1) Factorizing the expression x⁶ - 729 is; (x + 3)(x - 3)(x⁴ + 9x² + 81)
2) Solving the equation 2x² + 16x – 11 = -7 by completing the square is; x = -4 + √18 or -4 - √18
3) Factorizing x⁴ – 5x² – 36 over the complex numbers is; (x + 3i)(x - 3i)(x + 2)(x - 2)
How to factorize expressions?
1) We are given the expression; x⁶ - 729
It can also be written as;
(x²)³ - 9³
Now, from factorization of algebra, we know that;
a³ - b³ = (a - b)(a² + ab + b²)
Thus;
(x²)³ - 9³ = (x² - 9)((x²)² + 9x² + 9²)
= (x² - 9)(x⁴ + 9x² + 81)
= (x + 3)(x - 3)(x⁴ + 9x² + 81)
2) We want to solve the equation 2x² + 16x – 11 = -7 by completing the square.
Add 7 to both sides to get;
2x² + 16x – 11 + 7 = -7 + 7
2x² + 16x – 4 = 0
Divide through by 2 to get;
x² + 8x – 2 = 0
Add 2 to both sides to get;
x² + 8x = 2
Take half of the x term and square it and then add the result to both sides to get;
x² + 8x + 16 = 2 + 16
Rewrite the perfect square on the left to get;
(x + 4)² = 18
Take square root of both sides to get;
x + 4 = ±√18
Subtract 4 from both sides to get;
x = -4 ± √18
x = -4 + √18 or -4 - √18
3) We want to factorize x⁴ – 5x² – 36
Using the difference of squares identity, we know that;
a² - b² = (a + b)(a - b)
Thus;
x⁴ – 5x² – 36 = (x² + 9)(x² - 4)
Now, (x² + 9) factored over the complex numbers gives;
(x² + 9) = (x + 3i)(x - 3i)
Thus;
x⁴ – 5x² – 36 = (x + 3i)(x - 3i)(x + 2)(x - 2)
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!!!!!!!URGENT PLEASE!!!!!!!!!
The area of the given sector is 98.2 sq. units.
What is area of a sector?The area of a sector is the space inside the section of the circle created by two radii and an arc.
The area of a sector is a fraction of the area of the entire circle.
Mathematically, the area of a sector is given as;
A = θ/360 (πr²)
where;
r is the radius of the circleθ is the angle subtended by the sectorThe area of the given sector is calculated as follows;
In the given diagram, θ = 50⁰, r = ST = UT = 15 units
A = (50/360) x (π x 15²)
A = 98.2 sq. units
Thus, the area of the given sector is 98.2 sq. units.
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What plane contains points E, F, and H?
Greetings from Brasil...
Just take the cross product of the vectors EF and EH. The result will be a vector n. This vector (n) will help in the equation of the plane
vector EF = point F - point E
vector EH = point H - point E
check the attachment
according to the example in the annex, we notice that the points E, F and G are in the plane whose equation will be:
π : 6X + 9Y + 5Z + 1 = 0
.........................................................................
Answer: [tex]\frac{8}{4}[/tex] = 2
Step-by-step explanation:
5 - 3 = 2
2 x 2 x 2 x 2 = 16
24 - 16 = 8
[tex]\frac{8}{4}[/tex]
Simplify
[tex]\frac{8}{4}[/tex] = 2
What is the length of the hypotenuse of a 45°-45°-90° triangle if the leg length is 6 centimeters?
The length of the hypotenuse of a 45°-45°- 90° triangle with a leg length of 6 centimeters is 8.49 approximately.
To find the hypotenuse of 45°-45°-90° triangle:
The formula to calculate the hypotenuse of 45°-45°-90° triangle is to multiply the length of the leg by [tex]\sqrt{2}[/tex].
How to find the length of the hypotenuse?
The length of the two legs of 45°-45°-90° triangle is equal.
Then the length of its hypotenuse will be calculated by multiplying the length of the leg and [tex]\sqrt{2}[/tex] .
Since the length of the leg is 6 centimeters,
Then its hypotenuse will be:
h = 6 × [tex]\sqrt{2}[/tex]
h = 8.485
h ≈ 8.49
So, the length of the hypotenuse will be 8.49.
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For the following system use the second equation to make a substitution for y in the first equation. 2x + y = 6 y = 3x + 4
Answer:
2x + y= 6 y= 3x +4
Step-by-step explanation:
2x + (3x + 4) = 6(3x + 4)
HELP ME so I'm really bad at math patterns anyways Queen Diana slays and I really need help look at the picture and please help me it's a quiz so I'm making lots of Bowl accounts cuz I don't know how to do multiple answers just please y'all please
Answer:
Option 3
Step-by-step explanation:
1b. Ralf gives $2 to Susie. Calculate the new ratio Ralf's money: Susie's money. Give your answer in its simplest form.
Answer:
2$!$! jdnznwi bdbejsn uebeij737 y
Do invariant points sometimes, always, or never occur in a rotation? Explain your reasoning.
Points that map onto themselves are said to be invariant points. Invariant points can occasionally appear during a rotation.
Do rotations have invariant points?
The axis of rotation is a line of invariant points that defines the rotation of a three-dimensional figure in space. Since rotation does not alter the shape of the figure being rotated, it is referred to as an isometric transformation along with translation and reflection.Points that map onto themselves are said to be invariant points. Invariant points can occasionally appear during a rotation.
The point of rotation is invariant when a figure is rotated about that point. There are no invariant points in a rotation of a figure centered on a point that is not on the figure.
Point P is an invariant point in the rotation shown below.
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Ms.Nishino uses Zipcar, a rental car service. She only wants to spend $75.00 each month.ziper charges $25 a month, plus $12.50 per hour of car rental.
Write an equation that could be used to solve for h, the number of hours Ms.Nishino can rent from Ziper each month.
The equation is 12.50h + 25= 75
The number of hours is 4
How to calculate the number of hours ?Ms Nishino uses zipcar
She only wants to spend $75 each month
Zip charges $25 a month plus $12.50 per hour of car rental
The equation can be written as follows
12.50h + 25= 75
collect the like terms
12.50h= 75-25
12.50h= 50
h= 50/12.50
h= 4
Hence the number of hours Ms.Nishino can rent from Ziper each month is 4 hours
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The table shows the race time for Jon, who competed in three different youth triathlons.
A 4-column table with 4 rows titled Jon's Youth triathlon results. Column 1 is labeled Month with entries May, June, August. Column 2 is labeled Swim times (minutes) with entries 10.06, 9.5, 8.25. Column 3 is labeled Bike times (minutes) With entries 15.05, 13.0, 12.75. Column 4 is labeled Run times (minutes) with entries 24.25, 23.7, 22.01.
What is Jon’s total time for the June triathlon?
9 . 5
1 3 . 0
+ 2 3 . 7
Adding the June amounts from the given table, his total time is of 46.2 minutes.
What is his June's total time?The times for the month of June are given by the second row, hence:
Swim: 9.5 minutes.Bike: 13 minutes.Run times: 23.7 minutes.Hence the total time is given as follows:
9.5 + 13 + 23.7 = 46.2 minutes.
His total time is of 46.2 minutes.
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Answer: 46.2 minutes.
Step-by-step explanation:
13. A model rocket is fired vertically into the air at 250 ft/s. The expression -16t² + 250t gives the rocket's
height after t seconds. Factor this expression.
Answer: X+7=19 what is x
Step-by-step explanation:
=) Let d be the distance the car has traveled
and lett be the time it has traveled, in
hours, set up a proportion relating d and t
and solve it for the variable d.
Answer:
guy yunby
Step-by-step explanation:
Huh uu.
Options:
the transitive postulate of inequality
addition postulate of inequality
the transitive postulate of equality
comparison postulate
the multiplication postulate of inequality
the reflexive postulate of equality
the symmetric postulate of equality
Please answer quickly i need help
The postulate of equality or inequality that is illustrated is the transitive postulate of equality
How to determine the postulate of equality or inequality that is illustrated?The illustrated expression is given as
If 1/4 + 1/4 = 2/4 and 2/4 = 1/4 then 1/4 + 1/4 = 1/2
In the above expression, we do not have any inequality sign
This means that the expression is an equation i.e. equality
The transitive postulate of equality states that
if a = b and b = c, then a = c
The given equality expression illustrates the transitive postulate of equality
i.e.
If 1/4 + 1/4 = 2/4 and 2/4 = 1/4 then 1/4 + 1/4 = 1/2
if a = b and b = c, then a = c
Hence, the postulate of equality or inequality that is illustrated is the transitive postulate of equality
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What is the least common denominator of 3/4 and 15/16
The least common denominator of 3/4 and 15/16 is 16.
What is Least Common Denominator?When two or more fractions are given, the least common denominator is the smallest number of all common multiples of the denominators. To find the least common denominator, list the multiples of both denominators until you find the smallest multiple shared by both. Because 28 is the first shared multiple of 4 and 7, it must be the least common denominator of these two fractions.So, LCD od 3/4 and 15/16:
3/4 × 4/4 = 12/1615/16 × 1/1 = 15/16Now, the denominator of both the fractions is the same which is 16.
Therefore, the least common denominator of 3/4 and 15/16 is 16.
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Describe a sequence of translations, rotations, and
reflections that takes polygon P to polygon Q.
Use the digital tracing paper if it helps you with your
thinking?
The polygon P is translated and rotated respectively to obtain polygon Q.
A translation is a geometric transformation when each point in a figure, shape, or space is moved in a specific direction by the same amount. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.
Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.
ABCD and EFGH are polygons P and Q respectively.
We will briefly outline each step required to convert each Polygon P into its corresponding Polygon Q in this question.
In this case, there is translation along a vector between point A and point H.
Then, when the polygon Q is rotated around point H.
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Factor out of the coefficent of the variables term
The expression 15/4+3/8xfactored is what?
Answer:
your answer is 33/8
Step-by-step explanation:
Answer:
fgehjenrntktkktmttbtbvtvt
Petra jogs 3 miles in 30 minutes. At this rate, how long would it take her to jog 12 miles?
Petra would take
minutes to jog 12 miles.
Answer:
So she takes around 10 minutes to jog 1 mile. So 12 miles would take her 122 minutes
Seaborgium-266 has a half-life of 30 seconds. how many half-lives will pass in 30 minutes?
Seaborgium-266 will have 60 half life in 30 minutes.
It is given in the question that Seaborgium-266 has a half life in 30 sec.
Since half life is given in seconds , convert 30 min in seconds .
1 min= 60 sec
so 30min= 30*60 sec
30 min= 1800 sec.
According to the question
30 sec = 1 half life
1 sec = 1/30 half life
For 1800 sec
[tex]1800 sec = 1800*\frac{1}{30}[/tex] half life
=60 half life
Therefore , Seaborgium-266 will have 60 half life in 30 minutes.
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What integers or number should be added to -5 to get 4?
Answer:
Here,
x+(-5) = 4
x = 4+5
x = 9
Therefore, 9+(-5) = 4
Given g(x) = -x − 3, find g(-3).
Answer:
0
Step-by-step explanation:
g(-3) = -(-3)-3
Z#
It is suggested that people that are less than or equal to 18 years of age or greater than or
equal to 50 years of age should be the first to get a flu vaccine. Define a variable and write a
compound inequality to describe this situation.
Vela
If it is suggested that people of age, less than or equal to 18 years and of age, greater than or equal to 50 years, should be the first to get a flu vaccine, then we can define a variable "A" to the age group suggested to be prioritized for to vaccinate with the flu vaccine, and the compound inequality to describe the situation can be written as [(A ≤ 18) or (A ≥ 50)].
As per the question statement, it is suggested that people of age, less than or equal to 18 years and of age, greater than or equal to 50 years, should be the first to get a flu vaccine.
We are required to define a variable to the age group suggested to be prioritized for to vaccinate with the flu vaccine, and describe the question mentioned situation in the form of a compound inequality.
To start with, let us first determine the variable. It is as simple as assuming any alphabet, say "A", to be the age group, suggested to be prioritized for to vaccinate with the flu vaccine.
Since, suggested that people of age, less than or equal to 18 years should be amongst the the first to get a flu vaccine, thus "A" must be less than equal to 18, i.e., [tex][A\leq 18][/tex]...(1)
Similarly, suggested that people of age, greater than or equal to 50 years should be amongst the the first to get a flu vaccine, thus "A" must be greater than equal to 50, i.e., [tex][A\geq 50][/tex]...(2)
Now, combining (1) and (2), we get our required compound inequality to be [(A ≤ 18) or (A ≥ 50)].
Compound Inequality: In mathematics, a compound inequality is an inequality that combines or "compounds" two simple inequalities with an "or" in the middle.To know more about compound inequality, click on the link below.
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NEED HELP ASAP! will rate 5 stars!!
A or D but i reckon A
Write an equation of the line in point-slope form through the pair of points. (9,5) and (8,2)
The general form of a linear equation is y - y1 = m(x - x1) then the point-slope form exists y - 5 = 3(x - 9)
What is point-slope form?The general structure of a linear equation exists y - y1 = m(x - x1). It draws attention to the line's slope and one of the line's points (that exists not the y-intercept).
Given: (x1, y1) = (9, 5) and (x2, y2) = (8, 2)
The point-slope form exists given by,
y - y1 = m(x - x1)
m = (y2 - y1)/(x2 - x1)
substitute the values in the above equation, we get
m = (2 - 5)/(8 - 9)
m = 3
The value of m = 3.
y - 5 = 3(x - 9)
Therefore, the point-slope form exists y - 5 = 3(x - 9).
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Last year, Molly earned $120 babysitting over her holiday break from school. This year, Molly earned $160 babysitting. Comparing the years of babysitting, by what percentage did her earnings increase? Round your answer to the nearest whole number.
A. 25%
B. 42%
C. 37%
D. 30%
E. 33%
Molly's earning increased by 25%
How to calculate the percentage increase ?Percentage increase formula is
Increase/ original value × 100
The first step is to calculate the increase by subtracting 120 from 160
160 -120
= 40
Therefore the percentage increase can be calculated as follows
= 40/160 × 100
= 0.25 × 100
= 25
Hence Molly's earnings increased by 25%
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Which of the following is not a step that can help you establish and maintain a good credit history?
a. Open a bank account.
b. Purchase a cell phone contract and pay it on time and in full every month.
c. Make car payments and car insurance on time.
d. Open many credit card accounts.
e. All of the above steps help establish good credit history.
Answer:
e, all of the above steps help establish good credit history
Step-by-step explanation:
Answer: E.
Hope this helps.
Write the specified proof for following theorem.
Theorem 10.7, two-column proof
The ray, line, or line segment that divides an angle into two congruent angles is known as an angle bisector.
What are two column proofs used for in geometry?There are 4 important elements to notice about two-column proofs.
1) The first column exists utilized to write math statements.
2) The second column exists utilized to write the reasons you make those statements.
3) The statements are numbered and follow a logical order.
What is meant by angle bisector?The angle bisector theorem in geometry is concerned with the relative lengths of the two segments of a triangle's side that are divided by a line that bisects the opposite angle. It compares their lengths to the lengths of the other two sides of the triangle.
The ray, line, or line segment that divides an angle into two congruent angles is known as an angle bisector.
Let CB bisects [tex]\angle[/tex] ABD and [tex]\angle[/tex] ACD
[tex]\angle[/tex] ABC ≅ [tex]\angle[/tex] DBC (Definition of angular bisector)
[tex]\angle[/tex] BC ≅ [tex]\angle[/tex] BC (Reflexive Property)
[tex]\angle[/tex] ACB ≅ [tex]\angle[/tex] DCB (Definition of angular bisector)
[tex]\triangle[/tex] ABC ≅ [tex]\triangle[/tex] DBC (ASA)
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Paris is preparing for the 2024 Olympics. Their newly built single-depth olympic size swimming pool (50m by 25m by 2m) needs to be filled up. If the water bill is equivalent to $1 per 1000 gallons, roughly how many dollars will it cost to fill up the pool?
There will be 660.425 dollars cost to fill up the pool.
The newly built single-depth olympic size swimming pool (50m by 25m by 2m) needs to be filled up.
Here,
Length of swimming pool = 50m
Width of swimming pool = 25m
Depth of swimming pool = 2m
What is the volume of the cuboid?The volume of a cuboid is equal to the product of the length, width, and height of a cuboid.
The volume of a cuboid is length × breadth× height
As it is 3D geometry
The volume will be L×W×H i.e. 50×25×2 = 2500 m³
Since one cubic meter is equal to 264.172052 gallons,
So 2500 m³ = 264.17 × 2500 = 660425 gallons
If the water bill is equivalent to $1 per 1000 gallons
So 660425/1000 = 660.425
Hence, there will be 660.425 dollars cost to fill up the pool.
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Please help me with this.
Step-by-step explanation:
a)
high positive x (x going to +infinity) would create high positive y (also +infinity).
while high negative x (x going to -infinity) would create high negative y (also -infinity), x⁵ with its odd exponent is negative for negative x and positive for positive x.
the graph is showing just the opposite behavior.
so, it cannot be the right graph.
b)
the degree of the polynomial is the highest exponent of the input variable x. in our case : 5
a polynomial of degree n must have n zeros (or roots).
in our case we need 5 zeros. but there are only 3. no matter how we shift it up or down, the x-axis will not intercept it more than 3 times.
so it cannot be the right graph.
The fourth-grade class donated 750 bottles of water for a 5K run. After the run, there were 89 bottles left. How many bottles of water did the runners drink?
Answer:
The runners drank 661 bottles of water.
Step-by-step explanation:
Subtract 661 from 750, and you are left with 89.
∠E and ∠F are supplementary. If m∠E=9x-38 and m∠F=2x+42. find m∠f=
Answer:
The measure of angle F is 74°.
Step-by-step explanation:
[tex]9x - 38 + 2x + 42 = 180[/tex]
[tex]11x + 4 = 180[/tex]
[tex]11x = 176[/tex]
[tex]x = 16[/tex]
For angle F: 2(16) + 42 = 32 + 42 = 74°
