1. Illustrate an exterior angles
of a triangle and Name all the
exterior angles.


PLS NEED ANSWER ASAPPP

It is observed that the identity cos(a - B) and cos a cos B - sin a sin B are equal.

Trigonometric Identities are equality statements that use trigonometry functions and hold true for all values of the variables in the equation. There are numerous distinct trigonometric identities that relate to the side length and angle of a triangle.

We can use the identity for the cosine of a difference of two angles:

cos(a - B) = cos a cos B + sin a sin B

If we expand the right-hand side of this identity using the product-to-sum identities, we get:

cos a cos B + sin a sin B = cos a cos B + (cos a sin B)(sin a cos B) - (sin a sin B)(cos a cos B)

= cos a cos B - sin a sin B cos a cos B + cos a sin B sin a cos B

= cos a cos B - sin a sin B (cos^2 B + sin^2 B)

= cos a cos B - sin a sin B

We can see that this is the same as the expression cos a cos B - sin a sin B, which can be written as cos a cos B - sin a sin B = cos(a - B).

Therefore, we notice that cos(a - B) and cos a cos B - sin a sin B are equal.

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Answer:

it's electromagnetic radiatum

The length of the third side of the triangle, to the nearest hundredth, is approximately 54.75 units.

1. We have a triangle with two known side lengths: 43 and 67 units.

2. The angle included between these sides measures 27 degrees.

3. To find the length of the third side, we can use the Law of Cosines, which states that \(c^2 = a^2 + b^2\) - 2ab * cos(C), where c is the third side and C is the included angle.

4. Plugging in the known values, we get \(c^2 = 43^2 + 67^2\) - 2 * 43 * 67 * cos(27).

5. Evaluating the expression on the right side, we get \(c^2\) ≈ 1849 + 4489 - 2 * 43 * 67 * 0.891007.

6. Simplifying further, we have \(c^2\) ≈ 6338 - 5156.898.

7. Calculating \(c^2\), we find \(c^2\) ≈ 1181.102.

8. Finally, taking the square root of \(c^2\), we get c ≈ √1181.102 ≈ 34.32.

9. Rounding to the nearest hundredth, the length of the third side is approximately 34.32 units.

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Answer:

176.3

Step-by-step explanation:

have a nice day! :D.

first one:

Let's simplify the expression step by step:

4(a+5) - 5(a^2-4a+7)

= 4a + 20 - 5a^2 + 20a - 35 (distributing the 4 and -5)

= -5a^2 + 24a - 15 (combining like terms 4a and 20a, and combining 20 and -35)

So the simplified expression is -5a^2 + 24a - 15.

second one:

3(c-4) - 5(c^2+4c-8)

= 3c - 12 - 5c^2 - 20c + 40 (distributing the 3 and -5)

= -5c^2 - 17c + 28 (combining like terms 3c and -20c, and combining -12 and 40)

So the simplified expression is -5c^2 - 17c + 28.

Answer:

1. -5a^2+24a-15

2. -5c^2-17c+28

Step-by-step explanation:

1.

Distribute: 4a+20-5a^2+20a-35

Subtract the numbers: 4a-15-5a^2+20a

Combine like terms: 24a-15-5a^2

Rearrange terms: -5a^2+24a-15

2.

Distribute: 3c-12-5c^2-20c+40

Add the numbers: 3c+28-5c^2-20c

Combine like terms: -17c+28-5c^2

Rearrange terms: -5c^2-17c+28

Hope this helped!!!

Good luck!!!

Answer:

7 + 1 + 1 + 1 = 10

Step-by-step explanation:

This question is not very clear as to what is required, or any possible limitations. One possible solution is listed below, hope it does help.

Using the numbers 1, 6, and 7, you can get the number 10 through the following equation:

7 + 1 + 1 + 1 = 10

By adding 7 with three instances of 1, you obtain 10.

Answer: step by step

Step-by-step explanation:

not totally sure what you're asking but in this equation p=2

Option (C) is the correct choice. The distance from the bottom of the building to the point where the ladder is touching the building for triangle is 15 feet.

Distance of ladder 1 touching the building from its base i.e., 27 feet.

Distance from base of building and ladder 1 touching ground is 18 feet.

The distance, along the ground, from the bottom of the ladder to the building is 10 feet.

=> similarly, for ladder 2 = let us take it as x feet.

10 feet for ladder 2.

Therefore,

\(\frac{27}x} =\frac{18}{10}\)

270 =18x

x = 270/18

x = 15feet is the distance from the bottom of the building to the point where the ladder is touching the building for triangle.

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Answer:

(x - 3)² + (y + 3)² = 9

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

the radius r is the distance from the centre to a point on the circle.

given (3, - 3 ) is the centre and (3, 0 ) is a point on the circle

since the x- coordinates of both points are 3 then r is the absolute value of the difference of the y- coordinates, that is

r = | - 3 - 0 | = | - 3 | = 3

then equation of circle is

(x - 3)² + (y - (- 3) )² = 3² , that is

(x - 3)² + (y + 3)² = 9

Answer:

\(Change = \$8.82\)

Step-by-step explanation:

Given

\(Basketball = \$25.57\)

\(Air\ Pump = \$15.61\)

\(Amount = \$50\)

Required

Determine the change received

First, we need to calculate the total amount spent

\(Total = \$25.57 + \$15.61\)

\(Total = \$41.18\)

This implies that Natalie pays a total of $41.18

Next, we calculate the change as thus:

\(Change = Amount - Total\)

\(Change = \$50 - \$41.18\)

\(Change = \$8.82\)

Hence, the change is $8.82

Answer:

y=7/3x

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-7-0)/(-3-0)

m=-7/-3

m=7/3

y-y1=m(x-x1)

y-0=7/3(x-0)

y=7/3(x)

y=7/3x

Equation of the line through (0,0) and (-3,-7) is y=7/3x

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We need to find the equation of the line through (0,0) and (-3,-7)

m=-7/-3=7/3

Now let us find the y intercept

-7=7/3(-3)+b

b=0

So the equation is y=7/3x

Hence, equation of the line through (0,0) and (-3,-7) is y=7/3x

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Answer:

$85.60

Step-by-step explanation:

In this question, we need to find the price of the calculator after tax.

We know the cost of the calculator is $80 and the sales tax is 7%

To find your answer, we would multiply 80 by 1.07:

80 · 1.07 = 85.60

The total cost of the calculator is $85.60

After 10 years with a Compound interest rate of 1.9%, the amount in Carrie's account will be approximately $1777.87.

The amount that will be in Carrie's account after 10 years with compound interest, we can use the formula Pt = P0 ⋅ (1 + r)^t.

Given:

P0 = $1480 (initial deposit)

r = 1.9% = 0.019 (interest rate as a decimal)

t = 10 (number of years)

Substituting these values into the formula, we get:

Pt = $1480 ⋅ (1 + 0.019)^10

Using a calculator, we can evaluate the expression inside the parentheses:

(1 + 0.019)^10 ≈ 1.201223

Now we can calculate the final amount in Carrie's account:

Pt ≈ $1480 ⋅ 1.201223

Pt ≈ $1777.87

Therefore, after 10 years with a compound interest rate of 1.9%, the amount in Carrie's account will be approximately $1777.87.

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Using the binomial distribution, we have that:

a) 0.1024 = 10.24% probability that the marketing representative must select 4 people to find one who attended the last home football game.

b) 0.2621 = 26.21% probability that the marketing representative must select more than 6 people to find one who attended the last home football game.

c) The expected number of people is 4, with a variance of 20.

For each person, there are only two possible outcomes. Either they attended a game, or they did not. The probability of a person attending a game is independent of any other person, which means that the binomial distribution is used.

Binomial probability distribution  

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)  

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

The expected number of trials before q successes is given by:

\(E = \frac{q(1-p)}{p}\)

The variance is:

\(V = \frac{q(1-p)}{p^2}\)

In this problem, 0.2 probability of a finding a person who attended the last football game, thus \(p = 0.2\).

Item a:

Thus:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{3,0}.(0.2)^{0}.(0.8)^{3} = 0.512\)

\(0.2(0.512) = 0.1024\)

0.1024 = 10.24% probability that the marketing representative must select 4 people to find one who attended the last home football game.

Item b:

This is the probability that none of the first six went, which is P(X = 0) when n = 6.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{6,0}.(0.2)^{0}.(0.8)^{6} = 0.2621\)

0.2621 = 26.21% probability that the marketing representative must select more than 6 people to find one who attended the last home football game.

Item c:

The expected value is:

\(E = \frac{q(1-p)}{p} = \frac{0.8}{0.2} = 4\)

The variance is:

\(V = \frac{0.8}{0.04} = 20\)

The expected number of people is 4, with a variance of 20.

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The value of a is 5/9 if  y = a(x - 2)(x + 6) and (3,5) is a point on the graph.

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

It is given that:

A quadratic relation has the equation y= a(x - s )(x – t).

y = a(x - 2)(x + 6) and (3,5) is a point on the graph

Plug x = 3 and y = 5

5 = a(3 - 2)(3 + 6)

a = 5/9

The parabola has zeros of 4 and -2 and a y-intercept of 1

y= a(x - s )(x – t)

0= a(4 - s )(4 – t)

0= a(-2 - s )(-2 – t)

1= a(0 - s )(0 – t)

No solution.

Similarly, it can find the equation of the parabola in the remaining part,

Thus, the value of a is 5/9 if  y = a(x - 2)(x + 6) and (3,5) is a point on the graph.

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Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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Answer:

Step-by-step explanation:

X: -2, -1, 0, 1, 2,...

Y: -2, -1, 0, 1, 2,...

(y=x)

Answer:

\( - 8(45) + 482 = - 360 + 482 = 122\)

Answer:

Length of each side of regular hexagon = 19 inches

Step-by-step explanation:

When the length of all sides is equal and measure of all angles is equal . it is known as Regular hexagon. In a regular hexagon, each inside angle is 120 degrees.

Perimeter of Regular hexagon = 6a

where a is each side of regular hexagon

According to the given information

Perimeter of regular hexagon = \(\frac{342}{3}\)

                                                  = 114 inches

Perimeter of regular hexagon = 6a

                                          114   = 6a

                                           19   =  a

Length of each side of regular hexagon = 19 inches

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Answer:

\(\boxed{\sf x = 80}\)

Step-by-step explanation:

A quadrilateral inscribed in a circle has opposite sides equal to 180.

So,

x + x + 20 = 180

2x + 20 = 180

Subtracting 20 from both sides

2x = 180 - 20

2x = 160

Dividing both sides by 2

x = 80

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▹ Answer

x = 80

▹ Step-by-Step Explanation

x + x + 20 = 180

2x + 20 = 180

2x = 180 - 20

2x = 160

x = 80

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

Answer:

Explanation:

The period of the given sinusoidal wave for the shown graph is 10, as the wave is repeating its values after 10 units.

The most common way that many things change state in nature is represented by a sine wave or sinusoidal wave. A sine wave demonstrates how a variable's amplitude fluctuates over time.

Thus, the period of the given sinusoidal wave for the shown graph is 10, as the wave is repeating its values after 10 units.

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Answer:

student loan

Step-by-step explanation:

read then re read

Answer:

student loan

Step-by-step explanation:

its college

Answer: Turtle Camera

Step-by-step explanation:

The Turtle is the closest to 0, at around 5. Everything else is higher.

Hope that helped,

-sirswagger21

P.S. Please mark this as brainliest answer, it would help a lot!

Relative to sea level, turtle camera is the highest.

A fraction that has the numerator higher than or equal to the denominator is said to be an improper fraction.

Given:

The table lists the locations of four underwater cameras relative to sea level.

Dolphin camera = -12.33 feet.

Fish camera = -15.33 feet.

Manatee camera = -8.5 feet.

Turtle camera = -5.5 feet.

That means, the turtle camera is highest.

Therefore, turtle camera is highest.

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Answer:

number7 9452.425 and number 4 2 hrs

Step-by-step explanation:

85+15 is 100 so to get one hundred percent you alr have 85 but you need to find 15

find what 30percent of 400 it is 120 if hes going 60 mph:

120/60 is 2

so it took him 2 hrs