The equations which show direct proportion between a and b are:
a=2b and a=b/2.
What is direct proportion?Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. It is represented by the proportional symbol, ∝. In fact, the same symbol is used to represent inversely proportional, the matter of the fact that the other quantity is inverted here.
Example: x and y are two quantities or variables which are linked with each other directly, then we can say x ∝ y. When we remove the proportionality symbol, the ratio of x and y becomes equal to a constant, such as x/y = C, where C is a constant.
Given, two variables a and b
If two variables a and b are in direct proportion
then,
a/b = constant.
1. a = b²
a/b = b
which is not constant
⇒ a is not in direct proportion with b.
2. a = 2b
a/b = 2
which is constant
⇒a is in direct proportion with b.
3. a = b/2
a/b = 1/2
which is constant
⇒ a is in direct proportion with b.
4. a=b+2
a/b = 1+2/b
which is not constant
⇒ a is not in direct proportion with b.
5. a = 2/b
ab = 2
⇒a is inversely proportional to b.
Hence, In equation a=2b and a=b/2, a is directly proportional to b.
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Evaluate the expression x2+y210 when x = 6 and y = 8.
A:100
B: 1 2/5
C: 2 4/5
D: 10
Simplify:-
[tex]x {}^{2} - 5x + 6 \div x {}^{2} +3x - 10 \\ [/tex]
Guys help me please.
Step-by-step explanation:
[tex] = {x}^{2} \div {x}^{2} + 3x - 5x + 6 - 10 \\ = 1 - 2x - 4 \\ = - 2x - 4 + 1 \\ = - 2x - 3 \\ = - 1(2x + 3)[/tex]
HI,HOPE THAT IS HELPFUL.
6x+2y=2, y=-3x+1 substitution step by step???
Answer:
Answer below!
Step-by-step explanation:
since y = -3x + 1, you can just plug those numbers in on the first equation.
6x + 2(-3x+1) = 2 (see how I replaced y into -3x + 1)
then distribute 2.
6x - 6x + 2 = 2, subtract 2 to both sides
6x - 6x = 0, combine x
0 = 0 (this means it has an infinite amount of solutions)
Write a polynomial function in standard form
-6,0,0,2
Ms. Marcus estimates that 330 people will attend the school play. There was an actual total of 400 people who attended the school play. Find the percent of error.
Answer:
17.5%
Step-by-step explanation:
Subtract one value from the other. (i does not matter the sign)
400 − 330 = 70, so his error is 70
Now find the Percentage Error:
Divide by the exact value and make it a percentage:
70/400 = 0.175 = 17.5%
For the function below, write the differential.
f(x) = ln(1 + x^2)
dy = ( ) dx
Calculate dy for the given values of x and dx.
x = 2 and dx = 0.2
dy =
How accurate is dy in approximating Δy (i.e., what is their difference) to the nearest thousandth?
The dy for the given values of x and dx is dy = 0.5632, and their difference to the nearest thousandth is 0.0005.
The difference between dy and Δy can be determined by subtracting dy from Δy and taking the absolute value. In this case, dy approximates Δy to the nearest thousandth with a difference of 0.0005. This is a very small difference, indicating that dy is an accurate approximation for Δy.
The accuracy of dy can be attributed to the fact that the function f(x) = ln(1 + x^2) is a smooth function, meaning that the rate of change at a point (i.e., the derivative) is nearly constant. This allows dy to accurately approximate the change in y, Δy, over a small interval of x. Furthermore, the choice of dx = 0.2 is a small enough value that it does not significantly affect the accuracy of the approximation.
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The function f(x) = 225(1.29)", represented in the table, shows the number of people (in thousands) who own a cell phone device in a certain country where x is the number of years after 2010.
Year
Number of Cell Phone Owners
(in thousands)
2010 2012 2014 2016 2018
225 375 623 1,037 1,725
Find the average rate of change from 2012 to 2018 and interpret its meaning in terms of the context. (1 point)
-225; represents the average depreciation in cell phone owners from 2012 to 2018
225; represents the average growth in cell phone owners from 2012 to 2018
-37.5, represents the average depreciation in cell phone owners from 2012 to 2018
37.5, represents the average growth in cell phone owners from 2012 to 2018
Therefore , the solution of the given problem of function comes out to be f(x) = 2871 thousands.
What is meant by the word function?A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of inputs that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x). The input has an x in it.
Here,
Given :
=> f(x) = 225(1.29)×
After 10 year number of years x =10
=> f(x) = 225(1.29)¹⁰
=> f(x) = 12.76 * 225
=> f(x) = 2871 thousands.
Therefore , the solution of the given problem of function comes out to be f(x) = 2871 thousands.
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During a sale at the market, steaks sold for $2 and watermelons sold for $1.50. Declan spent $10 and bought a total of 6 steaks and watermelons. How many of each did he buy?
Answer:
Step-by-step explanation:
During a sale at the market, steaks sold for $2 and watermelons sold for $1.50. Declan spent $10 and bought a total of 6 steaks and watermelons. How many of each did he buy?
Let us represent
Steaks = x
Water melons = y
Our system of equations is given as:
x + y = 6.. Equation 1
x = 6 - y
During a sale at the market, steaks sold for $2 and watermelons sold for $1.50.
$2× x + 1.5 × y = $10
2x + 1.5y = 10... Equation 2
Substitute
2(6 - y) + 1.5y = 10
12 - 2y + 1.5y = 10
12 - 10 = 2y - 1.5y
2 = 0.5y
y = 2/0.5
y = 4
Write a real life scenario that is represented by the integer 15.
Answer:
15 buttholes
Step-by-step explanation:
Write the quadratic equation in standard form
Answer:
it would be 2x^2 +4x+8=0
Highschool Algebra: Indicated Operation.
(-ab2)(-6ab2)(3ab)
Answer:
-18a^3b^5
Step-by-step explanation:
First do -ab^2*-6ab^2=-6a^2b^4
Then multiply that by 3ab=-18a^3b^5
Can you help me do this exercice that I don't know how to do it, can you help me for this homework ?
After simplifying each expression, we get (2+5a - 10 b), (8a² - 15ca +2c),
(11- 2a+b) and (a+ b) respectively.
What is simplification?
The word simplify means to write an expression, equation or problems
in the simplest form so as to easy to evaluate it. we simplify an expression by removing the parenthesis and collecting like terms.
How can we simplify the expression given in question?
exercise 1.
given, A = 7 - 4a + 7a - 3b -5 -7b +2a
We collect the like term and get
A= 7 - 5 -4a +7a +2a -3b- 7b
A = 2 + 5a -10b
next, given B = 4a × 2a -5c - c +8c -3c × 5a
B = 8a² -6c +8c - 15ca
B = 8a² -15ca +2c
exercise 2.
given, A = 7 + [(2- a) -( 2+a) +9] + (b-5)
at first, we remove the parenthesis and get
A= 7 + [2-a - 2 -a+ 9] +b- 5
A = 7 + 9- 2a +b- 5
after collecting the like term
A = 11- 2a + b
given, B = 15 - [(7-b) - 9- (a-17)]
B = 15 - [7- b- 9 - a+17]
B = 15 - [15 - b -a]
after removing the parenthesis
B = b +a
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A person invested \$5,600$5,600 in an account growing at a rate allowing the money to double every 6 years. How long, to the nearest tenth of a year would it take for the value of the account to reach \$72,500$72,500?
Answer:
22.2 years
Step-by-step explanation:
Doubling formula is given as:
P(t) = Po × (2)^t/k
Where
Po = Initial amount invested = $5600
P(t) = Amount after time t = $72500
k = Time it takes to double = 6 years
t = Time in years = ??
Hence:
72500 = 5600 × (2)^t/6
Divide both sides by 5600
72500/5600 =( 5600 × (2)^t/6)5600
12.946428571 = (2)^t/6
Take the In of both sides
In 12.946428571 = In (2)^t/6
In 12.946428571 = t/6 In (2)
Divide both sides by In 2
In 12.946428571/In 2 = t/6
3.6944822628 = t/6
Cross Multiply
t = 6 × 3.6944822628
t = 22.166893577 years
Approximately
t = 22.2 years
Therefore, it would take 22.2 years
Pls answer this question
Answer:
1) (B) 25/18 ft³
2) (C) 1/216 ft³
Step-by-step explanation:
1) 1 2/3 x 5/6 x 1 = 5/3 x 5/6 x 1 = 25/18 ft³
2) 1/6 x 1/6 x 1/6 = 1/216 ft³
Chelsea wants to determine the number of people in her school who read news reports on the Internet daily. She asks five people in her language arts class. Which improvements could Chelsea make to her sample to increase the validity of the results
The three choices are increase the sample size, pick individuals from various grade levels and in all language arts classes, pick the fourth student.
what is sample size?
The number of observations utilized to calculate estimates for a given population is referred to as the sample size. From the population, a sample size was chosen. The term "sample size" describes the number of subjects or observations that make up a study. n is typically used to represent this number.
The three choices are increase the size of the sample, pick individuals from various grade levels and in all language arts classes, pick the fourth student.
It's important to take into account the following data:
The sample size should be raised in order to boost the result validity, The students should be chosen from among the various grade levels and For all language kinds, a student should be chosen every fourth student.
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Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Jayden was excited to get his test back for his
parents to sign He scored a 105%. He
received the extra 5 points for showing his work.
Which decimal represents his test score?
Answer:
1.05
Step-by-step explanation:
100% is 1.0, therefore 105% will be 1.05.
Explanation:
Think of 105% as 105.0%
Now remove the percent sign to get 105.0
Lastly, move the decimal point two spots to the left to get to 1.05
Percentages that are over 100% convert to decimal values larger than 1; on the flip side, percentages that are under 100% are between 0 and 1.
More Examples:
76% = 0.76
18% = 0.18
255% = 2.55
PLEASE HELP!!! WILL MARK AS BRAINLISTS!!!
PLEASE HELP!!! WILL MARK AS BRAINLISTS!!!
PLEASE HELP!!! WILL MARK AS BRAINLISTS!!!
PLEASE HELP!!! WILL MARK AS BRAINLISTS!!!
PLEASE HELP!!! WILL MARK AS BRAINLISTS!!!
PLEASE HELP!!! WILL MARK AS BRAINLISTS!!!
PLEASE HELP!!! WILL MARK AS BRAINLISTS!!!
PLEASE HELP!!! WILL MARK AS BRAINLISTS!!!
The limit is x---->4-
The negative show that x approaches from the left
Now
As x approaches 4 from the left ... Means This number should be less than 4 (<4) but really close to 4.
Let's pick a Number
Say 3.99
Substitute this... You have
3.99/3.99-4
3.99/-0.01
If we choose x to be 3.999
we will have
3.999/-0.001
Notice the pattern... As x approaches 4 from the left... This limit will approach NEGATIVE INFINITY
Why?
As you approach 4 from the left... 3.9,3.99,3.999... You notice that the denominator becomes negative and EXTREMELY SMALL... and when you divide by an extremely small Number..... You'll get a relatively HUGE VALUE(You can try this... Use a calc... Divide any number of choice by a very small number... say.. 0.0000001.... You'll get a huge result
In our case... The denominator is negative... So it Will Approach a very Huge Negative Number
Hence
Answer.. X WILL APPROACH NEGATIVE INFINITY.
Vertical asymptotes are the zeroes of the denominator of a function
The denom. is x-4
Equate to zero to get the asymptote
x-4=0
x=4
Hence... There will be a vertical asymptote at x=4.
Have a great day!
Answer: -3
Step-by-step explanation: x divided by x = 1 and 1 - 4 = -3
What is the answer to |60| ____|-60|
Answer:
=
Step-by-step explanation:
Equal too, you are finding the absolute value of both of them which means getting rid of any signs that is attached to them. 60 = 60
Answer:
|60| = |-60|
Step-by-step explanation:
| | means absolute value
The absolute value of any number is that number but in its positive form
So the absolute value of 60 is 60
The absolute value of -60 is positive 60
60 is equal to 60 therefore |60| = |-60|
A survey was given to a random sample of 195 residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. Of those surveyed, 117 respondents said they were in favor of the plan. Determine a 95% confidence interval for the proportion of people who favor the tax plan.
Answer:
(0.5415 ; 0.6785)
Step-by-step explanation:
Sample size, n = 195
Number of samples who werw in favor, x = 117
Phat = 117 / 195 = 0.609 = 0.61
The confidence interval :
Phat ± Margin of error
Margin of Error = Zcritical * √(phat(1-phat)/n)
Zcritical at 95% = 1.96
1 - phat = 1 - 0.61 = 0.39
Margin of Error = 1.96 * √((0.61*0.39)/195) = 0.0685
Confidence interval :
Lower boundary : 0.61 - 0.0685 = 0.5415
Upper boundary : 0.61 + 0.0685 = 0.6785
(0.5415 ; 0.6785)
Question 7 (Essay Worth 5 points)
(08.03)Consider the following pair of equations:
y = -2x + 8
y = X-1
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Answer:
x=3
Step-by-step explanation:
Why? well this is simple. Just subtitute x-1 into y in the equation above.
Please help me on this :/
Answer:
4. obtuse
5. right
6. obtuse
6. acute
Step-by-step explanation:
4. not a triangle, 2+4 = 6
5. 100 + 576 = 26^2 -> right
6. 8, 16 < 36 -> obtuse
7. 43.6 > 42.25 -> acute
If r || s, then which angles must be congruent (geometry)
Find m
2B, rounded to the nearest degree. Please help me
Answer:
∠ B ≈ 53°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan B = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{4}{3}[/tex] , then
∠ B = [tex]tan^{-1}[/tex] ([tex]\frac{4}{3}[/tex] ) ≈ 53° ( to the nearest degree )
What are the first 3 triangular numbers?
The depiction of numbers as an equilateral triangle organized in a series is known as a triangular number sequence. These numerals follow a 1, 3, 6 order.
Explain the term triangular numbers?A number that may be expressed as the sum of the initial n positive integers is referred to as a triangular number.
For instance, the fact that 6 may be expressed as 1+2+3, being sum of the initial three positive integers, indicates that it is a triangular number. If one takes the sum of the initial positive integer to be the first element, then sum of the earliest two positive integers to be the second element, then so on, triangular numbers comprise a sequence. In this scenario, n signifies the position of such a triangular number with in sequence if a number equals the sum of the initial n positive integers. Triangles can be formed from triangular numbers.Thus, the first three triangular numbers 1, 3, 6.
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An operator works a basic fortnight at a basic
rate of $8. 95 and earns $671. 25. Determine the
basic fortnight for the operator.
just the answer pls
To determine the basic fortnight for the operator, we need to divide the operator's earnings by their basic rate of pay.
$671.25 ÷ $8.95 = 75.05
The basic fortnight for an operator is the number of fortnights the operator has worked at their basic rate of pay. In this case, the operator has earned $671.25 at a basic rate of $8.95 per fortnight. To determine the basic fortnight, we need to divide the operator's total earnings by their basic rate of pay.
$671.25 ÷ $8.95 = 75.05
So, the operator has worked 75.05 basic fortnights. It means he has been working for 75.05*14=1053 days. This is the number of days the operator has worked at their basic rate of pay. It is important to note that this calculation assumes that the operator has not earned any overtime pay or other bonuses.
$671.25 ÷ $8.95 = 75.05
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PLEASE HELP WILL MARK BRAINLIEST
[tex]x = 140°[/tex]
hope it helps UwU
Answer:
X = 140 degrees
Step-by-step explanation:
Those lines and angles look identical, so I'll just assume they are
40 degrees on one side should be the same on the other side (if identical). So that means we can just subtract 40 from 180 (because 180 is equal to a flat line), so the answer would be 180-40 =140 degrees
Please hurry its timed
The correct option regarding the high tide and the low tide is given as follows:
B. high tide at 6 a.m. and 6 p.m., depth of 28 ft.
low tide at 12 midnight and 12 noon, depth of 20 ft.
What is the definition of the cosine function?The cosine function is defined as follows:
g(x) = acos(bx+c)+d.
The coefficients have these following roles:
a: amplitude.b: The period is of 2π/B.c: phase shift.d: vertical shift.The amplitude for this problem is of 4, with a vertical shift of 24, hence the low and high tides are given as follows:
Low: -4 + 24 = 20 ft.High: 4 + 24 = 28 ft.The function is reflected over the x-axis, due to the multiplication by the negative number, hence the low tide is at midnight.
The period of the function is given as follows:
2π/(π/6) = 12 hours.
Thus the low tide also happens at noon, meaning that option B is correct.
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The slope of a line that is perpendicular to y = -1 is not defined.
True
False
Answer:
True
Step-by-step explanation:
TRUE. y = -1 is a horizontal line. A line perpendicular to this horizontal line is a vertical line whose slope is not defined.
How do I find parameter?
Answer:
Depending of the figure that you are trying to find perimeter on, you just add up all the sides of that figure.
Answer:
The perimeter is the distance around a figure.
Step-by-step explanation:
For example, if I have a square where each side is 5 inches. The perimeter would be 20 inches. 5 + 5+ 5 + 5, a square has four sides and each side length is 5 inches.