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3 years ago

The figures below show a pattern.

Mathematics

1 answer:

yarga [219]3 years ago

7 0

Answer:

The number of blocks in the nth figure will be (3n + 1).

Step-by-step explanation:

See the attached figure where few arrangements are there.

The number of blocks in the first arrangement is (3 + 1)

Now, the number of blocks in the second arrangement is (3 × 2 + 1)

Again, the number of blocks in the third arrangement is (3 × 3 + 1)

So, the pattern says that the number of blocks in the nth arrangement will be (3 × n + 1) = (3n + 1) (Answer)

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A right triangle has a hypotenuse length of 60, and one side length of 24. Do the side lengths form a Pythagorean triple? Explai

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You can test this using the equation: a^2 + b^2 = c^2.

24^2 + b^2 = 60^2

576 + b^2 = 3,600

b^2 = 3,024

b = 54.999

Since b is not a whole number, the side lengths do not form a Pythagorean triple.

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3 years ago

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3 years ago

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Twice a first number decreased by a second number is 22. The first number increased by four times the second number is - 7.

AnnZ [28]

Answer:

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3 years ago

Find the value of x and y. Show all your work neat and in order.

Mazyrski [523]

Answer:

x = 21°

y = 29°

Step-by-step explanation:

a) Solving for x

Note that:

(3x - 3)° and 60° are Alternate interior angles, and alternate interior angles are equal to each other, hence:

3x - 3 = 60° (Alternate interior angles)

Add 3 to both sides

3x - 3 +3 = 60 + 3

3x = 63°

x = 63°/3

x = 21°

b) Solving for y

Notes that:

(3x - 3)° and (4y + 4)° are Consecutive interior angles and the sum consecutive interior angles is 180°

3x - 3 + 4y + 4 = 180°

3x + 4y - 3 + 4 = 180°

3x + 4y + 1 = 180°

Note that x = 21

Hence

3(21) + 4y + 1 = 180°

63 + 1 + 4y = 180°

64 + 4y = 180°

Subtract 64 from both sides

64 - 64 + 4y = 180° - 64

4y = 116°

y = 116/4

y => 29°

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3 years ago

What is your sister’s total cost under each of the two plans?2. Suppose your sister doubles her monthly usage to 3,500 minutes a

chubhunter [2.5K]

Answer:

(1) The total cost under Plan A is $92 and the total cost under Plan B is $515.

(2) The total cost under Plan A is $92 and the total cost under Plan B is $1,030.

Step-by-step explanation:

The question is incomplete, so the complete question is below:

$A\ cell \ phone \ company\ offers\ two \ different \ plans.$

$Plan\ A\ costs\ \$92\ per\ month\ for\ unlimited\ talk\ and\ text.\ Plan\ B\ costs \ $0.20\ per\ minute\ plus\ \$0.10\ per\ text\ message\ sent.$ $You\ need \ to\ purchase \ a \ plan \ for\ your \ 14-year-old \ sister$ $.Your\ sister\ currently \ uses\ 1,750 \ minutes\ and \ sends\ 1,650 \ texts\ each \ month.$ $(1) What\ is\ your \ sister's\ total\ cost\ under \ each\ of\ the\ two\ plans?$

$(2) Suppose\ your\ sister\ doubles\ her\ monthly\ usage \ to\ 3,500\ minutes \ and\ sends\ 3,300 \ texts.$ $What \ is \ your \ sister's \ total \ cost \ under \ each \ of \ the \ two \ plans?$

Now, to find (1) total cost for each of the two plans. (2) Total cost under each of the two plans, if sister doubles her monthly usage to 3,500 minutes and sends 3,300 texts.

As, the Plan A is for unlimited talk and text

Cost of the Plan A = $92.

Now, to find the cost under Plan B:

According to question:

Rate of call per minute is $0.20 and per text is $0.10.

Calls she uses currently is 1,750 minutes and text 1,650.

So, to get the cost of Plan B:

$0.20\times 1750+0.10\times 1650$