All categories

3 years ago

A rectangle has a perimeter of 23 cm. Its area is 33 cm2. Determine the

Mathematics

1 answer:

SCORPION-xisa [38]3 years ago

5 0

Answer:

length = 6 cm; width = 5.5 cm

Step-by-step explanation:

Let the length = x. Let the width = y.

We use the formulas for area and perimeter using x and y, and the given values.

area = length * width

perimeter = 2(length + width)

xy = 33

2(x + y) = 23

Solve the first equation for x:

x = 33/y

Substitute 33/y for x in the second equation.

2(33/y + y) = 23

66/y + 2y = 23

Mulrtiply both sides by y.

66 + 2y^2 = 23y

2y^2 - 23y + 66 = 0

(2y - 11)(y - 6) = 0

2y - 11 = 0 or y - 6 = 0

y = 11/2 = 5.5 or y = 6

xy = 33

x * 11/2 = 33

x = 33 * 2/11

x = 6

Answer: length = 6 cm; width = 5.5 cm

You might be interested in

On a coordinate plane, kite W X Y Z is shown. Point W is at (negative 3, 3), point X is at (2, 3), point Y is at (4, negative 4)

Aloiza [94]

The perimeter of the kite is (10 + 2√53) units if the kite and the coordinates of the kite are point W is at (-3, 3), point X is at (2, 3), point Y is at (4, -4), and point Z is at (-3, -2).

<h3>What is quadrilateral?</h3>

It is defined as the four-sided polygon in geometry having four edges and four corners. Kite is quadrilateral, in which. Two pairs of congruent sides, and it has one pair of opposite congruent angles.

The figure is missing.

On a coordinate plane, kite WXYZ is shown (please refer to the picture)

We have a kite and the coordinates of the kite are:

Point W is at (-3, 3), point X is at (2, 3), point Y is at (4, -4), and point Z is at (-3, -2).

Using the distance formula we can find the distance between coordinates:

$\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Distance between W and X:

$\rm WX=\sqrt{(2+3)^2+(3-3)^2}$

WX = 5 units

Similarly, distance between X and Y:

XY = √53 units

YZ = √53 units

ZW = 5 units

Perimeter = sum of the all sides

Perimeter = 5 + √53 + √53 + 5

Perimeter = (10 + 2√53) units

Thus, the perimeter of the kite is (10 + 2√53) units if the kite and the coordinates of the kite are point W is at (-3, 3), point X is at (2, 3), point Y is at (4, -4), and point Z is at (-3, -2).

Learn more about the quadrilateral here:

brainly.com/question/6321910

#SPJ1

4 0

1 year ago

Is f(x) continuous at x equals 4? Why or why not? A. No, f(x) is not continuous at x equals 4 because ModifyingBelow lim Wit

soldier1979 [14.2K]

<u>Corrected Question</u>

Is the function given by:

$f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right$

continuous at x=4? Why or why not? Choose the correct answer below.

Answer:

(D) Yes, f(x) is continuous at x = 4 because $Lim_{x \to 4}f(x)=f(4)$

Step-by-step explanation:

Given the function:

$f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right$

A function to be continuous at some value c in its domain if the following condition holds:

f(c) exists and is defined.

$Lim_{x \to c}$ f(x)$ exists.

$f(c)=Lim_{x \to c}$ f(x)$

At x=4

$f(4)=\dfrac{1}{4}*4+1=2$

$Lim_{x \to 4}f(x)=2$

Therefore: $Lim_{x \to 4}f(x)=f(4)=2$

By the above, the function satisfies the condition for continuity.

The correct option is D.

3 0

3 years ago

1.work out 1/2 + 5/6

Serggg [28]

1. First find the LCD of the two fractions.
They share the denominator 6.
Turn 1/2 into a fraction with a denominator of 6.
2*3=6, so 1*3=3
3/6
Now add.
Leave denominators alone, but add numerators.
3+5=8
8/6
Now simplify.
Divide both by 2.
8/2=4
6/2=3
4/3 is your answer or 1 1/3
2. Multiply straight across.
3*2=6
4*7=28
6/28
Simplify
You get 3/14 as your answer.

3 0

3 years ago

Why did the rug roll up around his girl friend

andre [41]

This is for real questions

8 0

3 years ago

Read 2 more answers

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unkno

spin [16.1K]

The other endpoint is (1, -17).

The midpoint formula is:

$m=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Using our midpoint and endpoint, we have:
$(6, -11) = (\frac{11+x_2}{2}, \frac{-5+y_2}{2})
\\
\\6=\frac{11+x_2}{2} \text{ and } -11=\frac{-5+y_2}{2}
$

For the first equation (to find the x-coordinate) we will multiply both sides by 2:
$6\times2=\frac{11+x_2}{2}\times 2
\\
\\12=11+x_2$

Subtract 11 from both sides:
12 - 11 = 11+x₂ - 11
1 = x₂

For the second equation (the y-coordinate) we multiply both sides by 2:
$-11\times2=\frac{-5+y_2}{2}\times 2
\\
\\-22=-5+y_2$

Add 5 to both sides:
-22+5 = -5+y₂ + 5
-17 = y₂

This means that (x₂, y₂) is at (1, -17).

4 0

3 years ago