Answers
Answer:
1. a)x² + y² = 29 ------------------(1)
y² - x² = 23 ----------------(2)
y² = 23 + x²
Using the value of y² in the first equation:
x² + y² = 29
x² + (23 + x²) = 29
2x² = 6
x² = 3
x = √3
Using the value of x in equation (2)
y² - x² = 23
y² - 3 = 23
y² = 26
y = √26 and x = √3
b) ( 1 - 12x) / 3 < 0 = 1-12x < 0 = x > 1 / 12
(1-x) / 2 ≤ (3-x) 3 = 3 - 3x ≤ 6 - 2x = -3 ≤ x
In these 2 equations, the value of x will be the values of x common to both the inequalities
Since the second equation starts at a much lower value than the first equation, and they are both going up, all the values for the first equation will also stand for the second equation
Hence, the value of x for the given system of equations is
x > 1/12
2.
3x² - 7x + 2 ≥ 0
3x² -6x -1x + 2 ≥ 0 (splitting the middle term)
3x(x - 2) -(x - 2) ≥ 0
(3x - 1)(x-2) ≥ 0
(3x-1) ≥ 0 or (x-2) ≥ 0
x ≥ 1/3 or x ≥ 2
Written above are the 2 solutions for the given equation
4.
We are given that Sin α = (2√3) / 3 or 2/√3
According to the pythagorean law:
sin²α + cos²α = 1
4 / 3 + cos²α = 1
cos²α = (3-4)/3
cos²α = -1/3
cos α = √(-1/3) or i / √3 since √-1 is also known as i
Cosec α = 1/ Sin α
Cosec α = 1 / (2/√3)
Cosec α = √3 / 2
Sec α = 1 / cos α
Sec α = 1 / √(-1/3)
Sec α = (√3) / (√-1)
Since (√-1) is also known as i , we can write this as:
Sec α = (√3) / i
Tan α = Sin α / Cos α
Tan α = (2√3 / 3) / (i / √3)
Tan α = (2√3 * √3) / 3 * i)
Tan α = 2 / i
Cot α = 1/Tan α
Cot α = 1 / (2 / i)
Cot α = i / 2
Related Questions
How many times greater was the temperature in Miami (45) than the lowest in San Diego (25)
Answers
Answer:
The temperature in Miami is 9/5 times the temperature in San Diego.
Step-by-step explanation:
Ratios
To compare the temperature in Miami (45) with the temperature in San Diego (25), we use the division or ratio between both numbers:
[tex]\displaystyle \frac{45}{25}[/tex]
Simplify the fraction dividing by 5:
[tex]\displaystyle \frac{9}{5}[/tex]
Since the relation between them is 9/5, it means the temperature in Miami is 9/5 times the temperature in San Diego.
Psychology 101: Is it normal for school age people to have crushes on their teachers or professors?
Answers
Answer:
it is normal, but not right to act upon
what is an equation of the line that passes through the point (8,2) and is parallel to the line 5x-4y=36
Answers
Answer:
y=5/4x-8
Step-by-step explanation:
put ito slope intercept form and then using the slope put y intercept in order for it to be true
The required equation of line will be y = 1.25x - 8.
It is given that a line passes through a point (8,2) and is parallel to the line 5x - 4y= 36.
We have to find out the equation of the line.
What is the general equation of a line ?
The equation of a line is y = mx + c , where m = slope of line.
As per the question ;
The line is parallel to another line 5x -4y = 36.
∴ 5x - 4y = 36
4y = 5x - 36
diving by 4 on both sides ;
y = (5/4)x - (36/4)
y = 1.25x - 9
After comparing with the general equation of a line y = mx + c. We found that value of slope m = 1.25.
So, the parallel line will have the same slope.
∴ y = 1.25 x + c
As the line passes through point (8,2) , hence x = 8 and y =2. After putting this value in the above equation we get ,
2 = 1.25 × 8 + c
∴ c = 2 - 10 = - 8
c = - 8
And the final equation of the line will be ,
y = 1.25 x - 8.
Thus , the required equation of line will be y = 1.25x - 8.
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Which is the equation of a line that has a slope of -3 and passes through point
(-3,-1)
Answers
Answer:
Use y-y1 = m*(x-x1) where m = slope and (x1,y1) is the point.
Step-by-step explanation:
found the info on a random website
Aiden needs 3.7 pounds of plaster for a project. He can choose from the 2 packages shown. Round the weight of each package of plaster to the nearest tenth.
Answers
Answer:
The answer is 3.8 and 2.5
Step-by-step explanation:
Lol
1+1 what the answer is
Answers
Answer:
1+1 = 2
Step-by-step explanation:
HELP ANSWER AS FAST AS U CAN
Acceptance into an acting workshop is highly competitive. Last year only 2 out of every 15 applicants were accepted into the workshop. This year the work shop accepted 40 out of 600 possible applicants.
Compare this years acceptance rates to that of last years rate. Is this years acceptable rate higher or lower or equal to last year’s acceptance rate? Explain your reasoning.
Answers
Answer:
is this a test
Step-by-step explanation:
kshsjwoo2o1k1 snsn
The 24 students in Mr. Brown's homeroom sold 72 magazine subscriptions. The 28 students in Mrs. Garcia's homeroom sold 98 magazine subscriptions. Whose homeroom sold more magazine subscriptions per student? Be sure to include examples as you explain your reasoning. *
Answers
Answer:
see below
Step-by-step explanation:
Mr. Brown
72 magazines/ 24 students = 3 magazines per student
Mrs. Garcia
98 magazines/ 28 students = 3.5 magazines per student
Mrs. Garcia sold more per student
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is fifteen more than the second. Find the measures of the three angles.
Answers
29jsfsouodpolfkldsfmdsfsdfdssfsdfsadfsd I GOT THE ANSWER IT IS 5
Answer:x=45 y=60 x=75
Step-by-step explanation:
Jill made 20 muffins.she put them into 3 boxes and has two muffins left . How many are in each box if they contain the same amount of muffin
Answers
Answer:
6 muffins
she can fit 6 into each box because 20 divided by 3 is eighteen with a remainder of 3. 18 goes into 3 6 times.
whats is the 39th triangular number
Answers
Answer:
The 39th triangle number is 780
F(x)=3x-1 g(x) x^3 -5x^2
Find (f o g)(x)
Answers
============================================
Work Shown:
f(x) = 3x-1
f(x) = 3( x ) - 1
f( g(x) ) = 3( g(x) ) - 1 ... replace every x with g(x)
f( g(x) ) = 3(x^3-5x^2) - 1 ... plug in g(x) = x^3-5x^2
f( g(x) ) = 3x^3-15x^2-1
(f o g)(x) = 3x^3-15x^2-1
What is a solution of 3(x + 4) - x > 4?
A. -6
B. -5
C. -4
D. -3
(Please help I don’t understand)
Answers
Answer: -4 Please mark brainliest if I am right :D
Step-by-step explanation:
Let's solve your inequality step-by-step.
3(x+4)−x>4
Step 1: Simplify both sides of the inequality.
2x+12>4
Step 2: Subtract 12 from both sides.
2x+12−12>4−12
2x>−8
Step 3: Divide both sides by 2.
2x/2 > -8/2
x>−4
Answer:
x>−4
Answer:
C.-4
Step-by-step explanation:
3(x)+3(4)-x>4
3x+12-x>4
2x>-8
2x/2>-8/2
x>-4
2. Given 3,989, 825;
round to the nearest
ten thousand, hundreds, and thousands
Answers
Answer:
then thousand -3,990,000
hundred -3,989,800
thousands-3,990,000
hope this helped :)
Let p = log10 x, q = log10 y, and r = log10 z. (The 10s are base numbers.)
Write the expression log10 (x / y^2 √z) in terms of p, q, and r.
Please show work! I have the answer ( p- (2q + 1/2 r) ), but I need to show my work.
Answers
Answer:
(p / q^2 √r)
Just make x, y, z into p, q, r.
Very simple!
Your firm needs $630 for one quarter to finance a deficit. Interest charges are 2% per quarter. Your bank
requires a 10% compensating balance. How much must your firm borrow in order to obtain the needed funds?
$700.00
$705.00
O $693.00
$715.91
Answers
Hope this helps
Sally's class went to the zoo. Out of the 24 students at the zoo, 5/8 wanted to see the penguin exhibit. How many students wanted to see the exhibit?
Answers
Answer:
15 kids wanted to see the penguins
Step-by-step explanation:
get the denominator to 24 by multiplying the top and bottom by 3. (3×5=15)
Tim read 70% of his book containing 230 pages how many pages does he have left
Answers
Considering the whole book as 100%, there’s 30% left.
Then, 30% of 230 = 0,3*230 = 69 pages.
Hope you’re all right! Stay safe!
69 Pages are left to read by Tim.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Total pages= 230
Percentage of reading = 70%
So, number of Pages Tim reads
= 70 /100 x 230
= 161 pages
Hence, number of pages left = 230- 161 = 69 pages
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There are more than 7,000 languages spoken in the world today, and, on average, one of them disappears every ten days. What does that mean for the future of language diversity? What about the future of cultural diversity
Answers
Answer:
One language disappears every ten day. Each language has history and culture that vanishes. This will affect the future of language and cultural diversity because people aren’t trying to save theses languages and culture. Imagine if the English language disappeared. Plenty of English speaking countries’ cultural would also disappear. Plus, lots of these languages know one knows about. The future of language diversity would be bland, for only big languages would exist. Therefore, the disappearance of languages will affect language because people don’t try to save culture, and there’d be no language diversity in the future.
The disappearance of languages at such a rapid pace has significant implications for both language diversity and cultural diversity.
Language diversity is essential as it reflects the richness and complexity of human communication and expression. Each language carries unique ways of perceiving and understanding the world, and its loss means losing a vast amount of cultural and intellectual knowledge.
When languages disappear, the world loses diverse perspectives, traditional knowledge systems, folklore, literature, and linguistic diversity itself.
Furthermore, language is deeply intertwined with cultural diversity. Language shapes and is shaped by culture, and it serves as a vehicle for transmitting cultural practices, values, beliefs, and traditions across generations. When a language vanishes, it often signifies a loss of cultural identity and can lead to the erosion of cultural practices and knowledge associated with that language. The extinction of a language can disrupt intergenerational transmission of cultural heritage, affecting not only linguistic diversity but also cultural diversity.
The consequences of language extinction extend beyond the loss of knowledge and cultural heritage. Language is an integral part of personal and collective identity. When a language dies, it can cause a sense of disconnection, loss, and alienation for the speakers and their communities. Language loss can also exacerbate social and economic inequalities, as marginalized communities often face language-based discrimination and exclusion.
To preserve language diversity and cultural diversity, concerted efforts are needed. Governments, communities, linguists, educators, and language enthusiasts can play a crucial role in documenting endangered languages, revitalizing them through language revitalization programs, promoting bilingual education, and creating platforms for language preservation and intercultural exchange. Recognizing the value of linguistic and cultural diversity is essential for fostering understanding, tolerance, and respect among different communities.
Overall, the future of language diversity and cultural diversity depends on our collective commitment to preserving, revitalizing, and celebrating the vast array of languages and cultures that enrich our world.
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help me please i need help
Answers
Answer:
I have NO IDEA
Step-by-step explanation:
???????????????????????????/?
Someone give me an actual answer and not for the points...
At a Halloween fair, you see a huge Ferris wheel. There are ten seats on the wheel, with two people placed on each seat. Every minute, a seat passes by the exit platform. The Ferris wheel opened for 30 minutes at 11 a.m. and doubled its speed after fifteen minutes. How many people rode the wheel during this time?
Answers
Answer:
i believe 90 would be your answer.
Step-by-step explanation:
There are 10 seats and 2 people on each
2 times 10 = 20
the wheel was open for a total of 45 min
since every minute people are being switched out you have to do 2 times 10 4 times witch gives you 80 and the last 5 min you count 2 for each min and then your final answer will be 90.
50 POINTS!!! PLEASE HELPPPPP
Plot 1 2/5, −1/2, and −2 1/10 on the number line.
Answers
Answer:
the answer is -1 1/5
Step-by-step explanation: 7/5
Answer:
-1 1/5
Step-by-step explanation:
Model the unknown number situation by writing an algebraic expression.
the difference of a number and one hundred
n-100
100 - n
n + 100
100 +n
Answers
Answer:
number 1 or A i got it
Step-by-step explanation:
Answer: The answer you are looking for is A on edge
Step-by-step explanation: Pls Mark me Brainilist! I know that this is for sure Right!
Jamie has a sprinkler than covers a circular area with diameter 16 feet. What is the area of lawn that the
sprinkler covers?
Answers
Answer:
64π or 201.0619298297
Step-by-step explanation:
Area of a circle: πr²
To find r, the radius of the circle, take the diameter (16) and halve it to get 8. You can now place 8 into the equation to get π8². Square 8 to get 64. You now now have π64, or 201.0619298297.
How do I solve -0.4r=16?
Answers
Answer:
r = -40
Step-by-step explanation:
1. Move constants to the other side of the equation
r = 16/-.04
2. Simplify (by calculator)
You can use a calculator and plug in 16/-.04
r = -40
2. Simplify (by fraction)
You can turn -.4 into a fraction.
-.04 = - 4/10
r = 16/-(4/10)
r = 16*10/-4
r = -40
Please hurry its urgent Thank you
The function f(x) is graphed on the coordinate plane
What is f(-2)
A)-4
B)-2
C)4
D)0
Answers
1.Find the missing angle
2.what is the measure of angle 1
3.what is the measure of angle 2?
Answers
Subtract using the number line.
57−(−17)
Answers
Answer:
74
Step-by-step explanation:
Using the Additive Inverse, it is the same as saying 57+17 = 74
please give brainliest, have a nice day
Answer:
Hi there!
Your answer is
74
Step-by-step explanation:
Two negatives equal a positive.
57 + 17=74
Hope this helps!
!!! PLEASE ANSWER NOW!!!
A square has side length 4 cm. What is its area?
Answers
Answer:
16 cm
Step-by-step explanation:
4 × 4 = 16 cmI hope this helps!
Answer:
16cm
Step-by-step explanation:
To find area of a square, multiply a side by itself.
4 x 4 = 16
A right triangle has hypotenuse with length 8 inches. If one leg is 5 inches long, how long is the other leg?
Answers
Using Pythagoras theorem,
[tex]\sf a^2 + b^2 = c^2[/tex]
Where [tex]\sf a[/tex] and [tex]\sf b[/tex] are the two legs of the triangle, and [tex]\sf c[/tex] is the Hypotenuse.
Putting the given values:
[tex]\sf 5^2 + b^2 = 8^2 \\ \longrightarrow \sf b^2 = 64 - 25 \\ \longrightarrow \sf b^2 = 39 \\ \longrightarrow \sf b = \sqrt{39}\:\:inches[/tex]
Hence, the length of the other leg is,
[tex]\leadsto \underline{\boxed{\mathfrak{\pink{\sqrt{39}\:\:inches}}}}[/tex]
