Let's begin by identifying key information given to us:
Numbers of apples = 35
Number of oranges = 30
Total number of fruits = 65
The ratio of apples to oranges is given by:
[tex]\begin{gathered} 35\colon30 \\ \text{Divide through both sides by the common factor ''5''. We have:} \\ \frac{35}{5}\colon\frac{30}{5}\Rightarrow7\colon6 \\ =7\colon6 \end{gathered}[/tex]4. Simplify the radical expression.
Answer: Hello Love I believe the answer is the LAST one
Step-by-step explanation:
y + 7 > 22 solve the inequality for y and simplify your answer as much as possible
Answer:
y > 15
Step-by-step explanation:
y + 7 > 22 ( subtract 7 from both sides )
y > 15
Answer the question in the photo for EASY points ( 20 points )
Answer: 7921 123569 5410
Step-by-step explanation:
1. 7912
2. 123569
3. 5210
Find the area and perimeter of a rectangle with vertices at (-1, 2), (3, 2),
(3.-5), and (-1,-5).
The area of the rectangle is A = L w, A = 4 * 3√5 = 12√5 Unit²
What is rectangle short answer?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.the points (-1 , 2) and (3 , 2 ) form one the of the rectangle w = [tex]\sqrt{( 3 + 1 )^{2} + ( 2 - 2 )^{2} }[/tex]
= [tex]\sqrt{4^{2} + 0 }[/tex]
= √ 16
= 4
The length can be obtained by finding distance between the points (-1,2) and ( -1, - 5) = [tex]\sqrt{( -1 -2 )^{2} + ( -5 + 1)^{2} }[/tex]
= [tex]\sqrt{(-3)^{2} + ( -6)^{2} }[/tex]
= √9 + 36
= √45 = 3√5
The perimeter of the rectangle is: P = 2( w + L) = 2( 4 + 3√5) ⇒ 8 + 6√5 unit
The area of the rectangle is A = L w, A = 4 * 3√5 = 12√5 Unit²
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graph the proportion y = -4x
Answer in the attachment
a scientist observes a congenital birth defect in a breed of cats and predicts that in a cross between heterozygotes, 25% of the kittens will be born with the birth defect. she surveys several litters, and finds that 44 out of 128 kittens have the defect. to see if her hypothesis is correct, she decides to use chi-square analysis and determines that the expected number of unaffected kittens should be:
The expected number of unaffected kittens should be 84
Find the below calculation of chi square:
Category Affected Unaffected Total
Observed values 44 84 128
Expected Ratio 1 3 4
Expected Values, E 32 96
Deviation, D 12 -12
Deviation Squared 14 144
D^2/E 4.5 1.5 6
X^2 6
Degrees of freedom - 1
Unaffected number of kittens:
Observed values for Affected=44
Total=128
25% of the 128 are affected.
The unaffected proportion is,
Total-Observed values for Affected kittens
=128-44
=84
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Let f be the function given by f(x) = x + [tex]\frac{\sqrt{x+1} }{x-1}[/tex]
Find and simplify f(3).
Responses
A f(3) = 5
B f(3) = 3 + 2[tex]\sqrt{2}[/tex]
C f(3) = 3 + [tex]\sqrt{2}[/tex]
D f(3) = 4
By evaluating f(x) in x = 3, we will get that:
f(3) = 4
Thus the correct option is D:
How to evaluate the function in x = 3?Here we have the following function:
[tex]f(x) = x + \frac{\sqrt{x + 1} }{x - 1}[/tex]
We want to get f(3), and to get that, we just need to replace all the "x" in the equation by the number 3, we will get:
f(3) = 3 + (3 + 1)/(3 - 1)
f(3) = 3 + √4/2 = 4
With this, we can conclude that the correct option is D:
f(3) = 4.
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HELPPPPP SAT QUESTION
The value of x in the angles is equal t0 15
Angles on a Straight line
To solve this problem, we can simply apply the theorem that states the sum of angles in a straight line is equal to 180 degrees.
This implies that;
[tex]AOF + FOG + GOB = 180^0[/tex]
substituting the values into the equation;
[tex]AOF + FOG + GOB = 180^0\\(5x -15) + 90 + 2x = 180[/tex]
Let's solve for x
[tex]5x - 15 + 90 + 2x = 180\\7x + 75 = 180\\7x = 105\\x = 15[/tex]
The value of x that makes the angles equal to 180 degrees is 15.
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8. Find the area of the regular polygon.
14 in
5.2 in
The area of a regular polygon is 84.87 in²
What is the regular polynomial?A polygon with congruent sides and equal angles is referred to as a regular polygon. Equilateral triangles, squares, regular pentagons, and more are examples of regular polygons.
In this case Formula of the area of the equilateral triangle is ( [tex]\sqrt{3\\}[/tex]×a²)/4
where a is the length of the side of triangle.
Here the length of the side of the polygon(triangle) is 14in.
So the area of the equilateral triangle is (√3xa²)/4.
And a=14 in the above equation.
So the area of the regular polygon is: (√3x14x14)/4 =84.87 in²
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you are constructing a 12 cubic feet box that is open at the top. the material used to construct the bottom costs $3 per square foot and the material used to construct the sides is $1 per square foot. what dimensions should you use to minimize the cost of the materials? set up and solve using the lagrange method.
The length and breadth should be 2 feet each and height should be 3 feet to minimize the cost of the materials.
Let consider the length of the box =x
considering a square bottom ,
length = breadth = x
and let the height =h
The surface area of the box is
SA = x² + 4xh ( box is open from top )
cost of 1sq feet material for bottom =$3
cost of 1sq feet material for sides =$1
The cost functions can be written as
C = 3x² + 1(4xh)
C = 3x² + 4xh
Also the volume equation is
x²h = 12
h = 12/x²
substituting the value of h into the cost function.
C = 3x² + 4x (12/x²)
C = 3x² + 48/x
C = (3x³ + 48)/ x
Take the derivative of C and set it equal to zero. So we get
6x³ - 48 = 0
x³ = 48/6 = 8
x = 2
∴ h = 12/x²
h = 12/4
h = 3
This is the value of x and h that minimizes the cost.
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In a math class with 22 students, a test was given the same day that an assignmentwas due. There were 14 students who passed the test and 13 students who completedthe assignment. There were 6 students who failed the test and also did not completethe assignment. What is the probability that a student chosen randomly from theclass passed the test and completed the homework?
Let:
A = students who passed the test = 14
B = students who completed the assignment = 13
N = Total students = 22
(A⁺ ∩ B⁺) = 6
P(A ∪ B) = 1 - 6/22 = 8/11
P(A ∩ B) = P(A) + P(B) - P(A ∪ B) = 14/22 + 13/22 - 8/11 = 1/2
P(A|B) = P(A ∩ B)/P(B) = (1/2)/(13/22) = 11/13 ≈ 0.85 ≈ 85%
What would you multiply by to decrease a number by 13%?
Answer:
To decrease it by 13% we will multiple (100-13 = 87) .
Step-by-step explanation:
Multiply the decimal form of the number (in this case 13) to the number.
For example: 13% of 50
13% can also be said as 0.13 in decimal form.
50*0.13=6.5
13% of 50 is 6.5.
Sean is buying 9/16 pound of tea at a tea shop. Write the amount as a decimal.
Step-by-step explanation:
A decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point.
Answer: 9/16 as a decimal is 0.5625
9-16-as-a-decimal-is-0.5625
Let's look into the two methods to write 9/16 as a decimal.
Explanation:
Method 1: Writing 9/16 as a decimal using the division method
To convert any fraction to decimal form, we just need to divide its numerator by denominator.
Here, the fraction is 9/16 which means we need to perform 9 ÷ 16
This gives the answer as 0.5625. So, 9/16 as a decimal is 0.5625
Method 2: Writing 9/16 as a decimal by converting the denominator to powers of 10
Step 1: Find a number such that we can multiply by the denominator of the fraction to make it 10 or 100 or 1000 and so on.
Step 2: Multiply both numerator and denominator by that number to convert it into it's an equivalent fraction.
Step 3: Then write down just the numerator, putting the decimal point in the correct place, that is, one space from the right-hand side for every zero in the denominator.
9/16 = (9 × 625) / (16 × 625) = 5625/10000 = 0.5625
Irrespective of the methods used, the answer to 9/16 as a decimal will always remain the same.
You can also verify your answer using Cuemath's Fraction to Decimal Calculator.
Thus, 9/16 as a decimal is 0.5625
f(x)=x^2+x and g(x)=1/x+1 find the rules for (f o g)(x) and (g o f)(x) and give the domain of each composite function
The composite functions of (f o g)(x), (g o f)(x) and their domains in the function f( x ) = x² + x and g( x ) = 1/(x+1) are (x+2) / (x+1)², Domain: {x|x ≠ -1 } and 1/(x² + x + 1 ), Domain: {x|x ∈ R } respectively.
What are the composite result function and domain of (f o g)(x) and (g o f)(x) in the given function?A function is simply a relationship that maps one input to one output.
Given the data in the question;
f( x ) = x² + xg( x ) = 1/(x+1)(f o g)(x) = ?(g o f)(x) = ?First, set up the composite result function (f o g)(x).
(f o g)(x) = f( g(x) )
f( x ) = x² + x
f( g(x) ) = f( 1/(x+1) ) = ( 1/(x+1) )² + 1/(x+1)
Apply product rule to simply
f( g(x) ) = 1² /(x+1)² + 1/(x+1)
f( g(x) ) = (1 + x + 1 )/ (x+1)²
f( g(x) ) = (x+2) / (x+1)²
Next, find the domain by equating the denominator to 0 and solve for x.
x + 1 = 0
x = -1
Domain: {x|x ≠ -1 }
For (g o f)(x), set up the composite result function (g o f)(x).
(g o f)(x) = g( f(x) )
g( x ) = 1/(x+1)
g( f(x) ) = g( x² + x ) = 1/( (x² + x) + 1 )
g( f(x) ) = 1/( (x² + x) + 1 )
g( f(x) ) = 1/(x² + x + 1 )
Next, find the domain by equating the denominator to 0 and solve for x.
x² + x + 1 = 0
x = ( -1±√(1² - 4 ×(1×1) ) / (2 × 1 )
x = (-1±i√3)/2
x = (-1+i√3)/2, (-1-i√3)/2
Hence,
Domain is set of all real numbers.
Domain: {x|x ∈ R }
Therefore the composite functions and their domain are (x+2) / (x+1)², Domain: {x|x ≠ -1 } and 1/(x² + x + 1 ), Domain: {x|x ∈ R }.
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if three buckets of capacities 15 litre,18 litre and 24 litre can fill a drum in exact number of times, find the least capacity of the drum.
There are two questions to be solved, therefore, I'll solve the buckets one first and then I'll solve the other one. To solve both we need to apply LCM (least common multiple).
There are three buckets with differente capacities, one with 15 litres, one with 18 litres and one with 24 litres. Since they can fill a drum in an exact number of times, this means that the capacity of the drum is a multiple of the capacity of each bucket, therefore we should break each number into their multiples and find the common ones as shown below.
[tex]\begin{gathered} 15\text{ = 3}\cdot5 \\ 18\text{ = 2}\cdot3\cdot3 \\ 24\text{ = 2}\cdot2\cdot2\cdot3 \end{gathered}[/tex]We now need to multiply all the common multiples:
[tex]\text{least capacity = 2}\cdot2\cdot2\cdot3\cdot3\cdot5\text{ = }360\text{ litres}[/tex]For the second problem we have three items a book, a pen and a box. They cost respectively 36, 45 and 54. We need to then find the smallest sum of money that could buy a exact number o each item. We need to apply LCM once again as shown below:
[tex]\begin{gathered} 36\text{ = 2}\cdot2\cdot3\cdot3 \\ 45\text{ = 3}\cdot3\cdot5 \\ 54\text{ = 2}\cdot3\cdot3\cdot3 \end{gathered}[/tex]We now need to multiply all the common multiples:
[tex]\text{least sum of money = 2}\cdot2\cdot3\cdot3\cdot3\cdot5\text{ = }540[/tex]16. Given that Angle 1 and Angle 2 form a linear pair, find the measure of both angles if m<1 = (5x + 9)° and
m<2= (3x + 11).
x =
m<1 =
m<2=
Answer: [tex]x=20, m\angle 1=109^{\circ}, m\angle 2=71^{\circ}[/tex]
Step-by-step explanation:
Angles that form a linear pair add to 180 degrees, so:
[tex]5x+9+3x+11=180\\\\8x+20=180\\\\8x=160\\\\x=20\\\\\implies m\angle 1=5(20)+9=109^{\circ}\\\\\implies m\angle 2=180^{\circ}-109^{\circ}=71^{\circ}[/tex]
y = 2 |x|
Graph the following linear inequalities
Mathematical expressions known as linear inequalities compare two expressions using the inequality symbol. The expression may be either a numerical or an algebraic expression, or it may be both.
What is meant by linear inequalities?Addition, subtraction, multiplication, and division are the four types of operations that can be performed on linear inequalities. Equivalent inequality refers to linear inequalities with the same solution. Both equality and inequality are subject to laws. For inequality involving smaller than or equal to () and greater than or equal to (), all the principles listed below apply. Let's look at some of the key inequality rules for all these operations before learning how to solve linear inequalities.
As with multi-step linear equations, start by separating the variable from the constants when resolving multi-step linear inequalities with one variable. According to the laws of inequality, it is crucial that we remember to flip the inequality sign when multiplying or dividing with negative values while resolving multi-step linear inequalities.
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How many blocks would be in the 10th figure? (figure 1 is 1 block) figure 11 figure 15 figure 19 figure 22
The 10th figure will have 19 blocks.
What is Arithmetic Progression?An arithmetic progression (AP) is a sequence in which the differences between each successive term are the same. The formula Tₙ = a+(n-1)d finds the general term (or) nth term of an AP whose first term is 'a' and the common difference is 'd'.
In the given figures,
Figure 1 has 1 block.
Figure 2 has 3 blocks.
Figure 3 has 5 blocks.
We have to find the number of blocks in the 10th figure.
The number of blocks in the figures are forming an arithmetic progression of 1,3,5.....with a common difference of 2.
So the 10th term of AP can be calculated as,
[tex]T_{10} = 1 + (10 -1)2[/tex]
[tex]T_{10} = 1 + 9*2[/tex]
[tex]T_{10} = 19[/tex]
Therefore, the 10th figure will have 19 blocks.
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PLEASE HELP ASAP! THANK YOU!
The scalar factor is of 6.
What is the scalar factor?
A scale factor is the ratio between corresponding measurements of an object and a representation of that object. in simple words how big or small is one object compared to another.
We are given two triangle and the measurements of the corresponding sides of the triangle.
side of one triangle is 4 and side of another triangle is 24.
To find the scalar factor we divide the two
We get the answers as 6
Hence the scalar factor is of 6
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Scientists are drilling a hole in the ocean floor to learn more about the Earth's history. Currently, the hole is in the shape of a cylinder whose volume is approximately 4200 cubic feet and whose height is 2.1 miles. Find the radius of the hole to the nearest hundredth of a foot. (Hint: Make sure the same units of measurement are used.)
The radius of the hole to the nearest hundredth of a foot is 2.88 feet.
What is radius?
The separation between a circle's centre and circumference is called the radius.Its diameter is halved that of the circle.The path that leads from a circle's centre to one of its points.The separation between a circle's centre and a certain point upon that circle.The volume of the cylinder, V = 4200 cubic feet
Height, H = 2.1 miles = 11088 feet
The volume of the cylinder is given by the formula, V =πr²H
Putting values in the formula to find out radius,
4200=πr²(11088)
r²=[(11088)π]/4200
r²=8.2938
r=2.879~2.88 feet
The radius of the hole to the nearest hundredth of a foot is 2.88 feet.
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Can someone help me and explain this please. I don’t understand what to do.
Answer:
The answer is 3 or 3/1
Step-by-step explanation:
The equation you use is m=y2-y1/x2-x1
Answer:
Slope = 3
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
Define two points on the line from the given table:
[tex]\textsf{Let}\:(x_1,y_1)=(2,7)[/tex][tex]\textsf{Let}\:(x_2,y_2)=(4,13)[/tex]Substitute the defined points into the formula:
[tex]\implies \textsf{Slope}=\dfrac{13-7}{4-2}=\dfrac{6}{2}=3[/tex]
Note:
The change between each y-value is 6.The change between each x-value is 2.Therefore, the question may require you to enter 6/2 into the answer boxes. However, the slope of the line is 3.
If cx-d+f, then x is equal to
(f + d)/c.
First get rid of -d on the left side by adding d to both sides
cx - d = f --> cx = f + d
Then remove c from the left side by dividing both sides by c.
cx = f + d --> x = (f + d)/c
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State the power function that the graph of f resembles for large values of x. Find the end-behavior for the function. Write your results using limit notation
Notice that:
[tex]\begin{gathered} \lim _{x\rightarrow\infty}\frac{2x^2(x-5)^2}{x^4}=\lim _{x\rightarrow\infty}\frac{2(x-5)^2}{x^2} \\ =\lim _{x\rightarrow\infty}\frac{2(x^2-10x+25)}{x^2} \\ =\lim _{x\rightarrow\infty}(\frac{2x^2}{x^2}-\frac{10x}{x^2}+\frac{25}{x^2}) \\ =\lim _{x\rightarrow\infty}(2-\frac{10}{x}+\frac{25}{x^2}) \\ =\lim _{x\rightarrow\infty}2-\lim _{x\rightarrow\infty}\frac{10}{x}+\lim _{x\rightarrow\infty}\frac{25}{x^2} \\ =2-0+0 \\ =2 \end{gathered}[/tex]Which means that, for large values of x:
[tex]2x^2(x-5)^2\approx2x^4[/tex]Since the function:
[tex]f(x)=2x^4[/tex]is a 4th degree monomial, with positive coefficient, then it keeps growing as x grows. Then, we know that:
[tex]\lim _{x\rightarrow\infty}2x^2(x-5)^2=\infty[/tex]Which means that the end behavior is such that f(x) approaches infinity as x approaches infinity.
On the other hand, for large negative values of x, the function is also positive. Then:
[tex]\lim _{x\rightarrow-\infty}2x^2(x-5)^2=\infty[/tex]how dose a value that is greater than 100 of the orangianl value less than1 of the orangilal value copare the oraginal value
If a value that is is greater than 100% of the original value will always be larger than original value.
If a value is less than 1% of the original value will always be less than the original value.
Given,
A value that is greater than 100% of the original value.
And it is 1% less than the original value.
We have to compare these values with the original value;
That is,
A value that is greater than 100% of the original value,
eg;
130% of 20 = 20 × 130/100 = 26
26 is greater than 20.
That is,
If a value that is is greater than 100% of the original value will always be larger than original value.
Next,
It is 1% less than the original value.
eg;
1% of 20 = 1/100 × 20 = 0.2
0.2 is less than 20
That is,
If a value is less than 1% of the original value will always be less than the original value.
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What is the slope of the line on the graph
Which point represents -(-7)−(−7)minus, left parenthesis, minus, 7, right parenthesis on the number line?
The final point where -(-7)−(−7) number after simplification lie is 14
In the above question it is given,
-(-7)−(−7)
We need to find the position of this number on the number line.
A number line is a visual depiction of numbers on a straight line in mathematics. A number line's numerals are arranged in a sequential manner at equal intervals along its length. It is often displayed horizontally and can be infinitely expanded in any direction.
To do that, we will first simplify the given numbers by using the sign rules of the real numbers
According to the sign rule of real numbers,
(i) (-) x (-) = +
(ii) (-) x (+) = -
(iii) (-) +(-) = -
(iv) (+) + (+) = +
Now using the above sign rules, we will simplify the given number
-(-7)−(−7)
-(-7)+ [-(−7)]
7 + 7
Now, on the number line, we'll move 7 steps in the positive direction of 0, we'll be on 7. Again from 7 we'll take next 7 steps in the same direction and we'll reach the point 14.
Hence, 14 is the final point where -(-7)−(−7) number after simplification lie.
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zimak bought 3 xylobars and 5 5 yackities from the intergalactic candy store for 1.75 jeejunu paid1.88 and got 4 xylobars and 1 yackity how much would dado pay for 1 xylobar and 2 yackities
For 1 xylobar and 2 yackities Dado would pay $0.61 .
In the question ,
it is given that
Zimak paid $1.75 for 3 xylobars and 5 yackities .
let the price of 1 xylobar = x
and let the price of 1 yackities = y
According to the question
3x+5y=1.75 ...(i)
Jeejunu paid $1.88 for 4 xylobars and 1 yackity .
So , equation becomes
4x+y=1.88 ...(ii)
y = 1.88-4x
substituting it in equation (i), we get
3x + 5(1.88 - 4x) = 1.75
3x + 9.4 - 20x = 1.75
20x-3x = 9.4 - 1.75
17x = 7.65
x = 7.65/17
x = 0.45
So, the price of 1 xylobar = $0.45
put x = 0.45 in y= 1.88-4x , we get
y = 1.88 - 4(0.45)
y = 1.88 - 1.8
y = 0.08
So , the price of 1 yackity is $0.08 .
So, For 1 xylobar and 2 yackities , Dado would pay
= x+2y
= 0.45 + 2(0.08)
= 0.45+0.16
= 0.61
Therefore , for 1 xylobar and 2 yackities Dado would pay $0.61 .
The given question is incomplete , the complete question is
Zimak bought 3 xylobars and 5 yackities from the intergalactic candy store for $1.75 . Jeejunu paid $1.88 and got 4 xylobars and 1 yackity . How much would dado pay for 1 xylobar and 2 yackities ?
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I need answer to this equation with working ASAP
5.104 ÷ 0.016
Answer:
319
Step-by-step explanation:
hope this helps
The compound interest formula states that if P dollars are invested at an annual interest rate of r, compounded n times per year, then A, the amount of money presentIf $10.500 is invested at 8 % compounded monthly, how much will this investment be worth in 22 years? Round youranswer to two decimal placesafter tyears, is given by A = P(1+2)
Step 1
State the compound interest formula
[tex]A=P(1+\frac{r}{n})^{t\times n}[/tex]where;
[tex]\begin{gathered} P=10500 \\ r=\frac{8}{100}=0.08 \\ t=22 \\ n=12 \end{gathered}[/tex]Step 2
Find the amount after 22 years
[tex]A=10500(1+\frac{0.08}{12})^{12\times22}[/tex][tex]\begin{gathered} A=10500\times5.778587511 \\ A=\text{ \$60675.16887} \\ A\approx\text{ \$60675.17} \end{gathered}[/tex]Answer;
[tex]\text{ \$60675.17}[/tex]If a+ 1/a = 5 then find the value of; i) a² + 1/a² ii) a³ + 1/a³
Answer:
23
110
Step-by-step explanation:
We have a + 1/a = 5
(a + 1/a)² = a² + (1/a²) + 2.a.1/a = a² + (1/a²) + 2
But (a + 1/a)² = 5² = 25
So a² + (1/a²) = 25 - 2 = 23
(a + 1/a)³ = a³ + 3a²(1/a) + 3a(1/a)² + (1/a)2
= a³ + 1/a³ + 3a + 3/a
= a³ + 1/a³ + 3(a + 1/a)
= a³ + 1/a³ + 3(5)
= a³ + 1/a³ + 15
But (a + 1/a)³ = 5³ = 125
So
a³ + 1/a³ + 15 = 125
a³ + 1/a³ = 110
Answer:
23 and 110
Step-by-step explanation:
using the expansion
(a + b)² = a² + 2ab + b² , then
a + [tex]\frac{1}{a}[/tex] = 5 ( square both sides )
(a + [tex]\frac{1}{a}[/tex] )² = 5²
a² + 2(a × [tex]\frac{1}{a}[/tex] ) + [tex]\frac{1}{a^2}[/tex] = 25
a² + 2(1) + [tex]\frac{1}{a^2}[/tex] = 25
a² + 2 + [tex]\frac{1}{a^2}[/tex] = 25 ( subtract 2 from both sides )
a² + [tex]\frac{1}{a^2}[/tex] = 23
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using the expansion
(a + b)³ = a³ + b³ + 3ab(a + b) , then
a + [tex]\frac{1}{a}[/tex] = 5 ( cube both sides )
(a + [tex]\frac{1}{a}[/tex] )³ = 5³
a³ + [tex]\frac{1}{a^3}[/tex] + 3(a × [tex]\frac{1}{a}[/tex] )(a + [tex]\frac{1}{a}[/tex] ) = 125
a³ + [tex]\frac{1}{a^3}[/tex] + 3(1)(5) = 125
a³ + [tex]\frac{1}{a^3}[/tex] + (3 × 5) = 125
a³ + [tex]\frac{1}{a^3}[/tex] + 15 = 125 ( subtract 15 from both sides )
a³ + [tex]\frac{1}{a^3}[/tex] = 110