Assuming that a 390 foot tall giant redwood grows vertically, if I walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be 39°, how far from the base of the tree am I?

Answer:

(a) 22 inches

(b) 770 inches

(c) 26,950 inches

Step-by-step explanation:

(a) To find the perimeter of the drawing, we add up the lengths of all four sides:

Perimeter of drawing = 7 + 4 + 7 + 4 = 22 inches

(b) The length and width of the actual garden are 35 times larger than the dimensions in the drawing. This means that the actual length is 7 x 35 = 245 inches and the actual width is 4 x 35 = 140 inches. To find the perimeter of the actual garden, we add up the lengths of all four sides:

Perimeter of actual garden = 245 + 140 + 245 + 140 = 770 inches

(c) When the dimensions of the garden are multiplied by 35, the perimeter of the garden will also be multiplied by 35. This is because each side will increase by a factor of 35, so the total length of all four sides will increase by a factor of 35 as well. Therefore, the new perimeter will be:

New perimeter = 35 x Perimeter of actual garden = 35 x 770 = 26,950 inches

Therefore , the solution of the given problem of unitary method comes out to be rectangle's size is 7/12 square inches.

The objective can be accomplished by using what was variable previously clearly discovered, by utilizing this universal convenience, or by incorporating all essential components from previous flexible study that used a specific strategy. If the anticipated claim outcome actually occurs, it will be feasible to get in touch with the entity once more; if it isn't, both crucial systems will undoubtedly miss the statement.

Here,

=>  A = L x W,

where A is the area, L is the length, and W is the breadth, is the formula for calculating the area of a rectangle.

Inputting the numbers provided yields:

=>  A = (7/4) x (1/3)

These fractions can be made simpler by eliminating any shared variables in the numerator and denominator before being multiplied. Since 7 and 3 are both prime integers in this instance, there are no shared factors to cancel.

The new numerator and denominator can then be obtained by multiplying the numerators and denominators, respectively. Thus, we get:

=>  A = (7 x 1) / (4 x 3)

When we multiply the numerator by the remainder, we obtain:

=> A = 7/12

The rectangle's size is 7/12 square inches as a result.

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The solution to the given quadratic equation is expressed as:

x = (-1 ± √5)/2

The general form of expression of a quadratic equation is:

y = ax² + bx + c

Where the solution is given by the quadratic formula:

x = [-b ± √(b² - 4ac)]/2a

The given quadratic equation is expressed as:

-3x² + 1 = 3x - 2

Rearranging in standard form is:

3x² + 3x - 3 = 0

Thus, the solution is:

x = [-3 ± √(3² - 4(3 * -3))]/2(3)

x = [-3 ± √(9 + 36)]/6

x = (-1 ± √5)/2

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The probability of the maximum number of black hats that could be present in the group is 2.

Since the probability of selecting a student with a green hat is the highest, it is likely that there are more green hats than any other color. Let's assume that there are 7 green hats. If there are 7 green hats, then there are only 5 hats left for the remaining colors. However, we know that there are only 2 red hats and 1 blue hat, leaving a maximum of 2 hats for the black color. Therefore, the greatest possible number of black hats in the group is 2, which would give a total of 2 red hats, 1 blue hat, 7 green hats, and 2 black hats. In conclusion, if the probability of selecting a student with a green hat is the highest, then the greatest possible number of black hats in the group is 2.

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Answer:

24x - 6y + 21

Step-by-step explanation:

3( 8x - 2y + 7 )

Multiply each term in the bracket by 3

= (3 x 8x) - ( 3 x 2y) + (3 x 7)

= 24x - 6y + 21

The value of the expression 34 - 9 x 2 is 16.

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed in an expression. These rules help to ensure that mathematical expressions are evaluated correctly and consistently. The order of operations is typically summarized by the acronym PEMDAS, which stands for:

Parentheses: Perform operations inside parentheses first.

Exponents: Evaluate exponents (powers and square roots, etc.) next.

Multiplication and Division: Perform multiplication and division, from left to right.

Addition and Subtraction: Perform addition and subtraction, from left to right.

In the given questions,

In this case, there are no parentheses or exponents, so we move on to multiplication before subtraction.

We perform the multiplication first, following the rule of performing multiplication before addition or subtraction.

9 x 2 = 18

Then, we subtract the result from 34:

34 - 18 = 16

Therefore, the value of the expression 34 - 9 x 2 is 16.

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Answer:

To find the surface area of a square pyramid, you need to find the area of the base and the area of the four triangular faces, and then add them together.

First, let's find the length of one side of the base of the pyramid:

Perimeter of the square base = 4 x side length

48 inches = 4 x side length

Side length = 12 inches

Now we can find the area of the base:

Area of the base = side length squared

Area of the base = 12 inches x 12 inches

Area of the base = 144 square inches

Next, we need to find the area of each triangular face. To do this, we need to find the length of the slant height of the pyramid. We can use the Pythagorean theorem to do this:

Slant height squared = height squared + (1/2 base length) squared

Slant height squared = 8 inches squared + (6 inches) squared

Slant height squared = 64 inches squared + 36 inches squared

Slant height = square root of (64 + 36) inches

Slant height = 10 inches

Now we can find the area of each triangular face:

Area of a triangular face = (1/2 base length) x slant height

Area of a triangular face = (1/2 x 12 inches) x 10 inches

Area of a triangular face = 60 square inches

Finally, we can add the area of the base and the area of the four triangular faces together to find the total surface area of the pyramid:

Total surface area = Area of the base + (4 x Area of a triangular face)

Total surface area = 144 square inches + (4 x 60 square inches)

Total surface area = 384 square inches

Therefore, the surface area of the pyramid is 384 square inches.

The distance of the satellite from station A is approximately 47 miles

The satellite is approximately 911 miles above ground

Let the distance from station A to the satellite be a and the distance from the station B to the satellite be a + 48

Using trigonometry

tan 87 degrees = height of the satellite above the ground, h / a

tan 87 degrees = h / a

h = a * tan 87

while

tan 84 degrees = h / a + 48

h = (a + 48) tan 84

substituting for h

a * tan 87 = (a + 48) tan 84

a (tan 87 - tan 84) = 48 tan 84

a (9.567) = 48 tan 84

a = 48 tan 84 / 9.567

a = 47.436

The distance of the satellite from station A is approximately 47 miles

The height above ground

h = a * tan 87

h = 47.436 * tan 87

h = 910.857 miles

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The distance the plane traveled from point A to point B is approximately 8.15 miles or 43056 feet (rounded to the nearest tenth of a foot).

An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are typically measured in degrees or radians, and they are used to describe the amount of rotation or turning between two lines or planes. In a two-dimensional plane, angles are usually measured as the amount of rotation required to move one line or plane to coincide with the other line or plane.

Let's first draw a diagram to visualize the problem:

                    /  |

                  /     |

                 /       |P (plane)

                /        |

               /         |

              /          | h = 6900 ft

            /            

           / θ2.        |  

         /                |

       /                  |

   B ___/θ1__  _|___ A

           d

We need to find the distance the plane traveled from point A to point B, which we'll call d. We can use trigonometry to solve for d.

From point A, we have an angle of elevation of 16° to the plane. This means that the angle between the horizontal and the line from point A to the plane is 90° - 16° = 74°. Similarly, from point B, we have an angle of elevation of 27° to the plane, so the angle between the horizontal and the line from point B to the plane is 90° - 27° = 63°.

Let's use the tangent function to solve for d:

x = h / tan(74°) = 19906.5 ft

d - x = h / tan(63°) = 23205.2 ft

So,

d = x + h / tan(63°) ≈ 43111.7 ft ≈ 8.15 miles.

Therefore, the distance the plane travelled from point A to point B is approximately 8.15 miles or 43056 feet (rounded to the nearest tenth of a foot).

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The vertex form of the quadratic equations in standard form are, respectively:

Case 9: y = 2 · (x + 2)² - 12

Case 10: y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11: y = 3 · (x - 4 / 3)² - 16 / 3

Case 12: y = - 3 · (x - 3)²

Case 13: y = (x - 4)² + 3

Case 14: y = (x - 1)² - 7

Case 15: y = (x + 3 / 2)² - 9 / 4

Case 16: 2 · (x + 1 / 4)² - 1 / 8

Case 17: y = 2 · (x - 3)² - 7

Case 18: y = - 2 · (x + 1)² + 10

In this problem we find ten cases of quadratic equation in standard form, whose vertex form can be found by a combination of algebra properties known as completing the square. Completing the square consists in simplifying a part of the quadratic equation into a power of a binomial.

The two forms are introduced below:

Standard form

y = a · x² + b · x + c

Where a, b, c are real coefficients.

Vertex form

y - k = C · (x - h)²

Where:

Now we proceed to determine the vertex form of each quadratic equation:

Case 9

y = 2 · x² + 4 · x - 4

y = 2 · (x² + 2 · x - 2)

y = 2 · (x² + 2 · x + 4) - 12

y = 2 · (x + 2)² - 12

Case 10

y = - (1 / 2) · x² - 3 · x + 3

y = - (1 / 2) · [x² + (3 / 2) · x - 3 / 2]

y = - (1 / 2) · [x² + (3 / 2) · x + 9 / 16] + (1 / 2) · (33 / 16)

y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11

y = 3 · x² - 8 · x

y = 3 · [x² - (8 / 3) · x]

y = 3 · [x² - (8 / 3) · x + 16 / 9] - 3 · (16 / 9)

y = 3 · (x - 4 / 3)² - 16 / 3

Case 12

y = - 3 · x² + 18 · x - 27

y = - 3 · (x² - 6 · x + 9)

y = - 3 · (x - 3)²

Case 13

y = x² - 8 · x + 19

y = (x² - 8 · x + 16) + 3

y = (x - 4)² + 3

Case 14

y = x² - 2 · x - 6

y = (x² - 2 · x + 1) - 7

y = (x - 1)² - 7

Case 15

y = x² + 3 · x

y = (x² + 3 · x + 9 / 4) - 9 / 4

y = (x + 3 / 2)² - 9 / 4

Case 16

y = 2 · x² + x

y = 2 · [x² + (1 / 2) · x]

y = 2 · [x² + (1 / 2) · x + 1 / 16] - 2 · (1 / 16)

y = 2 · (x + 1 / 4)² - 1 / 8

Case 17

y = 2 · x² - 12 · x + 11

y = 2 · (x² - 6 · x + 9) - 2 · (7 / 2)

y = 2 · (x - 3)² - 7

Case 18

y = - 2 · x² - 4 · x + 8

y = - 2 · (x² + 2 · x - 4)

y = - 2 · (x² + 2 · x + 1) + 2 · 5

y = - 2 · (x + 1)² + 10

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Answer:12

Step-by-step explanation:

i did it :)

Using trigonometric identities, we found that sec Φ = -7/(2√10), sin Φ = 3/7, tan β = √11/5, and sin β = √11/6 for the given values of csc Φ, cot Φ, and sec β.

1. We can start by using the Pythagorean identity to find the values of sin Φ:

[tex]sin^2[/tex] Φ + [tex]cos^2[/tex] Φ = 1

Since csc Φ = 1/sin Φ, we can substitute and solve for sin Φ:

1/(7/3) = sin Φ

sin Φ = 3/7

Next, we can use the fact that cot Φ = cos Φ/sin Φ:

cot Φ = cos Φ/(3/7) = - (2√10)/(3)

Simplifying this expression, we get:

cos Φ = - (2√10)/(3) * (3/7) = - 2√10/7

Finally, we can use the fact that sec Φ = 1/cos Φ:

sec Φ = 1/(- 2√10/7) = -7/(2√10)

2. We can use the fact that sec β = 1/cos β to find the value of cos β:

sec β = 6/5

cos β = 5/6

Next, we can use the Pythagorean identity to find the value of sin β:

[tex]sin^2[/tex] β + [tex]cos^2[/tex] β = 1

sin β = √(1 - [tex]cos^2[/tex] β) = √(1 - 25/36) = √(11/36) = √11/6

Finally, we can use the fact that tan β = sin β/cos β:

tan β = (√11/6)/(5/6) = √11/5

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Evaluating the linear equation in x = 19 we can see that the temperature was 5.76 degrees, so your answer is correct.

Here we have a linear equation that relates the wind temperature with the wind's velocity.

The linear equation is:

y = -0.36*x + 12.6

Where y is the temperature and x is the wind speed. We want to find the temperature when the speed is 19 miles per hour, to get it, just replace x by 19 in the linear equation above, then we will get:

y = -0.36*19 + 12.6

y = -6.84 + 12.6

y = 5.76

So your answer is correct.

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Answer:

true

Step-by-step explanation:

bcoz in iso triangle 2 sides are equal

and in equilateral all sides are equal

5 miles each day so 5×7=35 miles a week

Based on the employee contribution, the Traditional IRA is the better choice because the employee will be taxed at a lower rate on lower earnings in retirement than during employment. The Option A is correct.

The Traditional IRA allows the employee to make contributions on a pre-tax basis, which reduces the taxable income during the years of contribution. This reduces the tax liability during employment years in the 33% tax bracket. During retirement, the employee will be in the 15% tax bracket, which means they will pay a lower tax rate on the withdrawals from the Traditional IRA.

In contrast, the Roth IRA contributions are made with after-tax dollars, and the withdrawals during retirement are tax-free. Since the employee is currently in the 33% tax bracket, they will pay a higher tax rate on their current income than they would in retirement. Therefore, the Traditional IRA is a better choice for the employee in this scenario.

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Answer:

Rusty Raspberry's total earnings last year would be the sum of his earnings from playing baseball and his earnings from book royalties.

Earnings from playing baseball = $1,715,000

To calculate earnings from book royalties, we need to find out how much Rusty received in royalties for the 300,000 copies sold.

Royalties per book = 10% of $24 = $2.40

Total royalties for 300,000 books = $2.40 x 300,000 = $720,000

Therefore, Rusty Raspberry's earnings from book royalties last year = $720,000

Total earnings = Earnings from playing baseball + Earnings from book royalties

= $1,715,000 + $720,000

= $2,435,000

Therefore, Rusty Raspberry's total salary last year from the book and his baseball career was $2,435,000.

The value of the limit of the expression Limit x tend to π 1-sinx/2(π-x) ² is infinity (∝)

Given that

Limit x tend to π 1-sinx/2(π-x) ²

To solve this expression, we make use of

If limit of x to a+ of f(x) = limit of x to a- = L, then limit of x to a+ of f(x) = L

The interpretation is that we solve the expression by direct substitution

So, we have

Limit = 1 - sin(π)/2(π - π) ²

Evaluate the difference

Limit = 1 - sin(π)/2(0)²

Evaluate the exponent and the bracket

Limit = 1 - sin(π)/0

Divide

Limit = ∝

Hence, the limit of the expression is ∝

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Answer:

We can solve this expression using the order of operations, also known as PEMDAS:

2 + 77 + 2 + 4 + 18 + (9/4) + 5 + 23 + 78 + 33 - 76 - 4 + 12

First, we can simplify the fraction by adding the whole number and fraction parts:

2 + 77 + 2 + 4 + 18 + 2.25 + 5 + 23 + 78 + 33 - 76 - 4 + 12

Next, we can perform addition and subtraction from left to right:

= 187 + 2.25 + 68

= 257.25

Therefore, the value of the expression 2+77+2+4+18+9/4+5+23+78+33-76-4+12 is 257.25.

LOL the answer is 176.25

Therefore, the value of x is 9.

A triangle is a closed two-dimensional geometric shape that is formed by connecting three non-collinear points with three-line segments. The three line segments that connect the three points are called sides of the triangle, and the points themselves are called vertices. The angle formed between any two adjacent sides of a triangle is called an interior angle of the triangle. The sum of the interior angles of a triangle is always 180 degrees.

There are many different types of triangles, including equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles. An equilateral triangle is a triangle in which all three sides are equal, an isosceles triangle is a triangle in which two of the sides are equal, and a scalene triangle is a triangle in which none of the sides are equal. An acute triangle is a triangle in which all three interior angles are less than 90 degrees, an obtuse triangle is a triangle in which one of the interior angles is greater than 90 degrees, and a right triangle is a triangle in which one of the interior angles is exactly 90 degrees.

Given by the question.

According to Thel's theorems

[tex]\frac{5}{3} =\frac{15}{x}[/tex]

5x=45

x=9

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The true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.

It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.

To get to the current positioning, a rotation might not be sufficient.

It could be required to include a fictitious translation known as the object's location (or position, or linear position).

Together, the position and orientation completely explain where the object is situated in space.

Therefore, the true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

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Answer: 15 of those teachers are men

Step-by-step explanation: 2 out of 3, is of course written as 2/3

if 2/3 are women, this means 2/3 of 45 is 30, meaning 30 of the teachers are women, so if 30/45 are women, the remaining 15 are men

The total amount of money you will pay back when borrowing $1,000 for 4 years at an annual interest rate of 8% with annual compounding is $1,360.50.

The interest you receive is referred to as compound interest. Using simple math, you can see how this works: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year.

A = P*(1 + r/n)[tex]^(^n^*^t^)[/tex]

A is the total amount

P is the principal (initial amount borrowed), which is $1,000 in this case

r is the annual interest rate expressed as a decimal, which is 0.08 (8%)

n is the number of times the interest is compounded per year, which is usually 12 (monthly compounding) or 1 (annual compounding)

t is the time in years, which is 4 in this case

Assuming that the interest is compounded annually (n=1), we can plug in the values and simplify:

A = 1000*(1 + 0.08/1)¹⁴

= 1000(1.08)⁴

= 1000*1.3605

= $1,360.50

the total amount of money you will pay back when borrowing $1,000 for 4 years at an annual interest rate of 8% with annual compounding is $1,360.50.

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Answer: decrease in the GDP by 2.5%.

Step-by-step explanation:

Answer:

Assuming that the expression is asking for the tangent of 1 radian, we can use the tangent half-angle formula to find an exact value:

tan(1) = 2tan(1/2) / (1 - tan^2(1/2))

To find tan(1/2), we can use the half-angle formula for tangent:

tan(1/2) = sin(1) / (1 + cos(1))

We cannot simplify this expression any further without a calculator. Therefore, the exact value of tan(1) is:

tan(1) = 2sin(1) / (cos(1) - cos^2(1) + 1)

Again, we cannot simplify this expression any further without a calculator.

For the second expression, we are asked to find the value of:

tan(arctan(6/4))

By definition, tan(arctan(x)) = x for all x, so we have:

tan(arctan(6/4)) = 6/4 = 3/2

Therefore, the exact value of the expression tan(6/4) is 3/2.

Answer:

Equation: y= -3/4x+15/2

Step-by-step explanation:

The points given: (-2,9) and (2,6)

Slope ,m=y2-y1/x2-x1=6-9/2-(-2)= -3/(2+2)

slope ,m= -3/4

Equation: y-y1=m(x-x1)

Equation: y-6= -3/4(x-2)

y-6= -3/4x+3/2

y= -3/4x+3/2+6

y= -3/4x+15/2

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Answer:

Z(1.16)

Step-by-step explanation:

Let's start by expressing "Z increased by 16%" using algebra.

Let Z be the original value of some quantity.

To increase Z by 16%, we need to add 16% of Z to Z:

Z + 0.16Z

Simplifying this expression by factoring out Z, we get:

Z(1 + 0.16)

Combining like terms, we have:

Z(1.16)

Therefore, "Z increased by 16%" can be expressed algebraically as:

Z increased by 16% = Z(1.16)

Answer:

p= -3-1/2

p= -7/2

Step-by-step explanation:

(you transpose the fraction /take the liketerms)

( you transpose your fraction will change the sign and become negative then -3-0.5or -3-1/2=-7/2.)then you substitute to the original equation 1/2+p=-3 check your answer .

Answer:

24328.49 cm

Step-by-step explanation:

as (A = π r²). r is 88 so and is 24328.49cm

Answer:

Step-by-step explanation:

You want to know which set of equations could be combined in such a way as to result in the equation 3x = 18.

To obtain a term of 3x, the second equation must be subtracted from the first. That will result in 3x +2y = 18, not the equation of interest.

A term of 3x can be obtained by adding twice the first equation to the second:

  2(x +y) +(x -2y) = 2(4) +(10)

  3x = 18 . . . . . as required

A term of 3x can be obtained by subtracting the second equation from the first. That will result in 3x +2y = 18, not the equation of interest.

These equations are dependent. The second is the opposite of the first. They have an infinite number of solutions, not the single solution of the system of equations of interest.