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3 years ago

Given that a = 4.8 × 104 and that b = 8 × 10−3

Mathematics

1 answer:

Paha777 [63]3 years ago

8 0

Answer:

3.84 * 10^0

Step-by-step explanation

Given the following values;

a = 4.8 × 104 and that b = 8 × 10−3

We are to find the product ab

ab = (4.8 × 10^4)(8 × 10^−3)

ab = (4.8*8)(10^4 * 10^-3)

ab = 38.4 * 10^(4-3)

ab = 38.4 * 10^-1

ab = 3.84 * 10 * 10^-1

ab = 3.84* 10^0

<em>Hence the product in standard form is expressed as 3.84 * 10^0</em>

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Write the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10).

Serjik [45]

Answer:

$\displaystyle f(x)=x^2+2x+2$

Step-by-step explanation:

<u>System Of Linear Equations </u>

In this problem, we'll need to solve a 3x3 system of linear equations because we have three unknowns and three conditions.

We are required to find the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10)

The general quadratic function can be written as

$\displaystyle f(x)=ax^2+bx+c$

We need to find the values of a,b, and c. Let's use the first condition, i.e. f(-1)=1

$\displaystyle f(-1)=a(-1)^2+b(-1)+c$

$\displaystyle f(-1)=a-b+c$

$\displaystyle a-b+c=1.....[eq\ 1]$

Now we use the second condition f(1)=5

$\displaystyle f(1)=a(1)^2+b(1)+c$

$\displaystyle f(1)=a+b+c$

$\displaystyle a+b+c=5.......[eq\ 2]$

Finally, we use the third condition f(2)=10

$\displaystyle f(2)=a(2)^2+b(2)+c$

$\displaystyle f(2)=4a+2b+c$

$\displaystyle 4a+2b+c=10....[eq\ 3]$

We put together eq 1, eq 2, and eq 3 to form the system

$\displaystyle \left\{\begin{matrix}a-b+c=1\\ a+b+c=5\\ 4a+2b+c=10\end{matrix}\right.$

Adding the first two equations we have

$\displaystyle 2a+2c=6$

$\displaystyle a+c=3$

And also

$\displaystyle b=2$

Using the above equation and the value of b in the third equation, we have

$\displaystyle \left\{\begin{matrix}a+c=3\\ 4a+c=6\end{matrix}\right.$

Subtracting the first equation from the second

$\displaystyle 3a=3$

$\displaystyle a=1$

And therefore

$\displaystyle c=2$

Now we have all the values, the quadratic function is

$\displaystyle \boxed{f(x)=x^2+2x+2}$

6 0

3 years ago

Help meh plssss ( btw on question 2 its yes or no )

IgorLugansk [536]

The sum should be 9/32

5 0

3 years ago

Wrote the number in 2 other forms 15,409

myrzilka [38]

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4 0

4 years ago

Read 2 more answers

During a certain week, the mean price of gasoline in the New England region was $3.796 per gallon. A random sample of 32 gas sta

Ymorist [56]

Answer: the probability that the mean price for the sample was between $3.781 and $3.811 that week is 0.94122

Step-by-step explanation:

Given that;

sample size n = 32

mean μ = $3.796

standard deviation σ = 0.045

P(3.781 < x" < 3.811) = ?

Standard Error S.E = σ/√n = 0.045/√32 = 0.007955

z value for 3.781, z = x-μ/S.E = (3.781-3.796)/0.007955 = -1.8856 ≈ -1.89

z value for 3.811, z = x-μ/S.E = (3.811-3.796)/0.007955 = 1.8856 ≈ 1.89

P(3.781 < x" < 3.811) = P( -1.89 < z < 1.89)

= P(z < 1.89) - P(z < -1.89)

from z-score table

⇒ 0.9706 - 0.02938

⇒ 0.94122

Therefore the probability that the mean price for the sample was between $3.781 and $3.811 that week is 0.94122

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3 years ago

Liam is given numbers to cpmpare. Which comparison statement is true

liberstina [14]

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3 years ago

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