.

This implies that, side TC and side AT meets at Tat right angles and TC is parallel to OA.

Also AT is parallel to TO.

This shows that COAT is a rectangle.

8 0

3 years ago

6th grade math i mark as brainliest

Svetllana [295]

Answer:2

Step-by-step explanation: .5 multiplied by 2. This equals .25, multiply 8 and .25.

8 0

3 years ago

The area of a rectangle is 980 in squared. the ratio of the length to the width is 5 : 4. find the length and the width.

ella [17]

Answer: The length of the rectangle is 35 in.

The width of the rectangle is 28 in.
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Explanation:
_________________________________________________________
The formula for the area, "A", of a rectangle:

Area (A) = length (L) * width (w) ;

that is: " A = L * w " ;

A = 980 in² (given);

ratio of the length to the width is: " 5 : 4 " (given);

→ Find the length (L) and the width (w).
_________________________________________________________

→ 980 in² = (5x) * (4x) ;

in which: " 980 in² " is the area of the triangle;

" 5x" = the length (L) of the rectangle, for which we shall solve;

" 4x" = the width (w) of the rectangle, for which we shall solve.
_______________________________________________________
If we find solve for "x" ; we can solve for "5x" and "4x" (the "length" and the "width", respectively); by plugging in the solved value for "x" ;
_______________________________________________________

→ 980 in² = (5x) * (4x) ;

↔ (5x) * (4x) = 980 in² ;

→ (5x) * (4x) = (5) * (4) * (x) * (x) = 20 * x² = 20x² ;

→ 20x² = 980 ;

Divide each side by "10" ; by canceling out a "0" on each side of the equation:

→ 2x² = 98 ;

Now, divide each side of the equation by "2" ;

→ 2x² / 2 = 98 / 2 ;

to get:

→ x² = 49 ;

Now, take the "positive square root" of each side of the equation; (since a "length or width" cannot be a "negative value") ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ ⁺√(x²) = √49 ;

to get:

→ x = 7 ;
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Now, we can solve for the "length" and the "width" ;

→ The length is: "5x" ;

5x = 5(7) = " 35 in " ;
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→ The width is: "4x" ;

4x = 4(7) = "28 in."
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Let us check our answer:

→ A = L * w ;

→ 980 in² = ? 35 in. * 28 in. ?? ;

Using a calculator: "35 * 28 = 980" . Yes! ;
____________________________________________________
{ Also note: " in * in = in² " ? Yes! } .
____________________________________________________

3 0

3 years ago

Please answer questions from the following images!

Lelechka [254]

Can you send more information about this problem

6 0

3 years ago

On a special right triangle if the sides are 6 and 6 then what is the hypothinus

Black_prince [1.1K]

We are talking about a right triangle so the phytagoras equation can be used:
$a^{2} + b^{2} = c^{2}$
$6^{2} + 6^{2} = 36 + 36 = 72 = c^{2}$
$\sqrt{ c^{2} } = \sqrt{72} =8.48528...$
So the hypothinus is equal to approximately 8.49

4 0

3 years ago