2. The sum of the interior angles in a quadrilateral is 360°. Determine the value of x in
the diagram on the right.

Answer:

1)  -5x² + 13x + 6

2) B(x)  =(4x + 1 )(2x + 3)

  A(x) = (5x +2)(3-x)

Step-by-step explanation:

1) Expand the equation by using distributive property. Then simplify  by combining the like terms.

A(x) = (3 -x)2² - (x -3)(7x+ 4) - 18 + 2x²

         = (3 - x)4 - [x*7x + x*4 - 3*7x - 3*4] - 18 + 2x²

         = 3*4 - x*4 - [7x² + 4x - 21x - 12] - 18 + 2x²

         = 12 - 4x - 7x² - 4x + 21x + 12 - 18 + 2x²

        = 2x² - 7x² -4x - 4x + 21x + 12 + 12 - 18

       = -5x² + 13x + 6

B(x) = (3x + 2)² - (x - 1)²

Identities:

(a + b)² = a² + 2ab + b² ; Here a =3x & b = 2

(m -n)² = m² - 2mn + n² ; Here m = x & n = 1

2) B(x) = (3x)² + 2*3x*2 + 2² - [x² - 2*x*1 + 1]

      = 9x² + 12x + 4 - [x² - 2x + 1]

      = 9x² + 12x + 4 - x²+ 2x - 1

     = 9x² - x² + 12x + 2x  + 4 - 1

     = 8x² + 14x +3

Product = 8*3 = 24

Sum = 14

Factors = 2 , 12    {2*12 = 24 & 2 +12= 14}

    = 8x² + 2x + 12x + 3    {Rewrite the middle term}

    = 2x(4x + 1) + 3(4x + 1)      

   = (4x + 1 )(2x + 3)

  A(x) = - 5x² + 13x + 6

       = -5x² + 15x -2x + 6

       = 5x(-x +3) +2 (-x + 3)

       = (5x +2)(3-x)

4) B(x) - 3 = 8x² + 14x + 3 - 3

                = 8x² + 14x

                = 2x *4x + 2x *7

                =2x(4x + 7)

Hence proved.

                           B(x) = 3

            8x²  + 14x + 3 = 3

        8x² + 14x + 3 - 3 = 0

           8x² + 14x         = 0

              2x(4x + 7)     = 0

2x = 0   or    4x + 7 = 0

 x = 0   or          4x = -7

                            [tex]\sf x = \dfrac{-7}{4}[/tex]

  x = 0 or    [tex]\sf \dfrac{-7}{4}[/tex]

Answer:

96 years

Step-by-step explanation:

let Jorge's age be x

then the quotient of his age and 3 is x divided by 3 , so

[tex]\frac{x}{3}[/tex] - 2 = 30 ( add 2 to both sides )

[tex]\frac{x}{3}[/tex] = 32 ( multiply both sides by 3 to clear the fraction )

x = 3 × 32 =96

Jorge is 96 years old

1) Unit Rate of the given options are;

$0.05 for 1 ounce

24 bottles per case

16 ounces per bottle

2) Rate of the given options are;

5 bottles for $5

$1 per 16 ounces

A unit rate (or unit ratio) describes how many units of the first type of quantity corresponds to one unit of the second type of quantity. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second.

Meanwhile, a rate is the ratio between two different units of measure.

Thus;

1) Unit Rate of the given options are;

$0.05 for 1 ounce

24 bottles per case

16 ounces per bottle

2) Rate of the given options are;

5 bottles for $5

$1 per 16 ounces

3) The option that is neither a unit rate nor a rate is; 36 bottles

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The Quadratic equation modeled is  [tex]3x^{2} -4x+1=(3x-1) (3x-1)[/tex].

Quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is [tex]y=ax^{2} +bx+c[/tex], where a, b, and c are numbers and a cannot be 0.

the given equation Much easier to understand with the symbol              [tex]3x^{2} -4x+1=(3x-1) (3x-1)[/tex]

[tex]3x^{2} -4x+1= 9x^{2} -6x+1\\6x^{2} -2x=0[/tex]

That is how I interpreted the "tile" set up.

Now count up the factors:  

These are (4 -x) and ( x +1) factor of  Quadratic equation.

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The equation 3(4x + 12) = 2(6x + 8) has no solution because the variable x was neglected as it equals 0.

It should be noted that the equation given is illustrated as:

3(4x + 12) = 2(6x + 8)

Open the parentheses

12x + 36 = 12x + 16

Collect like terms

12x - 12x = 16 - 36

0 = -20

Therefore, it has no solution.

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Answer: it is upside down

Step-by-step explanation:

cant see the problem

Answer:

250 minutes.

Step-by-step explanation:

1/5=50/x

cross product

5*50=1*x

250=x

Cameron's current service charge of $0.95 per song, and the new service charge of $0.89 per song and $12 fee for joining, gives;

To Formulate

The charges for songs on the current music service is, C1 = 0.95•s

The charges for the new download service is, C2 = 12 + 0.89•s

Where the $12 is the joining fee

When the cost is the same for both service, we have;

C1 = C2

Which gives;

The equation to represent when the cost for both service is the same is therefore;

0.95•s = 12 + 0.89•s

Computing;

The number of songs that gives the same costs is therefore;

0.95•s = 12 + 0.89•s

12 = 0.95•s - 0.89•s = 0.06•s

s = 12 ÷ 0.06 = 200

Interpreting the solution;

The interpretation is, the cost of songs downloaded on both service will be the same, when 200 songs are downloaded.

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As for the answer, the length of the three sides was x=4.

Let [tex]x[/tex] be the length of the two sides that are the same.

Then the third side would be 2x-3

The perimeter of the triangle will come from adding all of the sides together and setting it equal to the value given, 13.

That is,

x + x + (2x-3)=13

4x-3=13

4x=13+3

4x=16

x=4

The length of each of the common sides is 4, making the third side 5, to get a total perimeter of 13.

The hypotenuse of a right-angled triangle is its longest side, the base is its lower side, and the perpendicular, which stands next to the right angle, is its standing line.

You may determine the sides of a right-angled triangle using a number of techniques, such as the Pythagoras theorem or the triangle's perimeter.

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Step-by-step explanation:

gradient = slope or several other words.

it describes how strongly a line (or tangent to a bent curve) is going up or down or ... if it is changing at all.

it is represented by the ratio

(y coordinate change / x coordinate change)

when going from one point on the line to another.

in our case, when going from A to B we have

x changes by -2k (from 3k to k).

y changes by -11 (from 8 to -3).

so, the gradient or slope is

-11/-2k = 3

11/2k = 3

11 = 3×2k = 6k

k = 11/6

A = (33/6, 8) = (11/2, 8)

B = (11/6, -3)

The mean is  79.5.

The standard deviation is 3.99

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(82 + 78 +  80 +  72 +  85 +  80) / 6 = 477 / 6 =  79.5

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group.

In order to determine the standard deviation, take the following steps:

Determine the mean of the observation:79.50

Determine the difference between each value and the mean and then square the result: (82 - 79.5)² + (78 - 79.5)² + (80- 79.5)² + (72- 79.5) ²+ (85- 79.5)² + (80- 79.5)² = 6.25 + 2.25 + 0.25 + 56.25 + 30.25 + 0.25 = 95.5

Determine the mean of the sum of the squared differences and then find the square root of the mean:

√95.5 / 6 = 3.99

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The equation of the line is x = 5

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, let's find the slope and y-intercept

(5, 0)(5, - 2)

m = -2 - 0 / 5 - 5

m = -2 / 0

m = infinity

Hence,  It is a vertical line, since the x is the same for both of them, and it is equal to  both times.

Therefore, the equation of the line is x = 5

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Answer:

nnk;'/mnhjjfn;h;;vhxpycoyyoly,

Step-by-step explanation:

I]o]ogi-gogoig]gogh]o]v]b]bob]b]k k k lgg]goghjppkngghhjjl

No generalizations can be made because the sample size is too small. Therefore, the correct option is option A.

A restaurant is an institution of business which prepares and provides clients with food and beverages. Although many restaurants now provide take-out as well as food delivery services, meals are often served and consumed on the premises.

A restaurant serves breakfast, lunch, and dinner. The restaurant offers a daily special. To estimate the percentage of customers who order the daily specials, the restaurant selected a random sample of customers who had lunch during 2 month period. From the results, the restaurant determined that 25% of these customers ordered the daily special. No generalizations can be made because the sample size is too small.

Therefore, the correct option is option A.

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By the commutative property, the value of the expression 7 x 2 x 7 x 5 is 490

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

7 x 2 x 7 x 5

The above expressions are grouped by the product sign

This means that the factors of the expressions can be rearranged by the commutative property

So, we have

7 x 7 x 2 x 5

Group the factors

So, we have

(7 x 7) x (2 x 5)

Evaluate the products

So, we have

49 x 10

Evaluate the products

So, we have

490

Hence, the value of the expression 7 x 2 x 7 x 5 is 490

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Answer:

Ramon deposited $204 monthly

Step-by-step explanation:

Step 1: Firstly convert 2 years to month

1 year = 12 month

∴ 2 years = 24 month

Step 2: Divide $4896 by 24

➟ 4896 ÷ 24

➟ 204

The company must produce 25 t-shirts to break even.

Here, we are given that a company producing t-shirts charges $125 for the design and set up plus $5 per tee.

This means-

fixed cost of producing the t-shirts = $125

Variable cost of producing a t-shirt = $5

Let x be the number of t-shirts produced

Thus, the total cost of producing t-shirts will be-

Total cost = 125 + 5x

Further, the selling price of 1 t-shirt = $10

Thus, selling price of x t-shirts = $10x

Now, at the break even point, the profit is 0, this implies-

Selling price = cost price

⇒ 10x = 125 + 5x

10x - 5x = 125

5x = 125

x = 125/5

x = 25

Thus, the company must produce 25 t-shirts to break even.

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Total number of boys in class are 172

A linear equation is an algebraic equation of the form y=mx+b involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

We have total  number of students in class = 410

We assume that the number of boys in class = X

Number of girls in class is  66 more then boys we assume total number of girls = X+66

If we add number of girls and boys then we found total strength of classX+X+66=4102X+66=4102x=344X=172

Number of boys = 172

Number of girls =238

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The total change in the stock market from the beginning based on the information will be 171 1/4 points.

It should be noted at the beginning of the day the stock market goes down 50 1/2 points and stays at this level for most of the day and at the end of the day the stock market goes up 120 3/4 points from the low at the beginning of the day.

Therefore, the total change in the stock market from the beginning will be the difference between the fractions that are given. This will be:

= 120 3/4 - (- 50 1/2)

= 120 3/4 + 50 1/2

= 171 1/4

Therefore, the total change in the stock market from the beginning based on the information will be 171 1/4 points.

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The value of 'x' and 'y' is '1' and '3' , respectively.

The substitution method is the algebraic method to solve simultaneous linear equations.

The first step in the substitution method is to find the value of any one of the variables from one equation in terms of the other variable.

Lets solve the given linear equations:

7x − 2y = 1     ... eq. (1)

3x + 4y = 15  ... eq. (2)

By equation 1 we got,

x = (1 + 2y)/7

Now, we will put x = (1 + 2y)/7 in equation 2,

3x + 4y = 15

3 [(1 + 2y)/7] + 4y = 15

 3/7 × (1 + 2y) = 15 - 4y

        3(1 + 2y) = 7(15 - 4y)

           3 + 6y = 105 - 28y

       6y + 28y = 105 - 3

                34y = 102

                    y = 102/34

                     y = 3

Now, put the value y =3 in equation 1,

              7x - 2y    =  1  

           7x - (2×3)   =  1

                 7x - 6   =  1

                      7x   =  1 + 6 = 7

                      7x   =  7/7

                        x  =  1

Hence, the value of x is 1 and y is 3.

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Answer:

y=4x-2

Step-by-step explanation:

m=[tex]\frac{8}{2}[/tex]=4

2=4(1)+b    2=4+b      -2=b

The required block diagram that shows how much distance Scarlett is away from the home is shown in the image attached.

As given in the question Scarlett left her house at time zero and drove to the store, which is 3 blocks away, at a speed of 1 block per minute.
Then she stopped and went into the store for 4 minutes.
she drove in the identical at a rate of 5 blocks per minute until she got to the bank, which is 15 blocks away from the store.

Here,
1 Approach, Scarlett moves with the speed of a block per minute
Total distance travel = 3 block

Approach 2 Scarlett moves with the speed of 5 blocks per minute for 3 minutes
Total distance travel = 15 block
Approach 3 Scarlett moves with the speed of 3 blocks per minute for 1 minute
Total block traveled = 3 + 15 = 18

Now, Approach 3 is to retrace the path at the rate of 3 blocks per minute,
All these calculations is been shown in the block diagram.

Thus, the required block diagram that shows how much distance Scarlett is away from the home is shown in the image attached.

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Answer:

The answer is 6.

Step-by-step explanation:

A negative and a negative makes a positive when the problem is written as
x - (-x)

So 2 - (-4) equals 2 + 4

which is simply 6

Answer:

6

Step-by-step explanation:

Two negatives cancel out a positive.

2-(4) should turn into 2 +4

2+4 =6

Answer: 8.25 miles in 2 3/4 hours

Step-by-step explanation:

Answer:

he traveled 900 feet

Step-by-step explanation:

250 + 650 = 900

Mr. Carter traveled a total distance of 900 feet from his boat to where he ended up.

Here, we have to find the total distance that Mr. Carter traveled from his boat to where he ended up, we need to calculate the sum of the distances above and below sea level.

The distance above sea level is 250 feet (his house boat's level), and the distance below sea level is 650 feet (where he ended up after jumping).

Total distance traveled = Distance above sea level + Distance below sea level

Total distance traveled = 250 feet + 650 feet

Total distance traveled = 900 feet

Mr. Carter traveled a total distance of 900 feet from his boat to where he ended up.

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Answer:

x<-5/4 or x>2

Step-by-step explanation:

-4x -11 > 5

    +11   +11

-4x>5

/      /

-4   -4   Switch the sign when divided by a negative.

x<-5/4

8x - 7 > 9

    +7   +7

8x>16

/      /

8    8

x>2

The area of a sidewalk that surrounds a rectangle of 4 ft by 6 ft  is 56 ft²

The given situation can be depicted in the attached picture.

Recall the formula to calculate the area of a rectangle:

  A = l ⨉ w

Where:

l = length

w = wide

In the attached picture, the area of the sidewalk is the one with green color.

Notice that:

Area of sidewalk = area of bigger rectangle – area of smaller rectangle

Parameters of the bigger rectangle:

l = 6 + 2 + 2 = 10 ft.

w = 4 + 2 + 2 = 8 ft.

Area of bigger rectangle = 10 x 8 = 80 ft²

Parameters of the smaller rectangle:

l = 6 ft.

w = 4 ft.

Area of bigger rectangle = 6 x 4 = 24 ft²

Hence,

Area of sidewalk = 80 - 24 = 56 ft²

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Using scientific notation, the first step in simplifying the expression is given by:

a. Addition and subtraction requires the terms to be "like terms" with the same power of the base 10, so you would need to change the second number to (0.026 x 10^5).

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

For two numbers in scientific notation to be added or subtracted, they need to have the same exponent, which removes options b and c.

Moving the second number for 10^3 to 10^5 would be equivalent to a multiplication by 100, hence we have to divide by 100 at the base, that is:

2.6 x 10^3 = (2.6/100) x 10^5 = 0.026 x 10^5.

Hence option a is correct.

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