Identify the transformation that carries the figure onto itself.

A) reflect across the line y = 7 and rotate 270° clockwise about (−7, 8)

B) reflect across the line x = 7 and rotate 270° clockwise about (−7, 8)

C) reflect across the line y = −7 and rotate 540° clockwise about (−7, 8)

D) reflect across the line x = −7 and rotate 540° clockwise about (−7, 8) '

Answer:  D. 7

Step-by-step explanation:

The value of the composite function f(g(x)) is 2(x-8)^2

Composite functions are functions in another function. Given the following functions

f(x)=2x^2 and

g(x)=x-8

Determine f(g(x))

f(g(x)) = f(x-8)

f(x-8) = 2(x-8)^2

f(g(x)) = 2(x-8)^2

Hence the value of the composite function f(g(x)) is 2(x-8)^2

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The number of days that this solution will probably last would be = 8 days.

To calculate the number of days the solution will last the following is taken into consideration.

The parameters given which are not in ml should be converted to ml as follows;

2 Oz of Lidocaine to ml = 2×29.6=59.2ml

½tsp of banana flavouring;

= 1/2×4.92

= 2.5ml

Therefore the total volume of the solution = 100+59.2+2.5 = 161.7ml

But 2×10 = 1 day

20ml = 1 day

161.7ml = X

Make X the subject of formula;

X = 161.7/20

= 8.1

= 8 days.

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To be able to simplify the given expression, let's recall some of the trigonometric identities.

1. sin²θ + cos²θ = 1

2. 1 + tan²θ = sec²θ

From those identities above, we can replace the numerator and denominator in the given expression with their equivalent value. Thus, the expression becomes:

Now, sec²θ is also just equivalent to 1/cos²θ. So, we can rewrite the expression as:

Then, applying the rules of dividing fractions, the expression becomes:

Therefore, the equivalent expression is cos²θ. (Option 1)

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The number of square meters that the space that Araceli rents is, is 30. 66 square meters.

The space that Araceli rents has a rectangular space so to find the area of the rectangular space that Araceli rents, we need to multiply the length by the width.

The given width is 4. 2 meters and the length is 7. 3 meters.

The area of the space in square meters is therefore :

Area = Length × Width

Area = 7. 3 meters × 4. 2 meters

Area = 30. 66 square meters

In conclusion, the space that Araceli rents has an area of 30. 66 square meters.

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The area of the segment is 9( π-2) units²

The area of a figure is the number of unit squares that cover the surface of a closed figure.

A segment is the area occupied by a chord and an arc. A segment can be a major segment or minor segment.

Area of segment = area of sector - area of triangle

area of sector = 90/360 × πr²

= 1/4 × π × 36

= 9π

area of triangle = 1/2bh

= 1/2 × 6²

= 18

area of segment = 9π -18

= 9( π -2) units²

therefore the area of the segment is 9(π-2) units²

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The degree of the polynomial is 14

The polynomial is given as:

y^2+7x^14-10x^2

Here, we assume that the variable of the polynomial is x

The highest power of x in the polynomial y^2+7x^14-10x^2 is 14

Hence, the degree of the polynomial is 14

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Answer:

-2 would be right next to -3 because its negative and -1 would be right next to -2, 2 would be two points away from 0 bc its a whole number

The domain, range, x-intercept, or y-intercept of g(x) = f(x + 4) + 8. The features of g depend on the corresponding features of f.

Given the function g(x) = f(x + 4) + 8, let's examine its features:

Domain:

The domain of the function g will be the same as the domain of the function f, which depends on the restrictions or constraints of f.  However, it is important to note that shifting the input by 4 units (x + 4) does not inherently change the domain unless there are specific restrictions imposed by f.

Range:

Similar to the domain, the range of the function g will depend on the range of the function f.

x-intercept:

The x-intercept of a function is the point where the graph intersects the x-axis, meaning the y-coordinate is zero (y = 0). To find the x-intercept of g(x), we set g(x) = 0 and solve for x.

0 = f(x + 4) + 8

By subtracting 8 from both sides:

-8 = f(x + 4)

Since the exact value of x that makes f(x + 4) equal to -8. The x-intercept will depend on the behavior of f.

y-intercept:

The y-intercept of a function is the point where the graph intersects the y-axis, meaning the x-coordinate is zero (x = 0). To find the y-intercept of g(x), we substitute x = 0 into the function:

g(0) = f(0 + 4) + 8

g(0) = f(4) + 8

Again, the specific value of f(4) will depend on the behavior of the function f.

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The perimeter of the rectangle is 4h + 6

An algebraic expression can be defined as an expression that is composed of terms, variables, coefficients, constants and factors.

These expressions are also made up of arithmetic operations, such as;

The formula for calculating the perimeter of a rectangle is expressed as;

Perimeter = 2( l + h)

Where;

l = 3 + h

Substitute the values

Perimeter = 2( 3 + h+ h)

expand the bracket

Perimeter = 2(3 + 2h)

Perimeter = 4h + 6

Hence, the expression is 4h + 6

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Answer: Yes they are in the same proportion

The ratio 2:6 reduces fully to 1:3 after dividing both parts by 2

2/2 = 1

6/2 = 3

It's similar to saying 2/6 = 1/3

Also, the ratio 7:21 reduces to 1:3 because we divide both parts by 7

7/7 = 1

21/7 = 3

Therefore, 2:6 and 7:21 are effectively the same ratio.

Answer:

Yes, 2:6 and 7:21 are proportional

Step-by-step explanation:

Both 2:6 and 7:21 equal to 1:3

Given :

Two similar triangles ΔABC and ΔSTU .

To Find :

The value of x.

Solution :

Since, ΔABC and ΔSTU are similar, so ratio of their sides are equal.

\(\dfrac{AB}{AC} = \dfrac{SU}{ST}\\\\\dfrac{x}{21}=\dfrac{13}{5}\\\\x = \dfrac{21\times 13}{5}\\\\x = 54.6\)

Therefore, value of x is 54.6 .

Answer:

x ≤ 10

Step-by-step explanation:

The current amount of the sale is 96

The sale is 120

It was decreased by 20%

20/100 × 120

= 0.2 × 120

= 24

The amount of the current sale is

120-24

= 96

Hence the amount of the current sale which is calculated by subtracting 24 from 120 is 96

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Andy would pay $23.94 more in finance charges compared to Brett, given their respective APRs, average daily balances, and monthly percentage rates.

To calculate the monthly percentage rate (MPR) from the given annual percentage rate (APR), we divide the APR by 12.

For Brett:

APR = 12.6%

MPR = 12.6% / 12 = 1.05%

For Andy:

APR = 16.2%

MPR = 16.2% / 12 = 1.35%

Next, we can calculate the finance charge for each individual using the formula: finance charge = average daily balance * MPR.

For Brett:

Finance charge = $7,980 * 1.05% = $83.79

For Andy:

Finance charge = $7,980 * 1.35% = $107.73

To find the difference in the finance charges between Andy and Brett, we subtract Brett's finance charge from Andy's finance charge:

Difference = $107.73 - $83.79 = $23.94

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Answer:

A. the angular speed is 3771.4 rad/min

b. 5921 rpms

Step-by-step explanation: I just got this same question right on a test.

Answer:

B is correct because there cannot be negative people in a cafeteria.

Step-by-step explanation:

We can use the formula for the volume of a cylinder: V = Ah, where A is the base area and h is the height.

Substituting the given values, we have:

720 cm³ = 36 cm² x h

Simplifying, we can divide both sides by 36 cm²:

20 cm = h

Therefore, the height is 20 cm.

A: There are 33,216 possible passwords. The probability of having a 5 character password ending in 0 is 2.7%. The probability of having an all digit password is 0.16%.

The total number of possible passwords can be calculated by multiplying the number of options for each character. There are 26 uppercase letters and 10 digits, so for a 4 character password there are 26 x 26 x 10 x 10 = 67,600 possible combinations. For a 5 character password there are 26 x 26 x 10 x 10 x 10 = 336,960 combinations. Therefore, there are 33,216 possible passwords if the password must be 4-5 characters long and contain at least one digit. The probability of having a password which is 5 characters long and ends in a zero is 2.7%. This is calculated by dividing the number of possible passwords that end in 0 (1,680) by the total number of possible passwords (33,216). The probability of having an all digit password is 0.16%. This is calculated by dividing the number of possible all digit passwords (5,120) by the total number of possible passwords (33,216).

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Answer:

a. the ratio is 1:2

b. its equivalent to the fraction 1/2

c. there would be 10 triangles

d. therw would be 45 triangles since the number of parallelograms is double the number of triangles

Answer:

See explanation.

Step-by-step explanation:

a) Simply divide the number of triangles by the number of paralellograms.

3/6

b) 3/6 is equal to 1/2.

1/2

c) Multiply 2 by 10 to get 20. Now, you also have to multiply 1 by 10.

10/20

d) There are three shapes for every instance of the ratio. Divide 90 by 3.

30

Hope this helped!

To determine how the surface area of a rectangular prism changes when all dimensions are quadrupled, we need to compare the original surface area to the new surface area.

The original surface area of the rectangular prism is given by:

SA_original = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the prism, respectively.

In this case, the dimensions of the original box are:

Length (l) = 3 ft

Width (w) = 6 ft

Height (h) = 5 ft

Substituting these values into the formula, we have:

SA_original = 2(3)(6) + 2(3)(5) + 2(6)(5)

            = 36 + 30 + 60

            = 126 square feet

Now, if we quadruple all the dimensions of the box, the new dimensions would be:

Length (l_new) = 4(3) = 12 ft

Width (w_new) = 4(6) = 24 ft

Height (h_new) = 4(5) = 20 ft

The new surface area of the enlarged box is given by:

SA_new = 2(l_new)(w_new) + 2(l_new)(h_new) + 2(w_new)(h_new)

       = 2(12)(24) + 2(12)(20) + 2(24)(20)

       = 576 + 480 + 960

       = 2016 square feet

Comparing the original surface area (SA_original = 126 sq ft) to the new surface area (SA_new = 2016 sq ft), we can see that SA_new is 16 times greater than SA_original.

Therefore, the correct answer is:

1. The new surface area would be 16 times the original surface area.

Answer:

it is 37.

Step-by-step explanation:

125 - 88 is 37

Answer:

5,000

Step-by-step explanation:

\(\frac{1}{7}*\frac{5}{5-9} \frac{10}{0-9} *\frac{10}{0-9} * \frac{10}{0-9}\)

Answer:

2.Post Office, Library, Park, Town Hall

3.2/6, 3/9, 4/12, 6/18

4. less than 1/2 in.: 1/8, 5/16

equal to 1/2 in.:8/16

more than 1/2 in.:5/8, 9/16, 15/16

Step-by-step explanation: Comment if you want the explanation.

Therefore, Kallie will need to use a total of 6 teaspoons of water conditioner for all the water in 12 fish tanks.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign, with the expression on the left being equal to the expression on the right. Equations are used to represent various relationships and situations in mathematics and other fields, and are solved to find the values of variables that make the equation true.

Here,

First, we need to determine the total amount of water in all 12 fish tanks. Since each fish tank is filled with 20 quarts of water, the total amount of water in all 12 fish tanks is:

12 fish tanks * 20 quarts per fish tank = 240 quarts of water

To convert quarts to gallons, we divide by 4 (since there are 4 quarts in a gallon):

240 quarts / 4 quarts per gallon = 60 gallons of water

Now, we can use the given conversion factor to determine how many teaspoons of water conditioner are needed for 60 gallons of water. Since for every 10 gallons of water, Kallie uses 1 teaspoon of water conditioner, for 60 gallons of water, she will use:

60 gallons / 10 gallons per teaspoon = 6 teaspoons of water conditioner

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Answer:

The number A(t) of pounds of salt in the tank at time t = \(\frac{3t(100 - t)}{25}\)

Step-by-step explanation:

Given - A large tank is filled to capacity with 400 gallons of pure water. Brine containing 3 pounds of salt per gallon is pumped into the tank at a rate of 4 gal/min. The well-mixed solution is pumped out at a rate of 8 gals/min.

To find - Find the number A(t) of pounds of salt in the tank at time t.

Proof -

Given that,

Capacity of water = 400 gallons

rate in flow = 4 gal/min

rate out flow = 8 gal/min

Concentration in = 3 lbs/gal

Concentration out = (Amount of salt at time t )/ (Solution in tank at time t)

Now,

Let

A(t) = Amount of salt in the tank at time t

Now,

Initially tank has 400 gallons of water, So

A(0) = 0 ................(1)

Now,

Rate of change in the amount of salt = \(\frac{d}{dt} A(t)\)

                                                             = (Rate in flow )( Concentration In) - (Rate out flow )( Concentration out)

                                                             = (4) (3) - (8) (\(\frac{A(t)}{400 - 4t)}\)

                                                             = 12 - \(\frac{2A(t)}{100 - t)}\)

⇒\(\frac{d}{dt} A(t)\) + \(\frac{2A(t)}{100 - t)}\) = 12

Now,

Integrating Factor, I.F = \(e^{\int {\frac{2}{100 - t} } \, dt }\)

                                    = \(e^{-2ln(100 - t)}\)

                                    = (100 - t)⁻²

⇒I.F = (100 - t)⁻²

The solution becomes

A (I.F) = ∫ (I.F)(12) dt + C

⇒A (100 - t)⁻² = ∫12(100 - t)⁻² dt + C

⇒A (100 - t)⁻² = -12(100 - t)⁻¹ (-1) + C

⇒A(t) = \(12(100 - t)+ C(100 - t)^{2}\)

Now,

We have A(0) = 0

⇒C = -12/100

∴ we get

A(t) = 12(100 - t) - \(\frac{12}{100}\) (100 - t)²

     = 12(100 - t) [ 1 - \(\frac{100 - t}{100}\) ]

     = 12(100 - t) (\(\frac{t}{100}\))

     = \(\frac{3t(100 - t)}{25}\)

⇒A(t) = \(\frac{3t(100 - t)}{25}\)

∴ we get

The number A(t) of pounds of salt in the tank at time t = \(\frac{3t(100 - t)}{25}\)