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3 years ago

The reciprocal of a fraction less than 1 is always a fraction greater than 1.why is this?

1 answer:

4 0

First of all, you know that a fraction is smaller than 1 if the top number is smaller than the bottom. It works both ways, meaning that if the top number is larger than the bottom number, the fraction is greater than 1.

So, for example, a fraction less than 1 can be expressed as
(x-1)/x
because the top number is smaller than the bottom number.

The reciprocal can be found by flipping the top and the bottom, so the reciprocal is
x/(x-1)

x is always greater than x-1, so in the reciprocal, the top number will be larger than the bottom number. That means it will always be greater than 1.

Hope this helps!
(Sorry if this is confusing)

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Is x + 3 a factor of P(x) = x³ - 5x² + 3x + 9 ? Explain.

Ksju [112]

Answer:

Step-by-step explanation:

using the Factor theorem.

If (x + h) is a factor of f(x) then f(- h) = 0

for factor (x + 3) then evaluate P(- 3)

P(- 3) = (- 3)³ - 5(- 3)² + 3(- 3) + 9 = - 27 - 45 - 9 + 9 = - 72

since f(- 3) ≠ 0 then (x + 3) is not a factor of P(x)

4 0

2 years ago

Angle 1 and angle 2 are vertical angles. If m angle 1 = (8x+12)° and m angle 2 = (3x+37)° find the measure for each angle.

laila [671]

Vertically opposite angles are always equal.

Given angles are (8x+12)° and (3x+37)°

=> (8x+12)° = (3x + 37)°

=> 8x - 3x = 37-12

=> 5x = 25

=> x = 25/5 = 5°

Angle 1 = (8x+12)° = (8(5)+12) = 40+12 = 52°

Angle 2 = (3x + 37)° = (3(5)+37)° = 15+37 = 52°

8 0

2 years ago

If 25% of a number is 12, what is 75% of that number?

snow_tiger [21]

Answer:

Step-by-step explanation:

$\frac{0.25}{0.75} =\frac{12}{x} \\$

$0.75 *12=9$

$\frac{9}{0.25} =36$

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3 years ago

Kyle Charges $75 plus $65 per hour for tractor work. How many hours does he work to earn at least $335?

strojnjashka [21]

Answer:

Hi there!

Your answer is

Kyle must work at LEAST 4 hours to earn 335$

Step-by-step explanation:

kyles charge:

75+65H>=335

-75

65H>=260

/65

H>=4

Plug back in!

75+65(4) >= 335?

335>=335 YES!

Hope this helps

7 0

3 years ago

A map shows that the vertices of a backyard are $W\left(-100,-70\right),\ X\left(-100,0\right),\ Y\left(0,0\right),$ and $Z\left

vichka [17]

i need a picture to answer this

Step-by-step explanation:

bc i said so

4 0

2 years ago