Given:
x gets larger and larger in the negative direction.
To find:
The polynomial function which gets larger and larger in the negative direction.
Solution:
In options a, c and d, degree of polynomials are even and leading coefficient is positive. So,
[tex]f(x)\to \infty\text{ as }x\to -\infty[/tex]
In option b, degree of polynomial is odd and leading coefficient is positive. So,
[tex]f(x)\to -\infty\text{ as }x\to -\infty[/tex]
Therefore, the function in option b, [tex]f(x)=6x^3+4x^2-15x+32[/tex] gets larger and larger in the negative direction as x gets larger and larger in the negative direction.
Hence, the correct option is b.
We want to see which polynomial function gets larger and larger as the variable increases in the negative direction. We will see that the correct option is d: f(x) = 8x^6 + 1
Here you need to remember two things.
As the larger the exponent is, the faster the polynomial grows.
When we evaluate a negative number in an even exponent, the outcome is always positive.
Then the polynomials that get larger and larger as x increases in the negative direction are all the polynomials with a even leading exponent, particularly, the one that increases faster is the one with the largest leading exponent, which is:
d. f(x) = 8x^6 + 1
If you want to learn more, you can read:
https://brainly.com/question/23792383
what the answer and how you got it
-2x/7=3x-46
Answer:
x=14
Step-by-step explanation:
-2x/7=3x-46
7(-2x/7)=7(3x-46)
-2x=21x-322
-23x=-322
x=14
Joseph is shopping for school supplies. He can buy a box of 24 pens for $4.32 or a box of 36 pens for $5.76. Which is a better buy? Explain your reasoning.
Answer:
the better one to buy is a box of 36 pens for $5.76. because it is cheaper per pen.
Step-by-step explanation:
4.32 / 24 = 0.18 cents a pen
5.76 / 36 = 0.16 cents a pen
F(x) = x^2 and g(x) = 2x-3 What is the value of g(4) + f(-3)?
Answer: 66
Step-by-step explanation:see attachment.
If this helps you please rate brainest
On a snowy day, only 7/12 of the students attended Calvin Middle School. Among the students that missed school, about 4/5 students call the school to inform the school office. What was the fraction of all students that called in to inform the school about missing school this day?
Answer:
1/3 of all the students called in to inform the school about missing school this day
Step-by-step explanation:
4/5 = students that call the school to inform the school office
only 7/12 attended Calvin Middle School
To get the number of students that missed Calvin Middle School = 1 - number of students that attended Calvin Middle School
= 1 - 7/12 = (12-7) / 12
= 5 /12
The fraction of all students that called in to inform the school about missing school this day is:
5/12 x 4/5 = 1/3
Please evaluate the given equation, and then see how many solutions the equation has. No. 1
here I am! dunno if this is the question you meant but you haven't gotten an answer here yet.
Answer:
B) Exactly one solution. (-3.5)
Step-by-step explanation:
5x + 8 - 7x = -4x + 1
combine like terms
5x - 7x + 8 = -4x + 1
-2x + 8 = -4x + 1
add 4x to both sides
-2x + 4x + 8 = -4x + 1 + 4x
2x + 8 = 1
subtract 8 from both sides
2x + 8 - 8 = 1 - 8
2x = -7
divide both sides by 2.
x = -3.5
3.5, clearly, is only one number.
What is 1 3/4 divided by 3?
Answer:
7/12 is the answer
Susan received $27 for 6 hours of work. Ricky received $14.25 for 3 hours of work. Which statement is true about there hourly rate? Answer choices: A:Susan's rate was closer to $5.00 B:Susan's rate was $0.70 more per hour C: Rickys rate was 0.25 more per hour D:Ricky was paid at half Susan's rate
Answer: C. Rickys rate was 0.25 more per hour" .
Step-by-step explanation:
Susan received $27 for 6 hours of work. Susan's rate we hour will be:
= $27/6
= $4.5
Ricky received $14.25 for 3 hours of work. Ricky's rate will be:
= $14.25/3
= $4.75
From the option given, the correct option is C "Rickys rate was 0.25 more per hour" .
This is because $4.75 - $4.5 = $0.25
The table shows what time the sunrise and
sunset occurred on dates in October. Based
on the data, what is the total number of
minutes of daylight recorded across these
dates?
Answer:
There are 2,802 minutes of daylight recorded across these dates.
Step-by-step explanation:
Elapsed Time
Elapsed time is the amount of time that passes from the start of an event to its finish.
We have to recall 1 hour has 60 minutes. Another useful fact is that from a specific time AM to the same time PM there are 12 hours or 720 minutes.
Let's find the minutes of daylight recorded day by day.
Oct, 4th:
From 7:26 am to 7:26 pm there are 720 minutes. Since the sunset time is 13 minutes less, the minutes of daylight are 720 - 13 = 707 minutes.
Oct, 6th:
From 7:27 am to 7:27 pm there are 720 minutes. Since the sunset time is 18 minutes less, the minutes of daylight are 720 - 18 = 702 minutes.
Oct, 8th:
From 7:28 am to 7:28 pm there are 720 minutes. Since the sunset time is 21 minutes less, the minutes of daylight are 720 - 21 = 699 minutes.
Oct, 10th:
From 7:30 am to 7:30 pm there are 720 minutes. Since the sunset time is 26 minutes less, the minutes of daylight are 720 - 26 = 694 minutes.
The total minutes of daylight is 707 + 702 + 699 + 694 = 2,802 minutes
There are 2,802 minutes of daylight recorded across these dates.
find the greastest common factor of 10,30,and 45.
===================================================
Explanation:
Find the prime factorization of each value. A factor tree may help.
10 = 2*5
30 = 2*3*5
45 = 3*3*5
We see that '5' is found in each of the factorizations. This is the only factor that shows up in all three values, and it only shows up one time. So that's why 5 is the GCF.
Which equation could be represented by the number line?
A. -5 + 6 = 1
B. -6 + 5 = -1
O c. 1 +(-7) = -6
D. 1 + (-6) = -5
Help!!!
Answer:
I think it’s C
Step-by-step explanation:
Solve for the indicated variable.
L = M - N for N
A culture of bacteria has an initial population of 12000 bacteria and doubles every 6 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P t =P 0 ⋅2 d t , where P_tP t is the population after t hours, P_0P 0 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 17 hours, to the nearest whole number?
Answer:
85,524 bacteria
Step-by-step explanation:
Given the population of bacteria modelled by the equation where;
[tex]P_t = P_0\cdot 2^{\frac{t}{d}[/tex]
P0 is the initial population
t is the time in hours
d is the doubling time
If the culture of bacteria has an initial population of 12000 bacteria, this means that;
at t = 0, P0 = 12000
substitute into the modelled function
[tex]P_t = P_0\cdot 2^{\frac{t}{d}\\\\P_t = 12000\cdot 2^{\frac{0}{d}\\\\\\P_t =12000\cdot 2^{0}\\\\P_t = 12000[/tex]
If the population doubles every 6 hours
at t = 6, Pt = 24000
[tex]P_t = P_0\cdot 2^{\frac{t}{d}\\\\\\24000 = 12000\cdot 2^{\frac{6}{d}\\\\\\\\24000/12000 = 2^{\frac{6}{d}\\\\\\\\[/tex]
[tex]2 = 2^{\frac{6}{d} }\\1 = 6/d\\d = 6\\[/tex]
Next is to get the population of bacteria in the culture after 17 hours
at t = 17, Pt = ?
[tex]P_t = P_0\cdot 2^{\frac{t}{d}\\\\P_t = 12000\cdot 2^{\frac{17}{6}\\\\\\\\P_t = 12000\cdot 2^{ 2.833 }\\P_t = 12000\cdot 2^{ 2.833 }\\P_t = 12000 * 7.127\\P_t = 85,524.3[/tex]
Hence the population of bacteria in the culture after 17 hours, to the nearest whole number is 85,524 bacteria
Answer:Pt 85526.2769 = 85526
Step-by-step explanation:
A taxi ride cost a flat fee of of $5.00 plus an additional $1.75 per mile. How many miles would a person
travel if they paid $15.50?
Answer:
6 miles
Step-by-step explanation:
15.50-5 is 10.50 and 10.50/1.75 is 6
hope this helped also could i get brainliest?
x³+y³+z³
if you can answer this ill give you Brainliest
Answer:
This expression reminds me a lot of Fermat's last theorem x^n+y^n=z^n where n is three(odd). Which is one of many famous diophantine equations such as the well known pythagorean theorem a^2+b^2 = c^2. Where one of the variables should be even, and all are coprime. The parity is odd since it has a remainder and is not evenly divisible. It has been proven that Fermat's last theorem does not have any real solutions because you would need a complex number to cancel out the cubes. You will also see that x^n+y^n=z^n does not have any solutions if n>=3. This cannot be factored either since the numbers are rational.
An expert diver is looking for a particular species of fish along the coast line. He dives 25 feet below the surface of the ocean. Then he dives down 10 more feet. He swims back up 7 feet and down another 3 feet before he finds the species of fish he is looking for. What was the depth at which the diver finds the fish?
Answer:
31
Step-by-step explanation:
Depth Changes:
1. down 25 feet
2. down 10 feet
3. up 7 feet
4. down 3 feet
If we form this into an equation, we get:
25+10-7+3 = 31
Please help me with this and show the steps. Will give brainliest if correct.
Answer:
X =1/(b2x+2b)
Step-by-step explanation:
bx2 +2x +1/b = 0
bx2+2x=1/b
bx2(b) +2bx = 1
x(b2x+2b)=1
x=1/(b2x+2b)
An object is thrown off a 256-foot-tall building, and the distance of the object from the ground is measured every second. The function that models the height, h, of the object after t seconds is h(t) = –16t2 + 96t + 256. Determine the time when the object hits the ground
Answer:
The object hits the ground 8 seconds after launch.
Step-by-step explanation:
Let [tex]h(t) =-16\cdot t^{2}+96\cdot t + 256[/tex], where [tex]h[/tex] is the height of the object above the ground, measured in feet, and [tex]t[/tex] is time, measured in seconds. We notice that given expression is a second-order polynomial and hence, there are two roots, one of them corresponding to the instant when the object hits the ground. If [tex]h(t) = 0[/tex], we get the following expression:
[tex]-16\cdot t^{2}+96\cdot t +256 = 0[/tex] (Eq. 1)
Roots are found by applying the Quadratic Formula:
[tex]t_{1,2} = \frac{-96\pm\sqrt{96^{2}-4\cdot (-16)\cdot (256)}}{2\cdot (-16)}[/tex]
[tex]t_1 = 8\,s[/tex] or [tex]t_{2} = -2[/tex]
Only the first root offer a solution that is physically reasonable. Thus, the object hits the ground 8 seconds after launch.
2. JI. has coordinates J(-6, 1) and Z(-4, 3). Find the coordinates of the midpoint.
Answer:
(- 5, 2 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
Here (x₁, y₁ ) = (- 6, 1) and (x₂, y₂ ) = (- 4, 3) thus
midpoint = [tex]\frac{-6-4}{2}[/tex], [tex]\frac{1+3}{2}[/tex] ) = ( [tex]\frac{-10}{2}[/tex], [tex]\frac{4}{2}[/tex] ) = (- 5, 2 )
How many times greater
is 1.837 X 10^9 than
3.6x10^5
Answer:
1.837 X 10^9 is 5103 times greater than 3.6x10^5
Step-by-step explanation:
1.837 X 10^9 =
Calculate the value
Solution
1,837,000,000
3.6x10^5
Evaluate the power
3.6 x 100,000
Multiply the numbers
360,000
Solution
360,000
Divide
1,837,000,000 / 360,000
Solution
5102.77778
Round
5103
1,837,000,000 > 360,000
Choose all the number sentences that have a difference less than 7,650?
A) 12,355 – 4,575
B) 19,345 – 12,000
C) 21,675 – 13,055
D) 24,356 – 18,560
E) 10,500 – 3,560
factor: a^2+b^2–c^2+2ab
Rearrange the polynomial:
a^2–2ab+b^2 - c^2
((a-b)(a-b))-c^2
(a-b)^2-c^2
Set x =a-b and y=c. The formula becomes
x^2-y^2
factoring this polynomial, we get
(x+y)(x-y)
Substituting back, we get:
(a+b+c)(a+b-c)
Let’s multiply it out to check:
A^2 -ab ac
- ab B^2 -bc
-ac bc -c^2
Answer:
(a + b + c)(a + b - c)Step-by-step explanation:
Use of formula:
(a+b)^2 = a^2 + 2ab + b^2a^2 - b^2 = (a + b)(a - b)Factoring the expression
a^2 + b^2 – c^2 + 2ab =(a^2 + 2ab + b^2) - c^2 = (a + b)^2 - c^2 =(a + b + c)(a + b - c)What type of graph is best to use to compare two sets of data over time?
Answer:
Line graphs.
Step-by-step explanation:
If you have two sets of data, the easiest graph to use would be a line graph. You can insert information and tell which line represents each category. Line graphs are also specifically used to compare data that changes over time.
I hope this helped you out!! Have a nice day :3
Answer:
line graphs
Step-by-step explanation:
i got 100
write the decimal expansion of 16 by 3125
Answer:
That will be 0.00512
How do I slove this eqaution, and whats the answer?
-3(n+6)+10=-9
Answer:
[tex]n = \frac{1}{3}[/tex]
Step-by-step explanation:
Apply the distributed property, so it now looks like this: -3n + -18 + 10 = -9Combine like terms: -3n + -8 = -9Simplify: -3n - 8 = -9Add 8 to each side, so it now looks like this: -3n = -1Divide each side by -3 to cancel out the -3 next to n. It should now look like this: n = 1/3I hope this helps!
A summer camp wants to buy some new boats. It costs $381 to buy a new canoe and $354 to buy a new rowboat. How much more does it cost to buy a canoe than a rowboat?
Answer:
28$ more
Step-by-step explanation:
To answer this you'll need to subtract $354 out of $381.
You should get 27 (or $27).
That means that the canoe costs $27 more then the rowboat.
________________________________________________
Sorry if this is unhelpful.
Write a sequence with five terms with a third term is six
Answer:
2, 4, 6, 8, 10
Step-by-step explanation:
This is a sequence that answers the question. Hope it helped
Which of the following happens when 21.63 is multiplied by 10^3?
A. The digit in the tens place moves to the hundredths place.
B. The digit in the tens place moves to the thousandths place.
C. The digit in the hundredths place moves to the tens place.
D. The digit in the hundredths place moves to the hundreds place
Answer: C. The digit in the hundredths place moves to the tens place.
Step-by-step explanation:
In 21.63,
place value of 2 = tens
Place value of 1 = ones
Place value of 6 = tenths
Place value of 3 = hundredths
21.63 × 10^3 = 21.63 × 1000 = 21630
From here , we can see that the digit in the hundredths place which is 3 has moved to the tens place.
Therefore, C is the answer.
The local meteorologist claims that the temperature is going to steadily drop over the next 4 hours. If the temperature changes by the same amount each hour, and it changes by a total of -28°F, how much will it change each hour? Explain how you got your answer in two or more complete sentences. plz answer with a real answer will give brainlyest
Answer:
-7°F/hour.
Step-by-step explanation:
If the total change is -28°F, and we know it took 4 hours, we just have to divide the total change by hours taken to get the change per hour.
So we do the following: [tex]\frac{-28F}{4} = -7F/h[/tex]
So the temperature changes (drops) by -7°F/hour.
; the boy to girl ratio is 10 to 8. If there are 16 girls in the class, how many boys are there?
Answer:
There are 20 boys
Step-by-step explanation:
Which relation is a function?
Answer:
b
Step-by-step explanation: