Use the definition of inverses to determine whether f and g are inverses.

Answer:

the answer is y=mx+c

Step-by-step explanation:

where the answer is the coefficient of the gradient which is x

Answer:

If Tonia eats 1/8 of the cake, then the fraction of the cake left is:

1 - 1/8 = 7/8

If Trinny eats 1/6 of the cake, then the fraction of the cake left is:

1 - 1/6 = 5/6

Since Tonia and Trinny have identical cakes, the amount of cake left is the same for both of them. Therefore, the amount of cake left is:

(7/8 + 5/6) / 2 = 41/48

So there is 41/48 of the cake left.

Answer:

i believe by creating radii of equal lengths.

Step-by-step explanation:

it gives a path to create an angle congruent to angle APB. The angle APB would have the same radii (BP and AP) and the same width as the congruent angle that would be created.

Wish you good luck.

The ratio of the amount charged in Mathematics to Consumer Studies is 4:5.

To find the ratio of the amount charged in Mathematics to Consumer Studies, we need to divide the amount charged in Mathematics by the amount charged in Consumer Studies.

The amount charged in Mathematics is R280 per month, while the amount charged in Consumer Studies is R350 per month.

Therefore, the ratio of the amount charged in Mathematics to Consumer Studies can be calculated as:

280 / 350

To simplify this ratio, we can divide both the numerator and denominator by their greatest common divisor, which in this case is 70.

Dividing 280 by 70 gives us 4, and dividing 350 by 70 gives us 5.

So, the simplified ratio of the amount charged in Mathematics to Consumer Studies is:

4/5.

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The exact circumferences of the inscribed and circumscribed circles for the given polygons are 8π cm and 15π cm, respectively.

To find the exact circumference of a circle inscribed or circumscribed by a polygon, we can use the Pythagorean theorem to determine the diameter of the circle.

In the case of an inscribed polygon, the diameter of the circle is equal to the diagonal of the polygon. Let's consider the polygon with a diagonal of 8 cm. If we draw a line connecting two non-adjacent vertices of the polygon, we get a diagonal that represents the diameter of the inscribed circle.

Using the Pythagorean theorem, we can find the length of this diagonal. Let's assume the sides of the polygon are a and b. Then the diagonal can be found using the equation: diagonal^2 = a^2 + b^2. Substituting the given values, we have 8^2 = a^2 + b^2. Solving this equation, we find that a^2 + b^2 = 64.

For the circumscribed polygon with a diagonal of 15 cm, the diameter of the circle is equal to the longest side of the polygon. Let's assume the longest side of the polygon is c. Therefore, the diameter of the circumscribed circle is 15 cm.

Once we have determined the diameter of the circle, we can calculate its circumference using the formula C = πd, where C is the circumference and d is the diameter.

For the inscribed circle, the circumference would be C = π(8) = 8π cm.

For the circumscribed circle, the circumference would be C = π(15) = 15π cm.

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Answer:

Relative frequency of selecting a 2 = 8/50 = 0.16 = 16%

Step-by-step explanation:

You are selecting a random number between 1 and 5, and you perform this task 50 times.

Out of these 50 times, the outcome "2" appears 8 times.

Therefore the relative frequency of selecting the number 2 is:

f(2) = 8/50 = 0.16 which is 16%

Answer:

Step-by-step explanation:

x=0.5, y=12.

x=3, y=2.

x=4, y=1.5.

x=6, y=1.

Answer:

30

Step-by-step explanation:

22/33=20/x

cross multiply

22x=33x20

22x=660

x=660/22

x=30

Answer:

a. Y(t) = At³ + Be^t + Ct² + Dt + E

b. Y(t) = At + B + Ce^t + Dsin(t) + Ecos(t)

c. Y(t) = Aet + Bte^t + Csin(t) + Dcos(t)

d. Y(t) = At³ + Bt² + Ct + D + Ecos(2t) + Fsin(2t)

e. Y(t) = At² + Bt + C + Dsin(t) + Ecos(t) + Fsin(t) + Gcos(t)

f. Y(t) = Aet + Bte^-t + Ccos(t) + Dsin(t) + E + Ft + G

The value of y in the figure is

35.134 degrees

The value of y is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The figure shows a right angle triangle of

opposite = 19

adjacent = 27

The angle is calculated using tan, TOA let the angle be y

tan y= Opposite / Adjacent

tan y = 19 / 27

y = arc tan (19/27)

y = 35.134 degrees

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Answer:

  -3

Step-by-step explanation:

You want the multiplier of the second equation that would result in eliminating the x-terms when the first equation is multiplied by 7 and added to the multiplied second equation.

The desired multiplier will have the effect of making the coefficient of x be zero when the multiplications and addition are carried out. If k is that multiplier, the resulting x-term will be ...

 7(-3x) +k(-7x) = 0

  -21x -7kx = 0 . . . . . . simplify

  3 +k = 0 . . . . . . . . . divide by -7x

  k = -3 . . . . . . . . . . subtract 3

The multiplier of the second equation should be -3.

__

Additional comments

Carrying out the suggested multiplication and addition, we have ...

  7(-3x -7y) -3(-7x +10y) = 7(-56) -3(1)

  -49y -30y = -395

  y = -395/-79 = 5

The solution is (x, y) = (7, 5).

In general, the multipliers will be the reverse of the coefficients of the variable, with one of them negated. Here the coefficients of x are {-3, -7}. When these are reversed, you have {-7, -3}. When the first is negated, the multipliers of the two equations are {7, -3}. That is, the second equation should be multiplied by -3, as we found above.

Note that if you subtract the multiplied equations instead of adding, you can use the reversed coefficients without negating one of them. The choice of where the minus sign appears (multiplication or subtraction) will depend on your comfort level with minus signs.

The number of minus signs in this system can be reduced by multiplying the first equation by -1 to get 3x +7y = 56.

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The total volume of the dill spears is approximately 1013 cm³.

To find the total volume of the dill spears, we can use the formula for the volume of a cylinder, which is given by V = πr²h,

where V is the volume, r is the radius of the base, and h is the height of the cylinder.

First, let's find the radius of the base.

Since the area of the base is given as 45 cm², we can use the formula for the area of a circle,

A = πr², to solve for the radius.

Rearranging the formula, we have r = √(A/π).

Given that the area of the base is 45 cm², we can substitute this value into the formula to find the radius:

r = √(45/π) ≈ 3 cm (rounded to the nearest centimeter)

Now that we have the radius and the height of the jar, we can calculate the volume of the jar using the formula V = πr²h:

V = π(3²)(13) ≈ 1173 cm³ (rounded to the nearest cubic centimeter)

However, we need to subtract the volume of the pickle juice that was drained from the jar.

We are given that the amount of pickle juice is 160 cm³, so the total volume of the dill spears is:

Total volume = Volume of jar - Volume of pickle juice = 1173 cm³ - 160 cm³ = 1013 cm³

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The interval for the graphed function that has a local minimum of 0 is [-2, 0].

To determine the interval for the graphed function that has a local minimum of 0, we need to examine the behavior of the graph around the x-values where it crosses the x-axis.

We know that the graph crosses the x-axis at -2.5, 0, and 3. Since the local minimum occurs at 0, we need to find the interval where the graph is decreasing to the left of 0 and increasing to the right of 0.

From the given information, we can determine the following:

The graph is decreasing between -2.5 and 0 because it crosses the x-axis at -2.5 and 0, and the minimum value is at (-1.56, -6).

The graph is increasing between 0 and 3 because it crosses the x-axis at 3, and the maximum value is at (1.2, 2.9).

The correct option is [–2, 0].

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Question

On a coordinate plane, a curved line with minimum values of (negative 1.56, negative 6) and (3, 0), and a maximum value of (1.2, 2.9), crosses the x-axis at (negative 2.5, 0), (0, 0), and (3, 0), and crosses the y-axis at (0, 0). Which interval for the graphed function has a local minimum of 0? [–3, –2] [–2, 0] [1, 2] [2, 4]

The coterminal of 4π/3 angle measure are 10π/3 and -2π/3

We add or subtract integer multiples of 2π.

So, 4π/3 + 2π = 10π/3 is one coterminal angle, and

4π/3 - 2π = -2π/3 is another coterminal angle.

To convert 125.67° to degree, minute, and second measure:

125.67° = 125° + 0.67°

Since there are 60 minutes in 1 degree, we can multiply 0.67 by 60 to get the minutes:

0.67° × 60 = 40.2'

Since there are 60 seconds in 1 minute, we can multiply 0.2 by 60 to get the seconds:

0.2' × 60 = 12"

So, 125.67° is equivalent to 125° 40.2' 12".

To find the degree measure equivalent to 10π/13 rounded to the nearest hundredth of a degree, we can divide 10π/13 by π and then multiply by 180° to convert from radians to degrees:

(10π/13) / π * 180° ≈ 138.46° (rounded to the nearest hundredth).

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a) The factored expression for h(t) is -16t(t - 10), obtained by factoring out a common factor of -16 and a common factor of t from the original expression -16t^2 + 160t.

b) Both the original expression -16t^2 + 160t and the factored expression -16t(t - 10) yield the same result of 144 when evaluated at t = 1, confirming the correctness of the factoring.

a) To factor out a common factor with a negative coefficient from the expression h(t) = [tex]-16t^2 + 160t[/tex], we can rewrite it as:

h(t) = [tex]-16(t^2 - 10t)[/tex]

Now, let's focus on factoring the quadratic expression inside the parentheses. We can factor out a common factor of t:

h(t) = -16t(t - 10)

Therefore, the factored expression for h(t) is -16t(t - 10).

b) To check the factoring by evaluating both expressions for h(t) at t = 1, we substitute t = 1 into the original expression and the factored expression and compare the results.

Using the original expression:

h(1) = [tex]-16(1)^2 + 160(1)[/tex]

h(1) = -16 + 160

h(1) = 144

Using the factored expression:

h(1) = -16(1)(1 - 10)

h(1) = -16(1)(-9)

h(1) = 144

Both expressions yield the same result of 144 when evaluated at t = 1. Therefore, the factoring is correct.

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Answer:

C. 335

Step-by-step explanation:

We will need a system of equations to determine how many senior citizen tickets were sold, where

First equation:

The sum of the revenues earned from the adult and senior citizen tickets equals $8579.00:

(price of adult tickets * quantity) + (price of senior citizen tickets * quantity) = total revenue earned

Since adult tickets cost $22/adult, senior citizen tickets cost $13/senior citizen, and the total revenue earned is $8579.00, our first equation is given by:

22A + 13S = 8579

Second Equation:

The sum of the quantities of adult and senior citizen tickets equals the total number of ticket sold:

quantity of adult tickets + quantity of senior citizen tickets = total quantity of tickets sold

Since the theater sold 527 tickets in total, our second equation is given by:

A + S = 527

Method to Solve:  Elimination:

We can solve for S by first eliminating.  To eliminate A, we'll first need to multiply the second equation by -22:

Multiplying -22 by A + S = 527

-22(A + S = 527)

-22A - 22S = -11594

Now we can add this equation to the first equation to find S, the number of senior citizen tickets:

Adding 22A + 13S = 8579 to -22A - 22S = -11594:

    22A + 13S = 8579

+

   -22A - 22S = -11594

----------------------------------------------------------------------------------------------------------

(22A - 22A) + (13S - 22S) = (8579 - 11594)

(-9S = -3015) / -9

S = 335

Thus, 335 senior citizen tickets (answer C.)

Optional:  Find A (the number of adult tickets sold) to check the validity of our answers:

We can find A by plugging 335 for S in any of the two equations in our system.  Let's use the second one:

Plugging in 335 for S in A + S = 527:

(A + 335 = 527) - 335

A = 192

Thus, 192 adult tickets were sold.

Checking the validity of our answers:

Now we can check that our two answers for S and A are correct by plugging in 335 for S and 192 for A in both of the equations in our system and seeing if we get the same answer on both sides:

Plugging in 335 for S and 192 for A in 22A + 13S = 8579:

22(192) + 13(335) = 8579

4224 + 4355 = 8579

8579 = 8579

Plugging in 335 for S and 192 for A in A + S = 527:

192 + 335 = 527

527 = 527

Thus, our answers for S and A are correct.

What is needed to be congruent to show that ABC=AXYZ is AC ≅ XZ. option D

Given that in ΔABC and ΔXYZ, ∠X ≅ ∠A and ∠Z ≅ ∠C.

We are to select the correct condition that we will need to show that the triangles ABC and XYZ are congruent to each other by ASA rule..

ASA Congruence Theorem: Two triangles are said to be congruent if two angles and the side lying between them of one triangle are congruent to the corresponding two angles and the side between them of the second triangle.

In ΔABC, side between ∠A and ∠C is AC,

in ΔXYZ, side between ∠X and ∠Z is XZ.

Therefore, for the triangles to be congruent by ASA rule, we must have AC ≅ XZ.

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To find the value of x, we can set the two angle measures equal to each other and solve for x.

Given:

mZA = (4x - 2)°

mZB = (6x - 20)°

Setting them equal to each other:

4x - 2 = 6x - 20

Now, we can solve for x:

4x - 6x = -20 + 2

-2x = -18

Dividing both sides by -2:

x = -18 / -2

x = 9

Therefore, the value of x is 9.

Answer:

The answer is 9.

Step-by-step explanation:

We need to use the fact that the sum of the angles in a triangle is 180 degrees. Let A, B, and C be the three angles in the triangle. Then we have:

mZA + mZB + mZC = 180°

Substituting the given values, we get:

(4x - 2)° + (6x - 20)° + mZC = 180°

Simplifying the left side, we get:

10x - 22 + mZC = 180°

Next, we use the fact that angles opposite congruent sides of a triangle are congruent. Since we know that segment AC and segment BC are congruent, we have:

mZA = mZB

Substituting the given values and simplifying, we get

4x - 2 = 6x - 20

Solving for x, we get:

x = 9

Therefore, the value of x is 9.

The square root of 184 is approximately 13.5647. It is a non-repeating, non-terminating decimal.

The square root is obtained by finding the number that, when multiplied by itself, equals 184. In this case, 13.5647 multiplied by itself is approximately equal to 184. To explain the answer further, the square root is a mathematical operation that determines the value which, when multiplied by itself, gives the original number.

In the case of 184, the square root is an irrational number, meaning it cannot be expressed as a fraction or a terminating decimal. The approximate value of 13.5647 is derived using numerical methods or a calculator. This value represents the principal square root of 184, and it is positive since the square of a negative number would yield a positive result.

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Answer:

The square root of 184 is expressed as √184 in the radical form and as (184)½ or (184)0.5 in the exponent form. The square root of 184 rounded up to 5 decimal places is 13.56466. It is the positive solution of the equation x2 = 184. We can express the square root of 184 in its lowest radical form as 2 √46.

Square Root of 184: 13.564659966250536

Square Root of 184 in exponential form: (184)½ or (184)0.5

Square Root of 184 in radical form: √184 or 2 √46

Answer:

Step-by-step explanation:

To determine if the point (4,1) is a solution for the system of equations, we need to substitute the values of x and y from the point into both equations and check if the equations hold true.

For the first equation, y = -x + 5, we substitute x = 4 and y = 1:

1 = -(4) + 5

1 = -4 + 5

1 = 1

The equation holds true for the first equation.

For the second equation, y = 2x - 7, we substitute x = 4 and y = 1:

1 = 2(4) - 7

1 = 8 - 7

1 = 1

The equation also holds true for the second equation.

Since the point (4,1) satisfies both equations, it is indeed a solution to the system of equations.

When 2 items are selected without replacement from a population of 6 items, there are 15 possible samples that can be formed. Option A.

To determine the number of possible samples when 2 items are selected at random without replacement from a population of 6 items, we can use the concept of combinations.

The number of combinations of selecting k items from a set of n items is given by the formula C(n, k) = n! / (k! * (n-k)!), where n! represents the factorial of n.

In this case, we have a population of 6 items and we want to select 2 items. Therefore, the number of possible samples can be calculated as:

C(6, 2) = 6! / (2! * (6-2)!) = 6! / (2! * 4!) = (6 * 5 * 4!) / (2! * 4!) = (6 * 5) / (2 * 1) = 15. Option A is correct.

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The mean of the distribution used in this problem is 3.5.The answer is B. 3.5.

To find the mean of the distribution used in this problem, we need to calculate the expected number of troubles that can be repaired on the same day out of the first five reported. The likelihood of a trouble being repaired on the same day is given as 0.70.

The expected number of troubles repaired on the same day can be calculated by multiplying the probability of each event by the number of trials. In this case, we have five trials (the first five troubles reported) and a probability of 0.70 for each trial.

Expected number of troubles repaired on the same day = Probability of repair on the same day * Number of trials

= 0.70 * 5

= 3.5

This means that, on average, out of the first five troubles reported, we can expect 3.5 of them to be repaired on the same day based on the past data and the given likelihood. So, the correct answer is B. 3.5.

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Answer:

Step-by-step explanation:

To find the total revenue in each market, we can calculate the product of the sale volumes and sale prices per unit using matrices.

Let's represent the sale volumes as a matrix V and the sale prices per unit as a matrix P:

V = [6000 9000 1300]

[12000 6000 17000]

P = [3.50]

[2.75]

[1.50]

To calculate the total revenue in each market, we need to perform matrix multiplication between V and P, considering the appropriate dimensions. The resulting matrix will give us the total revenue for each product in each market.

Total revenue = V * P

Calculating the matrix multiplication:

[6000 9000 1300] [3.50] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]

[12000 6000 17000] [2.75] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]

Performing the calculation:

[60003.50 + 90002.75 + 13001.50] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]

[120003.50 + 60002.75 + 170001.50] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]

Simplifying the calculation:

[21000 + 24750 + 1950] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]

[42000 + 16500 + 25500] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]

[47650] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]

[84000] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]

Therefore, the total revenue in Market I is GHS 47,650 and the total revenue in Market II is GHS 84,000.

Step-by-step explanation:

x = width

Raul    x   then    6x   then  finally   3x

Jen     x   then 5 x

5x   versus 3x

5x/3x = 1  2/3 wider

Answer:

25

Step-by-step explanation:

5+5+5+5+5=25

Answer:25

Step-by-step explanation:

Vinay buys "two thousand seven" fruits.

To find the number of fruits that Vinay buys, we need to determine the place value of 2 in the number 37,523 and add 7 to it.

In the number 37,523, the digit 2 is in the thousands place.

The place value of 2 in the thousands place is 2,000.

Adding 7 to the place value of 2, we get:

2,000 + 7 = 2,007.

Therefore, Vinay buys 2,007 fruits.

In number names, we can write 2,007 as "two thousand seven."

So, Vinay buys "two thousand seven" fruits.

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Answer:

The overall average nickel content of the rock samples is approximately 7.97%.

Step-by-step explanation:

To find the overall average nickel content of the rock samples, we need to take into account the number of samples from each location. Since we know the average nickel content of each set of samples, we can use a weighted average formula:

overall average nickel content = (total nickel content from first location + total nickel content from second location) / (total weight of samples from both locations)

To calculate the total nickel content from each location, we need to multiply the average nickel content by the number of samples:

total nickel content from first location = 8.43% x 1 sample = 8.43%

total nickel content from second location = 7.81% x 6 samples = 46.86%

To calculate the total weight of the samples from both locations, we need to add up the number of samples:

total weight of samples from both locations = 1 + 6 = 7

Now we can substitute these values into the formula and calculate the overall average nickel content:

overall average nickel content = (8.43% + 46.86%) / 7 ≈ 7.97%

Therefore, the overall average nickel content of the rock samples is approximately 7.97%.