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My name is Ann [436]
3 years ago
12

Factorize the following expression ab-a-b+1

Mathematics
1 answer:
dolphi86 [110]3 years ago
5 0

Group 'em together

a b − a + 1 − b

a b − a = a ( b − 1 )

Notice that there will be a 1 as without it it'll simply be  ab

1 − b = 1 ( 1 − b )

Notice that it doesn't match with the upper one... so we'll change the signs

1 ( 1 − b ) = − 1 ( b− 1 )

(try to multiply them now!!

Jot them down in one expression

a ( b − 1 ) − 1 ( b − 1 )

You get!!!!!!

( a − 1 ) ( b − 1 )

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A tub filled with 50 quarts of water empties at a rate of 2.5 quarts per minute. let w = quarts of water left in the tub and t =
Sholpan [36]

This is a linear relationship. The slope-intercept form of the linear equation is:

y=mx+c

Where,

  • m is the rate of change (positive if increasing rate and negative if decreasing rate)
  • c is the y intercept, or the initial value

<u><em>Rate of change is 2.5 quarts per minute (it is decreasing so m is -2.5)</em></u>

<u><em>Initial value is 50 quarts, so c is 50.</em></u>

Plugging in the values we get y=-2.5x+50.


Changing variables to w instead of y and t instead of x, gives us,

w=50-2.5t. Where w is warts of water left in the tub and t is the time in minutes.


There is no viable solution when t=30 because at t=20, w=0 (0=50-2.5(20)). It means after 20 minutes, there is no water left. So t=30 minutes doesn't make sense.


ANSWER:

Modelling equation: w=50-2.5t

When t=30, there is no VIABLE solution

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3 years ago
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The amount of radioactive uranium changes with time. The abscissas and ordinates of the points given are the time and amoung of
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The answer is <span>A. f(t) = 100(0.25)t
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4 0
3 years ago
Help please!!! AHAHSBHSBDR​
Degger [83]

Answer:

a = 8/29 thus: Step 1 is wrong!

Step-by-step explanation:

Solve for a:

8 - a/2 = 3 (4 - 5 a)

Hint: | Put the fractions in 8 - a/2 over a common denominator.

Put each term in 8 - a/2 over the common denominator 2: 8 - a/2 = 16/2 - a/2:

16/2 - a/2 = 3 (4 - 5 a)

Hint: | Combine 16/2 - a/2 into a single fraction.

16/2 - a/2 = (16 - a)/2:

(16 - a)/2 = 3 (4 - 5 a)

Hint: | Make (16 - a)/2 = 3 (4 - 5 a) simpler by multiplying both sides by a constant.

Multiply both sides by 2:

(2 (16 - a))/2 = 2×3 (4 - 5 a)

Hint: | Cancel common terms in the numerator and denominator of (2 (16 - a))/2.

(2 (16 - a))/2 = 2/2×(16 - a) = 16 - a:

16 - a = 2×3 (4 - 5 a)

Hint: | Multiply 2 and 3 together.

2×3 = 6:

16 - a = 6 (4 - 5 a)

Hint: | Write the linear polynomial on the left hand side in standard form.

Expand out terms of the right hand side:

16 - a = 24 - 30 a

Hint: | Move terms with a to the left hand side.

Add 30 a to both sides:

30 a - a + 16 = (30 a - 30 a) + 24

Hint: | Look for the difference of two identical terms.

30 a - 30 a = 0:

30 a - a + 16 = 24

Hint: | Group like terms in 30 a - a + 16.

Grouping like terms, 30 a - a + 16 = (-a + 30 a) + 16:

(-a + 30 a) + 16 = 24

Hint: | Combine like terms in 30 a - a.

30 a - a = 29 a:

29 a + 16 = 24

Hint: | Isolate terms with a to the left hand side.

Subtract 16 from both sides:

29 a + (16 - 16) = 24 - 16

Hint: | Look for the difference of two identical terms.

16 - 16 = 0:

29 a = 24 - 16

Hint: | Evaluate 24 - 16.

24 - 16 = 8:

29 a = 8

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 29 a = 8 by 29:

(29 a)/29 = 8/29

Hint: | Any nonzero number divided by itself is one.

29/29 = 1:

Answer: a = 8/29

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