Rational fraction is a fraction where a and/or b are fractions and b is not equal to 0.
What is rational fraction?Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers; they can be found in any field K. Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. The domain of a rational function is the set of all numbers except the zeros of the denominator since polynomials are defined everywhere.
Given Data
a_____________ is a fraction where a and/or b are fractions and b is not equal to 0.
A rational fraction is a fraction where a and/or b are fractions and b is not equal to 0.
Example 1. f(x) =[tex]\frac{x}{x-3}[/tex]
The denominator has only one zero, x = 3.
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A carpenter has 2 pipes which are 60 dm and 72 dm long respectively. he cuts them into equal lengths. what is the greatest possible length of each pipe?
Using greatest common factor (GCF), the greatest possible length of each pipe is 12 dm.
The greatest common factor (GCF) of a set of numbers is defined as the largest common positive integer that divides each number into equal parts with zero remainder.
If a carpenter has 2 pipes which are 60 dm and 72 dm long, respectively and he cuts them into equal lengths, then the greatest possible length of each pipe is the GCF of 60 and 72.
60 : 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
72 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 24, 36, 72
common factors : 1, 2, 3, 4, 6, 12
GCF = 12
Hence, he should cut the two pipes into 12 dm long.
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ind the radius of a circle that has a circumference of 16.
r = 4
r = 8
r = 12
r = 16
8 units is the radius of the circle with a circumference of 16π.
What is the radius of the given circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The circumference of a circle is expressed mathematically as;
C = 2 × π × r
Where r is radius and π is constant pi ( π = 3.14 )
Given the data in the question;
Circumference C = 16πRadius r = ?To find the radius of the circle, plug the given value into the circumference formula and solve for r.
C = 2 × π × r
16π = 2π × r
r = 16π / 2π
r = 16/2
Radius r = 8
Therefore, the radius of the circle is 8.
Option B is the correct answer.
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Choose the equation that represents the graph.
graph of a line passing through points negative 2 comma 0 and 0 comma negative 4
y = −2x − 4
y = 2x + 4
y = −2x + 4
y = 2x − 4
Answer:
The equation is y=2x+4.hope it's solved
A pole 9 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Ella measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.
r(x) = 8/9x - 17; r(x) = 15
Answer: 0.049382716
Step-by-step explanation: SOLVE FOR R, X
x=
4
1215
=303
4
3
=303.75
r=
81
4
≈0.049382716
All of the following represent three multiplied by six except:
03x6
03-6
O3(6)
3:6
Help please
Answer:
Except the last one 3:6 because its not multiplied by six but divided. Therefore the correct answer is the last one
Step-by-step explanation:
hope it helps
< A and < B are supplementary angles. If m m < B= (2x+30), then find the measure of < A.
Answer:
m<A = 50°
Step-by-step explanation:
supplementary angles add up to 180°
m<B = 2x + 30
we don't know m<A, so we'll say the value of it is x
2x + 30 + x = 180°
3x + 30 = 180
3x = 150
x = 50
plug this value back in for x
m<B = 2(50) + 30 = 130
m<B = 130°
m<A = x = 50
m<A = 50°
to prove these are supplementary angles, 130 + 50 = 180
What is the value of |−13|?
Answer:
+ 13
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
when you see the absolute value and the number is negative or positive it is just the whole number inside
The area of the compound shape below is 92 cm². Find the value of x.
Answer:
Step-by-step explanation:
Ling painted a picture of a local historic landmark for her history project. First, she painted a statue using a mix of black and white paint. Then, she painted a stone building using double the amount of black paint and double the amount of white paint. Which structure was a darker shade of gray?
Answer: Neither They were the same shade of Grey.
Step-by-step explanation:
it’s the right answer trust me
Color would be the same for both statue and stone buildings.
Let's, consider paint black as = x
and paint white as = y
If both the paints are mixed then paint z which is grey is formed.
Represented as,
x(black) + y(white) = z(grey)
Whereas, for the stone building double the amount of black and white colors are being used,
2x + 2y = 2z, coating of grey color would be also double.
Canceling 2 from both sides,
x + y = z
x(black) + y(white) = z(grey)
Therefore color would be the same for both statue and stone buildings.
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In Exercises 3 and 4, plot the points in a coordinate plane. Then determine whether
AB and CD are congruent.
3. A(-7, 1), B(-4, 1), C(3, -5), D(3, -2)
4. A(1, -1), B(1, 1), C(3, -4), D(5,-4)
AB is congruent to CD as an angle in front of them is congruent so, the sides are also congruent.
What is congruency?If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence. In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.So, all coordinates are shown on the graph as follows:
(Refer to the image attached below)
Now, we can see that in the 4th quadrant, two triangles are formed that are ABE and CDE.
We can see that:Then, we can conclude that:
AB ≅ CD (Angle in front of them is similar so, the sides are also similar)Therefore, AB is congruent to CD as an angle in front of them is congruent so, the sides are also congruent.
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HELP PLEASE!! I’ll give
The square root x^4= x^2
factor the triminal
3x squared -15x+12
Given mn, find the value of x.
(8x-7)°
(9x-28)°
Answer: top: x= -15 bottom: x= -37
Step-by-step explanation: First you need to get x by itself so for example on the top one you would do 8-8 to get x alone and then you would also do -7- 8 because whatever you do to one side you have to do to the other.
Hope this helped!!!
one out of every 9 light bulbs is defective. What constant of proportionality relates defective bulbs to total bulbs?
the constant of proportionality that relates defective bulbs to total bulbs is 1 / 9.
We are given that 1 bulb out of every 9 bulbs is defective.
So, this means that if there is a total of 9 bulbs, then 1 bulb in it will be defective.
Let us assume:
Total bulbs = 9
So, this implies that:
Defective bulbs = 1
Constant of proportionality = Defective bulbs / Total bulbs.
Substituting the values in this, we get that:
Constant of proportionality = 1 / 9
Therefore, we get that, the constant of proportionality that relates defective bulbs to total bulbs is 1 / 9.
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In the equation
2H₂ + 102 →→ 2H₂O
if you change the 2H₂ to 3H2 molecules and balance the equation, which statement is correct?
If you change the 2H₂ to 3H₂ molecules and balance the equation the equation will produce three molecules of water.
The provided chemical equation is,
2H₂ + O₂ → 2H₂O.
Changing 2H₂ with 3H₂
The chemical equation becomes,
3H₂ + O₂ → 2H₂O.
By doing this, the equation has become completely imbalanced,
So first we will balance it,
3H₂ +3/2O₂ → 3H₂O
Now, there will be 3 molecules of water formed.
As we observe the reaction more closely, we can see that the number of atoms of all the elements are equal on both the sides of the reaction.
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If you multiply two polynomials, will you always get a polynomial? Try combining some polynomials to answer your question. Use the ones given by your teacher or make up your own polynomials. Keep a record of what polynomials you tried, and the results. When you think you have an answer to your question, explain your reasoning using equations, graphs, visuals, calculations, words, or in any way that will help others understand your reasons.
Polynomials are closed under the multiplication operation, meaning that the result of the multiplication between two polynomials will always be a polynomial.
How to multiply polynomials?To multiply polynomials, we first apply the distributive property, multiplying all terms, then we combine the like terms, that is, adding all the terms that have the same exponents.
Since all the factors of the multiplications will be of polynomial terms, the results of the multiplication will be polynomial, and so will the like terms combined, hence polynomials are closed under the multiplication operation.
One example of multiplication of polynomials is given as follows:
(x² - 1)(x² + 1) = x²x² + x² - x² - 1 = x^4 - 1.
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Given that [tex]\alpha , \beta[/tex], roots of [tex]4x^{2} - x + 1 = 0[/tex], without finding the value of [tex]\alpha , \beta[/tex] ; evaluate
a. [tex]\beta x^{2} +\alpha x^{2} -\alpha \beta[/tex]
b. [tex]\frac{\alpha }{\beta } + \frac{\beta }{\alpha }[/tex]
Considering the product and the sum of the roots of the quadratic function, the numeric value of the expressions are given as follows:
1. [tex]\beta x^2 + \alpha x^2 - \alpha\beta = \frac{1}{4}(x^2 - 1)[/tex]
2. [tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = -\frac{7}{4}[/tex]
What are the product and the sum of the roots of the quadratic function?A quadratic function is defined according to the following rule:
y = ax² + bx + c.
In which a and b are the coefficients of the equation.
Supposing that the equation has roots [tex]\alpha[/tex] and [tex]\beta[/tex], the product and the sum of the roots of the quadratic function are given as follows:
[tex]\alpha\beta = \frac{c}{a}[/tex][tex]\alpha + \beta = -\frac{b}{a}[/tex]In this problem, the equation is:
4x² - x + 1.
Hence the coefficients are:
a = 4, b = -1, c = 1.
Then the product and the sum of the roots of the quadratic function are given as follows:
[tex]\alpha\beta = \frac{1}{4}[/tex][tex]\alpha + \beta = \frac{1}{4}[/tex]Then the numeric values for the expressions can be found as follows:
[tex]\beta x^2 + \alpha x^2 - \alpha\beta = x^2(\alpha + \beta) - \alpha\beta = \frac{1}{4}x^2 - \frac{1}{4} = \frac{1}{4}(x^2 - 1)[/tex]
For the second expression:
[tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = \frac{\alpha^2 + \beta^2}{\alpha\beta} = 4(\alpha^2 + \beta^2)[/tex]
The sum of the squares of the roots is:
[tex]\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta[/tex]
Hence:
[tex]\alpha^2 + \beta^2 = \frac{1}{16} - \frac{1}{2} = -\frac{7}{16}[/tex]
Then:
[tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = -\frac{28}{16} = -\frac{7}{4}[/tex]
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PLEASE HELP
Name the reciprocal you will use to multiply
-6/5k=12
Answer:
-5/6
Step-by-step explanation:
The reason why the reciprocal is -5/6 is because to isolate the variable with a fraction attached is to multiply it by swapping the numerator and denominator. Also making sure that if the number is a negative, to multiply the number by another negative to cancel it out.
A football team lost 14 yards on their first play then lost another 7 yards on the next play. What integer represents the total change in yards for the two plays?
Answer:
- 21
Step-by-step explanation:
They lost 14 yards, then lost and additional 7 more. You would simply add and make it a negative number due to the key word " lost ".
The equation would look like this: -14 + ( -7 ).
Another way to solve this equation is to multiply. ( + ) x ( - ) = -.
Your equation will the look this this: -14 - 7.
Now you just solve.
Thus, your answer should be - 21.
Hopes the helps!
Have a great day.
Answer: -21
Step-by-step explanation:
.A football team will lose an additional 7 yards if they lost 14 on their first play.
. Since the first play resulted in a loss of 14 yards, the integers that reflect the overall change in yards for the two plays are negative.
.In the second play, we score 14 points but lose 7 yards, which is a loss of 7 points.
.Negative 14 + Negative 7 = Negative 21, which is the overall change in yards.
. Hence, the answer would be -21 yards.
. -21 would be the correct integer that will represent the the total change in yards for the two plays.
Give crown and 10 points please please i need for now
1.
1- I, 2- II, 3- III, 4-IV, 5- V, 6- VI, 7- VII, 8- VIII, 9- IX, 10- X.
2.
26 = 10+10+5+1 = XXVI
17 = 10 + 5+2 = XVII
29 = 10+ 10+ 9 = XXIX
30 = 10+10+10 = XXX
3.
15 = XV
21 = XXI
26= XXVI
33 = XXXIII
35= XXXV
44 = XLIV
49 = XLIX
50 = L
4.
70 = LXX
80= LXXX
83 = LXXXIII
89 = LXXXIX
90= XC
100= C
5.
date today X / X/ XXXXII = 10/10/2022
the year 2022 = XXXXII
Hey, could someone help me out on this?
2. we want to estimate the mean of a population. a random sample of subjects is selected and the sample mean is computed. what is the probability that the sample mean is within 3 units of the true mean if the standard error is 1.8?
Given,
Sample mean = ±3 of true mean
Standard error = 1.8
Therefore,
Required probability of sample mean being within 3 units of the true mean is,
P ( sample mean - 3 < mean < sample mean + 3 )
= P [( sample mean - 3 ) - mean / 1.8 ] < mean - sample mean / 1.8 < [ ( sample mean + 3 ) - mean / 1.8 ]
= P ( - 1.67 < ∉ < 1.67)
= P (∉ < 1.67) - P( ∉ < 1.67)
= 0.952 - 0.047
= 0.905
Hence, the probability that the sample mean is within 3 units of the true mean if the standard error is 1.8 is 0.905.
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two cards are drawn without replacement from a standard deck of 52 playing cards. what is the probability of choosing a diamond and then, without replacement, a black card? express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
13/102
Step-by-step explanation:
We start with 52 playing cards. Of these 52 cards, 13 are diamonds, So the probability of a diamond is 13/52, or 1/4. There are now 51 cards left. Since the diamond is a red card, there are 26 black cards. So the probability of a black card is 26/51. Multiplying 1/4 and 26/51, and then simplifying, we have 13/102.
Rick sells sherriff badges to all of his friends. He earns a 25% commission on his sales per week. This past week she sold $ 100.00 worth of badges. How much did he make in commission total?
PLEASE HELP ! :)
1. G(X)=1/4x+1
what is g(-16)?
g(-16)=
In many cases, when we evaluate functions, we just have to replace x with a given value and simplify the expression.
Solving the Question[tex]g(x)=\dfrac{1}{4}x+1[/tex]
⇒ To solve for g(-16), plug in -16 as x:
[tex]g(x)=\dfrac{1}{4}(-16)+1\\\\g(x)=-4+1\\\\g(x)=-3[/tex]
Answerg(-16) = -3
Write the slope-intercept form of the equation of each line given the slope and y-intercept. Slope = 3/5, y-intercept = 0
Answer:y=3/5x
Step-by-step explanation:
just plug 3/5 in and you don’t need to add the 0
Picture attached below, and it's not a rectangle. It's a pentagonsolve a and b
a)
The perimeter is given by
[tex]2x+3+4x+5+3x+15+40[/tex]b)
Then we simplify by summing similar terms we obtain that the expression of the perimeter is
[tex](2x+4x+3x)+(3+5+15+40)[/tex][tex]9x+63[/tex]can you simplify 27/7
When we divide 27 by 7, we have 3; 3 * 7 = 21
27 - 21 = 6; we have a remainder of 6
Divide the remainder by 7, we have 6/7
Therefore, we have:
[tex]3\frac{6}{7}[/tex]when playing roulette at a casino, a gambler is trying to decide whether to bet $ on the number or to bet $ that the outcome is any one of the possibilities . the gambler knows that the expected value of the $ bet for a single number is . for the $ bet that the outcome is , there is a probability of of making a net profit of $ and a probability of losing $. a. find the expected value for the $ bet that the outcome is . b. which bet is better: a $ bet on the number or a $ bet that the outcome is any one of the numbers ? why?
The answers to both the subparts with the help of probability are:
(A) The $15 wager's expected value is a loss of $3.16.(B) Since the bet on a single number has a higher expected value, it is better.What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is equal to the variety of possible outcomes: the total number of outcomes that could occur. For instance, there is only one way to get a head and there are a total of two possible outcomes, so the probability of flipping a coin and getting heads is 1 in 2 (a head or tail).So, Item A:
The probability of earning $75 is 5/38.The likelihood of losing $15 is 33/38.The expected value is the total of each result times the associated probability, so:
[tex]E(X)=75 \frac{5}{38}-15 \frac{33}{38}=\frac{75(5)-15(33)}{38}=-3.16[/tex]The $15 wager should have a value of -3.16 dollars.
Item B:
The wager on a single number has an expected value of $-0.79 (or -$0.79).The best wager is a bet on a single number because it is higher than the expected value of the bet on multiple numbers.Therefore, the answers to both the subparts with the help of probability are:
(A) The $15 wager's expected value is a loss of $3.16.(B) Since the bet on a single number has a higher expected value, it is better.Know more about probability here:
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The complete question is given below:
When playing roulette at a casino, a gambler is trying to decide whether to bet $15 on the number 34 or to bet $15 that the outcome is any one of the five possibilities 00 comma 0 comma 1 comma 2 comma or 3. The gambler knows that the expected value of the $15 bet for a single number is negative 0.79 cents. For the $15 bet that the outcome is 00 comma 0 comma 1 comma 2 comma or 3, there is a probability of StartFraction 5 Over 38 EndFraction of making a net profit of $75 and a StartFraction 33 Over 38 EndFraction probability of losing $15. a. Find the expected value for the $15 bet that the outcome is 00 comma 0 comma 1 comma 2 comma or 3. b. Which bet is better: a $15 bet on the number 34 or a $15 bet that the outcome is any one of the numbers 00 comma 0 comma 1 comma 2 comma or 3? Why?