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3 years ago

What figure can be made with exactly 420 squares?

Mathematics

1 answer:

Natali [406]3 years ago

4 0

5. The 5th figure will have 30 tiles.
6. The 6th figure will have 42 tiles.
7. The pattern is non-linear (quadratic).
8. The 20th figure can be made with 420 tiles.

_____
The Nth figure is made with n*(n+1) tiles. To answer question 8, you must solve
.. n(n +1) = 420
.. n^2 +n -420 = 0
.. (n +21)(n -20) = 0
.. n = 20 or -21 . . . . the negative solution is extraneous

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Where is most of the mass in the universe found

xeze [42]

Answer:

The milky way galaxy

Step-by-step explanation:

It contains approximately 200 billion stars, and weighing about 1.7 trillion times the mass of the sun

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4 years ago

If your machine takes up 350sq. ft. and you are asked to scale down a drawing onto a 8" x 10" piece of paper what is your percen

Mnenie [13.5K]

Answer:

the scale is 630:1 = 0.16%

80inch^2 of 50400inch^2 however = 0.16%

Step-by-step explanation:

350ft^2 = 50400inches 8 x 10 = 80inches = 50400/80 = 630

50400/9 =5600 we distribute

5600/80 = 7

showing us that 7 x 9 = 63 where 63 x 80 = 5040 1/100th

1 = 630

7x9x 80 = 1/100 of 50400

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Proves that every every 10000 the percentage goes down 0.00011%

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4 years ago

George has $49 which he decides to spend on x and y. commodity x costs $5 per unit and commodity y costs $11 per unit. he has th

FromTheMoon [43]

We are given the equations:

Rewrite eqtn 1 explicit to y:

11 y = 49 – 5 x

Substitute eqtn 3 to eqtn 2:

u = 3 x^2 + 6 [(49 – 5x) / 11]^2

u = 3 x^2 + 6 [(2401 – 490 x + 25 x^2) / 121]

u = 3 x^2 + 14406/121 – 2940x/121 + 150x^2/121

u = 4.24 x^2 – 24.3 x + 119.06

Derive then set du/dx = 0 to get the maxima:

du/dx = 8.48 x – 24.3 = 0

solving for x:

8.48 x = 24.3

x = 2.87

so y is:

y = (49 – 5x) / 11 = (49 – 5*2.87) / 11

y = 3.15

Answer:

<span>George will choose some of each commodity but more y than x.</span>

7 0

3 years ago

What are the steps to my answer?

stepan [7]

Answer:

Step-by-step explanation:

f[g(x)]=(2x)²+3(2x)-3...substitute the values of g(x) into the function f(x)
f[g(x)]=4x²+6x-3...simplified

7 0

2 years ago

PLEASEPLEASE ANSWER

IRINA_888 [86]

Answer:

x = 7

Step-by-step explanation:

A triangle's total interior angle measurement will equal 180°.

Set all measurements equal to 180:

(82) + (9x - 6) + (6x - 1) = 180

Simplify. Combine like terms:

(82 - 6 - 1) + (9x + 6x) = 180

(82 - 7) + (15x) = 180

(75) + 15x = 180

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, Subtract 75 from both sides of the equation:

15x + 75 = 180

15x + 75 (-75) = 180 (-75)

15x = 180 - 75

15x = 105

Next, divide 15 from both sides of the equation:

(15x)/15 = (105)/15

x = 105/15

x = 7

7 is your value for x.

3 0

3 years ago