The length of each side of triangle ABC is 21.36 units (side a) and 22.88 units(side c or hypotenuse).
To find the length of side a in triangle ABC, we can use the tangent function, since we know the length of side b and the measure of angle A:
tan(A) = opposite / adjacent
tan(A) = a / b
tan(69) = a / 8.2
Multiplying both sides by 8.2, we get:
a = 8.2 * tan(69)
Using a calculator to evaluate sin(69), we get:
a ≈ 21.36
To find the length of the hypotenuse, c, we can use the Pythagorean theorem.
c² = a² + b²
c² = 21.36² + 8.2²
c ≈ 22.88
Therefore, the length of side a is approximately 21.36 units while the length of the hypotenuse, c, is 22.88 units.
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please solve this fast
Write the following equation in standard form. Identify the related conic. x' + y2 - 8x - 6y - 39 = 0
The standard form of the equation is (x' - 8x) + (y - 3)^2 = 48
To write the equation in standard form and identify the related conic, let's rearrange the given equation:
x' + y^2 - 8x - 6y - 39 = 0
Rearranging the terms, we have:
x' - 8x + y^2 - 6y - 39 = 0
Now, let's complete the square for both the x and y terms:
(x' - 8x) + (y^2 - 6y) = 39
To complete the square for the x terms, we need to add half the coefficient of x (-8) squared, which is (-8/2)^2 = 16, inside the parentheses. Similarly, for the y terms, we need to add half the coefficient of y (-6) squared, which is (-6/2)^2 = 9, inside the parentheses:
(x' - 8x + 16) + (y^2 - 6y + 9) = 39 + 16 + 9
(x' - 8x + 16) + (y^2 - 6y + 9) = 64
Now, let's simplify further:
(x' - 8x + 16) + (y^2 - 6y + 9) = 8^2
(x' - 8x + 16) + (y - 3)^2 = 8^2
(x' - 8x + 16) + (y - 3)^2 = 64
Now, we can rewrite this equation in standard form by rearranging the terms:
(x' - 8x) + (y - 3)^2 = 64 - 16
(x' - 8x) + (y - 3)^2 = 48
The equation is now in standard form. From this form, we can identify the related conic. Since we have a squared term for y and a constant term for x (x' is just another variable name for x), this equation represents a parabola opening horizontally.
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I dont understand this
Answer:
x=66
Step-by-step explanation:
180-114=66
Interior angles on the same side of transversal are supplementary (180°).
So,
x + 114° = 180°
=> x = 180° - 114°
=> x = 66°
What inequalities satisfy the region R in the diagram?
Answer:
y ≤ -x - 4
x > -1
y ≥ 4
Step-by-step explanation:
For the sloped line, we can see that the y-intercept is -4 and the x-intercept is -4.
This means at x = 0, y = - 4 and at y = 0, x = -4. We also see that the bottom of the line is shaded and that the line is not broken.
Thus, the inequality is; y ≤ -x - 4
For the vertical line, we can see it has only an x-intercept at x = - 1. We also see that the line is broken which means the equal to symbol is not part of the inequality. Also, the shaded part is to the right. Thus, the inequality is:
x > -1
For the horizontal line, we see that it has only a y-intercept at y = 4. We also see that the line is not broken which means the equal to symbol is part of the inequality. Also, the shaded part is above. Thus, the inequality is:
y ≥ 4
Therefore, the inequalities that satisfy the region R are:
y ≤ -x - 4
x > -1
y ≥ 4
10 boys to 12 girls ratio
Answer: 10:12
Step-by-step explanation:
Find an equation that fits this graph:
Answer:
y = -2/3x + 4
Step-by-step explanation:
Use formula for slope given two points.
m = (y2 - y1)/(x2 - x1)
The two points are (0, 4) and (6, 0)
m = (0 - 4)/(6 - 0)
m = -4/6
m = -2/3
y = -2/3x + b
The y-intercept b is 4.
In a shoe store window, Sandy sees a sign announcing 25% off all sandals in stock. She finds a pair she likes that was originally priced at $45. If Sandy buys this pair of sandals on sale, how much will she pay?
a)11.25 b)22.50 c)33.75 d) 56.25
how to convert 40 pounds in kg?
As per the conversion, the weight of 40 pounds is equivalent to a weight of 18.14 kilograms.
Converting measurements can sometimes be a tricky task, especially when we need to convert from one unit to another. One common conversion that we often encounter is the conversion of pounds to kilograms. In this guide, we will explain step by step how to convert 40 pounds into kilograms.
First, we need to understand the basic unit of measurement for both pounds and kilograms. Pounds are a unit of measurement commonly used in the United States and the United Kingdom to measure weight. Kilograms, on the other hand, are the standard unit of measurement for weight in the International System of Units (SI).
To convert 40 pounds to kilograms, we need to use the following formula:
1 pound = 0.45359237 kilograms
Using this formula, we can calculate the equivalent weight in kilograms for 40 pounds. We simply multiply 40 by 0.45359237 to get:
40 x 0.45359237 = 18.14374948 kilograms
So, 40 pounds is equivalent to 18.14374948 kilograms (rounded off to the nearest hundredth) we get 18.14 kilograms.
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What is the ratio of y to x represented by the line in the graph? Plssss help me will give BRAINLIEST!!
Volume kubus dengan panjang rusuk 2 cm?
Answer:
8 cm³Step-by-step explanation:
➡️ Volume = r³
➡️ 2³
➡️ 8
= Sisi × Sisi × Sisi
= 2 Cm × 2 Cm × 2 Cm
= 4 Cm × 2 Cm
= 8 Cm .
Maka, volumenya 8 Cm.
answer these 3 questoins
Answer:
b) m = 1/2
c) m = 3
d) m = 1/3
Step-by-step explanation:
b) rise = 1, run = 2; m = rise/run, so m = 1/2
c) rise = 3, run = 1; m = rise/run, so m = 3
d) rise = 1, run = 3; m = rise/run, so m = 1/3
ab = 6 BC= 12 what is the lenghth of ac
Work out x^2- 2x
when x =4
Answer:
8
Step-by-step explanation:
\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)
why are convenience samples used so frequently in nursing research, when a random sample would allow for greater generalizability?
Convenience samples are often used in nursing research because they are easy and convenient to obtain.
Nurses often have limited time and resources to conduct research, so they may opt for convenience sampling to save time and effort. Additionally, convenience samples may be useful for studying rare populations or situations where random sampling is not feasible.
However, convenience samples are not representative of the larger population and may lead to biased results. Therefore, the use of convenience samples should be carefully considered, and efforts should be made to increase the generalizability of the research findings through appropriate statistical analysis and interpretation.
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which of the following is not a characteristic of the normal probability distribution?a.the mean of the distribution can be negative, zero, or positive.b.the distribution is symmetrical.c.the mean, median, and mode are equal.d.the standard deviation must be 1.
The statement d. The standard deviation must be 1. is not a characteristic of the normal probability distribution.
What is characteristic of probability distribution?An illustration of a probability distribution shows the anticipated results of potential values for a certain data generation procedure.
The mean, standard deviation, skewness, and kurtosis of probability distributions are used to identify their various forms and features. The normal distribution, which is regularly used in banking, investing, science, and engineering, is the most widely used distribution.
Since, the standard deviation does not have to be 1 for a normal distribution.
Hence, the correct answer is d. The standard deviation must be 1.
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Convert the repeating decimal into a fraction: 0.555
Using Cramer's Rule, the solution to the system of equations
6x−5y=−4−7x+3y=−1
can be written in the form (DxD,DyD).
What is the value of Dx?
Using Cramer's rule it is found that Dx = -34.
In Cramer's rule, we have three matrices.
x is a matrix in which the first column is the coefficients that multiply x, and the second are the coefficients on the right side of the equality.y is a matrix in which the first column is composed by the coefficients on the right side of the equality and the second is the coefficients that multiply y.M is a matrix in which the first column is the coefficients that multiply x, and the second is the coefficients that multiply y.In this problem, the system is:
\(6x - 5y = -4\)
\(-7x + 3y = -1\)
Matrix x is given by:
\(x = \left[\begin{array}{ccc}6&-4\\-7&-1\\\end{array}\right]\)
It's determinant is given by:
\(Dx = 6(-1) -(-4)(-7) = -6 - 28 = -34\)
Thus, Dx = -34.
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HELP PLEASE Stem Leaf 16 2 56 3 8 4 5 6 7 2 3 0004 The stem and leaf plot shows the ages of people at the library. How many people are under the age of 40? 2 3 4
Answer: the answer is 2 I believe
Step-by-step explanation:as you look at “stem” and go down to the number 4. You count below that. So 8, and 6. That’s 2 numbers :) hope this helps!
The stem and leaf plot shows the ages of people at the library. 2 people are under the age of 40.
The duration of a being's or thing's existence; the length of its existence or life up until the moment being discussed or alluded to age. A time frame for humans that begins at birth and is measured in years.
This time frame is typically characterised by a specific stage or level of physical or mental development as well as the potential for legal responsibility. The stem and leaf plot shows the ages of people at the library. 2 people are under the age of 40.
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A car is traveling along a road that makes a 13° angle with the ground. Find the elevation of the car on a stretch of road that extends horizontally 125 meters. Round your answer to the nearest tenth.
Answer:
Therefore, the elevation of the car on the stretch of road, rounded to the nearest tenth, is approximately 29.7 meters.
Step-by-step explanation:
To find the elevation of the car on a stretch of road that extends horizontally 125 meters, we can use trigonometry.
Given:
Angle of the road = 13°
Horizontal distance = 125 meters
We can use the tangent function to calculate the elevation:
tan(angle) = opposite / adjacent
In this case, the opposite side represents the elevation, and the adjacent side represents the horizontal distance.
Let's denote the elevation as "e". The equation becomes:
tan(13°) = e / 125
To solve for "e", we can rearrange the equation:
e = 125 * tan(13°)
Using a calculator, we can evaluate this expression:
e ≈ 125 * tan(13°) ≈ 29.7
PLEASE HELPP
use the spinner to find the odds in favor of stopping on a multiple of 6
For the function f(x)=x^2-7x+6, find x when f(x)= -4
Answer:
50
Step-by-step explanation:
f(-4) = (-4)² - 7(-4) + 6
= 16 + 28 + 6
= 50
Suppose you buy one contract for september 2019 delivery. if the contract closes in september at a level of 4.10, what will your profit be?
If you buy one contract for September 2019 delivery and the contract closes in September at a level of 4.10, your profit will be $100.
A futures contract is an agreement to buy or sell a certain underlying asset at a predetermined price on a predetermined date. In this case, you are buying a futures contract for corn with a delivery date of September 2019. The contract price is currently 4.00. If the contract closes in September at a level of 4.10, you will be able to buy the corn at the lower price of 4.00 and then sell it at the higher price of 4.10, resulting in a profit of $0.10 per bushel. Since each contract is for 5,000 bushels, your total profit will be $100.
Here is a table showing the steps involved in calculating your profit:
| Step | Calculation | Result |
|---|---|---|
| Contract price | 4.00 | |
| Market price | 4.10 | |
| Profit per bushel | 4.10 - 4.00 | $0.10 |
| Total profit | $0.10/bushel * 5,000 bushels | $100 |
As you can see, your profit will be $100 if the contract closes in September at a level of 4.10.
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PLEASE HELP ME WITH THIS QUESTION AND PROVIDE AN EXPLANATION PLEASE
FIND A UNIT RATE!!!!
Answer:
No
Step-by-step explanation:
No, it is not because the 3 dollars is a steady price. A expression will look like 7n+3. Since the 3 dollars is a steady price you can never have a unit rate.
Answer:
It's proportional
Step-by-step explanation:
10-3=7 7/1 = 7
17 - 3= 14 1 4/2 = 7
31 - 3 = 28 28/4 = 7
38 -3 = 35 35/5 = 7
73 - 3 = 70 70/10 = 7
What is the value of x?
Enter your answer in the box.
x = []
A spring has a natural length of 30.0 cm. If a 20.0-N force is required to keep it stretched to a length of 42.0 cm, how much work W is required to stretch it from 30.0 cm to 36.0 cm? (Round your answer to three decimal places.) W = ______ J
The amount of work required to stretch the spring from 30.0 cm to 36.0 cm is 1.411 joules, which can be rounded to three decimal places.
According to Hooke's Law, the amount of work required to stretch or compress a spring by a certain amount is given by the formula:
W = (1/2) k (x2 - x1)²
where W is the work done (in joules), k is the spring constant (in newtons per meter), x1 is the initial displacement (in meters), and x2 is the final displacement (in meters).
In this case, the spring has a natural length of 30.0 cm, which is equivalent to 0.3 meters. To find the spring constant, we can use the fact that a 20.0-N force is required to keep it stretched to a length of 42.0 cm, which is equivalent to 0.42 meters.
Using Hooke's Law, we have
F = k (x2 - x1)20.0 N
= k (0.42 - 0.3) m
=> k = 80.0 N/m
Now we can use Hooke's Law again to find the amount of work required to stretch the spring from 30.0 cm to 36.0 cm, which is equivalent to 0.36 meters.
Using Hooke's Law, we have:
F = k (x2 - x1)W
= (1/2) k (x2 - x1)²W
= (1/2) (80.0 N/m) (0.36 - 0.3) m²W
= 1.411 J
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If the figures on the graph are similar to each other, which statement is TRUE
Side Cd corresponds to EP
There is at least one similarity transformation that will map ABCD to EFGH
The corresponding sides of the figures are equal in length
ABCD=EFGH
Based on the information in the graph and the figures, we can infer that a true statement about these figures is: There is at least one similarity transformation that will map ABCD to EFGH.
How to identify the transformations that relate these two figures?According to the information in the graph, we can show that the figures ABCD and DEFG are similar in shape. In fact, we could say that ABCD is a smaller scale than DEFG, because their sides and angles are similar.
However, this figure has some transformations, in particular the most notorious transformation is the rotation that has been given to it in the form of a mirror due to the fact that its longest side is to the left and not to the right like the DEFG figure.
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4 consecutive odd integers with a sum of 3048
Answer:
The integers you seek are:
759, 761, 763, 765
since
759 + 761 + 763 + 765 = 3048.
Hope this helps!
Which of the following formulas which of the following formulas defines an arithmetic sequence?
a) tn = 5 + 14
b) tn= 5n² + 14
c) tn= 5n(n+14)
d) tn= 5n + 14
The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.
In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.
Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.
Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.
Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.
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HELP ASAP PLEASE
Kristen Lynn sells college textbooks on commission. She gets 4% on the first
$5000 of sales, 8% on the next $5000 of sales, and 12% on sales over
$10,000. In July of 1997 Kristen's sales total was $13,500.
Answer:
Step-by-step explanation:
5000 at 4% =200 (5000*0.04)
5000 at 8% = 400 (5000*0.08)
3,500 at 12% = 420 (3500*0.12)
200+400+420 = 1020
Her commission is 1,020 dollars :)
How many flags can we make with 7 stripes, if we have 2 white, 2 red, and 3 green stripes? Justify. You are creating a 4-digit pin code. How many choices are there in the following cases? (a) With no restriction. (b) No digit is repeated. (C) No digit is repeated, digit number 3 is a digit 0. Note: Justify your answers
We can make 35 flags with 7 stripes if we have 2 white, 2 red, and 3 green stripes.
(a) There are 10,000 choices for a 4-digit pin code with no restrictions.
(b) There are 10 choices for the first digit, 9 choices for the second digit, 8 choices for the third digit, and 7 choices for the fourth digit, for a total of 5040 choices with no digit repeated.
(c) There are 9 choices for the first digit (excluding 0), 8 choices for the second digit (excluding the first digit and 0), 1 choice for the third digit (which must be 0), and 7 choices for the fourth digit (excluding the first two digits and 0), for a total of 504 choices with no digit repeated and digit number 3 as a digit 0.
To find the number of flags, we use the formula for combinations with repetition: C(n+r-1,r), where n is the number of colors (3), r is the number of stripes (7), and C is the binomial coefficient. Substituting, we get C(3+7-1,7) = C(9,7) = 9!/(7!2!) = 36. However, we must subtract 1 for the case with all green stripes, leaving us with 35 flags.
(a) For each digit, there are 10 choices (0-9), so the total number of choices is 10 x 10 x 10 x 10 = 10,000.
(b)We can choose the first digit in 10 ways. Once that digit is chosen, we have 9 choices for the second digit (all digits except the one we chose for the first digit). Similarly, we have 8 choices for the third digit and 7 choices for the fourth digit. Therefore, the total number of choices is 10 x 9 x 8 x 7 = 5040.
(c) We can choose the first digit in 9 ways (all digits except 0). Once that digit is chosen, we have 8 choices for the second digit (all digits except the first digit and 0). The third digit must be 0, so there is only 1 choice for it. Finally, we have 7 choices for the fourth digit (all digits except the first two digits and 0). Therefore, the total number of choices is 9 x 8 x 1 x 7 = 504.
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Angle A and Angle B are complementary angles. If Angle A = (2x+4) ° and Angle B = (x-1)°, then find the measure of angle A
Complementary angles are two angles whose measures add up to 90 degrees. Therefore, the measure of Angle A is 62 degrees.
Two angles are said to be complementary if their sum is exactly 90 degrees. Angles A and B are shown to be complimentary in this instance. Additionally, the expressions for Angles A and B in terms of 'x' are provided.
The total of the angles can be expressed mathematically as follows:
Angle B = 90° plus Angle A.
Angles A and B's supplied expressions are substituted into the equation to yield the following result: (2x + 4) + (x - 1) = 90°
By combining like terms, we can simplify the equation:
2x + 4 + x - 1 = 90°
3x + 3 = 90°
Next, we remove 3 from both sides of the equation to isolate 'x':
3x = 90° - 3 3x = 87°
We multiply both sides of the equation by 3 to determine the value of 'x':
x = 87° / 3 x ≈ 29°
Now that we know what 'x' is worth, we can add it back into the formula for Angle A to determine how much it is:
Angle A equals (x + 4)° Angle A equals (x * 29)°
Angle A=58+4
Angle A is equal to 62 degrees.
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