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Svetach [21]
3 years ago
13

A square is changed into a rectangle by increasing the length of the square by 5 units to be (x + 5) and increasing the width by

3 units to be (x + 3). Write a simplified expression that represents the area of the resulting rectangle in square units?
Mathematics
1 answer:
gladu [14]3 years ago
4 0
Area of the rectangle = x^2 + 8x + 15 square units

Explanation:

Length = x + 5
Breadth = x + 3

Area = l x b = (x + 5)(x + 3) = x(x + 3) + 5(x + 3) = x^2 + 3x + 5x + 15 = x^2 + 8x + 15 square units
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I really am confused on how to write a proof.
kvasek [131]

Since ABCD is a parallelogram, the opposite sides will be parallel and equal,

\begin{gathered} AB=CD \\ BC=AD \end{gathered}

Consider that AC acts as a transversal to the parallel lines AB and CD, so we can write,

\begin{gathered} \angle CAD=\angle ACB\text{ (Alternate Interior Angles)} \\ BC=AD\text{ (Opposite sides of parallelogram)} \\ \angle ADB=\angle CBD\text{ (Alternate Interior Angles)} \end{gathered}

So by the ASA criteria, the triangle AED is congruent to the triangle CEB,

Then the corresponding parts of the triangles will be equal,

\begin{gathered} AE=CE \\ BE=DE \end{gathered}

Hence Proved.

8 0
1 year ago
The Bishop family celebrated a birthday by dining out at a local restaurant. Their bill was $97.45. Mr. Bishop would like to lea
serg [7]
97.45 • 0.18 = 17.54. 97.45 + 17.54 = 114.99. I think this is right.
6 0
4 years ago
Read 2 more answers
Which expression represents the prime factorization of 108?
ankoles [38]

Answer:

2×2×3×3×3

Step-by-step explanation:

●108=

•2×54

•2×27

•3×9

• 3×3

Writing the prime numbers;

108=2×2×3×3×3

4 0
2 years ago
Using the Division algorithm to find q and r such that 3662 = q·16+r , where 0 ≤ r < 16 . What if we take c = −3662 instead o
bagirrra123 [75]

Answer:

a) If c=3662 then q=228 and r=14.

b) If c=-3662, then q=-229 and r=2

Step-by-step explanation:

a) Observe that 229*16=3664, since r must be in the interval [0,16), then 229 doesn't work, but 228*16=3648 and 3662-3648=14.

Then 3662=228*16+14.

b) Observe that -228*16=-3648 and -3648-14=-3662, but r= must be positive. Then -228 doesn't work.

But observe that -229*16=-3664 and -3664+2=-3662. So -3662=-229*16+2

4 0
3 years ago
<img src="https://tex.z-dn.net/?f=%282%2F3%29%5E%7B3%7D" id="TexFormula1" title="(2/3)^{3}" alt="(2/3)^{3}" align="absmiddle" cl
tiny-mole [99]

Answer:

\frac{8}{27}

Step-by-step explanation:

(\frac{2}{3} )^3 = \frac{2^3}{3^3} = \frac{2 \times 2 \times 2}{3 \times 3 \times 3} = \frac{8}{27}

8 0
3 years ago
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