The solution to the expansion of each polynomial is;
1. (x + 9)(x² - 9x + 81) = x³ + 729
2. (y² - 7)(y⁴ - 7y² + 49) = y⁶ − 14y⁴ + 98y² - 343
3. (x² - 5)(x⁴ + 5x² + 25) = x⁶ - 125
4. (8x - 9y)(64x² + 72xy + 81y²) = 512x³ - 729y³
5. (10m - 11) (100m² + 110m + 121) = 1000m³ - 1331
How to expand polynomials?
1) We want to expand the polynomial;
(x + 9)(x² - 9x + 81)
= x³ + 729
2) We want to expand the polynomial;
(y² - 7)(y⁴ - 7y² + 49)
Multiplying out gives;
y⁶ −7y⁴ + 49y² −7y⁴ + 49y² - 343
Combining like terms gives;
y⁶ − 14y⁴ + 98y² - 343
3) We want to expand the polynomial;
(x² - 5)(x⁴ + 5x² + 25)
Multiplying out gives;
x⁶ - 125
4) We want to expand the polynomial;
(8x - 9y)(64x² + 72xy + 81y²)
Multiplying out gives;
512x³ - 729y³
5) We want to expand the polynomial;
(10m - 11)(100m² + 110m + 121)
Multiplying out gives;
1000m³ - 1331
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Find a polynomial function with leading coefficient 1 that has the given zeros, multiplicities, and degree. zero: 1, multiplicity: 2 zero: 2, multiplicity: 2 degree: 4
Polynomial expression for the given conditions is formulated in the equation
y(x)=1*(x-2)^3(x-0)^2
The polynomial for the conditions with leading coefficient 1 that has the given zeros, multiplicities, and degree. Zero: 2, multiplicity: 3 Zero: 0, multiplicity: 2 Degree: 5 is given as
According to the given condition
The given conditions to write the polynomial equations are as follows
Zero 2 and Multiplicity 3
Zero 0 and Multiplicity 2
Degree of polynomial expression = 5
The leading coefficient of polynomial expression = 1
Let us consider the polynomial equation has only one variable and hence in the general form we can write the equation of polynomial as follows
From the general form of polynomial expression as shown in equation (1) we can write
Polynomial expression for the given conditions is formulated in the equation
y(x)=1*(x-2)^3(x)^2-------(2)
So the polynomial for the conditions given in the question is expressed as
y(x)=1*(x-2)^3(x)^2
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Find the exact solution of x.
X²=16
X=4
No solution
X=_+4
X=-4
Answer:
(-4, 4)
Step-by-step explanation:
x can be either negative 4 or positive 4. A negative number squared is a negative number times a negative number, which will be a positive number.
What is the solution to the equation below? 4+square root of x =10
Please help with problem 24
Answer: Domain: All real numbers
Range: y<-2, y>=0
Step-by-step explanation:
Domain: All real numbers ==> x can be less than zero and greater than or equal to zero.
Range: y<-2, y>=0
-x-2, x>0
-x-2+2, x>2
-x, x>2
x, x<-2
y, y<-2
-x, x<=0
x, x>=0
y, y>=0
Answer:
Step-by-step explanation:
Domain 5
range 2
Name a point that is collinear with the given points.
Answer: Three or more points that lie on the same line are called collinear point.
Example : the points A, B and C lie on the line m. They are collinear
Step-by-step explanation: i really hope this helps somehow (: btw lmk if i am wrong
In a survey of 232 professional athletes, it was found that 121 of them owned a convertible, 100 of them owned a giant screen tv, and 93 owned a sporting goods store. 18 owned a convertible and a store, 38 owned a tv and a store, and 54 owned a covertible and a tv. 5 owned all three items. how many athletes did not own any of the three items? how many owned a covertible and a tv, but not a store? how many athletes owned a convertible or a tv? how many athletes owned exactly one type of item in the survey? how many athletes owned at least one type of item in the survey? how many owned a tv or a store, but not a convertible?
In a survey of 232 professional athletes, 23 athletes do not own any of the three items. 49 owns a convertible and a tv, but not a store. 163 athletes owns a convertible or a tv. 109 athletes owns exactly one type of item in the survey. 209 athletes owns at least one type of item in the survey. 55 owns a tv or a store, but not a convertible.
Using Venn diagram, a diagram used to present the relationship between sets in a logical form, we analyze the given information.
athletes who do not own any of the three items = 232 - (121 + 100 + 93) +(54 + 38 + 18) - 5 = 23
athletes who owns a convertible and a tv, but not a store = 54 - 5 = 49
athletes who owns a convertible or a tv = (121 + 93) - (18 + 38 - 5) = 163
athletes who owns exactly one type of item in the survey = (121 - 54 - 18 + 5) + (100 - 38 - 54 + 5) + (93 - 18 - 38 + 5) = 109
athletes who owns at least one type of item in the survey = 121 + 100 + 93 - 54 - 38 - 18 + 5 = 209
athletes who owns a tv or a store, but not a convertible = (100 - 54 -38 + 5) + (93 - 18 - 38 + 5) = 55
See attached photo for reference.
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5x+3-2x=7x+3 sometimes always never
The true statement is sometimes true
How to determine the true statement?The equation is given as
5x + 3 - 2x = 7x + 3
Evaluate the like terms on each side of the equation
So, we have
3x + 3 = 7x + 3
Evaluate the like terms on both sides
4x = 0
Divide both sides by 4
x = 0
This means that the equation is only true when x = 0
Hence, the true statement is sometimes true
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determine whether the data described are discrete or continuous. relative humidity levels in operating rooms at local hospitals.
The data for relative humidity levels in operating rooms at local hospitals must be continuous.
For given question,
Continuous data is a type of numerical data that refers to the unspecified number of possible measurements between two points.
These numbers are not always clean and tidy like those in discrete data, as they're usually collected from precise measurements.
Variables in these data sets often carry decimal points.
When values in a data set are countable and can only take certain values, it is called discrete data.
In this question,
we need to find the type of data for relative humidity levels in operating rooms at local hospitals.
The data records of relative humidity levels carry decimal points.
Therefore, the data for relative humidity levels in operating rooms at local hospitals must be continuous.
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A = 1/4 0b^3c
need this rn algebra 1 will give a lot of points
Answer: c=[tex]\frac{4A}{b^3}[/tex]
Step-by-step explanation:
A = 1/4b^3c
A*4=4*1/4b^3c
4A=4/4b^3c
4A=b^3c
c=4A/b^3
c=[tex]\frac{4A}{b^3}[/tex]
Nathan and Steven stacked boxes on a shelf. Nathan lifted 13 boxes and Steven lifted 15 boxes. The boxes that Nathan lifted each weighed 12 lb more than the boxes Steven lifted.
Let s represent the weight of the boxes that Steven lifted.
Which expression represents the total number of pounds Nathan lifted?
A. s + 12
B. 15(s+12)
C. 12(s+13)
D. 13(s+12)
Answer:
we assume the two boys lifted the same amount of weight of boxes. Let s be the weight of the boxes Steven lifted. Hence,
Step-by-step explanation:
13 ( s+12) = 15 s
where s + 12 means that the box lifted by Nathan weighed 12 more than that of Steven.
we solve,
s = 78 pounds
such that Nathan's is 90 pounds.
you would like to investigate whether smokers are more likely than nonsmokers to get lung cancer. you take the students in your class, select half at random and tell them to smoke a pack of cigarettes each day, and you tell the other half not to ever smoke. fifty years from now, you will analyze whether more smokers than nonsmokers got lung cancer. is this an experiment or an observational study? experiment observational study summarize at least three practical difficulties with this planned study.
The following given task is an experiment.
What do we mean by an experiment?An experiment is a procedure that is carried out to support or refute a hypothesis, or to determine the efficacy or likelihood of something that has never been tried before. Experiments shed light on cause-and-effect relationships by demonstrating what happens when a specific factor is changed. Experiments vary greatly in goal and scale, but they all rely on repeatable procedures and logical results analysis. Natural experimental studies are also available.So,
The following given task is an experiment.
Telling someone to start smoking a pack of cigarettes every day endangers their health. The other half, who are told not to smoke, may do so at their leisure. In the end, it will be difficult to track who smoked and who did not over the course of 50 years, and whether they did so consistently.Therefore, the following assignment is an experiment.
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How many lengths of wire, each are 3 7/8 inches long , can be cut from a 25ft roll?
Number of [tex]3\frac{7}{8}[/tex] inches length wire that can be cut from 25ft roll is 77
Given,
The total length of the roll =25 foot
Length of each wire = [tex]3\frac{7}{8}[/tex] inches
First we have to convert mixed fraction to simple fraction
[tex]3\frac{7}{8}=\frac{31}{8}[/tex] inches
Convert foot to inches
25 foot = 25×12 =300 inches
Number of [tex]3\frac{7}{8}[/tex] inches length wire that can be cut from 25ft roll = Total length of the roll/ Length of each wire
=300÷[tex]\frac{31}{8}[/tex]
=77.41
≈77
Hence, the number of [tex]3\frac{7}{8}[/tex] inches length wire that can be cut from 25ft roll is 77
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I need help with decimals asap 100 points
need help fast
Answer:
f. 8.0
g. 34.4
h. 83.8
i. 121
j. 35.2
Step-by-step explanation:
f. 4.1 + 3.9 = 8.0
g. 23.1 + 7.6 + 3.7 = 34.4
h. 53.2 + 3.1 + 27.5 = 83.8
i. 11.1 + 17.3 + 92.6 = 121
j. 24.1 + 7.9 + 3.1 = 35.2
how do I turn this into an equation to solve for x
To solve the for x the equation will be 3x° = 80° - x° and the value of x is 20°.
When two or more lines meet at a common point it is known as intersecting lines.
According to the question we have been given that there are two lines who are intersection at a point. And we have been given measure of two angles.
Let the first angle be given as ∠A and the second angle be given as ∠B.
The measure of angles given to us are :
∠A = 3x° and ∠B = (80 - x)°
We know that when two lines intersect then the vertically opposite angles are equal, that is
∠A = ∠B
Putting the required values we get
3x° = 80° - x°
4x° = 80°
x = 20°
Hence the value of x = 20°. Thus the measure of ∠A = 60° and ∠B = 60°
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Help asap! 45 pts!
What is the third reason in the angle proof?
∠2≅∠3 because ∠1≅∠2 and ∠1≅∠3. Hence proved.
Given that, AD bisects ∠BAC and ∠1≅∠3.
What is an angle bisector?An angle bisector is defined as a ray, segment, or line that divides a given angle into two angles of equal measure. The word bisector or bisection means dividing one thing into two equal parts.
Since AD bisects ∠BAC, ∠BAD=∠DAC.
That is ∠1≅∠2 (AD bisects ∠BAC into two equal angles)
Since ∠1≅∠2 and ∠1≅∠3 (given)
We get, ∠2≅∠3
∠2≅∠3 because ∠1≅∠2 and ∠1≅∠3. Hence proved.
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a student records the repair cost for 1717 randomly selected tvs. a sample mean of $73.10$73.10 and standard deviation of $16.01$16.01 are subsequently computed. determine the 90�% confidence interval for the mean repair cost for the tvs. assume the population is approximately normal.
Therefore, the 90% confidence interval for the mean repair cost for the VCRs is ($82.40,$90.12).
What do you mean by the term Repair cost?Subject to the exclusions outlined in this clause, the repair cost is defined as the cost of the parts and labor required to fix or replace any covered component as a result of a covered mechanical breakdown. We reserve the right to substitute components of comparable sort and quality, whether they are new, OEM, swapped, rebuilt, remanufactured, or used. The suggested retail price of a part of a like type and quality, or the manufacturer's indicated retail price for Your Vehicle, whichever is higher, may not be exceeded when pricing out parts. A current, widely used flat-rate labor guide will be used to calculate labor costs. According to state-specific rules, the Repair Cost includes the necessary taxes related to the covered Mechanical Breakdown.
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Solve the equation for the red variable.
please help :(
Answer:
V = [tex]\frac{Bh}{3}[/tex]
Step-by-step explanation:
B = 3 × [tex]\frac{V}{h}[/tex] ( multiply both sides by h to clear the fraction )
Bh = 3V ( divide both sides by 3 )
[tex]\frac{Bh}{3}[/tex] = V
Tammy earns 51 dollars per week working part time at a book store. She makes one dollar more for each book that she sells. The amount, A(in dollars), that Tammy earns in a week If she sells b books is given by the following function A(b)= 51+bHow much does Tammy earn in a week if she sells books?
I dont understand how to do this.
Drag and drop the range of each data set into the boxes
The range of data set 1 is 20 and the range of data set 2 is 25.
From the given figure, the observations in data set 1 are 20, 25, 25, 25, 30, 30, 30, 35, 35 and 40.
The observations in data set 2 are 35, 40, 40, 45, 45, 45, 50, 50, 55 and 60.
What is the range?In statistics, the range of a set of data is the difference between the largest and smallest values, the result of subtracting the sample maximum and minimum. It is expressed in the same units as the data.
From data set 1:
Highest observation = 40 and lowest observation = 20.
So, range = 40-20=20
From data set 2:
Highest observation = 60 and lowest observation = 35.
So, range = 60-35=25
Therefore, the range of data set 1 is 20 and the range of data set 2 is 25.
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The Nile river is 4,160 miles long.the Amazon river is 25/26 as long as the Nile river.how long is the Amazon river
Step-by-step explanation:
Multiple the ratio by Nile river distance
Evaluate the expression 11-8 on top and on bottom is 1+7•2
Answer:
1/5
Step-by-step explanation:
because 3/15
Hey there!
(11 - 8)/(1 + 7 * 2)
= (3)/(1 + 14)
= 3/15
≈ 3 ÷ 3 / 15 ÷ 3
≈ 1/5
≈ 0.2
Therefore, your answer should be:
1/5 or 3/15
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
(2.3 x 105)(1.5 x 104) in scientific notation plssss ASAP
By using scientific notation we calculated (2.3[tex]\times[/tex]10⁵)(1.5 [tex]\times[/tex]10⁴) we got 345 [tex]\times[/tex]10⁷.
Given that,
(2.3[tex]\times[/tex]10⁵)(1.5 [tex]\times[/tex]10⁴)
By using scientific notation
The scientific notation allows us to express extremely large or extremely small numbers by multiplying them by single-digit integers and by 10 raised to the power of the corresponding exponent. The exponent is either positive or negative depending on how big or little the number is.
Now, we calculate
(2.3[tex]\times[/tex]10⁵)=2.5[tex]\times[/tex]100000=230000
(1.5 [tex]\times[/tex]10⁴)=1.5[tex]\times[/tex]10000=15000
Now,
=230000[tex]\times[/tex]15000
=3450000000
=345 [tex]\times[/tex]10⁷
Therefore, By using scientific notation we calculated (2.3[tex]\times[/tex]10⁵)(1.5 [tex]\times[/tex]10⁴) we got 345 [tex]\times[/tex]10⁷.
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There are 5 adults and 8 children in a group. what is the total cost for the group to ride the Ferris wheel??
If a group of 5 adults and 8 children, went for a ride of the Ferris wheel, and if the ticket cost $1 per person, irrespective of age, then total cost of tickets for the whole group will be $13.
As per the question statement, a group of 5 adults and 8 children, went for a ride of the Ferris wheel and the ticket costed $1 per person, irrespective of age.
We are required to calculate the total cost of tickets for the whole group.
Since the ticket cost was same for persons of all ages, therefore, total members of the group who wanted to ride the Ferris wheel was
(8 + 5) = 13.
As per the Unitary method, we have to calculate the value of 13 tickets from the data on the value of a single ticket provided to us in the question statement, i.e., we simply need to multiply the number of tickets with the cost of a single ticket to obtain our desired answer.
Therefore, cost of 13 tickets with each ticket costing $1 is [tex](13*1)=13[/tex] Dollars.
Unitary Method: In Mathematics, the unitary method is a technique of solving a problem, where first, we find the value of a single unit, and then find the required value by multiplying the value of the single unit.To learn about Unitary Method, click on the link below.
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Find the distance between the pair of points. Round to the nearest tenth, if necessary. (-4,-5) (0,5)
The distance between the two points ( − 4 , - 5 ) and ( 0 , 5 ) is 10 units.
We are given the two points:
( − 4 , - 5 ) and ( 0 , 5 )
We need to find the distance between the two points.
The formula for distance is given as:
Distance = √ (x₂ - x₁)² + (y₂ - y₁)²
Substituting the values, we get that:
Distance = √ ( 0 + 4 )² + ( 5 + 5)²
Distance = √ ( 4 )² + ( 10 )²
Distance = √ 16 + 100
Distance = √ 116
Distance = 2 √29 units.
Therefore, we get that, the distance between the two points ( − 4 , - 5 ) and ( 0 , 5 ) is 2 √29 units.
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Marko can bike at an average speed of 534 minutes per mile. He bikes at this speed for 8614 minutes.
How many miles does Marko bike?
Answer:
Marko bikes approximately 16.13 miles.
A very slow rate.
Step-by-step explanation:
average speed = 534 minutes per mile
time taken = 8614
d = t/s
distance = 8614 / 534
= 16.13 miles
f(x) = (½)x + 3
Rate of change ?
End behavior?
The rate of change is 1/2.
the end behavior of the function is:
as x → ∞, f(x) → ∞
as x → -∞, f(x) → -∞
What is the rate of change?
Here we have a simple linear function:
y = (1/2)*x + 3
Remember that for a general linear function we have:
y = a*x + b
Where a is the rate of change and b is the y-intercept.
Then comparing our function with the general one, we can see that the rate of change is 1/2.
Now, because the rate of change is positive, we can see that when x tends to infinity the function also tends to infinity.
And when x tends to negative infinity also does f(x).
Then the end behavior of the function is:
as x → ∞, f(x) → ∞
as x → -∞, f(x) → -∞
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Which letter is at position (1, 3)?
OA. S
OB. M
OC. U
OD. N
Answer:
u has position brobjdidiodd
Given AB where A (3,4) and B (-1,-2), translate left 2 and up 1, then rotate 90 degrees clockwise about the point C(1,3). Graph and list the coordinates of A"B"
pls help urgently!!!!
The coordinates of the ends of the line segment A''B'' are A''(x, y) = (3, 3) and B''(x, y) = (- 1, 7), respectively. The graph of the line segment is attached aside.
What are the coordinates of the image of a line segment?
In this problem we must find the coordinates of a new line segment, generated after making translations and rotation, two kinds of rigid transformations. First, determine the coordinates of the ends of the line segments by translation formula:
A'(x, y) = (3, 4) + (- 2, 1)
A'(x, y) = (1, 5)
B'(x, y) = (- 1, - 2) + (- 2, 1)
B'(x, y) = (- 3, 1)
Second, determine the coordinates of the ends of the line segment by using the rotation formula:
A''(x, y) = O(x, y) + ((A'x - Ox) · cos θ - (A'y - Oy) · sin θ, (A'x - Ox) · sin θ + (A'y - Oy) · cos θ)
A''(x, y) = (1, 3) + ((1 - 1) · cos (- 90°) - (5 - 3) · sin (- 90°), (1 - 1) · sin (- 90°) + (5 - 3) · cos (- 90))
A''(x, y) = (1, 3) + (2, 0)
A''(x, y) = (3, 3)
B''(x, y) = O(x, y) + ((B'x - Ox) · cos θ - (B'y - Oy) · sin θ, (B'x - Ox) · sin θ + (B'y - Oy) · cos θ)
B''(x, y) = (1, 3) + ((- 3 - 1) · cos (- 90°) - (1 - 3) · sin (- 90°), (- 3 - 1) · sin (- 90°) + (1 - 3) · cos (- 90))
B''(x, y) = (1, 3) + (- 2, 4)
B''(x, y) = (- 1, 7)
The coordinates of the ends of the line segment A''B'' are A''(x, y) = (3, 3) and B''(x, y) = (- 1, 7), respectively. The graph of the line segment is attached aside.
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Becky feeds her cat 55 g of cat food per day. About how many ounces of cat food will she feed her cat in 4 weeks? {1 oz ≈ 28.3 g}
13.6 oz
54.4 oz
1.9 oz
220 oz
The ounces of cat food she will feed her cat in 4 weeks is 54.4 oz
How to determine the number of feet?The given parameters are
1 oz = 28.3 g
1 day = 55 g
For 4 weeks, the amount would be
1 * 7 * 4 days = 55 g * 4
So, we have
28 days = 1540 g
Rewrite as
4 weeks =1540 g
Recall that 1 oz = 28.3 g
So, we have:
4 weeks = 54.4 oz
Hence, the ounces of cat food will she feed her cat in 4 weeks is 54.4 oz
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