The power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]
For given question,
We have been given a function g(x) = 4x / (x² + 2x - 3)
We need to find a power series for the function, centered at c, for c = 0.
First we factorize the denominator of function g(x), we have:
[tex]\Rightarrow g(x)=\frac{4x}{(x-1)(x+3)}[/tex]
We can write g(x) as,
[tex]\Rightarrow g(x)=\frac{1}{x-1}+\frac{3}{x+3}\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1+\frac{x}{3} }\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1-(-\frac{x}{3} )}\\[/tex]
We know that, [tex]\frac{1}{1-x}=\sum{_{n=0}^\infty}~{x^n}[/tex] if |x| < 1
and [tex]\frac{1}{1-(-\frac{x}{3} )}=\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n[/tex] if [tex]|\frac{x}{6}| < 1[/tex]
[tex]\Rightarrow g(x)=-\sum{_{n=0}^\infty}~x^n+\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n\\[/tex] if |x| < 1 and if [tex]|\frac{x}{6}| < 1[/tex]
[tex]\Rightarrow g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex] if |x| < 1
Therefore, the power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]
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Marcus loves baseball and wants to create a home plate for his house. Marcus needs to calculate the area of the home plate at the ball field so he can reconstruct it when he gets home. Calculate the area of the polygon.
72.5 in2
75.5 in2
83 in2
96 in2
Answer:
83in²
Step-by-step explanation:
This can also be expressed as;
Area of polygon=Area of ∆ABF +Area of rectangle BCDF + Area 0f ∆DEF
For ∆ABF;
Area of ∆ABO=∆AOF
Area of ∆ABF=2×Area of ∆ABO
Area of ∆ABO=1/2×Length×height
=1×4×7/2=28/2=14in
But area of ∆ABF=2×Area of ∆ABO
Area=2×14in=28in.
Area of rectangle;
Area=length×breadth
Area=5in×8in=40in.
Area of ∆DEF=2×Area of ∆EFG
Area=1/2× base× height
Area=1×2.5×6/2
Area=15/2=7.5in.
But area of ∆EFG=2×7.5in
=15in.
Area of polygon=28in+40in+15in=83in
√32x+1
= 9x-2 minta tolong dengan ini
We have:
√32x + 1 = 9x - 2
<=> √32x - 9x = -2 - 1
<=> (√32 - 9)x = -3
<=> x = -3/(√32 - 9) = (27+12√2)/49
ANSWER: x = (27+12√2)/49
P/s: i'm not pretty sure
Ok done. Thank to me :3
If a1=6 and a5=12, what does a3=?
a3=9
assuming the pattern is constant, a3 is right in the middle of a1 and a5 so the answer would be right in the middle of 6 and 12. the average of 6 and 12 is 9, so a3=9.
hope this helps!
help me 20 points and I will mark brainlyist
A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
What is a line plot?A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.
What is a mean?A mean is also referred to as an arithmetic average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.
Mathematically, the distance between the means of both classes A and B is given by:
Distance = Mean of class A - Mean of class B
Distance = 12 - 4
Distance = 8.
The mean absolute deviation (MAD) for class A is given by:
MAD A = 1/9[2(9 - 12) + (10 - 12) + (11 - 12) + (12 - 12) + (13 - 12) + (14 - 12) + 2(15 - 12)]
MAD A = 1/9[2(3) + (2) + (1) + 0 + (1) + (2) + (1) + 2(3)]
MAD A = 1/9[6 + 2 + 1 + 1 + 2 + 1 + 6]
MAD A = 1/9 × [18]
MAD A = 18/9
MAD A = 2.
Also, the mean absolute deviation (MAD) for class B is given by:
MAD B = 1/9[2(1 - 4) + (2 - 4) + (3 - 4) + (4 - 4) + (5 - 4) + (6 - 4) + 2(7 - 4)]
MAD B = 1/9[2(3) + 2(2) + (1) + (0) + (1) + (2) + 2(3)]
MAD B = 1/9[6 + 4 + 1 + 0 + 1 + 2 + 6]
MAD B = 1/9 × [18]
MAD B = 18/9
MAD B = 2.
Therefore, distance between the means = four (4) times the MAD.
Distance = Means × MAD
8 = 4 × 2.
In conclusion, we can infer and logically deduce that there is no overlap and the distance between the means of both players A and B is between one (1) times the MAD and five (5) times the MAD.
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Deion misses 4% of the free throws he attempts in a seaon. how many total free throws did he attempt if he missed 17
He has thrown 425 free throws if he missed 17
How to determine the total number of free throws?The given parameters are:
Proportion of free throw missed, p = 4%
Number of free throw missed, n = 17
Let the total number of throws be N.
So we have
n = p * N
Substitute the known values in the above equation
17 = 4% * N
Divide both sides by 4%
N = 425
Hence, he has thrown 425 free throws if he missed 17
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find the value of n: [tex]\frac{10n}{-5} = -4[/tex]
Answer:
n = 2
Step-by-step explanation:
cross multiply
-5 times -4 = 20
10n = 20
n = 2
[tex]\bf{Move \ the \ negative \ symbol \ to \ the \ left. }[/tex]
[tex]\boldsymbol{\sf{-\dfrac{10n}{5}=-4 \ \ \longmapsto \ \ [Split] }}[/tex]
[tex]\boldsymbol{\sf{-2n=-4 }}[/tex]
[tex]\bf{Divide \ both \ sides \ by \ -2. }[/tex]
[tex]\boldsymbol{\sf{n=\dfrac{-4}{-2} }}[/tex]
[tex]\bf{Two \ negatives \ make \ a \ positive. }[/tex]
[tex]\boldsymbol{\sf{n=\dfrac{4}{2} \ \ \longmapsto \ \ [Split] }}[/tex]
[tex]\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \underline{n=2}}}}}[/tex]
Harvey is analyzing the production cost of a new product launched by his company. The initial production cost was $1,050. The production cost is at its lowest amount, $250, for 200 items, and thereafter increases as the number of items increases. Which of the following graphs represents the production cost of the product?
It would be the bottom left graph
Initial production: 1050
so the graph will be started at 1050 which makes top right graph incorrect
Next, the money at the lowest was 250 which makes the top left and bottom right incorrect.
leaving only the bottom right graph to be correct
Answer:
Graph Y
Step-by-step explanation:
Given information:
Initial production cost = $1,050Lowest production cost = $250 for 200 itemsProduction cost increases after 200 items.The x-axis shows number of items in hundreds.The y-axis shows the cost in dollars.The initial production cost is when the number of items is zero.
Therefore, the y-intercept of the graph will be (0, 1050).
The lowest production cost is the minimum point of the curve.
Therefore, the vertex of the graph will be (2, 250).
The only graph that satisfies these conditions is graph Y (attached).
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When one organism gains a benefit at the expense of a second organism and causes them harm is called:
A. patasitism
B. Mutualism
C. Commensalism
D. Predation
When one organism gains a benefit at the expense of a second organism and causes them harm is called:
A. Parasitism
B. Mutualism
C. Commensalism
D. Predation
Answer:
Step-by-step explanation:
a
Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given.
Reason: AAS Postulate
∠KJI≅ZJX is the additional information.
What are the AAS congruency criteria?
⇒ AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent
We have been given that
⇒ kJ=ZJ
⇒∠KJI=∠ZJX (vertically opposite angle)
And we require one more angle which can't be on the non-included side
so we have only one angle that can satisfy this
⇒∠JIK=∠JXZ
⇒ Now we can say that △KJI ≅ △ZJX is congruent with AAS congruency criteria
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3 bells ring at interval of 12,15 and 18 minutes.Respectively they all ring together at 6am,at what time will they ring together? again?
The least common multiple of two or more natural numbers is the least common multiple of all of them. This concept has historically been linked to natural numbers, but can be used for negative integers or complex numbers.
We calculate the least common multiple, by simultaneous decomposition, this method consists of extracting the common and non-common prime factors, therefore
The lcm of 12,15, 1812 - 15 - 18 | 2 6 - 15 - 9 | 2 3 - 15 - 9 | 3 1 - 5 - 3 | 3 1 - 5 - 1 | 5 1 - 1 - 1 |L.c.m.(12,15,18)= 2² × 3² × 5 = 180 min
The least common multiple of 12, 15, and 18 is 180.
Convert the minutes to hours, for this we apply the rule of 3:
x = 180 * 1 / 60 = 3 hrAs the bells all together ring at 6 am, so we add
6 a.m + 3 = 9Answer: The bells are rung together again at 9 in the morning.
Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces.
Carries two brothers each ate 4 pieces, the rest of carries family ate 14 pieces and there were 14 pieces remaining given that Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces. This can be obtained by multiplying the fractions given with the total number.
Find the required number of pieces:From the question it is given that,
Carries family broke a package of graham crackers into 32 pieces.
Therefore total number of pieces will be 32 pieces.
First it is said that,carries two brothers each ate 1/8 of the pieces
This means that out of 32, 1/8 of the pieces were ate by the two brothers.
1/8 of 32 = 1/8 × 32 = 4 pieces
⇒ Carries two brothers each ate 4 pieces
Next it is said that,the rest of the family ate 7/16 of the pieces
This means that out of 32, 7/16 of the pieces were ate by the rest of the family
7/16 of 32 = 7/16 × 32 = 14 pieces
⇒ the rest of carries family ate 14 pieces
To find the remaining pieces add the number of pieces ate by both carries brothers and the rest of the family and subtracting from the total number of pieces.remaining pieces = 32 - (4 + 14) = 32 - 18 = 14 pieces
⇒ there were 14 pieces remaining
carries two brothers each ate 4 piecesthe rest of carries family ate 14 piecesthere were 14 pieces remainingHence Carries two brothers each ate 4 pieces, the rest of carries family ate 14 pieces and there were 14 pieces remaining given that Carries family broke a package of graham crackers into 32 pieces.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces.
carries two brothers each ate ____ pieces
the rest of carries family ate ____ pieces
there were ____ pieces remaining
Russ is solving an equation where both sides are linear expressions. he sets the expressions equal to y and graphs the system finding that they are the same line. how should russ interpret this outcome?
The correct option (D).
There are infinitely many intersection points.
What is liner equation?a two-variable equation that, when plotted on a graph, results in a straight line.
What does intersection point mean?The term "point of intersection" refers to the intersection of two lines.
According to the given information:Russ is attempting to solve an equation whose two sides are both linear expressions.
He graphs the system and finds that they are on the same line after setting the expressions to y.
Since both lines are the same, there are an endless number of junction places.
Russ should therefore consider the outcome to be option (D) There are a limitless number of intersections.
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I understand that the question you are looking for is:
Russ is solving an equation where both sides are linear expressions. He sets the expressions equal to y and graphs the system finding that they are the same line. How should Russ interpret this outcome? There are no intersection points. There is exactly one intersection point. There are exactly two intersection points. There are infinitely many intersection points.Russ is solving an equation where both sides are linear expressions. He sets the expressions equal to y and graphs the system finding that they are the same line. How should Russ interpret this outcome?
A. There are no intersection points.
B. There is exactly one intersection point.
C. There are exactly two intersection points.
D. There are infinitely many intersection points
The graph of y=√x is shifted 2 units down and 3 units left. Which equation represents the new graph?
A. y=√x-2-3
B. y=√x+2-3
C. y=√x+2+3
D. y=√x+3+2
the equation that represents the new graph is:
g(x) = √(x - 3) - 2
Which equation represents the new graph?
Here we start with the function:
y = f(x) = √x
First, we shift it 2 units down, then the new equation will be:
g(x) = f(x) - 2
Now we apply a horizontal shift, this time we shift the graph 3 units to the left, then the new equation is:
g(x) = f(x - 3) - 2
Now we replace f(x) = √x to get:
g(x) = √(x - 3) - 2
That is the equation that represents the new graph.
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A locker combination consists of two non-zero digits. the digits in a combination are not repeated and range from 2 through 9. event a = the first digit is an odd number event b = the second digit is an odd number if a combination is picked at random with each possible locker combination being equally likely, what is p(b|a) expressed in simplest form? a. b. c. d.
The P(B|A) expressed in the simplest form will be (B) 2/7.
What is probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.To find the P(B|A) expressed in the simplest form:
Given -
Event A = the first digit is less than 5Event B = the second digit is less than 5Total possible numbers = 2,3,4,5,6,7,8,9
Let the value of the number be AB.
The total possible values below 5 are 2,3, and 4.The probability of the first digit is less than 5, P(A) = 3/8.The second digit is less than 5, P(B/A) = 2/7.Therefore, the P(B|A) expressed in the simplest form will be (B) 2/7.
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The complete question is given below:
A locker combination consists of two non-zero digits. The digits in a combination are not repeated and range from 2 through 9.
Event a = a first digit is an odd number
Event b = the second digit is an odd number
If a combination is picked at random with each possible locker combination being equally likely, what is P(B/A) expressed in the simplest form?
A.1/4
B.2/7
C.4/9
D.1/2
The line represented by 2y = x + 8 is dilated by a scale factor of k centered at the origin, such that the image of the line has an equation of y-1/2x=2. What is the scale factor?
The scale factor of the given dilation transformation is calculated as; 1/2
How to use the scale of dilation?We know that from transformation that a dilation is a non - rigid transformation that produces similar figures.
If two lines are similar, then the lines are parallel and parallel lines always have the same slope.
Thus;
Line A has the formula; 2y = x + 8
Writing it in slope intercept form gives us;
y = 0.5x + 4 ------(1)
Thus;
slope of the line A is m = 0.5
y-intercept of the line A is b = 4
Line B has the equation;
y - ¹/₂x = 2
Rearranging in Slope Intercept form gives us;
y = ¹/₂x + 2
Thus;
slope of the line B is m = 0.5
y-intercept of the line B is b = 2
Now, it should be noted that the y-intercept of line A multiplied by the scale factor k must be equal to the y-intercept of line B. Thus;
4k = 2
k = 2/4
k = ¹/₂
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x^-19x-39=0 complete the square
The resulting equation on completing the square is (x+19/2)^2 = 39 + (19/2)^2
Completing the square method for a quadQuadratic equation are equations that has a leading degree of 2. Most quadratic equations have 3 terms.
Given the quadratic equation x^2-19x-39 = 0
Add 39 to both sides to have:
x^2 - 19x - 39 + 39 = 0 + 39
x^2 -19x = 39
Complete the square of the resulting
x^2-19x+(19/2)^2 = 39 + (19/2)^2
(x+19/2)^2 = 39 + (19/2)^2
x + 19/2 = ±√39 + (19/2)^2
x = ±√39 + (19/2)^2 - 19/2
Hence the resulting equation on completing the square is (x+19/2)^2 = 39 + (19/2)^2
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A line has a slope of 2 and passes through the point -3, 6 what is the equation in slope intercept form
Answer:
y=2x+12
Step-by-step explanation:
The table can be used to determine the solution to the system of equations, 2y − x = 8, and y − 2x = −5.
A table with 6 columns and 2 rows. The first column, Original System has 2 y minus x equals 8 and y minus 2 x equals negative 5. The second column, Equivalent System, has 2 y minus x equals 8 and negative y plus 4 x equals 10. The third column, Sum of equations in Equivalent System, has 3 x equals 18. The fourth column, Solution to System, is blank. The fifth column, New System Using Sum, has2 y minus x equals 8 and 3 x equals 18. The sixth column, Solution to New System is blank.
Which solution can be used to fill in both blanks in the table?
The solution to the system and the solution that fills the blank space is (6, 1)
System of equationsThis are also known as a set of simultaneous equations, also known as a system of equations which is a finite set of equations for which common solutions
Given the following system of equations
2y − x = 8, and
y − 2x = −5.
From equation 2;
y = -5 + 2x ............. 3
Substitute equation 2 into equation 1 to have:
2(-5+2x) - x = 8
Expand to have:
-10 +4x -x = 8
-10 + 3x = 8
3x = 8 + 10
3x = 18
Divide both sides
by 3
3x/3 = 18/3
x = 6
Substitute x = 6 into equation 3
y = -5 + 2x
y = -5 + 2(3)
y = -5 + 6
y = 1
Hence the solution to the system and the solution that fills the blank space is (6, 1)
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Answer:
Its D (6,7)
Step-by-step explanation:
If a polynomial function, f(x), with rational coefficients has roots 0, 4, and 3 startroot 11 endroot, what must also be a root of f(x)?
Answer:
-3√11
Step-by-step explanation:
If the coefficients of a polynomial are rational, any irrational root will have a conjugate that is also a root.
Irrational rootsThe root 3√11 is irrational, so its conjugate, -3√11, will also be a root.
__
Additional comments
The conjugate of a root of the form a+√b or a+bi will be the same form with the sign changed: a-√b or a-bi.
The conjugate of 3√11 = 0 +√99 will be 0 -√99 = -3√11.
__
A quadratic with rational coefficients can only have irrational roots of the form a±√b, where 'a' and 'b' may be any rational number.
3 - √11 also be a root of f(x).
What is Polynomial function ?A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.
According to the given Information:Get the conjugate of any irrational zero if you want rational coefficients.
The conjugate of 3 + √11 is 3 - √11
x = 3 +√ 11
Subtract 3 on both sides
x minus 3 = 3 + √11 - 3
x - 3 = √11
By squaring on both sides
(x - 3)² =√ 11
Now subtract 11 on both sides
(x - 3)² - 11 = 0
To factor use the difference of squares
u² minus v² = (u minus v) (u plus v)
[(x - 3) - 11][(x - 3) + 11] = 0
We get,
(x - 3) - 1 = 0 or (x - 3) + 11 = 0
Solve for x - 3 and x
Add √11 on both sides of first equation and subtract √11 on both sides of second equation
x minus 3 = √11 or x minus 3 = - √11
By adding 3 on both sides
x = 3 + √11 or x = 3 - √11
As a result,
the root of 3 - √11 must likewise be f(x).
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pls helpp
1. There are 3 1/2 groups of students ready to load buses for a field trip. Each group will fill one bus 2/5 of the students on each bus are boys. How many buses would it take to carry only the boys.
2. Mark is going to a pool party. It is 2 3/4 miles from his house. Mark decides to ride his bicycle, but he has a flat tire 2/3 if the way there. How far is Mark from his house?
We know that there are (3 + 1/2) groups, such that each group fill one bus.
2/5 of the students are boys, then the number of groups that we can make only with boys is:
(2/5)*(3 + 1/2) = 6/5 + 1/5 = 7/5 = 5/5 + 2/5 = 1 + 2/5
Then you can make one and a little less than a half of a group, which means that you need 1 and 2/5 of a buss to transport the boys, rounding that to the a whole number, you will need 2 busses to only transport the boys.
How far is Mark from his house?The original distance is:
D = (2 + 3/4) miles.
But Mark only covers 2/3 of that distance, then we have:
d = (2/3)*D = (2/3)*(2 + 3/4) miles = (4/3 + 2/4) miles
d = (4/3 + 1/2) miles = (8/6 + 3/6) miles = (1 + 5/6) miles
Mark is at (1 + 5/6) miles of his house.
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You are constructing a metal border of uniform width for a rectangular wall mirror that measures 20 inches by 24 inches. You have 416 square inches of metal to use. What is the greatest possible width * of the border
Answer:
The frame will be 4 inches in width
Step-by-step explanation:
The length of the outside is 24+2x
The width of the outside is 20+2x
(24+2x)(20+2x) - 20(24) = 416
480 + 40x + 48x + 4x2 - 480 = 416
4x2 + 88x - 416 = 0
x2 + 22x - 104 = 0
(x+26)(x-4) = 0
x = -26 or x=4
The frame will be 4 inches in width
Please help!!!
The diagram to the right shows a square pyramid. The point C is the centre of the base, and TC is perpendicular to the base. (More information in the screenshot)
(i) The measures of the angles are m ∠ TCM = m ∠ TCQ = m ∠ CMQ = 90°.
(ii) The lengths of sides CM and CQ are 2 cm and 2√2 cm, respectively.
(iii) The angle between the side face and the base is equal to θ = cos⁻¹ (2 / MT) and the angle between the slant edge and the base is θ = cos⁻¹ [2√2 / √(4 + MT²)].
How to analyze a right pyramid
In this problem we have a right pyramid as line segment TC is perpendicular to the base PQRS, which means that any line coplanar with PQRS is perpendicular to line segment TC. i) the measures of the angles are m ∠ TCM = m ∠ TCQ = 90°.
Besides, the base PQRS is a square, which is equivalent to four right triangles with angles 45° - 45° - 90° and each triangle can be divided into two right triangles. Hence, the measure of the angle CMQ is 90°.
ii) The length of the sides can be found by the 45-45-90 theorem, which states that the length of the hypotenuse is √2 times the length of any of the legs:
CQ = (√2 / 2) · PQ
CQ = (√2 / 2) · (4 cm)
CQ = 2√2 cm
CM = (√2 / 2) · (2 √2 cm)
CM = 2 cm
iii) The angle between the side face, one of them contains the line segment MT and the base can be found by the following inverse trigonometric relation: (value of the pyramid height is missing)
θ = cos⁻¹ (CM / MT)
θ = cos⁻¹ (2 / MT) (1)
Similarly, the angle between the slant edge and the base is found by Pythagorean theorem and inverse trigonometric relation: (value of the pyramid height is missing)
θ = cos⁻¹ (CQ / TQ)
θ = cos⁻¹ [2√2 / √(QM² + MT²)]
θ = cos⁻¹ [2√2 / √(4 + MT²)] (2)
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Firewood can be sold in cords. the wood is cut into equal lengths and stacked evenly in a rack. which geometric shape can be used as a model to calculate the volume of the cord of wood?
To estimate the volume of the chord of wood, since the wood exists cut into equal lengths and stacked evenly in a rack then we can use a cylinder as a model.
What is a cylinder?In mathematics, a cylinder exists as a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases exist normally circular (like a circle) and the center of the two bases exists joined by a line segment, which exists named the axis.
A cylinder exists as a closed solid that contains two parallel circular bases joined by a curved surface.
To calculate the volume of the chord of wood, since the wood exists cut into equal lengths and stacked evenly in a rack then we can use a cylinder as a model.
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help help help help help help help help help help help
Solving the quadratic equation we conclude that:
The maximum height is 45ft.The rocket is 18 seconds in the air.How to get the maximum height of the rocket?
The height of the rocket is defined by the quadratic equation:
[tex]d = 90t - 5t^2[/tex]
The maximum height is what we get in the vertex of the quadratic equation, such that for this quadratic equation, the vertex is at:
[tex]t = -90/(2*-5) = 9[/tex]
So the maximum height is what we get when we evaluate in t = 9:
[tex]d = 90*9 - 5*9^2 = 45[/tex]
The maximum height is 45ft.
How to get the time in the air?Now we need to solve the equation for the largest value of t:
[tex]d = 90*t - 5t^2 = 0[/tex]
Rewriting it, we get:
[tex]0 = 90*t - 5*t^2\\\\0 = t*(90 - t*5)[/tex]
The maximum solution is what we get when:
0 = 90 - t*5
t = 90/5 = 18
The rocket is 18 seconds in the air.
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Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°
Prove: △HKJ ~ △LNP
Triangles H K J and L N P are shown. Triangle L N P is smaller and to the right of triangle H K J.
Statement Reason
1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° 1. given
2. m∠H + m∠J + m∠K = 180° 2. ?
3. 30° + 50° + m∠K = 180° 3. substitution property
4. 80° + m∠K = 180° 4. addition
5. m∠K = 100° 5. subtraction property of equality
6. m∠J = m∠P; m∠K = m∠N 6. substitution
7. ∠J ≅ ∠P; ∠K ≅ ∠N 7. if angles are equal then they are congruent
8. △HKJ ~ △LNP 8. AA similarity theorem
Which reason is missing in step 2?
CPCTC
definition of supplementary angles
triangle parts relationship theorem
triangle angle sum theorem
Answer:
triangle angle sum theorem
Step-by-step explanation:
The missing statement is one that justifies the sum of the angles in a triangle being 180°.
That justification is provided by the ...
triangle angle sum theorem
How would I solve this, converting the left side to a square root? -16 = r^3
[tex]-16=r^3\implies \sqrt[3]{-16}=\sqrt[3]{r^3}\implies \sqrt[3]{-16}=r\implies \sqrt[3]{-2^4}=r \\\\\\ \sqrt[3]{(-2)^3\cdot 2^1}=r\implies -2\sqrt[3]{2^1}=r\implies -2\sqrt[3]{2}=r[/tex]
Ben, Rob, Kelly, Carla and Manu organised a pizza party for their business group, They ordered one vegetarian, one cheese, and one Nutella pizza. After the party, three-fourths of vegetarian pizza, five-eights of cheese pizza, and 11/12 of
Nutella pizza are remaining. Once all guests left, they decided to split the pizza equally among themselves, what
fraction of the whole pizza does each person get?
Answer:
11/24 ths each
Step-by-step explanation:
Add the portions left...then divide by the five of them
3/4 + 5/8 + 11/12 = ? must find common denominator (24) and convert
(18 + 15+22) / 24 = 55/24 now divide by 5 (which is the same as mult by 1/5)
55/24 * 1/5 = 55/120 now simplify to 11/24
The table below shows the depth of water in a bathtub as it is being filled over time. The data can be modeled by a linear equation where x is the elapsed time in minutes and y is the depth of the water in inches. What does the y-intercept of the linear equation that models the data indicate?
The y-intercept of the linear equation that models the data indicates that:
There was 1 inch of water on the tub when the water was turned on.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, when x changes by 1, y changes by 2, hence the slope is of 2. Hence, since when x = 1, y = 3, when x = 0, y = 3 - 2 = 1, which means that the y-intercept is of 1, and the correct interpretation is:
There was 1 inch of water on the tub when the water was turned on.
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an empty rectangular tank is 80 cm long and 60 cm wide. water flows into the tank at a rate of 24 liter per minute. how long will it take to fill the tank to a height of 50 cm?
By definitions of volume and flow rate, it will take a time of 10 minutes to fill the tank to a height of 50 centimeters.
How long will it take to fill the tank at constant rate?
Herein we find the case of a rectangular tank being filled with water at constant flow are, which is dimensionally speaking, volume by time. We know that dimensions of the tank are described in centimeters, whereas flow rate is described in liters per minute. Please notice that a liter is equal to 1000 cubic centimeters:
t = [(80 cm) · (60 cm) · (50 cm) · (1 L / 1000 cm³)] / (24 L / min)
t = 10 min
By definitions of volume and flow rate, it will take a time of 10 minutes to fill the tank to a height of 50 centimeters.
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On a rectangular soccer field, Sang is standing on the goal line 20 yards from the corner post. Jazmin is standing 99 yards from the same corner post on the nearest adjacent side of the field. What is the distance from Sang to Jazmin?
A. 119
B. 101
C. 10,201
D. 1,980
The distance from Sang to Jazmin is 101 yards.
What is the distance from Sang to Jazmin?
From the discussion in the question, we can see that the positions of Sang and Jazmin can be construed to give a rectangle. We know that the rectangle is a four sided figure.
The diagonal is a line that is drawn from one side of the four sided figure to another. Hence we can be able to apply the Pythagoras theorem to obtain the distance from Sang to Jazmin.
From;
c^2 = a^2 + b^2
c = √a^2 + b^2
c = √(20)^2 + (99)^2
c = 101 yards.
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