Solve for an angle in right triangles
Please help! Thank you!

3. -x + 2 < 3x - 6

=3x +x < 2 + 6

=4x < 8

=x > 8/4

=x > 2

4. 3v - 12 > 5v + 10

= 5v-3v > 10+12

=2v > 22

= v < 22/2

=v < 11

The possible lines indicates that the slopes of the lines are;

\(\begin{tabular}{ | c | c | }\cline{1-2}Line& Slope\\ \cline{1-2}A & -1/3 \\\cline{1-2}B & -1\\\cline{1-2}C & -5/4 \\\cline{1-2}\end{tabular}\)

The slope m of a line with coordinate points (x₁, y₁), (x₂, y₂) is; m = (y₂ - y₁)/(x₂ - x₁).

The possible coordinate points on the lines, obtained from a similar question on the internet are;

Line A; (2, 6), (8, 4)

Line B; (-5, 7), (1, 1)

Line C; (-6, -3), (-2, -8)

The slopes of the lines can be found using the formula for the slope of a line, which can be presented as follows;

The slope of line A = (4 - 6)/(8 - 2) = -2/6 = -1/3

The slope of line B = (1 - 7)/(1 - (-5)) = -6/6 = -1

The slope of line C = (-8 - (-3))/(-2 - (-6)) = -5/4

Please find attached the drawing of the lines, obtained from a similar question on the internet created with MS Excel

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Answer:

Answer and Explanation: Given polynomial expression is: (5x2+3x−5)−(x2 −6x−4) ( 5 x 2 + 3 x − 5) − ( x 2 − 6 x − 4).

Step-by-step explanation:

Answer:

25x^2 -20x +4

Step-by-step explanation:

(5x-2)^2

FOIL

(5x-2)(5x-2)

25x^2 -10x -10x +4

25x^2 -20x +4

The missing measures for the triangle are given as follows:

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

\(\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}\)

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle B is obtained as follows:

m < B + 81 + 33 = 180

m < B = 180 - 114

m < B = 66º.

Then the relation is:

26/sin(81º) = a/sin(33º) = b/sin(66º).

Then the value of a is obtained as follows:

26/sin(81º) = a/sin(33º)

a = 26 x sine of 33 degrees/sine of 81 degrees

a = 14.3.

The value of b is obtained as follows:

26/sin(81º) = b/sin(66º)

b = 26 x sine of 66 degrees/sine of 81 degrees

b = 24.

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To find the constant, k, for the growth formula y = 350cht, we can use the given information about the growth of bacteria. We are given that the bacteria population grows from 350 to 2000 in 1.5 hours.

Let's substitute the given values into the growth formula:

2000 = 350 * e^(k * 1.5)

To solve for k, we need to isolate it on one side of the equation. We can divide both sides of the equation by 350:

2000/350 = e^(k * 1.5)

5.714 = e^(1.5k)

Next, we take the natural logarithm of both sides of the equation to eliminate the exponential function:

ln(5.714) = ln(e^(1.5k))

ln(5.714) = 1.5k

Finally, we can solve for k by dividing both sides of the equation by 1.5:

k = ln(5.714)/1.5

Calculating this value will give us the constant, k, for the growth formula.

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To find the office hours for a specific Pro Guide, users can visit the Pro Guides website and navigate to the "Contact Us" or "Support" section.

Typically, this information is readily available on the website and is easy to locate. It's important to note that office hours may vary depending on the specific Pro Guide, so users should check the website for updated information.Being able to visit with Pro Guides during their office hours is a valuable resource for users who are seeking to improve their skills in competitive gaming. It provides a direct line of communication between users and experienced coaches, allowing users to receive personalized feedback and guidance tailored to their individual needs.

Pro Guides is a platform that offers educational resources and personalized coaching for gamers looking to improve their skills in competitive gaming. One of the benefits of using Pro Guides is the opportunity to connect with experienced coaches or "Pro Guides" during their office hours. Office hours are designated times when coaches are available to answer questions, provide feedback, and offer guidance to users who are seeking help.

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Answer:

1 apple

Step-by-step explanation:

Answer:

3.26$

Step-by-step explanation:

Simply subtract one from another to find the difference in the cost.

Answer:

y=-7x+16

Step-by-step explanation:

y-y=m(x-x1)

y-2=-7(x-2)

y-2=-7x+14

+2 +2

y=-7x+16

The product below when expression x => 0 is equivalent to 0. If any of the factors in the product is equal to 0, the entire product becomes 0. When x is greater than or equal to 0, the first factor, x - a, becomes 0 and thus the entire product becomes 0.

When x is greater than or equal to 0, the expression will evaluate to 0 because any product that involves 0 is equal to 0. Therefore, the entire expression becomes 0 regardless of the values of a, b, and c. This is because multiplying any non-zero number by 0 gives a result of 0.

It is important to note that this only holds true when x is greater than or equal to 0. If x is less than 0, then the value of the expression will depend on the values of a, b, and c.

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Answer:

x ~0.9

Step-by-step explanation:

To solve for (x) in the given right triangle, use the trigonometric ratios, which are the following,

\(sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}\)

Each of the sides of a triangle is named with respect to the given angle. In this problem, one is given the side opposite to the given angle, and the side adjacent to it. Use the ratio of tangent (tan) to solve for the unknown side.

\(tan(83)=\frac{7}{x}\)

Manipulate the equation so that it is solved for (x),

\(x=\frac{7}{tan(83)}\)

x ~ 0.859

Check the picture below.

To find the function values, we need to substitute the given values of x into the function:

a) f(2) = 95(0.84)^2 ≈ 66.96

This means that after 2 hours, there are approximately 66.96 milligrams of medicine remaining in the person's bloodstream.

b) f(6) = 95(0.84)^6 ≈ 35.33

This means that after 6 hours, there are approximately 35.33 milligrams of medicine remaining in the person's bloodstream.

To determine an appropriate domain for the function, we need to consider the context of the problem. The function represents the amount of medicine remaining in a person's bloodstream after taking a dose of medication, so the domain should be the set of non-negative real numbers, since the amount of medicine cannot be negative and time cannot be negative. Therefore, an appropriate domain for the function is [0, ∞).

Interpretation: The function f(x) = 95(0.84)^x models the amount of medicine, in milligrams, remaining in a person's bloodstream after x hours of taking the medication. For example, after 2 hours, there are approximately 66.96 milligrams of medicine remaining in the person's bloodstream.

After taking a dose of medication, the amount of medicine remaining in a person's bloodstream, in milligrams, after x hours can be modeled by the function

To find:

Interpret the given function values and determine an appropriate domain for the function.

Solution:

The general form of an exponential function is

Where, a is the initial value, 0<b<1 is decay factor and b>1 is growth factor.

We have,

Here, 110 is the initial value and 0.83 is the decay factor.

It means, the amount of medicine in the person's bloodstream after taking the dose is 110 milligrams and the amount of medicine decreasing in the person's bloodstream with the decay factor 0.83 or decreasing at the rate of (1-0.83)=0.17=17%.

We know that an exponential function is defined for all real values of x but the time cannot be negative. So, x must be non negative.

We know that  for any value of x. So,  for all values of x.

Therefore, domain of the function is  and the range is .

Hope this helps!!!

GTPex-

Answer:

8x=y or y=8x

Step-by-step explanation:

So 8 is the number of hours,

we can interpet x for the amount of practice he goes to. For example if hee goes,

for example if he goes to 2 practices the equation will be =

8(2)=Y.... 8(2)=16

16 is the number of miles he runs for 2 practice

We can insert the number of practice he goes to into X

The application rate is 3 (per DM$).

The given below table shows the monthly production volume, direct materials, direct labor, and manufacturing overheads for the past three months at Gizzard Wizard (GW):

Month Prod. Volume DM ($)DL ($)MOH ($)May 1000$400.00$600.00$1200.00

June 400160.00240.00480.00

July 1600640.00960.001920.00

By using DM$ to apply overhead, we have to find the application rate. We know that the total amount of manufacturing overheads is calculated by adding the cost of indirect materials, indirect labor, and other manufacturing costs to the direct costs. The formula for calculating the application rate is as follows:

Application rate (per DM$) = Total MOH cost / Total DM$ cost

Let's calculate the total cost of DM$ and MOH:$ Total DM$ cost = $400.00 + $160.00 + $640.00 = $1200.00$

Total MOH cost = $1200.00 + $480.00 + $1920.00 = $3600.00

Now, let's calculate the application rate:Application rate (per DM$) = Total MOH cost / Total DM$ cost= $3600.00 / $1200.00= 3

Therefore, the application rate is 3 (per DM$).

Hence, the required answer is "The application rate for GW is 3 (per DM$)."

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the approximate distance from Denver to Chicago using the proportional relationship is approximately 312.5 miles.

To approximate the distance from Denver to Chicago using a proportional relationship, we need a known distance and its corresponding ratio. Let's assume we have the distance from Denver to a different city and its corresponding ratio to the distance from that city to Chicago.

Let's say the distance from Denver to City X is 800 miles, and the distance from City X to Chicago is 500 miles. We can set up the proportion:

Distance from Denver / Distance from City X = Distance from City X / Distance from Chicago

Substituting the values:

800 miles / 500 miles = 500 miles / Distance from Chicago

To find the distance from Chicago, we cross multiply:

800 miles * Distance from Chicago = 500 miles * 500 miles

Distance from Chicago ≈ (500 miles * 500 miles) / 800 miles

Calculating this expression:

Distance from Chicago ≈ 312.5 miles

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To linearize the expression f(x) = (1 - x^2)^2 * sin(2x) around x = 0.25, we can split the function into two parts and linearize each part separately.

Let's split the function into two parts:

Part 1: \((1 - x^2)^2\)

Part 2: sin(2x)

For Part 1, we can linearize it by considering only the first-order term, which is the derivative of \((1 - x^2)^2\) evaluated at x = 0.25. The derivative is given by:

f1'(x) = \(2(1 - x^2)(-2x) = -4x + 4x^3\)

Evaluating f1'(x) at x = 0.25, we get:

\(f1'(0.25) = -4(0.25) + 4(0.25)^3 = -1 + 0.25^2 \approx -0.9375\)

So, the linearized form of Part 1 is approximately -0.9375x.

For Part 2, sin(2x) is already a linear function. Hence, the linearized form of Part 2 is sin(2x).

Combining the linearized forms of both parts, the linearized expression of f(x) around x = 0.25 is approximately:

f(x) ≈ -0.9375x * sin(2x)

This linearization provides an approximation of the original function near x = 0.25, where the function can be well-approximated by a linear function.

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The local maximum and minimum values of the function are as follows: maximum at (smaller x value), minimum at (larger x value), and there are no saddle points.

To find the local maximum and minimum values of the function, we need to analyze its critical points, which occur where the partial derivatives are equal to zero or do not exist.

Let's denote the function as f(x, y) = -8 - 2x + 4y - x^2 - 4y^2. Taking the partial derivatives with respect to x and y, we have:

∂f/∂x = -2 - 2x

∂f/∂y = 4 - 8y

To find critical points, we set both partial derivatives to zero and solve the resulting system of equations. From ∂f/∂x = -2 - 2x = 0, we obtain x = -1. From ∂f/∂y = 4 - 8y = 0, we find y = 1/2.

Substituting these values back into the function, we get f(-1, 1/2) = -9/2. Thus, we have a local minimum at (x, y) = (-1, 1/2).

There are no other critical points, which means there are no local maximums or saddle points. Therefore, the function has a local minimum at (x, y) = (-1, 1/2) but does not have any local maximums or saddle points.

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5/6 - 1/9=?/? - ?/? = ?/? , value of each (?/?) is

5/6 -1/9 =15 /18 -2/18 =13 /18.

As given,

5/ 6 - 1/9 =?/? -?/? =?/?

Convert the given terms into like terms

Least common multiple of (6,9)=18

Value of each ( ?/?)

(5/6 ) × ( 3/3) -(1/9) × (2/2)

= 15 /18 - 2/18

= 13 /18

Therefore,5/6 - 1/9 = ?/? - ?/? = ?/? , value of each (?/?) is equal to

5/6 -1/9 = 15 /18 -2/18 = 13/18.

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Answer:

X<_ -15.6 (first one)

Step-by-step explanation: I think

Answer:

1#

Step-by-step explanation:

enjoy

Answer:

20

Step-by-step explanation:

Plugin x = 10 and y = 5 in the expression.

x + 2y = 10 + 2*5

          = 10 + 10

          = 20

Answer: ABC is not a right angled triangle

Step-by-step explanation:

total = 22cm

22-8-5= 9cm

Hypotuneus = 9 cm since its the longest angle

pythagoras theorum = a2+b2=c2

so we need to see if 8² +5² =9²

64+25 need to be 81 (9² )

but its 64+25=89

therefore it is not a right angles triangle.

The prism in the picture has 6 sides, three are shown.

We will have to calculate the area of each of them and sum.

The front and back surfaces are the same and are a trapezoid with height 12 cm, base 27cm and top 6cm.

We can use the area formula for trapezoid:

Where, "a" and "b" are the base and top, and "h" is the height.

So:

So we have the area of the front surface 198 cm², since the back is the same we have two surfaces.

The top surface is a rectangle with dimensions 30 cm and 6cm, so its area is:

It is 180 cm².

The surface at the right is also a rectangle with measures 30cm and 20cm, so:

600 cm².

The surface of the left not appearing in the picure is also a rectangle and have measures 13cm and 30cm, so the area is:

390 cm².

And the last is the bottom one, which is also a rectangle, with measures 27cm and 30cm.

810 cm².

Now that we have all the areas,

When the cosine of an angle (0) is 3/5 and the angle lies in quadrant 4, the exact value of the sine of that angle is -4/5.

To find the exact value of sin(0), we can utilize the Pythagorean identity, which states that \(sin^2(x) + cos^2(x) = 1,\) where x is an angle in a right triangle. Since the terminal side of the angle (0) is in quadrant 4, we know that the cosine value will be positive, and the sine value will be negative.

Given that cos(0) = 3/5, we can determine the value of sin(0) using the Pythagorean identity as follows:

\(sin^2(0) + cos^2(0) = 1\\sin^2(0) + (3/5)^2 = 1\\sin^2(0) + 9/25 = 1\\sin^2(0) = 1 - 9/25\\sin^2(0) = 25/25 - 9/25\\sin^2(0) = 16/25\)

Taking the square root of both sides to find sin(0), we have:

sin(0) = ±√(16/25)

Since the terminal side of (0) is in quadrant 4, the y-coordinate, which represents sin(0), will be negative. Therefore, we can conclude:

sin(0) = -√(16/25)

Simplifying further, we get:

sin(0) = -4/5

Hence, the exact value of sin(0) when cos(0) = 3/5 and the terminal side of (0) is in quadrant 4 is -4/5.

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Note the correct and the complete question is

Q- Find the exact value of sin(0) when cos(0) =3/5 and the terminal side of (0) is in quadrant 4​ ?

Proportion of pregnancies that last fewer than 276 days is approximately 0.7340 or 73.40%.

Given, mean (μ) = 266 days and standard deviation (σ) = 16 days.

Let X be the length of pregnancies, then X follows the normal distribution with mean (μ) = 266 and standard deviation (σ) = 16.

We need to find the probability that a pregnancy lasts fewer than 276 days i.e. P(X < 276).

To find this probability, we standardize the variable X using the standard normal distribution formula:

z = (x - μ) / σ

where z is the standard normal random variable.

Substituting the given values, we get:

z = (276 - 266) / 16 = 0.625

Using a standard normal distribution table or calculator, we can find that the probability of a standard normal random variable being less than 0.625 is approximately 0.7340.

Therefore, the proportion of pregnancies that last fewer than 276 days is approximately 0.7340 or 73.40%.

Explanation: This means that out of 100 pregnancies, around 73 pregnancies will last fewer than 276 days.

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Answer:

he can order 2 of the extra toppings

the following expression i.e. (1.8x10⁹) (6.7 x 10¹²) in Scientific Notation is 120.6×\(10^{20}\) and a=120.6 and b=20

Scientific notation:

Scientific notation is a method of presenting very large or very small numbers in a more simplified format. We know that whole numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper. Furthermore, the numbers found after the decimal point needed to be represented in a more straightforward manner.

(1.8x10⁹) (6.7 x 10¹²) = 120.6×\(10^{20}\)

Given (1.8x10⁹) (6.7 x 10¹²) =a x \(10^{b}\)

a x \(10^{b}\)= 120.6×\(10^{20}\)

a=120.6 and b=20

Therefore,the following expression i.e. (1.8x10⁹) (6.7 x 10¹²) in Scientific Notation is 120.6×\(10^{20}\) and a=120.6 and b=20

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A simple random sample of 500 voters would be an appropriate method for a pollster to use in this situation.

In this method, each voter in the town is assigned a unique identifier and a list of all unique identifiers is created. Then, using a random number generator or a random number table, 500 unique identifiers are selected and those individuals are surveyed.

This method ensures that each voter in the town has an equal chance of being selected, so that the sample is representative of the population of voters. It also eliminates any potential biases that may be introduced if the pollster were to select individuals based on certain criteria (such as age, gender, or location).

By using a random sample, the pollster can have a good estimate of the true population parameter (voter preferences) with a high degree of confidence.

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Answer:

The sequence is defined by the formula an = 3n(-2), where n is a positive integer. To determine if the sequence is increasing, decreasing, or not monotonic, we need to look at the difference between successive terms.

Let's calculate the first few terms of the sequence:

a1 = 3(1)(-2) = -6

a2 = 3(2)(-2) = -12

a3 = 3(3)(-2) = -18

The difference between successive terms is:

a2 - a1 = -12 - (-6) = -6

a3 - a2 = -18 - (-12) = -6

Since the difference between successive terms is always the same (-6), the sequence is decreasing, and the answer is B. decreasing.

The correct answer is option C i.e. 0.15 - 0.02 to 0.15 + 0.02

The correct calculation for a 95% confidence interval for the true proportion of all US adults who feel a gym membership is a necessity is:

Margin of error = z√(p(1-p)/n)

where z is the z-score corresponding to the desired level of confidence (95% in this case), p is the sample proportion (0.15), and n is the sample size (1522).

From a standard normal distribution table, the z-score for a 95% confidence level is approximately 1.96.

Substituting these values into the formula, we get:

Margin of error = 1.96 * √(0.15*(1-0.15)/1522) ≈ 0.02

Therefore, the 95% confidence interval is:

0.15 - 0.02 to 0.15 + 0.02

which simplifies to: [0.13, 0.17]

So, the correct answer is option C.

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