An inequality relating 100n and n³ is 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.
What is inequality?An inequality is comparison of two values, showing if one is less than, greater than, or simply not equal to another value.
Since 100n and n³ for n = 1, 2, 3, . . . 9, 10, 11 are 100, 200, 300, . . . 900, 1000, 1100 and 1, 8, 27, . . . 729, 1000, 1331 respectively.
Therefore, an inequality relating 100n and n³ will be 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.
Induction hypothesis:
Suppose 100n ≤ k³ for some positive integer k ≥ 10.
We need to show that 100( k + 1 ) ≤ ( k + 1 )³ = k³ + 3k² +3k + 1.
Note 100( k + 1 ) = 100k + 100 ≤ k³ + 100
≤ k³ + 3k² (∵ k ≥ 10 )
≤ k³ + 3k² + 3k
≤ k³ + 3k²+3k + 1
So 100( k + 1 ) ≤ ( k + 1 )³, which is true.
Hence by the principle of mathematical induction, 100n ≤ k³ for every integer k ≥ 10.
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Describe the graph of a quadratic function below given in table form
Translate to an equation then solve the equation. Seven times the difference of some number and 2 amounts to the quotient of 196 and 14. (Type the question using x as the variable. Do not simplify.) x= ____
Answer:
x = 4
Step-by-step explanation:
7 * ( x-2) = 196/14
7x -14 = 14
7x = 28
x = 4
1.9^4 × 10 × 2.9 x 10^1
3779.309 is the answer....
Michael went to the game store there was so much games he wanted and if one of them was $42.29 and the other one was $87.99 and he had $142 how much would he have left
Answer:
$11.72
Step-by-step explanation:
Add: $42.29 + $87.99 = $130.28
Subtract: $142 - $130.28 = $11.72
Answer:
he would have spent 131.08 dollars meaning he has 11.72 dollars left.
Step-by-step explanation:
Denise and Stacey went to a carnival. The admission fee was $6 per person. Each ride at the carnival costs c dollars. The game booths charged g dollars for each game. Both Denise and Stacey went on 7 rides each. Stacey played 3 games, while Denise played 2 games. Which expression represents the total amount of money that Denise and Stacey spent at the carnival?
The total amount of money that Denise and Stacey spent at the carnival is 12 + 14c + 5g dollars.
What is total amount?
The amount that you get when you add several numbers or things together.
The total amount of money that Denise and Stacey spent at the carnival will be money spent on admission + ride + game.
Total amount = 2 * 6 + 2 ( 7 * c ) + ( 3 * g + 2 * g )
= 2 * 6 + 14 * c + 5 * g
= 12 + 14c + 5g dollars.
Therefore, the total amount of money that Denise and Stacey spent at the carnival is 12 + 14c + 5g dollars.
The questions seems incomplete, its option could be:
12 + 14c + 5g 12 + 14g + 5c 12 + 7g + 5c 12 + 7c + 5g.
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What is the solution to the equation below? Round your answer to two decimal places. 3e2x + 12 = 42
Answer:
X= 5.52
Step-by-step explanation:
1. Solve the equation:
e×2x + 12= 42
x=15/e
2. Round x=15/e to the required place
x=5.52
Answer:
X=1.15
Step-by-step explanation:
Suppose you want to test the effectiveness of a certain drug for treating a disease that said you wanted to see if using the drug is better the standard treatment used to like 150 patients to give the drug and 150 patients to give the standard treatment name at least five factors you should control for in your samples to make the test more random
Five factors that should be controlled are the dose of the medicine, the time the patients take this medicine, their diet, the stage of this disease and medicine composition.
Why should some factors be controlled?This is done to avoid bias or imprecise results.
What factors should be controlled?Factors related to the medicine itself and factors that can affect the results should be controlled. This includes:
The dose given to the patients.The stage of the disease that should be similar for all patients.The medicine compositon and manufacturer.The number of day patients take the medicine.The patients' diet.Learn more about medicine in:https://brainly.com/question/21486381
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helppp im stuck :(
Hope you guys help me
Answer:
[tex]y=-\dfrac{1}{2}x+2[/tex]
Step-by-step explanation:
Define two points on the line:
[tex]\textsf{let}\:(x_1,y_1)=(0,2)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(4,0)[/tex]
Use the slope formula and the defined points to find the slope:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-2}{4-0}=-\dfrac{1}{2}[/tex]
Substitute the found slope and one of the points into the point-slope form of a linear equation:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-2=-\dfrac{1}{2}(x-0)[/tex]
Simplify:
[tex]\implies y-2=-\dfrac{1}{2}x[/tex]
[tex]\implies y=-\dfrac{1}{2}x+2[/tex]
Evaluate 3a-5b when a=-3 and b=-2
Answer: 1
Step-by-step explanation:
Substituting in the given values,
3a-5b=3(-3)-5(-2)=-9+10=
Which expression is equivalent to (1−sinβ)(1+sinβ)/cos2β for all values of β for which (1−sinβ)(1+sinβ)/cos2β is defined?
Select the correct answer below:
tan2β
tanβ+secβ
tanβ
sec2β
1
Work Shown:
[tex]\frac{(1-\sin(\beta))(1+\sin(\beta))}{\cos^2(\beta)}\\\\\frac{1-\sin^2(\beta)}{\cos^2(\beta)}\\\\\frac{\cos^2(\beta)}{\cos^2(\beta)}\\\\1\\\\[/tex]
Therefore, [tex]\frac{(1-\sin(\beta))(1+\sin(\beta))}{\cos^2(\beta)}=1\\\\[/tex] is an identity for all values of β for which the original expression is defined. I used the difference of squares rule for the 2nd step. Then I applied the pythagorean trig identity for the 3rd step.
To purchase 13700 worth of restaurant equipment for her business Maria made a down payment of 1500 and took out a business loan for the rest after 3 years of paying monthly payments of 371.16 she finally paid off the loan
What was the total amount Maria ended up paying for the equipment
How much internet did Maria pay on the loan
The total amount Maria ended up paying for the equipment will be $14,861.76. And The interest of Maria on the loan will be 8.48%.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
To purchase 13700 worth of restaurant equipment for her business.
Maria made a down payment of 1500 and took out a business loan for the rest, after 3 years of paying monthly payments of 371.16 she finally paid off the loan.
The total amount Maria ended up paying for the equipment will be
Total amount = 371.16 × 3 × 12 + 1500
Total amount = $14,861.76
The interest of Maria on the loan will be
Interset = [(14861.76 – 13700) / 13700] x 100
Interset = 8.48%
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which system of the equation is represents by the graph?
¿A qué porcentaje anual se han impuesto Q. 8000.00 que en 32 días han producido Q. 140.00? ¿ A qué porcentaje anual se han impuesto Q. 8000.00 que en 32 días han producido Q. 140.00 ?
Based on the amount being taxed, the period of taxation, and the tax, the annual percentage of tax is 19.96%.
What is the annual tax percentage?Assuming this rate was x, the following formula would apply:
Annual rate/ 365 days a year x number of days x amount to be taxed = Tax amount
Solving gives:
x/365 x 32 x 8,000 = 140
701.369863x = 140
x = 140 / 701.369863
= 19.96%
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(1)
Mrs Tan had $3756 to spend on furniture. She bought a sofa set for $1195 and 6 chairs at $128 each.
(a) How much did she spend altogether?
(b) How much money did she have left?
(Marshall Cavendish/ Pupil's book My Pals Are Here! Maths 4A 3rd Edition)
solve the following inequality:
ALGEBRA 1
Answer:
[tex]m \leqslant 10 \: or \: m > 4[/tex]
Step-by-step explanation:
[tex] \frac{m - 2}{3} \leqslant - 4 \\ \frac{m - 2}{3} \times 3 \leqslant - 4 \times 3 \\ m - 2 \leqslant - 12 \\ m - 2 + 2 \leqslant - 12 + 2 \\ m \leqslant 10[/tex]
OR
[tex]3m - 8 > 4 \\ 3m - 8 + 8 > 4 + 8 \\ 3m > 12 \\ \frac{3m}{3} > \frac{12}{3} \\ m > 4 [/tex]
3 is less than w and 9 is greater than w
The complete question is
"Write the inequality when 3 is less than w and 9 is greater than w."
The inequality become as 3 < w < 9.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Given information ;
when 3 is less than w and 9 is greater than w.
Thus, the inequality will be ;
3 < w < 9
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IN THE GIVEN FIG, FIND THE VALUE OF x.
The answer is simple
First find the angle measures of first triangle:
statement:
we know that the sum of 45 and 30 sums up to the opposite angle and that is equal to 75, then to find the next remaining angle:
180-(75+20)=85
The you find the supplement of 85:
180-85=95
so x = 95
Hope it helps
help awdaWdawdadawdaWDaSwdaWDawdas
Answer:maybe c or d??
Step-by-step explanation:
Find the value of x.
2x
70
120
Question 6 of 10
sin 30º = √3/2 and cos 30º = 1/2
O A. True
OB. False
f of x is equal to 4x divided by the quantity of x minus 16 end quantity.
The zero of the equation is 0. Since degree of denominator is greater than degree of numerator, therefore, the horizontal asymptote is y=0
Asymptotes and zeros of a functionThe zero of the function is the point where the function is zero
Given the function below
f(x) = 4x/x-16
For the zeros
0 = 4x/x -16
4x = 0
x = 0
Hence the zero of the equation is 0
The vertical asymptote is the point where the denominator is zero
x - 16 = 0
x = 16
Since degree of denominator is greater than degree of numerator, therefore, the horizontal asymptote is y=0
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3. Measure the length of each leg and
the hypotenuse of this triangle:
AD =
units
AE=
units
DE=
units
Correct!
Check
The length of each leg and the hypotenuse of this triangle will be:
AD = 2 units.
AE = 2 units.
DE = 2.8 units
How to compute the hypotenuse?From the information given and the attached diagram, the value or AD and AE are 2 units respectively.
The value of DE will be calculated as the square root of 2² + 2². This will be:
= 2² + 2² = 8
= ✓8 = 2.8
Therefore, the correct options are 2, 2, and 2.8 units.
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The length of a golden rectangle is 35 cm. Find the width to the nearest centimeter.
17cm
25cm
22cm
29cm
16cm
Answer:
22 cm
Step-by-step explanation:
First we need to know that The golden number
= (1+√(5))÷2
= 1.61803398875 (in decimal)
………………………………………………
We get the length of a golden rectangle
by multiplying its width by the golden number itself.
Then
The width = 35÷ 1.61803398875
=21.631189606245
Need help with this geometric question
Answer: QN=19
Step-by-step explanation:
Diagonals of an isosceles trapezoid are congruent, so NQ=PM.
By the segment addition postulate, NQ=QR+RN=3x+7.
So,
[tex]6x-5=3x+7\\\\3x-5=7\\3x=12\\\\x=4[/tex]
So, [tex]QN=3(4)+7=\boxed{19}[/tex]
Given: angle 2 and angle 4 are vertical. Prove angle 2 congruent to angle 4
Need help quick!
The diagram shows that ∠2 and ∠4 are the vertical angles.
What are vertical angles?Vertical angles are the angles that are opposite of each other when two lines cross.
The statements are:
1. < 2 & < 4 are vert. angles
2. Lines M & N intersect at P
3. < 2 & < 3 are a linear pair
4. m < 2 + m < 3 = 180
5. <3 and < 4 are a linear pair
6. m < 3 + m <4 =180
7. m < 2 + m < 3 = m < 3 + m < 4
8. m < 2 = m < 4
9. < 2 =~ <4
Here are the reasons:
1. Given
2. Def of vertical angles.
3. Def of. Linear pair
4. Angle addition postulate
5. Def of a linear pair
6. Angle addition postulate
7. Substitution property
8. Subtraction property
9. Def of =~ angles.
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Answer: View the picture below!
Step-by-step explanation: Just did the assignment!
Two numbers are in the ratio 3:8.
The larger number is 96, find the
sum of the numbers
Answer:
The sum of the numbers is 132
Step-by-step explanation:
First find the smallest number
3/8=x/96 2(96)=8x 288=8x x=36Thus, you found the smallest number
then there sum given as 96+36=132
x + 4 = x2? Assume x greater-than 0
Answer:
The value comes out to be
[tex]x=\frac{1}{2}+\frac{\sqrt{17}}{2}[/tex]
Step-by-step explanation:
The quadratic equation is an equation containing a single variable of degree [tex]2[/tex]. Its general form is [tex]ax^{2} +bx + c=0[/tex].
The discriminant is the part of the quadratic formula underneath the square root symbol: b²- 4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
The equation we are given is :[tex]x+4=x^{2} \\x^{2} -x-4=0\\[/tex]
We know the formula as :
[tex]x=[-b[/tex]±[tex]\sqrt{b^{2}-4ac}][/tex] ×[tex]\frac{1}{2a}[/tex]
[tex]x=[-(-1)[/tex]±[tex]\sqrt{(-1)^{2} -4(1)(-4)}][/tex]×[tex]\frac{1}{2(1)}[/tex]
[tex]x=\frac{1}{2}[/tex] ±[tex]\frac{\sqrt{17} }{2} }[/tex]
Since [tex]x[/tex]≥[tex]0[/tex]
Other negative option is neglected
[tex]x=\frac{1}{2}+\frac{\sqrt{17}}{2}[/tex]
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Given f(x)=2x^2-1 and g(x) =3x-5 what is f-g
[tex]f(x)-g(x)=(2x^{2}-1)-(3x-5)=2x^{2}-1-3x+5=\boxed{2x^{2}-3x+4}[/tex]
Graph the equation.
Y= - 3/2x
Answer:
Step-by-step explanation:
What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)?
y – 1=-3/2(x + 3)
y – 1=-2/3(x + 3)
y – 1=2/3(x + 3)
y – 1=3/2(x + 3)
The equation of the line parallel to given line and passing through (-3, 1) will be y – 1 = (3/2)(x + 3). Then the correct option is D.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The slope of the parallel lines are equal.
m = (2 + 4) / (2 + 2)
m = 6/4
m = 3/2
Then the equation of the line will be
y = (3/2)x + c
The line is passing through (-3, 1). Then the value of c will be
1 = (3/2)(-3) + c
c = 9/2 + 1
Then the equation will be
y = (3/2)x + 9/2 + 1
y – 1 = (3/2)(x + 3)
Then the correct option is D.
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