rewrite the function g(x)=2x^2+16x+6 in vertex form by completing the square

The factor of the polynomial f(x) graphed on the coordinate plane is

(x - 1).

What is factor of the polynomial?

A polynomial with coefficients in a certain field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization.

A polynomial can be factored by expressing it as the product of two or more components; this is somewhat the opposite of multiplying.

From the given graph we can see that, graph crosses x - axis at points

x = 1 and x = 8.

That means x = 1, 8 are the zero of the polynomial.

Since, if x = a is a zero of the polynomial, then (x - a) is the factor of the polynomial.

As x = 1, 8 are zero of the polynomial so (x - 1) and (x - 8) are the factors of the polynomial.

Hence, from the given options (x - 1) is factor of the polynomial.

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The value needs to be added to x²+10x+6 to complete the square is 19.

Perfect square trinomials come in the form a² + 2ab + b², which is equal to (a + b)².

In the presented trinomial, we can immediately find that a = x, and b² = c,

We know that a = x, and , 2ab = 2bx.

Now, 2bx and 30x are corresponding terms, 2bx = 30x.

Take the coefficient of x = 10

Divide by 2

10/2 =5

Then Square it

5 x 5=25

Add this to make a perfect square trinomial;

x² + 10x + 25

In the given equation we need to add 19 to make the perfect square trinomial; x² + 10x + 25.

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Answer:

Maximum height of 32 feet after 1.25s

Step-by-step explanation:

The solution of the linear equation:

(2x + 6)/5 = 4x - 3

is x = 7/6

Here we have the following equation:

(2x + 6)/5 = 4x - 3

To solve this, we need to isolate x in one of the sides of the equation, we can start by multiplying both sides by 5.

2x + 6 = 5*(4x - 3)

Expanding the right side we get:

2x + 6 = 20x - 15

Now you can see that this is a simple linear equation, now we need to group like terms:

6 + 15 = 20x - 2x

21 = 18x

Now we can divide both sides by 18 to get:

21/18 = x

Finally, if we divide both numerator and denominator of the fraction by 3, we get:

21/3 = 7

18/3 = 6

Then 21/18 = 7/6

Finally, we conclude that the solution is:

x = 7/6

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Answer:

The slope is 5.

Step-by-step explanation:

[tex]m = \frac{1 - 6}{ - 1 - 0} = \frac{ - 5}{ - 1} = 5[/tex]

In completing the square method, considering the equation X^2 - 5x = 6 the student should add 25 / 4 to both sides of the equation

The quadratic equation is an equation of the form

ax^2 + bx + c

The completing the square method is on of the methods of solving equations of the form above

The factor to be added on the both sides of the equation while using the completing the square method is

(b / 2a)^2

compared to the equation in the problem X^2 - 5x = 6 it is

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Step-by-step explanation:

E=29

G = 180-29-107= 44

F = 180-29-29 = 122

H = 180-29-29 = 122

S = 180-107 = 73

M = 107

C = 73

D = 107

T = 73

B = 107

N = 73

K = 44

A = 360-44-44-107 = 165

O = 180-44 = 136

P = 44

J= 136

Answer: 4x + 29

Step-by-step explanation: add the like terms together.

Answer:

39 inches

Step-by-step explanation:

the triangle has all equal angles

this means it is equilateral and this also means all the sides are equal

so take 2 sides and set them equal to each other to find x

21 - x = x + 5

now solve

add x to both sides

21 = 2x + 5

subtract 5 to both sides

16 = 2x

divide everything by 2

8 = x

now flip it

x = 8

plug this is to one of the equations and multiply that by 3

8 + 5 = 13

13 * 3 = 39

that is the perimeter

Answer:

4 times the difference of x and 2 is 4(x-2)

Answer:

B: [tex]3\frac{6}{8}[/tex]

Step-by-step explanation:

we multiply numerator by numerator and denominator by denominator

6/8x5/1

30/8

3 6/8

Hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

We start by developing an equation for Line 1, and then use that to find the equation for Line 2.  We'll use the form of an equation for a straight line:

 y = mx + b,

where m is the slope and b the y-intercept (the value of y when x=0).

Line 1

Determine the slope, m, by calculating the "Rise/Run" between the two points (-3,-7) and (5,3).

Line up the two points from left to right (based on x) and then calculate:

  Rise:  (3 - (-7)) = 10

   Run:  (5 -(-3) = 8

The slope, m, is Rise/Run or (10/8)

The equation becomes y = (5/4)x + b

We could calculate b, the y-intercept, by entering one of the two given points and solving for b, but the only thing we need from this line is it's slope, m.  Slope is (5/4), which we'll use in the next step:  Line 2.

[Note:  Out of curiosity, here is the calculation for b:  Use point (5,3) in y = (5/4)x + b and solve for b.   3 = (5/4)*5 + b.  3 = (25/4) + b  b = -13/4.  This means that Line 1 is y = (5/4)x -(13/4)]

Line 2

The slope of a line perpendicular to the first is the "negative inverse" of the first line.  In this case, line 1's slope of (13/8) would become a slope of -(8/13) for line 2.

    Line 2:  y = -(8/13)x + b

We'll calculate b for this line by enetering the single point provided,  (-4,-2), and solving for b:

          y = -(8/13)x + b

        -2 = -(8/13)*(-4) + b

          -2 = (32/13) + b

          -2 - (32/13) =  b

b = -(26/13) - (32/13)

b = -(58/13)

The new line perpendicular to Line 1 and passing through (-4,-2) is:

          y = -(8/13)x -(58/13)

See attached graph.

The probability of getting 2 yellow apples and 1 red apple is 18/35 which is the D option.

This is a question of permutations and combinations.

Given that:-

Number of yellow apples = 4

Number of red apples = 2

We have to find the probability of getting 2 red apples and 1 yellow apple.

Number of ways of getting 2 yellow apples = [tex]^4C_2=6[/tex]

Number of ways of getting 1 red apple = [tex]^3C_1=3[/tex]

Total number of ways of finding 3 apples from 7 apples = [tex]^7C_3=35[/tex]

Hence,

Probability of getting 2 yellow apples and 1 red apple = 6*3/35 = 18/35.

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Answer:

x=-9

Step-by-step explanation:

-2x+5=23

-5 on both sides

-2x=18

/-2 on both sides

x=-9

The equation that could solve how many hours it will take for the second car to catch up to the first car is 55t = 120 + 40t.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

If the first car is going 40 mi/h, and has a 120 mile head start, then the distance it covers at time = t is,

d1 = 120 + 40t

If the second car is going 55 mi/h, you want to know the amount of time it will catch the first car, then, their distance must be equal.

d2 = 55t

d1 = d2

120 + 40t = 55t

Simplify the equation of t.

55t - 40t = 120

15t = 120

t = 8

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Answer:

58

Step-by-step explanation:

PEMDAS!

1) 20/2 = 10

2) 10*5+8

3) 10*5 = 50
4) 50 + 8 = 58

Answer is 58, hope this helps ;)

The number 1.41421356 is not a rational number.

What is a rational number?

A number that can be expressed as a ratio is called a rational number. This indicates that it may be expressed as a fraction, where the numerator (the number on top) and denominator (the number on the bottom) are both whole numbers.

The given number is 1.41421356

The square root of 2 has the approximate value of 1.41421356

The number is non-terminating and non-repeating decimals.

That's why the given number is not a rational number.

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The temperature of the hottest day in Oklahoma in Celsius to the nearest tenth of a degree is 48.89 degrees.

The process of converting a temperature value from one unit to another is known as temperature conversion. On scales like Kelvin, Celsius, Fahrenheit, etc., we measure temperature. The freezing point and boiling point of water, respectively, are 273.15K and 373.15K on the Kelvin scale. The freezing point and boiling point of water, respectively, are 32°F and 212°F on the Fahrenheit scale. The freezing point and boiling point of water, respectively, are 0°C and 100°C on the Celsius scale.

Given, The hottest day recorded in Oklahoma was 120° Fahrenheit

F=(9/5)C+32

120=(9/5)C+32

(9/5)C=88

C=48.89

Therefore, the temperature of the hottest day in Oklahoma in Celsius to the nearest tenth of a degree is 48.89 degrees.

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The chief of police use sample statistical study  to estimate the number of people above the age of 18 who are using illegal substances in town.

In the given question,

The chief of police in statville wanted to estimate the number of people above the age of 18 who are using illegal substances in town.

He obtained 200 random names of statville residents from a computer database and sent his officers to survey these people about substance abuse.

Once the results came in, he calculated the margin of error and got an estimate of the percentage of residents who use illegal substances.

We have to explain what type of statistical study the chief of police use.

In the given question chief of police wants to check number of people who using illegal substances in town above the age of 18. So he take  200 random names from a computer database. That means he take the sample of 200 random people.

As we know that a sample is a selection from a larger population of individuals, things, or things that are used for measurement. To enable us to extrapolate the research sample's findings to the entire population, the sample must be representative of the population.

So we can say that the chief of police use sample statistical study  to estimate the number of people above the age of 18 who are using illegal substances in town.

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Answer: Sample Study

No because there’s a great risk of obtaining biased answers.

Answer:

2 3/16

Step-by-step explanation:

It's simple math :D

NOVEMBER QUOTE!

Ooo! It's fall and thanksgiving time! I gotta get prepared for Thanksgiving and so my friends will come over! Fun! - Ash the Fox

(sorry that ones so long- ;-;)

Answer:

SAS

Step-by-step explanation:

∠CBA ≌ ∠DBA are equal by SAS

The standard error with "mean of 7 for some characteristic of interest and a standard deviation of 9.6 and a sample is drawn from this population of size 64" is 1.2.

Standard deviation of the theoretical distribution of a large population of such estimates is equal to the standard error, which is a measure of an estimate's statistical accuracy. The population mean's likelihood to differ from a sample mean is indicated by the standard error of the mean, or simply standard error. It reveals how much the sample mean would change if a study were to be repeated with fresh samples drawn from a single population.

Here,

Sample size=64

Standard deviation= 9.6

Error=Standard deviation/Sample size

=σ/√n

=9.6/√64

=9.6/8

=1.2

The sample is taken from this population of 64 people, with a mean of 7 for some relevant characteristics, a standard deviation of 9.6, and a standard error of 1.2.

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Answer:

Step-by-step explanation:

firstv= block second one

secondblock third one

and so on

The probability of randomly drawing a value greater than 3.0 from a z-distribution is 0.0013

The Z-score, commonly referred to as the standard score, expresses how far away from the mean an object is.

An element that is below the mean is indicated by a z-score that is less than 0.

An element bigger than the mean is indicated by a z-score greater than 0.

An element that is equal to the mean is represented by a z-score of 0.

P(Z > a) = 1-P(Z<a)

Let's say we want to know, for instance, the likelihood that a z-score will be higher than 3.00.

We learn from the table, that

P(Z < 3.00) = 0.9987.

Therefore,

P(Z > 3.00) = 1 - P(Z < 3.00)

= 1 - 0.9987

= 0.0013.

Therefore, the probability of randomly drawing a value greater than 3.0 from a z-distribution is 0.0013

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Answer: 0.04536

Step-by-step explanation:

Based on the information, the person traveled 117.8 feet by the Ferris wheel.

Circumference = π×diameter

Keep the values in formula and perform multiplication to find the circumference of the wheel

Circumference = 50π

On 1 complete revolution of 360 degrees, the distance covered = 50π

So, revolution of 270 degrees, the distance covered will be = (50π/360) × 270

Performing multiplication and division on Right Hand Side of the equation

The distance traveled = 117.8 feet

Hence, the person travelled 117.8 feet.

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