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3 years ago

Solve the equation using the zero-product property (2x-8)(7x+5)=0

Mathematics

2 answers:

alexandr1967 [171]3 years ago

8 0

Answer:

x = 4 and x = -5/7

Step-by-step explanation:

The zero product property states that if ab =0, then a =0 or b = 0 or both a and b equal to zero.

We are given (2x - 8)(7x + 5) = 0

Using the property, we can write it as

(2x - 8) = 0 or (7x + 5) = 0

Now we have to solve for x.

Let's solve the first one.

2x - 8 = 0

Add 8 on both sides, we get

2x - 8 + 8 = 8

2x = 8

Dividing both sides by 2, we get

2x/2 = 8/2

x = 4

Now let's solve the second one.

7x + 5 =0

Subtract 5 on both sides, we get

7x = -5

Dividing both sides by 7, we get

x = -5/7

Therefore, the solutions are x = 4 and x = -5/7

Iteru [2.4K]3 years ago

7 0

If xy=0 assume that x and y=0
so
(2x-8)(7x+5)=0
assume
2x-8=0 and 7x+5=0
solve each

2x-8=0
2x=8
x=4

7x+5=0
7x=-5
x=-5/7

so x=-5/7 or 4

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A student pays for 8.9 pounds of apples with a 10$ bill. Its $1.09 per pound. How much change does the student receive? What do you do first to solve the problem?

Answer:

$0.299

Step-by-step explanation:

Given that :

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3 years ago

The half-life of a certain tranquilizer in the bloodstream is 47 hours. How long will it take for the drug to decay to 93% of

GaryK [48]

Answer:

It will take 4.84 hours for the drug to decay to 93% of the original dosage.

Step-by-step explanation:

We are given that the half-life of a certain tranquilizer in the bloodstream is 47 hours.

The given exponential model is: $A = A_0 e^{kt}$

Now, we know that A becomes half after 47 hours which means that;

$A = 0.5 A_0$

Using this in the above equation we get;

$A = A_0 e^{kt}$

$0.5 A_0 = A_0 e^{(k\times 47)}$ where t = 47 hours

$\frac{0.5 A_0}{A_0} = e^{(47k)}$

$0.5 = e^{47k}$

Taking log on both sides we get;

$ln(0.5) = ln(e^{47k})$

$ln(0.5) =47k$

$k = \frac{ln(0.5)}{47}$

k = -0.015

Now, the time it will take for the drug to decay to 93% of the original dosage is given by;

$0.93 = e^{kt}$ where t is the required time

$0.93 = e^{(-0.015 \times t)}$

Taking log on both sides we get;

$ln(0.93) = ln(e^{-0.015t})$

$ln(0.93) =-0.015t$

$t = \frac{ln(0.93)}{-0.015}$

t = 4.84 hours

Hence, it will take 4.84 hours for the drug to decay to 93% of the original dosage.

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4 years ago

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nirvana33 [79]

Answer:

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Step-by-step explanation:

u = arcsin(0.391) ≈ 23.016737°

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You can also use the trig identity ...

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and you can find cos(u) as cos(arcsin(0.391)) ≈ 0.920391

or using the trig identity ...

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Then ...

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<em>Comment on the solution</em>

These problems are probably intended to have you think about and use the trig half-angle and double-angle formulas. Since you need a calculator anyway for the roots and the division, it makes a certain amount of sense to use it for inverse trig functions. Finding the angle and the appropriate function of it is a lot easier than messing with trig identities, IMO.

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