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3 years ago

Simplify the expression with using scientific notation (4 times 10 8)2

Mathematics

1 answer:

kifflom [539]3 years ago

8 0

The scientific notation:

$a\cdot10^n\\\\1\leq a < 10;\ n\in\mathbb{Z}$

$(4\cdot10^8)^2=4^2(10^8)^2=16\cdot10^{8\cdot2}=16\cdot10^{16}\\\\=1.6\cdot10\cdot10^{16}=1.6\cdot10^{17}$

Used:

$(a\cdot b)^n=a^n\cdot b^n\\\\(a^n)^m=a^{n\cdot m}\\\\a^n\cdot a=a^{n+1}$

Answer: (4 × 10⁸)² = 1.6 × 10¹⁷

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Which value of x satisfies both -9x + 4y = 8 and -3x − y = 4 given the same value of y?

liq [111]

Answer:

Step-by-step explanation:

Since y will have same value, y doesn't really matter. Thus,

We can solve for y in the 2nd equation as:

-3x - y = 4

-3x - 4 = y

Now we can plug it into the first and solve for x:

-9x + 4y = 8

-9x + 4(-3x - 4) = 8

-9x - 12x - 16 = 8

-21x = 8 + 16

-21x = 24

x = 24/-21

x = -8/7

Correct answer is C.

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2 years ago

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Simplify 10(N + 3).<br><br> 10N + 30<br> 10N + 13<br> 10N + 3

In-s [12.5K]

10(N + 3)

= 10N + 30

Hence, the answer is A.

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3 years ago

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Find the dimensions of the rectangle with area 256 square inches that has minimum perimeter, and then find the minimum perimeter

mezya [45]

Answer:

Dimensions: $A=a\cdot b=256$

Perimiter: $P=2a+2b$

Minimum perimeter: [16,16]

Step-by-step explanation:

This is a problem of optimization with constraints.

We can define the rectangle with two sides of size "a" and two sides of size "b".

The area of the rectangle can be defined then as:

$A=a\cdot b=256$

This is the constraint.

To simplify and as we have only one constraint and two variables, we can express a in function of b as:

$b=\frac{256}{a}$

The function we want to optimize is the diameter.

We can express the diameter as:

$P=2a+2b=2a+2*\frac{256}{a}$

To optimize we can derive the function and equal to zero.

$dP/da=2+2\cdot (-1)\cdot\frac{256}{a^2}=0\\\\\frac{512}{a^2}=2\\\\a=\sqrt{512/2}= \sqrt {256} =16\\\\b=256/a=256/16=16$

The minimum perimiter happens when both sides are of size 16 (a square).

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2 years ago

I don't understand plz help

Rasek [7]

Answer:

The equation that represent x, the height of the sign is;

$2a = 3x$

Step-by-step explanation:

Given that the area of the triangular yield is A square feet

and it has a base length of 3 feet.

also the height is represented by x;

$b = 3ft \\ h = x$

Recall that the area of a triangle can be written as;

$a = \frac{1}{2} bh$

substituting the given;

$a = \frac{1}{2} \times 3 \times x \\ a = \frac{3}{2} x \\ 2a = 3x$

Therefore, the equation that represent x, the height of the sign is;

$2a = 3x$

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2 years ago

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Tom caught 4 fish and his son caught 12 fish. The number of fish that Tom’s caught was what percent of the number of fish his so

Fofino [41]

Answer:

33.3 % (Approx) percent of fish that Tom’s caught of the number of fish his son caught .

25% is the percent of the total amount Tom caught.

Step-by-step explanation:

Formula

$Percentage = \frac{Part\ value\times 100}{Total\ values}$

Part First

As given

Tom caught 4 fish and his son caught 12 fish.

Here

Part value = 4

Total value = 12

Put in the formula

$Percentage = \frac{4\times 100}{12}$

$Percentage = \frac{400}{12}$

Percentage = 33.3 % (Approx)

Therefore the 33.3 % (Approx) percent of fish that Tom’s caught of the number of fish his son caught .

Second Part

As given

Tom caught 4 fish and his son caught 12 fish.

Total number of fish caught = 4 + 12

= 16

Part value = 4

Total value = 16

Put in the formula

$Percentage = \frac{4\times 100}{16}$

$Percentage = \frac{400}{16}$

Percentage = 25%

Therefore the 25% is the percent of the total amount Tom caught.

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2 years ago