The volume of a pyramid whose base is a right triangle is 1071 units
3
3
. If the two legs of the right triangle measure 17 units and 18 units, find the height of the pyramid.

Answer:

The exact value of cos(45°) is √(2) / 2.

Step-by-step explanation:

Answer:

Answer:√2/2=cos45

√2/2×√2/√2=2/2√2

1/√2

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

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A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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B

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A

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We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

Answer:

shown below

Step-by-step explanation:

9 different possible tiles to choose, but there are duplicates of two types of tiles. Out of 9 tiles, two of them are S. Therefore, the probability you choose an S is 2/9 (however much percent that is).

You'd reverse the math for letters other than P:

Out of 9 tiles, two of them are P. 9 minus 2 is seven. Seven out of 9 characters are not the letter P. Therefore, the probability you choose any letter other than P is 7/9 (however much percent that is).

Answer:

$88

Step-by-step explanation:

8:30 - 12:30 is 4 hours so 4 hour x 15.75 is 63 than add 25 and its a total of 88

Answer:

4/8 or reduced 1/2

Step-by-step explanation:

It's 4/8 or reduced as 1/2 because there are 4 even numbers 2, 4, 6, 8

Answer:

do you solve for y or x or anything on these if so, i can do them. i just need them in chat

Step-by-step explanation:

The pH value of water when the H₃O⁺ is 1.0 x 10⁻⁷ will be 7.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The pH value of any ion is given as,

pH = - log [H₃O⁺]

The ions of H₃O⁺ is 1.0 x 10⁻⁷. Then the pH value is given as,

pH = - log [H₃O⁺]

pH = - log [1.0 x 10⁻⁷]

pH = - log [10⁻⁷]

pH = - (-7) log 10

pH = 7

The pH value of water when the H₃O⁺ is 1.0 x 10⁻⁷ will be 7.

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Answer:

x²(x-1)(x-2)

Step-by-step explanation:

Have a nice day/night :)

Answer:

Step-by-step explanation:

250 students are in the 6th grade have a good night it is night hear if you live in America east side 10:34 PM

The matrix P represents the projection onto the line x₁ = -2x₂. The matrix Q represents the projection onto the coordinate axis x₁. And the matrix P is a 2x2 matrix, and the matrix Q is also a 2x2 matrix.

To find the matrix of the orthogonal projection in ℝ² onto the line x₁ = -2x₂, we can follow these steps:

Start by finding a vector that represents the line x₁ = -2x₂. Let's call this vector v. We can choose a point on the line, such as (1, -1), and use it to define the vector v as v = (1, -1).

Normalize the vector v by dividing it by its magnitude to obtain a unit vector u in the direction of the line. The magnitude of v is √(1² + (-1)²) = √2. Therefore, u = (1/√2, -1/√2).

Construct the matrix P by taking the outer product of the unit vector u with itself: P = uuᵀ.

The matrix P represents the projection onto the line x₁ = -2x₂.

Now let's find the matrix of the projection onto the coordinate axis x₁.

The coordinate axis x₁ is represented by the vector (1, 0).

Normalize the vector (1, 0) to obtain a unit vector in the direction of the x₁ axis. The magnitude of (1, 0) is 1, so the unit vector in the x₁ direction is (1/1, 0) = (1, 0).

Construct the matrix Q by taking the outer product of the unit vector with itself: Q = qqᵀ.

The matrix Q represents the projection onto the coordinate axis x₁.

To summarize:

The matrix P represents the projection onto the line x₁ = -2x₂.

The matrix Q represents the projection onto the coordinate axis x₁.

The matrix P is a 2x2 matrix, and the matrix Q is also a 2x2 matrix.

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Answer: 26

Step-by-step explanation:

26 + 26 = 52

52 + 3 = 55

55 divided by 5 = 11

Hope this helped : )

Answer:

127.38

Step-by-step explanation:

Answer:

127.38

Step-by-step explanation:

15 x 3 = 45

(102.38 + 45) - 20 = 127.38

Answer:

speed

1)the distance travelled by a body per unit time is known as speed.

2) speed is speed, or something how fast is going,

3) while velocity is speed how fast something is going in a specific direction.

average speed

1) average speed is the speed added up and divided by number of speed .

2)the average of all the instantaneous speed in a give time interval.

3) the average speed as the duration of the time interval approaches zero.

Answer:

5/12

Step-by-step explanation:

The tangent of an angle is the opposite side divided by the adjacent side, and in this case that would be 5 / 12. Hope this helps!

Answer:

\( \frac{5}{12} \)

Step-by-step explanation:

\( \because \tan (\beta) = \frac{AC}{BC} \\\\

\huge\purple {\boxed {\therefore \tan (\beta) = \frac{5}{12}}} \)

B 1/2

Step-by-step explanation:

Answer:

\(\large\boxed{\tt x^{\circ}= 90^{\circ}}\)

Step-by-step explanation:

\(\textsf{We are asked to find the value of x.}\)

\(\textsf{The value of x is an angle for this triangle.}\)

\(\textsf{Note that we are given 2 other angles, we can use what is given to us to solve for x.}\)

\(\large\underline{\textsf{What is a Triangle?}}\)

\(\textsf{A Triangle is a shape with 3 sides, and 3 angles. Sometimes these can be congruent,}\)

\(\textsf{other times, and most of the time they're not. These are called Equilateral}\)

\(\textsf{Triangles. Every Triangle consists of 3 angles that add up to 180}^{\circ}. \ \textsf{If the angles}\)

\(\textsf{don't add up to 180}^{\circ}, \ \textsf{then the shape is not a triangle.}\)

\(\textsf{Now that we know a Triangle has 3 angles that add up to 180}^{\circ}, \ \textsf{we can create an}\)

\(\textsf{equation where x is the \underline{subject}.}\)

\(\large\underline{\textsf{Solving;}}\)

\(\textsf{All 3 angles add up to 180}^{\circ}, \ \textsf{let's create an equation.}\)

\(\tt 180^{\circ} = 37^{\circ} + 53^{\circ} + x^{\circ}\)

\(\textsf{To make x the subject, move x to the other side of the equation by subtracting x.}\)

\(\tt 180^{\circ} - x^{\circ}= 37^{\circ} + 53^{\circ} + x^{\circ} - x^{\circ}\)

\(\textsf{We should also move 180}^{\circ} \ \textsf{to the other side of the equation as well.}\)

\(\tt 180^{\circ} - 180^{\circ} - x^{\circ}= 37^{\circ} + 53^{\circ} -180^{\circ}\)

\(\underline{\textsf{We should have;}}\)

\(\tt- x^{\circ}= -180^{\circ} + 37^{\circ} + 53^{\circ}\)

\(\textsf{We should remove the negative for x by dividing the whole equation by -1.}\)

\(\frac{\tt- x^{\circ}= -180^{\circ} + 37^{\circ} + 53^{\circ}}{-1} \rightarrow \tt x^{\circ}= 180^{\circ} - 37^{\circ} - 53^{\circ}\)

\(\underline{\textsf{Simplify the right side of the equation;}}\)

\(\large\boxed{\tt x^{\circ}= 90^{\circ}}\)

Answer:

x=7

Step-by-step explanation:

x^2=14x-49

x^2-14x+49=0

(x-7)^2=0

x-7=0

x=7

Answer:

x = 7

Step-by-step explanation:

First, you can start by subtracting 14x - 49 from both sides to get 0 on the left side:

x^2=14x-49

-(14x - 49) -(14x - 49)

x^2 - 14x + 49 = 0

Now, we can realize that this equation resembles a perfect square trinomial, which would be in the form a^2 - 2ab + b^2. This factors to (a - b)^2. We can say that x^2 corresponds to a^2 and 49 corresponds to b^2. We can wrote two equations to solve for a and b:

a^2 = x^2

a = x

b^2 = 49

b = 7

This means we can factor x^2 - 14x + 49 into (x - 7)^2.

Now we can use the zero product property:

(x - 7)^2 = 0

x - 7 = 0

x = 7

Answer:

10\(\pi\)

Step-by-step explanation:

Length of arc = \(\frac{theta }{360} * 2\pi r\)

= \(\frac{150}{360} * 2 \pi * 12\\\)

= \(10\pi\)

\(\text{Given that,}\\\\A(x_1,y_1) = (-3,6)~~ \text{and}~ B(x_2,y_2) =(10,-8)\\\\AB = \sqrt{(x_2-x_1)^2 + (y_2 -y_1)^2}\\\\~~~~~=\sqrt{(10+3)^2 + (-8-6)^2}\\\\~~~~~=\sqrt{13^2 + 14^2}\\\\~~~~~=\sqrt{365}\\\\~~~~~=19.105~ units\)

Answer:

one solution, x= -4

Step-by-step explanation:

Answer:

One solution, x = -4

Step-by-step explanation:

6x + 32 = -2x -- Minus 6x from both sides

32 = -8x -- Divide -8 on both sides

-4 = x

Answer:

12.5

Step-by-step explanation:

49.00/3.92=12.5

Answer:

B

Step-by-step explanation:

the height of the triangle formed by the diagonal and base of the TV screen.

The height of the TV is approximately 15.6 inches.

(26 inches / √2) = 18.8 inches

(18.8 inches * √2) = 26 inches

Height = (26 inches / 18.8 inches) * 18.8 inches

Height = 15.6 inches

Step 1: Calculate the hypotenuse of the triangle formed by the diagonal and base of the TV screen.

Hypotenuse = diagonal / √2

Hypotenuse = 26 inches / √2

Hypotenuse = 18.8 inches

Step 2: Calculate the diagonal of the triangle formed by the hypotenuse and base of the TV screen.

Diagonal = hypotenuse * √2

Diagonal = 18.8 inches * √2

Diagonal = 26 inches

Step 3: Calculate the height of the triangle formed by the diagonal and base of the TV screen.

Height = diagonal / base

Height = 26 inches / 18.8 inches

Height = 15.6 inches

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given data:

The function

represents the number of farms in the United States t years since 1950.

to find How many years after 1950 will the number of farms in the United States be 2,180,000.

put t=59.

then,

thus, after 59 the number of farms in the United States will be 2,180,000.

The the function to estimate the average age of employee of a company is A(s)=0.285s + 59  , then the average age of employee in 2003 is 65.27 and in 2009 is 66.98

To estimate the average age of an employee in 2003, we need to find the value of A(s) when s = 22  ;

because the number of years between 2003 and 1981 is = 22 years ;

So , A(22) = 0.285×22 + 59 = 65.27  ;

The average age of an employee in 2003 is approximately 65.27.

To estimate the average age of an employee in 2009,

we need to find the value of A(s) when s = 28

because the number of years between 2009 and 1981 is = 28 years ;

So , A(28) = 0.285×28 + 59 = 66.98  ;

The Average age of employee in 2009 is approximately 71.48.

The given question is incomplete , the complete question is

The function​ A(s) given by ​A(s)=0.285s + 59  can be used to estimate the average age of employee of a company in the year 1981 to 2009. Let​ A(s) be the average age of an​ employee, and "s" be the number of year since​ 1981; that​ is, s=0 for 1981 and s=9 for 1990. What is the average age of the employee in 2003 and in​ 2009 ?

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Answer:

Well, Your answer is 12 units.

Because, It was on edgunity

Good Luck with your homework!!~

Answer:

Hello There. The answer to this is The length of W'X' will be exactly given by, 12 unit. Explanation: The Rectangle WXYZ is dialated by a factor of 12/5 to form the rectangle W'X'Y'Z'. So, if the length of WX is 5 unit, the length of W'X' will be exactly given by, the lenght WX x Dialation factor. = (5 x 12/5) unit. = 12 unit

Hope It Helps! :) ♡

ItsNobody~

The correct answer is (c) 3.767.

To calculate the standard deviation of a combined sample, we need to use the formula for the pooled standard deviation. This formula takes into account the sample size and standard deviation of each group to calculate an overall standard deviation. The formula is:

s_pooled = sqrt(((n1 - 1)s1^2 + (n2 - 1)s2^2 + ... + (nk - 1)sk^2)/(n1 + n2 + ... + nk - k))

where n is the sample size, s is the standard deviation, and k is the number of groups.

Using the values from question 43, we can calculate the pooled standard deviation for all three lakes:

s_pooled = sqrt(((9 - 1)(2.6)^2 + (12 - 1)(1.7)^2 + (8 - 1)(3.9)^2)/(9 + 12 + 8 - 3))

= sqrt(232.02/26)

= 3.767

Therefore, the standard deviation of the combined group is approximately 3.767.

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Answer:

Step-by-step explanation:

8:2 doubled is 16:4