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3 years ago

Find the axis of symmetry of 2x^2 + 12x + 16 Show your work

Mathematics

1 answer:

raketka [301]3 years ago

6 0

The vertex form:

$y=a(x-h)^2+k\\\\(h,\ k)-vertex$

The axis of symetry is x = h.

$y=ax^2+bx+c\to h=\dfrac{-b}{2a}$

We have

$y=2x^2+12x+16\to a=2,\ b=12,\ c=16$

Substitute:

$h=\dfrac{-12}{(2)(2)}=\dfrac{-12}{4}=-3$

<h3>Answer: x = -3</h3>

You might be interested in

If a tellemarketer made 200 phone calls and 35 customers signed up what is the relative frequency of getting a customer and not

Snezhnost [94]

Answer:

82.5% and 17.5%

Step-by-step explanation:

The telemarketer made 200 phone calls and only 35 people signed up. Therefore, we need to find the amount of people who didnt.

200 - 35 = 165

165 people did not sign up.

This meants that the frequency of getting a customer is 35/200 and not is 165/200. In percentages,

The relative frequency of not getting a customer is 82.5%

The relative frequency of getting a customer is 17.5%

6 0

3 years ago

Prove that the roots of x2+(1-k)x+k-3=0 are real for all real values of k

masha68 [24]

Answer:

Roots are not real

Step-by-step explanation:

To prove : The roots of x^2 +(1-k)x+k-3=0x

+(1−k)x+k−3=0 are real for all real values of k ?

Solution :

The roots are real when discriminant is greater than equal to zero.

i.e. b^2-4ac\geq 0b

−4ac≥0

The quadratic equation x^2 +(1-k)x+k-3=0x

+(1−k)x+k−3=0

Here, a=1, b=1-k and c=k-3

Substitute the values,

We find the discriminant,

D=(1-k)^2-4(1)(k-3)D=(1−k)

−4(1)(k−3)

D=1+k^2-2k-4k+12D=1+k

−2k−4k+12

D=k^2-6k+13D=k

−6k+13

D=(k-(3+2i))(k+(3+2i))D=(k−(3+2i))(k+(3+2i))

For roots to be real, D ≥ 0

But the roots are imaginary therefore the roots of the given equation are not real for any value of k.

6 0

2 years ago

A student wants to report on the number of movies her friends watch each week. The collected data are below: 2 14 1 2 0 1 0 2 Wh

Sunny_sXe [5.5K]

The student's friend watch 1.5 movies every week.

Data provided to us {2, 14, 1, 2, 0, 1, 0, 2}.

Number of data values = 8

Sorted or rearranged data {0, 0, 1, 1, 2, 2, 2, 14}

Median of the data provided;

Median is the mid point value of the data provided to us, but as in this case there are 8 data provided (even number of data), we will take the average of the 2 mid values of the data.

Mid Values = 1 and 2

$\bold{Median=\dfrac{1+2}{2} = 1.5}$

Mean of the data provided;

$Mean=\dfrac{Sum\ of\ all\ data\ values}{Number\ of\ data\ values} \\\\Mean= \dfrac{(0+0+1+1+2+2+2+14)}{8}\\\\Mean=2.75$

As we know, The data values provided are 0, 1 and 2, and there is 14 as well in the data which is the maximum value in the data provided to us but the value is far from the other data values provided to us. Therefore, the data value 14 is considered to be an outlier.

An outlier is the maximum value that increases the mean, which makes it larger than it should be.

If we were to compute the mean without the outlier,

$Mean=\dfrac{Sum\ of\ all\ data\ values}{Number\ of\ data\ values} \\\\Mean= \dfrac{(0+0+1+1+2+2+2)}{7}\\\\Mean=1.1428$

Now, we have understood that the mean is sensitive to outlier can be easily manipulated. thus, mean is not the right option to go for in this case.

Therefore, the median value of 1.5 is the right option.

Hence, the student's friend watch 1.5 movies every week.

To know more visit:

brainly.com/question/1363341

3 0

2 years ago

Read 2 more answers

Consider the following regression line: T e s t s c o r e ^ = 698.9 − 2.28 S T R . You are told that the t-statistic on the slop

Amiraneli [1.4K]

Answer:

0.52

Step-by-step explanation:

Given the regression line :

Test score^ = 698.9 - 2.28STR

T statistic on slope Coefficient = 4.38

The standard error on slope Coefficient :

2.28 / 4.38

= 0.5205479

= 0.52

6 0

2 years ago

Zachary has nickels, dimes and quarters in his piggy bank. He has 58 coins with a total value of $6.50. There are twice as many

kari74 [83]

Answer:

nickel = 16

dimes = 32

quarters = 10

Step-by-step explanation:

Given that,

number of coins Zachery have in his piggy bank = 58

total money Zachery have in his piggy bank = $6.50

Suppose number of nickel = x

number of dimes = 2x

number of quarters = y

1 nickel = $0.05

1 dime = $0.10

1 quarter = $0.25

<h3>Equation 1</h3>

x + 2x + y = 58

3x + y = 58

<h3>Equation 2</h3>

x(0.05) + 2x(0.10) + y(0.25) = 6.50

0.05x + 0.2x + 0.25y = 6.50

0.25x + 0.25y = 6.50

y = 58 - 3x

<h3>put value of y in equation 2</h3>

0.25x + 0.25(58 - 3x) = 6.50

0.25x + 14.5 - 0.75x = 6.50

-0.5x = 6.50 - 14.5

-0.5x = -8

x = 16

y = 58 - 3x

y = 58 -3(16)

y =10

number of nickel = x = 16

number of dimes = 2x = 32

number of quarters = y = 10

5 0

2 years ago