Value of [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.
What do you mean by algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
There are 3 main types of algebraic expressions which include:
Monomial Expression
Binomial Expression
Polynomial Expression
An algebraic expression which is having only one term is known as a monomial.
Given expression:
a + 4/a = 4
We need to simplify the above expression and will find the value of a.
[tex]a+\frac{4}{a}=4[/tex]
⇒ [tex]\frac{a^2+4}{a}=4[/tex]
⇒ [tex]a^{2}+4=4a[/tex]
⇒ [tex]a^2-4a+4=0[/tex]
⇒ [tex]a^2-2a-2a+4=0[/tex]
⇒ a(a-2) -2(a-2) = 0
⇒ (a-2)(a-2) = 0
⇒ a = 2
Now, substitute this value of a in expression , [tex]a^5-\frac{1}{a^5}[/tex]
[tex]2^5-\frac{1}{2^5}[/tex]
= 32 - 1/32
= [tex]\frac{1024-1}{32} =1023/32 = 31.97[/tex]
Therefore, value of [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.
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the faa now figures the average checked bag to weigh 30 pounds. this is up from a previous figure of 26 pounds. find the amount of increase and the percent of increase, to the nearest whole percent.
The amount of weight of bag increase is 4 pounds. The percent of increase is 13,33 %. The result is obtained by calculating the change of two numbers.
How to find the percent of change?A number can increase or decrease to another number. This change can be counted by subtracting the first number from the second number. If the result is positive, it is an increase. If the result is negative, it is a decrease.
The percent of change would be the ratio of the amount of change to first number times 100.
Given the first figure of bag is 26 pounds and the last figure is 30 pounds.
What is the amount of increase?What is the percent of increase?The amount of increase is subtracting 26 from 30.
30 - 26 = 4 pounds.
The percent of increase is
[tex]= \frac{4}{30} \times 100[/tex] %
[tex]= 0.1333 \times 100[/tex] %
[tex]= 13.33[/tex] %
Hence, the amount of weight of bag increase is 4 pounds. The percent of increase is 13,33 %.
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a telephone call arrived at a switchboard at random within a one-minute interval. the switch board was fully busy for 15 seconds into this one-minute period. what is the probability that the call arrived when the switchboard was not fully busy?
The chance that the call arrived when the switchboard was not completely busy is 0.75.
Probability is a branch of mathematics that studies the likelihood of a random event occurring.
It is given that the switchboard is fully busy for the first 15 seconds, that means it is not busy for the next 15 seconds to 60 seconds
Therefore the probability that calls arrived when the switchboard was not fully busy is
P(15< x < 60) = ∫_15^60▒f(x)dx
= ∫_15^60▒〖1/60 dx〗
=1/60 ∫_15^60▒〖1.dx〗
= 1/60 [ x ]6015
= (60 – 15)/60
= 45/60
= ¾
= 0.75
Therefore the probability that the call arrived when the switchboard was not fully busy is 0.75
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Compute the the directional derivative Da(f) of f(x, y) = xy + x³ at the point (1, 2) and
in the direction of (1,-1).
The pages of a book are numbered consecutively from 1 to 100. What is the sum of all the digits used in numbering the pages of the entire book?
5050
Step-by-step explanation:
1+2+3+.....+100 add all the numbers and u get that
Expand and simplify (3x + 4)(2x + 3)
Answer:
6x^2+17x+12
Step-by-step explanation:
(3x+4) * (2x+3)
3x * 2x = 6x^2
3x * 3 = 9x
+4 * 2x = +8x
+4 * +3 = +12
6x^2+ 9x+8x +12
Simplify:
6x^2+17x+12
when two pipes fill a pool together, they can finish in 4 hours. if one pipe fills half of the pool and then the other takes over and finishes filling the pool, the pool will fill in 9 hours. how long would it take each pipe to fill the pool if it were working alone?
Time taken by pipe 1 to fill the pool is 6 and by pipe 2 is 12.
Here we have to find the time taken by each pipe to fill the pool.
Formula to find the work:
w = r × t
where
w = is the work done
r = is the rate of work done
t = is the time taken to do the work
For pipe 1 working alone to fill 1 pool, the work done is 1
w1 = r1 t1
1 = r1 × t1
t1 = 1/r1
For pipe 2 working alone to fill 1 pool, the work done is 1;
w2 = r2 t2
1 = r2 × t2
t2 = 1/r2
From the question, it would take 9 hours if each pipe took turns filling half the pool. That is;
t1/2 + t2/2 = 9
t1 + t2 = 18
However, if both pipes worked together, it would take 4 hours for each pipe. That is;
w1 + w2 = w
r1t1 + r2t2 = 1
4r1 + 4r2 = 1
r1 + r2 = 1/4
As we know from the above:
r1 = 1/t1 and r2 = 1/t2
So;
1/t1 + 1/t2 = 1/4
(t2 + t1)/ t1 t2 = 1/4
t1 + t2 = 18
So
t1 t2 = 72
The only factors of 72 that satisfy the conditions
t1 + t2 = 18
t1 . t2 = 72
are 6 and 12.
Therefore, pipe 1 will take 6 hours, and pipe 2 will take 12 hours.
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a fence is to be built to enclose a rectangular area of 310 square feet. the fence along three sides is to be made of material that costs 4 dollars per foot, and the material for the fourth side costs 14 dollars per foot. find the dimensions of the enclosure that is most economical to construct.
The dimension for the enclosure that is most economical to construct will be length=11.13 feet and width=27.85 feet.
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.
A=l*b
=310
b=310/l
total cost=(8b+4l+16l)
=8b+20l
=8*310/l+20l
t=2480/l+20l
t'=20-2480/l²
t'=0
20l²=2480
l²=124
l=11.13 feet
b=310/11.13
b=27.85 feet
The enclosure's length and width, which add up to 11.13 feet and 27.85 feet respectively, will be the most cost-effective dimensions to build.
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The temperature on a summer afternoon is 85°F. Define a variable and write an expression to find the temperature after it changes. Then evaluate your expression for a decrease of 11 degrees Fahrenheit.
The expression that can be used to find the temperature after it changes is 85°F + C
How to find a change in temperature?Temperature refers to the degree of hotness or coldness of a body at a particular time. It is measured in degree Celsius, degree Fahrenheit an Kelvin.
The instrument used to measure temperature is a thermometer.
Temperature on a summer afternoon = 85°FDecrease in temperature = -11°Flet
C = change in temperatureThe change in temperature = 85°F + C
= 85°F + (-11°F)
= 85 - 11
= 74°F
Therefore, the new temperature after a decrease in 11°F is 74°F
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How much money does he earn when he sells 35 wooden toys? Emilio builds and sells homemade wooden toys for $12 each. The festival he is attending charges $50 to set up his booth. How much money does he earn when sells 35 wooden toys?
After selling 35 wooden toys and after cutting the expense of setting up his booth, Emilio earns $370.
What is BODMAS?
BODMAS, often known as the order of operations, is a method for carrying out operations in an arithmetic expression. Math is all about logic and some established principles that facilitate our computations. BODMAS is one of those commonly used rules for consolidating expressions with multiple operators.
Solution Explained:
A/Q, The price of one toy is $12
The cost of setting up the shop is $50
Therefore, the amount Emilio earns after selling 35 toys is:
(12 X 35) - 50
= 420 - 50
= 370
Hence, Emilio earns $370
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Can anyone write the equation of the graph?
Y+2=1/4 x in standard form
Answer:
-[tex]\frac{1}{4}x[/tex] + y = -2
Step-by-step explanation:
Standard form: Ax + By = C
y + 2 = [tex]\frac{1}{4} x[/tex]
Rearrange terms:
1. Subtract 2 from both sides
y = [tex]\frac{1}{4} x[/tex] - 2
2. Subtract [tex]\frac{1}{4} x[/tex] from both sides
-[tex]\frac{1}{4}x[/tex] + y = -2
I really need help with this parallel lines and transversal equations find each angle measure 1-8
Answer:
1 = 88
2 = 92
3 = 88
4 = 92
5 = 92
6 = 88
7 = 92
8 = 88
Step-by-step explanation:
10x + 2 = 14x - 50
52 = 4x
18 = x
Which rational number is equivalent to 0 . ¯¯¯¯¯¯ 36 ?
The rational number is equivalent to 0.36 is 9/25
How to determine the equivalent rational number?From the question, we have the following decimal number that can be used in our computation:
Decimal number = 0.36
To start with, we need to express the decimal number as a fraction
This is represented as follows:
So, we have the following representation
Decimal number = 36/100
Change the label of the above representation to rational number
Rational number = 36/100
Simplify the rational number (divide the numerator and the denominator by 2)
Rational number = 18/50
Simplify the rational number (divide the numerator and the denominator by 2)
Rational number = 9/25
Hence, the equivalent rational number is 9/25
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1) What is the slope of the following graph?
Answer:[tex]\frac{3}{-2}[/tex]
Step-by-step explanation:
slope= [tex]\frac{rise}{run}[/tex]
start at (0,1)
go up 3 units
then go left 2 units
slope= [tex]\frac{3}{-2}[/tex]
you can answer any 17 questions from a total of 20 questions on an exam. in how many different ways can you select the questions?
With the help of probability we can say that there are 1140 ways.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .acc to our question-
permutation= 20!/ (20-17)!ncr= 20!/ 17!(20-17)!=1140Hence,we can say that there are 1140 ways.
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how do i work this out please?
By evaluating the linear equation we will see that:
A = -3
B = 4
And the correct line is the purple one.
How to get the values of A and B?We know that the points (0, A) and (B, 0) lie on the line 3x - 4y = 12
To find the value of A, we can replace the values of the point on the line, so we get:
3*0 - 4*A = 12
-4*A = 12
A = 12/-4 = -3
A = -3
To get the value of B we do the same thing.
3*B - 4*0 = 12
B = 12/3
B = 4
So the points are (0, -3) and (4, 0).
Then the correct line is the purple one.
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What is the length of the hypotenuse in 2 decimal places
a statistical quality control process for cereal production measures the weight of a cereal box. the population standard deviation is known to be .06 ounces. in order to achieve a 97% confidence with a margin of error of .02 ounces, how large a sample should be used?
The sample size that should be used is 43.
Given that;
The weight of a cereal box is measured as part of a statistical quality control process for the manufacture of cereal. It is understood that the population standard deviation is 0.06 ounces. To attain a margin of error of and a confidence level of 97% 0.02 ounces.
By considering the confidence level scenario, we get to solve how large a sample should be utilized.
The significance level is (α) = 0.03 ( 97% confidence level )
The critical value is (z*) = 2.17 ( From z-table )
The population standard deviation (σ) = 0.06
The margin of error (E) = 0.02
Therefore, the required sample size is;
n = [(z* × σ)/E ]²
n = 42.383
n ≅ 43
Finally, the sample size that should be used is 43.
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Complete the table and answer the questions that follow. (If a root occurs twice, count it twice; if
thrice, count it three times, and so on. The first one is done
Polynomial Equation
1. (x+1)² (x-5) = 0
2. X-9 0
3. (x+8) (x-8)= 0
4. x² + 3x +2=0
(x+1)(x+2) = 0
5. (x² - 4x + 4)(x-3)²
(x-2)(x-2)(x-3)(x-3) = 0
6. 2
7. (x-3)(x + 1)(x - 1) = 0
8. (x²-4)(x-3)³ = 0
(x+2)(x-2)(x-3)(x-3)(x-3)=0
9. x(x-4)(x + 5)(x - 1) = 0
10. (x + 1)5 (x - 1)² =0
Degree
3
Real Roots of the
Equation
-1 (2times); and 5
Number of Real Roots
3
An equation of the form P=0 is referred to as a polynomial equation. P is a polynomial with coefficients in some field, typically the field of the rational numbers. A polynomial equation, on the other hand, can include a number of variables. The phrase polynomial equation is typically preferred over algebraic equation when discussing situations with multiple variables.
What is Polynomial Equation ?One or more variables, coefficients, and non-negative integer exponents of variables make up a polynomial, which is an expression. A mathematical statement that has a "equal to" symbol between two algebraic expressions with equal values is called an equation.
Sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials.
4x² + 6x + 21=0 where 4x²+6x+21 is considered as a polynomial expression which is written on the left side and has been fixed to make the polynomial expression equal to zero to form a complete polynomial equation.
1 Already answered
2 Degree:1 Real Roots of an equation:8 Number of Real Roots:1
3 Degree:2 Real Roots of an equation:2,-2 Number of Real Roots:2
4 Degree:5 Real Roots of an equation:-1,1-3,-3,-3 Number of Real Roots:5
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What is the range of the following function
The range of the given function is y ≥ 0 which is option B.
From the graph:
Some points (-1,1),(-2,2),(0,0),(1,1),(2,2)
Range is defined as the set of y values or outputs.
range = 0,1,2,3 ......
Means range starts from zero to infinite(0 to all positive values.
so range = y ≥ 0
Therefore range of the given function is y ≥ 0 which is option B.
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Can someone please help !
[tex]\huge\begin{array}{ccc}BT=21\\DC=10.2\end{array}[/tex]
If BT is the midsegment of ΔMAH and DC is the midsegment of ΔBTH, then MA, BT and DC are parallel.
Therefore the segments form the proportion:
[tex]\dfrac{HM}{MA}=\dfrac{HB}{BT}=\dfrac{HD}{DC}[/tex]
BT is the midsegment of ΔMAH, therefore
[tex]HB=\dfrac{1}{2}HM[/tex]
DC is the midsegment of ΔBTH, therefore
[tex]HD=\dfrac{1}{2}HB=\dfrac{1}{2}\cdot\dfrac{1}{2}HM=\dfrac{1}{4}HM[/tex]
Substitute:[tex]\dfrac{HM}{42}=\dfrac{\frac{1}{2}HM}{BT}[/tex]
cross multiply
[tex]HM\cdot BT=42\cdot\dfrac{1}{2}HM[/tex]
divide both sides by HM
[tex]\boxed{BT=21}[/tex]
[tex]\dfrac{HM}{42}=\dfrac{\frac{1}{4}HM}{DC}[/tex]
cross multiply
[tex]HM\cdot DC=42\cdot\dfrac{1}{4}HM[/tex]
divide both sides by HM
[tex]\boxed{DC=10.5}[/tex]
What is the image point of (-8, 1) after the transformation 7x-axis R180°?
The image point of (-8, 1) after the transformation D₂ о R180° is equal to (16, -1).
What is a rotation?A rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).
For a dilation with a scale factor of 2, we have:
Point A (-8, 1) → (-8 × 2, 1 × 2) = Point A' = (-16, 2)
By applying a rotation of 180° to the given point, the coordinates of its image is given by:
(x, y) → (-x, -y)
Points A' = (-16, 2) → Points A' = (-(-16), -(1)) = (16, -1).
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Complete Question:
What is the image point of (-8, 1) after the transformation D₂ о R180°?
What number should go in the empty boxes to complete the calculation for finding the product of
To do the multiplication, we multiply 0.63 by each of the digits & decimal places of 0.24 (and align the products that we get) then add them together.
0.63 x 4 = 2.52, therefore the first missing spot is a 2.
0.63 x 2 = 1.26, therefore the second missing spot is a 2 (the 0 is so that the decimal point can be aligned for the result.)
Answer: Box 1: 2 Box 2: 2
Step-by-step explanation:
So, for box one it would be 2 because 3 x 4 = 12, put the 2 on the bottom and the 1 on the 6, then 6 x 4 + 1 = 25, then put the 5 on the bottom and the 2 on the top, then 4 x 0 + 2 = 2, so the answer would be 2.
For box 2, 252 + 1?60 = 0.1512, so we have to find the missing number. So, 2 + 0 = 2, so put the two on the bottom, then 5 + 6 = 11, so put the 1 on the bottom and the other 1 on the 2 from the first box, so 2 + 1 = 3, plus 2 more would equal 5, so the second box would be 2.
Hope this helps!
ASAP!! Brainliest to first answer
3x - 2/3x = 14
Answer:
x = 6
Step-by-step explanation:
Given equation,
→ 3x - (2/3)x = 14
Now the value of x will be,
→ 3x - (2/3)x = 14
→ (9/3)x - (2/3)x = 14
→ ((9 - 2)/3)x = 14
→ (7/3)x = 14
→ 7x = 14 × 3
→ x = 42/7
→ [ x = 6 ]
Hence, the value of x is 6.
which of the following quantitative research methods uses a relatively small group of people for testing and is most helpful in obtaining data that are representative of the whole population? a.) in-depth interviews b.) secondary data analysis c.) natural experiments d.) random sampling
In-depth interviews are a quantitative research method that uses a relatively small group of people for testing and is most helpful in obtaining data representative of the whole population. The correct option to this question is A.
Although you can use all of these techniques in your comprehensive customer experience management strategy, in-depth interviews can help you gather the information that can give you rich insights into the experiences and preferences of a large sample of your target audience.
An extensive amount of data can be gathered on the behavior, attitude, and perspective of the interviewers through in-depth interviews, a qualitative data collection technique.
Researchers and subjects are free to explore additional topics and alter the course of the interview when necessary during in-depth interviews. It is an independent research methodology that can use a variety of approaches depending on the needs of the study.
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3-107. Find common denominators and calculate each of the following sums.
b. +3
What is the least common multiple of 8 and 4? Of 5 and 3?
T
d. Explain how finding the least common multiple of two numbers can help
you add fractions.
Answer:
LCM(8,4)=8.LCM(5,3)=15. LCM can be used to create equivilant fractions, meaning you can add fractions with much more efficiency.
Step-by-step explanation:
Four different linear functions are shown below. Drag the representation of each function in order from greatest y intercept ti least y intercept
Order of greatest y intercept to least y intercept,
1). A linear function has been given as,
y = [tex]\frac{1}{2}[/tex]x + 4
Y intercept = 4
2). The graph,
Y intercept = (2)
3). Graph represented by table
Y intercept = 1
4). A line passes through two points (-2, -3) and (4, 0)
Y intercept = -2
What is Y- intercept?
It is the total distance from the origin and the intersection of y axis and the formed line. It may be positive, negative or zero.
From the graph,
y-intercept = (2)
A line passes through two points (-2, -3) and (4, 0),
Slope of the line = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
= [tex]\frac{0-(-3)}{4-(-2)}[/tex]
= 1/2
Equation of a line passing through a point (x', y') and slope = m
y - y' = m(x - x')
If the point is (4, 0) and slope = 1/2
y - 0 = 1/2 ( x - 4 )
y = 1/2x - 2
y-intercept of this line = (-2)
A linear function has been given as,
y = [tex]\frac{1}{2}[/tex]x + 4
Comparing it with the slope intercept equation,
y = mx + b
b = y-intercept = 4
From the given table,
For x = 0, f(x) = 1
Therefore, y-intercept = 1
Order of greatest y intercept to least y intercept,
1). A linear function has been given as,
y = [tex]\frac{1}{2}[/tex]x + 4
Y intercept = 4
2). The graph,
Y intercept = (2)
3). Graph represented by table
Y intercept = 1
4). A line passes through two points (-2, -3) and (4, 0)
Y intercept = -2
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Find the measure of the exterior angle.
The measure of the exterior angle as shown in the triangle is 140°.
What is exterior angle?
Exterior angle is the angle between a side of a polygon and an extended adjacent side.
Exterior angle theorem: The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
From the diagram below, applying the theorem above,
k = 64+76k = 140°Hence, the exterior angle is 140°.
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A jar contains only pennies, nickels, dimes, and quarters. There are 26 pennies, 12 dimes, and 19 quarters. The rest of the coins are nickels. There are 70 coins in all. How many of the coins are not nickels? If n represents the number of nickels in the jar, what equation could you use to find n? of the coins are not nickels.
Answer:
57 coins are not nickels.
Equation: n + 57 = 70
Step-by-step explanation:
To find how many coins are not nickels, just add up the pennies, dimes, and quarters all together:
26 + 12 + 19 = 57 coins are not nickels.
The equation you could use to find n (nickels) would be:
n + 57 = 70
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What is the constant of variation, k of the direct variation, y=kx,through (5,8)
Constant of variation, k of the direct variation is 8/5.
Equation -> y = kx
Point (x,y) = (5,8)
Putting the value in the equation,
8 = 5k
k = 8/5
Hence, k = 8/5.
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