Answer:
If I calculated correctly, the tangent line is horizontal where x ≈ -5.3 + 9.3i, and -5.3 - 9.3i
I'm somewhat concerned at having gotten complex numbers, and strongly recommend going through the steps to see if I missed anything. I checked it myself and don't see any errors.
Step-by-step explanation:
You can do this by taking the derivative of the function and solving for zero:
f(x) = 2x³ + 32x² + 220x + 11
f'(x) = 6x² + 64x + 220
f'(x) = 2(3x² + 32x + 110)
We can't factor that further, so let's do it the long way, starting by letting f'(x) equal zero:
0 = 2(3x² + 32x + 110)
0 = 3x² + 32x + 110
0 = 9x² + 96x + 990
0 = 9x² + 96x + 256 + 734
0 = (3x + 16)² + 734
(3x + 16)² = -734
3x + 16 = ± i√734
3x = -16 ± i√734
x = (-16 ± i√734) / 3
x ≈ (-16 + 27.9i) / 3, and (16 - 27.9i) / 3
x ≈ -5.3 + 9.3i, and -5.3 - 9.3i
I'm always wary when I end up with complex numbers. I'd suggest double checking everything here, but I'm fairly certain I did everything correctly.
A bicycle was reduced by 20%. The reduced price was £100. What was the original price?
Answer:
£125
Step-by-step explanation:
Let the original price be x
Reduction = 20%
Price after reduction = (100 - 20)% = 80%
80% of x = £ 100
[tex]\frac{80}{100}x = 100\\\\x=100*\frac{100}{80}\\\\[/tex]
x = 125
Original price = £125
Which of the following sets of numbers could represent side
lengths of a right triangle?
Select one:
15 cm, 18 cm. 33 cm
15 cm, 20 cm, 25 cm
15 cm, 16 cm, 17 cm
15 cm, 15 cm, 18 cm
9514 1404 393
Answer:
(b) 15 cm, 20 cm, 25 cm
Step-by-step explanation:
Because you know that the triple (3, 4, 5) is a Pythagorean triple, you know that every multiple of it will also give side lengths of a right triangle. Multiplying that triple by 5 gives (15, 20, 25), matching the 2nd choice on the list.
__
Comments on other choices
You also know that (3, 4, 5) is the only Pythagorean triple that has constant differences, so 15, 16, 17 cannot be a right triangle. (It is very nearly an equilateral triangle.)
A right triangle with same-length sides will have a hypotenuse that is √2 times that length, so no right triangle will have two equal integer legs and an integer hypotenuse.
The lengths 15, 18, 33 form a straight line, not even a triangle.
__
For those who insist on seeing an equation:
15^2 +20^2 = 225 +400 = 625 = 25^2 . . . 15, 20, 25 will form a right triangle
The number of registered vehicles on the road in a country is constantly increasing. In 2009, there were approximately 220 million registered vehicles. This represents a
2% increase over 2002. How many registered vehicles were there in the country in 2002?
Answer:
10000
Step-by-step explanation:
Simplify 2(5*)
What is the answer
Answer:
the answer is 10 multiply maybe
Tina ate 21 starbursts. If she ate 35% of the package of Starbursts, how many Starbursts are in the package?
Show your work
Answer:
60 starbursts
Step-by-step explanation:
We can set up an equation to find the answer. 21/x=0.35/1 because we're trying to find how many starbursts make up 100% of the package. So then to solve, we take 21x1 and then divide that by 0.35. From this we find that x=60.
What is 29 to the power of x to the power of 15
Answer:
29 to the power of 15x
Step-by-step explanation:
Rules of exponents:
Multiply exponents.
15*x=15x
Therefore 29 to the power of 15x
Which measures are the sides lengths of a right triangle?
a)4cm 12cm 8cm
b)5cm 12cm 10cm
c)16cm 4cm 6cm
d)30cm 12cm 6cm
Answer:
b)
Step-by-step explanation:
a) 4+12>8
12+8>4
4+8=12
NO
b) 5+12>10
10+5>12
12+10>5
YES
c) 16+4>6
6+4<16
NO
d) 30+12>6
12+6<30
NO
Write a system of equations and solve. Three times the first number minus two times the second number equals -7. The second number equals one less than negative three times the first number.
Answer:
-1 and 2Step-by-step explanation:
Let the numbers be x and y
Three times the first number minus two times the second number equals -7:
3x - 2y = -7The second number equals one less than negative three times the first number:
y = -3x - 1Substitute y in the first equation and solve for x:
3x - 2(-3x - 1) = -73x + 6x + 2 = -79x = -9x = -1Find the value of y:
y = -3(-1) - 1 y = 3 - 1y = 2The numbers are -1 and 2
Convert to the given unit. 42 in. = ______ ft
Answer:
There are 12 inches in a foot 42/12(ft)Answer:
3.5
Step-by-step explanation:
42/12=3.5
The equation for the linear function is
y= BLANK1 x + BLANK 2
What are the blanks?
Answer:
Answer:y=x divided by 3 times 5.
Step-by-step explanation:
if you divide x for example 6 by 3, you will get 2 then multiply it by 5, you will get 10, which is y.
My salary is £28,860 per year. What is my hourly rate of pay if I work 37 hours a week
Answer:
pay rate £7.80
Step-by-step explanation:
28860 divide by 37 = 780
780 divided by 100 = 7.80
Equivalent expression for 18x-12x
Answer:
[tex](18x - 12x) = (18 - 12)x = \boxed{6x}✓[/tex]
Equivalent expression for (18x-12x) is 6x.
6x is the right answer.Simplify (3x^2+5x) + (6x-6x^2+2)
Answer:
-3x^2+11x+2
Step-by-step explanation:
hope this helps!
I dont know how to get people to answer but please i really really need help fast im begging anyone
Answer:
75 + m ≥ 495
m ≥ 420
Step-by-step explanation:
Simplify this expression
√108
Answer:
6√3
Step-by-step explanation:
3. Peri earned $27 for walking her neighbor's dog 3 times. If pe the same rate and earned $36, how many times did she wall neighbor's dog? Use a unit rate to find the unknown value. 27 36 3 time
Answer:
She walked neighbor's dog 4 times.
Step-by-step explanation:
It is given that:
Peri earned $27 for walking the dogs 3 times.
Unit rate = [tex]\frac{27}{3}[/tex]
Unit rate = $9 per dog
Now,
Peri worked at the same rate and earned $36.
Unit rate = [tex]\frac{Total\ earning}{Dogs\ walked}[/tex]
[tex]9 = \frac{36}{d}[/tex]
d= 36/9
d = 4
Therefore,
She walked neighbor's dog 4 times.
please i need your help!
Answer:
$104,912.76
Step-by-step explanation:
You will need to pay $603.92 every month for 30 years to payoff the debt.
Monthly Payment$603.92
Time to Pay Clear30.00 years
Total of 360 Payments$217,412.76
Total Interest$104,912.76
(Credits to ElectricPavlov)
Kate can read 12 pages in 8 minutes. How many minutes will it take her to read 30 pages? Write a proportion to this problem.
Answer:
12/8 = 30/x ... x =20minutes
Step-by-step explanation:
What is the first error Alycia made in her proof.
Answer: Alycia only established some of the necessary conditions for a congruence criterion.
Step-by-step explanation: Two triangles are congruent if their corresponding sides or/and corresponding angles are the same.
There are 5 ways to find out if the triangles are congruent.
The one Alycia used seems to be the one called Side-Angle-Side, which states that if two sides and its included angle is equal to the corresponding sides and angle of the other triangle, they are congruent.
For triangles ΔOPQ and ΔSTR to be congruent, using that theorem:
1) ∠O = ∠S
2) OP = TS
And
3) RS = OQ
So, Alycia's error is that she didn't prove RS = OQ, which would definitively conclude that both triangles are congruent.
Answer:
Alycia used a criterion that does not guarantee congruence.
Step-by-step explanation:
A proof is a formal description of how we can know that something is true based on the information from a mathematical scenario.
Each step of the proof is a transformation, a construction, or a statement about what we can conclude from earlier steps.
For a two-column proof we give a reason to justify each statement. Common reasons include geometric theorems, algebraic properties, and information given in diagrams.
Let's check the reason for each step and whether Alycia established the conditions for it.
Step 1
The diagram does support the claim that OP=ST=4
Step 1 is correct
Step 2
The diagram does support the claim that OP is parallel to ST because they both have an arrow mark.
Step 2 is correct.
Step 3
<O is indeed congruent to ∠S because they are alternate interior angles between parallel lines.
Step 3 is correct.
Step 4
In this step, Alycia claims that the triangles are congruent using a "side-angle" criterion. She did establish the conditions for claiming that the figures has one pair of congruent corresponding sides and one pair of congruent corresponding angles.
~From Step 1, we know OP is congruent to ST
~From step 2, we know O is congruent to S
(Segments and angles are congruent if and only if they have equal measures.)
However, side-angle congruence is not a valid reason for claiming that two triangles are congruent, so Alycia's reason is inappropriate.
Alycia used a criterion that does not guarantee congruence.
Which equation represents the graphed function?
O y = 4x - 2
O y = -4x - 2
Oy = -x-2
O y=-x-2
9514 1404 393
Answer:
y = 1/4x -2
Step-by-step explanation:
The line rises one unit from -2 to -1 as x changes from 0 to 4. The slope is ...
m = rise/run = 1/4
The y-intercept (b) is where the line crosses the y-axis, at y = -2.
The equation in slope-intercept form is ...
y = mx + b
y = 1/4x -2
Which sequence of transformation can be used to map parallelogram K l m n onto parallelogram k l m n
Answer:
I need to see it first please
PLEASE HELP MEAN A LOT I WILL GIVE BRAINLIEST
Answer:
Kim should'nt have put 2 because y would be bigger than 2
by-step explanation:
Myra’s flower bed has three types of flowers. There are 7 lilies, 5 tulips, and 6 zinnias. What does the ratio 5 : 13 represent in this situation? Use a model to show your work. Explain your reasoning.
Answer:
m
Step-by-step explanation:
The ratio 5 : 13 in this situation represents number of Lilies to the number of tulips and zinnias in Myra's flower bed.
A ratio shows us the number of times a number contains another number.
Given that Myra’s flower bed has three types of flowers. There are 7 lilies, 5 tulips, and 6 zinnias. Therefore, the ratio of number of Lilies to the number of tulips and zinnias are,
Ratio = Number of Lilies : Number of tulips and zinnias
Ratio = 5 : (7+6)
Ratio = 5 : 13
Hence, the ratio 5 : 13 in this situation represents number of Lilies to the number of tulips and zinnias.
Learn more about Ratios here:
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Kelly uses point p to represent the sum of 3.6 +(-2.4) on the number line.
3.6 + (-2.4) = p
Kelly says that point pis plotted to the right of both 3.6 and -2.4 on the number line because addition means you should move right on the
number line.
• Explain why Kelly's reasoning is incorrect.
• Explain how the location of p on the number line is related to the locations of 3.6 and -2,4 on the number line.
Determine the value of point p.
Enter your explanations and your answer in the box provided.
Answer:
Kelly is incorrect because she added the two numbers on the number line that made no since.
If Kelly had worked through the problem
P would have equaled 1.2
3.6+(-2.4) = 1.2 which is what p equals
The value of P is 1.2
The value of p is 1.2.
What is an absolute value?Absolute value of a number is the distance value from zero without considering sign of a number. It is also represented as |x|, where x is any number.
Given that the expression, 3.6 + (-2.4) = p
To find the value of p,
3.6 + (-2.4) = p
p = 1.2
Relation of p in number line with -2.4 and 3.6 ;
p = 1.2 in the number line is right side of -2.4 and left side of 3.6.
Whenever we add the positive numbers we get the sum of the number in the right side of both the positive number.
And whenever we add the negative numbers we get the sum of the number in left side of both of the negative number.
And when we add the positive and negative number then if
1) positive number > absolute value of negative number then sum of the numbers will be in the middle of the both number.
And 2) if positive number < absolute value of negative number then the sum of the numbers will be in the middle of both of the number.
Therefore the value of p is 1.2.
To learn more about the absolute value;
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Adriana is rock climbing. She started at an elevation of -36.5 meters relative to sea level and will finish at an elevation of 24 3/4 meters. Her climb is now 80% complete. Estimate her current elevation. Then find her actual elevation. Show your work.
Answer: -722 7/10
Step-by-step explanation:
5 - (-3 x 7 ) +8 ÷ 4
Answer:
21x+7
Step-by-step explanation:
hope this helps ! c:
The answer to 5 - (-3 x 7 ) +8 ÷ 4 is 21x+7
Hope it helped!
Jermaine is saving $60 per week for a new guitar. The amount he has saved, s, is represented by
the function S = 60w, where w is the number of weeks he has been saving. Which is a true
statement?
A The number of weeks Jermaine saved depends on the amount he saves each week.
B The cost of the guitar depends on the amount Jermaine saves each week.
C The amount of money saved depends on the cost of the guitar.
D The amount of money saved depends on the number of weeks Jermaine has saved.
Option' A
Option B
Option C
Option D
Answer:
D
Step-by-step explanation:
34.25 times what equal 342.5
Answer:
10 probably
Step-by-step explanation:
it looks like a multiple of 10 since decimal just moved 1 place. I'm no expert
Answer:
10
Step-by-step explanation:
342.5÷34.25 = 10
brain
Plzzz helps me for once!!! Graph y= -x/3 - 3/2.
Answer:
go to desmos it is a online graphing calculator
Step-by-step explanation:
Given any two functions f and g, which of the following statements is always true? (1 point)
O If z is in the domain of f. then must be in the domain of f - g.
Olf 2 is in the domain of f and 22 is in the domain of g, then the product, 222, must be in the domain of fg.
O If ac is in the domain of f + g. then I must be in the domain of f and 2 must be in the domain of 9
O fa is not in the domain of then a is not in the domain of g
Answer:
cccccc
Step-by-step explanation:
Given two functions f and g, we want to see which statement is always true.
The only true statement is the third one:
"If a is in the domain of f + g. then I must be in the domain of f and it must be in the domain of g"
So what we can do, is try to find counterexamples for the given statements, if we can't, then the statements are true.
Note that the statements are really badly written, so I will complete them in a way that makes sense.
a) "If z is in the domain of f. then must be in the domain of f - g"
False, if z is not in the domain of g, then we can't define:
(f - g)(z)
This would happen if:
g = 1/(x - z)
b) "lf 2 is in the domain of f and 22 is in the domain of g, then the product, 222, must be in the domain of fg"
False, lets replace:
2 = z
22 = k
And let's say that:
f(x) = 1/(x - z*k)
g(x) = x
Then we have:
f*g(x) = x/(x - z*k)
Clearly, z*k (or 222 as you wrote it) is not on the domain.
c) "If a is in the domain of f + g. then I must be in the domain of f and it must be in the domain of g"
True, it only can be on the domain of the sum of the two functions if it belongs to the domain of each one.
d) "if a is not in the domain of (f + g) then a is not in the domain of g"
This is false, because a could be in the domain of g and not be in the domain of f.
Then the only true statement is the third one.
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