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3 years ago

Explain how you know whether 1/15 is equal a terminating decimal or

Mathematics

1 answer:

Ulleksa [173]3 years ago

3 0

The lame answer is that you put it into a calcuator and see.

The more formal way you know is if, when the fraction is reduced, the denominator's only prime factors are 2s or 5s. If that's the case, the fraction will terminate. If you have any prime factor other than 2 or 5, it will repeat.

But knowing that "2 or 5 prime factor" idea would have to be something specifically taught in your class (or a prerequisite class).

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Joe works as a busboy making $7 per hour and as a theater usher making $9 per hour. Let b be the number of hours he works as a b

Vilka [71]

Answer:

The inequality describing the situation is:

$7b+9u>1500$

Step-by-step explanation:

Joe works as a busboy at the rate of = $7 per hour

Let the number of hours he works as a bus boy this month be = $b$ hours

∴ Amount Joe would make this month working as a busboy = $\$7\times b=\$7b$

Joe works as a theater usher at the rate of = $9 per hour

Let the number of hours he works as a theater usher this month be = $u$ hours

∴ Amount Joe would make this month working as a theater usher = $\$9\times u=\$9u$

Total amount Joe would make this month = $\$(7b+9u)$

His goal is earn more than $1500 this month.

∴ The situation can be represented in the following inequality:

$7b+9u>1500$

6 0

3 years ago

PLSS HELP ME!!! question 3x - 4/5= - 1/2 what is the value of x?

Minchanka [31]

Answer:

x = $\frac{1}{10}$

Step-by-step explanation:

Given

3x - $\frac{4}{5}$ = - $\frac{1}{2}$

Multiply through by 10, the lcm of 5 and 2 to clear the fractions

30x - 8 = - 5 ( add 8 to both sides )

30x = 3 ( divide both sides by 30 )

x = $\frac{3}{30}$ = $\frac{1}{10}$

7 0

3 years ago

Let v = (v1, v2) be a vector in R2. Show that (v2, −v1) is orthogonal to v, and use this fact to find two unit vectors orthogona

andrey2020 [161]

Answer:

a. v.v' = v₁v₂ - v₁v₂ = 0 b. (20, -21)/29 and (-20,21)/29

Step-by-step explanation:

a. For two vectors a, b to be orthogonal, their dot product is zero. That is a.b = 0.

Given v = (v₁, v₂) = v₁i + v₂j and v' = (v₂, -v₁) = v₂i - v₁j, we need to show that v.v' = 0

So, v.v' = (v₁i + v₂j).(v₂i - v₁j)

= v₁i.v₂i + v₁i.(- v₁j) + v₂j.v₂i + v₂j.(- v₁j)

= v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j

i.i = 1, i.j = 0, j.i = 0 and j.j = 1

So, v.v' = v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j

= v₁v₂ × 1 - v₁v₁ × 0 + v₂v₂ × 0 - v₂v₁ × 1

= v₁v₂ - v₂v₁

= v₁v₂ - v₁v₂ = 0

So, v.v' = 0

b. Now a vector orthogonal to the vector v = (21,20) is v' = (20,-21).

So the first unit vector is thus a = v'/║v'║ = (20, -21)/√[20² + (-21)²] = (20, -21)/√[400 + 441] = (20, -21)/√841 = (20, -21)/29.

A unit vector perpendicular to a and parallel to v is b = (-21, -20)/29. Another unit vector perpendicular to b, parallel to a and perpendicular to v is thus a' = (-20,-(-21))/29 = (-20,21)/29

8 0

2 years ago

The cost of a piece of carpet is dependent on its area, in square feet, as shown in the graph.

Bess [88]

Answer:

A. false

B. c = 2.258241758a - 1.923076923

C. $290

Step-by-step explanation:

Part B was solved using a graphing calculator

3 0

3 years ago

The area of a rectangle is 36 square inches, and its perimeter is 26 inches. What are the length and width of the rectangle?

gogolik [260]

Answer:

9 and 4

Step-by-step explanation:

5 0

2 years ago