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11 days ago

(6.8x10^2) x (1.3x10^-3) answer as standard form

Mathematics

1 answer:

Svet_ta [4.2K]11 days ago

6 0

Result:

0.884

Detailed steps:

Initially, calculate the exponents, perform the foil, combine like terms, and the resulting figure will be 0.884.

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Which are the solutions of x2 = –5x + 8? StartFraction negative 5 minus StartRoot 57 EndRoot Over 2 EndFraction comma StartFract

tester [3895]

Answer:

$x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}$

Detailed solution:

Given:

The problem to solve is:

$x^2=-5x+8$

Convert the equation into the standard quadratic form $ax^2+bx +c =0$ , where $a,\ b,\ and\ c$ represent constants.

So, by adding $5x-8$ to both sides, we get:

$x^2+5x-8=0$

Note that $a=1,b=5,c=-8$ .

The roots of this quadratic are found by applying the quadratic formula given as:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substitute $a=1,b=5,c=-8$ into the formula and calculate for $x$ .

$x=\frac{-5\pm \sqrt{5^2-4(1)(-8)}}{2(1)}\\x=\frac{-5\pm \sqrt{25+32}}{2}\\x=\frac{-5\pm \sqrt{57}}{2}\\\\\\\therefore x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}$

Hence, the roots are:

$x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}$

4 0

14 days ago

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Stackable polystyrene cups have a height h1=12.5 cm. Two stacked cups have a height of h2=14 cm. Three stacked cups have a heigh

AnnZ [3868]

Answer:

Approximately 59 stacked cups.

Step-by-step explanation:

We have the following measurements:

Height of one cup = 12.5 cm,

Height of two cups stacked = 14 cm,

Height of three cups stacked = 15.5 cm,

...and so on.

This situation can be described by an arithmetic sequence,

12.5, 14, 15.5,....

The first term is defined as a = 12.5,

with a common difference of d = 1.5 cm.

Thus, the height of x stacked cups is given by

$h(x) = a+(x-1)d = 12.5 + (x-1)1.5 = 1.5x + 11$

As per the problem,

h(x) = 200

⇒ 1.5x + 11 = 200

⇒ 1.5x = 189

⇒ x = 59.3333333333 ≈ 59.

Therefore, you will need approximately 59 stacked cups.

3 0

3 days ago

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Find the slope of a pipe that slopes down 2/5 inch per foot.

babunello [3607]

Answer:

$m=\frac{1}{30}$

Step-by-step explanation:

To determine the slope, divide the rise by the run to calculate the slope.

Note that

1 ft = 12 in

Let

y ----> the rise

x ----> the run

m ----> the slope

$m=\frac{y}{x}$

the values are given as

$y=2/5\ in$

$x=1\ ft=12\ in$

$m=\frac{y}{x}$

substituting these values gives

$m=\frac{(2/5)}{12}$

$m=\frac{2}{60}$

Simplifying further

$m=\frac{1}{30}$

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12 days ago

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Two players A and B play a marble game. Each player has both a red and blue marble. They present one marble to each other. If bo

Zina [3893]

Answer:

Step-by-step explanation:

Player A has a red marble and a blue marble, while Player B also has a red marble and a blue marble.

Therefore, the probability of selecting one marble is equal, at 0.5.

Due to the independence of A and B's choices, the joint event is calculated by multiplying the probabilities.

Let A represent the amount that player A wins.

If both players select one marble, the sample space can be considered as

(R,R) (R,B) (B,R) (B,B)

Probability 0.25 0.25 0.25 0.25

A's winnings 3 -2 -2 1

E(A) 0.75 -0.5 -0.5 0.25 = 0

Thus, the game is even, offering equal expected values for both A and B.

It does not influence the outcome whether you are A or B.

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12 days ago

Kevin and Brittany write an equation to represent the following relationship, and both students solve their equation. Who found

Inessa [3895]

Kevin, since the problem states a number (x) minus 20, and given that 20 is mentioned later, it indicates that it is the second number involved here.

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1 day ago