Which of the following is an equivalent form of the compound inequality −22 > −5x − 7 ≥ −3?A) −5x − 7 < −22 and −5x − 7 ≥ −3
B) −5x − 7 > −22 and −5x − 7 ≥ −3
C) −5x > −22 and −7 ≥ −3
D) −5x − 7 < −22 and −5x − 7 ≤ −3
Answers
The equivalent form of the compound inequality −22 > −5x − 7 ≥ −3 are A) −5x − 7 < −22 and −5x − 7 ≥ −3
What is a solution set to an inequality or an equation?
If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.
Then a Set of such values is called solution set to the considered equation or inequality.
The equivalent form of the given inequality can be obtained by dividing the inequality into two parts.
In this case, we are given -22 > -5x - 7 > -3.
The two parts are; -22 > -5x - 7 and -5x - 7 > -3.
Since the −5x − 7 and −22 have interchanged sides, the inequality sign also changes direction.
For part two, we have −5x − 7 ≥ −3 remains unchanged.
Therefore, The choice that reflects these parts is A)-5x - 7 < -22 and -5x - 7 -3
Hence, The equivalent form of the compound inequality −22 > −5x − 7 ≥ −3 are A) −5x − 7 < −22 and −5x − 7 ≥ −3
Learn more about inequalities here:
#SPJ2
Working;
Since the −5x − 7 and −22 have interchanged sides, the inequality sign also changes direction.
For part two, −5x − 7 ≥ −3 remains unchanged.
Related Questions
Evaluate x0 + y0 for x = 3 and y = 2.
How do you write an equation of a line that is parallel line to y=8x-8 through the point (5,2)
In a collection of 1050 flowers, 3/10 of them are red , 2/5 of them arewhite and the rest are yellow. Find the no. of red, white and yellow flowers
Please sb help and write it down on paper then send a pic❤️
Answers
Answer:
K=32J
Explanation:
Kinetic energy is given by:
K=12mv2
We are given that m=4kg and v=4ms.
⇒K=12(4kg)(4ms)2
=32Nm
=32J
Step-by-step explanation:
i have no idea if this helps or not
what is the solution to the system of equations
Answers
2x + 6y = -6 ...(1)
4x - 3y = -12 ...(2)
We can use the method of substitution or elimination to find the solution. I will use the method of substitution.
From equation (1), we can solve for x in terms of y:
2x = -6 - 6y
x = (-6 - 6y)/2
x = -3 - 3y
Now, substitute this value of x into equation (2):
4(-3 - 3y) - 3y = -12
-12 - 12y - 3y = -12
-15y = 0
y = 0
Substitute this value of y back into equation (1) to find x:
2x + 6(0) = -6
2x = -6
x = -3
Therefore, the solution to the system of equations is x = -3 and y = 0.
hope this helps
Answer:
x = -3, y = 0
Step-by-step explanation:
2x+6y=-6 equation1
4x-3y=-12 equation2
multiply equation2 by 2
2[ 4x-3y=-12]
8x - 6y = -24 equation3
add equations 1 & 3
2x+6y=-6
8x - 6y = -24
--------------------
10x = -30
x = -3
substitute x = -3 to any of the equations
I will use equation1
2x+6y=-6
2(-3) + 6y = -6
-6 + 6y = -6
6y = 0
y = 0
5/21
3/28
4/29
Answers
Answer: The probability that a student chosen at random has a brand X mobile phone given that he has a brand Y mobile phone is 4/29.
Step-by-step explanation:
Since, the total number of students, n(s) = 1,000
The number of students who have X mobile phones, n(X) = 420,
And, number of students who have Y mobile phones, n(Y) = 580,
Thus, the probability of the student that has Y phones,
While, the number of students who have both phones, n(X∩Y) = 80
Thus, the probability of the student who has both phones,
Hence, the probability that a student chosen at random has a brand X mobile phone given that he has a brand Y mobile phone.
Hence, the required probability is 4/29.
Answers
Answers
The balance of Albert is $2159.07; the balance of Marie is $2244.99, the balance of Hans is $2188.35, and the balance of Max is $2147.40. Marie is $10,000 richer at the end of the competition.
What is Compound interest?
Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.
To determine the balance of Albert’s $2000 after 10 years :
If the amount of $1000 at 1.2 % compounded monthly,
A = P(1 +r/n)ⁿ n = 10 years
here P = $1000 and r = 1.2
A = 1000(1 + 0.001)¹²⁰
A = $1127.43
If Albert $500 losing 2%
So 0.98 × 500 = $490
If $500 compounded continuously at 0.8%
So A = P
A = 500
A = 541.6
So the balance of Albert’s $2000 after 10 years :
Total balance = 1127.43 + 490.00+ 541.64 = $2159.07
To determine the balance of Marie’s $2000 after 10 years:
If 1500 at 1.4 % compounded quarterly,
A = 1500(1 + 0.0035)⁴⁰ = $1724.99
If $500 Marie’s gaining 4 %
So 1.04 × 500 = $520.00
So the balance of Marie’s $2000 after 10 years
Total balance = 1724.99 + 520.00 = $2244.99
To determine the balance of Hans’ $2000 after 10 years:
If $2000 compounded continuously at 0.9%
So A = 2000
A = $2188.3
To determine the balance of Max’s $2000 after 10 years :
If $1000 decreasing exponentially at 0.5 % annually
So A = 1000(1 - 0.005)¹⁰= $951.11
If $1000 at 1.8 % compounded bi-annually
So A = 1000(1 + 0.009)²⁰ = $1196.29
So the balance of Max’s $2000 after 10 years
Total balance = 951.11 + 1196.29 = $2147.40
Therefore, Marie is $10,000 richer at the end of the competition.
Learn more about Compound interest here :
#SPJ2
Answer:
Step-by-step explanation:
Albert:
$1000 earned 1.2% annual interest compounded monthly
= 1000 (1+.001)120
(periodic interest = .012/12 ,n is periods = 10yr x 12 mos)
$500 lost 2% over the course of the 10 years
= 500 (.98)
$500 grew compounded continuously at rate of 0.8% annually
= 500 e^008(10) 10 years interest .008 (in decimal form)
Add these three to see how Albert did with his investments
Answers
The equation is
y = 9x - 4x^2
y = -4x^2 + 9x
y = -x(4x - 9)
The steepest rate of change from x = 1 to x =2
x = -1 ; y = 0
x = 1 ; y = 2
x = 2 ; y = 0
x =3 ; y = -4
So, based from the table show, the steepest rate of change is C. equation, –3