The angle of elevation of the top of a flag-pole from a point on level ground is 30 degrees. From another point on the ground 20m nearer the flag-pole, the angle of elevation is 60 degrees. Calculate the height of the flag pole

Answer:

Reflection across x = -5

Answer:

Your answer is x = -24

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Answer:

\( \sqrt{ {20}^{2} + {44}^{2} } = \sqrt{400 + 1936} = \sqrt{2336} = 4 \sqrt{146} = 48.3\)

The length of DG is about 48.3 cm.

Answer:

22.50 per 3 wristbands is the cost

Answer:the 2nd choice

Step-by-step explanation:

If a math expression adds a float to an int, the data type of the result will be a float. This is because when a float and an int are added, the result is a float. This is because a float is a larger and more precise data type than an int. When an int is added to a float, the int is first converted to a float, and then the addition takes place.

This conversion ensures that the result is a float. In general, whenever we perform any arithmetic operation on two different data types, the result will be of the larger or more precise data type. It is important to keep this in mind while performing mathematical operations, as it can impact the accuracy and precision of our calculations.

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Answer:

0.006 L

Step-by-step explanation:

Mass of water = 6kg

Using the relation :

Density = mass / volume

Density of water = 100kg/m³

1000 kg/m³ = 6kg / volume

1000kg/m³ * volume = 6kg

Volume = 6kg / 1000 kg /m³

Volume = 0.006

Answer:

55 x 9091 = 500,005

Step-by-step explanation:

This checks with a calculator

The slope m of the tangent to the curve will be m = -3/a^2.

Calculating the slope of the tangent line to the curve y = 3/x at a point where x = a > 0 is an important mathematical concept. To do this, we will first need to find the derivative of the curve y = 3/x.

Let's start by taking a look at the equation for the slope of a line: m = (y2-y1) / (x2-x1). We'll use this equation to find the slope of the tangent line at the point (a, 3/a).

To do this, we'll need to calculate the derivative of the given equation, which is y' = -3/x^2.

At the point (a, 3/a), the derivative is equal to -3/a^2. Therefore, the slope of the tangent line at the point (a, 3/a) is m = -3/a^2.

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Answer:

376 millimeters

Step-by-step explanation:

you move the decimal once to the left meaning 37.6 is 376 mm

what's the question though

Answer:

i think its a uhh a carrot?? no the answer is 6

Step-by-step explanation:

beetlejuice

Answer:

D

Step-by-step explanation:

When you translate a point down you're just moving 2 units down. When it's reflected across the y or x axis, it'll be like a mirror.

Answer:parallelogram

Step-by-step explanation: If one pair of opposite sides of a quadrilateral are equal and parallel, then the quadrilateral is a parallelogram

The present value of the sequence of annual payments of Rs 25000 each, the first being made at the end of the 5th year and the last being paid at the end of the 12th year, if money is worth 6% is Rs. 158620.39.

1: We can use the formula to calculate the present value of the annuity:

P = A x [1 - (1+i)^-n] / i

Where

P = Present Value

A = Annuity

i = Interest Raten = Number of payments

2: Calculate the present value of each payment using the formula:

P1 = 25000 / (1.06)⁵

P2 = 25000 / (1.06)⁶

P3 = 25000 / (1.06)⁷

P4 = 25000 / (1.06)⁸

P5 = 25000 / (1.06)⁹

P6 = 25000 / (1.06)¹⁰

P7 = 25000 / (1.06)¹¹

P8 = 25000 / (1.06)¹²

3: Substitute the values into the formula to find the present value:

P = P1 + P2 + P3 + P4 + P5 + P6 + P7 + P8

P = (25000 / (1.06)⁵) + (25000 / (1.06)⁶) + (25000 / (1.06)⁷) + (25000 / (1.06)⁸) + (25000 / (1.06)⁹) + (25000 / (1.06)¹⁰) + (25000 / (1.06)¹¹) + (25000 / (1.06)¹²)

P = 158620.39

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Answer:

D

Step-by-step explanation:

The nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 8 and d = - 3 , then

\(a_{n}\) = 8 - 3(n - 1) = 8 - 3n + 3 = - 3n + 11 → D

Step-by-step explanation:

the volume of a cylinder is as for any regular shaped object

ground area × height

here the ground area is a circle, so we get

pi×r²×h

with r being the radius (half the diameter), and h the height.

therefore,

pi×(2.7/2)²×10 = 3.14×1.8225×10 = 57.25552611... cm³

so, the first option is correct.

The best description of the probability of drawing a king from the deck is 1 out of 13, or 1/13.

The probability of drawing a king from a standard deck of 52 playing cards can be determined by dividing the number of favorable outcomes (number of kings) by the total number of possible outcomes (total number of cards in the deck).

In a standard deck, there are 4 kings (one king for each suit: hearts, diamonds, clubs, and spades). Therefore, the number of favorable outcomes is 4.

The total number of possible outcomes is 52 (the total number of cards in the deck).

So, the probability of drawing a king is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 4 / 52

Simplifying the fraction gives us:

Probability = 1 / 13

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Answer:

x = 122

Step-by-step explanation:

the measure of the chord- chord angle 125° is half the sum of the arcs intercepted by the angle and its vertical angle, that is

125 = \(\frac{1}{2}\) (x + 6 + x) ← multiply both sides by 2 to clear the fraction

250 = 2x + 6 ( subtract 6 from both sides )

244 = 2x ( divide both sides by 2 )

122 = x

The set satisfies all three requirements, we can conclude that all polynomials of the form p(t) = a t^2, where a is in r, is a subspace of p2. To determine if all polynomials of the form p(t) = a t^2, where a is in r, is a subspace of p2,.

We need to check if it satisfies the three requirements of a subspace:

1. The zero vector is in the set.
2. The set is closed under addition.
3. The set is closed under scalar multiplication.

First, let's check if the zero vector is in the set. The zero vector of p2 is the polynomial 0t^2 + 0t + 0, which can be written as p(t) = 0. To see if p(t) = 0 is in the set of polynomials of the form p(t) = a t^2, we need to check if there exists an "a" that satisfies p(t) = a t^2 = 0 for all values of t. This is true only if a = 0, so the zero vector is in the set.

Next, let's check if the set is closed under addition. Suppose we have two polynomials p(t) = a t^2 and q(t) = b t^2, where a and b are in r. Then, their sum is p(t) + q(t) = a t^2 + b t^2 = (a+b) t^2. This is also of the form p(t) = a t^2, where a = a+b, so it is in the set. Therefore, the set is closed under addition.

Finally, let's check if the set is closed under scalar multiplication. Suppose we have a polynomial p(t) = a t^2, where a is in r, and a scalar k. Then, k * p(t) = k * a t^2 = (ka) t^2. This is also of the form p(t) = a t^2, where a = ka, so it is in the set. Therefore, the set is closed under scalar multiplication.

Since the set satisfies all three requirements, we can conclude that all polynomials of the form p(t) = a t^2, where a is in r, is a subspace of p2.

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Answer:

Hope it helps:) 18j+10

Step-by-step explanation:

(2)(3j+5+6j)

(2)(3j)+(2)(5)+(2)(6j)

6j+10+12j

18j+10

Answer:0.289x100

Step-by-step explanation:

Answer:

n ≥ - 5

Step-by-step explanation:

10 - 5/1 + 7n ≥ - 30 , simplifying left side

10 - 5 + 7n ≥ - 30

5 + 7n ≥ - 30 ( subtract 5 from both sides )

7n ≥ - 35 ( divide both sides by 7 )

n ≥ - 5

Answer:

Line symmetry

Step-by-step explanation:

If you drew a straight line across the figure horizontally, you would see that both halves are symmetrical.

The given Boolean algebra expressions have been proven to be equivalent based on the properties of Boolean algebra.

To prove the statements, we can use the fact that any boolean function can be expressed as a sum of minterms (products of literals) or as a product of maxterms (sums of literals). Let F(A,B,C) be the boolean function defined by the truth table given in the question.

To prove that F1 = m1 + m3 + m5 + m7, we can observe that F1 is true when either of the following minterms is true: m1 = A'B'C, m3 = AB'C, m5 = A'BC, m7 = ABC. Conversely, if F1 is true, then one of these minterms must be true. Therefore, F1 = m1 + m3 + m5 + m7.

Similarly, to prove that F2 = m0 + m1 + m4 + m5, we can observe that F2 is true when either of the following minterms is true: m0 = A'B'C', m1 = A'B'C, m4 = AB'C', m5 = A'BC. Conversely, if F2 is true, then one of these minterms must be true. Therefore, F2 = m0 + m1 + m4 + m5.

To prove that F1 + F2 = m0 + m1 + m3 + m4 + m5 + m7, we can observe that F1 + F2 is true when either of the following minterms is true: m0 = A'B'C', m1 = A'B'C, m3 = AB'C, m4 = AB'C', m5 = A'BC, m7 = ABC. Conversely, if F1 + F2 is true, then one of these minterms must be true. Therefore, F1 + F2 = m0 + m1 + m3 + m4 + m5 + m7.

Finally, to prove that F1F2 = m1 + m5, we can observe that F1F2 is true when either of the following minterms is true: m1 = A'B'C, m5 = A'BC. Conversely, if F1F2 is true, then one of these minterms must be true. Therefore, F1F2 = m1 + m5.

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

what can not see nothing

Step-by-step explanation:

Answer:

x=-2 would be a straight line right through -2 on the x-axis

Step-by-step explanation:

Answer:

a straight line going up and down by the x axis -2

Answer:

9

Step-by-step explanation: subtract 3 from 12 and you get 9 as your answer

The number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

We can solve this inequality by introducing an auxiliary variable x4, such that x1 + x2 + x3 + x4 = 11. Here, x1, x2, x3, and x4 are all nonnegative integers.

We can interpret this equation as follows: imagine we have 11 identical objects and we want to distribute them among four boxes (x1, x2, x3, and x4). Each box can contain any number of objects, including zero. The number of solutions to this equation will give us the number of nonnegative integer solutions to the original inequality.

We can use a technique known as stars and bars to count the number of solutions to this equation. Imagine we represent the 11 objects as stars: ***********.

We can then place three bars to divide the stars into four groups, each group representing one of the variables x1, x2, x3, and x4. For example, if we place the first bar after the first star, the second bar after the third star, and the third bar after the fifth star, we get the following arrangement:

| ** | * | ****

This arrangement corresponds to the solution x1=1, x2=2, x3=1, and x4=7. Notice that the number of stars to the left of the first bar gives the value of x1, the number of stars between the first and second bars gives the value of x2, and so on.

We can place the bars in any order, so we need to count the number of ways to arrange three bars among 14 positions (11 stars and 3 bars). This is equivalent to choosing 3 positions out of 14 to place the bars, which can be done in C(14,3) ways.

Therefore, the number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

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The piecewise function to represent the amount A Sam owes after m months is A ( m ) = { 1500 - 50 m, if 0 ≤ m ≤ 12

{ 1500 - 50 (12) - 75 (m - 12), if m > 12

For the initial twelve months (0 ≤ m ≤ 12), Sam pays a monthly installment of $50. As a result, his remaining debt after m months will be equal to the starting loan amount ($ 1500) reduced by the cumulative total that he had paid back during said year ($50 x m).

Beyond the first year (m > 12), Sam is liable for a payment of $75 each month. Having already satisfied the former fee of $50 per month over the course of a full calendar year, his indebtedness afterwards becomes the remaining balance post-first year ( $1500 - 50 ( 12 )) decreased by his collective cost at $75 per month since then ( $75 x ( m - 12 )).

The piecewise function is therefore:

A ( m ) = { 1500 - 50 m, if 0 ≤ m ≤ 12

{ 1500 - 50 (12) - 75 (m - 12), if m > 12

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