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
What is the solition of 8 +a = 13?
Answers
Answer:5
Step-by-step explanation:
Answer:
a=5
Step-by-step explanation:
1. Subtract 8 from 13 to isolate the variable
a=5
Most major ski resorts offer family programs that provide ski and snowboarding in- struction for children. The typical classes provide four to six hours on the snow with a certified instructor. The following data are the location and the daily rate at 6 ski resorts reported on January 20, 2006. Resort Location Daily Rate Beaver Creek Colorado $137 Deer Valley Utah $115 Diamond Peak California $95 Hunter New York $79 Mount Bachelor Oregon $83 Butternut Massachusetts $108 How many variables are in the data set? ______________ Use whole number, example 3
Answers
Answer:
2
Step-by-step explanation:
Given the data:
Resort___________Location _____Daily Rate
Beaver Creek_____ Colorado______ $137
Deer Valley________ Utah_________$115
Diamond Peak______California_____ $95
Hunter____________New York_____ $79
Mount Bachelor_____Oregon______ $83
Butternut________ Massachusetts__ $108
The dataset above has two variables wgjich corresponds to the characteristic of each distinct element in the dataset. The variables are usually recognized as columns in a tabular dataset. The variables in the dataset above are :
Location and Daily rate which are attributes of each distinct Ski Resorts which corresponds to elements of the data.
PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((
Answers
Answer:
28
Step-by-step explanation:
For the area, since it is 49, each side should be equal, so the sides are 7. To get perimeter, you add all the sides together, or since all four side are equal, take 7 and multiply it by 4.
Simplify the algebraic expression by combining like (or similar) terms.
-7x - 8y- 5x - 6y
Answers
Answer:
-12x - 14y
Step-by-step explanation:
First I would move them side by side so I can see it better so:
-7x - 5x - 8y - 6y
now combine the x values together and the y values together:
-12x - 14y
= -20x-6y
Is your answer
Plz make it a brainliest answer
Select the correct answer from each drop-down menu. Identify the investment type and complete the description. _____offer corporations a loan. Investors tend to choose this investment type because it offers______ and _____
1.a bonds 1.b real estate investment 1.c saving account 1.c stocks
2.a risk 2.b safety
3.a dividends base on company profits 3.b income based on an interest rate
Answers
Answer: bonds/safety/income based on an interest rate
Step-by-step explanation:
:)
Community Gym charges a $50 membership fee and a $70 monthly fee. Workout Gym charges a $190
membership fee and a $60 monthly fee. After how many months will the total amount of money paid to
both gyms be the same? What will the amount be?
After
months the amount paid to both gyms will be $
Answers
Answer:
14 month
Step-by-step explanation:
Lets create equations for these two gyms. I believe this is an algebra 1 problem.
Community Gym: y=70x+50
Workout Gym: y=60x+190
Because both gyms are equal to y, we can set them together and solve for x.
70x+50=60x+190
10x=140
x=14
You can find the cost by plugging in 14 into both of the equations. You get a cost of $1030 after 14 months
Therefore, after 14 months you will have paid the same amount for both gyms.
Answer:
x = 14 months, $1030
Step-by-step explanation:
The expressions are,
→ 70x + 50
→ 60x + 190
Forming the equation,
→ 70x + 50 = 60x + 190
Now required value of x will be,
→ 70x + 50 = 60x + 190
→ 70x - 60x = 190 - 50
→ 10x = 140
→ x = 140/10
→ [ x = 14 months]
The amount of money will be,
→ 70(14) + 50 = 60(14) + 190
→ 980 + 50 = 840 + 190
→ $1030 = $1030
Hence, it will take 14 months.
In a group of students, 30 played chess, 19 played volleyball, 25 played
basketball, 14 played both volleyball and chess, 8 played both baskethall
and volleyball, 15 played both basketball and chess and 5 played both
three events. How many played chess only, basketball only and volleyball
only? How many students are there in all?
Answers
Answer:
Explained below.
Step-by-step explanation:
Denote the events as follows:
C = chess
V = volleyball
B = basketball
The data provided is as follows:
n (C) = 30
n (V) = 19
n (B) = 25
n (C ∩ V) = 14
n (B ∩ V) = 8
n (B ∩ C) = 15
n (C ∩ V ∩ B) = 5
Consider the Venn diagram below.
The number of students who played only chess is marked in pink:
n (Only C) = 6
The number of students who played only volleyball is marked in blue:
n (Only V) = 2
The number of students who played only basketball is marked in orange:
n (Only B) = 7
The number of students who played all three is marked in grey:
n (C ∩ V ∩ B) = 5
Which expression can be used to find 80% of 120?
Answers
Answer: the expression (120/100)*80 results in 80% of 120
Step-by-step explanation:
pls help plz pls plz
Answers
Answer: c
i’m pretty sure it’s c
Answer:
B
Step-by-step explanation:
15 rows with 7 cookies is just multiplying, 15*7, to get how many cookies that's in the tray. There's also 9 trays, so we multiply (15*7) by 9
Find the value of x.
Answers
its 38 (sorry if i get u wrong)
Water freezes at 0 celcius and 32 fahrenheit
Answers
Answer:
true
Step-by-step explanation:
the freezing point of water will always be 0 degrees celsius
:)
Jade and Jackson are considering a $210,000 mortgage for 30 years at 5.7%. With this information, their monthly payment would be $1218.84.
If they make only the minimum payment each month, what is the total payback of this loan?
How much of this total payback is interest?
Answers
Answer:
Jade and Jackson
The total payback of this loan = $438,782.72
The interest of this total payback is $228,782.72
Step-by-step explanation:
a) Data and Calculations:
Mortgage = $210,000
Interest rate of mortgage = 5.7%
Monthly payment = $1,218.84
Using an online calculator for Mortgage Payoff, the Original Payoff Schedule is:
Monthly Pay = $1,218.84
Total Payments = $438,782.72
Total Interest = $228,782.72
Answer:
Step-by-step explanation:
1218.84⋅12⋅30=$438,782.40
The total interest paid is the total payback less the amount borrowed.
$438,782.40−$210,000=$228,782.40
Given: x - 6 > -2
Choose the solution set.
{x | x ∈ R, x > 4}
{x | x ∈ R, x > -8}
{x | x ∈ R, x < 4}
{x | x ∈ R, x < -8}
Answers
The first one is the answer
A landscaper needs to estimate the amount of material required for a project building a circular brick patio for a client. The diameter of the patio is 13m and one bundle of brick will cover 116ft^2. How many bundles does he need?
Answers
Answer:
13 bricks
Step-by-step explanation:
Given parameter:
Diameter of the patio = 13m
Area of one bundle of brick = 116ft²
Unknown:
The number of bricks that will cover the patio = ?
Solution:
To solve this problem, we must find the area of the patio first.
Area of the patio = π r²
r is the radius of the patio;
Radius = [tex]\frac{13}{2}[/tex]
So area = π x ( [tex]\frac{13}{2}[/tex]) ² = 132.75m²
Now, let us convert the Area of the brick from ft² to m²;
1ft² = 0.093m²
116ft² = 0.093 x 116 = 10.79m²;
The number of bricks required to cover the patio = [tex]\frac{132.75}{10.79}[/tex] = 12.3 bricks,
Realistically, about 13 bricks would be needed.
Work out this problem: 2x + 3x -12x Show you work
Answers
Answer:
-7x
Step-by-step explanation:
2x + 3x - 12x
Add 2x + 3x, resulting in 5x
5x - 12x = -7x
It's negative because the -12 is the bigger number.
Hope this helps :D
A game store sold 206 games last week for $26 each the store owner had a sales goal of $5,000 for the week how much did the store owner actually earn
Answers
Answer:
5356$
Step-by-step explanation:
206*26=5356
The formulas below are the cost and revenue functions for a company that manufactures and sells small radios.
C(x)= 64,000 + 45x and R(x) = 49x
a. Use the formulas shown to write the company's profit function, P, from producing and selling x radios.
b. Find the company's profit if 24,000 radios are produced and sold.
a. The company's profit function is P(x) =
(Simplify your answer.)
Answers
Add 38 and 29, then multiply by 2.
Answers
Answer:
134
Step-by-step explanation:
A carnival ride holds 30 people at a time. In one hour,
220 people went on the ride. It was full each time
except the last. How many times was the ride
completely filled?
Answers
Answer:
7
Step-by-step explanation:
What is 7.103 × 105 in standard notation?
Answers
Answer:
710300 is your answer if im not mistaken
Amy earns $12.50 per hour at her work. She uses the equation shown to calculate the number of hours, she worked last week
12.5h = 312.5 how many hours did Amy work last week?
Answers
Answer:
25
I hope this helps.
Answer:
Amy worked 25 hours
Step-by-step explanation:
To first start off we have the equation 12.5h= 312.5
from here, we divide by 12.5 to have h by itself inorder to find how many hours she worked as h stands for hours.
Once you divide 312.5 by 12.5 you get h=25
Once again, the h stands for hours, so this means that Amy worked 25 hours, and that for one hour she earned 12.5 dollars.
If you want to find how much money she made for example in 5 hours, all you have to do is plug in the 5 for h and multiply it by 12.50 to get how much she earned in that certain amount of hours!
Hope this helps! If you have any questions, feel free to ask! :)
How do i do this problem
Answers
Answer:
no clue
Step-by-step explanation:
I have done this for a million times and I always get this one wrong I need the correct answer
Answers
Answer:
A, B, and D.
Step-by-step explanation:
HEY!! remember that if a number has ^2, it basically means it's multiplied by itself. for example:
5^2 = 5 x 5
aka, 25.
You can use this to check each of the answers in your formula, like this:
if x=6, then:
x^2 < 100
6 x 6 = 36
36 < 100
A is one of your correct answers!
Also remember, if you multiply a negative by a negative, it becomes positive.
-5 x -5 = 25
-10 x -10 = 100
what is the constant proportionality of this graph
Answers
Answer:
0 to 10
Step-by-step explanation:
I multiplied a number by itself and got 324. What was the
number?
Answers
Answer:
18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
18 times 18 equals 324 and the number 18 is being multiplied by itself
quarter note + whole note + quarter note
Answers
Answer:
1 1/2 notes
Step-by-step explanation:
The sum of the angle measures of a quadrilateral is 360°.
write and solve an equation to find the value of x. Use a protractor to check the
reasonableness of your answer.
Answers
125+132+72+x=360
329+x=360
x=31
solve for brainliest A keem measured the capacity of a glass as
2 7 0 mL and the capacity of a Th e rm o s® a s
1 L. He said that the ratio 270 :1 compare s
the capacity of the glass with the cap a c i t y
of the Th e rm o s®. Is his reasoning corre c t ?
E x p l a i n .
Answers
Answer:
[tex]his \: reasoning \: is \: correct.[/tex]
Step-by-step explanation:
[tex]since \: the \: ratio \: of \: the \: glass \: to \:that \\ \: of \: the \: thermos \: is \: in \: the \: fraction : \\ \frac{2 7 0 mL }{1mL} \: which \: is \:270 mL : 1mL \\ then \: the \: keem \: is \: right.[/tex]
what is the slope.of the line passing points (1, -5) and (4, 1)
Answers
Answer:
[tex]\huge{\boxed{\sf{ 2 }}}[/tex]
Step-by-step explanation:
Let the points be A and B
A ( 1 , -5 ) [tex]\longrightarrow[/tex] ( x1 , y1 )
B ( 4 , 1 ) [tex]\longrightarrow[/tex] ( x2 , y2 )
Finding the slope :
Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]
Slope = [tex]\frac{1 - ( -5 )}{4 - 1}[/tex]
Slope = [tex]\frac{1+5}{4-1}[/tex]
Slope = [tex]\frac{6}{3}[/tex]
Slope = [tex]2[/tex]
Hope I helped!
Best regards!
~TheAnimeGirl
Explain why each of the following integrals is improper. (a) 4 x x − 3 dx 3 Since the integral has an infinite interval of integration, it is a Type 1 improper integral. Since the integral has an infinite discontinuity, it is a Type 2 improper integral. The integral is a proper integral. (b) [infinity] 1 1 + x3 dx 0 Since the integral has an infinite interval of integration, it is a Type 1 improper integral. Since the integral has an infinite discontinuity, it is a Type 2 improper integral. The integral is a proper integral. (c) [infinity] x2e−x2 dx −[infinity] Since the integral has an infinite interval of integration, it is a Type 1 improper integral. Since the integral has an infinite discontinuity, it is a Type 2 improper integral. The integral is a proper integral. (d) π/4 cot(x) dx 0 Since the integral has an infinite interval of integration, it is a Type 1 improper integral. Since the integral has an infinite discontinuity, it is a Type 2 improper integral. The integral is a proper integral.
Answers
Answer:
a
Since the integral has an infinite discontinuity, it is a Type 2 improper integral
b
Since the integral has an infinite interval of integration, it is a Type 1 improper integral
c
Since the integral has an infinite interval of integration, it is a Type 1 improper integral
d
Since the integral has an infinite discontinuity, it is a Type 2 improper integral
Step-by-step explanation:
Considering a
[tex]\int\limits^4_3 {\frac{x}{x- 3} } \, dx[/tex]
Looking at this we that at x = 3 this integral will be infinitely discontinuous
Considering b
[tex]\int\limits^{\infty}_0 {\frac{1}{1 + x^3} } \, dx[/tex]
Looking at this integral we see that the interval is between [tex]0 \ and \ \infty[/tex] which means that the integral has an infinite interval of integration , hence it is a Type 1 improper integral
Considering c
[tex]\int\limits^{\infty}_{- \infty} {x^2 e^{-x^2}} \, dx[/tex]
Looking at this integral we see that the interval is between [tex]-\infty \ and \ \infty[/tex] which means that the integral has an infinite interval of integration , hence it is a Type 1 improper integral
Considering d
[tex]\int\limits^{\frac{\pi}{4} }_0 {cot (x)} \, dx[/tex]
Looking at the integral we see that at x = 0 cot (0) will be infinity hence the integral has an infinite discontinuity , so it is a Type 2 improper integral