Which factor could be multiplied by the given function so that their product causes the graph of f(x) to decrease as x approaches negative infinity?
[tex]f(x)=(2x^2 + 5)(x - 7)[/tex]
Select all that apply.
• -3
• 0.2x
• 5x²
• [tex]-\frac{1}{2}(x + 8)[/tex]
• 4(2x - 7)
Answer:
5x²
-1/2( x+8)
Step-by-step explanation:
The dominant term is 2x^2 *x or 2x^3
We want to know what happens when x goes to negative ∞
2 ( -∞) ^3 → 2 * (-∞) → -∞
As long as we multiply by a positive number, we will still be approaching negative infinity ( or decreasing)
-3 is negative
.2x is negative when x approaches negative infinity
.5 x^2 = .5( -∞)^2 = 5 ( ∞) = ∞ which is positive
-1/2 x is the dominant term = -1/2(- ∞) = ∞ which is positive
4(2x) is the dominant term = 8(- ∞) = - ∞ which is negative
Answer:
3rd and 4th Choices.
[tex]\displaystyle 5x^2\text{ and } -\frac{1}{2}(x+8)[/tex]
Step-by-step explanation:
We are given the function:
[tex]f(x)=(2x^2+5)(x-7)[/tex]
And we want to determine the factor(s) that we can multiply to the above function that will cause the graph of f to decrease as x approaches negative infinity.
We can see that the dominant term will be:
[tex]2x^2(x)=2x^3[/tex]
Thus:
[tex]2(-\infty)^3\Rightarrow -\infty[/tex]
It is already decreasing (shifting towards negative infinity) as x approaches negative infinity.
In order to preserve this, then, the factors must be positive as x approaches negative infinity.
The first factor is -3.
-3 is always negative, so it will make f increase.
The second factor is [tex]0.2x[/tex].
[tex]0.2(-\infty)\Rightarrow -\infty[/tex]
This will also make f increase.
The third factor is:
[tex]5(\infty)^2\Rightarrow \infty[/tex]
This is positive, so it will allow f to remain decreasing as x approaches negative infinity.
The fourth factor is:
[tex]\displaystyle -\frac{1}{2}(-\infty+8)\Rightarrow -\frac{1}{2}(-\infty)\Rightarrow \infty[/tex]
This is also positive, so it will also allow f to remain decreasing.
Lastly, the fifth factor is:
[tex]4(2(-\infty)-7)\Rightarrow 4(-\infty)\Rightarrow -\infty[/tex]
This is negative, so it will make f increasing.
Therefore, our answers are the third and fourth choices.
The sum of three numbers is 52. The difference of the largest and the smallest is 48, and the sum of the two smaller numbers is 11, Find the numbers.
Answer:
41, -7, 18
Step-by-step explanation:
Let a = smallest number
b = second number
c = largest number
Then a + b +c = 52 c - a = 48 a + b = 11
11 + c = 52
c = 41 41 - a = 48
-a = 6
a = -7 -7 + b = 11
b = 18
Answer:
a=-7
b=18
c=41
Step-by-step explanation:
a+b+c=52
c-a=48
a+b=11
11+48=59
a+59=52
a=-7
George had 50.00 he bought a pair of pants for 39.59 and a tire for 8.75 what is the total amount of money that he has left
A caterpillar crawling in a straight line across a coordinate plane starts at point (-3,
-4) and ends at point (25, 38). Counting the start point and end point, how many
points with integer coordinates does the caterpillar touch?
9514 1404 393
Answer:
15
Step-by-step explanation:
In vector form, the equation of point p on the line can be written as ...
p = (-3, -4) +t(25 -(-3), 38 -(-4)) . . . . . for some scalar t
p = (-3, -4) +t(28, 42)
p = (-3, -4) +14t(2, 3)
where t takes on any value between 0 and 1.
If we let t = n/14 for some integer 0 ≤ n ≤ 14, then the coordinates of point p will be integers.
There are 15 values that n can have in the allowed range.
The caterpillar touches 15 points with integer coordinates.
On average, Haley is able to read 4 5/6 Chapters in the her book each week . How many weeks will it take Haley to read 9 2/3 Chapters
Answer:
2 weeks
Step-by-step explanation:
y = mx + b
y = total number of chapters read = [tex]9\frac{2}{3}[/tex]
m = number of chapters read per week = [tex]4\frac{5}{6}[/tex]
x = number of weeks = what we're solving for
b is not needed to find this solution
[tex]9\frac{2}{3}[/tex] = [tex]4\frac{5}{6}[/tex] x divide [tex]4\frac{5}{6}[/tex] from both sides
x = 2 weeks
I really need help I will give brainliest
Answer:
64 degrees
Step-by-step explanation:
All angles in a triangle plus each other equals 180. First find the missing angle of the triangle with 2 given angles. The missing angle is 64 degrees because 68 plus 48 is 116 and 180 - 116 is 64. Vertical angles are always congruent and the missing angle is vertical to the missing angle on the first triangle.
13 as prime or composite
Answer:
prime
gggghfsssddfdfv ut b dc t
Answer:
the number 13 is a prime number
14 less then 3 times a number is 31 written out and solved
Answer:
3x-14=31 ,= 15
Step-by-step explanation:
3x= 45
x= 45/3
x= 15
hope it helps
3x - 2 y = 10 and 7 x + 2 y = 30
Answer:
Your answer is (4,1)
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Hoped this helped!
brainly, please?
27 is smaller than 5 times a number increased by 7
Answer:
4
Step-by-step explanation:
this means that 5x+7=27
subtract 7 from both sides
5x=20
x=4
Odette solved this problem:
A piggy bank has nickles and dimes totaling $1.15. If the bank contains exactly 15
coins, how many of each coin are in the bank?
Complete the statement about Odette's solution.
Answer:
In Odette's solution, 7 is the number of
nickels and 8 is the number of dimes
Which expression shows -5 3/5+9 1/5 as the sum of integer and fractional parts?
Answer:
-5 + 9 + (-3/5) + 1/5
Step-by-step explanation:
A Solve the
1. The total number of books which were borrowed from a library from Monday to Sunday can be
modelled by the function F(x) = 200x + 542x² + 179x + 1605 and the number of visitors to the
library from Monday to Sunday can be modelled by G(x) = 100x + 321, where x is the number of
days since Monday Which of the following expressions correctly describes the average number of
books per visitor?
Answer:
?
Step-by-step explanation:
PLZ HELP!!
What is the ratio of a:b, knowing that a-b/a+b=3/5
Answer:
1 : 4
Step-by-step explanation:
5(a - b) = 3(a + b) = 5a - 5b = 3a + 3b
2a - 5b = 3b
2a = 8b
2/8 is 1/4 simplified
What is tan K? help pleasee
8/15
Hope this helps!
Answer:
[tex]\frac{8}{15}[/tex]
Step-by-step explanation:
[tex]Tan(k)=\frac{24}{45} =\frac{8}{15}[/tex]
Which statement is true regarding the intervals where the function is increasing and decreasing? The function is increasing from (–∞, 0). The function is increasing from (0, ∞). The function is decreasing from (–∞, 0). The function is decreasing from (–∞, ∞).
Step-by-step explanation:
mark me as a brainlist hope its helpful yo you
The function is increasing from (–∞, 0). Then the correct option is A.
What is increasing and decreasing of function?If the value of y increases as the value of x increases, then increasing function.
And if the value of y decreases as the value of x increases, then decreasing function.
From the graph, the function is increasing from (–∞, 0).
Then the correct option is A.
The complete question is attached below.
More about the increasing and decreasing of function link is given below.
https://brainly.com/question/14330051
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A taxi driver had 31 fares to and from the airport last Monday. The price for a ride to the airport is $4.50, and the price for a ride from the airport is $11. The driver collected a total of $289 for the day.
Answer:
(8,23)
Step-by-step explanation:
x+y=31
4.5x + 11y = 289
x = 31 -y
4.5(31 - y) + 11y = 289
139.5 - 4.5y + 11y = 289
6.5y = 149.5
y = 23
x = 31 - 23 = 8
The ordered pair, (x, y) = (8, 23).
What is an ordered pair?
An ordered pair exists as a composition of the x coordinate (abscissa) and the y coordinate (ordinate), containing two values noted in a fixed order within parentheses.
Given: A taxi driver had 31 fares to and from the airport last Monday. The price for a ride to the airport exists $4.50, and the price for a ride from the airport exists $11. The driver collected a total of $289 for the day.
x + y = 31........(1)
4.5x + 11y = 289 ........(2)
From (1), we get
x + y = 31
x = 31 - y
Substitute the value of x in (2), and we get
4.5x + 11y = 289
4.5(31 - y) + 11y = 289
Simplifying the above equation, we get
139.5 - 4.5y + 11y = 289
6.5y = 149.5
y = 23
substitute the value of y, in (1) then we get
x = 31 - y
x = 31 - 23 = 8
The value of x = 8 and y = 23.
Therefore, the ordered pair, (x, y) = (8, 23).
Complete question
A taxi driver had 31 fares to and from the airport last Monday. The price for a ride to the airport is $4.50, and the price for a ride from the airport is $11. The driver collected a total of $289 for the day. Let 2 represent the number of trips to the airport and y represent the number of trips from the airport. Write the ordered pair, (x, y) that represents the situation.
Find the measure of Angel 1 and 2.
What is the term-to-term rule for this sequence?
64, 32, 16, 8,4
Answer:
Divide previous term by 2
Step-by-step explanation:
Have a nice day :)
Answer:
every number is getting half one by one
Step-by-step explanation:
means getting divided by 2
have a cheerful day
PLEASE HELP!!!!!
A beach toy in the shape of a pyramid has a rectangular base with dimensions of 4 inches by 12 inches. The height of the rectangular pyramid is 10 inches. Sand fills half the volume of the beach toy. How many more cubic inches of sand is needed to finish filling the beach toy? Enter your answer in the box. ____in3
Answer:
80in3
Step-by-step explanation:
12 x 4 = 48
48 / 2 = 24
24 x 10 =240
240 / 3 = 80
So your answer is 80in3
Answer: 80in
Step-by-step explanation:
BRAINLIEST AND ALSO 40 POINTS!!!!
Answer:
WOAH Sapnap!
Step-by-step explanation:
A garden table and a bench cost $903 combined. The garden table costs $53 more than the bench. What is the cost of the bench?
For what value of q is the equation -13(9 + 4) = 79 + 16 true?
Answer:
False, because the left side (-169), is not equal to the right side (95).
please help !!!! The leg of a right triangle is 2 units and the hypotenuse is 5 units. What is the length, in units, of the other leg of the triangle?
3
Square root of 29
Square root of 21
7
Answer:
[tex]\sqrt{21}[/tex]
Step-by-step explanation:
Use the pythagorean theoreom, a^2+b^2=c^2.
We know the hypontenuse and one of the sdes
a^2+2^2=5^2
a^2+4=25
subract four from both sides to isolate variable
a^2=21
square root both sides and you have the answer of sq root 21!
Edit: the answer for your next question is the last one b/c it satisfies the Pythagorean Theorem
f(x) = -2x + 2
g(x) = 3x^2– 3x
Find f (4) and g(-3)
helpp please i would appreciate it
Answer:
f(4) = -6, g(-3) = 36
Step-by-step explanation:
To find f(#) or g(#), plug the number into each x of the equation.
f(x) = -2x + 2
f(4) = -2(4) + 2
Simplify the parentheses by multiplying.
f(4) = -8 + 2
Add.
f(4) = -6
g(x) = 3x² - 3x
g(-3) = 3(-3)² - 3(-3)
Simplify the exponent first.
g(-3) = 3(9) - 3(-3)
Simplify the parentheses by multiplying.
g(-3) = 27 + 9
Add.
g(-3) = 36
Will mark brainliest for correct answer, due soon!
circumference = pi*d
70cm*pi = 219.8cm
219.8cm × 240 rev = 52752 cm
52752cm/100 = 528m
Conduct a Pareto analysis for the number of minutes that flights are late in the accompanying data. Interpret the results. LOADING... Click the icon to view the Atlanta Airline Data. Conduct a Pareto analysis for the number of minutes that flights are late. 15127137130.3074601124.053619303 192644911620.5010780515.163538874 192426514270.6153514455.158176944
Answer:
Following are the solution to the given question:
Step-by-step explanation:
Please find the attached file for the solution:
20% of flights accounted for nearly 70 to 80% of delayed minutes.
How many times smaller will a number become if is it decreased by 20%?
Answer:
Step-by-step explanation:
I'm unsure why my answer was deleted, randomly deleted a thoroughly explained answer.
20% is 20/100, 1/5, or 0.2
The number will decrease by a factor of 5.
Answer:1.25
Step-by-step explanation: for example 100 decreased by 20 percent is 80 so 100 divided by 80 is 1.25
The letters of "BEARS" should be evenly spaced across a 60-inch-wide banner, with no margins. Each letter is 8 inches wide. How many inches (x) should exist between each pair of letters?
Answer:
The answer is 10 inches, because first we multiply the letters and how wide they are then subtract that from 60 then divide that by our spaces (4)
Step-by-step explanation:
Maliki is building a ramp with a base of 4 feet and a vertical height of 2 feet. What is the length of the ramp?
Answer:
2√5
Step-by-step explanation:
By applying Pythagoras (hypotenuse)^2=(Base)^2 +(Height)^2
The length of the ramp is approximately 4.47 feet.
What is the Pythagorean theorem?Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
If the base of the ramp is 4 feet and the vertical height is 2 feet, we can use the Pythagorean theorem to find the length of the ramp:
ramp length² = base² + height²
ramp length² = 4² + 2²
ramp length² = 16 + 4
ramp length² = 20
Taking the square root of both sides, we get:
ramp length = √20
Simplifying the square root of 20, we get:
ramp length ≈ 4.47 feet
Therefore, the length of the ramp is approximately 4.47 feet.
Learn more about Pythagoras's theorem here:
brainly.com/question/343682
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