Algebra 1 8. 2 worksheet characteristics of quadratic functions answer key
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The solution of the system is x = 5 and y = 40.

A simultaneous equation is anyone or more equations that can have the same number of unknowns and be solved concurrently. The system of equations is a simultaneous equation.

Given:

system of equations,

8x=x+35    {equation 1}

y=8x          {equation 2}

From equation 1,

8x = x+35

7x = 35

x = 5

Substituting the value of x to the equation 2,

And y  = 8(5)

y = 40

Therefore, the solution is x = 5 and y = 40.

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Negative bases are not often used in logarithms because they produce complex results. For example, if the base is negative and the exponent is positive, the result will be a complex number.

Logarithms are generally used to solve equations or simplify complex problems. Having a negative base would complicate this process, as it would introduce complex numbers or even imaginary numbers into the equation. Consequently, it is not feasible to use negative bases with logarithms. Furthermore, if both the base and the exponent are negative, the result is undefined. This means that it is not possible to evaluate the expression. Therefore, for these reasons, it is usually not practical to use negative bases when working with logarithms.

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Andrew intends to make a second batch of Sauce 1 and Sauce II with 3,180 green peppers and 5,560 hot chili peppers.

You've tried poblanos and like the heat they provide to homemade salsa, but you're ready to branch out. The good news is that there are more than 4,000 different varieties of chili peppers in the world, and more are constantly being created.

Andrew prepares hot salts. his first batch will have 4 chili peppers and 6 green peppers, while his second batch will contain 3 green peppers and 10 chili peppers. We therefore need to know how many of each he requires.

To give you an idea of how many peppers to use per bottle of hot sauce, we suggest using at least two really hot peppers per bottle for a sauce with a lot of heat. In addition, habaneros can be made with 4-6 peppers.

Therefore, 975 green peppers and 1,250 hot peppers are purchased by Andrew. He uses all of those peppers to make both types of sauce.

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The solution of the equation 3(2x - 7) = 3 is x = 4 and the equation has a single solution.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Therefore, let's solve the equation as follows:

3(2x - 7) = 3

open the bracket

3(2x - 7) = 3

6x  - 21 = 3

add 21 to both sides of the equation

6x  - 21 = 3

6x  - 21 + 21 = 3 + 21

6x = 24

divide both sides by 6

6x / 6 = 24 / 6

x = 4

Therefore, the equation has only one solution.  The solution of the equation is x = 4.

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Data collected at the same, or approximately the same point in time are  Cross- sectional data

In statistics and econometrics, cross-sectional data, or a cross section of a study population, is a type of data gathered by monitoring numerous subjects (such as individuals, firms, countries, or regions) at one point or throughout the course of time. It's also possible that the analysis disregards variations in time. Cross-sectional data analysis often entails contrasting the variations among pre-selected respondents.

For instance, if we wanted to determine the prevalence of obesity in a population, we could randomly select a sample of 1,000 people (also referred to as a cross section of that population), measure their height and weight, and then determine what proportion of that sample falls under the definition of obesity. With the use of this cross-sectional sample, we are able to get a current picture of that group. Be aware that based on a single cross-sectional sample, we cannot determine whether the prevalence of obesity is rising or falling; we can only describe the current proportion.

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The required values of x in the interval 0° ≤ x ≤ 360° are 146.1° and 326.1°, when the value of tan x is given.

The interval of angle is given as 0° ≤ x ≤ 360°.

The value of x for which tan x is given as, tan x = - 0. 6745.

We have tan negative in two of the four axes, they are second (90° - 180°) and fourth quadrants (270° - 360°).

So, tan x = - 0. 6745

x = tan⁻¹ (- 0. 6745) = -33.9

As periodicity of tan x is 180°, x = 180-33.9 = 146.1°

x = 360-33.9 = 326.1°

Thus, the required values of x in the interval 0° ≤ x ≤ 360° are 146.1° and 326.1°, when the value of tan x is given.

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The graph for the points (-6, 2), (-5, 1), (-4, 0), (-3, 1) and (-2, 2) is plotted as below.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is y=|x+4|.

Graph the absolute value using the vertex and a few selected points.

Plot the points (-6, 2), (-5, 1), (-4, 0), (-3, 1) and (-2, 2)

Therefore, the graph for the points (-6, 2), (-5, 1), (-4, 0), (-3, 1) and (-2, 2) is plotted as below.

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The next value in the sequence is 80.

In arithmetic, what are sequences?

Sequences are ordered sequences of numbers, also referred to as "terms," such as 2,5,8. Some sequences adhere to a particular pattern that can be exploited to make them infinitely long. For instance, 2,5,8 conforms to the pattern "add 3," thus we can now proceed with the sequence. Formulas for sequences can be used to locate any term inside the sequence.

What does a mathematical series mean?

A series is the cumulative total of a given set of terms in mathematics. However, considerably more generality is possible. Typically, these phrases refer to real or complex numbers.

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The correct sentence to describe in the parent function is,

⇒ Shifted up.

⇒ Horizontal stretch

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

The function is,

⇒ f (x) = x

Here, The graph of the parent function of f (x) = x is shown in figure.

Hence, We get;

The correct sentence to describe in the parent function is,

⇒ Shifted up.

⇒ Horizontal stretch

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The value of x and y is solved in the equation  7x + y = 17 and -9x - y = -21 to get

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

7x + y = 17

-9x - y = -21

adding the equations will result to

-2x + 0 = -4

x = 2

substitute x = 2 into 7x + y = 17

7x + y = 17

7 * 2 + y = 17

14 + y = 17

isolating y

y = 17 - 14

y = 3

therefore x = 2 and y = 3

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Answer:

x = 6.6

Step-by-step explanation:

Proportions:

6.8 ⇒ 8.2

5.5 ⇒ P

P = 8.2 * 5.5 / 6.8

P = 6.6    (Rounded to the nearest tenth)

The solution of the system of equation using elimination method is x = -2, y = -4

The elimination method is a method used to solve systems of linear equations. It involves manipulating the equations in such a way that one of the variables is eliminated, resulting in an equation in one variable that can be easily solved.

-2y = 2 - 3x --- (1)

-5y = 10 - 5x ---(2)

To eliminate y, multiply (1) by -5 and multiply (2) by -2. Then subtract the result. That is:

-5 × (-2y = 2 - 3x)   =>  10y = -10 + 15x

-2 ×(-5y = 10 - 5x)    => 10y = -20 + 10x

.......................................................................

                                      0 = 10 +5x

.........................................................................

0 = 10 +5x

5x = -10

x = -10/5

x = -2

put x = -2 in (1):

-2y = 2 - 3x

-2y = 2 -3(-2)

-2y = 2 + 6

-2y = 8

y = -8/2

y = -4

Thus, x = -2, y = -4

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Answer:

b = 13

Step-by-step explanation:

21 = b + 8   Subtract 8 from both sides

21 - 8 = b + 8 - 8

13 = b

Answer: 13

Step-by-step explanation:

He bought two books for $21, and one of the books was $8. With this, we know that if we subtract 8 from 21, we can get "b", or the cost of the other book

21 = b + 8

-8        -8

13 = b

b = 13

Therefore, b = 13, or $13 for the other obok

A factory produces 72 bottles of juices in one minute.

Meaning of rate:

A rate is a special ratio in which two words are expressed using different units. The price is $69 for 12 ounces of corn if a 12-ounce can costs that much. This is not a ratio of two comparable units, like shirts, for example. This is a ratio between the units of cents and ounces.

We must divide the quantity of bottles produced by the time it takes to make them in order to determine the factory's production rate in bottles per minute. The factory in this instance produced 360 bottles in 5 minutes, resulting in the following production rate:

= 360 bottles / 5 minutes

= 72 bottles/minute

This means that the factory produces 72 bottles of juice per minute.

Hence, the factory produces 72 bottles of juice per minute.

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The following question may be like:

A factory bottles 360 bottles of juice in 5 minutes. Find the factory's unit rate of bottles per minute.

Percent of the total amount a per the given list price, documentation fee , registration fee and other payment paid by Charles is given by :

Option c. 16.70%

Cost of his old 2004 Dodge Neon = $6591

Sales tax = 6.88%

Dealer gives 80% trade in price on hos car

After tax selling price of the car

= 6,591 × (80/100) × [ 1 - (6.88/100) ]

= $4910.03

= $4,910

Vehicle registration amount = $1,089

List price of car = $21,450

Documentation fee = $124

Total cost of the car

= $21,450 + $1,089 + $124

= $22,663

Net amount Charles needs to pay

= $22,663 - $4,910

= $17,753

Monthly payment at the rate of 12.28% compounded monthly for 3 years

= 17753 [ 12.28%( 1+ 12.28%)^3 / [( 1+ 12.28%)^3 -1 ]

= $592

Total amount paid by Charles

= $592 × 36

= $21,312

Total interest paid by Charles

= $21,312 - $17,753

= $3,559

Percent of the total amount

= ( $3,559 / $21,312 ) × 100

= 16.699%

= 16.70%

Therefore, the percent of the total amount paid by Charles is equal to Option c. 16.70%.

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Answer:

3/2

Step-by-step explanation:

slope is rise over run:

3/2

The description of the piecewise function y is -2x + 3.

It is necessary to optically estimate the coordinates of the points because not everything is visible (particularly for the leftmost point).

We have the following considerations, I believe:

(-6, 1.5) (-3, 3) (-3, 3)

(-3, 2) (1, 2) (1, 2)

(1, 1) (6, -9) (6, -9)

the basic function definition appears on all three segments.

y = ax + b

X is always a factor of a, which is the line function's slope.

When a point on a line moves from one end to the other, the ratio y/x shows how many units change when x moves by a specific number of units.

b represents the y-intercept, or the value of y when x = 0.

(-6, 1.5) is followed by the first part and then (-3, 3).

x is modified by +3 units (from -6 to -3).

y shifts by 1.5 or 3/2 units (from 1.5 to 3).

the line has a slope of 3/2/3, which is 3/(23) = 1/2.

supplying the initial portion

y = (1/2)x + b

When we solve for b using a single point's coordinates (for example, -3, 3), we obtain b:

3 = (1/2)×-3 + b

3 = -3/2 + b

6/2 + 3/2 = b

9/2 = b

total equation is

y = (1/2)x + 9/2 = (x + 9)/2

The second portion is a straight line with no slope at all.

y = 2

Third segment, from (1, 1) to (6, -9)

5 units are added to x. (from 1 to 6).

By, y shifts

y = -2x + 3.

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The system of equations for the stuffed animals should the company manufacture to maximize profit P in dollars is P = 20x + 30y

The term equation in math is called as an expression or a statement that comprises two algebraic expressions with the same value and are separated by an equal symbol in between them.

Here we know that we have to determine the number of each of three types of souvenirs to be made.

Here let us consider that x, y, and z denote the respective numbers of type-A, type-B, and type-C souvenirs to be made.

Here we know that the total amount of time that machine I is used is given by 2x + y + z minutes and must equal 180 minutes.

Here the known details will leads to the equation

=> 2x + y + z = 180

While we take the similar considerations on the use of machines II and III lead to the following equations which is written as

=> x + 3y+2z = 300

=> 2x + y + 2z = 240

Here we have also identified the the stuffed animals should the company manufacture to maximize profit P in dollars as,

=>  P = 20x+30y

Here we know that the subject to the constraints plush stuffing trim x ≥ 0 y ≥ 0.

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The factorization of -25-15mn is -5(5+3mn)

Factorising is the reverse process of expanding brackets. To factorise an expression fully, means to put it in brackets by taking out the highest common factors. The simplest way of factorising is: Find the highest common factor of each of the terms in the expression.

For example 5( 3x+ 2y+ 4z) can be expanded into 15x + 10y + 20z and moreover 15x + 10y + 20z can be transformed by finding the factors between each terms, here the factor is 5; 5( 3x + 2y +4z)

Similarly to factorize -25-15mn we find the factor that is common to -25 and - 15 . The common factor is -5.

therefore factorizing -25-15mn we bring -5 out of -25 and -5

= -5( 5+3mn)

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Answer: -3 AND 7

Step-by-step explanation: very important to include the and, as it that point could be to the right or left of (3,1)

A possible inequality to represent the amount Payton spent is x >15, and two examples of the possible amount of money Payton spent are $30 and $6.

This is a mathematical expression that represents a situation using symbols such as ≥ (greater or equal to) or < (less than).

A possible inequality is  15 >x or 15 <x, which means the amount of money spent was less than or more than 15.

Some possible values within this range are:

$10

$2

$6

$30

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Answer:

10/32

Step-by-step explanation:

10+8+14 = all dishes = 32

10 = how many plates

In a ratio: 10/32

Answer:

Step-by-step explanation:

To find out how much the man spent per shirt, you need to divide the total cost of the shirts by the number of shirts.We know that the man spent $250 on the suit and $398 on the four shirts. To find the total cost of the shirts, you can add these two amounts:$250 + $398 = $648To find the cost per shirt, you need to divide the total cost of the shirts by the number of shirts:$648 / 4 = $162So the man spent $162 per shirt.

The solution is Option A.

The inequalities have one common solution

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equations be represented as A and B

The value of A is

( 1/2 )x + 8 ≤ 10   be equation (1)

-3x - 24 ≤ - 36   be equation (2)

On simplifying the equation (1) , we get

Subtracting 8 on both sides of the equation , we get

( 1/2 )x ≤ 2

Multiply by 2 on both sides of the equation , we get

x ≤ 4

And , on simplifying the equation (2) , we get

Adding 24 on both sides of the equation , we get

-3x ≤ -12

Multiply by -1 on both sides of the equation , we get

3x ≥ 12

Divide by 3 on both sides of the equation , we get

x ≥ 4

So , the common solution to the inequalities is x = 4

Hence , the inequalities have solution at x = 4

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The seller ought to bring more medium-sized shirts because these are the best-selling size.

From the graph we can see that total small shirt sold = 160

Total number of sale of small shirt = 225

Now remaining shirts = Total small shirt sold/Total number of sale

Now remaining shirts = 160/225 × 100

Now remaining shirts = 71

Total medium shirt sold = 335

Total number of sale of medium shirt = 375

Now remaining shirts = Total shirt sold/Total number of sale

Now remaining shirts = 335/375 × 100

Now remaining shirts = 89

Total large shirt sold = 275

Total number of sale of large shirt = 325

Now remaining shirts = Total shirt sold/Total number of sale

Now remaining shirts = 275/325 × 100

Now remaining shirts = 85

Total X-large shirt sold = 125

Total number of sale of X-large shirt = 175

Now remaining shirts = Total shirt sold/Total number of sale

Now remaining shirts = 125/175 × 100

Now remaining shirts = 71

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The complete question is given below:

On expanding the expression "(1/2)(-2x + 4y)" , the equivalent expression is -x + 2y  .

An expression is defined as the sentence that have a minimum of two numbers or variables and at least one math operation in it.

For Example : 2x + 3y is an expression .

The expression is : "(1/2)(-2x + 4y)"   ;

By using distributive property which means that a(b+c) = ab + ac ,

we multiply by (1/2) with both the terms ;

⇒ (1/2)(-2x) + (1/2)(4y)  ;

Simplifying further ,

we have ;

⇒ -2x/2 + 4y/2  ;

Further simplifying we get ⇒ -x + 2y  ;

Therefore , the equivalent expression is -x + 2y  .

The given question is incomplete , the complete question is

Expand to write an equivalent expression:  (1/2)(-2x + 4y) .

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Student A is incorrect. The student started at 0 on the y-axis, did not need to move horizontally on the graph, and so moved horizontally to 2 on the x-axis. The student should have started at 0 on the x-axis, moved horizontally to the graph, and then moved vertically to -6, which student B did.

The value of x at which we want to find the numeric value of the function is given as follows:

x = 2.

Tracing a vertical line through x = 2, it will cross the graph of the function at y = -6, hence the numeric value is given as follows:

f(2) = -6.

Meaning that student B is correct.

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Answer:

it is There are 4 cups of water for each cup of sugar

Step-by-step explanation:

There are two possible options for points and distances:

In this problem we need to determine the location of point M and distances between points A, M and B. This can be done by means of differences on number line and algebraic equations:

M - A = x² - x

M - (- 14) = x² - x

M + 14 = x² - x

M = x² - x - 14

B - M = 5 · x + 4

35 - M = 5 · x + 4

M = 31 - 5 · x

Then, we eliminate M and find the solutions to the resulting quadratic equation:

x² - x - 14 = 31 - 5 · x

x² + 4 · x - 45 = 0

(x + 9) · (x - 5) = 0

x = - 9 or x = 5

Finally, we determine the possible values for M based on the fact that M is between - 14 and 35:

x = - 9

M = 31 - 5 · x

M = 31 - 5 · (- 9)

M = 31 - 45

M = - 14

AM = - 14 - 14

AM = 0

MB = 35 - (- 14)

MB = 49

x = 5

M = 31 - 5 · x

M = 31 - 5 · 5

M = 31 - 25

M = 6

AM = 6 - (- 14)

AM = 20

MB = 35 - 6

MB = 29

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