Susie is correct as it is not a right triangle
How to prove the nature of the triangle?According to Pythagoras theorem, In a right triangle ,the square of the hypotenuse side in a right-angled triangle equals the sum of the squares of the other two sides.Here let the hypotenuse side = 17 (longest )
Square of the hypotenuse side = 289
Squares of the other two sides = 12 * 12 = 144
=9 * 9 = 81
Sum of the squares of the other two sides = 144 + 81
= 225
So, here 225 ≠ 289
The square of the hypotenuse side of this triangle does not equal the sum of the squares of the other two sides. So this is not a right triangleThus, Susie is correct as it is not a right triangle.To learn more about Pythagoras theorem, refer:
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(A TEST I NEED IT ASAP)
1. Use each digit from 1 to 5 once to make the following equation true. ■ − ■ ■/■ = 3 ■/6
2. The sum of three mixed numbers is 8 2/5. The difference between the first number and second number is 1. The difference between the first number and third number is 2. What is the least number?
3. Tori plays the tuba. She plays for 4 1/2 measures, rests for 8 3/8 measures, plays for another 16 measures, rests for 2 1/4 measures, and plays for the rest of a 36-measure song. How long was the last section that she played?
Answer:
2
Step-by-step explanation:
-x+y≤-1
x + 2y ≥ 4
Graph the system of inequalities.
Answer:
Step-by-step explanation:
[tex]-x+y\leq -1\\x-y\geq 1\\x+2y\geq 4[/tex]
dark blue is the required region.
The function f(x)=9.25x + 3 represents the amount radda earns dog walking for X hours
Since the function f(x) = 9.25x + 3 represents the amount of money that Radda earns dog walking for x hours, Radda's earnings would increase by $12.25 each hour.
How to write a linear function for the total amount of money Radda earns?In Mathematics, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be used to model (represent) the total amount of money that is being earned by Radda for dog walking;
T = mx + b
Where:
T represents the total amount of money earned.m represents the rate of change (slope) per hour.x represents the number of hours or time.b represents the y-intercept or initial amount.Therefore, the required linear function that represents the total amount of money that is being earned by Radda for dog walking per hour is given by this mathematical expression;
f(x) = T = 9.25x + 3
When the number of hours Radda spend dog walking is equal to 1 (x = 1), the rate of change(slope) can be calculated as follows;
f(1) = T = 9.25(1) + 3
f(1) = T = 9.25 + 3
f(1) = T = $12.25.
In this context, we can reasonably infer and logically conclude that Radda's earnings increases each hour by $12.25.
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Complete Question:
The function f(x) = 9.25x + 3 represents the amount Radda earns dog walking for x hours. How much does Radda's earnings increase each hour?
Cone W has a radius of 6 cm and a height of 5 cm. Square pyramid X has the same base area and height as cone W.
Paul and Manuel disagree on the reason why the volumes of cone W and square pyramid X are related. Examine their arguments. Which statement explains whose argument is correct and why?
Manuel's argument is correct on why the volume of cone W and square pyramid are related . Paul used the incorrect base area to find the volume of square pyramid X. Then the correct option is C.
Define cone and square pyramid
A thick or empty device with an approximately round or elliptical base that tapers to a notch is known as a cone.
on the other hand ,
A three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called vertex) is called a square pyramid.
CalculationCone W has a radius of 6 cm and a height of 5 cm.
The base area of the cone will be
A = πr²
A = π (6)²
A = 113.04 square cm
Then the volume of the cone will be
V = (1/3) x base area x height
V = (1/3) x 113.04 x 5
V = 188.4 cubic cm
Square pyramid X has the same base area and height as cone W.
Then the volume of the square pyramid will be
V = (1/3) x base area x height
V = (1/3) x 113.04 x 5
V = 188.4 cubic cm.
Manuel's argument is correct on why the volume of cone W and square pyramid are related . Paul used the incorrect base area to find the volume of square pyramid X. Then the correct option is C.
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a 9 foot ladder is leaning against a wall. if the top of the ladder is sliding down the wall at a rate of
The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.
The well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^{2}+b^{2} =c^{2}[/tex]
Given that,
Length of the ladder is, [tex]l=9ft[/tex]
Let the top of ladder be at height of 'h' and the bottom of the ladder be at a distance of 'b' from the wall.
Now, from triangle ABC,
[tex]AB^{2} +BC^{2} =AC^{2}[/tex]
[tex]h^{2} +b^{2} =l^{2}[/tex]
[tex]h^{2} +b^{2}[/tex] = [tex]9^{2}[/tex]
[tex]h^{2} +b^{2}[/tex] = 81 (Equation-1)
Differentiating the above equation with respect to time, 't'.
So,
We can write,
[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = [tex]\frac{d}{dt}[/tex] (81)
[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = 0
[tex]2h\frac{dh}{dt} +2b\frac{db}{dt}[/tex] = 0
[tex]h\frac{dh}{dt} +b\frac{db}{dt}[/tex] = 0 (Equation-2)
In the above equation the term [tex]\frac{dh}{dt}[/tex] is the rate at which top of ladder slides down and [tex]\frac{db}{dt}[/tex] is the rate at which bottom of ladder slides away.
Let us assume,
h = 3 ft and db/dt = 3 ft/s
We can substitute values in equation-1,
[tex]3^{2} +b^{2}[/tex] = 81
9 + [tex]b^{2}[/tex] = 81
[tex]b^{2}[/tex] = 81-9
[tex]b^{2}[/tex] = 72
b = [tex]\sqrt{72}[/tex]
b = 8.48 ft
Now, plug in all the given values in equation (2) and solve for [tex]\frac{dh}{dt}[/tex]
3*[tex]\frac{dh}{dt}[/tex] + 8.48 * 3 = 0
3*[tex]\frac{dh}{dt}[/tex] + 25.44 = 0
3*[tex]\frac{dh}{dt}[/tex] = - 25.44
[tex]\frac{dh}{dt}[/tex] = -25.44/3
[tex]\frac{dh}{dt}[/tex] = - 8.48 ft/s
Therefore,
The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.
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8x + 2 = 26
can someone please help?..
Answer:
x = 3
Step-by-step explanation:
8x + 2 = 26
8x = 26 - 2
8x = 24
x = 24/8
x = 3
Check:
8*3 + 2 = 26
24 + 2 = 26
(Score for Question 1: of 3 points)
1. Represent each situation with an inequality.
(a) The sum of a number and 12 is at most -8.
(b) A number increased by -8 is greater than 12.
(c) -8 less than a number is no more than 12.
Answer:
Inequality for each part be
a) x + 12 ≤ -8
b) x - 8 > 12
c) x + 8 < 12
What do you mean by inequality?
In mathematics, an inequality is a relationship in which two numbers or other mathematical expressions compare unequal. Most commonly used to compare two numbers on the number line based on size.
The notation a < b means that a is less than b.
The notation a > b means that a is greater than b.
Let the number be x
According to the question:
a) The sum of a number and 12 is at most -8.
inequality become:
x + 12 ≤ -8
b) A number increased by -8 is greater than 12
inequality become:
x + (-8) > 12
⇒ x - 8 > 12
c) -8 less than a number is no more than 12
x - (-8) < 12
⇒ x + 8 < 12
Therefore, inequality for each part be
a) x + 12 ≤ -8
b) x - 8 > 12
c) x + 8 < 12
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If 24000 bricks of the same shape and size are required to build a wall of dimension 15m*6m*20m find the volume of each brick
The volume of each brick is 0.75m³
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object. It is measured in cubic units.
A brick has a cuboidal shape. This means the volume of a cuboid is given as:
V = l×b×h
This means volume = area × height
The volume of the whole wall is calculated as:
15× 6× 20 = 18000m³
Since there are 24000 bricks needed for the wall. The volume of each brick is therefore calculated as:
V =18000/24000
= 0.75m³
Therefore the volume of each brick is 0.75m³
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A random sample of 75 students at the University of Minnesota spend an average of $614 per month in rent
with a standard deviation of $219. The distribution is moderately skewed to the high end. Which of the
following statements are true?
i. 95% of students at the university spend $564 to $664 on rent.
ii. We are 95% confident that the average rent for students at the university is between $564 and $664.
iii. Because we cannot examine other characteristics of the students in the random sample, it is not
advisable to construct a confidence interval.
Oi only
O ii only
O iii only
Oi and ii
Oi, ii, and iii
Check Answer
The correct option is b) ii only
From the given data we can construct confidence interval. So, the statement that we are 95% confident that the average rent for students at the university is between $ 564 and $664 is true.
What is meant by distribution?
The methodical effort to account for how the owners of the labor, capital, and land inputs divide the country's income. Rent, wages, and profit margins have historically been the focus of economists' research into how these expenses and margins are set.
What are the 3 types of distribution?
The Three Types of Distribution
Intensive Distribution: As many outlets as possible. The goal of intensive distribution is to penetrate as much of the market as possible.Selective Distribution: Select outlets in specific locations. ...Exclusive Distribution: Limited outlets.What are the 5 factors of distribution?
Market, Product, Company, Channel, and Environment Related Factors are 5 Important Factors Affecting Distribution Channel Selection. The distribution of goods can be done through a variety of routes.
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Help with this plsssss !!!
Answer:
58
Step-by-step explanation:
There are 5 lines between 50 and 60
60 - 50 = 10
10 / 5 = 2
This means that each increment is 2.
We see the end of the box plot is above the fourth increment above 50.
4 x 2 = 8
50 + 8 = 58
what number is 16 2/3% more than 240
280 is the number which is 16 2/3% more than 240
What is the percentage?
It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We would receive 16 times 3 plus 2 if we converted 16 2/3 to an improper fraction. Then, we would divide this number by 3, getting 50/3, which is equal to 50/3 divided by 100, or 1/6.
(1/6) th of 240 = 240/6 = 40
40 more than 240 = 280
So, 280 is the number which is 16 2/3% more than 240
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Marco has $16.72. He spends $9.21 on a movie ticket. How much money does Marco have left?
Responses
A $7.68$7.68
B $7.51$7.51
C $7.48$7.48
D $7.61
Answer:
7.51
Step-by-step explanation:
16.72 - 9.21
Please Help!!!
Marshall wants to buy a car in five years worth $20,000. He finds a savings account with a simple interest rate of 4%. How much money must he put in the account now so he has $20,000 to buy the car in five years (round to the nearest dollar). SHOW ALL WORK
The amount of money he must put in the account is $16666.66
What is meant by interest rate?A portion of the total loan amount that the borrower is required to pay the lender as interest over a predetermined timeframe.
This year, the Bank of Canada quickly increased its policy rate, taking it from 0.25% in March 2022 to 4.25% in December 2022, and in the process, driving up mortgage and prime rates. An interest rate is the portion of a loan, deposit, or borrowing that must be paid in interest each period. The total amount of interest charged depends on the amount lent or borrowed, the interest rate, the frequency of compounding, and the length of time it was lent, deposited, or borrowed.
Given,
r=4%
T=5 years
Total amount=SI+P
=20000
SI+P=20000
SI=20000-P
SI=PTR/100
20000-P=(P×5×4)/100
2000000-100P=20P
120P=2000000
P=16666.66
Therefore, The amount of money he must put in the account is $16666.66.
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An aircraft is flying at altitude H when it begins its descent to an airport runway that is at a horizontal ground distance L from the airplane. Assume that the landing path is described by the cubic polynomial function y=ax3+bx2+cx+d where y(-L)= H and y(0)= 0.a. What is dy\dx at x= 0?b. What is dy\dx at x= -L?
a. [tex]\frac{dy}{dx} \ at \ x=0 \ is \ c.[/tex]
b. [tex]\frac{dy}{dx} \at x=-L \ is \ 3aL^2+2bL+c.[/tex]
a. The derivative of a cubic function
[tex]y=ax^3+bx^2+cx+d[/tex] is [tex]y'=3ax^2+2bx+c[/tex].
Plugging in x=0, we get y'=c. Thus, [tex]\frac{dy}{dx}[/tex] at x=0 is c.
b. Plugging in x=-L, we get [tex]y'=3a(-L)^2+2b(-L)+c[/tex].
Thus, [tex]\frac{dy}{dx}[/tex] at [tex]x=-L \ is\ 3a(-L)^2+2b(-L)+c.[/tex]
A derivative is a financial instrument that derives its value from an underlying asset. It is a contract between two or more parties that specifies conditions (such as the date, price, and quantity of the underlying asset) under which payments, or payoffs, are to be made between the parties. Derivatives can be used for a variety of purposes, such as hedging risk or speculating on the future price of an asset.
A function is a mathematical relation between two sets of numbers that assigns each element in one set to exactly one element in the other set. For example, the function f(x) = 2x+3 assigns each real number x to the real number 2x+3
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Helpp!! GIVING BRAINIEST
The value of the c in the function c = 19m - 15 when m=10 is 175.
What is a function?A relationship between a number of inputs and outputs is termed a function. In a function, which is an association of inputs, each input is associated to exactly one output. Each function has a domain, range, and co-domain.
Given the function;
c = 19m - 15,
where m represents the number of months and c represents the total number of car sent to New York.
To find the value of c:
when m = 10,
Substitute the value of m to the function;
c = 19 (10) - 15
c = 190 - 15
c = 175.
Therefore, the value of c is 175.
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Polly borrowed $285 for a new floor lamp. She will make 5 monthly payments of $62 to repay the loan. How much will she pay in interest?
Interest is the price you pay to borrow money or the cost you charge to lend money.
How do you calculate interest on a loan?Divide your interest rate by the number of payments you'll make that year. If you have a 6 percent interest rate and you make monthly payments, you would divide 0.06 by 12 to get 0.005. Multiply that number by your remaining loan balance to find out how much you'll pay in interest that month.If the payment plan is $62 per month for 5 months, then the whole payment will be: $310To calculate simple interest on a loan, take the principal (P) times the interest rate (R) times the loan term in years (T), then divide the total by 100. To use this formula, make sure you're expressing your interest rate as a percentage, not a decimal (i.e., a rate of 4% would go into the formula as 4, not 0.04).So, $10$ percent per annum means that $10$ percent interest will be charged yearly or annually over a principal amount or a loan. Note: If the rate of interest is $10$ percent per annum, then the interest calculated will be $10$ percent of the principal amount.To find the difference of 310 and 285, subtract 310 from 285. This will give you the added interest cost.
310-285 = 25
So, Polly will pay $25 in interest.
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Given h(x)=-5x-4 find h(3)
The value of the equation h(x) = -5x-4 is - 19 when h = (3).
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
The three primary forms of linear equations are point-slope, standard, and slope-intercept.
So, the equation we have is:
h(x) = -5x-4
Now, solve the equation when h = (3)
h(x) = -5x-4
h(3) = -5(3) -4
h(3) = -15 - 4
h(3) = - 19
Therefore, the value of the equation h(x) = -5x-4 is - 19 when h = (3).
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=630(1.06)^x
percentage rate increase by 206%
What is exponential growth?
An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases with time.
Consider a population of mice that increases exponentially every year by a factor of two, starting with 2 in the first year and increasing to 4 in the second, 8 in the third, 16 in the fourth, and so on. The population is rising by a factor of 2 per year in this example. If mice gave birth to four pups instead, you would then have 4, 16, 64, and 256.
Linear growth, which is additive, and geometric growth can be contrasted with exponential growth, which is multiplicative (which is raised to a power).
This equation represents exponential growth because the base is greater than 1, the function represents growth and Whenever the base is less than 1, the function represents decay.
The base 1.06 is greater than 1, hence The equation represents exponential growth.
The formula for exponential growth:
[tex]y=a(1+r)^{x}[/tex]
where,
f(x) = exponential growth function
a = initial amount
r = growth rate
x = number of time intervals
In this case, [tex]r=1.06+1 = 2.06[/tex]
which represents percentage rate increase by 206%
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lucy buys a $68 pair of shoes. she receives a 15% employee discount. if the sales tax is 6 1/4 %, how much does she pay for the shoes?
The amount that Lucy pays for the shoes is $61.56.
How to calculate the amount paid?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this situation, Lucy buys a $68 pair of shoes. she receives a 15% employee discount and the sales tax is 6 1/4. The amount paid will be:
= $68 - (15% × $68)
= $57.80
Addition of the sale tax will be:
= $57.80 + (6.5% × $57.80)
= $57.80 + $3.76
= $61.56.
The price is $61.56.
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please help meeeeeeee
Answer: B & A
Step-by-step explanation: I think?
57. Center: (0, 0); Radius: 3
You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is 7.
While it is an uncommon confidence level, find the critical value that corresponds to a confidence level of 95.9%.
(Report answer accurate to three decimal places with appropriate rounding.)
ta/2 = ±
The critical value that corresponds to a confidence interval of 95.9% is 1.99.
The distribution of the sample mean will be roughly normally distributed, according to the Central Limit Theorem, if we have an unknown population with a mean and standard deviation and adequately small random samples (n < 30) are chosen from the population with replacement.
Then, the mean of the sample means is given by,
μ(x) = μ
And the standard deviation of the sample means is given by,
σ = σ / [tex]\sqrt{n}[/tex]
In this case the sample selected is of size, n = 7.
As the sample size n = 7 < 30, the sampling distribution of sample mean will be approximately normal.
So, a z-interval will be used to estimate the population mean.
The confidence level is, 95.9%.
The value of α is:
∝ = 1 - confidence level
∝ = 1 - 0.959
∝ = 0.041
The critical value is:
[tex]z_{\frac{∝ }{2} }[/tex] = [tex]z_{\frac{0.041}{2} }[/tex]
[tex]z_{\frac{∝ }{2} }[/tex] = [tex]z_{0.0205}[/tex]
[tex]z_{\frac{∝ }{2} }[/tex] = -1.99
[tex]z_{1-∝/2}[/tex] = 1.99
Use a z-table.
Therefore,
The critical value that corresponds to a confidence interval of 95.9% is 1.99.
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Kevin has an annual salary of $41,732, and he earned $33.52 interest from his savings account. He also paid $1050 in student loan interest and contributed $3900 to an IRA retirement account. Calculate Kevin’s adjusted gross income.
Kevin's adjusted gross income is $36, 815. 52
What is adjusted gross income?Adjusted gross income is simply described as gross income minus certain adjustments from the income.
These adjustments includes;
Educator expensesStudent loan interestAlimony paymentsContributions to an account, etcIt is calculated as;
Adjusted gross income = sum total of income - expenses
Now, let's substitute the values into the formula, we have;
Adjusted gross income = $(41,732 + 33.52) - $(1050 + 3900)
Add the values
Adjusted gross income = $(41, 765. 52 - 4950)
Subtract the values
Adjusted gross income = $36, 815. 52
Hence, the value is $36, 815. 52
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1 hour 15 minutes. is what in minutes
Answer:
75
Step-by-step explanation:
I hour and 15 minutes in minutes is 75 minutes
1 hour = 60 minutes
you add 15 and you get
60+15=75
The answer would be 75 Minutes.
1 Hour = 60 Minutes
[tex]60 + 15 = 75[/tex] Minutes.
The angle formed between one side and another, always less than 180 degrees.
Answer:obtuse angle
Step-by-step explanation:
An obtuse angle is an angle of greater than 90° and less than 180°. It is bigger than an acute angle. It is smaller than a straight angle, which measures 180°. Angles are measured with a protractor obtuse angle is specifically present in hexagon and pentagon and others.
Solve the equation 6x² + 1 = 10x to the nearest tenth.
let $f(x)$ be a polynomial with integer coefficients. suppose there are four distinct integers $p,q,r,s$ such that $$f(p)
The smallest possible value of f ( t ) = 9 based on the values of p , q , r , s.
Given :
Let f ( x ) be a polynomial with integer coefficients. Suppose there are four distinct integers p , q , r , s such that f ( p ) = f ( q ) = f ( r ) =f ( s ) = 5. If t is an integer and f ( t ) > 5,
Let g(x) = f(x) − 5.
g(x) = (x−p)(x−q)(x−r)(x−s)h(x)
The condition f(t) > 5 translates to g(t) > 0.
Since p,q,r,s,t are distinct integers, the smallest possible positive value of (t−p)(t−q)(t−r)(t−s) is 4 :
the four numbers in the parentheses are all distinct integers ≠ 0, so the smallest value we can get from the product (−2)⋅(−1)⋅1⋅2. }
The smallest possible positive value of h(t) is 1, since we must have g(t)≠0.
Thus the smallest possible value of g(t) is 4, and therefore the smallest possible value of f(t) is 9, and it is achieved for t=2 if we have
f(x)=x(x−1)(x−3)(x−4)+5
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Full question ;
Let f(x) be a polynomial with integer coefficients. Suppose there are four distinct integers p,q,r,s such that f(p)=f(q)=f(r)=f(s)=5. If t is an integer and f(t)>5, what is the smallest possible value of f(t)?
g ranking/unranking algorithms to generate a uniform random binary string of length n with exactly k ones.
The solution is written in Python
binary = ""decimal = 13quotient = int (decimal / 2) remainder = decimal % 2binary = str(remainder) + binarywhile(quotient >0):decimal = int(decimal / 2)quotient = int(decimal / 2) remainder = decimal % 2binary = str(remainder) + binaryprint(binary)The given problem can be solved by using the rand() function that generates a random number over the range [0, RAND_MAX] and with the help of the value returned by this function, any number in any range [L, R] can be generated as (rand() % (R – L + 1)) + L. Follow the steps below to solve the problem:
Initialize an empty string, say S.
Iterate over the range [0, N – 1] and perform the following steps:
Store a random number in the range [0, 1] using rand() function.
Append the randomly generated 0 or 1 to the end of the string S.
After completing the above steps, print the string S as the resulting binary string.
This binary is to hold the binary string.
Next, we declare variable decimal, quotient and remainder (Line 2-4). We assign a test value 13 to decimal variable and then get the first quotient by dividing decimal with 2 (Line 3). Then we get the remainder by using modulus operator, % (Line 4). The first remainder will be the first digit joined with the binary string (Line 5).
We need to repeat the process from Line 3-5 to get the following binary digits. Therefore create a while loop (Line 7) and set a condition that if quotient is bigger than 0 we keep dividing decimal by 2 and calculate the quotient and remainder and use the remainder as a binary digit and join it with binary string from the front (Line 9-11).
At last, we print the binary to terminal (Line 13).
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Which choice is equivalent to the quotient shown here when x > 0?
98x³+√72x²
O A. TV₂
OB. √26x
7x
O C. 7
6
OD. √98x3 - 72x²
Answer:
A.[tex] \frac{7}{6} \sqrt{x} [/tex]
Step-by-step explanation:
Solution Given:
[tex] \sqrt{98{x}^{3} } \div \sqrt{72 {x}^{2} } [/tex]
Bye using indices formula
[tex] \sqrt{x} \div \sqrt{y} = \sqrt{ \frac{x}{y} } [/tex]
we get
[tex] \sqrt{ \frac{98{x}^{3} }{72 {x}^{2} } } [/tex]
[tex] \sqrt{ \frac{49 {x}^{3} }{ 36 {x}^{2} } }[/tex]
[tex] \sqrt{ \frac{{7}^{2} {x}^{3 - 2} }{{6}^{2} } } [/tex]
[tex] \frac{7}{6} \sqrt{x} [/tex]
The function below has at least one rational zero. Use this fact to find all zeros of the function. f(x)=7x^4 +27x^3 -40x^2 +x +5
The rational zeros of the function can be found using the Rational Zero Theorem. The possible rational zeros of the function are ±1, ±5, ±1/7, ±5/7.
Zeros:
x=-5, -1/7, 0, 1, 5
The Rational Zero Theorem states that if a polynomial function of degree n has integer coefficients, then the possible rational zeros of the function will be of the form ±p/q, where q is a factor of the leading coefficient and p is a factor of the constant term.
In this case, the degree of the polynomial is 4, which means that the leading coefficient is 7 and the constant term is 5. Thus, the possible rational zeros of the function will be of the form ±p/q, where p is a factor of 5 and q is a factor of 7. The factors of 5 are ±1 and ±5, and the factors of 7 are ±1 and ±7. This means that the possible rational zeros of the function are ±1, ±5, ±1/7, and ±5/7.
To find the zeros of the function, we can use the rational zeros we found and plug them into the original equation. We can then solve for the zeros and find that the zeros of the function are x=-5, -1/7, 0, 1, 5.
x=-5: 7(-5)^4 +27(-5)^3 -40(-5)^2 +(-5) +5= 0
x=-1/7: 7(-1/7)^4 +27(-1/7)^3 -40(-1/7)^2 +(-1/7) +5= 0
x=0: 7(0)^4 +27(0)^3 -40(0)^2 +(0) +5= 0
x=1: 7(1)^4 +27(1)^3 -40(1)^2 +(1) +5= 0
x=5: 7(5)^4 +27(5)^3 -40(5)^2 +(5) +5= 0
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