Answers
The coordinates of point C in the given right triangle ABC is (2, 2√3-2)
What is a triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
Given that, triangle ABC is a 30°-60°-90° triangle, where two vertices are A(-4, -2) and B(4, -2).
Now, AB=4-(-4)=8
AC=AB×sin60°= 8×√3/4√3
In right triangle ACD
AD=AC×cos30°
= 4√3×√3/2
= 6
Xc=6-4=2
Yc=AC×sin30°-2
= 4×3×1/2-2
= 2√3-2
The coordinates of point C(2, 2√3-2)
Therefore, coordinates of C(2, 2√3-2).
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Related Questions
Need help really please
Answers
Answer:
Step-by-step explanation:
No pressure. You just need to look for the number that when added to the other given number, will give the same as the sum on the other side.
For instance, The top-left question:
4+6 = x+8 (let x be the box)
x= 4+6-8
x=2.
OR, since 4 + 6 =10,
you look for a number when added to 8, that gives 10.
That number is 2.
Hope this helps :]
Find the missing values.
Select two answers.
Answers
Answer:
a= 12, b=4, Choices B and F
Step-by-step explanation:
2/2=1
8/2=4
12/2=6
How can credit cards be safer than cash? a. It is harder to lose a single credit card than a large number of bills. b. A credit card requires a signature, so it is impossible for anyone other than you to use. c. If a merchant does not hold up their end of an agreement, you can call the credit company and dispute the charges. d. Cash can be miscounted, but credit cards cannot.
Answers
If a merchant does not hold up their end of an agreement, you can call the credit company and dispute the charges. This way, credit cards can be safer than cash.
What is credit card?
A credit card is a small plastic payment card that is provided by a person's bank and enables the cardholder to pay a merchant for products and services depending on the cardholder's accumulated debt.
To be on the safe side in the event that a merchant breaches an agreement, a cardholder may contact the credit bureau to resolve the disputed charges.
So, this way credit cards can be safer than cash.
Hence, option C is the correct solution.
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1. Items a company has purchased and paid for, but has not used are called
A. advanced
B.purchased
C.prepaid
D. long-term liability
items.
Answers
Answer:
the ans is advanced
I hope you get your ans
9 Mr Karim had 2740 sacks of rice at first Mr Dani had 3560 sacks of rice at first. Mr Karim gave some sacks of rice to Mr Dani. In the end, Mr Dani had 4 times as many sacks of rice as Mr Karim. How many sacks of rice did Mr Karim have in the end?
Answers
Answer:
**DUE TOMORROW, NEED ANSWER ASAP**
NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).
a.) An ultraviolet telescope in space
b.) An optical telescope in a remote location in Michigan's upper peninsula
c.) A radio telescope in the Mojave desert in Arizona
d.) An x-ray telescope in the Andes mountains in Chile
e.) An optical telescope in space
Step-by-step explanation:
Hello can you help me solve
Answers
Answer:
(p o q) = 54
(q o p) = 68
Step-by-step explanation:
Another way to write is (p o q)(3) is p(q(3)). As you can see, you start with the inner function and 3 is an input in the q(x) function. Then, the output of this becomes the input of p(x) (the outer function), which yields a final output and the answer:
[tex]p(x) = 4x + 2\\q(x)=5x-2\\\\p(q(3))\\\\q(3)=5(3)-2=13\\p(13)=4(13)+2=54[/tex]
You do the same process for (q o p)(3), which can be written as q(p(3)), where you start with p(3) and then plug in this result as the input for q(x):
[tex]p(x)=4x+2\\q(x)=5x-2\\\\q(p(3))\\\\p(3)=4(3)+2=14\\q(14)=5(14)-2=68[/tex]
19. The mass of a radioactive element is 35
milligrams. The mass of the element decreases by
12.9% every year.
a. Write a function that represents this situation.
b. Predict the mass of the element in 4 years. Round
your answer to the nearest tenth.
c. Will the mass of the radioactive element ever be 0
milligrams? Explain.
Answers
a) The function that represents this situation is,
⇒ y = 35 (1 - 12.9%)ⁿ
Where, 'n' is number of years and 'y' is mass of element.
b) For 4 years, the mass of the element is, 19.95 milligrams
c) No, the mass of the radioactive element will never be 0 milligrams.
What is expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now,
The function that represents this situation is,
⇒ y = 35 (1 - 12.9%)ⁿ
Where, 'n' is number of years and 'y' is mass of element.
Now, For 4 years, the mass of the element is,
⇒ y = 35 (1 - 12.9%)ⁿ
⇒ y = 35 (1 - 12.9%)⁴
⇒ y = 35 (1 - 0.129)⁴
⇒ y = 35 (0.87)⁴
⇒ y = 35 × 0.57
⇒ y = 19.95 milligrams
No, the mass of the radioactive element will never be 0 milligrams.
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examine whether you can construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm. Justify your answer
Answers
You cannot construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm, as the sum of the lengths of the two smaller sides is not greater than the length of the larger side.
What is the condition for 3 lengths to represent a triangle?In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.
The lengths for this problem are given as follows:
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How long is a movie if it starts at 2:25pm and ends at 16:41 pm
Answers
Answer:
It would be a little over 2 hours or so since 16:41 is just 4:41.
2 hours and 16 minutes
Step-by-step explanation:
You're welcome.
Aubrey broke a cell sample into 15 batches, each way 1.3×10 to the -7th grams. How much did the original sample weigh? Use scientific notation to express your answer.
Answers
Answer:
Step-by-step explanation:
1.3 * 10 ^-7
is 0.00000013
0.00000013 times 15 is
0.00000195.
0.00000195 in scientific notation is
1.95*10^-6
what is the value of 8.4n - 3.2p, when n=4 and p=-2
Answers
Answer:
33.6-(-6.4)=40
Step-by-step explanation:
1. 8.4×4
2. 3.2x-2
3. 33.6-(-6.4)
4. 40
the two negatives become positive
Find the value of C that makes 16x^2 -24x + C a perfect square
Answers
The required value of C is 3 which makes 16x² - 24x + C a perfect square.
What is Perfect Square?A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.
The expression is given in the question, as follows:
16x² - 24x + C
(4x)² - 24x + C
As we know that the factoring identity:
(a - b)² = a² - 2ab + b²
After comparing, we have a = 4x and 2ab = 24x
Solving for b:
2(4x)b = 24x
b = 24x/8x
b = 3
So 16x² - 24x + 3 = (4x - 3)²
This means the required value of C is 3 which makes a perfect square.
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1. For
what value of x is the
3(x + 2)-2x = 12 true?
A. 6
B. 10
C. 12
D. 14
E. 18
1.4.1 Set
the equation
Answers
Answer: A. 6
Step-by-step explanation:
Answer: I think D.
Step-by-step explanation: why not pick D…..
Hope this helps^^
help please i don’t know what to do
Answers
Answer:
Add 3 and then multiply by 5.
Step-by-step explanation:
The problem looks like this to me:
[tex] \dfrac{m}{5} - 3 = 8 [/tex]
If this is correct, then the operations are:
Add 3 to both sides.
Multiply both sides by 5.
I don't see that answer. The picture is not very clear to me. What is the denominator of the fraction?
The area of a rectangular wall of a barn is 110 square feet. Its length is 12 feet longer than twice its width. Find the length and width of the wall of the barn.
width= =feet
Answers
The length and width of the rectangular wall of a barn given the area is 22 feet and 5 feet respectively.
What is the length and width of the wall of the barn?Area of the rectangular wall of a barn = 110 square feet
Width of the barn = w
Length of the barn= 2w + 12
Area of a rectangle = length × width
110 = (2w + 12) × w
110 = 2w² + 12w
equate to 0
2w² + 12w - 110 = 0
w² + 6w - 55 = 0
using factorization method of solving quadratic equation
w² + 11w - 5w - 55 = 0
w(w + 11) - 5(w + 11) = 0
(w - 5) (w + 11) = 0
w = 5 or w = -11
The width of the rectangular barn cannot be negative
Therefore,
Width of the barn = w
= 5 feet
Length of the barn= 2w + 12
= 2(5) + 12
= 10 + 12
= 22 feet
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Point V is somewhere on the line segment . If UV = 8, then find the length of .
Answers
Answer:
it is 3
Step-by-step explanation:
just subtract
f(1) = 25
f(n) = f(n-1)(-1/5)
f(3) = ??
Answers
Answer: = 1 (look at the image for the solution)
Step-by-step explanation:
Help with question 6:
Answers
If the quotient of two functions f(x) and g(x) is a constant, then their derivatives are proportional to each other.
How are g.f' and f.g' related?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
If the quotient of two functions f(x) and g(x) is a constant k, meaning f(x)/g(x) = k for all x, then it follows that:
f(x) = k.g(x)
Taking the derivative of both sides with respect to x, we get:
f'(x) = k.g'(x) + g(x).d(k)/dx
Since the constant k is a constant and not a function of x, its derivative with respect to x is zero, so we can simplify the equation to:
f'(x) = k.g'(x)
Thus, we can see that if the quotient of two functions f(x) and g(x) is a constant, then their derivatives are proportional to each other, with the constant of proportionality equal to k.
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if 30% of a number is 7, then what is 10% of the number ?
Answers
Answer:
70.0000
Step-by-step explanation:
aka 70%
Maya had $32. She spent all the money on buying 3 notebooks for x dollars each and 4
packs of index cards for y dollars each. If Maya had bought 5 notebooks and 5 packs of
index cards, she would have been short $18. Which system of equations represents this
situation?
O 3x + 4y = 32 and 5x + 5y = 50
O 3x+4y= 32 and 5x + 5y = 18
O 3x + 4y = 50 and 5x - 5y = 18
O 3x - 4y= 32 and 5x - 5y = 50
Answers
The system of equations which represents this
situation is 3x+4y= 32 and 5x + 5y = 18.
The correct answer choice is option B
Which system of equations represents the situation?Amount with Maya = $32
Amount spent on each notebook = x
Number of notebook = 3
Amount spent on each pack of index cards = y
Number of index cards = 4
Maya bought 5 notebooks and 5 packs of
index cards
$18 short = $32 - $18
= $14
3x + 4y = 32
5x + 5y = 14
In conclusion, the system of equation is 3x+4y= 32 and 5x + 5y = 18.
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Could anyone help with #1 and #2 PLEASE.
URGENT! DUE TOMORROW!!
Answers
Answer:
Do the graph Then Solve for y
Answer:
1. Yes, a graph of this relationship will be linear.
2. The y-intercept of the graph is (0, 2).
Step-by-step explanation:
1. The equation will be linear because it can be written in the standard form for the equation of a line. The standard form for the equation of a line is Ax + By = C. Eight can be subtracted from both sides of the equation to get 3x - 4y = -8, which fits the format for standard form. A, B, and C are integers, which includes negative numbers, zero, and whole numbers.
2. 3x - 4y + 8 = 0
3(0) - 4y + 8 = 0
-4y + 8 = 0
-4y = -8
y = 2
Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line.
2x+4<10
Answers
The solution set of the inequality is [3, ∝)
How to determine the solution setFrom the question, we have the following parameters that can be used in our computation:
2x + 4 < 10
Subtract 4 from both sides of the inequality
So, we have the following representation
2x + 4 - 4 < 10 - 4
Evaluate the like terms
2x < 6
Divide both sides by 2
x < 3
When represented as an interval notation, we have
[3, ∝)
See attachment for the inequality of the solution set
Hence, the solution is [3, ∝)
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All numbers less than 17 and greater than or equal to -8. into SET BUILDER NOTATION!!
Answers
In set builder notation, the set of all numbers larger than or equal to -8 and less than 17 can be written as:
{x | -8 <= x < 17}
An explanation of set builder notation?
A set of items can be mathematically expressed using the set builder notation. The set builder notation's syntax is {x | }, where x stands for one of the set's elements and the condition outlines the requirements that an element must meet in order to be included in the set.
In this instance, the set consists of all numbers higher than or equal to -8 and less than 17 in total. The set must satisfy the constraint
-8 <= x < 17,where x is a real value. This implies that x must exceed or equal to -8 and must be less than 17 to be a part of the set.
As a result, in set builder notation, the set of all numbers greater than or equal to -8 and less than 17 can be written as follows: {x | -8 <= x < 17}
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Which of the following statements proves the series 250 – 150 + 90 – 54 + … is geometric?
r equals five thirds
r equals three fifths
r equals negative three fifths
Answers
The given series is geometric when r equals negative three-fifths.
What is geometric series?
The geometric series refers to the total of terms with a common ratio between every pair of neighbouring terms. Geometric series can be of two different types: finite and infinite. The sequence is of the form {a, ar, ar², ar³, …….} where, a is the first term, and r is the "common ratio".
where, r = ar/a = (second term)/(first term)
Given, the series 250 – 150 + 90 – 54 + …
So, r = (-150)/250 = -3/5
or, r = 90/(-150) = -3/5
Hence, for the geometric series, r should be equal to negative three-fifths.
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A random sample of 40 hotel reviews is drawn from a large population of hotel customers. It's known that 30% of the population left the hotel 1 star, 20% left 2 stars, 20% left 3 stars, and 30% left 4 stars. Give the standard deviation of the hotel's star rating.The choices are:0.18910.18930.19040.1934
Answers
The closest answer choice is 0.76, which corresponds to 0.1934. So the answer is 0.1934.
We can calculate the variance of the hotel's star rating by using the formula:
variance = sum[(xi - mean)^2 * pi]
where xi is the rating (1, 2, 3, or 4), mean is the expected value of the rating, and pi is the proportion of the population that left that rating. Since we know the proportions of the population that left each rating, we can calculate the expected value of the rating as:
mean = 1(0.3) + 2(0.2) + 3(0.2) + 4(0.3) = 2.9
Then, we can calculate the variance as:
variance = (1 - 2.9)^2 * 0.3 + (2 - 2.9)^2 * 0.2 + (3 - 2.9)^2 * 0.2 + (4 - 2.9)^2 * 0.3
variance ≈ 0.57
Finally, the standard deviation is the square root of the variance:
standard deviation = sqrt(0.57) ≈ 0.756
Therefore, the closest answer choice is 0.76, which corresponds to 0.1934.
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There are 12 consecutive parking slots available in a hotel parking lot in how many ways can four distinct cars be packed so that at least one parking slot remains vacant between into cars
Answers
Answer:
4 different spots
Step-by-step explanation:
12 - 4 spaces in between = 8 spaces
8 spaces / 4 cars = 4 spots
4 spots and 4 cars = 4 different spots for each car
16
In fall 2006, Pace University in New York raised its annual tuition from $25,000 to $29,750. Freshman enrollment declined from 1,475 in fall 2005 to 1,130 in fall 2006. Assuming that the demand curve for places in the freshmen class at Pace did not shift between 2005 and 2006, use this information to calculate the price elasticity of demand LOADING... . Use the midpoint formula in your calculation.
Answers
Answer:The answer is 20000
Step-by-step explanation:
If f (x) = 5x - 4 find f(2).
10
48
2
6
Answers
Answer:
6
Step-by-step explanation:
f(2) = 10-4 = 6
Answer:
[tex] \sf \: d) \: 6[/tex]
Step-by-step explanation:
Given function,
→ f(x) = 5x - 4
We have to find,
→ The required value of f(2).
Now value of f(2) will be,
→ f(x) = 5x - 4
→ f(2) = 5(2) - 4
→ f(2) = 10 - 4
→ [ f(2) = 6 ]
Therefore, the answer is 6.
Marsha deposited $7,000 into a savings account 4 years ago. The simple interest rate is 2%. How much money did Marsha eam in interest?
Answers
Answer:
$560
Step-by-step explanation:
The formula for simple interest is:
I = Prt, where P is the principal, r is the interest rate, and t is the time (in years).
Plugging in the values, we get:
I = $7,000 * 2% * 4 years = $560
So, Marsha earned $560 in interest.
Is the graph of y = x² + 2 a straight line? Explain.
O No. The graph does not pass through (0, 0), so it is not a straight line.
O No. The graph passes through the points (0, 2), (1, 3), and (2, 6), which do not all lie on a straight line.
O Yes. The graph passes through (0, 0), so it is a straight line.
O Yes. The graph passes through the points (0, 2), (1, 3), and (2, 6), which all lie on a straight line.
Answers
Answer: No, the graph of y = x² + 2 is not a straight line. The graph is a parabola that opens upwards and has its vertex at (0, 2).
A straight line is defined by a linear equation, which is an equation that can be written in the form y = mx + b, where m and b are constants. In this equation, the coefficient of x (m) represents the slope of the line, and the constant term (b) represents the y-intercept. A straight line has a constant slope, which means that the rate of change of y with respect to x is constant.
In the case of y = x² + 2, the coefficient of x (x) is not a constant, but rather a variable, which means that the slope of the line changes as x changes. The graph of y = x² + 2 is a parabolic shape that opens upwards and has its vertex at (0, 2). The slope of the graph is not constant, but rather increases as x increases. This means that the graph does not represent a straight line, but rather a parabolic curve.
Step-by-step explanation:
