Determine which of the following terms is a function: a. (1,2) (2,4) (3,5) c. (1,2) (2,4) (2,6) b. (1,2) (2,3) (1,5) d. (1,2) (3,5) (3,7)

Answer:

Option A    

Step-by-step explanation:

Given : Equation [tex]y-1 = 2(x -2)[/tex]

To find : Which graph represents the given equation

Solution :

First thing we plot the graph of the equation.

We see that graph cuts at point (1.5,0) and (0,-3) to the coordinates.

From the given graph Option A graph cuts to these points.

Therefore, Option A is correct.

Refer the attached graph A.

ANSWER

We need to rewrite [tex]x+2y=6[/tex], in slope intercept form.

[tex]\Rightarrow 2y=-x+6[/tex],

[tex]\Rightarrow y=-\frac{1}{2}x+3[/tex]

The given equation has a slope of [tex]-\frac{1}{2}[/tex].

ANSWER TO QUESTION 1

We now the write given options also in slope intercept form.

For the first one, we have

[tex]y=-\frac{1}{2}x+5[/tex]

This first equation also has a slope  of [tex]-\frac{1}{2}[/tex].

Hence [tex]y=-\frac{1}{2}x+5[/tex] is parallel to [tex]x+2y=6[/tex].

ANSWER TO QUESTION 2:

The second equation is;

[tex]-2x+y=-4[/tex].

We need to write this one too in slope intercept form.

[tex]y=2x-4[/tex]

This second equation has a slope of 2

Since [tex]2\times -\frac{1}{2}=-1[/tex], the line [tex]-2x+y=-4[/tex]

is perpendicular to [tex]x+2y=6[/tex].

ANSWER TO QUESTION 3

We rewrite the equation [tex]-x+2y=2[/tex] in slope intercept form.

[tex]\Rightarrow 2y=x+2[/tex]

[tex]\Rightarrow y=\frac{1}{2}x+1[/tex]

This equation also has a slope of [tex]\frac{1}{2}[\tex]

since the slope of [tex]-x+2y=2[/tex] is not equal to the slope of [tex]x+2y=6[/tex], and the product of these two slopes [tex]\frac{1}{2} \times - \frac{1}{2} \ne -1[/tex], the two lines are neither parallel nor perpendicular.

QUESTION 4

The given line has equation [tex]x+2y=-2[/tex]. We rewrite this equation in the slope intercept form.

[tex]\Rightarrow 2y=-x-2[/tex]

[tex]\Rightarrow y=-\frac{1}{2}x-1[/tex]

This line has a slope of [tex]-\frac{1}{2}[/tex].

Since this slope is the same as the slope of the given line,

[tex]y=-\frac{1}{2}x-1[/tex] is parallel to  [tex]x+2y=6[/tex].

See graph in attachment.

Final answer:

To evaluate the given integral, split the function at x = 3 and integrate separately. The integral evaluates to 18, which makes the correct answer 18.

Explanation:

The function we're integrating is 1, which makes this the same integral as the one in example 3 on p. 178. To evaluate this integral, we need to split it at x = 3 and integrate the corresponding functions separately.

For x ≤ 3, the function is f(x) = 3. So, the integral from 0 to 3 of 3 dx equals 9.

For x > 3, the function is f(x) = 6 - x. Integrate this from 3 to 6: ∫(6 - x) dx = 6x - 0.5x^2. Evaluating this from 3 to 6 gives 9.

If its rounded it would be 73 degrees

To make a profit of at least $600, the number of bookends that need to be sold is calculated by adding the desired profit to the initial cost, and then dividing this sum by the net revenue per bookend. The result is approximately 144 bookends.

The subject of this problem is Mathematics, specifically a topic within business math called 'breakeven analysis' or 'cost-volume-profit analysis'. It involves calculating the point at which revenue from selling a product equals the costs associated with producing and selling that product. In this case, you have spent $154 to make wooden bookends, and you plan on selling them online for $8.50 each. Additionally, there's a $3.25 fee per bookend for wrapping and shipping, which you charge to your customers. Your goal is to make a profit of at least $600.

To calculate the number of bookends that need to be sold, we first find the net revenue per bookend. This is the selling price minus the shipping cost, which comes out to $8.50 - $3.25 = $5.25 per bookend. The desired profit is added to the cost of making the bookends to find the total required revenue, which is $600 + $154 = $754.

Finally, total required revenue is divided by the net revenue per bookend to find the number of bookends that need to be sold: $754 ÷ $5.25 = approximately 144 bookends (rounded up to the nearest whole bookend since we can't sell a fraction of a bookend). So, in order for your profit to be at least $600, you must sell at least 144 bookends.

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Answer:

C - Opposite sides are congruent  

D - Corresponding parts of congruent triangles are congruent

Step-by-step explanation:

A parallelogram is a quadrilateral whose both pairs of opposite sides are parallel. In a parallelogram, the 2 sets of opposite sides are congruent. Also it has 2 sets of opposite angles congruent.

Therefore, the following are necessary when proving the opposite sides of a parallelogram are congruent.

C - Opposite sides are congruent  

D - Corresponding parts of congruent triangles are congruent

we know that

if the lines bd and xy are parallel. then

[tex]y+70\°=180\°[/tex] --------> by consecutive interior angles

so

Solve for y

Subtract [tex]70\°[/tex] both sides

[tex]y+70\°-70\°=180\°-70\°[/tex]

[tex]y=110\°[/tex]

therefore

the answer is

[tex]y=110\°[/tex]

Answer:

Option C. y = 110°

Step-by-step explanation:

In this question BD and XY are two parallel line and a transverse is intersecting both the lines at A and E.

Now ∠BAE = ∠AEY = 70° [ alternate interior angles ]

and ∠EAD + ∠BAE = 180° [ supplementary angles ]

or y + 70° = 180°

⇒ y + 70 - 70 = 180 - 70

⇒ y = 110°

Therefore Option C. measurement of y = 110° is the answer.

The interval of x-values over which the function is increasing is (-3 , -1), the correct option is B.

A function is a law that relates two variables namely, a dependent and an independent variable.

A function always has a defined range and domain.

The x values and the corresponding function values are shown in the figure.

The x and y values are:

-6      -34

-5       3

-4      -10

-3      -11

-2      -6

-1        -1

0        -2

1        -15

The  interval of x-values over which the function is increasing has to be determined.

The first option is (-6, -3) , the function is not increasing in this interval.

The second option is (-3 , -1) , the function is increasing in this interval.

The third option is(–3, 0), the function is not increasing in this interval.

The fourth option is (–6, –5), the function is not increasing in this interval.

Your question seems incomplete, the complete question is attached with the answer.

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Answer:

The discriminant of the given polynomial is 0.

Step-by-step explanation:

The discriminant of a quadratic polynomial [tex]p(x)=ax^2+bx+c[/tex] is

[tex]D=b^2-4ac[/tex]

The given expression is

[tex]9x^2-18x+9[/tex]

Here,

[tex]a=9,b=-18,c=9[/tex]

The discriminant of a given polynomial is

[tex]D=(-18)^2-4(9)(9)[/tex]

[tex]D=324-324[/tex]

[tex]D=0[/tex]

Therefore the discriminant of the given polynomial is 0.

Answer:

To prepare for the unexpected, it is important to have a reserve fund set aside. Having a reserve fund is important, but it should not always be your first priority. If you have credit card or other debt, pay that off before you start to put your money in a reserve. Credit card debt has a high interest rate, while the money that you will save in your reserve probably won’t gain a lot of interest. Why not? When you choose a place to save your financial reserve, low risk is key. Remember that your financial reserve fund is for emergencies only. If you have an emergency and need to use it, do. Once you are back on your feet, replenish it. Also, once you have saved the amount you need, stop. Your extra savings will serve you better in an investment that yields higher interest.

Step-by-step explanation:

Words taken from the online site 1 on edge for "Why might a person need an emergency fund?"

The term “emergency fund” refers to helping those times when a person is in need of money. An emergency fund allows you to save on rarer credit interest.

What is emergency fund?

The term “emergency fund” refers to the person's use of money at the time of need. Emergency money is saving money. They improve our financial security and safety. The emergency money is a small amount of money. For example, home repairs, paying medical bills, trip planning.

An emergency fund is money kept in a bank account to cover unexpected expenses like medical bills or car or home repairs. An emergency fund can also assist you in the event of a lack of income due to a job loss or prolonged illness.

Hence, the significance of the emergency fund is aforementioned.

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The conversion factor to convert cups to liters is 0.237. When converting from cups to liters, multiply the number of cups by 0.237.

According to the conversion table provided, the conversion factor to convert cups to liters is 0.237. That means for every 1 cup, it equals approximately 0.237 liters. To convert from cups to liters, you simply multiply the number of cups by this conversion factor, 0.237.

For example, to find out how many liters is 2 cups, you do the multiplication: 2 cups * 0.237 = 0.474 liters.

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The complete question is given below:

Given : A table showing conversions for common units of capacity.

                              Units of  capacity  

Customary System Units                             Metric System Units

        1 gallon                                                           3.79 liters

        1 quart                                                            0.95 liters

         1 pint                                                              0.473 liters

         1 cup                                                              0.237 liters

What is the conversion factor to convert cups to liters?

The conversion factor to convert cups to liters, according to the given table, is that 1 cup equals 0.237 liters. To convert any amount of cups to liters, multiply the number of cups by 0.237.

The table in your question provides the conversion factors for common units of capacity, including the conversion of cups to liters in both the Customary and Metric systems.

According to the table, 1 cup is equivalent to 0.237 liters. This means that to convert any given number of cups to liters, you multiply the number of cups by 0.237.

For example, to convert 5 cups into liters, you would perform the following calculation: 5 cups × 0.237 = 1.185 liters. This conversion factor is useful in everyday scenarios such as cooking or reading a recipe that uses different measurement systems.

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Expression after the simplification is 62.5.

In mathematics, expression is the combining of variables with the application of operations and prescribed rules. It could take the shape of an equation, some numbers, etc.

Given, expression

55 - 4.5 +12

Simplifying,

first, add the numbers.

55 - 4.5 +12

= 67 - 4.5

= 62.5

Hence, the value of the expression is 62.5.

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The standard form of the equation of the parabola with focus at (1, 1) and directrix 'y = 7' is (x - 1)² = 12(y - 4). The vertex is found by determining the midpoint between the focus and directrix, and the 'a' value is found by calculating half the distance between the focus and directrix.

To find the standard form of a parabola given the focus and directrix, we'll use the definition of a parabola itself. A parabola is defined as the set of points that are equidistant from a point, known as the focus, and a line, known as the directrix.

The equation representing a parabola is: (x - h)² = 4a(y - k) where (h, k) is the vertex of the parabola and 'a' denotes the distance between the vertex and the focus or the vertex and the directrix.

The mid-point of the focus (1, 1) and the directrix y=7 gives the coordinates of the vertex. So, h = 1 and k = (1+7)/2 = 4.

Now, 'a' is half the distance between the focus and directrix, a = (7-1)/2 = 3.

So, the standard form of the equation is (x - 1)² = 12(y - 4)

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An algebraic description of the transformation that translates a point (x, y) nine units to the right and five units down is written as the new point (x + 9, y - 5).

The algebraic description of a transformation that translates a point (x, y) nine units to the right and five units down can be written as the following ordered pair: (x + 9, y - 5).

In this transformation, the x-coordinate of each point is increased by 9 units, reflecting a horizontal translation to the right, and the y-coordinate is decreased by 5 units, representing a vertical translation downwards. Thus, if you have a point (x, y), after the transformation, it becomes (x + 9, y - 5).

For example, if your initial point is (3, 4), after the transformation it would be at (3 + 9, 4 - 5) = (12, -1).

Answer: C. The amount earned is a function of the number of hours worked.

Explanation:

Since, a function is always the type of y= f(x), where x is independent variable and y is dependent variable which is dependent on the value of x.

Here,  a graph of Olivia's earning per hour is given.

Since, it is the obvious thing that the earning will depend on hours she works.

Thus, we can say that earning is dependent variable while hours is independent variable.

Therefore, earning makes the y-axis and number of hours makes the x-axis.

So, option C is correct.

Dublin is 3 hours ahead of Moscow.

The difference between how time is measured in different ways; the length of a period of time. the time difference between two or more distinct time zones in terms of clock time.

Given Dublin time = 11:30 am

Moscow  time = 2:30

we can military time and subtract.

11:30 a.m. = 11:30

2:30 p.m. = 2:30 + 12:00 = 14:30

14:30 - 11:30 = 3:00

Hence the time difference is 3 hours.

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Answer: 0.0625

Step-by-step explanation: