Answers
Answer:
To solve the first inequality, you need to subtract 6 from both sides of the inequality, to obtain 4n≤12. This can then be cancelled down to n≤3 by dividing both sides by 4. To solve the second inequality, we first need to eliminate the fraction by multiplying both sides of the inequality by the denominator, obtaining 5n>n^2+4. Since this inequality involves a quadratic expression, we need to convert it into the form of an^2+bn+c<0 before attempting to solve it. In this case, we subtract 5n from both sides of the inequality to obtain n^2-5n+4<0. The next step is to factorise this inequality. To factorise we must find two numbers that can be added to obtain -5 and that can be multiplied to obtain 4. Quick mental mathematics will tell you that these two numbers are -4 and -1 (for inequalities that are more difficult to factorise mentally, you can just use the quadratic equation that can be found in your data booklet) so we can write the inequality as (n-4)(n-1)<0. For inequalities where the co-efficient of n^2 is positive and the the inequality is <0, the range of n must be between the two values of n whereby the factorised expresion equals zero, which are n=1 and n=4. Therefore, the solution is 1<n<4 and we can check this by substituting in n=3, which satisfies the inequality since (3-4)(3-1)=-2<0. Since n is an integer, the expressions n≤3 and n<4 are the same. Therefore, we can write the final answer as either 1<n<4, or n>1 and n≤3.
Related Questions
A swimming pool that holds 10,000 gallons of water is being filled at a rate of 600 gallons per hour. The function h(x)=600x represents the amount of water in the pool after x hours. Find h(3.25).
Answers
Answer:
16.6
Step-by-step explanation:
In 3.5 hours, a total of 1950 gallons of water will be filled in swimming pool.
What is the general form of a linear function?The general form of a linear function is given as follows -
y = kx
or
y = kx + c
Given is a swimming pool that holds 10,000 gallons of water is being filled at a rate of 600 gallons per hour. The function h(x)=600x represents the amount of water in the pool after [x] hours.
The linear function that represents the amount of water in the pool after [x] hours is given by -
h[x] = 600x
Now, for x = 3.5, the amount of water in the pool will be -
h[3.25] = 600 x 3.25 = 1950 gallons of water.
Therefore, in 3.5 hours, a total of 1950 gallons of water will be filled in swimming pool.
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Find three different integer solutions to the equation -3x-y=-1
Answers
Answer:
The integers are -3, x, and -y
Step-by-step explanation:
The elevations, in feet, of three citites are marked on the number line shown below. The point 0 on the number line represents sea level. Which statement is true?
Answers
Answer:
cityQ
Step-by-step explanation:
City Q is located at the sea level
The statement that should be true is
City P is above sea level and City Q is below sea level.
What is the number line?The word "number line" in mathematics refers to a straight line where a number should be positioned at similar intervals or segments along with its length.
Given:
The point 0 on the number line represents sea level.
As, It should be presented in a horizontal style and be infinitely in any direction.
As a result, option c should be the statement that is true. City Q is below sea level, but City P is above it.
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how do I work out this problem
sofia opens a new savings account with a 2.25% simple interest rate. She deposited $3500 and earned $3696.88 total by the time she checked the account again. How long was the money left untouched in the savings account?
Answers
please help i will mark brainliest
Answers
Answer:(3,-5)
Step-by-step explanation:
Answer:
The answer will be
B. (3,-5)
2x+10=6(x-1) What does x equal
Answers
Answer:
x=4
Step-by-step explanation:
2x+10=6(x-1)
2x+10=6x-6
10=6x-2x-6
10=4x-6
16=4x
4=x
Tasnia had a piece of ribbon that was 6 ½ yards long. She used this ribbon to make bows. Each bow was made from a piece of ribbon that was ⅓ yard long. This situation can be represented by the equation 6 ½ ÷ ⅓ = 19 ½ . Which statement best describes what the quotient 19 ½ represents?
Answers
Answer: the number of bowss that can be made.
Step-by-step explanation:
You didn't give the options but let me help out.
We are told that Tasnia had a piece of ribbon that was 6 ½ yards long and that she used this ribbon to make bows. We are further told that each bow was made from a piece of ribbon that was ⅓ yard long and that this situation can be represented by the equation 6 ½ ÷ ⅓ = 19 ½.
The quotient gotten above simply means the number of bowss that can be made.
the following two triangles are congruent. Select the correct statement for the correct corresponding part that must be congruent.
Answers
Answer:
You are correct.
Step-by-step explanation:
y and j are the vertexes. Given that M and S are the corresponding parts of the 2 triangles, I would say you picked the right answer. But the question is ambiguous and there might be some hidden meaning why this is wrong. The reason might not stand up in a court of law, but instructors do hold the gun at your head.
Curse at it and move on.
How to calculate the H-Method of
f(x)= -2,5x² x0=4 ?
I really have no clue
Answers
Answer:
Yotmpocoa ngo ni ideate
Step-by-step explanation:
I need help with this, please!
Answers
Answer:g(x)=-x/2-6
Step-by-step explanation:plug it in
Lyla is rounding some numbers to the nearest tenth. Select the number that will have an 8 in the tenths place after rounding.
A. 5.74
B. 6.08
C. 7.79
D. 8.86
Answers
Answer:
c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
if u round 7.79 it will be 8 because 7 is greater than 5
??help me please now
Answers
Answer:
x^2+10x+24
Step-by-step explanation:
(x+6)×(x+4)
=x^2+4x+6x+24
=x^2+10x+24 (ans)
Only 5 and 6. Please help me need it for now
Answers
Answer:
5)1075000000
6)333.333333333
Step-by-step explanation:
5)4.3*10^3=4300
2.5*10^5=250000
6)3*10^6=3000000
9*10^3=9000
Step-by-step explanation:
5.)
(4.3 × 10³) × (2.5 × 10⁵)
10.75 × 10⁸
Please help ASAP! (Photo)
Answers
Answer:a sq+ b sq= c sq
Step-by-step explanation: add a and b and the answer is c
Determine whether the samples are independent or dependent. Upper A data set includes the age at marriage for 90 randomly selected married men and 90 randomly selected married women. nbsp Choose the correct answer below.
A. The samples are independent because there is a natural pairing between the two samples.
B. The samples are dependent because there is a natural pairing between the two samples.
C. The samples are dependent because there is not a natural pairing between the two samples.
D. The samples are independent because there is not a natural pairing between the two samples.
Answers
Answer:
D. The samples are independent because there is not a natural pairing between the two samples
explanation:
Independent samples do not affect each other as each group is selected randomly. They are common in statistical analysis, example: when there is a control group and an experimental group and the subjects for each group are different. In the above example, the samples do not depend on each other. There are 90 randomly selected married men in one group and 90 randomly selected married women in the other. The subjects are different in the two groups and so they do not affect each other. This is unlike dependent/paired samples where for example same subjects are used before and after a medication and therefore each group affects the other.
1/3 of a number is 4 less than 1/2 of the number, the number is
Answers
Answer:
12
Step-by-step explanation:
1/2x=3/4x−3⇒2x=3x−12⇒x=12
What is the value of this expression? Select all that apply (8.59 x 10^4) - (3.2 x 10^3)
Answers
Answer:
A. 8.27*10^4
D. 82,700
Step-by-step explanation:
if the original price was $19.99, estimate the new price by first rounding the original price
Answers
Answer: $20.00
Step-by-step explanation:
Answer:
When rounded the answer will be $20.00.
Step-by-step explanation:
Solve:
10 -0.75x < 7
Please and thank you
Answers
Answer:
The answer is x<4
But the girl over me just did it for points
Answer:
x<4
Step-by-step explanation:
NEED HELP ASAP!!!!!!! WILL GIVE BRAINLIEST!!!!!!
Rectangle ABCD is in the coordinate plane. Which of the following is a valid definition of a reflection of rectangle ABCD?
A. Every point X on ABCD is mapped to a new point X′ such that each length from X toX′ is the same.
B. Every point X on ABCD is mapped to a new point X′ such that the distance from X to the line of reflection is the same as the distance from X′ to the line of reflection.
C. Every point X on ABCD is mapped to a new point X′ such that the coordinates of X′ are opposites of the coordinates of X.
D. Every point X on ABCD is mapped to a new point X′ such that one coordinate of X′ is the same as in X and the other coordinate of X′ is the opposite of the other coordinate in X.
Answers
The definition of a reflection of rectangle ABCD is option D:
"Every point X on ABCD is mapped to a new point X' such that one coordinate of X' is the same as in X, and the other coordinate of X' is the opposite of the other coordinate in X".
When a reflection occurs, each point on the original shape is mapped to a new location on the reflected shape.
Option A states that every point X on ABCD is mapped to a new point X' such that each length from X to X' is the same. This definition does not capture the essence of a reflection because it doesn't consider the relationship between the original shape and its reflection.
Option B states that every point X on ABCD is mapped to a new point X' such that the distance from X to the line of reflection is the same as the distance from X' to the line of reflection.
Option C states that every point X on ABCD is mapped to a new point X' such that the coordinates of X' are opposites of the coordinates of X.
Option D correctly captures the nature of a reflection. This states that each point X on ABCD is mapped to a new point X' where one coordinate of X' is the same as in X, and the other coordinate of X' is the opposite of the other coordinate in X.
Therefore, option D is the valid definition of a reflection of rectangle ABCD.
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A cookie factory puts 2/5 of a barrel of flour into each batch of cookies. How much flour will the factory use for 5 batches?
Answers
Answer:
they would use 2 barrels of flour. or 10/5
Step-by-step explanation:
Answer:
2 barrels
Step-by-step explanation:
Just multiply 2/5 by 5
Hope it helps ^,^
Which of the following quadratic equations has no real solution?
A) x^2-6x-2=0
B) 4x^2+4x+1=0
C) x^2+3x-5=0
D) 2x^2-4x+3=0
Answers
Solve the system of linear equations by substitution. x=16−4y 3x+4y=8
Answers
Answer:
Solution: (-4,5)
Step-by-step explanation:
x=16-4y
3x+4y=8
-----
The 1st equation tells you x = 16-4y
---
Substitute that into the 2nd equation
and solve for "y":
3(16-4y)+4y = 8
48 - 12y + 4y = 8
-8y = -40
---
y = 5
---
Solve for "x"
x = 16-4y
x = 16-4*5
x = 16-20
x = -4
The given system of equations has (-4, 5) as its solution.
What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have the following system of equations -
x = 16 - 4y
3x + 4y = 8
Now, we can write -
3x + 4y = 8
3(16 - 4y) + 4y = 8
48 - 12y + 4y = 8
40 = 8y
y = 5
Then, we can write -
x = 16 - 20
x = - 4
Therefore, the given system of equations has (-4, 5) as its solution.
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If I charged 30$ a hair cut the whole year how many customers would I need to have to get 17,510$ and how many times would my customers have to see me within that year
Answers
Answer: Around 584 people would have to get a haircut at 30$, if you are looking for 17,510$
Step-by-step explanation:
Please help will mark brainliest if correct
Answers
Answer:
Step-by-step explanation:
The triangles can not be proven congruent.
We have AAA theorem ⇒ given triangles are similar for sure.
Which of the following describe 4/8
Answers
Answer:
4/8 is one half.
Step-by-step explanation:
4/8 -- 4 goes into both the numerator and denominator -- 4 goes into 4 one time and 4 goes into 8 two times.
Therefore, you have 1/2.
Answer:
4/8=.5 or 1/2
Step-by-step explanation:
4/8 can be reduced to 1/2
A soccer team won 11 games last year. This year they won 13 games. What was the percent increase in the number of games they won?
Answers
Answer:
About 18% increase
Step-by-step explanation:
Plz answer correctly! thnx! :)
Answers
state the slope and a point on the line y - 18 = 71.3(x +98)
explain how you got your answer
Answers
Answer:
slope = 71.3 and a point (0, 7005.4)
Step-by-step explanation:
the slope in an equation of the form y = mx+b, m is the slope so multiply 71.3 through the brackets and then add 18 to both sides and that is the equation in y=mx+b format and 71.3 is the slope and b os the y-intercept which turns out b=7005.4 and since its a y-intercept x = 0
Answer:
The slope is 71.3 and the point on the line is (h, k): (-98, 18)
Step-by-step explanation:
y - 18 = 71.3(x +98) is to be solved for the slope and a point on the line represented by this equation.
Refer to the point-slope formula y - k = m(x - h), where (h, k) is a point on the ine and m is the slope of the line.
Comparing y - 18 = 71.3(x +98) to
y - k = m(x - h),
we readily see that k = 18, h = -98 and m = 71.3
The slope is 71.3 and the point on the line is (h, k): (-98, 18)
A bird flies south. Its distance from its nest, as a function of time, is modeled by y=20x+1. Which statement best describes the function
Answers
Answer:the function is linear
Step-by-step explanation:
Answer:
it linear
Step-by-step explanation:
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