Prove the trig identity

cosec theta / cot theta + tan theta = cos theta

Answer:

C

Step-by-step explanation:

consistently goes down by 3.2 for the y value

Answer:

The watered area is approximately 3783 square feet.

Step-by-step explanation:

The area that is watered due to the rotation of the spankler is a circular section area (\(A\)), whose formula is:

\(A = \frac{\theta }{2}\times \frac{1}{360^{\circ}}\times 2\pi \times d^{2}\)

Where:

\(d\) - Water distance, measured in feet.

\(\theta\) - Rotation angle, measured in sexagesimal degrees.

Given that \(d = 85\,ft\) and \(\theta = 60^{\circ}\), the watered area is:

\(A = \frac{60^{\circ}}{2} \times \frac{1}{360^{\circ}}\times 2\pi \times (85\,ft)^{2}\)

\(A \approx 3783\,ft^{2}\)

The watered area is approximately 3783 square feet.

Answer:176

Step-by-step explanation:

6 times 29.33333333333333

We have that because the central angle is 90°, the sector represents 1/4 of a circle with a radius of 10 yd.

So, length of the safety rail is given by:

Where:

r = 10 yd

pi = 3.14

Substitute, we have:

The Answer is 15.7 yd

Next, area of the deck is given by:

Substitute the values:

The answer is 78.5 yd^2

Answer:

There is no photo to go off of

Step-by-step explanation:

Answer:

There isn't a photo so how we suppost to answer this..?

Step-by-step explanation:

In completing the square method, considering the equation X^2 - 5x = 6 the student should add 25 / 4 to both sides of the equation

The quadratic equation is an equation of the form

ax^2 + bx + c

The completing the square method is on of the methods of solving equations of the form above

The factor to be added on the both sides of the equation while using the completing the square method is

(b / 2a)^2

compared to the equation in the problem X^2 - 5x = 6 it is

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Answer:

x = 11 , CE = 98

Step-by-step explanation:

• If 2 chords are congruent, then they are equidistant from its centre , so

CE = FC , that is

10x - 12 = 8x + 10 ( subtract 8x from both sides )

2x - 12 = 10 ( add 12 to both sides )

2x = 22 ( divide both sides by 2 )

x = 11

Then

CE = 10x - 12 = 10(11) - 12 = 110 - 12 = 98

Answer:

I will solve each one and work from there:

A. 4(5-y) ≥80

     20-2y≥80

      -2y≥60

        y≥-30

B. 2(y-3) ≥ 8

    2y-6≥8

     2y≥14

     y≥7

c. 3y-4>1

   3y>5

     y>5/3

d.  -3/4 / 6y>1/4

      -3/4>1/4 x 6y

Notice how for each inequality it is y≥ or > abc

Although for d it is a number greater than 1/4 x 6y

Based off that i would assume that D is correct

Step-by-step explanation:

Answer:

Vertex: (-5,-4) Y-int: (0,21) X-int. = (-7,0), (-3,0)

Step-by-step explanation:

The digits missing from the equation are 100, 10 and 1 respectively. The solution has been obtained by using the concept of algebraic equation.

What is algebraic equation?

If a mathematical phrase has variables, constants, and algebraic operations, it is said to be "algebraic" (addition, subtraction, etc.). The expression must contain the equals sign and satisfy the algebraic equation.

We are given an expression as

3. 58 × 100[(3 × 1) + (5 × 0. 1) + (8 × 0. 01)] × 100

On multiplying, we get

= (3 × 100) + (5 × 10) + (8 × 1)

= 358

Hence, the digits missing from the equation are 100, 10 and 1 respectively.

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Answer:

Answer is A

Step-by-step explanation:

Hope it helps

In interval notation,  the interval of continuity of f(x) is (-∞, 2) ∪ (5, +∞)

A function is said to be continuous in an interval if all the values in the interval satisfy the function.

Since we have the function (x² - 4)/(x² - 7x + 10), we desire to find the interval in which it is continuous. So, we proceed as follows.

For the function f(x) = (x² - 4)/(x² - 7x + 10) to be continuous, then the denominator (x² - 7x + 10) ≠ 0

So, solving this inequality, we have

x² - 7x + 10 ≠ 0

x² - 2x - 5x + 10 ≠ 0

Factorizing, we have that

x(x - 2) - 5(x - 2) ≠ 0

(x - 2)(x - 5) ≠ 0

x - 2 ≠ 0or x - 5 ≠ 0

x ≠ 2 or x ≠ 5

Also, since the coefficient of x² is positive the function f(x) tends to ±∞.

So, the interval of continuity of f(x) is 2 < x and x > 5

So, the interval of continuity of f(x) is (-∞, 2) ∪ (5, +∞)

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The amount of the remittance from ABC is $1,960.

The given information states that merchandise is sold for $2,000 with terms of 2/10, n/30 to ABC. The terms 2/10, n/30 imply a 2% discount if payment is made within 10 days, with the full amount due within 30 days.

Since ABC sends a remittance on Dec. 26, it means the payment is made after the discount period but within the credit period. Therefore, ABC is not eligible for the discount of 2%.

To calculate the amount of the remittance, we simply subtract the discount from the total amount. In this case, the discount is $2,000 * 2% = $40. Thus, the remittance amount is $2,000 - $40 = $1,960.

In conclusion, the amount of the remittance from ABC is $1,960, as they did not qualify for the early payment discount.

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The price difference between the two brands when buying 700 g of hot chocolate is £0.85.

To find the difference in price between the two brands when buying 700 g of hot chocolate, we need to compare the prices per gram of each brand and calculate the total cost for 700 g.

Let's calculate the prices per gram for each brand:

Brand A: £2.65 for 140 g

Price per gram = £2.65 / 140 g = £0.01892857 per gram

Brand B: £3.10 for 175 g

Price per gram = £3.10 / 175 g = £0.01771429 per gram

Now, let's calculate the total cost for 700 g for each brand:

Brand A: £0.01892857 per gram * 700 g = £13.25

Brand B: £0.01771429 per gram * 700 g = £12.40

To find the difference in price, we subtract the cost of Brand B from the cost of Brand A:

£13.25 - £12.40 = £0.85

Therefore, the difference in price between the two brands when buying 700 g of hot chocolate is £0.85.

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On a test with a range of 110–410, these students received a mean score of 370 and a standard deviation of 50. What range would roughly 95% of the students' scores fall into, presuming a mound-shaped and symmetric distribution.

Any traits, figures, or amounts that may be gauged or counted are considered variables. Another name for a variable is a data item. Variables include things like age, sex, business income and expenses, birthplace, capital expenditures, class grades, eye color, and vehicle type.

A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, income, province of birth, school grades, and kind of dwelling. Categorical and numeric variables are the two basic types of variables that can be categorized.

The answers to the three shapes are:

Figure 7; perimeter = 16.2mm, area = 12.64 square mm

Figure 8; perimeter = 15.2inches, area = 9.61 square inches

Figure 9; perimeter = 21.47yards,  area = 16.81 square yards

Perimeter is the outside boundary of a plane shape.

Analysis:

for figure 7, perimeter = s + s + s = 3s = 3(5.4) = 16.2mm

                   Height of triangle = \(\sqrt{((5.4)^{2} - (2.7)^{2} }\) = 4.68

            Area of triangle = 1/2 base x height = 1/2 x 5.4 x 4.68 = 12.64\(mm^{2}\)

For figure 8, perimeter = b + b + a = 5.9 + 5.9 + 3.4 = 15.2 inches

                     Height of triangle = \(\sqrt{(5.9)^{2} - (1.7)^{2} }\) = 5.65inches

           Area of triangle = 1/2 base x height = 1/2 x 3.4 x 5.65 = 9.61\(inches^{2}\)

For figure 9, perimeter = b + a + c = 8.2 + 4.1 + 9.17 = 21.47yards

           Area of triangle = 1/2 x base x height = 1/2 x 8.2 x 4.1 = 16.81\(yards^{2}\)

In conclusion, the perimeter and area of the given shapes are:

Figure 7; perimeter = 16.2mm, area = 12.64 square mm

Figure 8; perimeter = 15.2inches, area = 9.61 square inches

Figure 9; perimeter = 21.47yards,  area = 16.81 square yards

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The average velocity over the given time intervals:

[4, 5] = 37.53 m/s

[4, 4.5] = 37.945 m/s

[4, 4.1] = 38.277 m/s

[4, 4.01] = 38.36 m/s

[4, 4.001] = 38.4 m/s

Speed ​​is the ratio of the displacement of an object to the time it has traveled. Speed ​​is a vector quantity with units such as km/hour, m/minute, m/second, and others.

The speed formula is v = S/t, with the following description.

v is velocity/speed (m/s).

S is the distance/displacement (m).

t is the time(s).

The distance (s) can be calculated using the formula S = v x t, the formula for time is t = S/v, which is distance divided by speed. While the average speed is defined as the displacement traveled within a certain time interval.

The average velocity formula can be written like this v = ∆x / ∆t with the following information.

v is the average speed (m/s-1).

∆x is the final-initial displacement (m).

∆t is the change in the end-start time (seconds)

From the formula above we can calculate the average speed.

time intervals.

h(t) = 45t – 0. 83t²

a. [4, 5]

v = ∆h / ∆t

\(=\frac{h_2-h_1}{t_2-t_1}\)

\(=\frac{(45\times 5-0.83(5)^2)-(45\times 4-0.83(4)^2)}{5-4}\)

\(=\frac{(225-20.75)-(180-13.28)}{1}\)

= 204.25 - 166.72

= 37.53 m/s

b. [4, 4.5]

v = ∆h / ∆t

\(=\frac{h_2-h_1}{t_2-t_1}\)

\(=\frac{(45\times 4.5-0.83(4.5)^2)-(45\times 4-0.83(4)^2)}{4.5-4}\)

\(=\frac{(202.5-16.8075)-(180-13.28)}{0.5}\)

\(=\frac{185.6925-166.72}{0.5}\)

\(=\frac{18.9725}{0.5}\)

= 37.945 m/s

c. [4, 4.1]

v = ∆h / ∆t

\(=\frac{h_2-h_1}{t_2-t_1}\)

\(=\frac{(45\times 4.1-0.83(4.1)^2)-(45\times 4-0.83(4)^2)}{4.1-4}\)

\(=\frac{(184.5-13.9523)-(180-13.28)}{0.1}\)

\(=\frac{170.5477-166.72}{0.1}\)

\(=\frac{3.8277}{0.1}\)

= 38.277 m/s

d. [4, 4.01]

v = ∆h / ∆t

\(=\frac{h_2-h_1}{t_2-t_1}\)

\(=\frac{(45\times 4.01-0.83(4.01)^2)-(45\times 4-0.83(4)^2)}{4.01-4}\)

\(=\frac{(180.45-13.3464)-(180-13.28)}{0.01}\)

\(=\frac{167.1036-166.72}{0.01}\)

\(=\frac{0.3836}{0.01}\)

= 38.36 m/s

e. [4, 4.001]

v = ∆h / ∆t

\(=\frac{h_2-h_1}{t_2-t_1}\)

\(=\frac{(45\times 4.001-0.83(4.001)^2)-(45\times 4-0.83(4)^2)}{4.001-4}\)

\(=\frac{(180.045-13.2866)-(180-13.28)}{0.001}\)

\(=\frac{166.7584-166.72}{0.001}\)

\(=\frac{0.0384}{0.001}\)

= 38.4 m/s

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Answer:

C

Step-by-step explanation:

Answer:

5x +9+2x+6+4x

=5x+2x+4x+9+6

=11x+15

Answer C

Answer:

Rearrange your equation

5x + 2x + 4x + 9+6

Add the like term of the equation

( 5x + 2x + 4x ) + (9+6)

11x + 15

Answer: 96

Multiply

3×6×7=126

2.5×4=10

(3)(-10)

Subtract

126-30=96

Answer:

96.

Step-by-step explanation:

Using order of operations:-  we deal with the parentheses first:

3 * (6 * 7 - 2.5 * 4)  Multiplying before the subtract in the parentheses:

= 3 * (42 - 10)       Now do the subtraction in the parentheses:

= 3 * 32

= 96.

Answer:One minute let me find a answer

Step-by-step explanation:

Answer:

the first option

Step-by-step explanation:

Answer: x < 4

Step-by-step explanation: To plot an inequality, find the number and go the way the sign is pointing.

In this problem...

The less than sign is pointing left, and the number is 4. We use an open circle because the sign is not equal to. If it was, we would of put a closed circle.

<, or > = Open circle (Not shaded)

≤, or ≥ = Closed circle (Shaded)

I attached a image to proof the answer is correct.

Let me know if you have any questions.

~ Lily, from Brainly.

The one-sample z-statistic for evaluating the hypothesis that unvaccinated people get COVID-19 is not 0.03 is -85.7. This statistic tested the hypothesis that unvaccinated people do not get COVID-19 at 0.03%.

In order to compute the one-sample z-statistic, we must first do a comparison between the observed proportion of COVID-19 instances in the placebo group and the expected proportion of 0.03. (p - p0) / [(p0(1-p0)) / n is the formula for the one-sample z-statistic. In this formula, p represents the actual proportion, p0 represents the predicted proportion, and n represents the sample size.

The observed proportion of COVID-19 instances among those who received the placebo is 162/18325 less than 0.0088. According to the received wisdom, the proportion that should be anticipated is 0.03. The total number of people sampled is 18325. After entering these numbers into the formula, we receive the following results:

z = (0.0088 - 0.03) / √[(0.03(1-0.03)) / 18325] ≈ (-0.0212) / √[(0.0291) / 18325] ≈ -85.7

As a result, the value of the z-statistic for just one sample is about -85.7. This demonstrates that the observed proportion of COVID-19 cases in the unvaccinated population is significantly different from the expected proportion of COVID-19 cases in that population.

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The design that resulted in the shortest line is the one that minimized the distance between the start and end points.

This can be achieved by using a straight line design, as it is the shortest distance between two points. In other words, the shortest line design is the one that does not have any curves or detours, and instead goes directly from the start point to the end point. This is because the shortest distance between two points is always a straight line, and any other design would result in a longer line. Therefore, the design that resulted in the shortest line is the one that used a straight line.

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We can solve this problem using a system of linear equations, have in mind the expression for simple interest:

Let x be the principal invested on the first account.

Let y be the principal invested on the second account.

We can solve the system by the method of substitution, isolate the variable y in equation (1):

Now, substitute (1) into equation (2) to get x-value:

Austin invested $16,000 on the first account.

Then, substitute the x-value in the equation (1) to get y-value:

Austin invested $14,000 on the second account.

Answer:

20

Step-by-step explanation:

Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.

And 18+3... 21, that is smaller than 21.

If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.

Answer:

It’s a.

Step-by-step explanation:

Plus have this...

YOU MATTER, BE YOU, don’t let anyone tell you otherwise. You are beautiful/handsome. You are one of a kind. you are here for a reason, be the reason someone lives today!

Spread this message of hope because I may need it but others need it most!

For every message like this I see I will give out 20 free points and if you put this on my questions I will give you more points. have a nice day!

The equation of the line from the given figure is y=-7.

We need to find the equation of the line from the given figure.

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x and y to form an algebraic equation, which is referred to as an equation of a line.

From the given figure, we can see that the line is passing through the point (0, -7).

The slope (m) of the line is 0.

Put m=0 and (0, -7) in y=mx+c and simplify.

That is, -7=c

Now, substitute c=-7 in y=mx+c.

Thus, y=-7

Therefore, the equation of the line from the given figure is y=-7.

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The difference quotient for the function is 8.

The function is given by:

f ( x ) = 8 x − 9, where h ≠ 0

To find f(a), substitute a for x in the function. So we have:

f ( a ) = 8 a − 9

To find f(a + h), substitute a + h for x in the function. So we have:

f ( a + h ) = 8 ( a + h ) − 9

The difference quotient can be found using the formula:

(f(a + h) - f(a))/h

Substituting the values found above, we have:

(8 ( a + h ) − 9 - (8 a − 9))/h

Expanding the brackets and simplifying, we have:

((8a + 8h) - 9 - 8a + 9)/h

= 8h/h

= 8

Therefore, the difference quotient for the function is 8.

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