The reduce algebraic fraction is [tex]\frac{y^2 + 1}{y + 3}[/tex]
What is algebraic fraction?Algebraic fraction are simply fractions with algebraic expressions on the top and/or bottom
We follow the step to reduce to algebraic fraction
[tex]\frac{y^3 - 3y^2 -3 }{y^2 - 9}[/tex]
Simplify the numerator
[tex]\frac{ (y - 3) )(y^2 + 1 )}{y^2 -9}[/tex]
Factor out the greatest common factor from each group
[tex]\frac{(y^3 -3y^2 ) = y -3}{y^2 - 9}[/tex]
Find out greatest common factor (GCF) from each group
[tex]\frac{y^2 (y + 3) + 1 (y - 3)}{y^2 - 9}[/tex]
Simplify the denominator and rewrite 9 as [tex]3^{2}[/tex]
[tex]\frac{( y - 3 ) (y^2 + 1 ) }{y^2 - 3^2}[/tex]
Since both terms are perfect squares, factor using the difference of squares formula
[tex]a^{2}- b^2 = (a +b ) (a -b)[/tex] where a = y and b = 3
[tex]\frac{( y - 3) (y^2 + 1 )}{(y + 3 ) (y -3)}[/tex]
Evaluate the equation and rewrite the expression
[tex]\frac{y^2 + 1}{y + 3}[/tex]
Therefore, the reduce algebraic fraction is [tex]\frac{y^2 + 1}{y + 3}[/tex]
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Each 31 students brought 75 aluminum cans to class for a recycling drive find how many cans the class collected
ANSWER
2325 cans
EXPLANATION
We are given that 31 students each brought 75 aluminum cans to class.
To find how many cans the class collected, we have to multiply the number of students by the number of cans collected by each student.
That is:
Number of cans = 31 * 75 = 2325
Therefore, 2325 cans were collected by the class.
2. Without dividing, use powers of 10 to write three division expressions that are each equivale
to 35.78 ÷ 6.
The three division expressions that are each equivale to 35.78 ÷ 6 is 0.5933[tex]\times10^1[/tex], 59.33[tex]\times10^{-1}[/tex] and 59.33[tex]\times10^{-2}[/tex].
In the given question we have to use the powers of 10 to write three division expressions that are each equivale to 35.78 ÷ 6.
The given expression is 35.78 ÷ 6
To express in power of 10 we have to firstly simplify the given expression.
To simplify the given expression we have to divide the 35.78 by 6.
So 35.78 ÷ 6 =5.9633
To express in the power of 10 we move the decimal point left and right.
When we move left the power is positive and when move right power is negative.
The first expression is 0.5933[tex]\times10^1[/tex]
The second expression is 59.33[tex]\times10^{-1}[/tex]
The third expression is 593.3[tex]\times10^{-2}[/tex]
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Consider the probability model with sample space (A,B,C} and P(A)=0.1, P(B)=0.1, P(C)=0.8.Then
The sum of all the possible events is 1, which means that all the events are independent of the others, in that case
P(A or C) = P(A)+P(C) = 0.1 + 0.8 = 0.9
P(B and C) = P(B)*P(C) = 0.1 * 0.8 = 0.08
what is seven and fifteen hundredths as a decimal
Seven hundredths is:
[tex]0.07[/tex]Fifteen hundredths is:
[tex]0.15[/tex]What is the length of one leg of the triangle? 11 units 11 startroot 2 endroot units 22 units 22 startroot 2 endroot units
Considering the given triangle is a right-angled triangle. Therefore, one side of the triangle is [tex]11\sqrt{2}[/tex] and the other side of the triangle is [tex]22\sqrt{2}[/tex]. Since we have to find one of the legs of the triangle, we can assume [tex]22\sqrt{2}[/tex] is the length of the hypotenuse and [tex]11\sqrt{2}[/tex] the length of one of the sides of the right-angled triangle.
Therefore, by Pythagoras' theorem,
[tex]\sqrt{ (22\sqrt{2}) ^{2} - (11\sqrt{2} )^{2} } =[/tex] length of one leg of the triangle = 26.95 units
Therefore, The length of one leg of the triangle is 26.95 units.
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Answer:
b…22
Step-by-step explanation:
A wedge has two smooth sloping faces; one face makes an angle 30° with the horizontal and the other makes an angle 60 with the horizontal. A small smooth pulley is fixed at the apex of the wedge. A light inextensible string passes over the pulley and lies parallel to the faces of the wedge. At each end of the string there is a particle of mass 0.3kg. The system is released from rest. Show that the tension in the string is 3/4(1+√3) N.
The tension in the string at rest calculating the force and friction is approximately 2 N.
For particle A ,
The forces perpendicular to the plane is
R - 3cos 30° = 0
⇒R = 3cos 30°
The resultant force acting horizontally is
T cos 30° - R sin 30°
Now we substitute the value of R and T we get:
⇒ [tex]\frac{3(1+\sqrt3)}{4} cos 30 -3cos30\text{ }sin30[/tex]
⇒3√3 / 8 + 9/8 -3√3 / 4
⇒0.475 N
For the particle B.
The forces perpendicular to the plane is
R - 3cos 60° = 0
⇒R = 3cos 60°
The resultant force acting horizontally is
T cos 60° - R sin 60°
Now we substitute the value of R and T we get:
Force = 0.275 N
Resultant tension in the string:
0.475 -0.275 = 0.2
The given tension in the string is 3/4(1+√3) N
or, tension =2.049..N
or, tension ≈ 2 N approx
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ITS URGENT PLEASE HELP ME AND SHOW THE STEPS
I WILL MARK BRAINLIEST
Answer:
No, Anthony is not correct.
Step-by-step explanation:
K is at (-4, 8), L is at (-7, 4), M is at (-2, 1)
KL
[tex] \sqrt{ {( - 4 - ( - 7))}^{2} + {(8 - 4)}^{2} } [/tex]
[tex] \sqrt{ {3}^{2} + {4}^{2} } = \sqrt{9 + 16} = \sqrt{25} = 5[/tex]
LM
[tex] \sqrt{ {( - 7 - ( - 2))}^{2} + {(4 - 1)}^{2} } [/tex]
[tex] \sqrt{ {( - 5)}^{2} + {3}^{2} } = \sqrt{25 + 9} = \sqrt{34} [/tex]
KM
[tex] \sqrt{ {( - 4 - ( - 2))}^{2} + {(8 - 1)}^{2} } [/tex]
[tex] \sqrt{ {( - 2)}^{2} + {7}^{2} } = \sqrt{4 + 49} = \sqrt{53} [/tex]
From these, it follows that KLM is not an isoceles triangle.
Justify [tex] \sqrt[3]{8} \times \sqrt[3]{8} = 16[/tex]using the properties of exponents in at least two different ways.
EXPLANATION
Given the cubic root:
[tex]\sqrt[3]{8}\cdot\sqrt[3]{8}[/tex]Rewriting 8 as 2^3:
[tex]=\sqrt[3]{2^3}\cdot\sqrt[3]{2^3}[/tex]Applying the property of roots:
[tex]\sqrt[3]{a^3}=a[/tex][tex]=2\cdot2=4[/tex][tex]\sqrt[3]{8}\cdot\sqrt[3]{8}=\sqrt[3]{8^2}=\sqrt[3]{64}=4[/tex]Select the correct image.
Which image shows triangle A dilated by a scale factor of 2 with a center at the origin?
The triangle ABC undergoes a dilation of scale factor 2 centered at the origin.
Dilation About the Origin
Given a point P(x,y), its dilation about the origin by a scale factor of k maps the point to a point P'(kx,ky).
If we are given the dilated point, then we can find the original point by dividing by the scale factor.
Triangle ABC was dilated by a scale factor of 2 about the origin mapping it to triangle A'B'C' with vertices A'(-4,4), B'(-4,6), and C(2,4).
The coordinates of triangle ABC are:
A=(-4/2,4/2) = (-2,2)
B=(-4/2,6/2) = (-2,3)
C=(2/2,4/2) = (1,2)
The coordinates of ABC are respectively (-2,2), (-2,3), and (1,2).
Hence the answer is the triangle ABC undergoes a dilation of scale factor 2 centered at the origin.
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Answer:i'm pretty sure it's the one to the right of the example
Step-by-step explanation:
Consider the polynomial function P given by p(x)=5x^3+8x^2-3x+1 evaluate the function at x=-2
To evaluate it at x = -2 substitute x by -2 in p(x)
[tex]p(-2)=5(-2)^3+8(-2)^2-3(-2)+1[/tex]Now let us find its value
(-2)^3 = -2 * -2 * -2
12 eggs for 3$ how much is the cost of each egg
Answer:
0.25
Step-by-step explanation:
3 / 12 = 0.25
Answer: 0.60
Step-by-step explanation:
I need help solving questions 28 and 34 by expanding and simplifying please
#28
The given expression is
[tex]\lbrack x+(y-2)\rbrack\lbrack x-(y-2)\rbrack[/tex]At first, we will simplify each square bracket
Note that, the + sign does not change the terms in the bracket but the - sign change the signs of the terms inside the bracket
[tex]\begin{gathered} \lbrack x+(y-2)\rbrack=\lbrack x+y-2\rbrack \\ \lbrack x-(y-2)\rbrack=\lbrack x-y+2\rbrack \end{gathered}[/tex]Now, we will multiply the 2 brackets
[tex]\begin{gathered} \lbrack x+y-2\rbrack\lbrack x-y+2\rbrack= \\ (x)(x)+(x)(-y)+(x)(2)+(y)(x)+(y)(-y)+(y)(2)+(-2)(x)+(-2)(-y)+(-2)(2)= \\ x^2-xy+2x+xy-y^2+2y-2x+2y-4 \end{gathered}[/tex]Now we will add the like terms
[tex]\begin{gathered} x^2+(-xy+xy)+(2x-2x)-y^2+(2y+2y)-4= \\ x^2-y^2+4y-4 \end{gathered}[/tex]a homeowner estimates that it will take him 16 days to roof his house. a professional roofer estimates that he could roof the house in 3 days. how long will it take if the homeowner helps the roofer?
If the homeowner helps the professional roofer they will do the job in 2.53 days
How to determine how long it takes to do the roofing jobLet the number of days to complete the job be x
The rate at which the homeowner will roof is x / 16
The rate at which the professional roofer will roof is x / 3
Adding the rates together gives
x / 16 + x / 3
19x / 48
The rate it will take them both to finish the job is
= 48 / 19
= 2.53 days
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If EG = 10 and EF = 4, thenFG = [?]
In the exercise we first formulate and then replace values to find an unknown;
It is important to first look at what data the exercise gives us and then place them in the correct way, it must coincide with what the graph shows us.
Erika sells bags of fresh coffee beans at a local food co-op. She created the table below that shows her last four sales. Based on Erika's data, what was the cost per pound of coffee?
By using division of decimal numbers, it is obtained that cost of 1 pound of coffee is $8.99
What is decimal number and division?
Decimal numbers are those numbers which consist of an integer part and a fractional part.
Decimal are of two types-
Terminating decimals are those decimals which has finite number of figures after decimal point
Non terminating decimals are those decimals which has infinite number of figures after decimal point.
Division is the process by which value of single unit can be calculated from the value of multiple unit
The number which is divided is the dividend, the number by which dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula in division
Divisor x Quotient + Remainder = Dividend
Here, division of decimal will be used
Cost of 5 pounds of coffee = $44.95
Cost of 1 pound of coffee = $[tex]\frac{44.95}{5}\\[/tex]
= $8.99
Cost of 8 pounds of coffee = $71.92
Cost of 1 pound of coffee = $[tex]\frac{71.92}{8}\\[/tex]
= $8.99
Cost of 14 pounds of coffee = $125.86
Cost of 1 pound of coffee = $[tex]\frac{125.86}{14}\\[/tex]
= $8.99
Cost of 20 pounds of coffee = $179.80
Cost of 1 pound of coffee = $[tex]\frac{179.80}{20}\\[/tex]
= $8.99
So cost of 1 pound of coffee = 8.99
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What is the property demonstrated below:1/6 x 6 = 1
Answer:
Multiplicative inverse property (because 6 is the inverse of 1/6)
[tex]\frac{1}{6}\cdot\frac{6}{1}=1[/tex]Which point shown on the grid is located at (-3,6)
If the coordinates of the points are (x, y), then the point lies in the 1st quadrant
If the coordinates of the point are (-x, y), then the point lies in the 2nd quadrant
If the coordinates of the point are (-x, -y), then the point lies in the 3rd quadrant
If the coordinates of the point are (x, -y), then it lies in the 4th quadrant
Since the given point is (-3, 6), then it should be in the 2nd quadrant
Since point B is in the 2nd quadrant, then
The answer is B the third answer
(
ctg 30° + 2 csc 60° - 3 cos 30°
The value of the expression ctg 30° + 2 csc 60° - 3 cos 30° is 5√3/6
The expression is calculated using trignometic values
ctg 30° + 2 csc 60° - 3 cos 30°
1/tan 30 + 2/sin 60 - 3 cos 30
1/(1/√3) + 2/(√3/2) - 3 (√3/2)
√3 + 4/√3 - 3√3/2
LCM is 2√3
(√3(2√3) + 2(4) - 3√3(√3) )/2√3
(6 + 8 - 9)/2√3
5/2√3
5√3/6
The value of the expression ctg 30° + 2 csc 60° - 3 cos 30° is 5√3/6
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HELP QUICKLY PLSSSSS
Answer:
5, 6, 7, 8
Step-by-step explanation:
substitute the values of x from the table into f(x)
f(1) = 1 + 4 = 5
f(2) = 2 + 4 = 6
f(3) = 3 + 4 = 7
f(4) = 4 + 4 = 8
the values of f(x) are 5, 6, 7, 8
Find the mean of these numbers: 5, 11, 2, 12, 4, 2Need solution :Dhave a good night ^^ from Philippines
Given:
5, 11, 2, 12, 4, 2
Required:
To find the mean of the given numbers.
Explanation:
Consider the given numbers
5, 11, 2, 12, 4, 2
Now the mean is
[tex]\begin{gathered} =\frac{2+2+4+5+11+12}{6} \\ \\ =\frac{36}{6} \\ \\ =6 \end{gathered}[/tex]Final Answer:
The mean is 6.
Give the information asked for to each problems Ax Styles Tags Assignments Calendar In each of the following state the Start Value Growth Value 1. C-5f + 32 Calts FE 2. Y= 4000 - 250x 3 х -3 0 6 у -9 3 -1 -5 3 4. x -4 4 8 Olo у 3 15 21 5. A financial account begins with $5900. Each week $300 is deducted. 6. Also point to the start value Apps Hus Type here to search
Explanation:
1) C = 5/9 f + 32
The start value is the constant = 32.
The start value = 32
Growth value = rate of change
Growth value = 5/9
2) y = 4000 - 250x
The start value is the constant = 4000
The start value = 4000
Which graph shows the solution for the system of linear inequalities?
2x - y ≥ -3
y < -2x + 4
The graph that represents the systems of linear equations 2x - y ≥ -3 and y < -2x + 4 is option d
How to interpret linear equation graphsinformation gotten from the question include
inequality graph showing shaded regions
rearranging the equation to be in the form
y = mx + c
2x - y ≥ -3
2x + 3 ≥ y
y ≤ 2x + 3
The two equations are
y ≤ 2x + 3
y < -2x + 4
some interpretation on the information from the question include
shading below a line is less thandotted lines mean the inequality do not have equal to, either less than or greater thanThe both inequalities are less than hence the shading for the both will be below the line
This interpretation helps to conclude that last options is the best choice
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people with type o-negative blood are universal donors. that is, any patient can receive a transfusion of o-negative blood. only 7.2% of the american population have o-negative blood. if we choose 10 americans at random who gave blood, what is the probability that at least 1 of them is a universal donor?
The probability that any given person is a universal donor is 7.2%. This means that the probability that a person is not a universal donor is 92.8%.This indicates that there is a 0.65 percent chance that at least 1 out of every 10 randomly selected individuals is a universal donor.
Now, if we choose 10 people at random, we can use the binomial distribution to calculate the probability that at least 1 of them is a universal donor. The binomial distribution tells us that the probability of getting exactly k successes in n trials is:
P(k; n, p) = (n choose k) p^k (1-p)^(n-k)
where n is the number of trials, p is the probability of success on a single trial, and k is the number of successes.
plugging in our values, we get:
P(1; 10, 0.072) = (10 choose 1) (0.072)^1 (1-0.072)^9
P(1; 10, 0.072) = 10(0.072) (0.928)^9
P(1; 10, 0.072) = 0.65
This means that the probability that at least 1 out of 10 people chosen at random is a universal donor is 0.65.
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Airen and Megan are making admission tickets to the White Station Middle School dance. So far they have made 231 tickets, and their plans are to make 330 tickets. What percent of the admission tickets has Airen and Megan produced so far? Solve the problem using the percent formula.
[tex]\huge\red{\mid{\underline{\overline{\textbf{EQUATION AND ANSWER}}}\mid}}[/tex]
_________________
Let's solve this simple percentage problem,
_________________DefinitionsPercentage - Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number.
Cross Multiplication - In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.
Division - Division, otherwise known as the inverse of multiplication separates a certain number into what it has been divided by.
_________________
Now that we understand the definition we can further solve this equation
[tex]\large\red{\mid{\underline{\overline{\textbf{Values}}}\mid}}[/tex]
[tex]231[/tex][tex]330[/tex]________________
Now we will add to solve this equation
[tex]\large\red{\mid{\underline{\overline{\textbf{Equtation}}}\mid}}[/tex]
[tex]\frac{x}{100}=\frac{231}{330}[/tex]
Now we will do cross multiplication
[tex]231\cdot100\\x\cdot330[/tex]
[tex]330x=231000[/tex]
Finally, we will do some division
[tex]x=70[/tex]
[tex]\large\red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}[/tex]
Airen and Megan are making admission tickets to the White Station Middle School dance. So far they have made 231 tickets, and their plans are to make 330 tickets. What percent of the admission tickets has Airen and Megan produced so far? Solve the problem using the percent formula.The answer is [tex]70%[/tex]%
Have a good day!Find the total surface area of this cone.
Leave your answer in terms of T.
25m
ما
8m
TT
Hint: Surface Area of a Cone = Tre + B
Where l = slant height, and B = area of the base
Enter
Given
[tex]\begin{gathered} r=8m \\ l=25 \end{gathered}[/tex]The given formula
[tex]\begin{gathered} Surface\text{ area of a cone =}\pi rl+B \\ where\text{ l is slant height} \\ and\text{ B is the area base} \end{gathered}[/tex]The base is circle
[tex]\begin{gathered} Area\text{ of a circle=}\pi r^2 \\ Area\text{ of a circle=}\pi8^2 \\ Area\text{ of a circle =64}\pi \end{gathered}[/tex]Now back to the given formula
[tex]\begin{gathered} Surface\text{ of area of cone=}\pi rl+B \\ B=64\pi \\ l=25 \\ r=8 \\ \end{gathered}[/tex][tex]\begin{gathered} Surface\text{ of area of cone =}\pi\times8\times25+64\pi \\ Surface\text{ofareaofcone=200}\pi\text{+64\pi} \\ Surface\text{ofareaofcone=264\pi} \end{gathered}[/tex]The final answer
[tex]264\pi m^2[/tex]
Lauren walks 400 m in 125 seconds what is her speed
Answer:
3.2 m/s
Step-by-step explanation:
If we use the equation distance/time=speed, we can find this pretty quickly.
Our distance is 400 m.
Our time is 125 s.
400/125=
3.2 m/s
can yall help me with this
Answer:
B
Step-by-step explanation:
If you see two negatives next to each other, just think of them as adding. So add 8 and 7, you get 15.
Write the explicit formula for the given arithmetic sequence in explicit form: a(n)=a(1)+d(n-1)
What is the result when the number 8 is increased by 25%?
Answer:
Step-by-step explanation:
Ok1
1. Put percent into numbers
25/100*8=
200/100=
2
2. Add
There was a increase of 2 dollars from 8$
8$+2$=
10$
Answer: 10$
Answer:10
note: please tell me if I'm wrong
hello!! Can someone please explain and solve this problem for me? I’m having a hard time understanding.. I believe you start with terminal point and then initial.. but the rest i have no clue
Find the component form of vector v with initial point (-6,2) and terminal point (7,-3).
The component form of vector v with initial point (-6,2) and terminal point (7,-3) is (13,-5).
What is component form of vector?The component form of a vector is represented as x, y >, where x denotes the direction of travel (right or left) and y denotes the direction of travel (up or down) of the vector. Any two-dimensional vector may be conceived of as exerting influence in two separate directions. In other words, it can be considered to have two pieces. Components are the individual pieces that make up a two-dimensional vector. A vector's elements show how that vector will act in a specific direction.
Here,
initial point A=(-6,2)
terminal point B=(7,-3).
AB=(Bx-Ax, By-Ay)
=(7-(-6), -3-2)
= (13, -5)
The component form of the vector v with the starting points (-6, 2) and terminal points (7, -3) is (13,-5).
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