Find the radius of the circle, if the big square is 30 square units more than the area of the small square.
Answers
Answer:
The area of a square is equal to the side length of the square squared. If the side length of the small square is "s" and the side length of the big square is "b", then we can write the following two equations to represent the area of the two squares:
Area of small square = s^2
Area of big square = b^2
Since the area of the big square is 30 units more than the area of the small square, we can write the equation:
b^2 = s^2 + 30
To find the radius of the circle, we need to find the side length of the small square. To do this, we can rearrange the equation above to solve for s:
s^2 = b^2 - 30
s = sqrt(b^2 - 30)
Now we just need to find the value of "b", which is the side length of the big square. To do this, we can use the fact that the big square is inscribed in the circle, so the side length of the big square is equal to the diameter of the circle. Let's call the diameter of the circle "d". Then we can substitute "d" for "b" in the equation above:
s = sqrt(d^2 - 30)
To find the radius of the circle, we just need to divide the diameter of the circle by 2, so the radius is equal to "d" divided by 2. Therefore, the radius of the circle is:
r = d/2 = sqrt(d^2 - 30)/2
So to find the radius of the circle, we just need to know the diameter of the circle. Can you provide the diameter of the circle in the question?:
The radius of the circle is: r = d/2 = sqrt(d^2 - 30)/2
What is area of circle?The area of a circle is π multiplied by the square of the radius. The area of a circle, (A) when the radius 'r' is given is πr2. π is approximately 3.142
Here, we have,
The area of a square is equal to the side length of the square squared. If the side length of the small square is "s" and the side length of the big square is "b", then we can write the following two equations to represent the area of the two squares:
Area of small square = s^2
Area of big square = b^2
Since the area of the big square is 30 units more than the area of the small square, we can write the equation:
b^2 = s^2 + 30
To find the radius of the circle, we need to find the side length of the small square. To do this, we can rearrange the equation above to solve for s:
s^2 = b^2 - 30
s = sqrt(b^2 - 30)
Now we just need to find the value of "b", which is the side length of the big square. To do this, we can use the fact that the big square is inscribed in the circle, so the side length of the big square is equal to the diameter of the circle. Let's call the diameter of the circle "d". Then we can substitute "d" for "b" in the equation above:
s = sqrt(d^2 - 30)
To find the radius of the circle, we just need to divide the diameter of the circle by 2, so the radius is equal to "d" divided by 2. Therefore, the radius of the circle is:
r = d/2 = sqrt(d^2 - 30)/2
So to find the radius of the circle, we just need to know the diameter of the circle.
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Related Questions
Dilate the line shown by a scale factor of 1/4 with the center as (-3,9). Graph the dilated line
Answers
On solving the provided question we can say that - the coordinates from the graphs will be P' = (0.0); Q' = (1,0); R' = (1,1); S' = (0,1)
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is r
A fixed point serves as the dilation's center.
Dk is used to represent dilation, where k is the scale factor.
Dk (x, y) = for a dilation centered on the origin (kx, ky)
Let's assume that you have a PQRS rectangle where
P = (0,0)
Q = (4,0)
R = (4,4)
S = (0,4)
You must multiply each coordinate by 1/4 to achieve the dilation of this PQRS to P'Q'R'S' with a scale factor of 1.
P' = (0.0)
Q' = (1,0)
R' = (1,1)
S' = (0,1)
You may plot both of these rectangles to see that they are the same size and are centered on the origin, but they have different shapes.
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Which graph represents the system of linear inequalities?
2x+y<1
y≥12x+2
Answers
The graph of the system of linear inequalities 2x + y < 1 and y ≥ 12x + 2 is attached.
What is an equation?An equation shows how two or more numbers and variables are related to each other.
The standard linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Inequalities is used for the non equal comparison of numbers and variables.
The graph of 2x + y < 1 and y ≥ 12x + 2 is attached.
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What is equivalent to " two more than three times a number is seven
Answers
Answer:
if it’s asking for a numerical answer it would be 1.67
(Rounded to the nearest two)
Step-by-step explanation:
(5b + 16)
(b + 32)°
What is the value of b ?
b =
Answers
Answer:
b = -8
Step-by-step explanation:
To determine the value of b, we can use the factoring method. We can factor the expression
(5b + 16)(b + 32) as (b + 8)(5b + 16).
Setting each factor to 0, we get b + 8 = 0 and 5b + 16 = 0.
Solving for b in the first equation, we get b = -8.
Substituting this value into the second equation, we get 5(-8) + 16 = 0, which simplifies to -40 + 16 = 0.
This equation is true only when the value of b is -8. Therefore, the value of b is -8.
Two exponential functions, f and g, are shown in the figure below, where g is a transformation of f.
19.
4-
2
4
x
Which of the equations given below describes the transformation of f?
OA. g(x) = f(x) - 4
OB.
g(x) = 4f(x)
O c.
g(x) = f(x) + 4
OD.
g(x) = -4f(x)
E
Answers
The transformation of f (x) exists g (x) = f (x) - 4.
What is meant by exponential functions?A mathematical function using the following formula is an exponential function: f (x) = an x. where x is a variable and an is a fixed amount known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.
A function that has a positive constant increased to a variable exponent, other than 1, is referred to as an exponential function. By solving at a certain input value, a function is assessed. When the beginning value and growth rate are known, an exponential model can be discovered.
We observed that:
f (0) = 2
For the function g (x) we have:
g (0) = -2
Therefore,
g (x) = f (x) - 4
Looking for intersection with axis and we have:
g (0) = f (0) - 4
g (0) = 2 - 4
g (0) = -2 (correct demonstration)
The transformation of f (x) is: A. g (x) = f (x) - 4
Therefore, the correct answer is option A. g (x) = f (x) - 4.
The complete question is;
Two exponential functions, f and g, are shown in the figure below, where g is a transformation of f.
Which of the rules given below shows the transformation of f?
A. g(x) = f(x) - 4
B. g(x) = f(x - 4)
C. g(x) = f(x) + 4
D. g(x) = f(x + 4)
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I eh need the Answer to this please i am timed!!
Answers
Answer:
pro tip: crop your screen before you post it....
I think it's B
I did this 2 years ago in middle school
The angle of elevation to the top of a Building in New York is found to be 4 degrees from the ground at a
distance of 1.75 miles from the base of the building. Using this information, find the height of the building.
Round to the nearest whole number.
Your answer is
Submit Question
feet.
Answers
The height of the building can be 649.44 ft
What is angle of elevation ?
angle of elevation states that the angle which is formed between line of sight and horizontal line.
Given, the base of the triangle is 1.75 mile. The angle opposite of the tall side, x, is 4 degrees.
height of the building is an unknown variable (x) .
tan(angle) = opposite length /adjacent length.
Opposite length is x, adjacent length is 1.75 mile, angle is 4 degrees.
tan(4º) = x / 1.75
rearrange for x
x = 1.75*tan(4º) = ~1.75*0.0699 miles.
x = ~0.123
Now to get feet, just multiply by 5,280 ft in one mile
Height of the building is 0.123 miles * 5280 ft/mile = 649.44 ft
Hence , The height of the building can be 649.44 ft .
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The dimensions of a picture frame can be represented as (x+4) inches and (x+3) inches. The value of the area, in square inches, of the picture frame is equal to the value of the perimeter, in inches
Answers
The wrist circumference in relation to height tells us how big our body frames are.
How is frame size calculated?The wrist circumference in relation to height tells us how big our body frames are. A man who is above 5' 5" tall and with a wrist measurement of 6" would be considered to have tiny bones.
The following chart can be used to establish whether a person has tiny, medium, or large bones by measuring their wrist with a measuring tape and comparing the results.
Women:
under 5'2" in height"
Medium wrist size is between5.5" and5.75" Small wrist size is less than5.5" "
Large is defined as a wrist size of 5.75 or greater."
between 5'2" and 5'5" tall
smaller than 6 inches around the wrist"
Bracelet size 6 is medium "Medium = wrist size between 6.25" and 6.5" Large
Over 5' 5" in height"
Small wrists measure less than 6.25", Medium wrists measure 6.25" to 6.5," and Large wrists measure over 6.5."
Example :
2(x + 3 ) + 2 (x + 4 ) = (x + 3 )( x + 4)
x² + 7x + 12 = 4x + 14
x² + 3x - 2 = 0
(x + 3 / 2 )² = 17 / 4.
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write 363 in the base-four system
Answers
Answer:
363 = 11223₄
Step-by-step explanation:
You want 363 written in base 4.
Base conversionWe can convert to base 4 by looking at the remainders from repeated division by 4:
363 ÷ 4 = 90 r 3
90 ÷ 4 = 22 r 2
22 ÷ 4 = 5 r 2
5 ÷ 4 = 1 r 1
1 ÷ 4 = 0 r 1
Writing the remainders in reverse order gives the base-4 number:
363 = 11223₄
What is the following difference?
2ab(√/192ab²)-5[√/81a¹b³
O-3ab √3ab²
O 18ab² (2/3a)-45a2b² (2√3b)
0-7ab(2√3ab²)
O
8ab(√3ab²-15ab² (2√3ab)
Answers
Expressions with equal values are considered equivalent expressions. the difference is 2ab(√/192ab²)-5[√/81a¹b³ is -7ab(2√3ab²)
what are expressions ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.
given
Rewrite the above expression as:
[tex]2ab\sqrt[3]{3*4^{3} *ab^{2} } - 5\sqrt[3]{3*3^{3} * a^{4}b^{5} }[/tex]
Evaluate the cube roots
[tex]2ab {4\sqrt[3]{3ab^{2} } } - 5 {3ab\sqrt[3]{3ab^{2} }[/tex]
Evaluate the differences
-7ab(2√3ab²)
Expressions with equal values are considered equivalent expressions. the difference is 2ab(√/192ab²)-5[√/81a¹b³ is -7ab(2√3ab²)
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Tell whether each system of equations has no solution, one solution, or infinitely many solutions. Show how you arrived at your conclusion for each.
a. y = 5x + 11 and y = 5x
b. y = 6x + 3 and y = 3x
c. x + 4y = 8 and y = -1/4x + 2
Answers
System of equations y = 5x + 11 and y = 5x has no solution, y = 6x + 3 and y = 3x has one solution and x + 4y = 8 and y = -1/4x + 2 no solution.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given system of equations are
a. y = 5x + 11 and y = 5x
Substitute the y value in first equation
5x=5x+11
So the system of equations y = 5x + 11 and y = 5x has no solution.
b. y = 6x + 3 and y = 3x
Substitute the y value in first equation
3x=6x+3
-3x=3
x=-1
y=-3
The system of equations has one solution
c. x + 4y = 8 and y = -1/4x + 2
x+4(-1/4x + 2)=8
x-x+2=8
The system of equations has one solution has no solution
Hence, system of equations y = 5x + 11 and y = 5x has no solution, y = 6x + 3 and y = 3x has one solution and x + 4y = 8 and y = -1/4x + 2 no solution.
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In the figure below, a surveyor put stakes at the lettered points. He used string to determine lengths of line segments and a transit to check that the angles at D and B were both right angles.
If CD = 3, CE = 5, DE = 4 and DB = 18, and:
AB/DB=BC/CD
AB =
units.
Answers
The length of segment AB is given as follows:
AB = 20 units.
What are similar triangles?Similar triangles are triangles that share these two features given as follows:
Congruent angle measures.Proportional side lengths.The similar triangles for this problem are given as follows:
ABD and CDE.
Hence the proportional relationship that can be established between the side lengths is given as follows:
AB/DE = BC/CD = AC/CE.
The side lengths are given as follows:
CD = 3, CE = 5, DE = 4, DB = 18.
As CD = 3 and DB = 18, using the segment addition postulate, we have that:
BC = BD - CB
BC = 18 - 3
BC = 15 units.
Hence the length AB is obtained as follows:
AB/4 = 15/3
AB/4 = 5
Applying cross multiplication, we have that:
AB = 4 x 5
AB = 20 units.
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please help!!! HURRY!!
Answers
please help!!! HURRY!!
Given that cot 0 =
5
-, find csc 0.
√11
Answers
According to the given cosecant function the value of csc 0 is equal to 6/5.
What is the cosecant function?The sine function has a reciprocal called the cosecant function. The cosecant function is the hypotenuse divided by the opposite side, just like the sine function is the opposite side divided by the hypotenuse. The hypotenuse and legs are terms for the two sides that are not at the right angle.
It is given that:
[tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]
According to trigonometric identity,
[tex]csc^2\ alpha - cot^2\alpha = 1\\csc^2\ 0 -\frac{11}{25} =1\\csc^2\ 0 = \frac{36}{25} \\csc\ 0= \frac{6}{5}[/tex]
Therefore the value of csc 0 is equal to 6/5.
Complete question;
Given that [tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]
find csc 0.
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Y intercept and slope
Answers
Answer: A y-intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.
Slope - A number that describes both direction and steepness of the line.
Step-by-step explanation: If a line intersects the y-axis at point 5 then its y-intercept will be c= 5. As we denote y-intercept with c.
The slope is denoted by m.
5 pizzas cost £35.00. How much do 3 pizzas cost?
Answers
Answer:£21.00
Step-by-step explanation:
One pizza: (£35/5) =£7
Three pizza's: (£7x3)=£21
Factor the expression y^2+8x+12
Answers
Answer: y^2+8x+12
Step-by-step explanation:
Pacquiao has inherited P6,000 from the death of his Grandma . He would like to use this money to buy his mom Dionisia a new bicycle costing P7,000 2 years from now. Will Pacquiao have enough money to buy the gift if he deposits his money in an account paying 8 percent compounded semi-annually?
Answers
Pacquiao will have enough money (a future value of up to P7,000) to buy the gift if he deposits his money (P6,000) in an account paying 8 percent compounded semi-annually.
What is the future value?The future value is the compounded present value at an interest rate.
The future value can be determined using an online finance calculator, FV table, or FV formula.
N (# of periods) = 4 (2 years x 2)
I/Y (Interest per year) = 8%
PV (Present Value) = P6,000
PMT (Periodic Payment) = P0
Results:
Future Value (FV) = P7,019.15
Total Interest = P1,019.15
Thus, in 2 years' time, Pacquiao will have P7,019 enough to buy his mom a new bicycle.
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Find the sum or difference (I will give you brainlist :D)
Answers
Step-by-step explanation:
1. Get rid of the parentheses since you don't need them.
2. Combine like terms, 3k^2, 4k^2, 4k, and -6k. This should lead you to 7k^2 -2k +12
To find the sum or difference we must know what k is however you can simplify the expression by rewriting and removing the parenthesis furthermore collecting the like terms to get the solution.
Attached photo shows the steps to the solution :P
solve the equation a^2x^2 = abx + 2b^2 using completing the square method
Answers
The solution to the equation is
x = b/a ± √(b^2/a^2) / a.
What is the equation?Generally, To solve the equation using the completing the square method, we first move all the terms to one side of the equation by subtracting abx and 2b² from both sides, giving us:
a²x² = abx + 2b²
Which is
a²x² - abx - 2b² = 0
Next, we need to add and subtract a term so that the left side of the equation can be written as a perfect square.
We need to find the square of half of the coefficient of the x term, which is -ab/2a.
So we add and subtract (ab/2a)^2 = (b^2/a^2) on the left side of the equation:
a²x² - abx - 2b² + (b²/a²) - (b²/a²) = 0
This gives us the left side of the equation as
(ax - b/a)² = b²/a².
We can then take the square root of both sides:
ax - b/a = ±√(b²/a²)
Finally, we can add b/a to both sides to get the solution:
x = b/a ± √(b²/a²) / a
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Select the correct answer
Answers
The domain of the given graph is (-∞ < x < ∞)
What is the domain of a function?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).
Given is a graph,
For f(x) = x, there is no restriction on x
Both the domain and range are the set of all real numbers.
Hence, The domain will be (-∞ < x < ∞)
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If you work for an airline need to sit a passenger every 30 seconds. If the doors open at 9:35 am, what time does the last passenger sit if there are 110?
Answers
Answer: 10:30 am
Step-by-step explanation: If you need to seat a passenger every 30 seconds, (half of a minute, which is 60 seconds), for every minute, 2 passengers will be seated. So, if you seat 2 passengers for a min each until you have seated 110 people, you will have taken up 55 minutes in total. (110 divided by 2 passengers a min). And finally, 55 minutes past 9:35 am would be 10:30 am. Hope this helps!
The student council is responsible for setting up the tables for
an awards banquet at the end of the year.
There are 144 people
who confirmed that they would attend the banquet.
The equation
8x +12y = 144 models this situation, where x is the number of
circular tables and y is the number of rectangular tables.
Find the x- and y-intercepts.
Answers
On solving the provided question, we can say that - here in the slope intercept [tex]2y / 2 = -4x /2 + 24 / 2 = > y = -2x + 12\\[/tex]
what is slope intercept?The point on the y-axis where the slope of the line passes is known as the intersection point in mathematics. the location on a line or curve where the y-axis crosses that point. This is demonstrated by putting y = mx+c as the equation for the straight line, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the slope (m) and y-intercept (b) of the line are highlighted. The slope is m, and the y-intercept is b for equations in the intercept form (y=mx+b). Additionally, certain equations may be recast to seem like slope intercepts. For instance, if y=x is rewritten as y=1x+0, the slope becomes 1 and the y-intercept becomes 0.
y = mx + c
m = slope, c = y-intercept
[tex]4x + 2y = 24\\2y = -4x + 24\\2y / 2 = -4x /2 + 24 / 2\\y = -2x + 12\\[/tex]
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Based on the experiment if a card is chosen 200 times how many times would you expect to pick a card without stripes?
Answers
The number of expected times to pick a card without strips is 130.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The percentage of stripes from the 120 times.
= 42/120 x 100
= 35%
Now,
Based on this experiment,
The number of strip cards out of 200 times.
= 35% of 200
= 35/100 x 200
= 35 x 2
= 70
The number of times to pick a card without strips.
= 200 - 70
= 130
Thus,
The expected number of times to pick a card without stripes is 130.
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The complete question is given below.
If some one makes and many slices of toast of toast as possible in 4 minutes and 40 seconds how many slices they can make?
Answers
Therefore , the solution of the given problem of expression comes out to be probably 4 slices.
Who or what is expression?In mathematics, it is possible can multiply, division, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression. Expressions and phrases can be contrasted.
Here,
you figure if a toaster takes about 1-2 minutes to toast a piece of bread and a toaster usually can fit 2 slices at a time i would say 4.
Preheat oven broil to high. Move oven rack to highest position.
Place sliced bread on an ungreased baking sheet. 4 slices of bread.
Broil bread for 1 minute, or until golden brown, then flip and broil for another 20-30 seconds. ...
Top with butter, jam, or any other favorite topping!
The temperature needed for the hot ambient air in a toaster, which makes the bread turn brown, is around 310°F (146°C). The heating element inside a toaster is a nickel-chromium alloy. The electrical current that runs through it heats it to make it red hot, with a temperature of 1,100°F to 1,200°F (519°C to 566°C).
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Where did Nathan make a mistake?
In Step 1, Nathan did not multiply
both terms in parentheses by-3.
In Step 2, Nathan did not simplify
5x 3x correctly.
In Step 3, Nathan did not divide
by the correct number.
In Step 4, Nathan did not simplify
correctly.
<->) -24
8
Answers
Answer:
The question is not detailed enough
Answer:
In step 2, Nathan did not simplify 5x - 3x correctly.
Step-by-step explanation:
In step 2, Nathan was one number off the correct simplification.
Can someone sole this please
Answers
The value of u is given by the equation u = 37°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the sum of total internal angles of a triangle be = 180°
Now , the triangle be ΔABC
The measure of ∠A = u + 4°
The measure of ∠B = u
The measure of ∠C = ( 180° - ( u + 41° ) ) ( angles on a straight line = 180° )
From the triangle theorem ,
u + 4° + u + ( 180° - ( u + 41° ) ) = 180° be equation (1)
On simplifying the equation , we get
2u + 184° - u - 41° = 180°
u + 143° = 180°
Subtracting 143° on both sides of the equation , we get
u = 37°
Therefore , the value of u is 37°
Hence , the value of u in the triangle is 37°
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Pls help! Step by step:)
Answers
Answer:
x = 15
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² = 9² + 12² = 81 + 144 = 225 ( take square root of both sides )
x = [tex]\sqrt{225}[/tex] = 15
Answer:
x = 15
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
From inspection of the given right triangle:
a = 9b = 12c = xSubstitute the given values into Pythagoras Theorem and solve for x:
[tex]\implies 9^2+12^2=x^2[/tex]
[tex]\implies 81+144=x^2[/tex]
[tex]\implies 225=x^2[/tex]
[tex]\implies \sqrt{x^2}=\sqrt{225}[/tex]
[tex]\implies x=15[/tex]
If m and n are positive integers, show that: 3 (m + n)! ≥ m! + n!
Answers
We can conclude the proof of inequality : 3 (m + n)! ≥ m! + n! below.
What is factorial?In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Mathematically, we can write -
[tex]$n! = n \times (n-1) \times \dots \times 1[/tex]
Given is the inequality -
3 (m + n)! ≥ m! + n!
We have -
3 (m + n)!
3 {(m + n)(m + n - 1)(m + n - 2) ....... (3)(2)(1)}
3 {m² + mn - m + nm + n² - n}(m + n + 2) ...... (3)(2)(1)
3 {m² + n² - m - n + 2mn}(m + n + 2) ........ (3)(2)(1)
3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1)
Now, for (m! + n!) --
(m! + n!) = m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)
It can be seen that -
3 {m(m - 1) + n(n - 1) + 2mn}(m + n + 2) ....... (3)(2)(1) ≥
m(m - 1) .... (3)(2)(1) + n(n - 1) ..... (3)(2)(1)
Hence, it can be seen that -
3 (m + n)! ≥ m! + n!
Therefore, we can conclude that 3 (m + n)! ≥ m! + n!.
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PLEASE HELP ME 2 QUESTIONS ARE LISTED DOWN BELOW
Answers
A) The linear equation is:
y = (3/4)*x + 3
B) The sets with only positive elements are:
{x| x ∈ N}{y| 0 < y < 1}{y| 3 ≤ y ≤22}How to write the linear equation?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Here, we do know that the y-intercept of the linear equation is (0, 3), then we know that b = 3.
Then the line is something like:
y = a*x + 3
We also know that the line passes through (-4, 0), then we can replace these values in the equation above to get:
0 = a*-4 + 3
4a = 3
a = 3/4
Then the linear equation is:
y = (3/4)*x + 3
In which sets all the numbers are positive?The sets where all the numbers are positive are:
{x| x ∈ N}
Where N is the set of the natural numbers, these are all the integers equal to or larger than 1, so all are positives.
{y| 0 < y < 1}
There we can see that y must be larger than zero, so all the elements are positive.
{y| 3 ≤ y ≤22}
Here the elements are between 3 and 22, so all of these are positve.
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