WILL GIVE BRAINLIEST! Consider the graph at right and answer the following questions.
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Answer:
a.)A and B are the intersection between the two curves. The x coordinate is the equation
[tex]f(x) = g(x)[/tex]
Let's solve it
[tex]\frac12 (x-2)^3 +1 = 2x^2-6x-3\\x^3-6x^2+12x-8+2=4x^2-12x-6\\x^3-10x^2+24x=0\\x(x^2-10x+24)=0\\x(x-4)(x-6)=0[/tex]
We can see that if we substitute x= 0 or x= 4 the equation is verified.
b. The equation has a third solution, x = 6, that is too far to the right to be visible in the graph.
c. the x coordinate of C is the solution of [tex]f(x)=0[/tex] or [tex]\frac 12 (x-2)^3 +1=0\\(x-2)^3 = -2\\(x-2) = -\sqrt[3]2[/tex]
At this point let's guesstimate the cubic root of 2 -let's say the cubic root of 2 is equal to 1plus an error e, and since we know how to calculate the cube of a binomial, let's build it.
[tex](1+e)^3 = 2 \rightarrow 1+3e+3e^2+e^3 = 2[/tex] Now, assuming the error is small enough, it's square and its cube gets even smaller. (if the error is 0.1, it's square becomes 0.01 and the cube 0.01), let's ignore them. [tex]1+3e=2 \rightarrow 3e=1 e= \frac13[/tex] So, going back to our equation, we can tell that the right hand side is [[tex]\mathbb{R}[/tex]]-(1+\frac13)[/tex] Not perfect, but good enough. Let's solve it now.
[tex]x-2= -1-\frac13 \rightarrow x=1-\frac13 = \frac23[/tex]
Which seems close enough from the photo.
c. Domain of both function are the whole Real set, since they're polynomials. Range of f(x) is again the whole real set, since it's an odd degree polynomial. g(x) is a parabula and its range is for y above the vertex y-coord, which is [tex]y>g(\frac32) = 2(\frac94)-6(\frac32)-3 = \frac92 -3(\frac62) -\frac62 = \frac92-4\frac62= -\frac{24-9}2 = -\frac{15}2[/tex]
Related Questions
GEOMETRY PROOFS!
Given: AB ≅ DB; AC ≅ DC
Prove: ABC ≅ DBC
refer to attachments
WILL GIVE BRAINLIEST! PLS HELP!
Answers
Given that
In ∆ ABD , AB = BD------(1)
=> Angle B = Angle D
Since the angles opposite to equal sides are equal.
=> Angle A = Angle D
and
BC bisects Angle B
=> Angle BCA = Angle CDB ----(2)
And
BC = BC (Reflexive Property) -----(3)
From Eqⁿ(1),(2)&(3) we have
BA = BD
< ABC = BCD
BC = BC ( Common Side)
Therefore, ∆ ABC =~ ∆ DBC
by SAS property
Hence, proved.
Additional comment:
The angles opposite to equal sides are equal.In two triangles , the two sides and the included angle of the first triangle are equal to the corresponding two sides and the included angle in the second triangle then they are congruent and this property is called Side-Angle-Side (SAS) Property.CPCT - Corresponding parts in the Congruent triangles are equal.Angle bisector divides the angle into two equal parts.The sum of two adajacent angles is 180° they are called Linear Pair.also read similar questions:Given: AD perpendicullar DB, DB perpendicullar BC, AB = CD Prove: AB||DC..
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given: AB ≈ DC ; AC ≈ DB PROVE: ABC ≈ DCB THE DIAGRAM SHOWS A 2 COLUM PROOF. ORDER THE REASONS SHOWN IN THE LIST TO MATCH THE STATEMENTS ......
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Which expressions are equivalent to
-1/3(12-9+6x)
Answers
Answer:
-2x-1
Step-by-step explanation:
first you simplify what is inside the parenthesis to get: -1/3(6x+3)
then, you distribute the -1/3 to each of the numbers inside the parenthesis to get: -2x-1
What is a trend line in math.
Answers
Answer:
Determining if a set of points exhibits a positive trend, a negative trend, or no trend at all.
A trend line, often referred to as a line of best fit, is a line that is used to represent the behavior of a set of data to determine if there is a certain pattern.
WATER The workers at the plant drink 38 gallons of water per day. Write an equation to find the number of gallons g the workers drink in any number of days d?
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Hope this helps
Solve. −6.6x=−4 What is the solution to the equation? Enter your answer as a simplified fraction in the box. x =
Answers
Answer:
20/33
Step-by-step explanation:
i took the test
Answer:
x = 20/33
Step-by-step explanation:
−6.6x = −4
Divide both sides by -6.6
x = -4/(-6.6)
x = 40/66
x = 20/33
Answer: x = 20/33
HELP PLEASE ASAP WILL GIVE BRAINLIEST
Farmer Hopt started with some alabers on her farm. She had 90 alabers after 5 months. After 16 months, she had 167 alabers. Assume a constant rate of change.
Write an equation in slope-intercept form for total alabers, y, after x months.
Answers
Answer:
[tex]y= 11x+35[/tex]
Step-by-step explanation:
Let's find the slope first. It took hopt 11 months (from 5 to 16) to grow 77 trees. It means that each month he grew [tex]\frac{77}{11} = 7[/tex] trees.
At this point you can use the point-slope form and re-write the equation or, let's think about it. It's a direct proportion. If at month 5 she has 90 trees, one month earlier she had 11 less. two month earlier, 22 less. 5 month earlier, or at x = 0 (ie, our intercept!) she had 55 less trees, or 90-55 = 35 trees
The equation is then [tex]y= 11x+35[/tex]
5. How is each centimeter on a ruler further divided?
tenths
fourths
sixteenths
O eighths.
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Mai skated x miles, and Clare skated farther than that. Write an expression for the distance Clare skated. Write an equation to represent the relationship between the distance Mai skated (x) and the distance Clare skated (y).
Whats the answer?
Answers
Answer:
X over y or x/y since y is claire and she skated more
Step-by-step explanation:
Pls brainliest
Plant A Plant B WeeksHeight (inches) WeeksHeight (inches) 06 04 28 27 Part A To graph the two linear relationships, you need to know which variable is the independent variable, x, and which is the dependent variable, y. Of the two variables, weeks and height, which is the independent variable and which is the dependent? Explain your answer.
Answers
Answer:
Weeks is the independent variable and height is the dependent variable.
Step-by-step explanation:
The height of the plant depends on the weeks the plant has been growing. So the height is the dependent variable. Because the number of weeks doesn't depend on anything, the number of weeks is an independent variable.
Dan and Paul share some money in the ratio 13:5.
Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1.
How much did Paul originally have?
Answers
Answer:
Dan had $104
Paul had $40
Step-by-step explanation:
13x-32=5x+32
8x=64
x=8
8*5=40
13*8=104
Enter an expression equivalent to (x^4 y^3 y)^2 in the form x^m y^n
Answers
Answer:
Step-by-step explanation:
As water evaporates from a bucket, its weight changes at a rate of -11/4 ounces per day.
what's the answer?
Answers
Answer:
the five differences are 24.88
Help. What is 90% decreased by 10% :/
Is it 81?
Answers
New value =
90 - Percentage decrease =
90 - (10% × 90) =
90 - 10% × 90 =
(1 - 10%) × 90 =
(100% - 10%) × 90 =
90% × 90 =
90 ÷ 100 × 90 =
90 × 90 ÷ 100 =
8,100 ÷ 100 =
81
Hope this helps :)
URGENTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT
Answers
Answer:
I don't think soo that it make a function
So the answer is A
PLZ HELP 100 POINTS AND DUE TODAY I WILL BE SO GRATEFUL!!
Answers
Answer:
A) 15(20x14) = 4,200
Step-by-step explanation:
20 pounds each day per horse
so 2 weeks is 14 days
which means 20x14
then there are 15 horse
so 15(20x14)
4,200
If y + 6 = 45, then y = 39
Answers
Answer:
True!
Step-by-step explanation:
The sum of the first 10 terms of a linear sequence is 5 and the sumof the next 10 terms is 215. Find the sequence.
Answers
Answer:
The first term of the sequence is -8.95 with a common difference of 2.1.
The sequence is:
-8.95, -6.85, -4.75, -2.65...
Step-by-step explanation:
We are given that the sum of the first ten terms of a linear sequence is 5, and the sum of the next ten terms is 215.
And we want to find the sequence.
Recall that the sum of an A.P. is given by:
S = k / 2 ( a + xk)
Where a is the first term, k is the number of terms, and x_k is the last term.
We can represent our term values with the direct formula:
Xn = a + d (n-1)
Where the first term, x₁ = a.
The sum of the first ten terms is 5. Hence, S = 5, k = 10, a = x₁ and x_k = x₁₀:
(5) = 10/2 (a+xk)
5 = 5(a+(a+9d))
2a + 9d = 1
The sum of the next ten terms (that is, from x₁₁ to x₂₀) is 215. Hence, S = 215 when k = 10, a = x₁₁, and x_k = x₂₀:
(215) = (10)/2 (a + xk)
215 = 5((a+d(11-1))+(a+d(20-1)))
2a + 29d = 43
This yields a system of equations:
[tex]\left \{ {{2a+9d=1} \atop {2a+29d=43}} \right.[/tex]
Solve:
(2a + 9d) + (-2a - 29d) = (1) + (-43)
-20d = -42
d = 2.1
Consequently:
a = 1/2(1-9d)
= 1/2(1-9(2.1))
= -8.95
In conclusion, the first term of the sequence is -8.95 with a common difference of 2.1.
The sequence is:
-8.95, -6.85, -4.75, -2.65...
Type the missing digit down below
63,927,_76 is divisible by 8.
Answers
Answer:
4
Step-by-step explanation:
Answer:
63,927,476 is divisible by 8.
What fraction of an hour is 15 minutes?
Give your answer in its simplest form.
Answers
Answer:
1/4
Step-by-step explanation:
15/60 = 1/4
Hello there! :)
15 minutes is 1/4 of an hour.
An hour is 60 minutes:
[tex]\frac{}{60}[/tex]
We have 15 minutes:
[tex]\frac{15}{60}[/tex]
Reduce your answer by dividing 15 and 60 by 15:
[tex]\frac{1}{4}[/tex]
Hope this helps!
~Just a determined gal
#CarryOnLearning
Please mark brainliest!!
[tex]Mysterious Nature[/tex]
Can someone please help!!
Answers
Answer:
d
Step-by-step explanation:
40 is the exact amount from a,b,back to c
hi guys pls answer this we will pass the tomorrow
Answers
Answer:
1. 25/24
2. 7/6
3. 4/3
4. 6/8 or 3/4
5. 5/4
1. 1
2. 1/4
3. 2/10 or 1/5
4. 7/3
5. 13/6
If Lucy runs 1 mile in 6
minutes, how many miles
will she run in 23 minutes?
Answers
C=pi/2 what is the area?
Answers
Answer:
A=1
Step-by-step explanation:
The formula to find the area of a circle is πr^2, meaning that you divide the diameter in half which is 1. So 1^1 is one. The area would be one.
Hope this helps :)
The area would be one, is, A=1.
What is area of circle?The area of a circle is π multiplied by the square of the radius. The area of a circle, (A) when the radius 'r' is given is πr2. π is approximately 3.142
here, we have,
C=pi/2
The formula to find the area of a circle is πr^2,
meaning that you divide the diameter in half which is 1.
So 1^1 is one.
The area would be one.
To learn more on area of circle click:
brainly.com/question/22964077
#SPJ2
5. Look at the shaded products. What pattern do you see?
Answers
Answer:
8+6+4
Step-by-step explanation:
Is this a function? I don’t think it is but I’m not sure.
Answers
Answer:
no
Step-by-step explanation:
the ratio 18:24 in its simplest form is?
Answers
Answer:
3:4
Step-by-step explanation:
18 = 2 * 3 * 3
24 = 2 * 2 * 2 * 3
HCF = 2 * 3 = 6
Divide by 6
18: 24 = 18÷6 : 24÷6
= 3 : 4
Answer:
it's 3:4
Step-by-step explanation:
18 ÷ 6 : 24 ÷ 6
3 : 24 ÷ 6
=3:4
use synthetic division to evaluate f(x)=x^3-6x+1 for x=6. f(6)=____
Answers
Given: x=6
By substituting value of x as 6 in the given expression, we get:
[tex]f(6) = {x}^{3} - 6x + 1[/tex]
[tex]→f(6) = {6}^{3} + (6 \times 6) - 1[/tex]
[tex]→f(6) = 216 - 36 + 1[/tex]
Now, using integer sign property,
[tex]→f(6) = 216 - 35[/tex]
[tex]→f(6) = 181[/tex]
Therefore, f(6)=181
Find the value of the variable(s) in each figure explain your reasoning.
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Answer:
...............................
help me please
−|a+b/2−c when a=123 , b=−1 , and c=−3
Enter your answer as a simplified fraction in the box.
Answers
Answer:
64
Step-by-step explanation:
123+(-1)/2-(-3)=
122/2=61
61+3=64
Pleaaaaaaaaaaaaaaaaaaaaaaase help me
Answers
Answer:
It would be the first one
Step-by-step explanation:
Start at 0 and the end shows 2.5