Find the value of x that makes the quadrilateral a parallelogram?

a) The function is continuous in it's entire domain.

b) The increasing and decreasing intervals for the function are given as follows:

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

In this problem, we have a piece-wise function which has the definition changing at x = 2, hence the continuity must be studied at x = 2.

The lateral limits for the function in this problem are defined as follows:

The second limit is also equals to the numeric value at x = 2, due to the equal sign in the definition, hence the function is continuous at x = 2 and for all other values in the domain.

The intervals of increase and decrease are given as follows:

The function for this problem is the piece-wise function A(x).

Item a asks if the function is continuous.

Item b asks when the function is increasing and when it is decreasing.

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Answer:

Slope: -1/2

Step-by-step explanation:

You can find the slope from this equation by adding 1/2 to each side of the equation since the way you find the slope of a line is by using: y = mx + b. The "m" must ALWAYS be on the right for it to be a valid slope equation, therefore, we have to use inverse operations for -1/2x to bring it to the right side.

Now, after we added 1/2x to each side, we get this equation:

-y = 1/2x + 3/4

We are not yet done since the y is accompanied by a negative 1, so, to isolate the variable, you use inverse operations once again and you get this equation:

y = -1/2x - 3/4

Therefore, the slope for this equation is -1/2.

Hope this helped! :D

Answer:

The ratio of the number of quarters to the number of dimes in the box is 9:10

Step-by-step explanation:

The image point of (0, 4) is (0, -4).

The intersection of the x- and y-axes creates the two-dimensional coordinate plane known as the cartesian plane. The origin is the point at where the x- and y-axes cross perpendicularly.

The Cartesian coordinate point (x, y) indicates that the distance from the origin is x in the horizontal direction and y in the vertical direction. The point is to the right of the origin if the sign of x is positive; otherwise, it is to the left.

Given points (0, 4)

to find image of the point (0,4) after a rotation of 180 degrees,

The initial coordinates (x, y) of a point become when we rotate it by 180 degrees around the origin (-x, -y).

So,

-0 is just 0 (since 0 is both negative and positive)

-(4) is -4

This makes our new point (0, -5).

Hence the image of point is (0, -4).

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Answer:

The mechanic spent 12 hours on the repair.

Step-by-step explanation:

The mechanic spent 12 hours on the repair.

The current value of property is 4000

The capitalization rate (also known as cap rate) is used in the world of commercial real estate to indicate the rate of return that is expected to be generated on a real estate investment property. Formula: Capitalization Rate = Net Operating Income / Current Market Value

Given here cap rate as 10% and income as 40000, Thus Current market value of property is = 40000/10

                                 =4000

Hence, The current value of property is 4000

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-2

Step-by-step explanation:

12x＝x+26

-13x＝26

x＝-2

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those provided

[tex]R(\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad S(\stackrel{x_2}{15}~,~\stackrel{y_2}{31}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{31}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{5}}} \implies \cfrac{ 24 }{ 10 } \implies \cfrac{12 }{ 5 }[/tex]

keeping in mind that perpendicular lines have negative reciprocal slopes

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{12}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{12}} ~\hfill \stackrel{negative~reciprocal}{ {\Large \begin{array}{llll} -\cfrac{5}{12} \end{array}} }}[/tex]

Step-by-step explanation:

the slope of a line is the ratio

y coordinate change / x coordinate change

when going from one point on the line to another.

the perpendicular slope is simply turning that ratio fraction upside down and flips the sign.

(5, 7) to (15, 31)

x changes by +10 (from 5 to 15).

y changes by +24 (from 7 to 31).

the slope (or gradient) is therefore

+24/+10 = 12/5

the perpendicular slope or gradient is then

-5/12

The percentage of the total marks that Edet gets is 60%

The percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

In this situation, the score of Edet will be:

= 48 + 52 + 46 + 46 + 44 + 52

= 288

Total score = 80 × 6

= 480

The percentage will be:

= 288 / 480 × 100

= 60%

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Answer: We can set up a system of equations to represent this problem. The first equation represents the total value of the nickels and dimes in terms of the number of nickels and dimes that Nevaeh has:

0.05x + 0.1y = 0.80

The second equation represents the total number of nickels and dimes that Nevaeh has in terms of the number of nickels and dimes that she has:

x + y = 11

To graphically solve this system of equations, we can use the slope-intercept form of the linear equations.

y = -2x + 22

y = -1/2 x + 8

The solution would be the point where the lines intersect , which x = 4, and y = 7 .

So she has 4 nickels, and 7 dimes.

Step-by-step explanation:

The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

We have to given that;

The table below shows the ratios of boxed donuts to the cost.

Donuts    A       4        5     C

Cost    13.80  27.60   B   55.20

Now, By definition of ratio, we get;

⇒ A / 13.80 = 4 / 27.60

⇒ A = 13.80 × 4 / 27.60

⇒ A = 2.00

And,

⇒ 4 / 27.60 = 5 / B

⇒ B = 5 × 27.60 / 4

⇒ B = 34.5

⇒ 4 / 27.60 = C / 55.20

⇒ C = 55.20 × 4 / 27.60

⇒ C = 8

Thus, The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

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Answer:

a

Step-by-step explanation:

i took the test :)

Answer: Your answer is 60 divided by 13 = 4.165.

Step-by-step explanation: You would have to divide 12 out of 50, and that would be a decimal of 4.166666666666667 So you need an aditional 10 items but then another additional suitcase there is an answer to this but it would come out as a decimal or fraction, so you would have to specify what type of object is going into these suitcases, most people would just deal with it and carry it in the hands lol.  

Answer: 4

Step-by-step explanation:

Let me get to know you:)

Answer:

Below

Step-by-step explanation:

0 ft -4.2 + 3.4 - 10 = -10.8 ft     or 10.8 ft below the surface

Answer:

- 7√10

Step-by-step explanation:

Step 1 : Take √10 common

2√10 - 5√10 - 4√10

= √10 ( 2 - 5 - 4 )

Step 2 : Subtract the numbers separately.

2 - 5 - 4

= 2 - 9

= - 7

Step 3 : Multiply √10 and - 7

√10 * - 7 = - 7√10

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.

Here,

the two numbers' primary factors are as follows:

-25[tex]b^{2}[/tex] + 15b

Common prime factors can be multiplied to determine the GCF:

=> -25[tex]b^{2}[/tex]  = -(5)(5) * [tex]b^{2}[/tex]

=> 15b = (5)(3)b

The expression can be factored in the following fashion because the GCF is 5b:

=> -(5)(5) * [tex]b^{2}[/tex] +  (5)(3)b

=> (5b)(-5b+3)

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

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A'(-2, -3) would result if A (2, -3) was reflected over the x axis. Point (2,3)'s representation under the x-axis is (2,-3). from the y-axis P image (-a,b).

Changing the sign of the value on the opposite axis, in this case the y-value, is all that is required to reflect a point such as (-2,3) across the x-axis in a question. As a result, this location has a y-value of 3. A positive number, this. A negative sign produces a result of -3.

While the Y coordinate remains the same when you reflect across the Y-axis, the X coordinate changes sign. Determining the reflection of (2, 3) across the Y-axis is therefore (-2, 3). The Y-coordinate of each point must be negative while reflecting across the X axis, but the X value must remain constant.

Therefore the correct answer is option a ) A'(-2, -3)

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Answer:

The answer is 0.26.

I wish you luck on your assignments.

Answer: 0.26

Step-by-step explanation:

1. The hundredths place is two digits from the decimal point

2. Look at the thousandths place and if it is larger or equal to 5 then we round up, otherwise we round down and the hundredths digit remains the same

3. 7 is larger than 5 therefore the hundredths place digit of 5 rounds to a 6

4. Our final answer is 0.26

The first equation will be multiplied by 3 and that of the second by 4.

An elimination method is a process of solving a system of linear equation, in this we make coefficients of the one variable equal and subtract the equations.

Given that are two equations to be solved by using elimination method,

-4x+4y = 32.....(i)

3x-y = 12......(ii)

To eliminate x, we will multiply eq(i) by 3 and eq(ii) by 4

-12x+12y = 96.....(iii)

12x-4y = 48....(iv)

Solving the equations, we get,

8y = 144

y = 18

Put y = 18 in eq (ii)

3x-18 = 12

3x = 30

x = 10

Hence, the first equation will be multiplied by 3 and that of the second by 4.

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Answer:

6,9 and 3 times respectively

Answer:

3.5 hours to read

Step-by-step explanation:

Before the trip, Tyler read 24 pages of his Philadelphia guidebook in an hour. The guidebook is 84 pages long. If he continued to read it at the same rate, how long did it take Tyler to finish reading the guidebook before his family's trip?

total pages / reading rate per hour

Equation: 84/24

Solution:  = 3.5 hours

a. The model represents exponential growth.

b. The annual percentage increase is 3%.

c. After 2390 decades the population was about 590000.

The formula for exponential growth is [tex]y = y_₀.e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_₀.e^{(-kt)}.[/tex]

Given, The population P(in thousands) of Austin Texas during a recent decade is approximated by [tex]y = 492(1.03)^t[/tex].

The model represents exponential growth as time can not be negative.

The annual percentage increase in the model [tex]y = 492(1.03)^t[/tex] is 3%

as 1.03×100% = 103%.

The time when the population was about 590000 since the beginning of a decade is,

[tex]590000 = 492(1.03)^t[/tex].

[tex](1.03)^t = 590000/492[/tex].

[tex](1.03)^t = 1199.1869[/tex].

[tex]log_{1.03}1.03^t = log_{1.03}1199.1869[/tex].

t = 2389.84 Or 2390 decades.

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The no. of customers they serve per day is equal to 14.

It is given that the total number of customers served in first year of business was 5110.

We have to find that what will be the average of servings per day ?

What do you mean by average ?

The average is the ratio of sum of all numbers to the total no. of numbers.

As per the question ;

Total number of people served in a year = 5110

We know that ;

1 year = 365 days

So ;

To calculate the average of servings per day we need to divide total number of servings by no. of days in 1 year.

i.e.,

Average of customers per day ;

= 5110 ÷ 365

= 14 customers per day

Thus , the no. of customers they serve per day is equal to 14.

Answer:

7/

Step-by-step explanation:

3/4 * 7/

3 can be crossed

Leaving 7/

Therefore , the solution of the given problem of perimeter comes out to be  PQRS  = 29 units.

The perimeter, or total length, of a shape is referred to as its perimeter in geometry. A shape's perimeter is calculated by summing the lengths of all of its sides and edges. By adding together the lengths of all a shape's sides, one may determine its perimeter.  The circumference of a field, for instance, will be 78 yards for a rectangle with dimensions of 24 yards long by 15 yards wide.

Here,

Given : PQRS has the length 12

and TUVW has length 15.

thus ,

To find the perimeter of PQRS:

we find,

TUVW = 35 units

and

PQRS = 35 - 6

=> PQRS  = 29

Therefore , the solution of the given problem of perimeter comes out to be  PQRS  = 29 units.

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Answer:

k = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

given variation equation

y = kx

to find k substitute y = 3 and x = 4 into the equation and solve for k

3 = 4k ( isolate k by dividing both sides by 4 )

[tex]\frac{3}{4}[/tex] = k

If you are dealt one card from a​ 52-card deck. The probability that you are not dealt a jack or a ten is 12/13.

Since there are 4 aces in a deck of card 52 first step is to find the number of cards  not aces in a deck of 52

Number of cards  not aces in a deck = 52 -4

Number of cards  not aces in a deck = 48

Now let find the probability that you won't draw an ace.

Probability = 48/52

Probability = 24/26

Probability = 12/13

Therefore we can conclude that the probability is 12/13.

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The annual cost if she chooses to make monthly payment is $1920 and money saved is $170

The given parameters that will help us to determine the incomes are

a)  Annual cost if she chooses to make one annual monthly installment is $1920

b) Money saved is she makes one annual payment is $(1920-1750)= $170

3) Volume of gas = 60 L

Efficiency rating = 10.2km/L

Average drive = Volume / Efficiency = 60/10.2 = 5.9km/L

b) Cost of gas = 149.9⊄⊄/L

Number of liters =60

= 60*149.9

=$8994

c) Constant gas price = $149.9⊄/L

Number of weeks /year = 52

=52*149.9

= $7795

4) Morgan pay $15/hr

Number of hours per week = 40

Gross monthly income = 40*15*4

=$2400

b)   Monthly income $2400

Amount left after deduction = 85%

=0.85*2400

Net income = $2040

In conclusion Mindley receives $1920 monthly and saves $170

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Answer:

Perimeter = 9x + 6

Step-by-step explanation:

Perimeter = x+14 + x-1 + x+5 + 3x + 2x-10 + x-2

Perimeter = 9x + 14 + 5 - 1 - 10 - 2

Perimeter = 9x + 19 - 13

Perimeter = 9x + 6

Answer:

dunno la saya , gak bisa bahasa ingeris