Answers
The set A satisfying the given inequality is A = (-[tex]\infty[/tex], -10].
What are some properties of an inequality relation?Following are some facts which are true for an inequality relation:
Equal numbers can be added or subtracted from both sides of an inequality without affecting the inequality sign.The Inequality sign is unchanged if both sides are multiplied or divided by a positive number, but when multiplied or divided by a negative number the inequality sign is reversed.[tex]\frac{5x-2}{8} - \frac{3x-5}{10} &\ge& x+y\\\\\Rightarrow\;\; \frac{13}{40}x + \frac{1}{4}&\ge& x+y\\\\\Rightarrow\;\;\;\;\;\; -\frac{27}{40}x &\ge & y - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\;\; -x &\ge & \frac{40}{27}\left( y-\frac{1}{4} \right).\hspace{1cm}(1)[/tex]
Since y ∈ B, -2 ≤ y ≤ 7. So,
[tex]\;\;\;\;\;\;\;\,-2 - \frac{1}{4}\; \le\; y - \frac{1}{4} \;\le\; 7 - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\; -\frac{9}{4}\; \le\; y - \frac{1}{4} \;\le\; \frac{27}{4}\\\\\Rightarrow\;\;\; -\frac{9}{4}\cdot \frac{40}{27} \;\le\; \frac{40}{27} \left( y-\frac{1}{4} \right) \;\le \;\frac{27}{4}\cdot \frac{40}{27}\\\\\Rightarrow\;\;\;\;\;\;\;\; -\frac{10}{3} \;\le\; \frac{40}{27}\left( y - \frac{1}{4} \right)\; \le\; 10.[/tex]
The set {-x | inequality (1) holds ∀ y ∈ B} is [10, [tex]\infty[/tex]) i.e.
10 ≤ -x ≤ [tex]\infty[/tex].
Multiplying -1 throughout gives
-10 ≥ x ≥ -[tex]\infty[/tex].
x, thus, lies in the range A = (-[tex]\mathbf{\infty}[/tex], -10}.
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Disclaimer: The question was incomplete. Please find the full content below.
QuestionFind the set A such that for x ∈ A
[tex]\frac{5x - 2}{8} - \frac{3x - 5}{10} \ge x + y[/tex]
∀y ∈ B = {y ∈ R | -2 ≤ y ≤ 7}.
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Related Questions
Help please I'll mark you as brainlist if the answer is correct
if (x + q) is a factor of two polynomials x2 + px + q and x2 + mx + n, then prove that a = n-q m-p
Answers
If (x + q) is factor of two polynomial [tex]x^2+px+q[/tex] and [tex]x^2+mx+n[/tex] than [tex]a = \frac{n - q}{m- p}[/tex].
x + a is factor of equations [tex]x^2+px+q[/tex] and [tex]x^2+mx+n[/tex]
What is a polynomial equation?Polynomial equation is equation of independent variables.
Putting it in both the equations
[tex]x^2+px+q=0[/tex]
[tex](-a)^2+p(-a)+q=0\\a^2-ap+q=0 ........(1)[/tex]
[tex]x^2+mx=n = 0\\(-a)^2+m(-a)+n=0\\a^2-am+n=0 .....(2)[/tex]
subtracting (2) from (1)
[tex]-am+ap+n-q=0[/tex]
[tex]a=\frac{n-q}{m-p}[/tex]
Thus, the required expression is [tex]a=\frac{n-q}{m-p}[/tex].
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Use the compound interest formulas A=P1+
r
nnt and A=Pert to solve the problem given. Round answers to the nearest cent.
Find the accumulated value of an investment of $25,000 for 3 years at an interest rate of 7% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.
Answers
The accumulated value of an investment if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously is $30731.4 $ , $30785.98 $30823.14 , 30841.95
What is Interest ?Interest is the amount received by a person as a result of investing certain amount of money for a certain period of time.
It is given that
Principal = $ 25000
Time = 3 years
Interest Rate = 7 %
The amount is given by
[tex]\rm A = P( 1+ \dfrac{r}{n}) ^{nt}[/tex]
Compounded semiannually
n = 2
Compounded Quarterly
n = 4
Compounded Monthly
n =12
Compounded Continuously
P = P₀ [tex]\rm e ^{rt}[/tex]
Therefore the accumulated value for
compounded Semiannually is
[tex]\rm A = 25000( 1+ \dfrac{7}{200}) ^{2*3}[/tex]
A = $30731.4
Compounded Quarterly
[tex]\rm A = 25000( 1+ \dfrac{7}{400}) ^{4*3}[/tex]
A = $30785.98
Compounded Monthly
[tex]\rm A = 25000( 1+ \dfrac{7}{1200}) ^{12*3}[/tex]
A = $30823.14
Compounded Continuously
[tex]\rm P = 25000 e ^{ 7 * 3 }[/tex]
P = $30841.95
Therefore the accumulated value of an investment if the money is
a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously is
$30731.4 $ , $30785.98 $30823.14 , 30841.95
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An equilateral triangle has the height BO= 80 cm. Considering, height BO splits the base (segment) AC into two equal segments of size x/2, find X.
Answers
Answer:
Given - an equilateral triangle
An equilateral triangle means all sides equal and all angle equal to 60°
In triangle BOA
sin 60° = OB/ AB
√3/2. = 80/AB
AB = 160√3/3
X = 160√3/3
find the gradient of the line joining the points (0,2) and (-2,-4)
Answers
Answer:
m = 3
Step-by-step explanation:
Gradient of a line is given by the formula
m= (y2-y1) /(x2-x1) which is change y divided by change in x
m = (-4-2)/(-2-0)
m = -6/-2
m = 3
Answer: the gradient is 3
Step-by-step explanation:
for a full explanation refer to the document and the ones written colorfully are the explanation. So, if you want just the workings they are the ones written in black.
and I drew an eye! Have a nice day!
Solve for x
3x² - 5x + 6 = 10 - 4x
Answers
Answer: [tex]-1, \frac{4}{3}[/tex]
Step-by-step explanation:
[tex]3x^{2}-5x+6=10-4x\\\\3x^{2}-x-4=0\\ \\ (x+1)(3x-4)=0 \\ \\ x=\boxed{-1, \frac{4}{3}}[/tex]
Answer:
x = -1
x = 4/3
Step-by-step explanation:
Hello!
First, let's convert the equation into Standard Form: [tex]ax^2 + bx + c = 0[/tex]
[tex]3x^2 - 5x + 6 = 10 - 4x[/tex][tex]3x^2 - x - 4 = 0[/tex]We can solve this by factoring the quadratic. We have to find two numbers that multiply to [tex]ac[/tex] but add up to [tex]b[/tex].
ac = -12b = -1The two numbers would be -4 and 3. We can expand -x to -4x + 3x, and then factor by grouping.
Factor[tex]3x^2 - x - 4 = 0[/tex][tex]3x^2 +3x - 4x - 4 = 0[/tex][tex]3x(x + 1) - 4(x + 1) = 0[/tex][tex](3x - 4)(x + 1) = 0[/tex]Use the Zero Product Property. Set each factor to zero and solve for x.
3x - 4 = 03x = 4x = 4/3x + 1 = 0x = -1The solutions to the quadratic are -1 and 4/3.
Find the measure of the remote exterior angle. m∠x=(198−5n)°m∠y=(5n+37)°m∠z=(n+7)°
Answers
The value of the angle ∠x will be ∠x = 128°. Then the correct option is C.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The triangle is given below.
The sum of the two interior angle is equal to the third exterior angle.
m∠x = (198 − 5n)°
m∠y = (5n + 37)°
m∠z = (n + 7)°
We know that
∠x = ∠y + ∠z
198 - 5n = 5n + 37 + n + 7
11n = 154
n = 14
Then the value of the angle ∠x will be
∠x = 198 – 5 × 14
∠x = 128°
Then the correct option is C.
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please help
PLEASE
Answers
Answer:
Step-by-step explanation:
4567890987654345678
How many significant digits are there in the number 237.16?
Answers
Answer:
3
Step-by-step explanation:
Frankie wants to build a path from one corner of his yard to the opposite corner. his yard measures 20 ft. x 32 ft. what will be the length of his path to the nearest tenth of a foot?
21.5 ft
25.0 ft
32.6 ft
37.7 ftfrankie wants to build a path from one corner of his yard to the opposite corner. his yard measures 20 ft. x 32 ft. what will be the length of his path to the nearest tenth of a foot?
21.5 ft
25.0 ft
32.6 ft
37.7 ft.
Answers
The length of his path to the nearest tenth of a foot is 37.7 ft option fourth is correct.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
We have:
Frankie wants to build a path from one corner of his yard to the opposite corner. his yard measures 20 ft. x 32 ft.
From the Pythagoras theorem:
Perpendicular(P) = 32 ft
Base(B) = 20 ft
H = √(32²+20²)
H = √1424
H = 37.7 ft
Thus, the length of his path to the nearest tenth of a foot is 37.7 ft option fourth is correct.
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Answer:
D) 37.7
Proof:
a-3/7 devided by 3-a/21
Answers
The answer is pretty simple but I put it in a picture below
Jackson took 8 fewer pictures on Saturday than he did on Friday. If he took 11 pictures on Friday, how many pictures did he take on Saturday?
Answers
Friday =11
Saturday =?
But, we know that the pictures he took on Saturday are eight times fewer than those he took on Friday.
Saturday = 11-8
= 3
∴ He took 3 pictures on Saturday.
Hope this helps >3
Which expressions are equivalent to the one below? Check all that apply.
In (e^2)
Possible Answers Below:
A.)2•In e
B.) 2
C.) 2e
D.) 1
Answers
Answer:
a and b
Step-by-step explanation: you can move the exponent to the front and lne is also equal to one times 2 = 2
please help! [4 x 3⁵ - 9 x (-7)] + 3³ (-4² +2²) - 11 Give your answer in simplest form.
Answers
Answer:
Please see the question below.
Step-by-step explanation:
In the expression "[4 x 3⁵ - 9 x (-7)]" I'm unclear if the "x" is a multiplication sign, or the variable x. I'll assume it is the variable x in my answer.
4 x 3⁵ = 972x
- 9 x (-7) = 63x
3³ (-4² +2²) = 27 (20) = 540
-11 = -11
========
Putting it all together:
972x + 63x + 540 -11
1035x + 529
Denver has a current temperature of -5°, while Barcelona has a current temperature of 54°. What is the difference in temperature between Denver and Barcelona?
Answers
Answer:
59°
Step-by-step explanation:
Difference=54-(-5)
=54+5=59
A 11 gram sample of a substance that’s used to treat thyroid disorders has a k- value of 0.125
Answers
The substance's half-life is 5.5 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.125
What is exponential decay?During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have an exponential function:
[tex]\rm N = N_oe^{-kt}[/tex]
Plug N = N⁰/2
[tex]\rm N_o/2 = N_oe^{-kt}[/tex]
[tex]\rm \dfrac{1}{2} = e^{-0.125t}[/tex]
Solving for t:
t = 5.54 ≈ 5.5 days
Thus, the substance's half-life is 5.5 days if the 11-gram sample of a substance that’s used to treat thyroid disorders has a k- the value of 0.125
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Help asap show your work!
Answers
Answer:
x = 4
Step-by-step explanation:
2
3
4
5
Which distance measures 7 units?
L
M
N
-8-7-6-5-4-3-2-1012
3
the distance between points L and M
the distance between points L and N
the distance between points M and N
the distance between points M and P
5 6 7 8
TIME REMAINING
56:41
Answers
Answer:
the distance between points M and P
Step-by-step explanation:
i did it
Simplify the expression
-17.8a-2.4a+25-19.5
Answers
Answer:
-20.2a+5.5
subtract the values with a in it and the ones without the a together.
The davidson family wants to expand its rectangular patio, which currently measures 15 ft by 12 ft. they want to extend the length and width the same amount to increase the total area of the patio by 160 ft2. which quadratic equation best models the situation? a = lw (15)(12) (x)(x) = (15)(12) 160 (15x)(12x) = (15)(12) 160 2(15 x) 2(12 x) = (15)(12) 160 (15 x)(12 x) = (15)(12) 160
Answers
Answer:
160
Step-Step Explaining:
So I Know This ⏩ ⏩
The circle above with center O has a circumference of 36. What is the length of minor arc AC? A) 9 B) 12 C) 18 D) 36
Answers
Answer:
A) 9
Step-by-step explanation:
⇒ Circumference of a Circle = 2πr
[tex]36=2\pi r[/tex]
[tex]r=\frac{36}{2} \pi[/tex]
[tex]r=\frac{18}{\pi }[/tex]
Length of arc = rθ
θ = angle AC = [tex]90^o[/tex]
Convert [tex]90^o[/tex] to radian
= [tex]\frac{90\pi }{180}[/tex]
= [tex]\frac{\pi }{2}[/tex]
length of arc = 18/π x π/2
= 9
I need more help I'm lazy (img included)
Answers
Answer:
B)20
Step-by-step explanation:
convert 900in to ft=75
1500/75=20boxes
There are 12 inches in a foot, so 1500 times 12 is 18000, 18000 divided by 900 is 20
someone help me get outta summer school slope? And y intercept?
Answers
A _______ random variable has infinitely many values associated with measurements.
Answers
Answer:
Continuous
A continuous random variable has infinitely many values, and those values can be associated with measurements on a continuous scale in such a way that there are no gaps or interruptions.
If the nth term of a sequence is 18-8n what is the 8th term
Answers
Answer:
[tex]a_{n} =18-8n\\a_{8} =18-8(8)=-46[/tex]
Answer:
-46
Step-by-step explanation:
(hello, I just answered your previous question--some stuff will sound similar because we are applying the same concept :) )
We know that the nth term of the sequence is 18 - 8n
the "nth" term of a sequence means that you can plug in the term place to get the term value (ex. if the nth term is n + 2, we can plug any term in {let's say, the eighth term, 8 + 2 = 10 ; to get our term's value} )
18 - 8n is sequence
18 - 8(8) is 8th term
18 - 64 is 8th term
-46 is the 8th term
hope this helps!! :)
The largest bubblegum bubble ever blown was 23 inches in diameter. What was its circumference?.
Answers
Answer:
[tex]C=23\pi[/tex] inches
or as a decimal
72.26 inches
Step-by-step explanation:
Formula for circumference: [tex]C=2\pi r[/tex]
Radius = [tex]\frac{d}{2}[/tex]
Altogether we get: [tex]C=2*\pi*\frac{d}{2}[/tex]
Which simplifies to: [tex]C=\pi d[/tex]
So now we can plug in 23 for [tex]d[/tex].
[tex]C=\pi*23[/tex]
Our final answer is:
[tex]C=23\pi[/tex] inches
or as a decimal
72.26 inches
Timothy has a savings account that he started five years ago to begin saving for college. The
savings account has an interest rate of 3% and has earned $225 in interest since he began the
account. How much money did Timothy start the account with when he originally opened the
savings account?
A. $1500.00
B. $33.75
C. $7500.00
D. $3375.00
of $18
Answers
Answer:
A. $1500.00
Step-by-step explanation:
Assuming this is a simple interest savings account.
Simple interest formula
I = Prt
where:
I = total interestP = principal amountr = interest rate (in decimal form)t = time (in years)Given:
I = $225r = 3% = 0.03t = 5 yearsSubstitute the given values into the formula and solve for P:
⇒ I = Prt
⇒ 225 = P(0.03 ×5)
⇒ 225 = P(0.15)
⇒ P = 225 ÷ 0.15
⇒ P = 1500
Therefore, Timothy started the account with $1500.00.
Subtract the following complex numbers:
(4+4i)-(13+17i)
OA. 9+21/
OB. -9+21/
OC. 9-13i
OD.-9-13i
Answers
We have been given (4 + 4i) - (13 + 17i) .after solving we get the correct option is A ) -9 - 13 i.
What are complex numbers?Complex numbers are those numbers that contain the imaginary and the real part.
We have been given (4 + 4i) - (13 + 17i) .
On removing the parenthesis
4 + 4 i - 13 - 17i.
On combine the real part and complex parts, we get
= 4 - 13 + 4i - 17 i.
= -9 - 13 i.
Therefore, The correct option is A ) -9 - 13 i.
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Use substitution to solve the following system of equations
2x + 3y = 18 AND X = y - 6
Answers
Answer:
y=6,x=0
Step-by-step explanation:
here's an attachment with how to solve
all natural numbers (N) are integers (Z), but not all integers are natural numbers true or false
Answers
True. All natural numbers N are integers Z, but not all integers are natural numbers.
Natural numbers:
Natural numbers starts from zero to infinity are all positive.All the natural numbers are whole numbers.It is denoted by NThe set of natural numbers are N = 1,2,3, ...Integers:
Integers are the whole numbers that contain positive numbers, zero and negative numbersIt is denoted by ZThe set of integers are Z = ... ,-3,-2,-1,0,1,2,3, ...Since natural numbers are all positive, N is positive integers but not all integers are natural numbers.
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The driving distance between Manchester and London is 195 miles. Farid intends to travel from Manchester to London by coach. The coach will leave Manchester at 3.30pm.
Farid assumes that the coach will travel at an average speed of 50mph
A)Using his assumption, work out Faris's arrival time at London.
It actually turns out that the coach has a lower average speed.
B)Describe how this affects the arrival time
Answers
Answer:
7:24pm
Step-by-step explanation:
At 50 mph, it will take 195/50 = 3.9 hours to reach London
3.9 hours = 3 .9 * 60 = 3 hours and 54 minutes(54 = 0.9 * 60 )
3:30 + 3:34 ==> 7:24
(one way to do this is to add up the hours and minutes separately so we get 6:84) Since 84 minutes = 1 hour and 24 minutes, just add 1:24 to 6 to get 7:24
Another way to do this is to see that if the distance was 200 miles, then it would take exactly 4 hours (200/50) to reach at 7:30pm But it is short by 5 miles. At the speed of 50mph, the time taken to travel 5 miles = 60/50 * 5 = 6 minutes so deduct 6 minutes from 7:30pm to get 7:24pm
If the train is slower average speed, then the arrival time is delayed beyond 7:24pm
