The factorized expression is (4/x³)(1/x² + 4).
The expression given to us is 4x^-5 + 16x^-3.We need to factorize the above expression.We need to use only the positive exponents.The number of times a number has been multiplied by itself is referred to as an exponent. There are four different sorts of exponents: positive, negative, zero, and rational/fractional. By interpreting the exponent as the total number of times the base number must be multiplied by the same base, one may determine the value of the number.We will use the laws of exponents.a^(-m) = 1/a^mWe can rewrite the expression as 4/x^5 + 16/x³.Now take out the common from the two terms.The expression becomes (4/x³)(1/x² + 4).Thus, we have successfully factorized the expression using only the positive exponents.To learn more about exponents, visit :
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Two yachts are 39 miles apart. As they travel towards each other, they pass each other after 20 minutes . Given one yacht travels 6 miles per hour faster than the other, find the speeds of both yachts.
Answer:
See below
Step-by-step explanation:
20 minutes = 1/3 hr
distance / rate = time
x = rate1 x+6 = rate2
39 mi / ( x + x+6 m/hr ) = 1/3 hr
39/(1/3) = 2 x + 6
x = 55.5 mi/hr x+6 = 61.5 mi/hr
please help me!!!!!!
Cube rolled = 50 times
1 or 2 came up = 19 times
In percentage, that is >>>
[tex]\begin{gathered} \frac{19}{50}=0.38 \\ 0.38\times100=38\% \end{gathered}[/tex]So, 1 or 2 occured 38% of the times where it should occur around 20% of the times.
Looking at the answer choice, third option (C) is right.
(7m - 2) (9m — 5)
(6n-1)
Answer:
Step-by-step explanation:
(7m - 2) the two would instantly become a negative so the answer would be 7m + -2.
same goes for (9m - 5) the five will become a negative and the answer would be 9m + -5.
Same also goes for (6n - 1) the one would become a negative so the answer would be 6n + -1. Your welcome!!!!!!!!!
Lexi is jogging from the library back to her home. The function y = -x + 8 shows Lexi's distance from home, where y is distance in miles and x is time in
minutes. Which statement is true of the graph of the function?
10
A. As the value of x increases, the value of y increases.
B. As the value of x decreases, the value of y stays the same.
C. As the value of x increases, the value of y decreases.
D. As the value of x decreases, the value of y decreases.
please help me with this question
Answer: 4x^2 + 2x + 3
Step-by-step explanation: long division method :)
Which of the following is a solution of x2 + 5x = −2?
5 plus or minus the square root of 33 divided by two
5 plus or minus the square root of 17 divided by two
negative 5 plus or minus the square root of 33 divided by two
negative 5 plus or minus the square root of 17 divided by two
A possible solution for the equation is -5 ± √17/2.
What is a quadratic equation?The term quadratic equation is a term that cold be used to be able to describe a polynomial of degree 2. A polynomial of degree 2 is one in which the highest power of the algebraic terms present in the equation is 2.
We can rewrite the equation as;
x^2 + 5x + 2 = 0
Now what we need to do is to solve the quadratic equation and obtain its value.
By solving the quadratic equation as it have been shown in the question above, e can see that one of the solutions of the equation is; negative 5 plus or minus the square root of 17 divided by two.
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If the data in a histogram is roughly symmetrical, what does that tell us about the mean and median?
To answer this question, first we need to properly understand the definition of median and mean, and also understand what it means to be "roughly symmetrical".
Let's start with the definition of median.
"the median is the value separating the higher half from the lower half of a data sample"
If we have an odd amount of elements in our dataset, the median is literally the middle element of our set.
Example:
[tex]\lbrace1,1,1,2,3,4,7,10,52\rbrace[/tex]We have four elements below 3, and four elements above 3, therefore, the median of this dataset is 3.
If we have an even amount of elements, the median is the mean between the two elements in the middle.
Example:
[tex]\lbrace1,1,1,1,2,2,7,15\rbrace[/tex]The elements in the middle are 1 and 2. This means our median is
[tex]\frac{1+2}{2}=1.5[/tex]1.5.
Now, let's understand the mean.
By definition, The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers, given by the sum of all elements divided by the amount of elements.
Examples:
[tex]\begin{gathered} \lbrace1,2,3\rbrace \\ \bar{x}=\frac{1+2+3}{3}=2 \\ \lbrace1,1,3,5,7,9,9\rbrace \\ \bar{x}=\frac{1+1+3+5+7+9+9}{7}=5 \end{gathered}[/tex]Now that we know what mean and median exactly are, let's try to understand what it means to be "roughly symmetrical".
When talking about histograms, Close to symmetric means the data are roughly the same in height and location on either side of the center of the histogram.
As the histogram gets closer to symmetric, the mean approaches the middle values, to be more specific, If the histogram is close to symmetric, then the mean and median are close to each other.
Since the statement says "roughly symmetrical" this is the only thing we can claim. If we have more values to the right in our roughly symmetrical distribution, the mean will be a little bit bigger than then median, and if we have more values to the left in our roughly symmetrical distribution, the mean will be a little bit smaller than then median.
If a die is rolled three times, what is the probability of
getting a 2 on the first roll, an odd number on the second
roll, and a number less than 5 on the third roll?
Answer:
probability of getting 2 = 1/6
probability of getting an odd number=3/6=1/2
probability of getting number less than 5 = 4/6=2/3
multiply probabilities:
1/6x1/2x2/3
=2/36
=1/18
5. Which function does NOT have a range of all real numbers?
a. f(x) = 3x
b. f(x) = -0.5x + 2
c. f(x) = 8 - 4x 8
d. f(x) = 3
jesse earns $6 an hour babysitting for his younger brother. his mom gave him $20 for an allowance. how many hours would jesse have to babysit to earn enoug money to buy a $80 football ticket?
Answer:
Step-by-step explanation:
10 hours. 80-20 is 60, which means he needs 60 more dollars. he makes 6 an hour, and 6x10 equals 60(what he needs) and that is your answer.
Joanna has a big paper due. yesterday, she started typing her hand-written draft. she typed 862 words of it and saved her work to continue later. if she types at a rate of 70 words per minute, and the paper is 1,562 words long, how much more time does she have to spend typing? a. 10 minutes b. 15 minutes c. 18 minutes
Answer:
10 minutes
Step-by-step explanation:
if 70 words = 1minute
862 words will be 862÷70=12.31 minutes
1,562 words will be 1562÷70=22.31 minutes
time needed to finish will be 22.31-12.31= 10 minutes
So the total time needed to finish will be 10 minutes
interior and exterior triangle angles
Answer:
∠ GHI = 17°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ HIJ is an exterior angle of the triangle , then
∠ HJI = ∠ GHI + ∠ IGH , that is
7x - 18 = 2x - 3 + 2x + 15
7x - 18 = 4x + 12 ( subtract 4x from both sides )
3x - 18 = 12 ( add 18 to both sides )
3x = 30 ( divide both sides by 3 )
x = 10
Then
∠ GHI = 2x - 3 = 2(10) - 3 = 20 - 3 = 17°
Tavon has a gift card for $150 that loses $3.50 for each 30-day period it is not used. He has another gift card for $130 that loses 3 for each 30-day period it is not used. a. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal. b. What will the value of each card be when they have equal value?
Part a
[tex]150-3.50x=130-3x\\\\20=0.50x\\\\x=40[/tex]
After fourty 30-day periods, the balances on the cards will be equal.Part b
[tex]150-3.50(40)=10[/tex]
$10Which equation exemplifies the Associative Property of Multiplication?
O4×(2x5)= (2x5)×4
O4x(2x5)=4x(5x2)
O4x(2x5)= (4x2)x5
O4x2x5=5x2x4
19
Step-by-step explanation:
35*44
5555
75*69
*1235
A theater has 22 rows of seats. the first row has 27 seats and each row has 3 seats more than the previous one. how many seats are in the theater total?
The number of total seats in the theater is 1287 seats.
How to calculate the value?The formula to find the sum in an arithmetic sequence will be:
= n/2 (a + l)
where n = total number
a = first term
l = last term
The last term which is the 22nd term will be:
= a + 21d
= 27 + 21(3)
= 27 + 63
= 90
The sum will be:
= n/2 (a + l)
= 22/2 ( 27 + 90)
= 11 × 117
= 1287 seats
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In which set(s) of numbers would you find the number-202/45Natural numberIntegerWhole numberReal numberIrrational number
Natural number: No, because when you divide -202/45 you do not get a integer.
Integer: No, for the reason given before.
Whole number: No, for the reason given before (it is not an integer)
Real number: Yes, because real numbers include negative fractions.
Irrational number: No, because you can write the number as a fraction of two integers.
You would find the number -202/45 in the set of the real numbers.
7y - 14 factor please
Answer:
7(y - 2)
Step-by-step explanation:
7y - 14 ← factor out 7 from each term
= 7(y - 2)
Answer:
7(y -2)
Step-by-step explanation:
Factorize:
Find the GCF.
7y= 7 * y
14 = 7 * 2
GCF = 7
7y - 14 = 7*y - 7*2
= 7*(y - 2)
Find upper and lower fences (SHOW ALL WORK and formulas used) Upper fence:________Lower fence:________
The upper fence and the lower fence are known as the upper limits and lower limits respectively. The upper fence and lower fence can be computed below
[tex]\begin{gathered} Q1=11 \\ Q3=15 \\ Interquartile\text{ range = 15-11=4} \\ \text{Lower fence=}Q1-1.5(4)=11-6=5 \\ \text{upper fence=}Q3+1.5(4)=15+6=21 \end{gathered}[/tex]You made a decision that you are doing to take care of the animals for the Claus family so they can go to a
warmer climate for their vacation this year. They will be on vacation the months of January and February. You will
be in North Pole, Alaska caring for their Reindeer, dogs, and hanging out with some of the Elves that take care of
things.
The weather for January 2022 and February 2022 are files found with the TGA.
Find the change in temperature (from the high and low) for the first day and last day of each month. How would
you have to pack for this trip?
(5 points)
2. What was the hardest part for you? Explain why.
By considering the climate of the North Pole, Alaska, the change in the Temperature, is 13°F and 14 °F on the 1st and last day of the month respectively.
Alaska experiences an average low temperature of 9°F (-13°C) and an average high temperature of 22°F (-5°C) in January. You should be able to see the little sun that is shining (just for 5 to 6 hours per day on average) since it is clear for roughly 60% of the days.
Alaska's typical February temperature ranges from a low of 12°F (-11°C) to a high of 26°F (-3°C). There is a little bit more cloud cover (approximately 50% of days) and roughly 8 hours of sunlight per day, which both contribute to this rise in temperatures.
Change in Temperature:
On 1st day of January , the Change in temperature = Highest Temperature - lowest temperature = 22°F - 9°F = 13°F
On the 1st day of February, and the last day of January, the Change in temperature = Highest Temperature - lowest temperature = 26°F - 12°F = 14 °F.
Claus needs to pack a lot for the vacation, as it is at the North Pole, Alaska, Considering the climate of the North Pole. She has to pack a lot winter clothes, lots of animal food, and sanitary.
The hardest part will take care of the animals, The majority of animals only require a warm, secure, and protected area to live in addition to enough food, drink, and exercise. Animals require care and attention to stay safe, happy, and healthy. They require wholesome food, pure water, and a cozy place to sleep. The majority of animals need frequent exercise to keep healthy.
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6 cups to 4 cups in simplest form
Answer:
3 cups to 2 cups
Step-by-step explanation:
6 divided by 2 = 3
4 divided by 2 = 2
and that equals 3 to 2 cups
help with this question
Answer:
a. x + 4
b. (x + 6)(x + 4) = x^2 + 10x + 24, so a = 10 and b = 24.
Deirdre is a member of a very small but high-class organization called Algebra Lovers Anonymous. She paid $10 in dues for each of her first 3 years as a member and $2 in dues each year after that. If Deirdre has paid a total of $38 in dues, for how many years has she paid $2 in dues?
For 4 years, Deirdre paid $2 in dues.
Deirdre paid each year for three years = 3 × 10 = 30.
Let's consider x as the number of years,
As Deirdre paid $2 for x years the value she paid will be 2x,
Deirdre paid = $2x (in x years)
Deirdre has paid $10 for three years each, a total of $38 in dues. So the final equation will be,
38 = 30 + 2x
38 - 30 = 2x
8 = 2x
x = 4
Thus, Deirdre has paid $2 in dues for 4 years.
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the largest of the following integers which divides each of the numbers of the sequence $1^5 - 1,\, 2^5 - 2,\, 3^5 - 3,\, \cdots, n^5 - n, \cdots$ is:
The sequence's numbers are all multiples of 30. Every number can be divided by 30.
If two integers are divided equally, leaving no remainder, then we say that one integer divides the other (we sometimes say, "with no remainder," but that is not technically correct). Mathematicians express this more explicitly as follows: If a and b are integers (with a not zero), then a divides b if c is an integer such that b = ac. Sequence: 1 51, 2 52,....., n 5n,....n 5n=n(n 4 1)=n(n1)(n1)(n+1)(n 2 +1)
At n=1, n 5, n=0, n=1, 2, 3, etc. Not attainable
Atn=2,n 5 −n=30 ∴ The sequence's numbers are all multiples of 30. Every number can be divided by 30.
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Find the exact value and the approximate value of the perimeter of the triangle
the perimeter of triangle is equal to the sum of all the side of the triangle,
The perimeter of given triangle is x+y+9+3
Solve for x and y,
Apply pythagoras theorem in triangle ADC,
[tex]\begin{gathered} AC^2=DC^2+AD^2 \\ y^2=81+AD^2^{} \\ AD^2=y^2-81 \end{gathered}[/tex]Now, in triangle ADB
Apply pythagoras,
[tex]\begin{gathered} AB^2^{}=BD^2+AD^2 \\ x^2=9+AD^2 \\ AD^2=x^2-9 \end{gathered}[/tex]Compare the value of AD from both the equation,
[tex]\begin{gathered} x^2-9=y^2-81 \\ x^2-y^2=-72 \end{gathered}[/tex]Now, in triangle ABC
[tex]\begin{gathered} BC^2=AB^2+AC^2 \\ 12^2=x^2+y^2 \\ x^2+y^2=144 \end{gathered}[/tex]Add the equation
[tex]\begin{gathered} x^2+x^2-y^2+y^2=-72+144 \\ 2x^2=72 \\ x^2=36 \\ x=6 \end{gathered}[/tex]Substitute x=6 in the above equation,
[tex]\begin{gathered} x^2_{}+y^2=144 \\ 36+y^2=144 \\ y^2=144-36 \\ y^2=108 \\ y=10.39 \end{gathered}[/tex]So, the value of the other side of triangle are 6, 10.39
Perimeter of triangle =sum of all sides of triangle
[tex]\begin{gathered} \text{Perimeter}=AB+BC+AC \\ \text{Perimeter}=AB+BD+CD+AC \\ \text{Perimeter}=6+3+9+10.39_{} \\ \text{Perimeter}=28.39 \end{gathered}[/tex]ANSWER : Perimeter is 28.39
How to find the size of angle x in a triangle
Answer:
it depends on the question
Usually if it a triangle with 2 angles and an x
you will add the 2 angles and rearrange to give the answer
Step-by-step explanation:
Hope this helps!!!
Answer:
A right triangle has one angle measuring 90 degrees. The side opposite this angle is known as the hypotenuse (another name for the longest side). The length of the hypotenuse can be discovered using Pythagoras's theorem, but to discover the other two sides, sine and cosine must be used. These are trigonometric functions of an angle.
In the diagram below, one of the angles is represented by the Greek letter θ. (pronounced "the - ta"). Side a is known as the "opposite" side and side b is called the "adjacent" side because of their positions relative to the angle θ.
The vertical lines "||" around the words below mean "length of."
So sine, cosine and tangent are defined as follows:
Step-by-step explanation:
So sine, cosine and tangent are defined as follows:
sine θ = |opposite side| / |hypotenuse|
cosine θ = |adjacent side| / |hypotenuse|
Find the value of (3 -1 × 4 -1 ) ÷ 2 -2 .
Answer: -3
Step-by-step explanation:
[tex](3-1*4-1) \div 2-2=\\\\(3-4-1)\div2-2=\\\\(-2)\div2-2=\\\\-1-2=\\\\-3[/tex]
5. Rachel typed 48 words in 3/4 minute. What is her typing speed in words per minute?
Please help! Please and thank you
Answer:
4
Step-by-step explanation:
Length time width times high , 8x8=16 square rooted equals 4
john is a quarterback. this year, he completed 350350350 passes, which is 70\pp, percent of all the passes he's attempted this year. how many passes has john attempted this year? passes
The number of passes that john has attempted this year is 500500500 passes
To solve this exercise the percentage formula and the procedure to be applied is as follows:
n= (% * nt) / 100
Where
% = percentagen= number portionnt = total of the number portionInformation about the problem:
% = 70%n = 350350350 passesnt =?Using the percentage formulate and isolating the total of the number portion (nt), we get:
n= (% * nt) / 100
nt = (n*100) / %
nt = (350350350* 100) / 70
nt = 500500500
What is a percentage?Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.
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After receiving her paycheck Karen lends her sister $21 buys groceries for $71 and pays her $85 gym membership if she is now left with $73 how much was her paycheck
After using Arithmetic we'll get - Total of her paycheck $250
What is Arithmetic ?
The study of the characteristics of the standard operations on numbers, including addition, subtraction, multiplication, division, exponentiation, and root extraction, constitutes the fundamental subject of arithmetic. Giuseppe Peano, an Italian mathematician, formalised arithmetic in the 19th century with the help of his Peano axioms, which are still crucial to the modern study of mathematical logic. There are only a few artefacts from the early history of mathematics that may have shown how addition and subtraction were first thought of. The best-known of them is the disputedly interpreted Ishango bone from central Africa, which dates from between 20,000 and 18,000 BC.
The Amount Karen spent:
She lends sister = $21
Buys Groceries = $71
Pays Gym membership = $85
After spending this much she left with $73
The paycheck she receive = 21 + 71 + 85 + 73
= $250
Hence , her paycheck was $250
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