For every integer n ≥ 8, =3x+5y for some nonnegative integers x,y. Prove the statement using the Well-Ordering Principle
Answers
For any integer n≥8, it is possible to represent n as 3x+5y, where x and y are non-negative integers.
Let P(n) be the statement that n can be represented as 3x+5y, where x and y are non-negative integers. We need to prove P(n) for all n≥8.
First, we will prove P(8). We can write 8 as 3+5, which means that we can represent 8 as 31+51. Hence, P(8) is true.
Assume that P(k) is true for all integers k such that 8 ≤ k ≤ n for some fixed n ≥ 8. We need to prove that P(n+1) is also true.
Let's consider two cases:
Case 1: n+1 is divisible by 3
In this case, we can write n+1 as 3(x+1)+5y, where x+1 and y are non-negative integers. Hence, P(n+1) is true.
Case 2: n+1 is not divisible by 3
In this case, we can write n+1 as 3(x-1)+5(y+2), where x-1 and y+2 are non-negative integers. Since n ≥ 8, we have x-1 ≥ 2. Hence, P(n+1) is true.
Therefore, by the principle of mathematical induction, P(n) is true for all n≥8.
For more questions like Integer click the link below:
https://brainly.com/question/490943
#SPJ11
Related Questions
What relationship do the ratios of sin x° and cos yº share?
a. The ratios are both identical (12/13 and 12/13)
b. The ratios are opposites (-12/13 and 12/13)
c. The ratios are reciprocals. (12/13 and 13/12)
d. The ratios are both negative. (-12/13 and -13/12)
Answers
The relationship between the ratios of sin x° and cos yº is that they are reciprocals. The correct answer is option c. The ratios of sin x° and cos yº are reciprocals of each other.
In trigonometry, sin x° represents the ratio of the length of the side opposite the angle x° to the length of the hypotenuse in a right triangle. Similarly, cos yº represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.
Since the hypotenuse is the same in both cases, the ratios sin x° and cos yº are related as reciprocals. This means that if sin x° is equal to 12/13, then cos yº will be equal to 13/12. The reciprocals of the ratios have an inverse relationship, where the numerator of one ratio becomes the denominator of the other and vice versa.
It's important to note that the signs of the ratios can vary depending on the quadrant in which the angles x° and yº are located. However, the reciprocal relationship remains the same regardless of the signs.
Learn more about hypotenuse here:
https://brainly.com/question/16893462
#SPJ11
find point G on AB such that the ratio of AG to GB is 3:2
Answers
The point G on AB such that the ratio of AG to GB is 3:2 is; G(4.2, 2)
How to partition a Line segment?
The formula to partition a line segment in the ratio a:b is;
(x, y) = [(bx1 + ax2)/(a + b)], [(by1 + ay2)/(a + b)]
We want to find point G on AB such that the ratio of AG to GB is 3:2.
From the graph, the coordinates of the points A and B are;
A(3, 5) and B(5, 0)
Thus, coordinates of point G that divides the line AB in the ratio of 3:2 is;
G(x, y) = [(2 * 3 + 3 * 5)/(2 + 3)], [(2 * 5 + 3 * 0)/(2 + 3)]
G(x, y) = (21/5, 10/5)
G(x, y) = (4.2, 2)
Read more about Line segment partition at; https://brainly.com/question/17374569
#SPJ1
6. use the table to find the unit rate with the specified units
PLEASE HELP I WILL MARK BRAINIEST
Answers
Answer:
75
Step-by-step explanation:
lok at the image for explanation, you just need to expand the table
A jar contains 17 blue cubes,4 blue spheres,5 green cubes,and 16 green spheres.what is the probability of randomly selecting a blue object or a cube? Give your answer as a fraction.
Answers
Answer:
The answer would be 3/16
Step-by-step explanation: Hope this helped
Answer:
13/21. that is 0.619
Step-by-step explanation:
there are 17 + 4 + 5 + 16 = 42 things in total.
p = probabililty.
p(blue object) = (17 + 4)/ 42
= 1/2.
p(cube) = (17 + 5) /42
= 11/21.
we have to subtract the things that are both blue and a cube:
there are 17 of those. that is p(blue and cube) = 17/42.
so our answer is (1/2) + (11/21) - (17/42)
= 13/21. that is 0.619
a convex pentagon has interior angles with measures $x 1$, $2x$, $3x$, $4x$, and $5x-1$ degrees. what is the measure of the largest angle?
Answers
The largest angle is $5^{th}$ angle which has a measure of $179.33$ degrees.
In a convex pentagon, the sum of all interior angles is equal to 540 degrees. Therefore, we can write the following equation:
$$x+2x+3x+4x+5x-1=540$$
Simplifying the equation, we get:
$$15x-1=540$$
$$15x=541$$
$$x=36.07$$
Now that we know the value of x, we can find the measure of each angle:
$1^{st}$ angle: $x=36.07$ degrees
$2^{nd}$ angle: $2x=72.14$ degrees
$3^{rd}$ angle: $3x=108.21$ degrees
$4^{th}$ angle: $4x=144.28$ degrees
$5^{th}$ angle: $5x-1=179.33$ degrees
Therefore, the largest angle is $5^{th}$ angle which has a measure of $179.33$ degrees.
Learn more about equation brainly.com/question/10413253
#SPJ11
Ayden is making smoothies. Each smoothie needs 1/4 cups of yogurt. He has 2 1/2 cups of yogurt. How many smoothies can he make?
A. 10 smoothies
B. 8 smoothies
C. 5 smoothies
D. 12 smoothies
Answers
Answer:
Ayden can make 10 smoothies
Step-by-step explanation:
1 cup of yogurt would be equal to four 1/4 cups.
2 cups of yogurt would be equal to eight 1/4 cups.
1/2 cup of yogurt would be equal to two 1/4 cups.
If two cups of yogurt equals eight 1/4 cups and 1/2 cup equals two 1/4, Ayden would be able to make 10 smoothies with the amount he has.
Split 1/2 into 2/4, then take the whole numbers and imagine putting 1/4 to make a whole. So then for the whole numbers you have 8/4, or 2.
8/4 plus 2/4 is 10/4 so you can make ten per each 1/4
x - 1/3 = 6
Give your answer as an improper fraction.
Answers
Answer:
19/3 (6 1/3)
Step-by-step explanation:
x = 6( or 18/3) + 1/3
x = 19/3
how many sides does a regular polygon have if one exterior angle measures 30
Answers
Answer:
12 sides
Step-by-step explanation:
the sum of the exterior angles of a polygon is 360°
since the polygon is regular then the exterior angles are congruent
number of sides = 360° ÷ 30 = 12
Answer:
12.
Step-by-step explanation:
is i get one point each 5 minutes how long until i get 50 points?
Answers
Answer:
250 minutes.
Step-by-step explanation:
1/5=50/x
cross product
5*50=1*x
250=x
Someone help pleaseeeee
Answers
Answer:
\(1. \: \: \: a = \frac{5}{7} \\ 2. \: \: \: 4 \\ 3. \: \: \: 15 {x}^{2} + 60x + 135 \\ 4. \: \: \: m = {75}^{o} \\ \)
Step-by-step explanation:
\(1. \: \: 7a - 8 = 13 \\ 7a - 8 + 8 = 13 + 8 \\ 7a = 5 \\ \frac{7a}{7} = \frac{5}{7} \\ a = \frac{5}{7} \\ \)
\(2. \: \: \: 4 = 2 \times 2 \\ 8 = 2 \times 2 \times 2 \\ 4 \\ \)
\(3. \: \: \: 15 {(x + 3)}^{2} \\ 15(x + 3)(x + 3) \\15 (x + 3)(x + 3) \\ 15 |x(x + 3) + 3(x + 3)| \\ 15 ({x}^{2} + 3x + 3x + 9 )\\ 15( {x}^{2} + 6x + 9) \\ {15x}^{2} + 60x + 135 \\ \)
\(4. \: \: \: m = {75}^{o} (opposite \: angles)\)
Write a formula for the volume V of a prism where B is the area of the base and h is height
Answers
Answer:
a pyramidal prism is 1/3 the volume of a similar rectangular prism of same base and height
so V=(1/3)bh
V=36
H=6
find area of base
36=(1/3)b6
36=2b
divide both sides by 2
18=b
the area of the base is 18 square units
Step-by-step explanation:
the answer is : V= B.h
Greg drew a scale drawing of a campground. The picnic area is 22 inches wide in the drawing. The actual picnic area is 33 yards wide. What scale did Greg use for the drawing?
Answers
Answer:
We need to find the ratio of the width of the actual picnic area to the width of the picnic area in the drawing. Since 1 yard is equal to 36 inches, we can convert 33 yards to inches by multiplying by 36:
33 yards x 36 inches/yard = 1188 inches
So the ratio is:
1188 inches / 22 inches = 54
This means that 1 unit in the drawing represents 54 units in real life. Therefore, the scale of the drawing is 1:54.
I believe 1.5 yards
(Brainliest for fastest right answer!!!) Which is correct?
Answers
Answer:
Step-by-step explanation:
ax² + bx + c = a(x - \(x_{1}\))(x - \(x_{2}\))
D = b² - 4ac
\(x_{12}\) = ( - b ± √D ) / 2a
~~~~~~~~~~~~
Let x² = y , then y² + 8y - 9
Find the roots of equation y² + 8y - 9 = 0
D = 64 + 36 = 100 = 10²
\(y_{1}\) = ( - 8 - 10) / 2 = - 9
\(y_{2}\) = ( - 8 + 10) / 2 = 1
y² + 8y - 9 = (y - 1)(y + 9) = (x² - 1)(x² + 9)
x² = 1 ⇒ \(x_{12}\) = ± √1
\(x^{4}\) + 8x² - 9 = (x - 1)(x + 1)(x² + 9)
The angle of elevation from Abby to the top of the Statue of Liberty is 70 ° . If the Statue of Liberty is 305 feet tall, how far is Abby standing from its base?
Answers
Answer:
Here
You can form a triangle joining the ship(C) to the base of statue of liberty(B) and its top of statue(A) which is again joined to the ship(C)
AB=BCtan(20)=305cot(20)----that's your answer.
Step-by-step explanation:
Work out the size of angle x.
Give reasons for your answer.
Answers
Answer:
80
Step-by-step explanation:
180 - 100 = 80
Answer:
d and h are the same so you will have 200cm divide that by 90 and covert the decimal into a fraction
Step-by-step explanation:
trust me i got it right
For f(x)=4x+1 and g(x)=x^2-5, find (f-g)(x).
Answers
The answer for given expressions is (f -g)(x) = -x² + 4x + 6.
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
To find (f-g)(x), we need to subtract g(x) from f(x) and simplify the expression.
f(x) = 4x + 1
g(x) = x² - 5
(f - g)(x) = f(x) - g(x)
= (4x + 1) - (x² - 5)
= -x² + 4x + 6
Therefore, the answer for given expressions is (f -g)(x) = -x² + 4x + 6.
To learn more about the quadratic equation visit:
brainly.com/question/28038123
#SPJ1
The lifting force, f, exerted on an airplane wing varies jointly as the area, a, of the wing's surface and the square of the plane's velocity, v. the lift of a wing with an area of 230 square feet is 14,100 pounds when the plane is going 240 miles per hour. find the lifting force on the wing if the plane slows down to 150 miles per hour.
Answers
The lifting force (f) is given by the formula, f = kav², where k is the constant of variation. It is given that the lifting force varies jointly as the area (a) of the wing's surface and the square of the plane's velocity (v).
f = kav² ----- (1)
The given values are:
a = 230 sq. ft.
v1 = 240 mph
f1 = 14100 lbs
v2 = 150 mph
We need to find the lifting force (f2) when the plane slows down to 150 miles per hour. Now, we need to find the value of the constant of variation (k). We have,
f1 = kav1²
14100 = ka (230) (240)²
14100 = ka (230) (57600)
14100 = 13248000a
k = 14100 / (13248000a) ----- (2)
We can substitute equation (2) into equation (1).We have,
f = 14100 / (13248000a) x a x v² ----- (3)
We can substitute the given values into equation (3).
We have,
f2 = 14100 / (13248000a) x a x 150²
f2 = 14100 / (13248000 x 230) x 150²
f2 = 563 / 5064 x 22500
f2 = 2493.24324324
The lifting force on the wing if the plane slows down to 150 miles per hour is 2493.24324324 pounds.
Answer: 2493.24324324.
To know more about variation visit:
https://brainly.com/question/29773899
#SPJ11
What is the slope of this line?
Enter
your answer as a whole number or a fraction in simplest
form in the box.
PLEASE HELP!! WILL MARK BRAINLIEST
Answers
Answer:
4/8 in simplist for would be 1/2
Step-by-step explanation:
the length f a rectangle is 3 ties its width, the perimeter of it is 24cm. what is the area of it?
Answers
Answer: 27cm²
Step-by-step explanation:
lets take the width as x and length as 3x( since length is 3 times the width)…
Perimeter of the rectangle is 24 cm( 2*(l+b))= 2×(3x+x):24
2×4x=24
8x=24
X( width): 24/8=3cm
Length= 3x: 3*3=9cm
Area of the rectangle: ( l*w)= 9×3: 27cm²
Answer:
Step-by-step explanation:
What is greater -3.2 or -3
Answers
Answer:
-3 is greater
Step-by-step explanation:
Have a good day :)
Directions: Use your graphing skills to answer the questions below.
According to the box-and-whisker plot shown above, identify the following:
1) The first quartile
2) The third quartile
3) The lowest, or minimum value (first #)
4) The highest, or maximum value (last #)
According to the box-and-whisker plot shown above, identify the following:
5) The 25th quartile
6) The 75th quartile
7) The range
Answers
We can see here that according to the box-and-whisker plot:
1) The first quartile = 20
2) The third quartile = 60
3) The lowest, or minimum value = 10
4) The highest, or maximum value = 90
What is box-and-whisker plot?A box-and-whisker plot, also known as a boxplot, is a graph that shows the distribution of data. It is a simple way to see the main features of a data set, such as the median, quartiles, and outliers.
For the second box-and-whisker, we have:
5) The 25th quartile = Lower quartile = 60
6) The 75th quartile = Upper quartile = 100
7) The range = Highest value - Lowest value = 120 - 40 = 60
Learn more about box-and-whisker plot on https://brainly.com/question/28098703
#SPJ1
The gross monthly salary of a permanent secretary is $6,583. Find his net annual salary after deductions of $1,475 were made monthly.
Answers
Answer:
oh my gosh they have it
Step-by-step explanation:
gLiZzY
IN A RECTANGLE PQRS , PR = 25 AND THE AREA IS 168. WHAT IS THE MEASURE OF PQ?
Answers
Answer:
the answer is 143
Step-by-step explanation:
just do 168 - 25 equals 143 , I'm sorry if I got this wrong I'm going based off what my 10th grade math teacher are taught me
Tom and Jane left for school, Tom walked to school on route A which was 4.5 kilometers while Jane walked to school on route B which was 8 kilometers 450 meters. How long did Jane take to reach to school than Tom?
Answers
Answer:
3.95 km
Step-by-step explanation:
The computation is shown below:
As both left for school
Tom walked to school on route A i.e. 4.50 kilometer
And, Jane walked to school on route B i..e 8 kilometers & 450 meters i.e. 8.45 kilometers
So, the more km that jane would take to reach to school as compared with Tom is
= 8.45 km - 4.50 km
= 3.95 km
Find the first five terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n=1. 10n+10
Answers
Answer:
20,30,40,50,60
Step-by-step explanation:
The sequence is given by the relation as follows :
\(a_n=10n+10\)
First term, n = 1
\(a_1=10(1)+10=20\)
Second term, n = 2
\(a_2=10(2)+10=30\)
Third term, n =3
\(a_3=10(3)+10=40\)
Fourth term, n = 4
\(a_4=10(4)+10=50\)
Fifth term, n = 5
\(a_5=10(5)+10=60\)
So, the first five terms of the sequence are 20,30,40,50,60
Select the correct answer.
Which expression is equivalent to this polynomial expression?
(5xy^2 + 3x^2–7) + (3x^2y^2 – xy^2 + 3y^2 + 4)
Answers
Answer:
Option B
Step-by-step explanation:
\((5xy^2 + 3x^2-7) + (3x^2y^2-xy^2 + 3y^2 + 4)\\\)
if we solve this lets rewrite it order
\(3x^2y^2-xy^2 + 3y^2 + 4+5xy^2+3x^2-7\)
\(3x^2y^2-xy^2 +5xy^2+3y^2+3x^2-7+4\)
\(3x^2y^2+4xy^2+3y^2+3x^2-4\)
The solution of the given polynomial is 3x²y² + 4xy² +3x² +3y² +3x²y² -3. The correct option is B.
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given that the expression is (5xy² + 3x²–7) + (3x²y² – xy² + 3y² + 4).
The polynomial can be solved as:-
E = (5xy² + 3x²–7) + (3x²y² – xy² + 3y² + 4)
E = 3x²y² + 4xy² + 3x² + 3y² -3
Hence, the solution of the polynomial would be 3x²y² + 4xy² +3x² +3y² +3x²y² -3.
To know more about polynomials follow
brainly.com/question/2833285
#SPJ2
I'm feeling nice today her is 15 points
just and me this riddle
what CAN'T you put in a pan?
Answers
Answer:
a human
Step-by-step explanation:
Answer:
hmmmm. I'm usually pretty good with riddles, but this ones got me stumped big time.
Please help Solve for x
(will give brainliest)
Answers
Answer: x = 62.5 degrees
Step-by-step explanation:
Angle DEC is adjacent to the angle measuring 137 degrees, which means their sum is 180 degrees. Therefore:
Angle DEC + 137 = 180
We can subtract 137 from both sides:
Angle DEC = 43 degrees
We know that the sum of the angles in a triangle is 180 degrees, so we can set up an equation for triangle DEC.
We know Angle D + Angle C + Angle E = 180, so we can plug in the values given for each.
Therefore, x + 5 + x + 7 + 43 = 180
We can combine like terms:
2x + 55 = 180
Subtract 55 from both sides:
2x = 125
Divide both sides by 2:
x = 62.5 degrees
Solve the given boundary-value problem.y" - 8y' + 16y = 0, y(0) = 1, y (1) = 0У(x) = _____.
Answers
The given boundary-value problem can be solved using the method of variation of parameters. the solution to the given boundary-value problem is у(x) = -e2x + 2e4x.
First, we need to find a particular solution of the homogeneous equation y" - 8y' + 16y = 0, which is yp(x) = c1e2x + c2e4x, where c1 and c2 are constants.
To find the particular solution, we can use the given boundary conditions y(0) = 1 and y(1) = 0. We solve for c1 and c2, and we get c1 = -1 and c2 = 2.
So, the particular solution is yp(x) = -e2x + 2e4x. The general solution of the boundary-value problem is then:
у(x) = c1e2x + c2e4x -e2x + 2e4x
= c1e2x + (c2 + 2)e4x.
By using the boundary conditions, we can find the value of c1 and c2:
у(0) = c1 + c2 + 2 = 1
у(1) = c1e2 + (c2 + 2)e4 = 0
Solving these two equations, we get c1 = -1 and c2 = 2.
Therefore, the solution to the given boundary-value problem is
у(x) = -e2x + 2e4x.
You can read more about parameters at https://brainly.com/question/29344078
#SPJ11
Given that p = 3, q= 5 and r= 7, work out the value of 2pqr.
Answers
Answer:
\(2pqr =2 (3)(5)(7) = 210\)
Answer:
210
Step-by-step explanation:
Substitute the values for their respective variables.
\(2pqr\\2(3)(5)(7)\\210\)