What is the domain of f?
A. {-4, -1, 0, 2, 7}
B. {-5, -4, -1, 0, 1, 2, 4, 7}
X
N
7
f(x)
C.
D. {5}
4
{-5, 0, 1, 2, 4, 7}

A translation 3 units left and 2 units up best describes the graph of  f(x) = log2(x + 3) + 2 as a transformation of the graph of g(x) = log2x

How to solve this problem?

f(x) = log2(x + 3) + 2 (given)

g(x) = log2x (given)

We need to describe the best statement for the graph

The graph is shown in the image

The following steps are shown to describe the graph.

The general equation of f(x) = log2(x-h)+k

When h > 0 (positive)

The graph of the base of the function shift to the right

When  h < 0 (Negative)

The graph of the base function shifts to the left.

When k > 0 (Positive)

The graph of the base function shifts upward.

When k < 0 (Negative)

The graph of the base function shifts downward

Here h = 3 , k = 2

Hence , a translation 3 units left and 2 units up describes the graph.

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We have evidence that this is not a symmetrical die, the standardized residuals is 9.5689

The die is tossed 1000 times

Given the observed value

x1 = 163

x2=178

x3=142

x4= 150

x5 = 183

x6 = 184

The mean = 163 + 178 + 142 + 150 + 183 + 184 / 6

= 1000 /6

= 166.67

Next we have to find the value of (observed value - Expected value)^2 / Expected value

x1 = (163-166.67)^2 / 166.67 = 0.081

x2 = (178-166.67)^2 / 166.67 = 0.7659

x3 = (142-166.67)^2 / 166.67 = 3.6598

x4 = (160 -166.67)^2 / 166.67 = 1.673

x5 = (183 - 166.67)^2 /  166.67 =  1.5938

x6 = (184-166.67)^2 / 166.67 =   1.7954

The standardized residuals = 0.081 + 0.7659 + 3.6598 +1.673 +1.5938 +1.7954 = 9.5689

Therefore, this is not a symmetrical die

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Applying DeMorgan's theorem to the expression overbar(overbar((overbar(a) overbar(b))) (overbar(c d))) results in (a b) + (c + d).

DeMorgan's theorem states that when two terms are combined with an AND operator (such as overbar(a) overbar(b)), the result is the two terms combined with an OR operator (such as a + b).

Similarly, when two terms are combined with an OR operator (such as overbar(c d)), the result is the two terms combined with an AND operator (such as c overbar(d)). Applying this theorem to the expression above results in (a b) + (c + d).

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The solution is D = 200 feet

The diameter of the circular store is = 200 feet

What is a Circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the diameter of the circle be represented as = D

Let the radius of the circular store be = r

D = 2r

Now , the area of the circular store be = A

The value of A = 31,415 feet²

The area of the circular store is given by the formula

Area of the circle = πr²

Substituting the values in the equation , we get

31415 = 3.1415 x r²

Divide by 3.1415 on both sides of the equation , we get

r² = 10000

Taking square roots on both sides of the equation , we get

r = 100 feet

Now , the diameter of the store = 2 x radius of the store

Diameter of the store D = 2 x 100 feet

Therefore , diameter of the store D = 200 feet

Hence , The diameter of the circular store is = 200 feet

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10 inches is the scale factor from the drawing to the actual billboard

A scale factor is a ratio of change from a drawing to real life. Typically, a scale factor is unit-less; a scale factor of 48 (or 1:48) is saying that for one unit on the page, it represents 48 of the same units in real life.

A scale factor is the ratio between corresponding measurements of an object and a representation of that object.

Scale drawings show an image either reduced or enlarged in size. The change between the original and the scaled drawing is generally represented by two numbers separated by a colon, like 10:1 (read as “ten to one”).

The difference between the ratio numbers represents the factor by which the scaled image is enlarged or reduced. So for a 10:1 scale ratio, a 1 inch (2.5 cm) drawing will be 10 inches (25 cm) in real life.

Methods are as follows :

Changing Scale Digitally-

Scan the image or snap a pic of it with your phone.

Insert the image into a suitable program or app.

Navigate to the image layout options.

Adjust the height and width under the “Scale” heading.

Save the scaled image and you’re done.

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The equation of the line that has the slope of 7/3 is:  y = (7/3) x - 27/49

Finding the slope and y-intercept is necessary to express the equation of a graphed line in y-intercept (y=mx+c) form, which can then be used to get the equation of the line. The ratio of y to x is known as the slope. A slope triangle should be drawn connecting any two spots you find along the line.

Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.

Given that,

slope (m) = 7/3

Putting (7,-9) into the equation: y =mx+c

or, -9 = (7/3) × (7) + c

or, -9 = 49 /3 + c

or, c = (-9) × (3/49)

or, c = -27/49

Thus, the equation becomes:

or, y = (7/3) x + -27/49

or, y = (7/3) x - 27/49

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The maximum area of the tile to contain both grounds is 12x²y²

From the question, we have the following parameters that can be used in our computation:

Area of ground A = 12x^2y sq. units

Area of ground B = 6xy^2sq units

Rewrite these areas properly

So, we have the following representation

Area of ground A = 12x²y sq. units

Area of ground B = 6xy² sq units

Express the areas as the products of their prime factors

This gives

Area of ground A = 2 * 2 * 3 * x * x * y

Area of ground B = 2 * 3 * x * y * y

From the above products, we have

Least common multiple = 2 * 2 * 3 * x * x *y * y

Evaluate the products

Least common multiple = 12x²y²

This represents the greatest area

Hence, the greatest area is 12x²y²

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Conditional problems are problems that involve one or more conditions that must be met in order for a certain action to be taken or a certain result to be obtained. The temperature of the solution in degrees Fahrenheit after x hours, is y = 1.5x - 100.

The required details for Conditional problems in given paragraph

This function models the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. The initial temperature of the solution is 100 °F, and the temperature decreases by 1.5 °F for each hour that passes. Therefore, the temperature of the solution after x hours can be found by subtracting 1.5x degrees from the initial temperature of 100 degrees.

For example, if we plug in x = 2 into the function, we get y = 1.5 * 2 - 100 = 3 - 100 = -97, which means that the temperature of the solution after 2 hours is -97 °F.

The other options listed are not correct because they do not correctly model the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. Option A is incorrect because it adds 1.5x degrees to the initial temperature, rather than subtracting it. Option B is incorrect because it adds 100 degrees to the temperature, rather than subtracting it. Option C is incorrect because it multiplies the initial temperature by 1.5x, rather than subtracting 1.5x degrees from it. Option D is incorrect because it adds 1.5 to the temperature, rather than subtracting 1.5x degrees from it.

what are conditional problems?

Conditional problems are often expressed using words like "if," "then," or "when." For example, a conditional problem might involve finding the value of a variable x if it satisfies a certain condition, such as "If x is greater than 5, then x is even." In this case, the problem specifies that x must be greater than 5 in order for it to be even.

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The two linear equations have the same slope, -2/3, and different y-intercepts, thus, the lines are parallel.

A general linear equation is written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

Two linear equations are parallel if both lines have the same slope and different y-intercepts.

And two lines are perpendicular if the product between the slopes is equal to -1.

In this case, we have the two linear equations:

y= -(2/3)*x - 3

y= -(2/3)*x + 6

So you can see that both linear equations have the same slope -2/3 and different y-intercepts, thus, the lines are parallel.

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Answer:

I cant see numbers sorry. post question again

The question is unclear.

The factor of the expression 8w - 16 will be 8 and (w - 2).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

A frequency table displays a sequence of scores in either increasing or decreasing order together with their occurrences as a way to compactly organize raw data.

The expression is given below.

⇒ 8w - 16

The factor of each term in the expression, then we have

8w = 8 x w

16 = 8 x 2

Then the expression is written as,

⇒ 8w - 16

⇒ 8 × w - 8 × 2

⇒ 8 × (w - 2)

⇒ 8(w - 2)

The component of the articulation 8w - 16 will be 8 and (w - 2).

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The correct option is B (f-g)(y)=8 y²-y+3

What exactly are function and example?

A rule is something that produces one output from one input, such as a function. Alex Federspiel was the source of the image. As an illustration, consider the equation y=x2. For every x input, there is only one y output. The fact that x is the input value leads us to say that y is a function of x.

Which four sorts of functions are there?

The classification of various types of functions can be done using four primary categories. All functions are based on the element: one to one, many to one, onto, one to one, and into.

Given that:

f(y)=5 y²-2y+1

g(y)=-3y²-y-2

(f-g)(y) = 8y²-y+3

Option b is correct

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The simplified expression of the fraction in its simplest form is -12a¹¹r⁻³

From the question, we have the following parameters that can be used in our computation:

\frac{3a^9r^{-3}}{-4(a^2)^{-1}}

Rewrite the above expression properly

So, we have the following representation

3a⁹r⁻³/(-4a²)⁻¹

Evaluate the expression in bracket

So, we have the following representation

3a⁹r⁻³/(-4a²)⁻¹ = 3a⁹r⁻³ * (-4a²)

Remove the brackets

This gives

3a⁹r⁻³/(-4a²)⁻¹ = 3a⁹r⁻³ * -4a²

Evaluate the products

So, we have the following representation

3a⁹r⁻³/(-4a²)⁻¹ = -12a¹¹r⁻³

Hence, the the fraction expression in its simplest form is -12a¹¹r⁻³

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Answer:

gh(b)

Step-by-step explanation:

Answer:

shifted to the right

Step-by-step explanation:

The following statements are true are more than 40% of the students at the school are freshmen or sophomores who plan to attend college.

Given :

emily surveyed all the students at her school to find out if they plan to attend college. the results are shown in the two-way frequency table. emily knows that the student body at her high school is distributed as follows: freshmen: 28 % sophomores: 26 % juniors: 24 % seniors: 22 %  .

Freshmen = 0.85

sophomores = 0.80

it is clearly visible that the freshmen or sophomores is greater than the 40 % .

Hence , more than 40% of the students at the school are freshmen or sophomores who plan to attend college.

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All the real numbers except 1 make the two expressions equal. Then the correct option is A.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expressions are given below.

[(x - 1)(x - 6)] / [4(x - 1)] and (x - 6) / 4

Simplify the expression [(x - 1)(x - 6)] / [4(x - 1)], then we have

⇒ [(x - 1)(x - 6)] / [4(x - 1)]

⇒ (x - 6) / 4

But at x = 1, the expression [(x - 1)(x - 6)] / [4(x - 1)] is not defined.

All the real numbers except 1 make the two expressions equal. Then the correct option is A.

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The picture of the (5, -1) beneath the same translation, in accordance with the stated statement, is (9, 6).

Each point in a graphic is moved the same distance within the same direction using a sort of transformation known as translation.

Translation in mathematics is the movement of a form in any direction—left, right, up, or down—without turning. They are congruent if the translated forms appear to be of the same size as that of the original ones. They have only changed their direction or directions.

The image of the translation is (9,-2).

The point is given as: P = (-6, -4)

The image of the point is: P' = (-2, 3)

The translation rule is calculated as:

T = x - 2 - (-6), y+3-(-4)

so,  T = x + 4, y + 7

So, the image of (5, -1) is:

the Image of the translation = 5 + 4, -1 + 7

Hence, the image of the translation is (9, 6).

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Answer:

f - 36

-3f - 23

are your prime polynomials.

Answer:

  2x² +5

Step-by-step explanation:

You want the width of a rectangle with a length of x+3 and an area of A(x) = 2x³ +6x² +5x +15.

The area is the product of length and width, so the width will be ...

  A = LW

  W = A/L = (2x³ +6x² +5x +15)/(x +3)

The cubic expression can be factored by grouping, so we have ...

  Area = (2x³ +6x²) +(5x +15)

  = 2x²(x +3) +5(x +3)

  = (2x² +5)(x +3)

Then the width is ...

  [tex]\text{width}=\dfrac{(x+3)(2x^2+5)}{x+3}=\boxed{2x^2+5}[/tex]

The width of the rectangle is 2x² +5.

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If the price of a latte is $4 and the price of a muffin is $2, then we can conclude that Julia can buy 5 lattes or 10 muffins ($20) if she chooses to buy only one of the two goods.

A price is the sum of money that one party pays or receives in exchange for another's goods or services. The cost of production may go by another name in certain circumstances. If the item is a "good" in a commercial transaction, the cost of the item will probably be referred to as its "price."

In this case, Allie receives a $20 gift card for the local coffee shop, where she only buys lattes and muffins. Here, we can conclude that Julia can buy 5 lattes. This will be 5 × $4 = $20 or 10 muffins which will be:

= 10 × $2

= $20

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Answer:

A

Step-by-step explanation:

Blue = River Y

Red = River Z

River Y equation: y = 18

River Z equation: y = 10 + 2x

Graph A represents this system of equations.

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The dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.

Given that:

Total surface area of the rectangular box or cuboid = 100 cm²

A rectangular box with largest volume is a cube.

The total surface area of a cube = 6 times square of one edge length.

Let the edge length = given dimensions; x, y, z

So,

x = y = z

6x^2 = 100

x^2 = 100 / 6

x = √ 100 / 6

x = 10 / √ 6 cm

x = 2.449 cm

Hence, dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.

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63 degrees is the angle.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given triangle is a right angle triangle.

The opposite side length is 85 and the adjacent side is 38.

Opposite side=85

Adjacent side=38.

Calculate Opposite/Adjacent

= 85/38= 2.236

Which is tanθ=2.236

Now tan inverse on both the sides

θ=tan⁻¹2.236

θ=tan⁻¹2

θ=63 degrees.

Hence, the angle is 63 degrees.

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Answer:

Step-by-step explanation:

log base (2) of (x^2 +5) = (3) can also be described as 2^3 = x^2 + 5

simplify: 8 = x^2+5

Subtract 5 from each side: 3 = x^2

square root: x = sqrt(3)

Answer:

Step-by-step explanation:

[tex]log(2)^{(x^2+5)}=3\\[/tex]

[tex]2^3 =x^2+5\\8-5=x^2\\x^2=3\\x=\pm\sqrt{3}[/tex]

Answer:

x- intercept = - 8 , y- intercept = 6

Step-by-step explanation:

to find the x- intercept let y = 0 in the equation and solve for x

3x - 4(0) = - 24

3x = - 24 ( divide both sides by 3 )

x = - 8 ← x- intercept

to find the y- intercept let x = 0 in the equation and solve for y

3(0) - 4y = - 24

- 4y = - 24 ( divide both sides by - 4 )

y = 6 ← y- intercept

The complete answer: A domain is a set of input data in a relationship.

The collection of all conceivable independent values that a function or relation may take is known as its domain.

An input value and an output value are matched in a relation.

A relation is a function where each input value yields one and only one output value.

Graphs, tables, and ordered pairs can all be used to represent functions. The domain is the set of input values,

while the range is the set of output values.

The domain of a function or relation is the set of all possible independent values that it can have.

Therefore,  a domain is a set of input data in a relationship.

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Answer:

[tex]2x^2+7x+C[/tex]

Step-by-step explanation:

Find the antiderivative of f'(x)=4x+7

[tex]\frac{4x^{1+1} }{1+1}+7x+C\\\frac{4x^2}{2}+7x+C\\ 2x^2+7x+C\\[/tex]

Answer:

To find the difference between the elevations of City A and City B, we need to subtract the elevation of City A from the elevation of City B. Since City A is located 15 meters below sea level, and City B is located 43 meters above sea level, the difference between their elevations is $43 - (-15) = 43 + 15 = 58 meters. Therefore, the difference between the elevations of City A and City B is 58 meters.

The probability that the first success occurs on trial number n = 3 is 0.032

Given:

probability of success on a single trial p = 0.80

trial number, n = 3

Recall the formula for the Geometric Probability Distribution

P(n) = p(1 - p)ⁿ⁻¹

where n is the number of the binomial trial on which the first success occurs and p is the probability of success on each trial

P(n) = p(1 - p)ⁿ⁻¹

P(3) = 0.8(1-0.8)³⁻¹

P(3) = 0.8(0.2)²

P(3) = 0.032

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