Answer:
0.83r + 0.91
Step-by-step explanation:
-0.17r + 0.91 + r
Combine like terms (so, that would be r)
0.83r + 0.91
y = f(x) has the derivative f'(x) = (x + 1)²(x + 3)(x² + 2mx + 5) with ∀x∈i.
find m so that g(x) = f(|x|) has exactly 1 extreme point
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Answer:
m ≥ -√5
Step-by-step explanation:
If g(x) = f(|x|) for x∈i, then g(x) = f(x) for x∈ℝ: x ≥ 0.
f'(x) is 5th-degree, so f(x) is 6th-degree, meaning it is generally U-shaped. Since we're only concerned with x ≥ 0, we want to make sure f'(x) has no real zeros of odd multiplicity such that x > 0. The given factors of f'(x) make it have real zeros at x = -3 and x = -1.
For the last factor, (x² +2mx +5) to have no positive real zeros of odd multiplicity, we must have m ≥ 0 or the discriminant ≤ 0. The discriminant is ...
d = b² -4ac = (2m)² -4(1)(5) = 4m² -20 . . . . . discriminant of the last factor
d ≤ 0 . . . . . . . . . . the condition for no real zeros
4m² -20 ≤ 0
m² -5 ≤ 0 . . . . . . divide by 4
m² ≤ 5 . . . . . . . . .add 5
|m| ≤ √5 . . . . . . . take the square root
This tells us there will be a positive real zero of multiplicity 2 in f'(x) when m = -√5, and there will be no positive real zeros for -√5 < m < 0
There will be no odd-multiplicity positive real zeros in the derivative function f'(x) as long as m ≥ -√5. This means the slope of f(x) is non-negative for x ≥ 0, hence f(|x|) has its only minimum at x=0.
_____
Additional comment
The multiplicity of the zeros of f'(x) is important because the derivative will only change sign where the multiplicity is odd. When the discriminant of (x²+2mx+5) is zero, the associated positive real zero will have multiplicity 2, hence f'(x) will not change sign there.
Select the statement that is true. (2 points)
a
0.688 < 0.602
b
0.688 > 0.602
c
0.688 = 0.602
d
0.602 > 0.688
Answer:
b is the answers for the question
Step-by-step explanation:
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A recipe for lemonade calls for 2 1/2 quarts of water. How many cups of water should you use for the recipe?
Answer:
10 cups
Step-by-step explanation:
1 quart=4 cups
Water flows into the tank at a rate of 3 litres per minute.
If the tank fills completely in 450 seconds , What is the capacity of the tank in ml?
rate = 3l/minute÷60 = 0.05l/s
t = 450s
capacity = ?
rate = c/t
c = rate*t
c = 0.05*450
c = 22.5litres.
c = 22500ml
How many groups of 3/8 can fit into 3/4. Notice it is not asking how many 1/8 you can fit
Answer:
2
Step-by-step explanation:
You can fit two groups of 3/8. 3/4 is equivalent to 6/8. 3/8 goes into 6/8 two times therefore the answer is two groups of 3/8.
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Expand and simplify 2(3x - 4) - 2(x - 5)
Answer:
(6x-8)-(-2x-10)
4x-18
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Answer:
m:3/2 b:0 or 1
Step-by-step explanation:
I believe its asking what the m and b is in this formula: mx+b
so 3/2 and 0 or 1?
Answer:
in Y = mX + b
in relation to Y = -3/2X + 0
m = -3/2
b = 0.
Which diagram shows only the first step of constructing the line perpendicular to
segment AB through point P?
Perpendicular lines are lines that meet at 90 degrees.
Diagram (D) shows the first step of constructing the perpendicular line.
To draw a perpendicular line, the first step is to draw two points equidistant to the point at which the perpendicular line will pass.
Assume that the point is P.
The following points represent the position of the two points
. P .
The diagram that shows this representation is (d)
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solve this please. i need an answer
Five students are running for Junior class president. They draw straws to see who will go first, second, etc. In how many different orders could they give their speeches?
===================================================
Explanation:
There are 5 choices for the first selection, 4 choices for the second, etc etc until we reach 1 for the last selection. We have the countdown {5,4,3,2,1}. We'll multiply those values together to get our answer.
5*4*3*2*1 = 120
This operation of starting with some integer, counting down and multiplying along the way, is done so very often that it's given a name which is "factorial". The shorthand notation is to use an exclamation mark. So we'd say 5! = 120
Miss lin bought 40 berry,strawberry,chocolate cookies.The ratio of number of berry cookie,strawberry cookie, chocolate cookie was 7;5;8.find the number of chocolate cookies.
Answer:
20 chocolate cookies
Step-by-step explanation:
7 +5 + 8 + x = 40
7+5+8= 20 cookies non chocolate
subtract 20 from both sides
40-20= 20 chocolate cookies
FRACTIONAL INDICIES - PLEASE HELP
Answer:
1) 2/5
b) 5/2
2) C
3) 1/3
4) X = - 3/2
5) middle right left
Please help :)
40 percent of the leaves are still green. If there are 12,000 total leaves, how many are no longer green?
Answer:
4,800
Step-by-step explanation:
40% of 12000 = 4800
Which one is the larger average rate, -3.142 or -0.5?
Answer:
The answer to this question is -3.142
given -3nsquared -n +14
find the first four terms of the sequence
Answer:
-3,n²,-n,14
Step-by-step explanation:
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QUICK QUESTION: What is the answer?
Answer:
2 AIF3... synthesis
Step-by-step explanation:
WELLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL
Violet bought snacks for her team's practice. She bought a bag of popcorn for $3.29 and a 15-pack of juice bottles. The total cost before tax was $27.14. Write and solve an equation which can be used to determine j, how much each bottle of juice costs.
How do you write an equation for this?
Answer:
popcorn 3.29$
popcorn + 15 pack juice = 27.14$
Step-by-step explanation:
15 pack juice= 27.14-3.29
15 pack juice=23.85
pack of juice=23.85/15
pack of juice=1.59$
The equation that shows the cost of each bottle of juice is 15j + 3.29 = 27.14 and the cost of each juice is $1.59
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let j represent the cost of each bottle of juice. The total cost before tax was $27.14, hence:
15j + 3.29 = 27.14
j = 1.59
The equation that shows the cost of each bottle of juice is 15j + 3.29 = 27.14 and the cost of each juice is $1.59
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Can you help work question number 4 please?
Step-by-step explanation:
if 2 sides are equal which means it is an Isosceles triangle
so,
→ 52 + 52 + c = 180
→ 104 + c = 180
→ c = 180 - 104
→ c = 76°
d = 52°
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Charlotte bought 25 cookies to share with her class, and 5 of them are oatmeal raisin. What percent of the cookies are oatmeal raisin?
Answer:
20%
Step-by-step explanation:
25 divided by 5 = 5
Convert to decimal
0.20
Convert to percentage
20%
Answer:
20%
Step-by-step explanation:
25 divided by 5=5
convert to decimal
0.20
convert to percentage
20%
Solve the proportion using the multiplication property of equality.
E 100
OL
m =
(Type an integer or a decimal.)
There are 40% more black balls than white balls in a bag.
Work out the ratio of black balls to white balls.
Give your answer in its simplest form.
Answer:
there are 40% black ball a
white ball we don't know
so, we let = x
40\100 × x
now we cutting
ans is 10x
Two rectangular flower beds are set next to each other as shown:
Flowerbed A has length x feet and width that is two feet more then five times it’s length
Write an expression for the area of Flowerbed A:
Expand this expression
Answer:
area = l x 5l + 2
Step-by-step explanation:
area equals length times 5 times the length plus two
The expression for the area will be equal to x(5x + 2).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Flowerbed A has length x feet and width that is two feet more than five times its length
Lenght = x
width = 5x + 2
Area = L x W
Area = x ( 5x + 2 )
Area = 5x² + 2x
Therefore, the expression for the area will be equal to x(5x + 2).
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Find the original price given the total amount and tax rate.
Total price: $128,500
Tax rate: 5.5%
What is the length of the missing sides?
Perimeter=14
What is 40% of 60? someone help pleaseee
Answer:
it is use a calculator and type 60 divided by .4
Answer:
24% or just 24
Step-by-step explanation:
if wrong pls forgive me
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what property does have to make it more suitable for water pipes than metal pipes?
Answer:
Copper
Explanation:
Copper would be beacuse it's non-toxic, it's antimicrobial, it's rustproof, and it is affordable.
One of Teddy's jobs at home is to pump gas for his family's sedan and truck. When he fills up the sedan with 12 gallons of gas, he notices that it costs him $50.28. How much does one gallon of gas cost? This is also called the unit rate. Explain how you found your answer.
Answer:
4.19$
Step-by-step explanation:
If 12 gallons cost 50.28$
then 1 gallon would be (50.28/12)$
which equals to 4.19$
The Teddy's jobs at home is to pump gas for his family's sedan and truck the cost of gas of one gallon is:
=> The unit rate is:
=> $4.19 per gallon
We have the following information available from the question is:
One of Teddy's jobs at home is to pump gas for his family's sedan and truck.
When he fills up the sedan with 12 gallons of gas, he notices that it costs him $50.28.
Now, According to the question:
The cost of gas of one gallon is:
=> The unit rate is:
50.28/12
=> $4.19 per gallon
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what is 2.04 + 0.07 as a answer
Answer:
2.11
2.04+0.07=2.11
Answer:
2.11
Step-by-step explanation:
2.04 + 0.07
2.11
Solved using: Math