Use completing the square to solve this quadratic equation x^2+8x+16=2

The recursive formula for the sequence f(1)=1, f(2)=9, f(3)=17, f(4)=25, f(5)=33 is aₙ₋ =aₙ₋₁ +d

We should know that a recursive sequence is a sequence in which the terms are gotten using one or more previous terms along with an initial condition.

The given sequence is f(1)=1, f(2)=9, f(3)=17, f(4)=25, f(5)=33

This forms an Arithmetic Progression (AP)

The terms are 1, 9, 17, 25, 33, ...

The common different is 9-1 = 8

The terms are

a₁, a₂+d, a₃+d, a₄+d, + .....+ aₙ+(n-1)d

Therefore the The recursive formula for the sequence f(1)=1, f(2)=9, f(3)=17, f(4)=25, f(5)=33 is aₙ₋ =aₙ₋₁ +d

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We will not be able to figure out the price of one can of each type of canned food in the same manner of operating on two equations.

This is because the equation are identical.

Let the dog food be represented by d.

Let the cat food be represented by c.

Since Carlos buys 4 cans of dog food and 6 cans of cat food for $12.00. This will be:

4d + 6c = 12

This cane b reduced to lowest term as 2d + 3c = 6

Then the next week, he purchased 2 cans of dog food and 3 cans of cat food for $6.00. This will be:

2d + 3c = 6

Since the equations are the same, we can't calculate the price.

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Answer:

Step-by-step explanation:

the answer is a

Answer:

$12.5

Step-by-step explanation:

500/40 = 12.5

The required linear function is

f(x) = -2x+ 7

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Let the linear function f(x) = ax + b

f(0) = 7

a [tex]\times[/tex] 0 + b = 7

b  =7

f(x) = ax + 7

f(3) = 1

3a + 7 = 1

3a = 1 - 7

3a  = -6

a = [tex]-\frac{6}{3}[/tex]

a = -2

The given linear function is

f(x) = -2x+ 7

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The solution of the equation 2.5x² − 1.95x − 225.6 = 0 will be negative 9.117 and 9.897.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given below.

2.5x² − 1.95x = 225.6

Simplify the equation, then we have

2.5x² − 1.95x = 225.6

2.5x² − 1.95x − 225.6 = 0

Then the solution of the equation is given as,

[tex]\rm x = \dfrac{-(-1.95) \pm \sqrt{(-1.95)^2 - 4 \times 2.5 \times (-225.6)}}{2 \times 2.5}[/tex]

Simplify the expression, then we have

x = [1.95 ± 47.537] / 5

x = (1.95 + 47.537) / 5, (1.95 - 47.537) / 5

x = 9.897, -9.117

The solution of the equation 2.5x² − 1.95x − 225.6 = 0 will be negative 9.117 and 9.897.

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The linear equation can be solved by using arithmetic operation the answer for 13 is 27/4 etc.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

13)

9/16 = x/12

x = 27/4

14)

(x - 13)/18 = 12/9

x = 37

15)

7/11 = 18/(x+1)

x = 191/7

16)

(3x-4)/14 = 9/10

x = 83/15

17)

17/15 = 10/(2x -2)

x = 92/17

18)

(x - 16)/(x + 6) = 3/5

x = 49

Thus, the linear equation can be solved by using arithmetic operation the answer for 13 is 27/4 etc.

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Answer: five beers' worth of alcohol in a bottle of wine.

Step-by-step explanation:

In order to have an equivalent amount of alcohol as red wine, we would need to consume approximately 6 bottles of beer.

To determine how many bottles of beer need to be consumed in order to have an equivalent amount of alcohol as red wine, we can compare the alcohol content in both beverages.

The red wine has a volume of 750 ml and an alcohol content of 12%. This means that the red wine contains 750 ml x (12/100) = 90 ml of alcohol.

The beer has a volume of 330 ml and an alcohol content of 5%. This means that each bottle of beer contains 330 ml x (5/100) = 16.5 ml of alcohol.

To find the number of beer bottles needed to match the alcohol content of the red wine, we divide the total amount of alcohol in the red wine by the amount of alcohol in one beer bottle:

The number of beer bottles:

90 ml / 16.5 ml = 5.45

Since we can't have a fraction of a beer bottle, we round up to the nearest whole number.

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The point [tex]B(1,8)[/tex]is not a solution of the given inequality. Whereas the points [tex]C(-5,10) \text { and } D(3,6) \\[/tex]are the solutions of the given inequality.

What is inequality?

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

It can be found out simply by substituting [tex](x, y)[/tex] values in the given equation

[tex]y < 2 x^2+3 x-5[/tex]

let us start with the point [tex]3(1,8)[/tex]

here [tex]x=1 \text { and } y=8[/tex] therefore [tex]y < 2 x^2+3 x-5[/tex]

[tex]8 < 2\left(1^2\right)+3(1)-5=2+3-5=0[/tex]

that means, [tex]8 < 0[/tex] which is an incorrect inequality, therefore the point

[tex]B(1,8)[/tex] is not a solution of the given inequality.

similarly, for [tex]C(-5,10)[/tex]

[tex]10 < 2(-5)^2+3(-5)-5=50+15-5=60[/tex]

that is [tex]10 < 60[/tex], which is correct.

therefore[tex]C(-5,10)[/tex] is a solution of the given inequality.

next[tex]D(3,6)[/tex]

[tex]6 < 2(3)^2+3(3)-5=18+9-5=22[/tex]

that is[tex]6 < 22[/tex], which is correct . Therefore the point D is a solution of the given inequality.

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Answer:

x = 45y + 650/2

Step-by-step explanation:

20x - 45y = 650

20x - 45y + 45y = 650 + 45y

20x = 650 + 45y

20x/20 = (650 + 45y)/2

x = 45y + 650/2

Thus, The value of x is 45y + 650/2

The biweekly pay is $1,385, the hourly rate of pay for 160 hours of work per month is $17.31, and the overtime rate of pay is $25.96.

It is given that, the annual pay is $36,010.

There are 52 weeks in a year. So, there are 26 biweeks in a year.

Then, the biweekly pay = (Annual pay)/the number of biweeks in a year

⇒ biweekly pay = (36,010)/26 = $1,385

There are 160 working hours in a month.

So, biweekly working hours = 160/2 = 80 (for two weeks in a month)

Then, the hourly rate of pay is calculated by

hourly rate of pay = biweekly pay/biweekly working hours

⇒ hourly rate of pay = 1,385/80 = $17.31

To calculate the overtime rate of pay, we need to know the number of overtime working hours and the multiplier.

Here we are finding the overtime rate per hour. So, we can find the overtime rate of pay by

overtime rate of pay = hourly rate of pay × multiplier

We have the overtime multiplier per hour as 1.5.

Then,

Overtime rate of pay = 17.31 × 1.5 = $25.96

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Hi!

The parrot starts off knowing 60 phrases at time 0.

This is the y intercept, it occurs at x = 0

A point is (x, y)

at 0, the line is equal to 60

the y intercept is (0, 60)

Each night, the parrot learns one bad phrase.  

Equation of a line given y intercept and slope is

y = mx + b

y (answer of equation)  = m (slope) x(input of equation) + b (y intercept)

Slope is 1 because every time a day passes, it learns a new phrase.

y = 1x + 60

y = x + 60

Hope this helps,

Jeron

The values of a, h and k for the  given quadratic function are:

a = -6, h = -5 and k = -1

What is vertex form?

This is one way of writing a quadratic function:

f(x) = a(x-h)² +k

(h, k) = vertex

a = vertical stretch

According to the given question:

We're given:

f(x)= -6x² - 60x - 151

To write a quadratic function in vertex form, we must complete the square.

⇒ Put parentheses around the first two terms containing x and x²:

f(x)= (-6x² - 60x) - 151

⇒ Factor out -6 (keeping the x's in the parentheses):

f(x)= -6(x² + 10x) - 151

⇒ To complete the square, add, inside the parentheses, the square of half the coefficient of x.

⇒ In this case, the coefficient of x is 10.

⇒ Half of this value is 5.

⇒ The square of 5 is 25.

⇒ Add this inside the parentheses:

f(x) =  -6(x² + 10x + 25) - 151

⇒ Now, we cannot randomly introduce a new value into a function. To balance the +25, subtract -6(25) outside the parentheses:

f(x) =  -6(x² + 10x + 25) - 151 - (-6 x 25)

f(x) =  -6(x² + 10x + 25) - 151 - (-150)

f(x) =  -6(x² + 10x + 25) - 151 + 150

f(x) =  -6(x² + 10x + 25) - 1

⇒ Finally, complete the square.

Remember: (a + b)² = a² + 2ab + b²

In this case, a is x, and b is 5:

f(x) = -6(x + 5)² - 1

On comparing with f(x) = a(x-h)² +k we get the values of a, h and k as:

a = -6

h = -5

k = -1

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Answer:

2/5

Step-by-step explanation:

Answer: 1953125

Step by Step:

5^9 and because it is an odd exponent it is a positive answer for this problem

Answer:

4

Step-by-step explanation:

it's the best because of my friend its the greatest factor

Answer:

x = 1/3

Step-by-step explanation:

12=7+15x

12-7=15x

5=15x

5/15=x

Simplify

x = 1/3

Answer:x=1/3 or x=0.3 I hope this helpful mark me brainlist if correct

Step-by-step explanation:

12=7+15x

Move the variable to the left-hand side and change its sign

12-15x=7

Then move the constant to the right-hand side and change its sign

-15x=7-12

Calculate the difference
-15x=-5

Divide both sides of the equation by -15

x=1/3 or x=0.3

Answer:

1000

Step-by-step explanation:

The distance between UFO and KA-12 is 1229.7 Km

Given,

Satellites KA-12 and SAL-11 have spotted a UFO.

Distance between Satellites KA-12 and SAL-11 = 900 km

Angle between UFO and SAL-11 = 60°

Angle between UFO and KA-12 = 75°

We have to find the distance between UFO and KA-12;

Here,

Consider as a triangle;

Sum of interior angles of a triangle = 180 degree

So,

The third angle here will be = 180 - 60 + 75 = 180 - 135 = 45°

Now, use sin rule;

x / sin 75 = 900 / sin 45

x = sin 75 × 900 / sin 45

x = 900 × 0.966 / 0.707

x = 869.4 / 0.707

x = 1229.7

That is,

UFO is 1229.7 Km far from KA-12

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The value of matrix multiplication is

a)    [tex]C = \begin{pmatrix}14&20\\ 32&46\end{pmatrix}[/tex]

b)  [tex]C = \begin{pmatrix}7&35\\ 8&42\end{pmatrix}[/tex]

c)  [tex]C = \begin{pmatrix}22&32\\ 26&38\end{pmatrix}[/tex]

d)  [tex]C =\begin{pmatrix}-3&-5\\ 34&52\end{pmatrix}[/tex]

What is multiplication of matrices?

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix

Given data ,

a)

Let the first be A

[tex]A = \left[\begin{array}{ccc}1 &2 \\ 3 & 4 \\\end{array}\right][/tex]

Let the second matrix be B

[tex]B = \left[\begin{array}{ccc}4 &6 \\ 5 & 7 \\\end{array}\right][/tex]

Now , the product of matrices A and B is C

where the matrix C is A x B

[tex]C = \begin{pmatrix}1\cdot \:4+2\cdot \:5&1\cdot \:6+2\cdot \:7\\ 3\cdot \:4+4\cdot \:5&3\cdot \:6+4\cdot \:7\end{pmatrix}[/tex]

On simplifying the matrix C , we get

[tex]C = \begin{pmatrix}14&20\\ 32&46\end{pmatrix}[/tex]

Therefore , the value of matrix is  [tex]C = \begin{pmatrix}14&20\\ 32&46\end{pmatrix}[/tex]

b)

Let the first matrix be A

[tex]A = \left[\begin{array}{ccc}3 &5 \\ 4 & 6 \\\end{array}\right][/tex]

Let the second matrix be B

[tex]B = \left[\begin{array}{ccc}-1 &0 \\ 2 & 7 \\\end{array}\right][/tex]

Now , the product of matrices A and B is C

where the matrix C is A x B

[tex]C = \begin{pmatrix}3\left(-1\right)+5\cdot \:2&3\cdot \:0+5\cdot \:7\\ 4\left(-1\right)+6\cdot \:2&4\cdot \:0+6\cdot \:7\end{pmatrix}[/tex]

On simplifying the matrix C , we get

[tex]C = \begin{pmatrix}7&35\\ 8&42\end{pmatrix}[/tex]

Therefore , the value of matrix is [tex]C = \begin{pmatrix}7&35\\ 8&42\end{pmatrix}[/tex]

c)

Let the first matrix be A

[tex]A = \left[\begin{array}{ccc}4 &6 \\ 5 & 7 \\\end{array}\right][/tex]

Let the second matrix be B

[tex]B = \left[\begin{array}{ccc}1 &2 \\ 3 & 4 \\\end{array}\right][/tex]

Now , the product of matrices A and B is C

where the matrix C is A x B

[tex]C = \begin{pmatrix}4\cdot \:1+6\cdot \:3&4\cdot \:2+6\cdot \:4\\ 5\cdot \:1+7\cdot \:3&5\cdot \:2+7\cdot \:4\end{pmatrix}[/tex]

On simplifying the matrix C , we get

[tex]C = \begin{pmatrix}22&32\\ 26&38\end{pmatrix}[/tex]

Therefore , the value of matrix is  [tex]C = \begin{pmatrix}22&32\\ 26&38\end{pmatrix}[/tex]

d)

Let the first matrix be A

[tex]A = \left[\begin{array}{ccc}-1 &0 \\ 2 & 7 \\\end{array}\right][/tex]

Let the second matrix be B

[tex]B = \left[\begin{array}{ccc}3 &5 \\ 4 & 6 \\\end{array}\right][/tex]

Now , the product of matrices A and B is C

where the matrix C is A x B

[tex]C = \begin{pmatrix}\left(-1\right)\cdot \:3+0\cdot \:4&\left(-1\right)\cdot \:5+0\cdot \:6\\ 2\cdot \:3+7\cdot \:4&2\cdot \:5+7\cdot \:6\end{pmatrix}[/tex]

On simplifying the matrix C , we get

[tex]C =\begin{pmatrix}-3&-5\\ 34&52\end{pmatrix}[/tex]

Therefore , the value of matrix is  [tex]C =\begin{pmatrix}-3&-5\\ 34&52\end{pmatrix}[/tex]

Hence , the matrix multiplication is solved and the results are given

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The town with the greater population density is C. Town A, with about 1,027 people per square mile.

Population density is the quotient of the number of individuals (population) living in a specified location divided by the geographic size of the area, usually measured in squared miles.

Towns          Population        Squared Miles        Persons/square mile

Town A         397,546                387                      1,027 (397,546/387)

Town B         264,108                 261                      1,012 (264,108/261)

Thus, we can conclude that Town A has a greater population density than Town B.

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Answer: B

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solve by Factoring 2x^2-9x=x^2-20. 2x2−9x=x2−20 2 x 2 - 9 x = x 2 - 20. Step 1. Move all the expressions to the left side of the equation.

:)

The margin of error, a statistic, is a measure of how much random sampling error there is in survey data.

The margin of error exists 0.07728.

A statistic known as the margin of error describes how much random sampling error there is in survey data. Less faith should be placed in a poll's results representing the outcome of a population census as the margin of error increases.

A survey's margin of error, also known as the confidence interval, is a measurement of error in the data, particularly when the sampling method of a survey is used. This indicator lets researchers know to what extent survey findings should be taken as representative of the entire community under study.

Given : n = 36

x-bar = 3222.2 g

s = 686.7

Confidence level 95%

The 2 - critical Valve = 2.03

A) Let the equation be

[tex]$S F=\sqrt{\frac{\bar{x}(1-\bar{n})}{n}}$$[/tex]

substitute the values in the above equation, we get

[tex]$& \Rightarrow \sqrt{\frac{(3222.2)(1-3222.2)}{100}} \\[/tex]

SE = 0.03807

B) Margin of error = (0.03807)(2 ×[tex]I_2[/tex] )

Margin of error = 0.07728

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Answer:

y= x +4

Step-by-step explanation:

2 point form : y -20 = x- 16

slope intercept form: y = x + 4

Answer:

-3

Step-by-step explanation:

3 times negative 1 is -3 since a positive times a negative is a negative

hopes this helps

Answer:

The y-intercept is 8.

Answer:

0.5

Step-by-step explanation:

-1+3(10-12)^3/-16

-1+3(-2)^3/-16

-1+(-24)/-16

.5

The point when reflected across the y-axis is (0, -9)

From the question, we have the following parameters that can be used in our computation:

Point = (0, -9)

Transformation = Reflect the point across the y-axis:

The rule of reflection across the y-axis is represented as

(x, y) = (-x, y)

Substitute the known values in the above equation, so, we have the following representation

Image = (0, -9)

Hence, the image is (0, -9)

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