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AlladinOne [14]
3 years ago
7

The length of a rectangle is seven units more than it's width if the width is doubled and the length is increased by two the are

a is increased by 42 square Units find the dimensiones of the original rectangle
Mathematics
2 answers:
My name is Ann [436]3 years ago
7 0

Answer:

length = 10 units; width = 3 units

Step-by-step explanation:

Let the width = w

Then the length is w + 7

Original area: w(w + 7)

Double the width: 2w

Increase the length by 2: w + 9

Area of new rectangle: 2w(w + 9)

Area of new rectangle = w(w + 7) + 42

2w(w + 9) = w(w + 7) + 42

2w^2 + 18w = w^2 + 7w + 42

w^2 + 11w - 42 = 0

(w + 14)(w - 3) = 0

w + 14 = 0 or w - 3 = 0

w = -14 or w = 3

A width cannot be negative, so we discard w = -14.

The original width is 3 units.

The length is 7 more than the width, so the length is 10 units.

Anit [1.1K]3 years ago
5 0

yup the guy below me Is right

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Step-by-step explanation:

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8 0
3 years ago
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12) Find the sum, S7, for the geometric series (1 + 5 + 25+ --- + 15625).
vfiekz [6]

Answer:

Find the (r) between adjacent members

a2/a1=+25/5=5

a3/a2=+125/+25=5

a4/a3=+625/+125=5

a5/a4=+3125/+625=5

a6/a5=+15625/+3125=5

The ration (r) between every two adjacent members of the series is constant and equal to 5

General Form: a

n

=a

1

×r

n-1

This geometric series: a

n

=5×5

n-1

The nature of this series

Sum of finite geometric series members

sum of a geometric series

The sum of our particular series

a 1-rn = 5 1-56 = 5 1-15625 = 5 -15624 =5×3906=19530

1-r 1-5 -4 -4

Finding the n

th

element

a2 =a1×r2-1  =a1×r1 =5×51 =25

a3 =a1×r3-1  =a1×r2 =5×52 =125

a4 =a1×r4-1  =a1×r3 =5×53 =625

a5 =a1×r5-1  =a1×r4 =5×54 =3125

a6 =a1×r6-1  =a1×r5 =5×55 =15625

a7 =a1×r7-1  =a1×r6 =5×56 =78125

a8 =a1×r8-1  =a1×r7 =5×57 =390625

a9 =a1×r9-1  =a1×r8 =5×58 =1953125

a10 =a1×r10-1  =a1×r9 =5×59 =9765625

a11 =a1×r11-1  =a1×r10 =5×510 =48828125

a12 =a1×r12-1  =a1×r11 =5×511 =244140625

a13 =a1×r13-1  =a1×r12 =5×512 =1220703125

a14 =a1×r14-1  =a1×r13 =5×513 =6103515625

a15 =a1×r15-1  =a1×r14 =5×514 =30517578125

a16 =a1×r16-1  =a1×r15 =5×515 =152587890625

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Find the surface area of the composite solid. Write your answer as a decimal.
IrinaK [193]

Answer:

283.5 cm squared

Step-by-step explanation:

The surface area of a solid is basically just the sum of the areas of all the exterior sides. In this figure, we have 3 congruent triangles at the top, 3 congruent rectangles on the sides, and 1 triangle at the base. We need to find all these areas.

<u>3 congruent triangles</u>:

The area of a triangle is denoted by: A = (1/2) * b * h, where b is the base and h is the height.

Here, the base of one triangle is 10 and the height is 4. So:

A = (1/2) * b * h

A = (1/2) * 10 * 4 = 20

Since there are 3 such triangles, multiply 20 by 3:

20 * 3 = 60 cm squared

<u>3 congruent rectangles</u>:

The area of a rectangle is denoted by: A = lw, where l is the length and w is the width.

Here, the length is 6 and the width is 10, so:

A = lw

A = 6 * 10 = 60

There are 3 such rectangles, so multiply 60 by 3:

60 * 3 = 180 cm squared

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Again we use the formula A = (1/2) * b * h for this area.

Here, the base is 10 and the height is 8.7, so:

A = (1/2) * b * h

A = (1/2) * 10 * 8.7 = 43.5 cm squared

Add all these together:

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The answer is thus 283.5 cm squared.

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For an absolute scale decide on the end (because it starts with 0) and then divide that range by the amount of squares to get your step height. I used 80000 as the end which resulted in steps of 4000 with each square.

With the relative scale its similar, round the max&min values of the data and decide on some step width (by dividing by your vertical graph height and rounding again). I used 3000 with 80000 and 20000 as the end and start of the axis.

Once you have your scale and both axis are labeled you only have to draw the points.

I added two pictures what the result should look like.

4 0
4 years ago
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