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2 years ago

Which two equations would be most appropriately solved by using the zero product property? Select each correct answer.

Mathematics

2 answers:

rusak2 [61]2 years ago

7 0

Anwser: 2x² + 6x = 0 and (x−3)(x+4)=0

LekaFEV [45]2 years ago

3 0

The zero product property tells us that if the product of two or more factors is zero, then each one of these factors CAN be zero.

For more context let's look at the first equation in the problem that we can apply this to: $(x-3)(x+4)=0$

Through zero property we know that the factor $(x-3)$ can be equal to zero as well as $(x+4)$ . This is because, even if only one of them is zero, the product will immediately be zero.

The zero product property is best applied to factorable quadratic equations in this case.

Another factorable equation would be $2x^{2}+6x=0$ since we can factor out $2x$ and end up with $2x(x+3)=0$ . Now we'll end up with two factors, $2x$ and $(x+3)$ , which we can apply the zero product property to.

The rest of the options are not factorable thus the zero product property won't apply to them.

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Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to

nikklg [1K]

Answer:

Part 1)

See Below.

Part 2)

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

Step-by-step explanation:

Part 1)

The linear approximation L for a function f at the point x = a is given by:

$\displaystyle L \approx f'(a)(x-a) + f(a)$

We want to verify that the expression:

$1-36x$

Is the linear approximation for the function:

$\displaystyle f(x) = \frac{1}{(1+9x)^4}$

At x = 0.

So, find f'(x). We can use the chain rule:

$\displaystyle f'(x) = -4(1+9x)^{-4-1}\cdot (9)$

Simplify. Hence:

$\displaystyle f'(x) = -\frac{36}{(1+9x)^{5}}$

Then the slope of the linear approximation at x = 0 will be:

$\displaystyle f'(1) = -\frac{36}{(1+9(0))^5} = -36$

And the value of the function at x = 0 is:

$\displaystyle f(0) = \frac{1}{(1+9(0))^4} = 1$

Thus, the linear approximation will be:

$\displaystyle L = (-36)(x-(0)) + 1 = 1 - 36x$

Hence verified.

Part B)

We want to determine the values of x for which the linear approximation L is accurate to within 0.1.

In other words:

$\displaystyle \left| f(x) - L(x) \right | \leq 0.1$

By definition:

$\displaystyle -0.1\leq f(x) - L(x) \leq 0.1$

Therefore:

$\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1$

We can solve this by using a graphing calculator. Please refer to the graph shown below.

We can see that the inequality is true (i.e. the graph is between y = 0.1 and y = -0.1) for x values between -0.179 and -0.178 as well as -0.010 and 0.012.

In interval notation:

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

4 0

2 years ago

The function f(x) is shown on the graph. On a coordinate plane, a curved line with 3 arcs, labeled f of x, crosses the x-axis at

brilliants [131]

Answer:

x = -2,1,3

Step-by-step explanation:

Given: The curved line represented by the function crosses the x-axis at and y-axis at

To find: value of x for which

Solution:

$f(x)=0$ = gives those values of x for which the curve represented by the given function cuts the x-axis.

According to question, the curve cuts the x-axis at

5 0

2 years ago

Read 2 more answers

Steve stayed after school for extra activities 55% of the 180 school days this year. How many days did Steve stay after school?

musickatia [10]

Answer:

11/20 or 99/180 days

Step-by-step explanation:

55/100 converted to ?/180

180/100=1.8

so you would do the same on the numerator which is 55*1.8=99

99/180= 33/60=11/20

7 0

2 years ago

Use the fact that the variance of a Poisson distribution is σ2=μ. The mean number of bankruptcies filed per hour by businesses i

lianna [129]

Answer:

Variance = 5

Standard deviation = 2.236

0.2650257

Step-by-step explanation:

For a Poisson distribution is σ² = μ.

Given that:

Mean , μ of bankruptcies files per hour = 5

μ = 5

For a Poisson distribution :

P(x = x) = (μ^x * e^-μ) / x!

The Variance and standard deviation :

Variance : σ² = μ = 5

Standard deviation = sqrt(variance) = sqrt(5) = 2.236

B.) Find the probability that at most three businesses will file bankruptcy in any given hour.

P( x ≤ 3) = P(0) + P(1) + P(2) + P(3)

P(x = 0) = (5^0 * e^-5) / 0! = 0.0067379

P(x = 1) = (5^1 * e^-5) / 1! = 0.0336897

P(x = 2) = (5^2 * e^-5) / 2! = 0.0842243

P(x = 3) = (5^3 * e^-5) / 3! = 0.1403738

0.0067379 + 0.0336897 + 0.0842243 + 0.1403738

= 0.2650257

6 0

2 years ago

Maria and Edwin have $23.00 each to spend at a book fair, where all students receive a 25% discount. They both want to purchase

Andreyy89

Maria : 26.50 - 0.25(26.50) = 26.50 - 6.625 = 19.88
19.87 + 0.10(19.87) = 19.87 + 1.99 = 21.86

Edwin : 0.75(26.50) = 19.88
1.10(19.88) = 21.86

and if they each have $ 23, then yes, they both ave enough money to buy the book. They both were correct in their calculations. Because taking 25% off, is the same as paying 75%.....and taking the discount price and subtracting 10% from that, is the same as multiplying by 110%. So they basically worked the same problem, just in a little different way...and they both ended up with the same answer

4 0

2 years ago