2. (5 pts) An angle, A, is 11 times larger than its supplement, B. Find the angles (be sure to say which is which).

The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

For more such questions on length

https://brainly.com/question/2217700

#SPJ8

Answer:

im just trying to get points im sorry

Step-by-step explanation:

The solution to the given polynomial in their degree are:

2a + 4a³ - 5a² - 1

= 4a³ - 5a² + 2a - 1

The leading coefficient is 4a³

4z - 2z² - 5z⁴

= -5z⁴ - 2z² + 4z

The leading coefficient is -5z⁴

(-3d² - 8 + 2d) + (4d - 12 + d²)

= -3d² - 8 + 2d + 4d - 12 + d²

= -2d² + 6d - 20

(y + 5) + (2y + 4y² - 2)

= y + 5 + 2y + 4y² - 2

= 4y² + 3y + 3

Learn more about polynomial:

https://brainly.com/question/4142886

#SPJ1

Answer:

269.75

Hope this helps:)

Step-by-step explanation:

Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

For more such questions on GCF

https://brainly.com/question/902408

#SPJ8

Considering the definition of a line, the equation of the line that passes through the point (-10, -1) and has a slope of -1/5 is

A linear equation o line can be expressed in the form y = mx + b

where

In this case, you know:

Substituting the value of the slope in the expression of a linear equation, y = mx + b, the line has the form: y=-1/5x + b

Replacing the value of the point in the expression of a linear equation, the value of the ordinate to the origin b can be obtained:

-1= -1/5×(-10) + b

-1= 2 + b

-1 -2= b

-3= b

Finally, the equation of the line is y= -1/5x -3.

Learn more about equation of a line:

brainly.com/question/20842634

#SPJ1

Answer:

E and F

Step-by-step explanation:

✔️To eliminate the variable y, we can multiply the first equation, -x + 4y = 1 by 7 and the second equation, 8x - 7y = 42 by 4. This will leave us with the variable x alone to solve for.

✔️Alternatively, we may decide to eliminate the variable x first by multiplying the first equation, -x + 4y = 1 by 8. Both equations would be equivalent, thus when we can easily eliminate the variable x leaving us with variable y to solve for.

The required reverse Euclidean algorithm is the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

Given that (5*x) mod 91 =32.

To solve the modular equation (5*x) mod 91 =32 using reverse Euclidean algorithm is to find the modular inverse of 5 modulo 91.

Consider  (5*x) mod 91 =32.

5x = 32(mod 91)

Apply the Euclidean algorithm to find GCD of 5 and 91 is

91 = 18 * 5 + 1.

Rewrite it in congruence form,

1 = 91 - 18 *5

On simplifying the equation,

1 = 91 (mod 5)

The modular inverse of 5 modulo 91 is 18.

Multiply equation by 18 on both sides,

90x = 576 (mod91)

To obtain the smallest positive  solution,

91:576 = 6 (mod 91)

Divide both sides by the coefficient of x:

x = 6 * 90^(-1).

Apply the Euclidean algorithm,

91 = 1*90 + 1.

Simplify the equation,

1 + 1 mod (90)

The modular inverse of 90 modulo 91 is 1.

Substitute the modular inverse in the given question gives,

x = 6*1(mod 91)

x= 6 (mod91)

Therefore, the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

Learn more about modular equation click here:

https://brainly.com/question/15055095

#SPJ1

Answer:

511121.09784 <33

Step-by-step explanation:

Calculator :)

556775.55444 - 45654.4566 = 511121.09784

Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].

To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).

The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.

In other words, the range of f(x) is (-∞, 5].

So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.

Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.

For such more questions on range

https://brainly.com/question/30389189

#SPJ8

Median = 6

Q₁ or first quartile = 4

Q₂ or third quartile = 8

Smallest data point  = 2

Maximum data point = 11

Box plots draw boxes from the first quartile to the third quartile. At the median, a vertical line passes through the box. The whiskers move from each quartile to the minimum or maximum.

The given numbers are: 2 , 3 ,5, 6 , 7 , 8 ,11

Number of terms = 9

Middle term = 9 + 1 / 2 = 5th term =7

The first quartile is the median of the data points to the left of the median.

2,3,5,6,

Number of Terms = 4

Median = 3 + 5 /2

             = 4th term = 6

The smallest data point is 2 and the largest data point is 11 .

Learn more about Quartile:

https://brainly.com/question/24329548

#SPJ4

Answer:

The answer is 17

Step-by-step explanation:

-15-2= -17

9514 1404 393

Answer:

  (c)  Not parallel: corresponding angles are not congruent

Step-by-step explanation:

The two angles shows are both "east" of the respective points of intersection, so are "corresponding" angles. If (and only if) lines r and s are parallel, corresponding angles are congruent. These angles have different measures, so lines r and s are not parallel.

hello

to solve for x, we have to simplify this equation

step one

collect like terms

step two

cross multipy both sides

step three

divide both sides by the coefficient of x

from the calculation above, the value of x is equal to 9

The area of ΔEFG is approximately 916 square centimeters.

Given that,

In ΔEFG

f = 88 cm ,

g = 18 cm

∠E=68°

To find the area of ΔEFG,

Use the formula:

Area = (1/2)xfxgxsin(∠E)

First, we need to convert the angle from degrees to radians.

We can do this by multiplying by π/180.

∠E = 68° * π/180 ≈ 1.19 radians

Next, we can plug in the values we have:

Area = (1/2)x88x18xsin(1.19)

        ≈ 915.56 cm²

Rounding this to the nearest square centimeter,

we get,

Area ≈ 916 cm²

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

Answer: (√2)(2) = 2√2

Step-by-step explanation:

To simplify the expression 3√2 - √2, you can factor out the common term √2:

3√2 - √2 = (√2)(3 - 1)

Now, subtract the numbers in parentheses:

(3 - 1) = 2

(√2)(2) = 2√2

Answer:

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle. In this case, the diameter is given as 14 cm, so we can substitute that into the formula:

C = π(14 cm)

Multiplying, we get:

C = 14π cm

So the circumference of the circle is 14π cm. The units are centimeters, since circumference is a length measurement.

The acceleration of the car is 8 m/s^2.

The figure shown in the question is the distance-time graph of a muscle car accelerating from a standstill. The table lists the coordinates of points on the graph.The following observations can be made from the graph and the table: The car is at rest at time t=0 and at distance x=0. It then starts accelerating, and its speed increases uniformly with time. The slope of the distance-time graph is the velocity of the car.

Since the velocity is increasing uniformly, the slope of the graph is a straight line with a positive slope. The area under the graph between two points gives the displacement of the car during that time interval. The displacement can be calculated as the product of the average velocity and the time interval. Using the coordinates in the table, we can calculate the average velocities for each time interval and the displacement during that interval.

(a) The average velocity of the car between t=0 and t=2 is equal to the slope of the graph between the two points (0,0) and (2,32). This can be calculated as the difference in distance divided by the difference in time:Average velocity = (32 - 0) / (2 - 0) = 16 m/sThe displacement during this time interval is given by the area under the graph between the two points:Displacement = (1/2) x 32 x 2 = 32 m

(b) The acceleration of the car is given by the slope of the velocity-time graph. Since the velocity is increasing uniformly with time, the velocity-time graph is also a straight line with a positive slope. The slope of the velocity-time graph is equal to the acceleration. We can calculate the slope of the velocity-time graph between two points using the coordinates in the table. For example, the slope between t=0 and t=2 is given by the difference in velocity divided by the difference in time:Slope = (16 - 0) / (2 - 0) = 8 m/s^2

for more search question acceleration

https://brainly.com/question/30595126

#SPJ8

\(\huge\blue{\mid{\fbox{\tt{\:ANSWER\:}}\mid}}\)

____________________

The graph,

Answer:

8483 ft²

Step-by-step explanation:

Subtract the area of the smaller circle from the area of the greater circle

Greater Circle area:

πr² = π × 140²

= 61583.2 ft²

Smaller Circle area:

= π × 130²

= 53099.8 ft²

Area of track:

61583.2 - 53099.8 = 8483.4ft²

= 8483ft² (to the nearest ft²)

Given:

There are given that the triangle, ABC.

Where:

Explanation:

According to the question, we need to prove that the isosceles triangle:

So,

From the concept of the isosceles triangle:

The isosceles triangle is defined when two sides of the length of any triangle are equal.

Then,

First, we need to find the length of the sides by using the distance formula:

So,

Then,

And,

Final answer:

Hence, the step and values of the sides are shown below;

And,

The side CA and AB is congruence by the definition of h

And,

Triangle ABC is an isosceles triangle by the the defination of b.

Answer:

Hello There!

According to the question,

Base=6

And

Height =4

Let's know the formula

\( \frac{1}{2} \times base \times height \\ so \\ \frac{1}{2} \times 6 \times 4 \\ \)

simplify 2 with 6 then it will look like this

\( \frac{1}{1} \times3 \times 4 \\ \\ \)

1 has no value so

\(3 \times 4 = 12 {ft}^{2} \\ \)

So third option

\(a = 12 {ft}^{2} \)

is correct.

\(\Large\textsf{Hope \: It \: Helped}\)

Answer:

Area = 12 sq ft

Step-by-step explanation:

The formula to find the area of a triangle is

1/2 bh so we will replace the letters with their number value

1/2 (6x4)

1/2 x 24 = 12

So, 12 is your answer!

Nate has a deductible of $1,000, which means he is responsible for paying that amount out of pocket before his insurance coverage kicks in. The cost of repairing his car is $7,000, which exceeds his deductible.

However, Nate's collision coverage limit is $5,000, which is the maximum amount his insurance will cover for repairs.

Since the cost of repairs exceeds Nate's coverage limit, he will have to pay the difference between the coverage limit and the actual repair cost.

In this case, Nate's out-of-pocket expenses would be $7,000 (repair cost) - $5,000 (coverage limit) = $2,000.

Therefore, Nate will have to pay a total of $2,000 out of pocket for this claim, which includes his $1,000 deductible and the additional $1,000 that exceeds his coverage limit.

For such more question on collision

https://brainly.com/question/7221794

#SPJ8

Answer:

Step-by-step explanation:

The vertex is at (-3, -1)  and the leading coefficient is negative ( because  the curve is inverted)

y = -a(x + 3)^2 - 1

One point on the curve is (-2, -3) so

-3 = -a(-2+3)^2 - 1

-3 = -a - 1

-a = -2

So we have

y = -2(x + 3)^2 -  1

y = -2(x^2 + 6x + 9) - 1

y = -2x^2 - 12x - 19.

Answer:

a = 2500mm

b = 5km

c = 2e+7

Step-by-step explanation:

Answer:

a)

1cm = 10mm

250cm = 250*10 = 2500mm

b)

1km = 1000m

5000m = 5000/1000 = 5km

c)

1km = 1000m

1m = 100cm

1km = 1000*100 = 100000cm

200km = 200*100000 = 20000000cm

Answer:

If Susie makes $10.25 an hour, and makes time and a half for overtime, she would make $410 from regular time. If she works 5 hours of overtime, she would make $76.90.

$410+$76.90=$486.90

In total, she would make $486.90.

To rewrite the expression -2(n-7) using the distributive property, we need to distribute the -2 to both terms inside the parentheses. The distributive property states that for any numbers a, b, and c:

a(b + c) = ab + ac

Applying this property to the given expression:

-2(n-7) = -2 * n + (-2) * (-7)

Simplifying further:

-2(n-7) = -2n + 14

Therefore, the rewritten expression is -2n + 14.

Answer:

Step-by-step explanation:

The current endpoints are ...

  V = (-9, 2)

  W = (-3, 6)

Put each of these in the translation formula to see where the image points are.

  (x, y) ⇒ (x+5, y-1)

  (-9, 2) ⇒ (-9+5), 2-1) = (-4, 1) . . . . point V ⇒ V'

  (-3, 6) ⇒ (-3+5, 6-1) = (2, 5) . . . . . point W ⇒ W'

The new end points are (-4, 1) and (2, 5), matching choices A and B.

option D 3,125!/(3,125-10)! is the correct expression, because it represents the number of ways to choose 10 people from a group of 3,125 people (without regard to order) and accounts for the fact that each person can win only once.

A. (3,125-10)!/3,125! is not the correct expression, because this would represent the number of ways that 10 people can be chosen from a group of 3,115 people (without regard to order) and doesn't account for the fact that each person can win only once.

B. (3,125-10)! 10!/3,125! is also not the correct expression, because this is the number of ways to choose 10 people out of 3,115 and then arrange them in a specific order of 10 gift cards, and this doesn't account that each person can win only once.

C. (3,125)!/(3,125-10)!10! is also not the correct expression, because this represents the number of ways to arrange 3,125 people, regardless of the fact that only 10 can win, and this doesn't account for the fact that each person can win only once.

Therefore, the correct expression is D. 3,125!/(3,125-10)!

To learn more about the expression:

https://brainly.com/question/1859113

#SPJ4

It is important to note that representativeness is not solely determined by the sampling method. Other factors, such as the size of the population

To determine whether the sample is likely to be representative of the population of her patients if she selects every third name on the list, we need to consider the characteristics of the population and the potential bias introduced by the sampling method.

Sampling every third name on the list is a form of systematic sampling, where every kth element is selected from the population. This method can introduce bias if there is a pattern or regularity in the list that aligns with the characteristic of interest. In this case, if there is a pattern in the list that correlates with the patients' characteristics, selecting every third name may not result in a representative sample.

For example, if the list is arranged in alphabetical order by last name, and there is a correlation between patients' last names and their medical conditions, then selecting every third name could introduce bias. It may result in an overrepresentation or underrepresentation of certain conditions depending on the distribution of last names.

To determine the representativeness of the sample, we need to assess whether the sampling method is likely to introduce systematic bias or if the list is randomly ordered. If the list is randomly ordered and there is no known correlation between the order of the list and the patients' characteristics, selecting every third name may provide a representative sample.

However, it is important to note that representativeness is not solely determined by the sampling method. Other factors, such as the size of the population, the specific characteristics of interest, and the variability within the population, also play a role.

To make a definitive assessment of the representativeness of the sample, further information about the list and the population would be needed. Without such information, it is challenging to determine whether selecting every third name on the list would result in a representative sample of the population of her patients.

for more such question on size visit

https://brainly.com/question/19429649

#SPJ8