The function after synthetic division f(x) = 4x3 + 3x2 − 16x − 12
Answers
Answer:
[tex]\huge\purple{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad \ \ \ }}[/tex]
»ANSWER«
(1) Write properties of function:
x intercept/zero:
[tex] x_{1} = \frac{3}{4} [/tex]
y intercept:
[tex]y = - 12[/tex]
domain:
[tex]( - \infty \: \infty )[/tex]
type of function: cubic fraction
standard form:
[tex]f(x) = 4 {x}^{3} - 3 {x}^{2} + 16x - 12[/tex]
factorize form:
[tex]f(x) = (4x - 3)( {x}^{2} + 4)[/tex]
even/odd/neither: neither
bounce/cross x axis:
[tex]x = \frac{3}{4} \: across[/tex]
increasing interval:
[tex]( - \infty \: \infty )[/tex]
decreasing interval: no
number of positive real zeros: 1
number of possible turning point: 2
order/degree: 3
leading term:
[tex]4x ^{3} [/tex]
leading coefficent: 4
constant term: -12
end behavior:
[tex]as \: x \: → \infty f(x) → \infty \: as \: x → - \infty f(x) → - \infty [/tex]
#CarryOnLearning
Related Questions
II. Solve the problems involving variations. Show your complete solution. (3 points each) 1. If y varies directly as the square of x, and y = 32 when x = 2, find y when x = 5. 2. The force of attraction (F) between two opposite electrical charges varies inversely as the square of the distance (d) between them. If F = 18 when d = 10, find F when d = 15. 3. If y varies jointly as x and z, find y if x = 3, k = 6 and z = 9
Answers
Answer:
see explanation
Step-by-step explanation:
(1)
y varies directly as x² then the equation relating them is
y = kx² ← k is the constant of variation
To find k use the condition y = 32 when x = 2
32 = k × 2² = 4k ( divide both sides by 4 )
8 = k
y = 8x² ← equation of variation
When x = 5 , then
y = 8 × 5² = 8 × 25 = 200
(2)
Given F varies inversely as d² then the equation relating them is
F = [tex]\frac{k}{d^2}[/tex] ← k is the constant of variation
To find k use the condition F = 18 when d = 10
18 = [tex]\frac{k}{10^2}[/tex] = [tex]\frac{k}{100}[/tex] ( multiply both sides by 100 )
1800 = k
F = [tex]\frac{1800}{d^2}[/tex] ← equation of variation
When d = 15 , then
F = [tex]\frac{1800}{15^2}[/tex] = [tex]\frac{1800}{225}[/tex] = 8
(3)
y varies jointly as x and z then the equation relating them is
y = kxz ← k is the constant of variation
when x = 3, y = 6, z = 9 ,then
y = 6 × 3 × 9 = 162
Sarah works for 8 minutes and for every 8 minutes she gains 23 coins everytime she works and she is saving for 2,000 coins in total. How many hours will it take Sarah to get 2,000 coins?
Answers
Answer:
11.59 hours {Basically 12 hours]
Step-by-step explanation:
Sarah's coin rate is 23 coins/8 minutes, or 2.875 coins/minute
Rate * Time(X) = Coins
(2.875 coins/min)*(X) = 2000 coins
X = (2000 coins)/(2.875 coins/min)
X = 695.65 minutes
(695.65 minutes)*(1 hour/60minutes) = 11.59 hours
Select all the functions whose output is 4 when the input is 16.
A.
y = 2x
B. y=x?
2
= x
C.
y = x + 12
D.
y = x - 12
E. y = 1
x
Answers
Answer:
Please check your post. I did the best I could.
Step-by-step explanation:
A. y = 2x 4 = 2*(16)? Nope
B. y=x? I don't understand the equation: y = x? 2 = x?????
C. y = x + 12 4 = 16 + 12? Nope
D. y = x - 12 Same???
E. y = 1 x 4 = 16? Nope
у — 3x 4
у > 4х +1
Anyone know the answe on how to solve this???
Answers
Answer:
Unbounded, infinite number of solutions
Step-by-step explanation:
1. Graph each inequality separately
2. Choose test point to determine which side of line needs to be shaded
3. The solution will be the the area where the shadings from both inequalities overlap
Since, the overlap almost covers the 2nd and 3rd quadrants there are an infintite number of solutions
I need help with this question
Answers
Answer:
2√14m
Step-by-step explanation:
Hypothenus = 9m
Second side = x
third side = 5m
Using Pythagoras theorem
9² = x² + 5²
81 = x² + 25
x² = 81 - 25
x² = 56
x = √56
= √4 × √ 14
= 2√14m
if the nth term of a sequence is n^2-5 what are the first three terms and the 10th term
Answers
Answer:
-4, -1, 4
95
Step-by-step explanation:
when n is 1
n² - 5 = 1² - 5
1 - 5 = -4
when n is 2
n² - 5 = 2² - 5
4 - 5 = -1
when n is 3
n² -5 = 3² - 5
9 - 5 = 4
10th term, when n is 10
n² - 5 = 10² - 5
100 - 5 = 95
completing the square: x^2+2x-7=8x
Answers
Answer: x = 7, x = -1
Step-by-step explanation: Move the term to the left side
x^2 + 2x - 7 = 8x
x^2 + 2x - 7 - 8x = 0
Combine like terms
x^2 + 2x - 7 - 8x = 0
x^2 - 6x - 7 = 0
x^2 - 6x - 7 = 0
a = 1
b = -6
c = -7
x = -(-6) + (-6)^2 - 4 x 1(-7)/ 2 x 1
Evaulate the Exponent
Multiply the numbers
Add the numbers
Evaluate the square root
Multiply the numbers x = 6 ± 8/2
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
x = 6 + 8/2
x = 6 - 8/2
Rearrange and isolate the variable to find each solution
x = 7
x = -1
X - 5V + 17 = 0 2x+ V + 1 = 0
Answers
Answer:
x= -[tex]\frac{10}{3}[/tex], v = [tex]\frac{7}{3}[/tex]
Step-by-step explanation:
x= - 10/3, v = 7/3
jus so u want to copy so u don't have to type ur self
-4x+ lly = 15
pls help me
x=2y
Answers
Answer:
y = 5
Step-by-step explanation:
-4(2y) +11y = 15
-8y + 11y = 15
3y = 15
y = 5
Which speed is the fastest? 4 miles in 1/3 hour 1/3 mile in 4 hours 1/2 mile in 3 hours
Answers
Answer: 4 miles in 1/3 hour
Step-by-step explanation:
Find a and b. А E b B 409 с D
Answers
Answer:
a = 70°, b = 140°
Step-by-step explanation:
use alternate interior angles
The interior angles of a straight line are 180°
a = 180°-110° = 70°
b = 180°-40° = 140°
//I'm sorry, but I'm not very fluent in English.
12/15 =10/13 true or false
Answers
Answer:
False.
Step-by-step explanation:
5+2x=2x+6
do anyone know the answer
Answers
Answer:
no solutions
Step-by-step explanation:
5+2x = 2x+6
Subtract 2x from each side
5+2x-2x = 2x+6-2x
5 = 6
This is not a true statement so there are no solutions
Am I right? Should I've to add more info?(only about Rectangle and Square)
Answers
Answer:
Yh its right.
Step-by-step explanation:
Have a great day!
Answer:
yeah it is correct
Step-by-step explanation:
and well hruu
WILL GIVE YOU 50 POINT
Find M AFE.
Answers
Answer:
The answer is C
Step-by-step explanation:
25 + 57 + 34 = 116, so at least 116, not 116.
The angle is close to 90+45 = 135
assuming with this, the asnwer is C
Answer:
B. 173
Step-by-step explanation:
just add them all up! for DFE, BFC has the same sign, which i assume means it is the same thing
Sonja has a bank account balance of $1400. Each week, her balance changes by-$85.25. She wants to keep the balance above $377. How many weeks will Sonja's balance remain above $377? Select from the drop-down menu to correctly complete the statement. Sonja's balance will remain above $377 Choose... v weeks.
Answers
Answer:
12 Weeks
Step-by-step explanation:
$1400 - $377 = $1023
1023 / 85.25 = 12 Weeks
Answer:
Its will take Sonja 12 weeks
Step-by-step explanation:
Find the measures of x and y
Answers
Answer:
x = 65°y = 25°Step-by-step explanation:
We can clearly see that 90 = x + 25. Let's solve for x.
=> 90 = x + 25=> x = 65°Since we found x, we can find y by substituting x in the equation 90 = x + y
=> 90 = x + y=> 90 = 65 + y=> y = 25°Conclusion:
Therefore, we found that:
x = 65°y = 25°Hoped this helped.
[tex]BrainiacUser1357[/tex]
Two squares are congruent if and only if:
A. any two corresponding angles are
congruent
B. two pairs of corresponding angles are
congruent
C. all four pairs of corresponding angles are
congruent
D. a side of one is congruent to a side of the
other
Answers
D) a side of one is congruent to side of the other
Coz in the question it specified that both the shapes are square so obviously all angles are equal (90°)
Now we only need one side of it congruent .
whats the slope of the line that passes through (3,-3) with the slope of 3?
Answers
Answer:
y=3x-12
Step-by-step explanation:
Assuming that you're asking what's the equation of the line that passes through (3, -3) with the slope of 3.
y-y1=m(x-x1)
y-(-3)=3(x-3)
y+3=3(x-3)
y=3x-9-3
y=3x-12
Can someone answer number 9 for and tell me if the others are correct i have a 64% in geometry trying to raise grade up to alteast 70%
Answers
Answer:
5, 6, 7, 8: correct
9: the Hi.nge theorem does not apply
Step-by-step explanation:
The Hi.nge theorem says that the side opposite the angle between two pairs of congruent sides is longer if the angle is larger. This theorem is applicable to problems 5-8, and your application is correct.
__
9) The Hi.nge theorem does not apply. The marked angles are not between the congruent sides. There is no necessary relation between the marked angles and the angles that are between the congruent sides, so no conclusion can be drawn regarding the relative lengths of AB and CD.
can somebody plsss help me 7qt= pt pls help meeee
Answers
Answer:
8.40665 Step-by-step explanation:
Luis has $4.00 from his allowance. He visits an arcade where soda costs $0.75 and video games cost $0.25. Which of the following expressions represents the amount of money Luis will have left if he buys one soda and plays "g" video games? *
5 points
4.00 - 0.25 - 0.75g
4.00 + 0.75 + 0.25g
4.00 - 0.75 - 0.25g
4.00 - 0.25 + 0.75g
Answers
Answer: c
Step-by-step explanation:
Cube root -125 over 216
Answers
Hope this helps
Help please
Simplify the difference quotient (f(x + h) − f(x) )/h if h ≠ 0.
f(x) = x2 + 38
Answers
Answer:
2x + h
Step-by-step explanation:
[tex]\frac{f(x+h)-f(x)}{h}[/tex]
= [tex]\frac{(x+h)^2+38-(x^2+38)}{h}[/tex]
= [tex]\frac{x^2+2hx+h^2+38-x^2-38}{h}[/tex]
= [tex]\frac{2hx+h^2}{h}[/tex]
= [tex]\frac{h(2x+h)}{h}[/tex] ← cancel h on numerator/ denominator
= 2x + h
What is an
equation of the line that passes through the point (-8, -1) and is
parallel to the line x– 4y = 4?
Answers
Answer:
y=1/4x + 1
Step-by-step explanation:
first equation,,y=1/4x - 1
G1 = G2
G2 = 1/4
y+1 /x+8 =1/4
4y = X + 8 -4
4y =x + 4
y = 1/4x + 1
A sandbox is a right rectangular prism
that is 6 ft long and 4 ft wide. The
sandbox can hold 48 ft of sand when
full. Lisa fills the sandboxfull of sand.
What is the height of the sand in the
sandbox?
Answers
Use the SAS Postulate to prove triangle W X Y approximately equal to triangle W Z Y space i f space stack W Z with bar on top approximately equal to stack W X with bar on top space a n d space angle Z W Y approximately equal to angle X W Y.
Answers
Hope you could get an idea from here.
Doubt clarification - use comment section.
3 out of every 5 students in Mrs. Wilson's class have brown eyes. There are 20 students in Mrs. Wilson's class. How many of the students in Mrs. Wilson's class have brown eyes?
Answers
Answer:
12
Step-by-step explanation:
So there is 3:5 right, so 20 divided by 5 equals 4, there are four 5's in 20. Then 4 multiplied by 3 equals 12. So there are 12 students that has BROWN EYES.
Hope I Helped You :)
In this diagram shown,
PQRS is a rectangle
Answers
Answer:
In the figure, PQRS is a rectangle. If the shaded area is 72 sq. cm,...In the figure, PQRS is a rectangle. If the shaded area is 72 sq. cm, find h
EXPLANATION
From the diagram, PQRS is a rectangle
Area of shaded part = 72sq.cm
But 72 = 3h - 4 + 6h - 4 + 4h
= 72 - 16h - 8
= 16h - 72 + 8
=16h = 80
h = 80/16
= 5cm
Given the figure below, which statement correctly completes the following? ABE and HCD are what type of angles
Answers
Angles are classified based on their measures.
Classification of angles
The following are the classification of angles
Acute AnglesRight AnglesObtuse AnglesStraight linesReflex AnglesThe smallest angle is 0 degrees and the largest is 360 degrees.
When the measure of an angle is less than 90 degrees, such angle is an acute angle
When the measure of an angle is exactly 90 degrees, such angle is a right angle
Angles greater than 90 degrees, but less than 180 degree are obtuse angles, while angles that measure exactly 180 degrees are straight lines.
The last type of angle is the reflex angle, and it has a measure between 180 degrees and 360 degrees (exclusive)
The question is incomplete, so I gave a general explanation
Read more about angles at:
https://brainly.com/question/17972372