BA61°830°СFind the side length of BC. Round your answers to the nearest whole number

Answer:

-18 2/3 or -56/3

Step-by-step explanation:

Using trigonometric function the length to the nearest foot of the shortest ladder that will safely reach a roof that is 23 feet high is calculated as 25 feet.

What are trigonometric functions?

Simply put, trigonometric functions—also called circular functions—are the functions of a triangle's angle. This means that these trigonometric functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given the angle a ladder makes with the ground should be no greater than 67°.

So the angle θ ≤ 67°.

Let us assume the angle to be equal to 67°

The height of the roof from the ground is 23 feet.

The ladder and wall form the right triangle where the ladder works as hypotenuse and the wall as perpendicular.

With the sine function, find the length of the ladder -

sin θ = perpendicular/hypotenuse

Let the length of ladder be x.

sin 67° = 23/x

x = 23/sin 67°

x = 23/0.920

x = 25 feet

Therefore, the length of the ladder is 25 feet.

To learn more about trigonometric functions from the given link

https://brainly.com/question/1143565

#SPJ1

Using Pascal's triangle and the difference quotient formula, we expand (x + h)^2 and simplify the expression to (2hx + h^2) / h. As h approaches 0, the term h becomes negligible, and we are left with 2x, which represents the derivative of x^2.

To use Pascal's triangle to find x^2 using the difference quotient formula, we can follow these steps:

1. Write the second row of Pascal's triangle: 1, 1.

2. Use the coefficients in the row as the binomial coefficients for (x + h)^2. In this case, we have (1x + 1h)^2.

3. Expand (x + h)^2 using the binomial theorem: x^2 + 2hx + h^2.

4. Apply the difference quotient formula: f(x + h) - f(x) / h.

5. Substitute the expanded expression into the formula: [(x + h)^2 - x^2] / h.

6. Simplify the numerator: (x^2 + 2hx + h^2 - x^2) / h.

7. Cancel out the x^2 terms in the numerator: (2hx + h^2) / h.

8. Divide both terms in the numerator by h: 2x + h.

9. As h approaches 0, the term h becomes negligible, and we are left with the derivative of x^2, which is 2x.

For more such questions on triangle

https://brainly.com/question/28470545

#SPJ8

Answer:

the first one is (23)

number 7 is ( 34.069)

Step-by-step explanation:

Answer:

5.5 (five and a half weeks)

Step-by-step explanation:

If she was withdrawing 20$ twice a week that means that she withdrew 40$ (20$x2) a week, and 220$ divided by 40$ is 5.5.

The nth term of the sequence -3, 0, 5, 10, 25, 5, 47 can be represented by the piecewise function:

nth term =

-3 + (n - 1) * 5, if n mod 5 ≤ 5

5 + (n - 1) * 15, if n mod 5 > 5

To find the nth term of a sequence, we need to identify the pattern or rule that governs the sequence. Upon analyzing the given sequence -3, 0, 5, 10, 25, 5, 47, we can observe the following:

The sequence starts with -3 and increases by 5 each time, except for the 5th term, where it increases by 15 (from 10 to 25). After the 5th term, the sequence starts again with 5 and continues to increase by 15 each time.

Based on this pattern, we can divide the sequence into two parts:

Part 1: -3, 0, 5, 10, 25 (increasing by 5 each time)

Part 2: 5, 20, 35, 50, 65 (increasing by 15 each time)

Now, to determine the nth term, we can consider the formula for arithmetic sequences:

nth term = first term + (n - 1) * common difference

For Part 1, the first term is -3 and the common difference is 5. Thus, the nth term for Part 1 is given by:

nth term = -3 + (n - 1) * 5

For Part 2, the first term is 5 and the common difference is 15. Therefore, the nth term for Part 2 can be expressed as:

nth term = 5 + (n - 1) * 15

However, since the sequence alternates between Part 1 and Part 2, we need to determine which part the nth term falls into. For that, we can use modular arithmetic:

If n mod 5 is less than or equal to 5, then the nth term is from Part 1.

If n mod 5 is greater than 5, then the nth term is from Part 2.

Let's calculate a few terms to illustrate this:

For n = 1, the sequence starts with -3, so the 1st term is -3.

For n = 2, we are still in Part 1, so the 2nd term is 0.

For n = 3, Part 1 continues, so the 3rd term is 5.

For n = 4, we are still in Part 1, so the 4th term is 10.

For n = 5, Part 1 ends, and the 5th term is 25.

For n = 6, the sequence starts with 5 in Part 2, so the 6th term is 5.

For n = 7, Part 2 continues, so the 7th term is 20.

For n = 8, we are still in Part 2, so the 8th term is 35.

Based on this analysis, we can conclude that the nth term for the given sequence is:

If n mod 5 ≤ 5:

nth term = -3 + (n - 1) * 5

If n mod 5 > 5:

nth term = 5 + (n - 1) * 15

Therefore, depending on the value of n and the remainder when divided by 5, we can use the appropriate formula to calculate the nth term.

​for such more question on sequence

https://brainly.com/question/30194025

#SPJ8

Answer:

HCF of 105 and 65 is 5.

LCM of 65 and 105 is 1365.

Answer:

H.C.F = 5

L.C.M = 1365

please give me a brainliest answer

Answer:

69

Step-by-step explanation:

first 135

second 135 - 20% = 135 - 27 = 108

third 108 - 20% = 108 - 21.6 = 86.4

fourth 86.4 -20% = 86.4 -17.28= 69.12

rounded 69

Answer:

2/5

Step-by-step explanation:

\( \frac{12}{30} = \frac{2 \times 6}{5 \times 6} = \frac{2}{5} \\ \)

Answer:

Step-by-step explanation:

In this question, we need to use the formula of means to solve the. We can set the number of beads Rajiv brings as X, and use the formula of mean to get the total number of beads that the Four(4) children have and the total number of beads that the Five(5) children have.

Four(4) children each have some beads, the mean number of beads is: 8

        4 * 8 = 32

We set the number of beads Rajiv brings as:

x, so the total number of beads that the Five(5) children have is:

32  +  x

The mean number of the Five(5) children is now: 9

      5  *  9   =  45

     32 +  x    =    45

      x  +  32  =    45

           -  32  =   -32

       x            =     13

By solving the above equation, you can get:

x  =  13

       13

Hope this helps!

Tthe triangle that is a reflection of the green triangle is figure 1

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

The figures

Where, we have:

This means that the triangle that is a reflection of the green triangle is figure 1

Read more about transformation at

brainly.com/question/4289712

#SPJ1

Answer:

4

Step-by-step explanation:

2+2 is 4 see. 2+1 is 3. So 2+2 is 4

The answer of the given question based on graphing and crafting is you will create a Mobius strip , and when we cut it into lengthwise  you will get a single, longer Mobius strip.

A Möbius strip is a one-sided surface with only one boundary component. It is named after the German mathematician August Ferdinand Mobius who discovered it in 1858.

A Mobius strip can be created by taking  rectangular strip of paper, giving it  half-twist, and then connecting two ends of  strip together to form  loop. The resulting loop will have interesting property of being non-orientable, which means that it only has one side.

If you take a strip of paper, put two half-twists in it, and glue the ends together, you will create a Mobius strip.

When you cut a Mobius strip length wise down the middle while hugging the right edge, you will get a single, longer Mobius strip that has two full twists instead of the original two half twists. This is because cutting down the middle of the Mobius strip results in flipping one of the twists, which combines with the original twist to create a double twist.

To know more about Length visit:

https://brainly.com/question/30625256

#SPJ1

Answer:

Step-by-step explanation:

$2.12 - $1.65 = $0.47
$0.47 x 65 = $30.55 profit.

This is an exercise in the formula to calculate the profits obtained from the sale of a product, it is an essential tool in the management of any business. By knowing the profits obtained from the sale of a product, business owners and managers can make informed decisions and adjust their business strategies to maximize their profitability.

Profit is calculated by subtracting the total costs of production from the total revenue earned from the sale of a product. Total production costs include not only the direct costs associated with manufacturing the product, but also indirect costs, such as advertising and marketing costs, the cost of packaging materials, and other overhead.

The total income obtained from the sale of a product is the product of the number of units sold by the sale price per unit. It is important to remember that the selling price per unit must be sufficient to cover both the direct and indirect costs of production, and to provide a reasonable profit.

Once the profit earned from the sale of a product has been calculated, business owners and managers can use this information to improve their profitability. If profits are low, they might consider lowering production costs, raising the selling price, or finding ways to sell more units. On the other hand, if profits are high, they might consider increasing their investment in advertising and marketing to attract more customers and expand their business.

In addition, profit calculation can also help business owners and managers assess the feasibility of launching a new product or expanding into new markets. By calculating total production costs and potential total revenue, they can determine if the new product or market is profitable and make informed decisions about whether to proceed with the launch or expansion.

The total cost of making the handles is the product of the number of handles times the cost per unit:

Total cost = 65 potholders × $1.65/potholder = $107.25

The total revenue from selling the handles is the product of the number of handles times the selling price per unit:

Total revenue = 65 potholders x $2.12/potholder = $137.8

Elmo's profit is the difference between total revenue and total cost:

Profit = Total Revenue - Total Cost

Profit = $137.8 - $107.25 = $30.55

Profit = $30.55

Answer:

alternate interior angles are congruent

The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.

To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.

Add the square of half of the coefficient of x to both sides of the equation:

x² + 2x + (2/2)² = 319 + (2/2)²

x² + 2x + 1 = 320

The left-hand side of the equation can now be factored as a perfect square:

(x+1)² = 320

This is the equation in the form (x+a)²=b, where a=1 and b=320.

Learn more about the perfect square here:

https://brainly.com/question/385286

#SPJ1

The complete question is as follows:

What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?

x² + 2x = 319

The Solution:

We are required to find the sum of

This also means that we should simplify

Therefore, the correct answer is option 2

The probability of the baseball player getting exactly 4 hits out of 10 times at bat is approximately 0.161, or 16.1%.

To calculate the probability of a baseball player getting exactly 4 hits out of 10 times he was up at bat, we need to use the binomial probability formula.

The binomial probability formula is given by:P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of getting exactly k hits

n is the total number of trials (in this case, the player's 10 times at bat)

k is the number of successful trials (in this case, 4 hits)

p is the probability of success in a single trial (in this case, the player's batting average, 0.298)

(1 - p) is the probability of failure in a single trial

Plugging in the values:

P(X = 4) = C(10, 4) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Using the combination formula C(n, k) = n! / (k! * (n - k)!):

P(X = 4) = 10! / (4! * (10 - 4)!) * (0.298)^4 * (1 - 0.298)^(10 - 4)

Calculating the values:

P(X = 4) ≈ 0.161

For more such questions on probability

https://brainly.com/question/1834572

#SPJ8

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 4 ( x +3) \\\\\\ y+11=4x+12\implies {\Large \begin{array}{llll} y=4x+1 \end{array}}\)

The equation is:

Work/explanation:

Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),

where m is the slope and (x₁, y₁) is a point on the line.

Plug in the data:

\(\rm{y-(-11)=4(x-(-3)}\)

Simplify.

\(\rm{y+11=4(x+3)}\)

Simplified to slope intercept:

\(\rm{y+11=4x+12}\)

\(\rm{y=4x+1}\) <- this is the simplified slope intercept equation

Answer:

=6 units squared

Step-by-step explanation:

area=1/2h(a+b)

        =1/2×2(4+2)

        =6

Answer: r

Step-by-step explanation:

Answer:

495.6 cm, or 4.956 m

Step-by-step explanation:

1:84 means that a centimeter on the drawing has to be multiplied 84 times in order to find the real length. Therefore, 5.9 x 84 = 495.6

Answer:

Step-by-step explanation:

We know that the sides in a square are equal length. We also know that you have to multiply length by width to get area. So if we know that the length of one side is 16 feet then all we have to do if multiply 16 by 16. Hence why the answer is 256 square feet of carpet.

Answer:

8x+20

36

Step-by-step explanation:

4(2x) + 4(5)

= 8x +20

Hence,

Substituting 2 into 8x+20:

8(2)+20

= 36

Feel free to mark it as brainliest :D

The weight of each chair is 7 pounds.

Specific numbers and their computations employing a variety of fundamental arithmetic operations are at the center of arithmetic mathematics. Algebra, on the other hand, deals with the limitations and guidelines that apply to all other types of numbers, including whole numbers, integers, fractions, functions, and so on. Arithmetic math serves as the foundation for algebra, which always adheres to its definition. A large range of subjects fall within the broad definition of mathematics, which encompasses a very broad range of topics. Beginning with the fundamentals like addition, subtraction, and division of numbers, they then move on to more complicated topics like exponents, variations, sequence, progression, and more. This part does touch on some of the mathematical formulas and mathematical sequence. Four essential mathematical operations—addition, subtraction, multiplication, and division—are covered in basic arithmetic.

Total weight = 63 pounds

Weight of the table = 35 pounds

Weight if 4 chairs = 63 - 35

= 28 pounds

Weight of one chair = 28/4

= 7 pounds

To know more about basic arithmetic ,visit:

brainly.com/question/16096936

#SPJ13

Answer:

-16

Step-by-step explanation:

\((32+9-1)+(-52+6-10) \\ \\ =(41-1)+(-46-10) \\ \\ =40-56 \\ \\ =-16\)

The length of segment GH is approximately 2.2

We have,

To find the length of segment GH, we need to calculate the distance between points G(-1, -4) and H(-3, -3).

The distance formula between two points \((x_1, y_1) ~and ~(x_2, y_2)\) in a coordinate plane is given by:

\(d = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}\)

Applying the formula to the coordinates of points G and H, we have:

d = √((-3 - (-1))² + (-3 - (-4))²)

d = √((-3 + 1)² + (-3 + 4)²)

d = √((-2)² + (1)²)

d = √(4 + 1)

d = √(5)

The length of segment GH is the square root of 5, which is approximately 2.24 when rounded to the nearest tenth.

Therefore,

The length of segment GH is approximately 2.2

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ1

Answer:

Grapes: 7/15 pound. Cherries: 1/6 pound.

Step-by-step explanation:

The total weight of the fruits is 7/10 of a pound. The weight of the grapes is 2/3 of the total weight. Therefore, the weight of the grapes is 2/3 * 7/10 = 14/30 = 7/15 of a pound. The weight of the cherries is 7/10 - 7/15 = 1/6 of a pound.