Write this equation in standard form.

x^2+y^2-6x-6y+2=0

Show work.

The simplified form of the given expression is x + a - 4

From the question, we are to simplify the given expression

From the given information, we have that

g(x) = x² - 4x,

Now,

We are to simplify

[tex]\frac{g(x)-g(a)}{x -a}[/tex]

First, we will determine g(a)

From the given function,

g(x) = x² - 4x

∴ g(a) = a² - 4a

Thus,

[tex]\frac{g(x)-g(a)}{x -a}[/tex] becomes

[tex]\frac{x^{2} -4x-(a^{2}-4a)}{x -a}[/tex]

[tex]\frac{x^{2} -4x-a^{2}+4a}{x -a}[/tex]

[tex]\frac{x^{2} -a^{2} -4x+4a }{x -a}[/tex]

Factoring

[tex]\frac{(x+a)(x-a)-4(x-a) }{x -a}[/tex]

Further factorization

[tex]\frac{(x-a)((x+a)-4) }{x -a}[/tex]

Dividing

((x +a) -4)

x + a - 4

Hence,

The simplification gives x + a - 4

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It is observed that f is a subset of A×B

A subset is a subset (another set or the same set). It is expressed as A⊆ B in the set notation to indicate that set A is a subset of set B.Set 1 is a subset of Set 2 if all of its components are included in Set 2. A set, as far as we are aware, is a clearly defined grouping of letters, objects, numbers, or anything else. Set 1 is a subset of Set 2 if Set 1 = A, B, C, and Set 2 = A, B, C, D, E, and F. This is because all the items in Set 1 are also present in Set 2.

Given that :A={1,2,3},B={7,8,9,10}andf={(1,7),(2,9),(3,8)}

A={1,2,3}

B={7,8,9,10}

A×B ={(1,7)(1,8)(1,9)(1,10)(2,7)(2,8)(2,9)(2,10)(3,7)(3,8)(3,9)(3,10)}

f={(1,7),(2,9),(3,8)}

A relation from a non-empty set  A to a non-empty set  B  is a subset of the Cartesian product A×B

It is observed that f is a subset of A×B

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4 Tangerines will balance 1 apple.

Given that

Weight of Apple is represented by: a

Weight of tangerine is represented by: t

Weight of Grapefruit is represented by: g

Weight of Banana is represented by: b

Consider 1st picture:

1 apple and 1 tangerine balance 1 grapefruit.

⇒ a+t = g                  ...(1)

Consider 2nd picture:

1 banana and 1 tangerine balance 1 apple.

⇒ b+t = a                  ...(2)

Consider 3rd picture:

2 grapefruits balance 3 bananas.

⇒ 2g = 3b

g = 1.5b                     ...(3)

The system of equations are:

First balance: a+t = g  

Second balance: b+t = a  

Third balance: g = 1.5b  

Putting the value of g from equation (3) to equation (1), we get

a+t = 1.5b                   ...(4)

Now, putting the value of b from equation (2) to equation (4), we get

a+t = 1.5(a-t)

1.5a - 1.5t = a+t

0.5a = 2t

a = 4t

Hence, one apple is balanced by 4 tangerines.

Refer to the full question given below in the image.

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The g graph exhibits a four-fold vertical stretch.

The graph of f (x)=[tex]x^{2}[/tex] is translated up to two units, then reflected in the X-axis.

The rule for g.

Identify the vertex​

The g graph exhibits a four-fold vertical stretch.

=> g = 4f(x) (x)

an X-axis reflection

=> g = - 4f(x) (x)

(X-axis reflection of (X, Y) is (x , - y)

a conversion two units higher

=> g = -4f(x) + 2

f(x) = x²

=> g = - 4x² + 2

Vertex is at  ( 2, 0)

What is a vertical stretch?

When a base graph is multiplied by a particular factor larger than 1, vertical stretch happens. As a consequence, the graph is stretched outward while keeping the input values (or x). We anticipate that the y values in a function's graph will be further away from the x-axis when it is vertically extended.

How to vertically stretch a function?

When given a function’s graph, we can vertically stretch it by pulling the curve outwards based on the given scale factor. Here are some things to remember when we vertically stretch functions:

Ensure that the values for x remain the same, so the base of the curve will not change.

This means that when applying vertical stretches on a base graph, its x-intercepts will remain the same.

Take note of the new critical points, such as the new maximum point of the graph.

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Answer:

350'000

Step-by-step explanation:

The real # is 369,852, so 350,000 is closest to all the other options.

Answer: 1/2

Step-by-step explanation:

If we have an equaton in a standard form, that is y = mx + b, our slope is m (the coefficient of x). So, let's transform 3x - 6y = 144 into the standard form.

3x - 6y = 144

-6y = - 3x + 144

y = -3/(-6)x - 144/6

y = (1/2)x - 24

As I mentioned above, the slope is the coefficient of x. Here our slope is 1/2.

Answer:

a: undefined

b: -15

c: 20

d: 25

Step-by-step explanation:

a: look at x -3 on graph, the left hand limit and right hand limits are different so it's undefined

b: look at x 0 on graph, there is open dot at -15 meaning the limit is there

c: look at x -7 on graph, there is open dot at 20 meaning the limit is there

d: look at x 5 on graph, the y is at 25 meaning the limit is there (it's normal here)

Answer:

n / 9  + 5 = 3

Step-by-step explanation:

The description of the relationship is a linear relationship, the equation is y = 301.7 - 2.158x and the actual selling price of the home is $275

The given parameter is in the attached figure

Also from the question, we have:

House price decreases by approximately every mile

The above implies that the relationship is an approximately linear relationship

From the table, we have

Coefficient constant = 301.7

Coefficient distance = -2.158

This means that

y-intercept = 301.7

Slope = -2.158

So, the equation is

y = y-intercept + slope * x

This gives

y = 301.7 - 2.158x

The interpretation of the slope and y-intercept in context are:

Slope implies that the house price decreases by 2.158 miles, and the y-intercept implies that the initial house price is 301.7

Here, we have

Residual =  -2.962

Miles = 11

This means that

Predicted price = 301.7 - 2.158 * 11

Evaluate

Predicted price = 277.96

So, we have

residual = actual - predicted

This gives

actual = residual + predicted

So, we have

actual = -2.962 +  277.96

Evaluate

actual = 275

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The absolute change or the car's value decreased by $1500.

The relative change: The value of the car decreased by 6.302 %.

The car's value dropped from $23,800 to $22,300 over the last year.

So, the initial price of the car is I = $23,800, and the final value of the car after a year is F = $22,300.

Therefore,

The Absolute change will be:

= I - F

= $23,800 - $22,300

= $1500

Hence, the car's value decreases by $1500.

Now, the relative change is the percentage by which the price decreased over the year.

So,

As the price decreased by $1500.

Let x be the relative change.

Then,

$ 23,800 × x/100 = $1500

238x = 1500

x = 6.302

Hence, the car's value decreased by 6.302% last year.

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The prices p that would yield a revenue of 7110 dollars are;

Lowest price = $0.895

Highest price = $119.105

We are told that the total revenue obtained by producing and selling x units is given by; R = xp.

Now, we are told that the demand equation for a certain product is given by p = 120 - 0.015x.

where;

p is the unit price (in dollars) of the product.

x is the number of units produced.

At a revenue of $7110, we will have;

(120 - 0.015x)x = 7110

120x - 0.015x² = 7110

0.015x² - 120x + 7110 = 0

Using quadratic equation calculator, we have;

x = 59.695 and 7940.305

Thus;

Lowest price = 120 - 0.015(7940.305) = $0.895

Highest price = 120 - 0.015(59.695) = $119.105

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Answer:4

Step-by-step explanation:

The graph of the function gives the type of function, (continuous or discrete function) the domain and the range as follows;

(A, 2A)

First graph;

Discrete function

Domain; {x| x = -8, -2, 3, 6}

Range; {y| y = 5, 4, -2, 7, }

Second graph

Continuous function

Domain; -4 < x < ∞

Range; 1 ≤ y < 9

(A3.A) 1. The slope of the graph is -1.5

2. The slope of the graph is 1.5

A function is an equation defining the relationship between input and output variables

(A, 2A)

A continuous function is one in which a continuous variation in the input values produces a continuous variation in the output. Therefore, a continuous function does not have discontinuity and it has a defined output within the interval in which it is contagious

A discrete function is one that have input values and output only at specified points, such that the function does not have inputs, and therefore, outputs at certain points.

The points in the scatter plot of the first graph are separate and not linked, such that the function is not contagious between any two x–values, which gives;

The function is a discrete function

The domain, which is the set of possible x–values is; {x| x = -8, -2, 3, 6}

The range is {y|y = 5, 4, -2, 7, }

The line joining the points on the second graph, indicates that the graph has values for all input or x–values

Therefore, the function of the graph is a continuous function

(A3. A) 1. Points on the graph are:

(0, 2), (2, -1)

The slope is given by the equation;

Slope = ∆y ÷ ∆x

Which gives;

2. The given function is; -3•x + 2•y = -6

To find the slope, the function is expressed in the slope and intercept form, y = m•x + c, as follows;

-3•x + 2•y = -6

2•y = 3•x - 6

Therefore;

2•y = 3•x - 6

y = (3•x - 6) = 1.5•x - 3

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The reciprocal of 3 7/8 is 8/31.

To find the reciprocal of a number, we invert the fraction by swapping the numerator and denominator.

Let's calculate the reciprocal of 3 7/8.

First, we need to convert the mixed number into an improper fraction. To do this, we multiply the whole number (3) by the denominator (8) and add the numerator (7). This gives us:

3 7/8 = (3 x 8 + 7) / 8 = 31/8

Now, to find the reciprocal, we invert the fraction:

Reciprocal of 31/8 = 8/31

Therefore, the reciprocal of 3 7/8 is 8/31.

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Answer: 25 is divisible by 5, so it is composite

Step-by-step explanation:

Answer: Smooth muscle contractions

answer:

the third one

We need to know about density to solve this problem. The density of the piece of metal is 5.9 g/[tex]cm^{3}[/tex], so option (c) is the correct answer.

Density is a substance's mass per unit volume. The symbol commonly used for density is ρ. Density can be calculated by dividing the mass by volume. In this question we know that mass of the metal piece is 124 grams and the volume is given to be 21 cubic centimeters. The density can be calculated by dividing the mass by volume of the metal piece.

density =mass/ volume= 124/21=5.90 g/[tex]cm^{3}[/tex]

Therefore the density of the piece of metal is 5.9 g/[tex]cm^{3}[/tex] , so option (c) is the correct answer.

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Answer: x = 7

Explanation - 4(5x-2)=2(9x+3)

20x-8=18x+6

20x-18x=6+8

2x=14

x=14÷2

x=7

Hello there!

Here we need to solve for x.

The first thing that we're going to do is this:

[tex]\implies\boldsymbol{4(5x-2)=2(9x+3)}[/tex]

[tex]\implies\boldsymbol{20x-8=18x+6}[/tex]

[tex]\implies\boldsymbol{20x=18x+14}[/tex]

[tex]\implies\boldsymbol{20x-18x=14}[/tex]

[tex]\implies\boldsymbol{2x=14}[/tex]

[tex]\implies\boldsymbol{x=7}[/tex]

Therefore x=7. I hope this helps you, feel free to comment if you have any queries :)

The number of different samples possible when the shopper selects a sample of 4 apples from the bag is 126.

Combinations are a method of calculating the overall results of an event where the order of the results is irrelevant. From the information, the bag of 9 apples contains 2 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag.

It should be noted that the question has to do with a combination. The number of different samples that are possible will be:

Number of apples = 9

Number to be selected = 4

= ⁹C₄

= 9! / (9 - 4)! 4!

= 9 × 8 × 7 × 6 / 4 × 3 × 2

= 126

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A bag of 9 apples contains 2 rotten apples and 7 good apples. A shopper selects a sample of 4 apples from the bag. How many different samples are possible?

The actual area of the guest bedroom is 240 square ft, if on a blueprint, a guest bedroom has dimensions 3 cm by 5 cm and the blueprint is drawn using the scale of ½ cm = 2 ft.

The minimal amount of coordinates required to specify any point within a mathematical space (or object) is known as the dimension in physics and mathematics. As a result, a line has one dimension (1D), since only one coordinate is required to specify a point on it, such as the point at 5 on a number line.

A surface, like the perimeter of a cylinder or sphere, has two dimensions (2D) because two coordinates are necessary to specify a point on it. For instance, both a latitude and a longitude are necessary to pinpoint a point on the surface of a sphere.

The dimensions are 3cm by 5 cm meaning length = 5cm and breadth = 3cm

Given that ½ cm = 2 ft, that is

1 cm = 4 ft

Using the conversion method

3 cm = 3 × 4

        = 12 ft

5 cm = 5 × 4

        = 20 ft

Actual area = 20 × 12 ft

                    = 240 square ft

Thus, the actual area of the guest bedroom is 240 square ft, if on a blueprint, a guest bedroom has dimensions 3 cm by 5 cm and the blueprint is drawn using the scale of ½ cm = 2 ft.

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The C-intercept is the point at which the function crosses the C-axis, then it is at t=0.

As we know two points on the line: (-20, 200) and (30,0), and we found previously the slope m=-4.

We can use the slope-intercept form of the equation of a line to find the C-intercept as follows:

Where (t,C) is any point on the line, m is the slope and b is the C-intercept.

By replacing the know values we can solve for b:

Therefore,

The value of x in the equation is 18. 98

Trigonometric identities are defined as mathematical equations relating to several trigonometric functions, holding true for all the values in the domain of the functions.

The several types of trigonometric identities includes;

It is important to note that the trigonometric ratios for major identities are;

sine = opposite/hypotenuse

tangent = opposite/adjacent

cosine = adjacent/hypotenuse

Given the equation;

x/25.75=sin47.5 degrees

Take the following steps to determine the value of 'x'

We have;

cross multiply

x = sin47.5  × 25. 75

Find the value of sin 47. 5 and substitute the value

x = 0. 7373 × 25. 75

multiply through

x = 18. 98

Hence, the value of x is  18. 98

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The complete question:

x/25.75=sin47.5 degrees

Find the value of x

nswer:

Explanation:

ere, we want to solve the given composuite function

What we have to do is to replace the x in f(x) with the entirety of g(x)

We have that as:

Now, we replace x in f(x) with 2x+9 as stated

We have that as:

The probability that a theft can happen in a room that is left unlocked based on the statistics of dorm rooms affected by theft, is 1.89%

To find the probability that a room will be subjected to theft if it is left unlocked, the formula is:
= Probability that dorm room is left unlocked x Probability of dorm room being affected by theft x Probability that a theft occurs in a unlocked room

The probability of an unlocked room being robbed is therefore:

= 0.75 x 0.03 x 0.842

= 0.0225 x 0.842

= 0.018945

= 1.89%

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1) Dividing the given formula by W we get:

2) We know that:

Therefore:

Then:

Substituting W=3/4ft and L=18ft in the given formula we get:

Answer:

1)

2)

Answer:

I'm not so very sure but I really need points