13. Tonia and Trinny are twins. Their friends give them identical cakes for their birthday. Tonia eats ⅛ of her cake and Trinny eats ⅙ of her cake. How much cake is left? ​

Answer:

52% used.

Step-by-step explanation:

13/25=52/100=52%

The estimated population of the state in the year 2022 is 19,280,700 people.

The given equation represents the population of a certain state as a function of time, where p is the population in thousands of people and t is the number of years since 2010.

The equation is given as p = 80.7t + 18,312.3.

To estimate the population of the state, we substitute the value of t into the equation. For example, if we want to estimate the population in the year 2022 (12 years since 2010), we substitute t = 12 into the equation:

p = 80.7(12) + 18,312.3

= 968.4 + 18,312.3

= 19,280.7.

The estimated population of the state in the year 2022 is 19,280,700 people.

We can estimate the population for any given year by substituting the corresponding value of t into the equation.

It's important to note that the population is given in thousands of people, so we multiply the final result by 1,000 to obtain the population in actual numbers.

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To find the area of a rectangle, we need to know its length and width. Let's solve the problem step by step:

Let's assume that the width of the rectangle is represented by "w" (in feet).

According to the given information, the length of the rectangle is 4 feet longer than its width, which means the length can be represented as "w + 4" (in feet).

The perimeter of a rectangle is calculated by adding up all the sides. In this case, the perimeter is given as 32 feet.

Since a rectangle has two pairs of equal sides (length and width), we can express the perimeter equation as the following:

2(length + width) = perimeter

Substituting the values into the equation, we get:

2(w + (w + 4)) = 32

Simplifying the equation, we have:

2(2w + 4) = 32

4w + 8 = 32

4w = 24

w = 6

Now we know that the width of the rectangle is 6 feet. To find the length, we can substitute this value back into the equation for the length:

Length = w + 4 = 6 + 4 = 10 feet

The width is 6 feet, and the length is 10 feet. Now we can calculate the area of the rectangle:

Area = Length × Width = 10 × 6 = 60 square feet

Answer: The area of the rectangle is 60 square feet.

The values in the expression is as follows:

a = 2

b = 0

c = -1

The expression can be solve using the exponential law. Therefore,

g = 2³ × 3 × 7²

h = 2 × 3 × 7³

Therefore, let's solve the following:

g/h = 2ᵃ × 3ᵇ × 7ⁿ

Therefore,

g = 2³ × 3 × 7² = 2 × 2 × 2 × 3 × 7 × 7

h = 2 × 3 × 7 × 7 × 7

Hence,

g / h =  2 × 2 × 2 × 3 × 7 × 7 / 2 × 3 × 7 × 7 × 7

Hence,

g / h = 2 × 2 / 7

g . h = 2² × 3° × 7⁻¹

Hence,

a = 2

b = 0

c = -1

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Answer:A' = (15, -15), B' = (9, -9), and C' = (15, -9)

Step-by-step explanation:

To dilate triangle ABC with a center of dilation at the origin (0,0) and a scale factor of 3, you need to multiply the coordinates of each vertex by the scale factor.

Let's calculate the coordinates of triangle A'B'C':

For point A:

x-coordinate of A' = scale factor * x-coordinate of A = 3 * 5 = 15

y-coordinate of A' = scale factor * y-coordinate of A = 3 * (-5) = -15

Therefore, A' = (15, -15)

For point B:

x-coordinate of B' = scale factor * x-coordinate of B = 3 * 3 = 9

y-coordinate of B' = scale factor * y-coordinate of B = 3 * (-3) = -9

Therefore, B' = (9, -9)

For point C:

x-coordinate of C' = scale factor * x-coordinate of C = 3 * 5 = 15

y-coordinate of C' = scale factor * y-coordinate of C = 3 * (-3) = -9

Therefore, C' = (15, -9)

Hence, the correct coordinates of triangle A'B'C' are A' = (15, -15), B' = (9, -9), and C' = (15, -9).

Answer:

$4929

Step-by-step explanation:

I assume the cost is proportional to the area.

15 ft × 20 ft = 300 ft²

25 ft × 26 ft = 650 ft²

650/300 = x/$2275

300x = 650 × $2275

x = $4929

Answer: $4929

Answer:

BC = 24 units

Step-by-step explanation:

This is an isosceles triangle which always has:

In this triangle, the legs CA and BA are congruent so CA = BA and the angles C and B are congruent to each other so angle C = angle B.

Thus, we can find x by setting CA and BA equal to each other:

(3x - 15 = x + 33) + 15

(3x = x + 48) - x

(2x = 48) / x

x = 24

Thus, x = 24

Since the length of BC is x and x = 24, BC is 24 units long.

Answer:

A) -1.5

Step-by-step explanation:

We can find the average rate of change of a function over an interval using the formula:

(f(x2) - f(x1)) / (x2 - x1), where

Thus, we can plug in (9, 3) for (x2, f(x2)) and (5, 9) for (x1, f(x1)) to find the average rate of change in f(x) on the interval [5,9].

(3 - 9) / (9 - 5)

(-6) / (4)

-3/2

is -3/2.

If we convert -3/2 into a normal number, we get -1.5

Thus, the average rate of change in f(x) on the interval [5,9] is -1.5

Answer:

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}[/tex]

In this case, we need to find the average rate of change on the interval [5, 9], so a = 5 and b = 9.

From inspection of the given graph:

Substitute the values into the formula:

[tex]\textsf{Average rate of change}=\dfrac{f(9)-f(5)}{9-5}=\dfrac{3-9}{9-5}=\dfrac{-6}{4}=-1.5[/tex]

Therefore, the average rate of change of f(x) over the interval [5, 9] is -1.5.

Answer:

A

Step-by-step explanation:

3x16

+

4x18
+

5x17

Ki Tae used 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides are each 15 meters long, while the remaining four sides are each 6 meters long.

Let's solve the problem step by step. We know that Ki Tae used a total of 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides have a length of 15 meters each.

Let's denote the length of the remaining four sides as "x."

Since the dog pen has six sides, we can set up an equation based on the total length of the fencing:

15 + 15 + x + x + x + x = 54

Simplifying the equation, we have:

30 + 4x = 54

Subtracting 30 from both sides, we get:

4x = 24

Dividing both sides by 4, we find:

x = 6

Therefore, each of the remaining four sides has a length of 6 meters.

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The calculated value of x to the nearest degree is 56

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

The triangle

The value of x can be caluclated using the following cosine rule

So, we have

cos(x) = 5/9

Evaluate the quotient

cos(x) = 0.5556

Take the arc cos of both sides

x = 56

Hence, the value of x to the nearest degree is 56

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By algebra properties, the simplified form of the complex fraction is - (x - 4) / [120 · (x - 1)].

In this problem we find the case of a complex fraction that must be simplified by algebra properties. A simple fraction must be found. First, write the entire expression:

[1 / (3 · x² - 3)] / [5 / (x + 1) - (x + 4) / (x² - 3 · x - 4)]

Second, factor the parts of the fraction:

[1 / [3 · (x - 1) · (x +1)]] / [5 / (x + 1) - (x + 4) / [(x - 4) · (x + 1)]]

[1 / [3 · (x - 1) · (x +1)]] / [[5 · (x - 4) - (x + 4)] / [(x - 4) · (x + 1)]]

Third, eliminate the rational fraction:

[(x - 4) · (x + 1)] / [- 120 · (x - 1) · (x + 1)]

Fourth, eliminate common binomials:

- (x - 4) / [120 · (x - 1)]

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Step-by-step explanation:

Let Peter's present age be "p" and his father's age be "x"

So, p = x-24 ;

5 years from now,

Peter's age will be (x-24) + 5 = x-19

His father's age will be x+5.

It is given that 3(x-19)= x+5.

3x - 57 = x + 5 => 2x = 62.

On solving, his father's present age (x) is 31.

So Peter's present age is (p) is x - 24 = 31 - 24 = 7.

Now going in the reverse oder to check the answer.

Peter's present is 7.

5 years from now, it will be 12.

His father's age is 31.

5 years from now, his age will be 36 (which is 3x12).

Hence , the answer to the given problem is 7

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:x=-28

Step-by-step explanation:

Distribute the 4 on the left side of the equation:

32 - 8x = 256

Move the constant term to the right side of the equation:

-8x = 256 - 32

-8x = 224

Divide both sides of the equation by -8 to isolate x:

x = 224 / -8

x = -28

Yuri is 2 years younger than triple Karina’s age

Answer:

yo

Step-by-step explanation:

i think its d

Answer:

(a) To find the average cost in 2011, substitute 11 for x in the function.

g(11) = -1,736.7 + 1,661.6 ln 11 = $2,247.64

The average cost in 2011 was $2,247.64.

(b) Using the graphing calculator, graph the function in the viewing window

[6, 15] by [1,000, 3,000].

The correct graph is B.

(c) A. The average cost increases at a slower rate as time goes on.

The function for which f(x) is equal to f⁻¹(x) is: C. [tex]f(x) = \frac{x+1}{x-1}[/tex]

In this exercise, you are required to determine the inverse of the function f(x) with an equivalent inverse function f⁻¹(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;

[tex]f(x) = y = \frac{x+6}{x-6} \\\\x=\frac{y+6}{y-6}[/tex]

x(y - 6) = y + 6

y = xy - 6x - 6

f⁻¹(x) = (-6x - 6)/(x - 1) ⇒ Not equal.

Option B.

[tex]f(x) = y = \frac{x+2}{x-2} \\\\x=\frac{y+2}{y-2}[/tex]

x(y - 2) = y + 2

y = xy - 2x - 2

f⁻¹(x) = (-2x - 2)/(x - 1) ⇒ Not equal.

Option C.

[tex]f(x) = y = \frac{x+1}{x-1} \\\\x=\frac{y+1}{y-1}[/tex]

x(y - 1) = y + 1

y - xy = x + 1

f⁻¹(x) = (x + 1)/(x - 1) ⇒ equal.

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The difference table for the sequence (-1, 6, 24, 56, 105, 174, 266) reveals a cubic pattern, where the third differences are constant at 3. Based on this pattern, the next term in the sequence is predicted to be 289.

The difference table for the given sequence (-1, 6, 24, 56, 105, 174, 266):

Term     |   First Difference   |   Second Difference   |   Third Difference

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

-1

6                         7

24                    18                                  11

56                   32                                 14                                   3

105                  49                                17                                   3

174                 69                                 20                                  3

266                92

To construct the difference table, we start by writing down the given sequence. Then, in the first column, we calculate the differences between consecutive terms. In the second column, we calculate the differences between the values in the first difference column. Similarly, in the third column, we calculate the differences between the values in the second difference column.

Analyzing the difference table, we observe that the third differences are constant at 3. This indicates a cubic pattern in the sequence, where the difference between consecutive terms is increasing by a constant amount each time.

To predict the next term, we take the last term of the sequence (266) and add the next difference (23) to it:

Next term = 266 + 23 = 289

Therefore, based on the pattern observed in the difference table, the next term in the sequence is predicted to be 289.

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We can complete the blanks with the following ratios:

(7.5 mi/1) * (1 mi/ 5280 ft) * (400ft/1 yd) * (3 ft/1 ft) =33 flags

Since we do not need a flag at the starting line, then 32 flags will be required in total.

To solve the problem, we would first convert 400 yds to feet and miles.

To convert to feet, we multiply by 3. This gives us: 400 yd * 3 = 1200 feet.

To convert to miles, we would have 0.227 miles.

Now, we divide the entire race distance by the number of miles divisions.

This gives us:

7.5 mi /0.227 mi

= 33 flags

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The function is continuous in the domain x ≥ 3/4

Here we have a root function:

f(x) = ⁴√(4x - 3)

This is an even degree root function, so we have problems when the argument is negative.

Then the allowed values (where the function is defined, and thus, continuous) are:

4x - 3 ≥ 0

4x ≥ 3

x ≥ 3/4

There the function is continuous.

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The required answers of the given questions are answered below.

a), b), c),  d)

A quadrilateral is geometric structure enclosed in 4 sides.

A) Because,

 1) the angle A = Angle D

 2) its has a common side

 3) the angle D = Angle B

 ∵ ΔEAB ≅ EDC

Thus, Both the triangle is congruent by ASA.

B.)

Jane conclusion is also write for AAA

because by angle E is congruent to angle B, implies angle F is congruent to angle C.

So that is why Jane conclude AAA.

C.) George conclusion is also perfect

George thinks the following conditions-

1) the angle A = Angle D

 2) its has a common side

 3) the angle D = Angle B

 ∵ ΔEAB ≅ EDC

Thus, Both the triangle is congruent.

Hence, Both the triangles are congruent by SSS.

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Answer:

all real numbers

Step-by-step explanation:

Try a negative number, a positive number and zero for x.

All of them work.

Answer: all real numbers