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3 years ago

What are the zeros of the quadratic function f(x) = 2x2 + 16x – 9?

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

8 0

Answer:

The zeros of the function are -0.488 and -7.39

Step-by-step explanation:

Given the quadratic function

f(x) = 2x²+16x-9

The zeros of the function is gotten at when f(x) = 0

2x²+16x-9 = 0

Using the general equation

x = -b±√b²-4ac/2a

From the equation, a = 2, b = 16 and c= -9

x = -16±√16²-4(2)(-9)/2(2)

x = -16±√256-72/4

x = -16±√184/4

x = -16+13.56/4

x = -16+13.56/4 and -16.13.56/4

x = --2.44/5 and -29.56/4

x = -0.488 and -7.39

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3 years ago

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A population of mice is increasing exponentially. On Monday there were 120 most. One month later there were 132 most. Ready func

djyliett [7]

Answer:

$y=120 * 1.1^x$ --- function

The monthly rate is 10%

Step-by-step explanation:

Given

Let

$x \to months$

$y \to mice$

So, we have:

$(x_1,y_1) = (0,120)$ --- Monday

$(x_2,y_2) = (1,132)$ --- One month later

Required

The function

The function is represented as:

$y=ab^x$

In $(x_1,y_1) = (0,120)$ , we have:

$120 = a * b^0$

$120 = a * 1$

$120 = a$

$a=120$

In $(x_2,y_2) = (1,132)$ , we have:

$132 = a * b^1$

$132 = a * b$

Substitute: $a=120$

$132 = 120 * b$

Solve for b

$b = \frac{132}{120}$

$b = 1.1$

So, the function is:

$y=ab^x$

$y=120 * 1.1^x$

To calculate the monthly rate (r), we have:

$y =a(1 + r)^x$

Compare to: $y =ab^x$

$1 + r = b$

Make r the subject

$r = b-1$

Substitute $b = 1.1$

$r = 1.1-1$

$r = 0.1$

Express as percentage

$r = 0.1*100\%$

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5 0

3 years ago

Thanks for the help

Brrunno [24]

The answer is B.

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4 0

3 years ago

Help with the question above please????

sukhopar [10]

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7 0

3 years ago

A researcher wants to see if birds that build larger nests lay larger eggs. He selects two random samples of nests: one of small

True [87]

Answer:

95% confidence interval for the difference between the average mass of eggs in small and large nest is between a lower limit of 0.81 and an upper limit of 2.39.

Step-by-step explanation:

Confidence interval is given by mean +/- margin of error (E)

Eggs from small nest

Sample size (n1) = 60

Mean = 37.2

Sample variance = 24.7

Eggs from large nest

Sample size (n2) = 159

Mean = 35.6

Sample variance = 39

Pooled variance = [(60-1)24.7 + (159-1)39] ÷ (60+159-2) = 7619.3 ÷ 217 = 35.11

Standard deviation = sqrt(pooled variance) = sqrt(35.11) = 5.93

Difference in mean = 37.2 - 35.6 = 1.6

Degree of freedom = n1+n2 - 2 = 60+159-2 = 217

Confidence level = 95%

Critical value (t) corresponding to 217 degrees of freedom and 95% confidence level is 1.97132

E = t×sd/√(n1+n2) = 1.97132×5.93/√219 = 0.79

Lower limit = mean - E = 1.6 - 0.79 = 0.81

Upper limit = mean + E = 1.6 + 0.79 = 2.39

95% confidence interval for the difference in average mass is (0.81, 2.39)

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3 years ago