The overnight temperature drops from 11°C to -2°C. B how many degrees has the temperature dropped?

Answer:

PO = 12

Step-by-step explanation:

given a tangent and a secant from an external point to the circle then

the product of the measures of the secant's external part and the entire secant is equal to the square of the measure of the tangent , that is

OP × OQ = NO²

OP × 27 = 18² = 324 ( divide both sides by 27 )

OP = 12

Answer: D. 145°

Step-by-step explanation:

Since it is a parallelogram given by the symbol, then angle B is equal to angle D which is 145°.

Answer:

37.98

Step-by-step explanation:

Taking into account the definition of a system of linear equations, on Sunday 77 adult tickets were sold.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

So, the system of equations to be solved is

a + c= 131

9.60a + 5.20c= 1020

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable c from the first equation:

c= 131 -a

Substituting the expression in the second equation:

9.60a + 5.20×(131 -a)= 1020

Solving:

9.60a + 5.20×131 -5.20a= 1020

9.60a + 681.2 -5.20a= 1020

9.60a -5.20a= 1020 - 681.2

4.4a= 338.8

a= 338.8÷ 4.4

a= 77

In summary, 77 adult tickets were sold that day.

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Answer:

Step-by-step explanation:

Converting between Fraction, Decimal, and Percent:

Fraction to Decimal: Divide the numerator by the denominator. The result is the decimal form.

Example: 1/4 = 1 ÷ 4 = 0.25

Decimal to Fraction: Write the decimal as a fraction by placing the decimal value over the appropriate power of 10.

Example: 0.75 = 75/100 = 3/4

Fraction to Percent: Divide the numerator by the denominator and multiply by 100.

Example: 1/3 = (1 ÷ 3) × 100 = 33.33...%

Percent to Fraction: Write the percent as a fraction with a denominator of 100 and simplify if necessary.

Example: 40% = 40/100 = 2/5

Decimal to Percent: Multiply the decimal by 100 and add the percent symbol (%).

Example: 0.75 = 0.75 × 100 = 75%

Percent to Decimal: Divide the percent by 100.

Example: 40% = 40 ÷ 100 = 0.4

a. The absolute maximum of g is 4.

The absolute minimum of g is -4.

b. The absolute maximum of h is 3.

The absolute minimum of h is -4.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of the polynomial function g shown above, we can logically deduce that its vertical asymptote is at x = 3. Furthermore, the absolute maximum of the polynomial function g is 4 while the absolute minimum of g is -4.

In conclusion, the absolute maximum of the polynomial function h is 3 while the absolute minimum of h is -4.

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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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For a collection of numbers to be considered a sequence, it is essential that they have a law of formation, are ordered in a specific manner, and can be either finite or infinite.

B: They have a law of formation:

A sequence is a set of numbers arranged in a specific order according to a rule or pattern. The numbers in a sequence are not random but follow a specific law of formation.

This law can be a mathematical formula, a recursive relationship, or any other systematic pattern that determines the values of the sequence. Without a well-defined law of formation, a collection of numbers cannot be considered a sequence.

C: They are ordered:

In a sequence, the numbers are arranged in a specific order or sequence. The order of the numbers is crucial and defines the pattern and structure of the sequence.

Each number in the sequence has a unique position or index that determines its place in the sequence. The order of the numbers allows us to identify the next number or predict the pattern of the sequence. Without the concept of order, the numbers would simply be a set of unrelated elements and not a sequence.

A: They may or may not be infinite:

Sequences can be finite or infinite. A finite sequence has a specific number of terms, and once the pattern or rule is established, the sequence ends.

On the other hand, an infinite sequence continues indefinitely, and its terms extend infinitely in one direction or both directions. Whether a sequence is finite or infinite depends on the context and the specific rule or pattern that governs its formation.

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Note: the translated question is:

To have a sequence it is essential that the numbers that form it:

A: be infinite

B: they have a law of formation C: they are ordered

Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.

Answer:

A''(-1, 1), B''(-4, 2), C''(-2, 4)

Step-by-step explanation:

When rotated 180°, the symbol of the coordinames change

i.e., if x = 2 it becomes x = -2 and if y = -4, it becomes y = 4

so the coordinates A(1, -1), B(4, -2), C(2, -4)

change to A''(-1, 1), B''(-4, 2), C''(-2, 4)

El movimiento en línea recta se refiere al desplazamiento de un objeto en una trayectoria rectilínea, es decir, sin cambios de dirección.

En este tipo de movimiento, la velocidad y la aceleración del objeto pueden variar, pero su dirección se mantiene constante a lo largo del recorrido.

El movimiento en línea recta puede ser uniforme o no uniforme. En el caso del movimiento uniforme, la velocidad del objeto es constante, lo que implica que el desplazamiento realizado en intervalos iguales de tiempo es también constante.

Por otro lado, en el movimiento no uniforme, la velocidad cambia a lo largo del tiempo, resultando en diferentes desplazamientos en intervalos de tiempo iguales.

La descripción matemática del movimiento en línea recta se basa en conceptos como la posición, la velocidad y la aceleración. La posición se refiere a la ubicación del objeto en relación a un punto de referencia, la velocidad representa la tasa de cambio de la posición y la aceleración indica la tasa de cambio de la velocidad.

El estudio del movimiento en línea recta es fundamental en la física y tiene aplicaciones en diversas áreas, como la mecánica, la cinemática, la dinámica y la física de partículas.

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Answer:

(90°/360°)π(3^2) = (1/4)(9π) = 9π/4 m²

The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-[tex]1)^2[/tex] + (-[tex]5)^2[/tex]) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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The customer would need to use more than 12.5 megabytes for Plan B to be a better deal. (Option 1) more than 12.5 megabytes).

To determine when Plan B would be a better deal than Plan A, we need to compare the charges for both plans based on the number of megabytes used.

Plan A is represented by the linear function y = 10x, where x represents the total number of megabytes used, and y represents the charge for the plan.

Plan B is represented by the linear function y = 4x + 75, where x represents the total number of megabytes used, and y represents the charge for the plan.

To find the point at which Plan B becomes a better deal, we need to find the x-value where the charge for Plan B is less than the charge for Plan A.

In other words, we need to find the x-value that satisfies the inequality:

4x + 75 < 10x

To solve this inequality, we subtract 4x from both sides:

75 < 6x

Then, we divide both sides by 6:

12.5 < x

Therefore, the customer would need to use more than 12.5 megabytes for Plan B to be a better deal.

This means that option 1) "more than 12.5 megabytes" is the correct answer.

For any value of x greater than 12.5, the charge for Plan B will be less than the charge for Plan A, making it a better deal for the customer.

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The probability of Lashonda winning a prize is 9/11.

To find the probability of Lashonda winning a prize, we can use the odds given. The odds in favor of Lashonda winning a prize are expressed as 9/2.

Odds are typically represented as a ratio of favorable outcomes to unfavorable outcomes.

In this case, the favorable outcomes are Lashonda winning a prize, and the unfavorable outcomes are Lashonda not winning a prize.

The odds in favor of Lashonda winning a prize can be written as 9:2, where 9 represents the favorable outcomes and 2 represents the unfavorable outcomes.

To calculate the probability, we add the favorable and unfavorable outcomes to get the total number of possible outcomes.

In this case, the total number of outcomes is 9 + 2 = 11.

The probability of Lashonda winning a prize can be calculated as the ratio of the favorable outcomes to the total number of outcomes:

Probability = Favorable outcomes / Total outcomes

Probability = 9 / 11.

Therefore, the probability of Lashonda winning a prize is 9/11.

In conclusion, based on the given odds in favor of Lashonda winning a prize being 9/2, the probability of Lashonda winning a prize is 9/11.

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Answer:The present worth of the project for Bronson Building Inc is $6,389,137.

In order to calculate the present worth, follow these steps:

1. The given information is:

Initial cost (first cost) = $18,000,000

Annual revenue = $5,000,000

Annual expenses = $2,000,000

Net annual cash flow = Annual revenue - Annual expenses = $5,000,000 - $2,000,000 = $3,000,000

MARR = 11%

Project duration = 18 years

Sale price at the end of the project = $8,000,000

2. To calculate the present worth, we first need to find the present value of the net annual cash flows using the MARR as the discount rate. Then, we will add the present value of the sale price and subtract the initial cost.

Present value of net annual cash flows (PV_ACF) = Net annual cash flow * [(1 - (1 + MARR)^(-duration)) / MARR]

PV_ACF = $3,000,000 * [(1 - (1 + 0.11)^(-18)) / 0.11] = $3,000,000 * 7.696 = $23,088,000

3. Find the present value of the sale price at the end of the project.

Present value of sale price (PV_SP) = Sale price / (1 + MARR)^duration

PV_SP = $8,000,000 / (1 + 0.11)^18 = $8,000,000 / 6.146 = $1,301,137

4. Calculate the present worth of the project.

Present worth = PV_ACF + PV_SP - Initial cost

Present worth = $23,088,000 + $1,301,137 - $18,000,000 = $6,389,137

Step-by-step explanation:

Answer:

Relative maximum at x=0; Relative minimum at x=8/3

Step-by-step explanation:

To find the relative maximums and the relative minimums, you must first find the first derivative of the function. The first derivative of this function is 6x^2-16x. Simply it and you get 2x(3x-8). X would be equal to 0 and 8/3. Next, make a number line where you put 0 and 8/3 have a value of zero.

        +                           -                                 +      

-------------------0----------------------------8/3-----------------------

Plug in a value of x<0 to get the region left of 0. Say we use -1, we get -2(-3-8), which is positive, meaning that it is increasing there. From 0 to 8/3, if we use 1, we get 2(3-8), which is decreasing. If we use 3, we get 6(9-8), which is increasing. From this, we can see that when x=0, the graph has a relative maximum. When x=8/3, the graph has a relative minimum.

The value of x is 5625 when √x + √y=138 and x-y=1656.

To solve for x using the given equations, we will use the method of substitution. Let's go through the steps:

Start with the equation √x + √y = 138.

We want to express y in terms of x, so solve for y in terms of x by isolating √y:

√y = 138 - √x

Square both sides of the equation to eliminate the square root:

(√y)² = (138 - √x)²

y = (138 - √x)²

Now, substitute the expression for y in the second equation x - y = 1656:

x - (138 - √x)² = 1656

Expand the squared term:

x - (138² - 2 * 138 * √x + (√x)²) = 1656

Simplify the equation further:

x - (19044 - 276 * √x + x) = 1656

Combine like terms and rearrange the equation:

-19044 + 276 * √x = 1656

Move the constant term to the other side:

276 * √x = 20700

Divide both sides of the equation by 276 to solve for √x:

√x = 20700 / 276

√x = 75

Square both sides to solve for x:

x = (√x)²

x = 75²

x = 5625

Therefore, the value of x is 5625.

By substituting this value of x back into the original equations, we can verify that √x + √y = 138 and x - y = 1656 hold true.

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Answer: 2,2

Step-by-step explanation:

trust me

The completed sequence would then be: 2, 4, 7, 9, 16, 19, 29.

To complete the given number sequence, let's analyze the pattern and identify the missing terms.

Looking at the given sequence 2, 4, 7, __, 16, __, 29, __, we can observe the following pattern:

The difference between consecutive terms in the sequence is increasing by 1. In other words, the sequence is formed by adding 2 to the previous term, then adding 3, then adding 4, and so on.

Using this pattern, we can determine the missing terms as follows:

To obtain the third term, we add 2 to the second term:

7 + 2 = 9

To find the fifth term, we add 3 to the fourth term:

16 + 3 = 19

To determine the seventh term, we add 4 to the sixth term:

__ + 4 = 23

Therefore, the missing terms in the sequence are 9, 19, and 23.

By identifying the pattern of increasing differences, we can extend the sequence and fill in the missing terms accordingly.

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Answer:

5) tan A = 0.42

6) Acute angle is less than 90°

7) Right angle is exactly 90°

8) Obtuse angle is greater than 90° but less than 180°

9) Straight angle is exactly 180°

10) Complementary angles add up to 90°

11) Supplementary angles add up to 180°

Step-by-step explanation:

tan A = opposite / adjacent

= 5/12

= 0.42

The value of cos E in the triangle is √2/2

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. Trigonometric ratio is only applied in right triangles.

Some of the trigonometric functions are ;

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

In the triangle taking reference from angle E, 5 is the opposite and 5 is the adjascent and 5√2 is the hypotenuse.

Therefore;

cos E = 5/5√2

cos E = 1/√2

rationalizing the value;

cos E = √2/2

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Answer:

That Platonic solid is a dodecahedron.

B is the correct answer.

1a. Compute NPV by calculating the present value of net cash flows and subtracting the investment amount.

1b. Compute PVI by dividing NPV by the investment amount.

2. Determine IRR by finding the discount rate corresponding to an NPV of zero.

3. Compare NPV, PVI, and IRR to identify the better financial opportunity.

1a. To compute the net present value (NPV) for each project, we need to calculate the present value of the annual net cash flows and subtract the amount to be invested. Using the present value of an annuity of $1 from the table, we can fill in the following values:

Wind Turbines:

Present value of annual net cash flows: $420,000 * 1.736 + $420,000 * 2.487 + $420,000 * 3.170 + $420,000 * 3.791

Less amount to be invested: $1,199,100

Net present value: NPV_Wind_Turbines = Present value of annual net cash flows - Amount to be invested

Biofuel Equipment:

Present value of annual net cash flows: $880,000 * 1.736 + $880,000 * 2.487 + $880,000 * 3.170 + $880,000 * 3.791

Less amount to be invested: $2,278,320

Net present value: NPV_Biofuel_Equipment = Present value of annual net cash flows - Amount to be invested

1b. The present value index (PVI) can be calculated by dividing the NPV by the amount to be invested:

Present Value Index = NPV / Amount to be invested

2. To determine the internal rate of return (IRR) for each project, we need to find the discount rate at which the NPV becomes zero. We can use the present value of an annuity of $1 from the table to calculate the present value factor for an annuity of $1. Then, we can find the discount rate that corresponds to an NPV of zero.

Wind Turbines:

Present value factor for an annuity of $1: Fill in the values from the table

Internal rate of return: IRR_Wind_Turbines = Discount rate corresponding to NPV = 0

Biofuel Equipment:

Present value factor for an annuity of $1: Fill in the values from the table

Internal rate of return: IRR_Biofuel_Equipment = Discount rate corresponding to NPV = 0

3. Based on the calculations of NPV, PVI, and IRR, we can compare the two projects. The project with the higher NPV, PVI, and IRR is considered the better financial opportunity. Both investments meet the minimum return criterion of 10%, but the project with the higher financial indicators is preferred.

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Answer:

m

Step-by-step explanation:

Answer: the answer is -4

Step-by-step explanation: the reason why the answer is -4 becaue all of the option is in correct.

The number line inequality that represents x > -7 is: Option D

In number line inequalities we know that:

A closed circle indicates "greater than or equal to" or "less than or equal to" .

Meanwhile an open circle indicates "greater than" or "less than".

A closed circle pointing to the right indicates  "greater than or equal to" while a closed circle pointing to the left indicates "less than or equal to,"

Similarly:

An open circle pointing to the right indicates "greater than" while An open circle pointing to the left indicates  "less than".

Thus , the correct number line that shows x > -7 is: Option D

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Answer:

x intercept : -1

y intercept : 3

Step-by-step explanation:

We have 3x - y = -3 ---eq(1)

The x intercept is the value of x when y = 0 in eq(1),

⇒ 3x - 0 = -3

⇒ x = -3/3

⇒ x = -1

The y intercept is the value of y when x = 0 in eq(1),

⇒ 3(0) - y = -3

⇒ -y = -3

⇒ y = 3

The equations of the asymptotes of the hyperbola are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.

To find the equations of the asymptotes of the hyperbola defined by the equation:

[tex]-25x^2 + 81y^2 + 100x + 1134y + 1844 = 0[/tex]

We can rewrite the equation in the standard form by isolating the x and y terms:

[tex]-25x^2 + 100x + 81y^2 + 1134y + 1844 = 0[/tex]

Rearranging the terms:

[tex]-25x^2 + 100x + 81y^2 + 1134y = -1844[/tex]

Next, let's complete the square for both the x and y terms:

[tex]-25(x^2 - 4x) + 81(y^2 + 14y) = -1844\\-25(x^2 - 4x + 4 - 4) + 81(y^2 + 14y + 49 - 49) = -1844\\-25((x - 2)^2 - 4) + 81((y + 7)^2 - 49) = -1844[/tex]

Expanding and simplify

[tex]-25(x - 2)^2 + 100 - 81(y + 7)^2 + 3969 = -1844\\-25(x - 2)^2 - 81(y + 7)^2 = -1844 - 100 - 3969\\-25(x - 2)^2 - 81(y + 7)^2 = -4913[/tex]

Dividing both sides by -4913:

[tex](x - 2)^2/(-4913/25) - (y + 7)^2/(-4913/81) = 1[/tex]

Comparing this equation to the standard form of a hyperbola:

[tex](x - h)^2/a^2 - (y - k)^2/b^2 = 1[/tex]

We can determine that the center of the hyperbola is (h, k) = (2, -7). The value of [tex]a^2[/tex] is (-4913/25), and the value of [tex]b^2[/tex] is (-4913/81).

The equations of the asymptotes can be found using the formula:

y - k = ±(b/a)(x - h)

Substituting the values we found:

y + 7 = ±(√(-4913/81) / √(-4913/25))(x - 2)

Simplifying:

y + 7 = ±(√(4913) / √(81)) × √(25/4913) × (x - 2)

y + 7 = ±(√(4913) / 9) × √(25/4913) × (x - 2)

Rationalizing the denominators and simplifying:

y + 7 = ±(5/9) ×(x - 2)

Finally, rearranging the equation to isolate y:

y = ±(5/9)x - 10/9 - 7

Simplifying further:

y = ±(5/9)x - 79/9

In light of this, the equations for the hyperbola's asymptotes are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.

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Answer:

[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]

Step-by-step explanation:

First, rewrite the given equation in the standard form of a hyperbola by completing the square.

Given equation:

[tex]-25x^2+81y^2+100x+1134y+1844=0[/tex]

Arrange the equation so all the terms with variables are on the left side and the constant is on the right side:

[tex]-25x^2+100x+81y^2+1134y=-1844[/tex]

Factor out the coefficient of the x² term and the coefficient of the y² term:

[tex]-25(x^2-4x)+81(y^2+14y)=-1844[/tex]

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:

[tex]-25(x^2-4x+4)+81(y^2+14y+49)=-1844-25(4)+81(49)[/tex]

Factor the two perfect trinomials on the left side and simplify the right side:

[tex]-25(x-2)^2+81(y+7)^2=2025[/tex]

Divide both sides by the number of the right side so the right side equals 1:

[tex]\dfrac{-25(x-2)^2}{2025}+\dfrac{81(y+7)^2}{2025}=\dfrac{2025}{2025}[/tex]

      [tex]\dfrac{-(x-2)^2}{81}+\dfrac{(y+7)^2}{25}=1[/tex]

        [tex]\dfrac{(y+7)^2}{25}-\dfrac{(x-2)^2}{81}=1[/tex]

As the y²-term is positive, the hyperbola is vertical (opening up and down).

The standard equation of a vertical hyperbola is:

[tex]\boxed{\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1}[/tex]

Therefore, comparing this with the rewritten equation:

The formula for the equations of the asymptotes of a vertical hyperbola is:

[tex]\boxed{y=\pm \dfrac{a}{b}(x-h)+k}[/tex]

Substitute the values of h, k, a and b into the formula:

[tex]y=\pm \dfrac{5}{9}(x-2)-7[/tex]

Therefore, the equations for the asymptotes are:

[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]