Explain how to use a pattern to find the product of a power of 10 and a decimal

Answers

Answer 1
Answer:

Decimal numbers are numbers that have fractional parts.

Take for instance the following products.

\mathbf{2.56 * 10^2 = 256}

\mathbf{2.56 * 10^3 = 2560}

\mathbf{2.56 * 10^(-3) = 0.00256}

\mathbf{2.56 * 10^(-2) = 0.0256}

Assume the power of 10 is n.

  • Notice that, when the n is positive, the decimal place moves forward n times.
  • Similarly, when n is negative, the decimal place moves backward n times.

So, patterns can be used to calculate the product of a decimal and a power of 10 by moving the decimal place forward or backward

Read more about patterns and decimals at:

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Answer 2
Answer:

Answer:

When we multiply a decimal by a number with power of 10, the decimal point moves to the right by the same number of zeros in the power of ten multiplier.

For example:

Multiplying 7.362 by 100.

As there are 2 zeroes in 100, we will move the decimal to 2 places in the right.

Hence, 7.362*100=736.2

Powers of 10 are like 10,100,1000 and so on.


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72 = r 90 Whats R in this equation

Answers

rmemeber you can do anything to an equaiton as longn as you do it to both sides
also x times 1/x=1 since x/x=1
also x times 1=x

72=r90
divide both sides by 90
72/90=r
0.8=r


r=0.8

What is the exact volume of a sphere that has a radius of 7.5ft

Answers

V=(4/3)(pi)r^3

r=7.5

V=(4/3)(pi)(7.5^3)
V=(4/3)(pi)(7.5^3)

V=(4/3)(pi)(421.875)

V=562.5pi ft^2


if you watnt to you can aprox pi=3.14

V=562.5*3.14

V=1766.25 ft^3

so answer is 562.5pi ft^3 or 1766.25 ft^3
since the equation for volume of a sphere is 4/3* π*r^3, you just plug in the radius. if you do this you get 4/3*421.875*π. multiply 4/3 and 421.875 and you get 562.5. now since it says EXACT, leave it in terms of pi; your answer would be 562.5π ft^3. if it said estimated or something along those lines then you would multiply by 3.14...... but since it says exact you leave pi alone.

16) Solve and graph the compound inequality.

Answers

B) 2x+1 < 7 and -2x +1 < 9
C) -4 < x < 3
D) -4 <[equal to] x <[equal to] 3

A nonlinear system of inequalities consist of two or more

Answers

b equations can be the correct ans

Final answer:

A nonlinear system of inequalities involves two or more inequalities that are not straight lines when graphed. They can include equations like quadratic or exponential equations. The solution is the set of points that satisfy all inequalities.

Explanation:

A nonlinear system of inequalities in mathematics consists of two or more inequalities that are not straight lines when graphed. These inequalities might include quadratic equations, exponential equations, or any other equations that do not form a straight line. For example, y > x^2 and y < -x are a nonlinear system of inequalities. The points (x, y) that satisfy all the inequalities in the system constitute the solution.

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The range of the function f(k) = k2 + 2k + 1 is {25, 64}. What is the function’s domain? A. {5, 8} B. {-5, -8} C. {3, 8} D. {4, 7} E. {4, 8}

Answers

Answer:

Option D

The domain of the function is: {4, 7}

Step-by-step explanation:

We know that for polynomial functions like f(k) = k^2 + 2k + 1 its domain and its rank are all real numbers. However, for this case we are told that the function range is: the set {25, 64}

This means that the function is bounded.

Then the domain of f(k) are all possible values of k such that f(k) belongs to the interval {25, 64}.

To find the limit values of k then we do f(k) = 25

k^2 + 2k + 1 = 25

k^2 + 2k -24 = 0

Now we factor the expression:

(k + 6)(k-4) = 0

Then k = 4 and k = -6.

Now we do f(k) = 64

k ^ 2 + 2k +1 = 64\n\nk ^ 2 + 2k -63 = 0

We factor the expression:

(k + 9)(k-7) = 0

k = -9 and k = 7.

Finally we search between the options given an interval that matches.

The option that matches is option D {4, 7}

Finally, the domain of the function is: {4, 7}

7. What percent of 75 is 27?

Answers

The percentage of 75 that 27 is, is 36 percent.

What percent of 75 is 27?

If we have two numbers A and B, and we want to find the percentage of B that A is, we can use the formula:

P = 100%*(A/B)

Here we have:

A = 27

B = 75

Reaplacing that in the formula above, we will get:

P = 100%*(27/75)

P =  36%

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Answer:

36 %

Step-by-step explanation:

x% = x/100

27/75 = x/100

100 · 27/75 = 100 · x/100

2700/75 = x

36 = x

36%