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3 years ago

I know the right answer to this I just don't know how to get it, please help.

1 answer:

7 0

$\bf \cfrac{x^2+5x+6}{x+4}\cdot \cfrac{x^2+x-12}{x^2+x-2}\implies \cfrac{\underline{(x+2)}(x+3)}{\underline{x+4}}\cdot \cfrac{\underline{(x+4)}(x-3)}{\underline{(x+2)}(x-1)}
\\\\\\
\cfrac{(x+3)(x-3)}{x-1}$

and yes, the restrictions are -4, -2 and 1.

the original expression has such restrictions because if ever "x" becomes one of those values, one of the denominators will turn to 0 making the fraction undefined.

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Can someone please helpp.

nika2105 [10]

1. Over a period of 6 years (from 1980 to 1986) the house gained a value of 12000 dollars (109k-97k). 12000/6 gives you a rate of 2000 dollars per year. Because the initial price at t=0 is 97000, the function is 97000+2000t

6 0

3 years ago

Four doughnuts and 4 coffees cost $12. The cost of the 4 coffees is half the cost of the 4 doughnuts. What is the cost of each c

tangare [24]

The cost of each coffee is $1.05

8 0

3 years ago

Let θ

konstantin123 [22]

Answer:

θ is decreasing at the rate of $\frac{21}{16}$ units/sec

or $\frac{d}{dt}$ (θ) = $\frac{-21}{16}$

Step-by-step explanation:

Given :

Length of side opposite to angle θ is y

Length of side adjacent to angle θ is x

θ is part of a right angle triangle

At this instant,

x = 8 , $\frac{dx}{dt}$ = 7

( $\frac{dx}{dt}$ denotes the rate of change of x with respect to time)

y = 8 , $\frac{dy}{dt}$ = -14

( The negative sign denotes the decreasing rate of change )

Here because it is a right angle triangle,

tanθ = $\frac{y}{x}$ -------------------------------------------------------------------1

At this instant,

tanθ = $\frac{8}{8}$ = 1

Therefore θ = π/4

We differentiate equation (1) with respect to time in order to obtain the rate of change of θ or $\frac{d}{dt}$ (θ)

$\frac{d}{dt}$ (tanθ) = $\frac{d}{dt}$ (y/x)

( Applying chain rule of differentiation for R.H.S as y*1/x)

$sec^{2}$ θ $\frac{d}{dt}$ (θ) = $\frac{1}{x}$ $\frac{dy}{dt}$ - $\frac{y}{x*x}$ $\frac{dx}{dt}$ -----------------------2

Substituting the values of x , y , $\frac{dx}{dt}$ , $\frac{dy}{dt}$ , θ at that instant in equation (2)

2 $\frac{d}{dt}$ (θ) = $\frac{1}{8}$ *(-14)- $\frac{8}{8*8}$ *7

$\frac{d}{dt}$ (θ) = $\frac{-21}{16}$

Therefore θ is decreasing at the rate of $\frac{21}{16}$ units/sec

or $\frac{d}{dt}$ (θ) = $\frac{-21}{16}$

3 0

3 years ago

Assume the reserve requirement is 10%. First National Bank receives a deposit of $5,400. If there is no slippage, how much could

d1i1m1o1n [39]

Given:

Reserve requirement = 10%
Deposit = $5400

Find:

money the supply could expand = ?

Solution:

Money Supply = Monetary Base × Money Multiplier

Before we determine the money supply, the money multiplier must already be determined. Therefore:
$5400 (0.10) = $540

In this case, adding the two will give us the money supply
$5400 + $540 = $5940

Nevertheless, not all money is lent out or spent. Kept money reduces the money supply.

The restrain to the growth of the money supply when deposits expand are identified by 2 factors:

1. The amount above (excess reserves) what they are required to hold are being kept.

2. Their income rises as the public has the penchant to hold more cash as their income.

8 0

3 years ago

Find three consecutive odd integers such that the sum of the first is two less than the second,and three more than the third is

Lunna [17]

Answer:

the three consecutive odd integers are 9, 11, and 13.

Step-by-step explanation:

Let's say that the first odd integer is x. The second consecutive odd integer would have to be x+2. (It would not be x+1 because that would result in an even integer. The sum of any two odd numbers is even.) The third consecutive odd integer would be (x+2) +2 or x+4.

The sum of the first, twice the second, and three times the third can be written as:

x+2(x+2)+3(x+4)

This equals 70. We can now distribute and solve for x:

x+2(x+2)+3(x+4)=70

x+2x+4+3x+12=70(distribute)

6x+16=70(combine like terms)

6x=54(subtract 16 from both sides)

x=9(divide by 9)

Thus, the three consecutive odd integers are 9, 11, and 13

hope this helps :)

4 0

3 years ago

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