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3 years ago

Simplify the following rational expression and state for what values they are undefined.

Mathematics

2 answers:

Svetllana [295]3 years ago

8 0

Answer: d - 2 and d cannot equal 8

Step-by-step explanation: To simplify this rational expression, start by factoring both the numerator and the denominator.

So factoring the numerator in this problem, we have a

trinomial that factors as the product of two binomials.

So we are looking for factors of +16 that add to -10 which are -8 and -2.

So we have (d - 8)(d - 2) in the numerator.

The denominator doesn't factor however.

So we have $\frac{(d - 8)(d - 2)}{(d - 8)}$ and the d - 8's cancel leaving us with d - 2.

The values d cannot be happen when the denominator is set equal to 0.

So we have d - 8 = 0 which means d = 8.

This means d = 8 wouldn't work!

QveST [7]3 years ago

3 0

Answer:

d-2 and d cannot = 8

Step-by-step explanation:

d^2 -10d+16

-----------------------

d-8

Factor the numerator

( d-8)(d-2)

-------------------

d-8

The undefined values occur when the denominator is equal to zero

d-8 = 0

d= 8

This means d cannot equal 8

Now cancel like terms in the equation ( d-8)

This yields d-2

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O Decrease 40 by ratio of 4:5

Reika [66]

A decrease in the ratio 4:5 implies that :

New quantity:Old quantity = 4:5

Let the new quantity be $\bf \: x$

$\bf∴ x : 40 = 4:5$

$= > \bf \frac{x}{40} = \frac{4}{5}$

$\bf = > 40 \times \frac{x}{40} = 40 \times \frac{4}{5}$

$\bf = > x = 8 \times 4$

$\bf = > x = 32$

So, the new quantity is 32

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3 years ago

As... Which of the following geometric series diverges?

Volgvan

Answer:

II and II only.

Step-by-step explanation:

The first series converges because the common ratio r is 0.8 (<1).

II diverges as |r| > 1.

III is an alternating series with r = -4 - that is |r| = 4 so it diverges.

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3 years ago

1. Taylor needs to purchase a car. The car Taylor plans to purchase costs $10,000. Taylor has saved $2,000 to use as a down paym

Alexxandr [17]

Answer:

a. The amount Taylor will need to finance is $8,000

b. The amount Taylor pays as interest in one year is $400

Step-by-step explanation:

The given parameters of the financing for the car are;

The cost of the car Taylor plans to purchase, C = $10,000

The amount Taylor has saved to be used as down payment, S = $2,000

The interest rate of the credit Taylor is offered = 5%

The duration given for repayment of the loan = 5 years

a. To purchase the car, the amount Taylor will need to finance, 'P', is given as follows;

P = C - S

∴ P = $10,000 - $2,000 = $8,000

b. The amount of interest on the loan in one year, 'I', is given by the following formula;

$I = \dfrac{P \times R \times T}{100}$

Where;

I = The interest payed

P = The principal amount taken as loan = $8,000

R = The interest rate = 5% APR

T = The time period the interest is applied = 1 year

Plugging in the values, we get;

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The interest Taylor will pay on the loan in one year, I = $4,00

7 0

4 years ago

Margo can purchase tile at a store for $0.79 per tile and rent a tile saw for $24. At another store she can borrow the tile saw

Monica [59]

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3 years ago

Heather is flying a kite at the park. The string makes an angle of 53° with the level ground. The kite is 28 meters above the gr

Snezhnost [94]

Answer:

35.06 meters

Step-by-step explanation:

This represents a right angled triangle.

The height of the kite above the ground represents the opposite side while the length of the string of the heather of the kite is the hypotenuse.

We need to find the hypotenuse, h.

We can use the sine part of the trigonometric function SOHCAHTOA:

sin(Ф) = opp / hyp

where opp is the side opposite the angle

hyp is the hypotenuse

=> sin(53) = 28 / h

h = 28 / sin(53)

h = 35.06 meters

The length of the string from the heather to the kite is 35.06 meters

3 0

4 years ago