What is the domain of the function graphed below?

The function g(x) is a translation of 3 units to the right and a vertical dilation by scale factor k = 2 of f(x), the graphs of both functions can be seen in the image at the end.

We know that g(x) is a transformation of the parent function f(x) = √x, such that:

g(x) = 2*f(x - 3)

g(x) = 2*√(x - 3)

Then we can see that g(x) is a translation of 3 units to the right followed by a vertical dilation of scale factor 2 of the parent function f(x).

So to graph g(x) you first need to move the whole graph of f(x) 3 units to the right, and then apply a dilation vertically.

The graph of g(x) and f(x) can be seen in the image below:

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Angle M corresponds to angle M' and

Side N'O' is the image of side NO

The vertices of each triangle must have a one-to-one correspondence. This phrase means that the measure of each side and angle of each triangle is equal to the side or angle of the other triangle.

Here it is given that Triangle MNO maps to triangle M'N'O'

We need to find that Angle M corresponds to which angle and the image of side NO

By one to one correspondence we get that

Angle M corresponds to angle M' and

Side N'O' is the image of side NO

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The equivalent equation is (4x² + 9)(4x² - 9) and the zero's are x =± 3 / 2 and x = ± 3 / 2i

The equivalent equation can be found by factoring. Factoring of a polynomial is the method of breaking the polynomial into a product of its factors.

Therefore,

f(x) = 16x⁴ - 81 = 0

Hence,

9 × 9 = 81

4x² × 4x² = 16x⁴

Therefore,

16x⁴ - 81  = (4x² + 9)(4x² - 9)

Hence,

The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0 (f(x) = 0).

The zero's of the function are as follows:

4x²  = 9

x² = 9 / 4

x =± 3 / 2

4x² = -9

x² = - 9 / 4

x =√-9 / 2

x = ± 3 / 2i

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There is a 9/25 chance that two numbers will be added together such that their total exceeds their product.

The set of positive numbers are:

{1,2,3,4,5}

We have to independently select two numbers from these sets.

We are trying to determine the likelihood that the sum is larger than the product of the integers.

When one of the chosen numbers is 1, the total will always be greater than the product because:

1*1=1 & 1+1=2

1*2=2 & 1+2=3

1*3=3 & 1+3=4

1*4=4 & 1+4=5

1*5=5 & 1+5=6

and so on.

If we select 2 as both numbers then,

2*2=4 & 2+2=4

Here sum and the product are equal.

If not, the product will be bigger than the sum.

Now, the first stage is to evaluate the total number of two combinations that are feasible:

We have 5 alternatives for the first number and 5 alternatives for the second number.

The product of the number of possibilities in each scenario yields the total number of combinations:

C= 5*5=25

The following combinations have a sum that is greater than the product :

1 and 1

1 and 2

1 and 3

1 and 4

1 and 5

2 and 1

3 and 1

4 and 1

5 and 1

So, we get 9 combinations.

So, Probability,p=9/25

Therefore it is concluded that the probability is 9/25.

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Answer:

The estimated result is 680, which suggests the calculator is incorrect.

answer choices would have helped, hope this helps :)

The graph depicts that at the end of the snowstorm, there was 5 inches of snow left. See the attached graph.

It is not be noted that the total amount of hours which the snow fell is:

2 + 9 = 11 hours.

Although the graph depicts a peak of 14 hours, recall that there were three hours when the snow didn't fall.

While the maximum depth of the snow was 11 inches.

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When two or more given triangles are congruent, this implies that the measures of their corresponding angles and sides are equal. So that the additional information required in the question is FG ≅ IJ.

When two or more given triangles are congruent, this implies that the measures of their corresponding angles and sides are equal. Thus the congruent relations of the triangles can be with respect to their angles or/ and sides.

The two given triangles in the question would be congruent with respect to the Side-Angle-Side (SAS) postulate if the condition below is true:

i.e FG ≅ IJ

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Answer:

555 m

Step-by-step explanation:

Because the model should have identical proportions to the real-life tower, the ratio between the height and shadow length of both diagrams should be the same.

Height (model)             Height (real)
-------------------------  =  ------------------------
Shadow (model)         Shadow (real)

Math:

 0.9 meters                   x
--------------------  =  ----------------------               <----- Ratio
 0.2 meters           123.3 meters

4.5 = x / 123.3 meters                                  <----- Divide 0.2 from 0.9

555 meters = x                                            <----- Multiply both sides by 123.3

The inverse function of g(x) is:

[tex]f(x) = -\frac{3}{x + 4}[/tex]

So the correct option is D.

Here we have the function:

[tex]g(x) = -\frac{3}{x} - 4[/tex]

Remember that two functions f(x) and g(x) are inverses if:

[tex]f(g(x)) = x\\g(f(x)) = x[/tex]

Then we must have:

[tex]g(f(x)) = -\frac{3}{f(x)} - 4 = x[/tex]

Solving for f(x), we get:

[tex]-\frac{3}{f(x)} - 4 = x\\\\ \frac{3}{f(x)} +4 = -x[/tex]

[tex]\frac{3}{f(x)} = -x - 4\\\\3 = (-x - 4)*f(x)\\\\\frac{3}{-x - 4} = f(x) = -\frac{3}{x + 4}[/tex]

Then the correct option is D.

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Answer:

Step-by-step explanation:

The probability that of the questions studied, all three were the test questions selected by the professor is 0.05.

We can find the probability by dividing the total number of favorable events by the total number of events.

The total number of events is given by [tex]6C_{3}[/tex].

The total number of favorable events is given by [tex]3C_{3}[/tex].

The probability is given by = Favorable events/Total number of events

= [tex]\frac{3C_{3}}{6C_{3}}[/tex]

= [tex]\frac{1}{\frac{(6)(5)(4)}{(1)(2)(3)} }[/tex]

= [tex]\frac{1}{(5)(4) }[/tex]

= 0.05

The probability that all three questions are selected by the professor for the test is found to be 0.05.

Therefore, we have found that the probability that of the questions studied, all three were the test questions selected by the professor is 0.05.

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Disclaimer: The question was incomplete, the complete question is attached below.

Question: A professor gave her students six essay questions from which she will select three for a test. A student has time to study for only three of these six questions. What is the probability that, of the questions studied, all three were the test questions selected by the professor?

The equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².

Based on the calculations, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5²

The equation of a circle.

Mathematically, the standard form of the equation of a circle is given by;

(x - h)² + (y - k)² = r²

Where:

h and k represent the coordinates at the center.

r is the radius of a circle.

The midpoint of the given points represents the center of this circle:

h = (4 + 4)/2 = 4

k = (5.5 + 10.5)/2 = 8

Next, we would determine the radius by using the distance formula for coordinates:

r = √[(x₂ - x₁)² + (y₂ - y₁)²]

r = √[(4 - 4)² + (10.5 - 5.5)²]

r = √[0² + 5²]

r = √25

r = 5 units.

Therefore, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².

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Answer:

================

The exponential growth function has:

When the function is reflected across the y-axis, we'll have no change to domain or range from what is described above.

Alissa is correct, the input values change to opposite, however the domain stays same - all real numbers.

It means Simon is correct with his statement.

The matching answer choice is C.

Answer:

Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input.

Step-by-step explanation:

Exponential Function

General form of an exponential function:  [tex]f(x)=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Reflection in the y-axis

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

As the exponential function is a growth function, b > 1.

If the exponential growth function has been reflected in the y-axis, the x variable is negative:

[tex]\implies f(x)=ab^{-x}[/tex]

Regardless whether the initial value [tex]a[/tex] (y-intercept) is positive or negative, the domain of an exponential function is (-∞, ∞) so it is unrestricted.

Therefore, if the function is reflected across the y-axis, the output value for each input value will change, but the domain itself will not change and will still be all real numbers.

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[tex] \frac{2}{y} = \frac{4}{2} [/tex]

[tex]4 = 4y[/tex]

[tex] \frac{4}{4} = y[/tex]

[tex]1 = y[/tex]

Hope it helps you any confusions you may ask!

Let's see

Verified

Answer:

240π cm³ (exact)

754 cm³ (approximate)

Step-by-step explanation:

I assume the shape of the cup is a cylinder. The height of the cylinder is 15 cm.

Think of a vertical rectangle that contains the vertical axes of the cylinder.

Two sides of the rectangle are diameters of the bases of the cylinder. The other two side are heights of the cylinder. The pencil is 17 cm long and is a diagonal of this rectangle. We can find the diameter of the base of the cylinder using the Pythagorean theorem.

In a rectangle that is 15 cm long, the diagonal measures 17 cm.

a² + b² = c²

15² + b² = 17²

b = 8

The diameter of the cup is 8 cm.

radius = 8 cm/2 = 4 cm

V = πr²h

V = π(4 cm)²(15 cm) = 240π cm³ (exact)

V = 754 cm³ (approximate)

The construction that is performed based on the information given will be D. construct a right angle.

It should be noted that construction simply means the accurate drawing of shapes, angles, and the line in geometry.

In this case, the construction that is performed based on the information given will be to construct a right angle.

It should be noted that a right angle has an angle of 90°.

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Answer:

17) 3

18) -5/4

19) 4/2 or 2

20) 1

21) 2/4 or 1/2

22) 4/7

23) -2/2 or -1

24) -1/3

Step-by-step explanation:

the easiest thing to do is go by rise over run and count the number of units, hope this helped!

Answer:

See below.

Step-by-step explanation:

The $2 charge is independent of the miles driven.  It cost $2 regardless of mileage.  The $0.20.half mile is the dependent variable.  The cost changes as a function of 1/2 miles driven.

Answer:

The file contains the solution to the above question

[tex]\sqrt[3]{125x^{10}y^{13} } +\sqrt[3]{27x^{10}y^{13} }[/tex]=[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} } = 8\sqrt[3]{x^{10}y^{13} }[/tex]

[tex]\sqrt[3]{125x^{10}y^{13} } +\sqrt[3]{27x^{10}y^{13} }[/tex]

Therefore,

125 = 5³

27 = 3³

Hence,

[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} }[/tex]

Hence,

Both cube root are the same now,

Therefore, we have to add them together.

[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} } = 8\sqrt[3]{x^{10}y^{13} }[/tex]

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Step 1. You need x isolated.
[tex]x < 13+7[/tex]

When you move a number from the left to right (and its addition or subtraction, the sign stays (< ≤ > and ≥ is signs).
x<20 or in words, x is less than 20, and cannot be 20.

Answer:

x < 20

Any number less than 20 is a solution

Step-by-step explanation:

x-7 < 13

The first step to solve this inequality is to add 7 to each side

x-7+7 < 13+7

x < 20

Any number less than 20 is a solution

Answer:

12/13

Step-by-step explanation:

     [tex]\sf Cos \ x = \dfrac{adjacent \ side \ to \ \angle x}{hypotenuse}\\\\[/tex]

              [tex]\sf = \dfrac{XY}{ZX}\\\\=\dfrac{36}{39}\\\\=\dfrac{36 \div3}{39 \div 3}\\\\=\dfrac{12}{13}[/tex]

your anwer would be 12/13 love

The perimeter of the quadrilateral illustrated is 30cm.

The information is incomplete. Therefore, an overview will be given. It should be noted ha perimeter simply means the addition of the sides given.

Let's assume that that we've a rectangle with length and width of 10 and 5cm.

The perimeter will be:

= 2(l + w)

= 2(10 + 5)

= 30cm

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∠5 ≅ ∠8 (vertically opposite angles)

Hence, ∠1 ≅ ∠8 by the transitive property.

When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.

Therefore, line e and f are parallel lines cut by the the transversal g.

∠1 ≅ ∠4(vertically opposite angles)

Hence,

∠4 ≅ ∠8(corresponding angles)

Since, ∠1 ≅ ∠4

Then, by substitution,

∠1 ≅ ∠8 (transitive property)

∠5 ≅ ∠8 (vertically opposite angles)

Therefore, ∠1 ≅ ∠8 by the transitive property.

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Using proportions, it is found that their bill before adding the tip was of $27.48.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

They paid a 20.2% tip, hence 120.2% = 1.202 of the price x is equals to $33.03, hence the bill before the tip is found as follows:

1.202x = 33.03

x = 33.03/1.202

x = $27.48.

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The reasons for the statement about the angles include:

3. Definition of linear pair.

4. Definition of supplementary angles.

5. Substitution.

6. Subtraction property of equality.

7. Definition of congruence.

The angles are supplementary because the angles 1 and 2, 2 and 3 form a linear pair and thus because of the definition of linear pair, they are supplementary angles.

The sum of angles of 1 and 2, 2 and 3 is equal to 180 because these pair of angles are supplementary angles. Supplementary angles are those angles whose sum is 180 degrees.

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A $2.00 base fare charge, and per-mile, and per-minute rates related as follows; 3•x + 7•y = 6.5 and 7•x + 14•y = 14, give the distance traveled in the third ride as 4.5 miles

The base fare = $2.00

Let x represent the per-mile rate, and let y represent the per-minute rate, we have;

The cost of Ryan's first taxi ride = $8.50

Distance traveled in the first ride = 3.0 miles

Time taken during the first ride = 7 minutes

Therefore;

2 + 3•x + 7•y = 8.5

Which gives;

3•x + 7•y = 8.5 - 2 = 6.5

Distance traveled in the second ride = 7.0 miles

Duration of the second ride = 14 minutes

The second ride cost = $16.00

Therefore;

2 + 7•x + 14•y = 16

Which gives;

7•x + 14•y = 16 - 2 = 14

Solving the above simultaneous equations by multiplying equation (1) by 2 then subtracting the result from equation (2) gives;

(7•x + 14•y) - 2 × (3•x + 7•y) = 14 - 2×6.5 = 1

x = 1

3•x + 7•y = 6.5

7•y = 6.5 - 3•x

7•y = 6.5 - 3×1 = 3.5

y = 3.5/7 = 1/2 = 0.5

Duration of the third taxi ride = 10 minutes

Cost of the third ride = $13.50

Therefore;

2 + 1×a + 10×y = $13.50

Where a is the distance traveled during the third ride, we have;

2 + 1×a + 10×0.5 = $13.50

2 + a + 5 = 13.5

a = 13.5 - 2 - 7 = 4.5

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The profit he would make in one week is  $30.

Profit is the total revenue less total cost.

Total revenue = price of one hot dog x number of hotdogs sold

$10.25 x 100 = $1025

Total cost = 950 +( 0.45 x 100)

950 + 45 = 995

Profit = 1025 - 995 = $30

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