How do you solve this??? I need it fast please help with steps.
(x+3)(x+1)^2(x−4)>0
Answers
Answer:
x < -3 or x > 4
Step-by-step explanation:
The product of the factors is 4th-degree, and the leading coefficient is 1 (positive).
The factors tell you the following about the zeros:
x = -3 . . . sign change from + to -
x = -1 . . . graph touches, but no sign change. - on either side of x=-1
x = 4 . . . sign change from - to +
__
The function will be positive for x < -3 and for x > +4.
_____
Additional comments
The value of the function is zero when any of its factors is zero. The value of a factor changes sign when the value of x changes from one side of the 0 to the other. For example, here, we have x+1 as a factor, so x=-1 is a zero. When x = -0.9, the factor is positive (-0.9 +1 = 0.1). When x = -1.1, the factor is negative (-1.1 +1 = -0.1). If this factor were to the first power, it would cause the value of the function to change sign at x=-1.
However, the factor (x+1) has an even power: (x+1)^2. That means when the factor is negative, its square is positive, and when the factor is positive, its square is positive. In short, the factor (x+1)^2 causes the function to be zero at x=-1, but does not make the function change sign there.
The product of all of these factors will result in a polynomial with x^4 as the highest-degree term. That means the function is of even degree. The leading coefficient is 1, so is positive, and the function will generally have a U-shape. The left-most (odd-degree) zero will be where the function changes sign from positive to negative. The right-most (odd-degree) zero will be where the function changes sign from negative to positive. Those zeros are x=-3 and x=+4, respectively. There are no places between these where the function changes sign, so these zeros are the ends of the regions where the function is positive (>0).
Related Questions
Mathematic 19 don’t understand
Answers
Answer:
1.75 x 10^3
Step-by-step explanation:
This is quite a simple question really, we just have to remember one thing, the exponent laws. When both exponents have the same base and are getting divided by each other, you subtract the exponents.
So in this case we have 10^8 on top divided by the 10^5 on the bottom, so now you just subtract the 5 from 8 and you get 3 as your final exponent. So your power would just be 10^3.
The final step is just dividing 7 by 4 which is 1.75
Combine the power and 1.75 together to get the correct notation
1.75 x 10^3
What is the slope of the line that passes through the points (-4, 3) and (6, -5).
Answers
Answer:
-4/5
Step-by-step explanation:
m=[tex]\frac{y2-y1}{x2-x1}[/tex]
m=[tex]\frac{-5-3}{6-(-4)}[/tex]
m=-8/10
m=-4/5
If Uber charges $12 for a ride plus $2 per mile, write an equation for the cost (where x is the miles)
Answers
Answer:
12 + 2x = y
Step-by-step explanation:
y would be the total cost
Answer:
$12 + $2 × x
Step-by-step explanation:
According to the 1991 census, there are about 43406932 people in our country who speak Urdu. Which of the following is the closest approximation of this number?
A 4 lakhs
B 43 lakhs
C 4 crores
D 43 crores
Answers
According to the 1991 census, there are about 43406932 people in our country who speak Urdu. Which of the following is the closest approximation of this number?
A 4 lakhs
B 43 lakhs
C 4 crores
D 43 crores
→ C 4 crores
Explaination :
2 - Unit place
3-tens place
9- hundred place
6 - thousand place
0- ten thousand place
4 - lakh place
3 - ten lakh place
4 - crore place
hence , closest approximation of this number is 4 crores.
Approximation of number is 4 crores.
What is Approximation?Anything that is similar to something else but not exactly equal to it is an approximation. By rounding, a number can be approximated. By rounding the values contained within a calculation prior to performing the operations, it can be approximated.
Given census of a country is 43406932
Adjusting numbers to the closest 10, 100, 1,000
To rough to the closest ten, check out at the digit during the tens section.
Look at the digit in the hundreds column to approximate to the nearest hundred. Take a look at the digit in the thousands column to determine the nearest thousand.
so the number to the closest is crore
Hence the closest approximation of this number is 4 crores.
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my Christmas present to you
Answers
and have a happy new year!
Use the quadratic formula to write a quadratic equation that has the solutions x=-4 ± 2/6.
Answers
Step-by-step explanation:
general formula
x²-(a+b)x+(ab)
where a is alpha
and b is beta
x=-4+2/6 or x=-4-2/6
x=-1/3 or x=-1
a+b=-1/3 + -1 =-4/3
ab= -1/3 x -1 =1/3
quadratic equation
x²-(-4/3)x + 1/3=0
x² + 4/3x + 1/3=0
multiply through by 3
3x² +4x +1=0
Answer:
general formula
x²-(a+b)x+(ab)
where a is alpha
and b is beta
x=-4+2/6 or x=-4-2/6
x=-1/3 or x=-1
a+b=-1/3 + -1 =-4/3
ab= -1/3 x -1 =1/3
quadratic equation
x²-(-4/3)x + 1/3=0
x² + 4/3x + 1/3=0
multiply through by 3
3x² +4x +1=0
First person to answer will get brainliest and it has to be in 4 or less minutes
Answers
The figure shows triangle DEF and line segment BC, which is parallel to EF:
Triangle DEF has a point B on side DE and point C on side DF. The line BC is parallel to the line EF.
Part A: Is triangle DEF similar to triangle DBC? Explain using what you know about triangle similarity. (5 points)
Part B: Which line segment on triangle DBC corresponds to line segment EF? Explain your answer. (3 points)
Part C: Which angle on triangle DBC corresponds to angle F? Explain your answer. (2 point
Answers
Part A: Yes, Triangle DEF and DBC are the same triangle, but DBC is smaller than DEF because it is just a cut off of DEF.
Part B: I am pretty sure it is angle C.
Part C: I am pretty sure it is angle D.
Answer:
Step-by-step explanation:
Part A.
m < B = m < E (corresponding angles, (BC parallel to EF))
m < C = m < F ( as above)
So triangles DBC and DEF are similar ( by 2 equal angles).
Part B.
Line segment BC ( as they are both opposite < D)
Part C.
< C as its in same relative position to < F.
HELP PLEASE
Use the value of the discriminant to determine the number and type of roots for the equation,
X^2 = 4x - 4
A. 2 real, irrational roots
B. 1 real, rational root
C. 2 complex roots
D. 2 real, rational roots
Answers
We are given –
[tex]\qquad[/tex] [tex]\twoheadrightarrow\bf x² = 4x -4[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\bf x² -4x +4 = 0[/tex]
Where, a = 1 ; b = -4 ; c = 4Let's find it's discriminant.
We know –
[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\bf Discriminant = b² - 4ac}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf Discriminant = (-4)² - 4 \times 1 \times 4[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf Discriminant = 16-16[/tex]
[tex]\qquad[/tex] [tex]\purple{\twoheadrightarrow\sf Discriminant =0 }[/tex]
If Δ (Discriminant) >0here are two separate real roots.If Δ (Discriminant) =0, there are two identical real roots.If Δ (Discriminant) <0, there are no real roots, but there are two complex roots.As we got –
Δ Discriminant is 0 that means , there are two identical real roots. Henceforth, Option (D) 2 real, rational roots – is correct.pls answer quickly
This line chart displays marks scored by Carol out of 100 in each subject. Which statement can be concluded from the chart?
A) history is her favorite subject
B) carol scored more in physics than English
C) Carol got the least marks in history
D) Carol scored the highest in math
Answers
Answer:
D) Carol scored the highest in math.
Step-by-step explanation:
Look at the chart and check each question.
A) history is her favorite subject - Wrong (This is about Marks Obtained, Not Favorite Subjects!)
B) carol scored more in physics than English - Wrong (In Physics, the score is 55 while in English, it is 65!)
C) Carol got the least marks in history - Wrong (History is at 48 while Biology is at 35!)
D) Carol scored the highest in math - Correct (The highest score is 80 which is Math!)
A lady is 5 years younger to her husband and he is 5 times as old as his daughter. If the daughter was 5 years old 3 years back, what is the present age of the lady? 25
45
35
30
Answers
Answer:
35
Step-by-step explanation:
5x (5+3)=40-5=35
someone pls help me!!!!
Answers
Answer:
-2
Step-by-step explanation:
The interval [-6. -4] refers to x values.
At x = -6, in the line in the middle of -4 and -8, y = 0 at the x axis
At x = -4, y = -4. We know this because when the function crosses x = -4, y = -4 at that point.
The average rate of change is equal to (change in y)/ (change in x) = (yfinal - yinitial) / (xfinal - xinitial) (or the other way around in terms of final and initial)
= (-4 - 0) / (-4 - (-6)) = -4 / (-4 + 6) = -4/2 = -2
[tex]\sf -(6-4x)[/tex]
Answers
Answer:
[tex] - (6 - 4x) = - 6 + 4x[/tex]
Answer:
[tex]-6+4x[/tex]
Step-by-step explanation:
[tex]-(6-4x)[/tex]
[tex]\mathrm{Distribute\:parentheses}[/tex]
[tex]=-\left(6\right)-\left(-4x\right)[/tex]
[tex]\mathrm{Apply\:minus-plus\:rules}[/tex]
[tex]-\left(-a\right)=a,\:\:\:-\left(a\right)=-a[/tex]
[tex]=-6+4x[/tex]
Write and solve a system of THREE inequalities that models the situation below.
Terrence is going to make and sell cupcakes and giant cookies as a fundraiser to earn money for his bank uniform. He sells the cupcakes for $1.25 each and the cookies for $0.75. He knows he will sell at least 10 cupcakes and 24 cookies. He wants to make at least $50. Find a possible combination of cupcakes and cookies he needs to sell to meet his goal.
Answers
Answer:
x = cupcakes
y = cookies
3x + 1y ≥ 205
x cupcakes at $3 each plus y cookies at $1 each is greater than or equal to $205
Step-by-step explanation:
Explain how to calculate 32% of 150
Answers
Answer:
32% of 150 is 48.Step-by-step explanation:
32% of 150=> 150 x 32/100=> 3 x 32/2=> 3 x 16=> 48Conclusion:
Therefore, 32% of 150 is 48.
Hoped this helped.
[tex]GeniusUser[/tex]
Troy assembles wooden toya at Tindall's Toy Shoppe. He is paid $1.46 for each snake, $1.11 ab each fan, and $1.74 for each teddy bear. Troy assembled 515 snakes, 982
fans and 669 teddy bears. What Is Troy's gross pay for this week? Round to the nearest cent.
Answers
Answer:
$3005.98
Step-by-step explanation:
did the math with calculator
Find the value of the variables.
Answers
Answer:
x = 90 degrees
y = 50 degrees
Step-by-step explanation:
The angle where x lies is a right angle, and right angles = 90 degrees. A triangle adds up to 180 degrees, so you add 90 and 40 together and then subtract that from 180 degrees.
: Andre poured 27 ounces of rice into 6 containers. If all containers have the same amount of rice, how many ounces are in each container?
Answers
27/6=4.5
Kaya rented a limousine for prom. There was a one-time charge of $100 plus an hourly rate of the total
cost for the night was $347.50. How many hours did Kaya rent the limo for?
Answers
Answer:
3 hours
Step-by-step explanation:
it is $100 for 1 hour right. Ok so forget about the hourly rates. Then you are left with $300. $300 total÷100 per hour = 3 hours.
Answer:
The total is 3 hours
Hope this help! good luck :)
you are going to wash a large glass window in a shape of a trapezoid. The lenghts of the bases of the window are 10 feet and 14 feet. the height is 8 feet. you can wash 6 square feet of the window in 1 minute. how long will it take you to wash the entire window
Answers
Answer:
16 minutes
Step-by-step explanation:
First we are going to want to find the area of the window. We then divide that by the amount of area you can wash per minute ( 6 square feet )
So first lets find the area.
We are told that the window is in a shape of a trapezoid.
The area of a trapezoid can be calculated using the formula A = [tex]\frac{a+b}{2} h[/tex]
Where a and b are the base lengths and h is the height
We are told that the length of the bases are 10 ft and 14ft so a and b = 10 and 14. We are also told that the window has a height of 8 so h = 8 .
We then plug these numbers into the formula to find the area
Recall formula: [tex]A=\frac{a+b}{2} h[/tex]
a = 10 , b = 14 and h = 8
plug in these values into formula
[tex]A=\frac{10+14}{2} 8[/tex]
add 10 and 14 to get 24
[tex]A=\frac{24}{2} 8[/tex]
simplify fraction : 24 / 2 = 12
[tex]A=(12)(8)[/tex]
multiply 12 and 8 to get 96.
A = 96 square feet.
To find how long it would take to wash the window we divide the total area of the window by the amount of area that can be washed per minute
Total area of window = 96
Area that can be washed per minute = 6
Time it would take to wash the whole window = 96 / 6 = 16 minutes
Which property of equality should Wade use to solve the equation StartFraction x Over 6 EndFraction = 3?
Answers
The property of equality Wade would use to solve the equation StartFraction x Over 6 EndFraction = 3 is multiplication property of equality.
Given:
StartFraction x Over 6 EndFraction = 3
x / 6 = 3
apply multiplication property of equality by crossing multiply
x = 3 × 6
x = 18
check:
x / 6 = 3
18 / 6 = 3
3 = 3
Therefore, the property of equality Wade would use to solve the equation StartFraction x Over 6 EndFraction = 3 is multiplication property of equality.
Learn more about property of equality:
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Answer:
C) Multiplication property of equality.
Step-by-step explanation:
Did the test, but it's because to cancel the division, you need to multiply. in this case, they'd multiply by six to cancel the fraction or x/6.
x/6=3
x/6x6=3x6
x=18
hope this helps
First correct answer= brainlist
Answers
Answer:
[tex]-a^2+ab[/tex]
Step-by-step explanation:
So the sentence can be written like this:
[tex]((a^2-b^2)+(a^2+ab+3b^2))-((a^2-2ab+b^2)+(2a^2+2ab+b^2))[/tex]
Now you can combine like terms in the first part of the equation and the second part:
[tex]((a^2+a^2)+ab+(-b^2+3b^2))-((a^2+2a^2)+(-2ab+2ab)+(b^2+b^2))[/tex]
Which leaves you with:
[tex](2a^2+ab+2b^2)-(3a^2+2b^2)[/tex]
Now distribute the negative to the second part of the equation:
[tex]2a^2 + ab + 2b^2-3a^2-2b^2[/tex]
Combine like terms again:
[tex](2a^2-3a^2)+ab+(2b^2-2b^2)[/tex]
Which becomes:
[tex]-a^2+ab[/tex]
Answer:
- a² + ab
Step-by-step explanation:
summing the first 2 expressions
a² - 2ab + b² + 2a² + 2ab + b² ← collect like terms
= 3a² + 2b² → (1)
summing the next 2 expressions
a² - b² + a² + ab + 3b² ← collect like terms
= 2a² + ab + 2b² → (2)
Subtracting (1) from (2)
2a² + ab + 2b² - (3a² + 2b²) ← distribute parenthesis by - 1
= 2a² + ab + 2b² - 3a² - 2b² ← collect like terms
= - a² + ab
if 3/15 is equivalent to 45/n. find n
Answers
Answer:
n = 225
Step-by-step explanation:
Multiply 15 by 15
Cross multiply
3n=675
Divide both sides by 3
n=675/3
n=225
"a deposit plus $8 per hour"
Answers
Answer:
d + 8/hr
Step-by-step explanation:
Does anyone know the answer to this the work is not needed unless you would like but Please please please answer :)
Answers
Can somebody please help me i need this urgently.
Answers
Answer:
multiple choice is worth 2
short response is worth 4
Step-by-step explanation:
23x + 10y = 86
28x + 5y = 76
solve by elimination
multiply the top by -1 and the bottom by 2
-23x + -10y = -86
56x + 10y = 152
add them
33x = 66
x = 2
with x = 2 plug x into one of the equations
23x + 10y = 86
23(2) + 10y = 86
46 + 10y = 86
10y = 40
y = 4
x = 2 and y = 4 so
multiple choice is worth 2
short response is worth 4
I do not understand
Answers
[tex]\huge \sf༆ Answer ༄[/tex]
Here's the solution ~
[tex] \sf \dfrac{5 {}^{6} }{5 {}^{1} } [/tex][tex] \sf 5 {}^{6 - 1} [/tex][tex] \sf {5}^{5} [/tex]While moving up on the rope-way, I noticed that the seat place in the opposite direction was numbered as 95. Behind it was number 0, then 1, 2 and so on. My seat place was numbered as 66. What number should I meet when I am in the middle of my one-way route?
Answers
The seat in the middle of the one-way route is 34
The seats are given as:
[tex]First= 0[/tex] --- the first seat behind the seat number 95
[tex]Last= 66[/tex] --- my seat
The seat number half-way would be:
[tex]Half = \frac{Last - First}{2} + 1[/tex]
This gives
[tex]Half = \frac{66- 0}{2} + 1[/tex]
Subtract 0 from 66
[tex]Half = \frac{66}{2} + 1[/tex]
Divide 66 by 2
[tex]Half = 33 + 1[/tex]
Add 33 and 1
[tex]Half = 34[/tex]
Hence, the seat in the middle of the one-way route is 34
Read more about median at:
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Charnise uses 3 gal. red paint to 5 gal. white paint to make pink paint. She
needs 24 gal. of pink paint. How many gallons of red paint will she need?
Answers
The method into creating pink paint is mixing 3 gallons of red paint and 5 gallons of white paint together. This mixture only creates 8 gallons of paint and she needs 16 more. List the factors of 16:
1, 2, 4, 8, and 16
We notice that 8 can be factored out of 16 and becomes:
16 / 8 = 2
If we multiply the sample by 3 (the one already counted plus the two extra), we can discover how much paint is needed. Multiply everything by 3:
3 x 3 = 9
5 x 3 = 15
So in this case, 15 gallons of white paint and 9 gallons of red paint are need and combine for 24 gallons in total.
The ratio of shoes sold to sandals sold was 9:5. If there were 72 shoes sold, how many
sandals were sold?
Answers
Answer:
40
Step-by-step explanation:
9x8 = 72
5x8 = 40
72:40 = 9:5
Hope that helps