Answers
The value of (p² + 1/p²) and (p + 1/p)²is 18 and 20 respectively.
The above question is from algebra section and is from the topic surds and indices.
One of the standard formula is
(a - b)² = a² - 2ab +b²
(i) Here the expression is
p - 1/p = 4 and we need to find the value of p² + 1/p²
(p - 1/p)² = p² + 1/p² -2p(1/p)
4² = p² + 1/p² - 2
16 + 2 = p² + 1/p²
p² + 1/p² = 18
(ii) we need to find the value of (p + 1/p)²
(a + b)² - (a - b)² = 4ab
(p + 1/p)² - (p - 1/p)² = 4p(1/p)
(p + 1/p)² - 4² = 4
(p + 1/p)² = 4 + 16
(p + 1/p)² = 20
Therefore, the value of (p² + 1/p²) and (p + 1/p)² is 18 and 20 respectively.
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Related Questions
solve the following equation. express your answer as both an exact expression and a decimal approximation rounded to two decimal places. use e = 2.71828182845905.
Answers
SOLUTION:
Case: Exponential equations
Given:
[tex]e^{3x-8}=102^{5x+5}[/tex]Required: To solve for x
[tex]\begin{gathered} e^{3x-8}=102^{5x+5} \\ Take\text{ }natural\text{ }logarithm\text{ }of\text{ }both\text{ }sides \\ ln(e^{3x-8})=ln(102^{5x+5}) \\ (3x-8)lne^=(5x+5)ln(102) \\ 3x-8=(5x+5)4.624972 \\ 3x-8=23.12x+23.12 \\ Collecting\text{ }like\text{ }terms \\ -23.12-8=23.12x-3x \\ -31.12=20.12x \\ x=-\frac{31.12}{20.12} \\ x=-1.54658754284 \end{gathered}[/tex]Final answer:
Exact value
[tex]x=-1.54658754284[/tex]To 2 decimal places
[tex]x\approx-1.55[/tex]What is 13^c^11?
O A. 91
OB. 105
C. 78
D. 120
Answers
78
1) Since we have a Combination, we can write out the following formula:
[tex]_{13}C_{11}=\frac{13!}{11!(13-11)!}=\frac{13\times12\times11!}{11!\text{ 2!}}=\frac{13\times12}{2}=78[/tex]Note that we canceled 11! on the numerator by the factorial of 11! on the denominator. And notice this is only possible when the order does not matter.
2) Hence, the answer is 78 because there are 78 combinations of 13 choosing 11.
f(x) = 2x2 + 6x - 4 9(2) = 573 – 6x2 – 3 Find (f +9)(2). O A. (f +g)(x) = -523 + 8x2 + 6x – 1 O B. (f +9)(x) = 5x3 + 2x2 – 7 O C. (f+g)(x) =1723 – 7 O D. (f + g)(x) = 5x3 - 4x2 + 6x - 7
Answers
Answer:
The function (f+g)(x) is:
[tex](f+g)(x)=5x^3-4x^2+6x-7[/tex]Explanation:
Given the functions;
[tex]\begin{gathered} f(x)=2x^2+6x-4 \\ g(x)=5x^3-6x^2-3 \end{gathered}[/tex]We want to find the function (f+g)(x);
[tex]\begin{gathered} (f+g)(x)=f(x)+g(x) \\ (f+g)(x)=(2x^2+6x-4)+(5x^3-6x^2-3) \\ (f+g)(x)=5x^3+2x^2-6x^2+6x-4-3 \\ (f+g)(x)=5x^3-4x^2+6x-7 \end{gathered}[/tex]Therefore, the function (f+g)(x) is:
[tex](f+g)(x)=5x^3-4x^2+6x-7[/tex]I need help figuring out what angle these degrees are
Answers
1) Looking at the picture we can state that
m∠1 = 57º and m∠2 = 180-57
m∠2 = 123º
We can state that according to the Same side interior angles that states that those angles ∠1 , and ∠2 are supplementary since those angles belong to lines that have been crossed by a transversal line t.
Suppose Latoya borrows$4000.00 at an interest rate of 18% compounded each year.Assume that no payments are made on the loan.Find the amount owed at the end of 1 year.Find the amount owed at the end of 2 years.
Answers
Answer:
[tex]\begin{gathered} A=\text{ \$4,720 at the end of 1 year} \\ A=\text{ \$5,570 at the end of 2 year} \end{gathered}[/tex]Step-by-step explanation:
The compound interest is represented by the following equation:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ where, \\ P=\text{ principal borrowed} \\ r=\text{ rate} \\ n=\text{ number of times compounded per time ''t''} \\ t=\text{ time in years} \end{gathered}[/tex]Therefore, if Latoya borrows $4000 at an interest rate of 18% compounded each year;
[tex]\begin{gathered} A=4000(1+\frac{0.18}{1})^1 \\ A=\text{ \$4,720 at the end of 1 year} \end{gathered}[/tex]Now, at the end of 2 years:
[tex]\begin{gathered} A=4000(1+\frac{0.18}{2})^2 \\ A=\text{ \$5,569.6 at the end of 2 year} \end{gathered}[/tex]What’s the equation passing threw the points? And is parallel to the line 3x+y=3
Answers
The parallel line 3x + y =3, can be write on y-intercept form:
Solve for y the equation:
3x + y = 3
y = 3 -3x
Now, two lines are parallel when they have the same slope. In this case for line y= 3 -3x, the slope is the number with the x.
Therefore, the slope is -3.
Use the slope intercept-form using slope=m=3 and the point (1,-7):
[tex]y-y_1=m(x-x_1)[/tex]Replace these values and solve for y:
[tex]y-(-7)=-3(x-1)[/tex][tex]y+7=-3x+3[/tex]Solving for x:
[tex]y=3x+3-7[/tex]The equation that passes through the point (1,-7) and is parallel to the line3x + y =3 is :
[tex]y=-3x-4[/tex]What is the value of 24 - 5²?Record your answer and fill in thebubbles on your answer document.Be sure to use the correct placevalue.
Answers
24 - 5²
24 - 25 (Raising 5 to the power of 2)
-1 (Subtracting)
The answer is -1.
-12- (-35)
If 3m+5=27, then the value of m is
Answers
Answer:
m=7 1/3 in mixed number or 22/3 in improper fraction
Step-by-step explanation:
3m+5=27 is your equation
You will have to subtract 5 on both sides and you will be left with
3m=22
After that you will divide three on both sides
Therefore the answer is m=7 1/3 or 22/3
A customer wants to put in a concrete driveway that is 10″ thick. How much concrete would it take to pour a driveway that measures 18′ by 42′? Express your answer in cubic yards.
Answers
The volume of concrete it would it take to pour a driveway that measures 18′ by 42′ and 10″ thick is equal to 23.33 cubic yard.
What is a conversion factor?In Mathematics, a conversion factor simply refers to a number that is typically used to convert a number in one (1) set of units to another, either by multiplying or dividing.
Additionally, an appropriate conversion factor to an equal unit of value must be chosen and used when it is necessary to perform any mathematical conversion.
Note: The double quotation mark " is a notation that represent inches while the apostrophe mark ' represents foot.
Next, we would convert the unit in inches to feet:
1 inch = 0.0833333 feet.
10 inches = 10 × 0.0833333 = 0.833333 feet.
For the volume of concrete required, we have:
Volume of concrete = Length × Width × Thickness
Volume of concrete = 18 × 42 × 0.833333
Volume of concrete = 629.999748 cubic feet.
Also, we would convert cubic feet to cubic yard:
1 cubic feet = 0.037037 cubic yard
629.999748 cubic feet = x cubic yard
Cross-multiplying, we have:
Volume of concrete = 629.999748 × 0.037037
Volume of concrete = 23.33 cubic yard.
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A train leaves Little Rock, Arkansas, and travels north at 90 kilometers per
hour. Another train leaves at the same time and travels south at 60 kilometers
per hour. How long will it take before they are 300 kilometers apart?
Answers
Answer: 240 ft to be sure
Step-by-step explanation:
Determine whether each pair of polygons is similar. OPTIONSSimilar, sides are proportional and angles are corresponding Similar, sides are proportional and angles are congruent Not similar, sides are not proportional and angles are congruent Not similar, sides are proportional and angles are not congruent
Answers
From the figure it can be observed that angles of both figure are equal to 90 degrees. So angles are congurent of polygons are conurent to each other.
Determine the ratio of corresponding sides of two polygon.
[tex]\frac{3}{4}[/tex]And
[tex]\frac{6}{9}=\frac{2}{3}[/tex]As sides of the polygons are not proportional to each other. So figure are not similar.
Thus correct option is,
Not similar, sides are not proportional and angles are congruent .
She earns $12 per hour working at a store.
She earns $30 per lawn mowed working for a landscaper.
Her goal is to earn $1,800 to pay her monthly expenses.
The situation can be modeled by the formula below, where represents the hours Tina works in the grocery store and represents the number of lawns mowed.
Answers
Answer:
Change Mixed fraction to improper fraction 2/9
Use the transformations of the graph of f(x) = x^2 to determine the graph of the function. h(x) = -(x+2)^2
Answers
Answer:
Step-by-step explanation:
The graph f(x) = x^2 is shifted along the OX axis to the left by 2 and reflected relative to this axis:
Santino tried to find the median from the following table, which shows the number of internet users in 2012 20122012 for the highest using countries. However, he made a mistake. Country China United States Japan India Brazil Number of internet users (in millions) 568 568568 254 254254 101 101101 152 152152 100 100100 Here is Santino's work: "The numbers are 568 568568, 254 254254, 101 101101, 152 152152, and 100 100100. There are 5 55 values, so the middle value is the 3 rd 3 rd 3, start superscript, start text, r, d, end text, end superscript value, 101 101101. The median is 101 101101 million internet users." What mistake did Santino make?
Answers
The median of the data set is 152 . Santino made the mistake of not arranging the numbers in the set.
The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.
It could be referred to as "the middle" value for a data set. The fundamental difference between the mean and the median when describing data is that the median is more representative of the "normal" value because it is not skewed by a tiny fraction of exceptionally big or small values. Due to the fact that income distribution can be very skewed, the median income, for instance, might be a better indicator of what is considered a "normal" income. Given that it is the most resilient statistic, the median is crucial to strong statistics.the numbers of the data when arranged are :
100 ,101 , 152 ,254 ,568
Here n =5
Median =(n+1)/2 th data
or , median = 3rd data
or, median =152
Therefore Santino did not arrange the data in ascending order to find the median. the correct median is 152.
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Answer:
Santino should have ordered the numbers from least to greatest before picking the middle number.
Step-by-step explanation:
I need help with this Struggling It asks to answer (a) and (b) Put these separately ^ so I know which is which
Answers
We are given that:
[tex](3x^5-\frac{1}{9}y^3)^4[/tex]a) We know that binomial theorem in summation form
[tex](a+b)^n=\sum ^{r=n}_{r\mathop=0}\begin{bmatrix}{n} \\ {r}\end{bmatrix}a^{n-r}\cdot b^r[/tex]Using the formula and substitute
[tex]a=3x^5,b=-\frac{1}{9}y^3\text{ and n=4}[/tex]Therefore,
[tex](3x^5-\frac{1}{9}y^3)^4=\sum ^{r=4}_{r\mathop=0}\begin{bmatrix}{4} \\ {r}\end{bmatrix}(3x^5)^{4-r}\cdot(-\frac{1}{9}y^3)^r[/tex]Hence, the sum in summation notation that he uses to express the expansion is
[tex](3x^5-\frac{1}{9}y^3)^4=\sum ^{r=4}_{r\mathop{=}0}\begin{bmatrix}{4} \\ {r}\end{bmatrix}(3x^5)^{4-r}\cdot(-\frac{1}{9}y^3)^r[/tex]b) Let us now write the simplified terms of the expansion.
Therefore,
Using Combination formula to expand the expression above
The combination formula is,
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]Where,
[tex]n!\text{ = n(n-1)(n-2)}\ldots3.2.1[/tex]Hence,
[tex]\begin{gathered} =\frac{4!}{0!\left(4-0\right)!}\mleft(3x^5\mright)^4\mleft(-\frac{1}{9}y^3\mright)^0+\frac{4!}{1!\left(4-1\right)!}\mleft(3x^5\mright)^3\mleft(-\frac{1}{9}y^3\mright)^1+\frac{4!}{2!\left(4-2\right)!}\mleft(3x^5\mright)^2\mleft(-\frac{1}{9}y^3\mright)^2 \\ +\frac{4!}{3!\left(4-3\right)!}\mleft(3x^5\mright)^1\mleft(-\frac{1}{9}y^3\mright)^3+\frac{4!}{4!\left(4-4\right)!}\mleft(3x^5\mright)^0\mleft(-\frac{1}{9}y^3\mright)^4 \end{gathered}[/tex]Simplifying the above, we have
[tex]=81x^{20}-12x^{15}y^3+\frac{2x^{10}y^6}{3}-\frac{4x^5y^9}{243}+\frac{y^{12}}{6561}[/tex]Hence, the simplified terms of the expansion are
[tex]81x^{20}-12x^{15}y^3+\frac{2x^{10}y^6}{3}-\frac{4x^5y^9}{243}+\frac{y^{12}}{6561}[/tex]what fraction of a day is 45 minutes
Answers
To be able to determine what fraction of a day is 45 minutes, let's first determine how many minutes are there in a day.
1 day
convert each fraction to its equivalent using the least common denominator 3/7 , 3/4
Answers
The least common denominator of 3/7 and 3/4 is 7*4=28, therefore:
[tex]\begin{gathered} \frac{3}{7}=\frac{3\cdot4}{7\cdot4}=\frac{12}{28}, \\ \frac{3}{4}=\frac{3\cdot7}{4\cdot7}=\frac{21}{28}. \end{gathered}[/tex]Answer:
3/7, option e.
3/4, option c.
Yoshi has played in 6 basketball games so far this season. Her points in each game aredisplayed in the table below.GamePoints181234562420142224What is the median of Yoshi's points per game?O 21None of the other answers are correctO 221920
Answers
Let us revise how to find the median
At first you must arrange the numbers from small to big
Let us do that
14, 18, 20, 22, 24, 24
We have 6 numbers we need to find the middle one because the median means middle number in a set of data
But there are 6 numbers the middle numbers are 20 and 22
So the median will be the average of the two number
[tex]\text{Median}=\frac{20+22}{2}=\frac{42}{2}=21[/tex]There is a very important note for the median
If the number of data is even the median will be the average of the middle two numbers as our question, but if the number of data is odd then the median will be the middle number.
The answer is the first choice
Martina is driving on a highway. She uses one gallon of gas every 30 miles she drives. The distance, D (in miles), she travels on g gallons of gas is given
by the following function.
D (g) = 30g
How far does Martina drive if she uses 3 gallons of gas?
Answers
Answer:
90 miles
Step-by-step explanation:
First the formula is solving for distance in miles. and is says distance = 30 x gallons. So if it's asking for how far she drives with 3 gallons, it's asking for her distance driven when using 3 gallons of gas. So the formula would be D = 30g. D = 30 x 3 is the formula, we have to put in 3 for g. When we do 30 x 3 we would get our answer as 90. Therefore our final answer is 90 miles.
Hugo averages 41 words per minute on a typing test with a standard deviation of 7.5 words per minute. Suppose Hugo's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then, X∼N(41,7.5).
Suppose Hugo types 45 words per minute in a typing test on Wednesday. The z-score when x=45 is ________. This z-score tells you that x=45 is ________ standard deviations to the ________ (right/left) of the mean, ________.
Correctly fill in the blanks in the statement above.
Answers
At x = 30, the result is -1.57. According to this z score, x = 30 is 1.57 standard deviations away from the mean. 41 At x = 30, the result is -1.57. According to this z score, x = 30 is 1.57 standard deviations away from the mean.
What is the z score and standard deviation?
In essence, standard deviation represents the degree of variability present in a given data collection. To compute the standard deviation, first, get the distance between each data point and the mean. After that, the discrepancies are squared, added up, and averaged. The variance is caused by this. The variance's square root yields the standard deviation.The Z-score, in contrast, indicates how far a given data point deviates from the mean. The Z-score is adverse for data points that are below the mean. 99% of the values in most sizable data sets have a Z-score between -3 and 3, which denotes that they are within three standard deviations of the mean either above or below.Given, the Normal distribution with,
mu = 41
sigma = 7
The z-score formula is
z score = (X - mu) / sigma
So , z score at X = 30 is
z score = (X - mu) / sigma = (30 - 41) / 7 = -1.57
At x = 30, the result is -1.57. According to this z score, x = 30 is 1.57 standard deviations away from the mean. 41 At x = 30, the result is -1.57. According to this z score, x = 30 is 1.57 standard deviations away from the mean.
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1. Anna is saving up for a new laptop. She currently has 2x² - 2x dollars saved in her bank account. After working at her part-time job, she is able to deposit another 11x + 15 dollars. She finally has enough money to buy the laptop, and so she withdraws x²- 5x + 3 dollars. How much money does she have left in her bank account after buying her laptop? SHOW ALL WORK!
Answers
1) Gathering the data
Anna currently has 2x² -2x dollars
Then She adds: 11x +15 dollars
And withdraw x²-5x +3 dollars
2) Let's rewrite that
2x² -2x
+11x +15
---------------------
2x² +9x +15 - (x² -5x +3)
2x² +9x +15
-x² +5x -3
---------------------
x² +14x +12
That's the amount of money Anna has left for her laptop: x² +14x +12 dollars
Use the information to find and compare ∆y and dy (Round your answers to three decimal places.)
y=4x^3 x=2 ∆x=dx=0.1
Answers
The values of derivatives Δy and dy are given as 0.48 and 4.8
The values of Δy and dy will be calculated using the formula Δy = f(x + Δx) - f(x) and dy = f'(x)dx. For calculating the values, we put the values which are given in the question that is
Δy = f(x + Δx) - f(x)
Δy = f(2 + 0.1) - f(2)
Δy = f(2.01) - f(2)
Δy = 4(2.01)³ - 4(2)³
Δy = 32.48 - 32
Δy = 0.48
Now, we have f(x) = 4x³, so we have f'(x) = 12x²
Now, dy = f'(x)dx
dy = 12x²dx
dy = 12(2)²(0.1)
dy = 4.8
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Explain how to simplify ( (a*)") using the properties of exponents.
Answers
Simplifying ((a*)"),
In this type of expression, we apply the properties of exponents under Power Rules.
Under the power rule property of exponents,
[tex]((A^x)^y)=A^{x\text{ }\cdot\text{ y}}[/tex]This says that to raise a power to a power you need to multiply the exponents.
Let's apply this rule to simplify the given expression,
((a*)") = a*"
The radius of a circle is 11ft. Find its area in terms of pi
Answers
Answer: A≈380.13ft²
Step-by-step explanation:
(Laws of Exponents with Integer Exponents LC) Create an equivalent expression for 9−7 • 95.
Answers
The expression 9⁻⁷ • 9⁵ when simplified is 9⁻²
How to evaluate the expression?The expression is given as
9−7 • 95.
Rewrite properly
9⁻⁷ • 9⁵
The base of the above expression are the same
i.e. Base = 9
This means that we can apply the law of indices
When the law of indices is applied, we have the following equation:
9⁻⁷ • 9⁵ = 9⁻⁷ ⁺ ⁵
Evaluate the sum in the above equation
So, we have
9⁻⁷ • 9⁵ = 9⁻²
Hence, the simplified expression of the expression given as 9⁻⁷ • 9⁵ is 9⁻²
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Zak jogs from his house to a lake. He then jogs 5 laps around the lake at a constant speed. The table shows thetotal amount of time, in minutes, Zak has been jogging after completing x laps.Which equation represents the time, m, in minutes, Zak has been jogging after completing x laps?A m = 12x + 5B m = 5x + 12C m = 24x + 5D m = 5x + 24
Answers
We are given Zak's laps jogged along with the minutes elapsed.
If the equation of a line is:
m = kx + b
Where m is the number of minutes.
k is the slope of the line
x is the Laps
b is the y-intercept (or where the line crosses the y-axis)
In order to get the equation of the relationship between Laps (x) and Minutes (m),
we need to calculate the slope k and intercept b.
The formulas for doing these are given below:
[tex]\begin{gathered} m=\frac{\sum(x_i-X)(y_i-Y)}{(x_i-X)^2} \\ \text{where,} \\ x_i=\text{data points of Laps x} \\ X=\text{ Average of the Laps x} \\ y_i=\text{data points of Minutes m} \\ Y=\text{Average of Minutes m} \end{gathered}[/tex]The formula for intercept (b) is;
[tex]b=Y-kX[/tex]where Y and X are the averages of m and x values from the table.
[tex]\begin{gathered} Y=\frac{\sum m}{n}\text{ (n is the number of data values of Y)} \\ Y=\frac{17+41+65}{3} \\ \\ Y=41 \\ \\ X=\frac{\sum x}{n}\text{ (n is the number of data values of X)} \\ X=\frac{1+3+5}{3} \\ \\ X=3 \end{gathered}[/tex]In order to be tidy and quick, a table is used to solve.
This table is shown in the image below:
Therefore, we can now calculate slope (m):
[tex]\begin{gathered} m=\frac{\sum(x_i-X)(y_i-Y)}{(x_i-X)^2} \\ \\ m=\frac{\mleft(-24\mright)\mleft(-2\mright)+0\mleft(0\mright)+\mleft(24\mright)\mleft(2\mright)}{4+0+4} \\ m=\frac{96}{8} \\ \\ m=12 \end{gathered}[/tex]Now that we have slope (k) = 12, we can get the intercept b
[tex]\begin{gathered} b=Y-kX \\ Y=41-12(3) \\ Y=41-36 \\ Y=5 \end{gathered}[/tex]Therefore, the equation is:
m = 12x + 5
The display shows the data set from a survey about time spent on social media in a day. Vertical box plot titled average time spent on social media in a day, with minutes labeled on the vertical axis. The minimum is at 5, and the maximum is at 80. The lower quartile is at 30, the median is at 50, and the upper quartile is at 60. Which of the following describes the data set? Categorical and bivariate Categorical and univariate Numerical and bivariate Numerical and univariate
Answers
The data-set in this problem is classified as follows:
Numerical and univariate.
What are the classification of variables?The variables can be classified as categorical or numerical as follows:
Categorical: The possible values assumed by the variable are labels, such as yes/no, good/bad, and so on...Numerical: The values assumed by the variable are numbers.In the context of this problem, the minimum, the maximum and the quartiles of the variable all assume numeric values, hence the variable is classified as numerical.
From the text, the variable under study is the time spent on social media in a day, as a function of minutes. Since the output of the study is a single variable, the study is called univariate.
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Answer:
Numerical and univariate.
Step-by-step explanation:
Find the solution set of the inequality
\qquad5x + 13 \geq -37.5x+13≥−37.
5x + 13 ≥ -37
Answers
The solution set of the inequality 5x + 13 ≥ -37 is represented by x≥-10
and internal notation is [-10,∞).
Given the inequality equation is 5x + 13 ≥ -37.
Now solve the equation.
⇒ 5x + 13 ≥ -37
Arrange the constant terms on one side.
⇒ 5x ≥ -37 - 13
Subtract the terms.
⇒ 5x ≥ -50
Now solve for x.
⇒ x ≥ -50/5
⇒ x ≥ -10
Hence the solution set is x ≥ -10.
So, the internal notation is [-10,∞).
Therefore, the solution set of the inequality is x ≥ -10.
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What is the total volume of all four gum balls?
Answers
Kaitlyn wants to buy Nikes but only brought $156.50 with her to the store. If the Nikes cost $209, what percent discount would she need in order to be able to afford the Nikes? Round your answer to the nearest whole percent.
Answers
Kaitlyn's money =$156.50
Nike's cost = $209
We have to write an equation:
The cost of the Nikes (209) multiplied by the percentage(x) in decimal form (divided by 100) must be equal to the money available (209)
209 x = 156.50
x = 156.50/209
x= 0.75
0.75 x 100 =75%
1- 75 = 25%
Percent discount= 25%
