Determine whether the given function is a polynomial function. If it's a polynomial function, state the degree. If not, state the reason why.
k(x) = –3x6 – 0.7x + x3
A. Yes; degree 10
B. No, because some range elements correspond to more than one domain element
C. No, because 0.7 isn't an integer
D. Yes; degree 6
ANSWER
The correct answer is option D.
EXPLANATION
The given function is
[tex]k(x)=-3x^6-0.7x+x^3[/tex]
This a polynomial function. All degrees are greater than or equal to zero.
The coefficient being decimals does not disqualify it from being a polynomial.
The highest degree of this polynomial is 6.
Therefore the correct answer is D
Please help asap 30 pts
7x > -35 |divide both sides by 7
x > -5
---------------------
3x ≤ 30 |divide both sides by 3
x ≤ 10
-5 < x ≤ 10
Answer: b.
A cheetah can go from a state of testing to running at 20 m/s in just 2 seconds. What is the cheetahs average acceleration?
5 times a number, subtracted from six, is triple the number
Final answer:
The algebraic equation based on the statement '5 times a number, subtracted from six, is triple the number' is 6 - 5x = 3x. Solving for 'x' gives us x = 3/4.
Explanation:
The student's question involves creating an algebraic equation based on a verbal statement. To translate the statement '5 times a number, subtracted from six, is triple the number' into an equation, let's use 'x' to represent the unknown number. The statement can be written as: 6 - 5x = 3x. To solve for 'x', we need to get all terms involving 'x' on one side and constants on the other. Here's how you can do it:
Add 5x to both sides of the equation to get: 6 = 3x + 5x
Combine like terms: 6 = 8x
Divide both sides by 8 to get the value of x: x = 6/8
Simplify the fraction: x = 3/4
Therefore, the number in question is 3/4.
Please help asap 27pts
[tex]7x\geq-56\qquad|\text{divide both sides by 7}\\\\x\geq-8\\-------------------------------\\9x < 54\qquad|\text{divide both sides by 9}\\\\x < 6\\\\Answer:\ d)\ -8\leq x < 6[/tex]
The 6 in 63 represents how many times the value of the 6 in 46?
In 63, 6 is in the tenths place, meaning it represrents the number 60.
In 46, 6 is in the ones place, meaning it represents the number 6.
So, given that, in the first example 6 is x times the value of 6 in the second example:
x = 60 / 6
x = 10
Hope it helped,
BioTeacher101
The value of the digit 6 in the number 63 is 10 times the value of the digit 6 in the number 46.
Explanation:In the number 63, the 6 is in the tens place, meaning it represents 60 (6 tens). In the number 46, the 6 is in the ones place, meaning it simply represents 6 (6 ones). Therefore, the 6 in 63 is 10 times the value of the 6 in 46.
Learn more about Place Value here:https://brainly.com/question/35447631
#SPJ2
if f(x)=4x^2-6 and g(x)=x^2-4x-8,find (f-g)(x)
a.(f-g)(x)=x^2-14
b.(f-g)(x)=5x^2-4x-14
c.(f-g)(x)=3x^2+4x+2
d.(f-g)(x)=3x^2-4x-2
c. Due to c. and the equation above would be equal just in a different arrangement
Answer:
[tex](f-g)(x)=3x^2+4x+2[/tex]
C is correct
Step-by-step explanation:
Given: [tex]f(x)=4x^2-6[/tex]
[tex]g(x)=x^2-4x-8[/tex]
To find : (f-g)(x)
[tex](f-g)(x)=f(x)-g(x)[/tex]
[tex]\Rightarrow (4x^2-6)-(x^2-4x-8)[/tex]
using Distributive property
[tex]\Rightarrow 4x^2-6-x^2+4x+8[/tex]
[tex]\Rightarrow 4x^2-x^2+4x+8-6[/tex]
Combine like term
[tex]\Rightarrow 3x^2+4x+2[/tex]
[tex](f-g)(x)=3x^2+4x+2[/tex]
Hence, The composite function is [tex](f-g)(x)=3x^2+4x+2[/tex]
The registration period for the race is under way, and as the word is getting out, the number of participants registering is growing exponentially. The numbers from the first two days of registration are shown in the table.
Use the data in the table and the general form of an exponential growth equation, y= a(1 +r)^x, to write an equation modeling the exponential growth of registrations, where x is the number of days since registration opened, a is the initial number of registrations, r is the rate of growth of registrations per day, and y is the total number of registrations.
y = a(1 + r)ˣ
a = 15 "initial" means what you started with on the first day
r = 6 the rate it increased is the slope ([tex](\frac{21 - 15}{2 - 1})[/tex]
y = 15(1 + 6)ˣ
Answer: y = 15(7)ˣ
What can the zeros and intercepts of a quadratic function tell you about real world relationships?
Suppose, we are given a function
[tex]f(x)=ax^2+bx+c[/tex]
Application of Zeros:
we know that
zeros are x-intercepts
We know that zeros are values of x for which f(x)=0
and it has very wide application
It is extremely useful in real world applications such as finance, astronomy, geology, architecture, or physics
For exp:
[tex]h(t)=-16t^2 + 96t + 112[/tex]
Zeros will help us to find time at which ball reaches to ground
so, we set h(t)=0
and then we can solve for t
value of t are zeros
Application of y-intercept:
we know that y-intercepts are values of y at which x=0
It's application can be population , finance and physics etc
For exp:
[tex]h(t)=-16t^2 + 96t + 112[/tex]
we can find initial height of object after plugging t=0
[tex]h(0)=-16(0)^2 + 96(0) + 112[/tex]
[tex]h(0)=112[/tex]
so, body dropped from 112 feet
A moving company has a truck filled for deliveries to four different sites. If the order of the deliveries is randomly selected what is the probability that is the shortest route?
As there are 4 different sites so we have 4! possible arrangements to choose from so it becomes = [tex]4\times3\times2\times1=24[/tex]
And there will be only 1 shortest route out of these.
So the probability that the route selected is the shortest route becomes = [tex]\frac{1}{24}[/tex]
The question involves finding the probability of randomly arranging deliveries to four sites such that the arrangement corresponds to the shortest route. With 24 possible arrangements, only one of which constitutes the shortest route, the probability is 1/24.
Explanation:This question involves the concept of permutations in probability. If delivery sites are being randomly selected, there are 4! (4 factorial) possible sequences for the deliveries, i.e., 4*3*2*1 = 24 different routes.
Assuming that only one of these combinations constitutes the shortest route, the probability of randomly selecting the shortest route is therefore 1 out of 24. To obtain this, you divide the number of favorable outcomes (1 - because there's only one shortest route) by the total outcomes (24 - from 4 factorial).
So, "the probability of selecting the shortest route randomly is 1/24".
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ3
In math what does it mean by Define the varible?
Final answer:
To define the variable in mathematics means to assign symbols to represent quantities that can take various values, either as numerical variables measurable in the same units or as categorical variables for classification purposes. This allows for the exploration of relationships and predictions of outcomes.
Explanation:
In mathematics, the term 'define the variable' refers to the process of assigning a symbol, typically a letter such as X or Y, to represent a quantity that can take on various values. Variables can be of different types, such as numerical variables which represent values measurable in the same units like time in hours or weight in pounds, and categorical variables which classify individuals or items into categories, such as political affiliation.
For example, in the equation of a line y=mx+b, x and y are variables with x usually representing the independent variable plotted along the horizontal axis, and y as the dependent variable plotted on the vertical axis. The variable m represents the slope of the line, and b represents the y-intercept, or the point where the line crosses the y-axis. By defining each variable, a mathematician or an economist can explore the relationship between quantities and predict outcomes.
An example in statistics would be letting X represent the number of children in a family, making it a numerical variable, where each specific number of children would be represented by a lowercase x (0, 1, 2, 3, etc.). Conversely, if Y represents someone's political party, each category (Republican, Democrat, Independent, etc.) is an example of a categorical variable, which does not make sense to average mathematically like numerical variables.
Some one pleasseee help xx
A.
600 : 2 = 300
300 : 2 = 150
150 : 2 = 75
75 : 5 = 15
15 : 5 = 3
3 : 3 = 1
600 = 2 · 2 · 2 · 5 · 5 · 3 = 2³ · 5² · 3
B.
1050 : 2 = 525
525 : 5 = 105
105 : 5 = 21
21 : 3 = 7
7 : 7 = 1
1050 = 2 · 5 · 5 · 3 · 7 = 2 · 5² · 3 · 7
600 = 2 · 2 · 2 · 5 · 5 · 3
HCF(600, 1050) = 2 · 3 · 5 · 5 = 150
Mrs.Bell has a 256-ounce bag of potting soil.What is greatest number 6-ounce pots she can completely fill with soil?
If x > 0 and y > 0, where is the point (x, y) located? On a coordinate plane
Answer:
its y
Step-by-step explanation:
is this work right?
Idk if I followed the PEMDAS right
yes you did a very good job
My favorite songstress gives away 25% of the sales of her signature fragrance collection to her charity. Last month her sales was $ 1,200. How much of her total sales did she donate?
Since she donates 25%, take 25% and multiply it by 1,200
[tex].25 * 1,200 = 300[/tex]
or,
[tex]\frac{1}{4} * 1,200 = 300[/tex]
The price of wheat in 1997 was 3.38 per bushel. In 1998,the price was 2.65 per bushel. Round the price per bushel of wheat for each year to the nearest tenth of a dollar
1997 = 3.40
1998 = 2.70
Select the slope-intercept form of an equation for a line with y-intercept –5 and slope 2.
Someone know the answer?
Answer: Choice A) (5+a)/(a-1)
Step-by-step explanation:
In the numerator, we originally have 3+x. Replace the x with a+2 and we get 3+x = 3+a+2 = 5+a. So the answer will have a numerator of 5+a.
The denominator in the answer will be x-3 = a+2-3 = a-1
Overall that's how the answer is (5+a)/(a-1)
Customers at Fair Weather Farmer's Market love to sample Ava's homemade strawberry jam. A jar of jam contains 12 ounces, and the sample size is 1 2 of an ounce. How many people can sample from one jar?
It is given that the sample size is half or [tex]\frac{1}{2}[/tex] of an ounce.
It is also given that a jar of jam contains 12 ounces.
Let the number of people who sample from the jar be "x". Then it is clear that:
[tex]\frac{1}{2}\times x=12[/tex]
Therefore, we will have [tex]x=\frac{12}{\frac{1}{2}}=12\times 2=24[/tex]
Therefore, 24 customers at Fair Weather Farmer's Market who love to sample Ava's homemade strawberry jam can sample from one jar.
Gia got some books from the library yesterday. She got 5 books today after returning 3. Gia now has 6 books. How many library books did gia begin with?
Answer:
4
Step-by-step explanation:
Given: Gia got some books from the library yesterday. She got 5 books today after returning 3. Gia now has 6 books.
To Find: How many library books did gia begin with.
Solution:
Let the number of library books gia begin with [tex]=\text{x}[/tex]
Number of books gia got today [tex]=5[/tex]
Number of books gia returned [tex]=3[/tex]
Total number of books Gia has [tex]=(\text{Total number of books is started with})+(\text{number of books gia got})-(\text{books gia returned})[/tex]
[tex]\text{x}+5-3[/tex]
[tex]\text{x}+2[/tex]
Total number of books gia has [tex]=6[/tex]
now,
[tex]\text{x}+2=6[/tex]
[tex]\text{x}=6-2[/tex]
[tex]\text{x}=4[/tex]
Hence number of books gia started with is 4
The number of books Gia started with is 4
Let the number of books she got yesterday = x
Total Number of books she has gotten = 6
Books she got today = 3
Number of books she returned = 5
Expressing this as an equation :
Total books gotten = (x + 5 - 3)
6 = x + 5 - 3
6 = x + 2
6 - 2 = x
x = 4
The number of books Gia started with is 4.
Learn more : https://brainly.com/question/18112348
solve the formula V = bh for h
V = bh Dividing both sides by "b" we get
(V / b) = h
Solving for h means to isolate h by move everything else to the other side of the equal sign.
V = b * h
[tex]\frac{V}{b} = \frac{b*h}{b}[/tex] divide both sides by b
[tex]\frac{V}{b} = h[/tex] h is now isolated
How many pounds of coffee worth $9 a pound should be added to 10 pounds of coffee worth $3 a pound to get a mixture worth $7 a pound
Please try to answer quickly thanks :)
The Distance between the 2 points is 15 units
One way that a company can raise money for expansion is to sell stock. When you buy a share of a company's stock, you become a shareholder, or part owner, of that company. The cost of a share is often represented in points, where each points represents one dollar. When a stock gains points, its shares increase in value, and when a stock loses points, its shares decrease in value. For instance, if a stock gains three points one day, each share of its stock is worth three dollars more than it was the day before. Positive decimal numbers are used to represent gains, and negative decimal numbers are used to represent losses.
On Monday, the closing value of a share of stock in Company ABC, was 74.01. On Tuesday, it closed at 73.67, and on Wednesday, it closed at 74.32. On Thursday, the change in stock value was -1.48. And, on Friday, Company ABC's stock gained 0.89 points. Answer the following questions based on Company ABC's stock performance this week.
If a shareholder owns 75 shares of Company ABC's stock, by what amount did their total stock value change on Wednesday?
well if he started his day on Wednesday with 75 end he ended with 74.32 he lost -0.68
of his share hope this helped theres alot of extra information in the question
Answer:
-0.68
Step-by-step explanation:
Identify the property that justifies the statement.
∠XYZ≅∠PDQ and ∠PDQ≅∠ABC, so ∠XYZ≅∠ABC.
Answer: Transitive property of Equality.
Therefore if ∠XYZ≅∠PDQ and ∠PDQ≅∠ABC then by transitive property of equality we have ∠XYZ≅∠ABC.
The law of transitivity tells that if a equals to b and b equals to c then a equals to c.
For example If Jane has same height of Susan and Susan has same height of Tina then Jane has same height of Tina.
The statement "∠XYZ ≅ ∠PDQ and ∠PDQ ≅ ∠ABC, so ∠XYZ ≅ ∠ABC" is justified by the Transitive Property of Equality, which indicates that the congruence of the first and third angle is established through their mutual congruence to the second angle.
Explanation:The property that justifies the statement "∠XYZ ≅ ∠PDQ and ∠PDQ ≅ ∠ABC, so ∠XYZ ≅ ∠ABC" is the Transitive Property of Equality. This property states that if a first thing is equal to a second thing, and the second thing is equal to a third thing, then the first thing is also equal to the third thing.
In the context of angles, if ∠XYZ is congruent to ∠PDQ, and ∠PDQ is congruent to ∠ABC, then by the Transitive Property, ∠XYZ must be congruent to ∠ABC.
Please show work and help!! Will give brainliest!!
Step 1. Since the power of 2 is even, the result will be positive
(3j^2k^3)^2(2j^2k)^3
Step 2. Use Multiplication Distributive Property
3^2(j^2)^2(k^3)^2(2j^2k)^3
Step 3. Simplify 3^2 to 9
9(j^2)^2(k^3)^2(2j^2k)^3
Step 4. Use the Power Rule
9j^4(k^3)^2(2j^2k)^3
Step 5. Use the Power Rule
9j^4k^6(2j^2k)^3
Step 6. Use Multiplication Distributive Property
9j^4k^6 * 2^3(j^2)^3 k^3
Step 7. Simplify 2^3 to 8
9j^4k^6 * 8(j^2)^3 k^3
Step 8. Use the Power Rule
9j^4k^6 * 8j^6k^3
Step 9. Take out the constants
(9 * 8)j^4j^6k^6k^3
Step 10. Simplify 9 * 8 to 72
72j^4k^6k^3
Step 11. Use the Product Rule
72j^4+6k^6+3
Step 12. Simplify 4 + 6 to 10
72j^10k^6 + 3
Step 13. Simplify 6 + 3 to 9
72j^10k^9
Your friend is 1.25 times taller than you. Your friend is 64.5 inches tall. How tall are you?
To do a problem like this, multiply the base height by the rate. So here is how you do it:
64.5 times 1.25
The easiest way is to get a calculator and plug in the equation
Your answer should be 80.625
*If you multiply by hand, remember to move the decimal back to the left three places.*
If m arc HAM = 265°, find the measure of the corresponding minor arc. circle Z with radius ZH, diameter MT, and point A opposite point H
If the major arc HAM is 265°, then the minor arc MH is: 360° - 265° = 95°
Major arc plus minor arc equals the full circle of 360°
Answer: 95°
Heidi's mom made flower arrangements for a party. She made 4 times as many rose arrangements as tulip arrangements. Heidi's mom made a total of 40 arrangements. How many flower arrangements of each type did Heidi's mom make?
32 rose arrangements and 8 tulip arrangements
8 times 4 = 32
8 + 32 = 40
Heidi's mom made 8 tulip arrangements and 32 rose arrangements. This was determined by setting up equations based on the given information and solving for the number of each type of arrangement.
With 4 times as many rose arrangements as tulip arrangements. Let's denote the number of tulip arrangements as T and the number of rose arrangements as R. According to the information, R = 4T and R + T = 40.
Substituting R in the second equation gives 4T + T = 40, which simplifies to 5T = 40. Solving for T, we find T = 8. Therefore, the number of tulip arrangements is 8. Substituting T = 8 into the equation R = 4T gives R = 32, meaning that there are 32 rose arrangements. Thus, Heidi's mom made 8 tulip arrangements and 32 rose arrangements for the party.