Answers
Answer:
1a: f(x) = x³ -6x² +9x -4
1b: no breaks; the function is defined everywhere
2a: (-∞, 5]
2b: y = -3; y = -1
2c: x → -∞, y → -3; x → ∞, y → -1
Step-by-step explanation:
1A:The factored form of f(x) is ...
f(x) = (x -4)(x -1)²
f(x) = (x -4)(x² -2x +1) = x³ -2x² +x -4x² +8x -4
f(x) = x³ -6x² +9x -4
__
1B:The function h(x) is defined for all values of x to be either f(x) or g(x). The function f(x) is a polynomial function, so has no breaks in its domain. The function g(x) is defined for all values of x, so has no breaks in its domain.
There are no breaks in the domain of h(x).
__
2A:See the attachment for a graph.
-∞ < y ≤ 5 . . . . range of f(x)
__
2B:The asymptote as x → -∞ is the asymptote of the exponential function. The exponential term has an asymptote of y=0, but shifting it down 3 units means the asymptote is 0 -3:
x → -∞, y → -3 . . . . asymptote is y = -3
The asymptote as x → ∞ is the asymptote of the rational expression. That is the ratio of the leading terms: -x²/x² = -1.
x → ∞, y → -1 . . . . asymptote is y = -1
__
2C:See part B.
Related Questions
Lucy borrowed $73,250 to purchase a home. The bank offered her an APR of 3.15% for a term length of 20 years. Excel calculates the monthly payment to be $411.77. If she were to pay only the minimum payment for the lifetime of the loan, how much will Lucy be paying in interest?
Answers
Amount Lucy will be paying in interest will be $38,596.2
Using the compound amount formula to get the amount after she will pay back after 20 years expressed as:
[tex]A =P(1+\frac{r}{n} )^{nt}[/tex]
A is the amount after 20 yearsr is the rate = 3.15% = 0.0315time in years = 20 yearsn is the compounding time = 12 (monthly)P is the amount borrowed = $73,250Substitute the parameters into the formula;
[tex]A=73,250(1+\frac{0.0315}{12} )^{20(12)}\\A= $73,250 (1.8761)\\A= \$137,421.49[/tex]
If Excel calculates the monthly payment to be $411.77, the amount paid for 20 years will be $411.77 * 240months = $98,824.8
Amount Lucy will be paying interest will be $137,421- $98,824.8 = $38,596.2
Learn more on compound interest here: https://brainly.com/question/24924853
here is a list of numbers: 8 7 12 7 11 10 7 12
a) find the median
b) the range
c) the mode
Answers
Answer:
Ascending order = 7,7,7,8,10,11,12,12
a) n = 8
= median = (n/2+(n/2+1)/2
= (4th term + 5th term)/2
= 8+10/2
= 9
b) range = 12-7 = 5
c) the mode = 7 (highest occuring value)
The median of the given list of numbers is 9.
The range of the given list of numbers is 5.
The mode of the given list of numbers is 7.
We have,
a) To find the median of a set of numbers, we arrange them in ascending order and determine the middle value.
If there is an odd number of values, the median is the middle number.
If there is an even number of values, the median is the average of the two middle numbers.
Arranging the numbers in ascending order: 7 7 7 8 10 11 12 12
There are eight numbers in this set, so the middle two numbers are 8 and 10.
Taking their average, the median is (8 + 10) / 2 = 9.
b) The range is the difference between the highest and lowest values in the set.
The lowest value is 7, and the highest value is 12.
So the range is 12 - 7 = 5.
c) The mode is the value that appears most frequently in the set.
In the given list, the number 7 appears three times.
Therefore,
The median of the given list of numbers is 9.
The range of the given list of numbers is 5.
The mode of the given list of numbers is 7.
Learn more about the median here:
https://brainly.com/question/28060453
#SPJ2
5x squared +1=4x-7 solve the equation using the quadratic formula
Answers
Answer:
Step-by-step explanation:
- B ± √ B2-4AC
x = ____________
2A
which will be
4 ± √ -144
x = _______
10
x =(4-√-144)/10=(2-6i)/5= 0.4000-1.2000
+
-
1. The amount M (in trillions of dollars) of mortgage debt outstanding in the United States from 1990
through 2009 can be approximated by the function M = f(0) = 0.0037(t + 14.979), where t = 0
represents the year 1990.
(a) Describe the transformation of the common function f(x) = x2. Then sketch the graph over the
intervalo s t < 19.
(b) Rewrite the function so that t = 0 represents the year 2000. Explain how you got your answer.
(c) Use the model from part (b) to predict the mortgage debt in the year 2014.
Answers
The give quadratic function is dilated by the given coefficient, and shifted
horizontally to the left.
(a) The transformation of the common function f(x) are;
f(t) is made more wider than f(x) f(t) is shifted more to the left than the common function f(x).Please find attached the required graph created with MS Excel
(b) Where t = 0, represent the year 2,000 we have;
f(t) = 0.0037·(t + 24.979)²(c) The mortgage debt in the year 2014 is M ≈ $5.622 trillion
Reasons:
The given function is f(t) = 0.0037·(t + 14.979)²
Year 1990 is t = 0
(a) The given common function is; f(x) = x²
The transformation of the quadratic function are;
The coefficient 0.0037 widens the common function such that f(t) is wider
than f(x).
The constant, 14.979 added to the variable, t, shifts the graph of the
common function horizontally to the left.
Therefore;
f(t) is wider and shifted to the left more than the common function f(x)Please find attached the required graph over the interval 0 ≤ t ≤ 19 created with MS Excel.
(b) The amount of mortgage debt in 2,000 is given as follows;
With t' = 0 represent the year 2,000, we have;
At year 1990, t' = -10
Which gives, t' = t + 10
From which we have;
f(t) = 0.0037·(t + 14.979)² = 0.0037·(t' + 10 + 14.979)² = 0.0037·(t' + 24.979)²
Therefore;
The function with t = 0 representing the year 2,000 is presented as follows;
f(t) = 0.0037·(t + 24.979)²
(c) In the year 2014, we have;
t = 2014 - 2000 = 14
Which gives;
f(14) = 0.0037·(14 + 24.979)² ≈ 5.622
The mortgage debt in the year 2014 is M ≈ $5.622 trillion dollars
Learn more about transformation of quadratic functions here:
https://brainly.com/question/15105480
Please help. Will mark Brainliest
Which statements go in boxes 2 and 3?
What is the proof for boxes 3 and 4?
Answers
Next is I, 3 and 5 must be equal since they are vertically opposite
Last is transitive property
Since 1 = 3 and 3 = 5, then 1 must equal 5
Please help for brainliest!!:)
Answers
Answer:
d)
Step-by-step explanation:
we know, that i = sqrt(-1)
so, i² = -1
i³ = -i
i⁴ = -i × i = - -1 = 1
i⁵ = i⁴×I = 1×i = i
and the cycle begins again for any higher exponents.
so, we find out what i^n is, by dividing n by 4 and look at the remainder.
remainder = 0, i^n = 1
remainder = 1, i^n = i
remainder = 2, i^n = -1
remainder = 3, i^n = -i
so, what is 139 in this regard ?
139 ÷ 4 = 34
remainder 3
so, i¹³⁹ = -i
a) 322 ÷ 4 = 80
remainder 2. not equivalent.
b) 304 ÷ 4 = 76
remainder 0. not equivalent.
c) 221 ÷ 4 = 55
remainder 1. not equivalent.
d) 239 ÷ 4 = 59
remainder 3. this IS equivalent.
39 round to the nearest hundred
Answers
2,983,562 to the nearest hurdreth
Answers
Answer:
2,983,562 if you mean hundredth
if to the nearest hundred then 2,983,600
Step-by-step explanation:
Can y’all please help me answer this, this My last question
Answers
Answer:
x ft is the answer since X = 10
so it means 10 ft
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Graph the image of the figure using the dilation given)
Answers
Answer:
[tex]I(-1,0) \to I \ ' \ (-0.25,0)\\\\J(-1,1) \to J \ ' \ (-0.25,0.25)\\\\K(2,2) \to K \ ' \ (0.5, 0.5)\\\\L(2,-1) \to L \ ' \ (0.5,-0.25)\\\\[/tex]
======================================================
Explanation:
The fraction 1/4 is equivalent to the decimal form 0.25
We multiply 0.25 with each coordinate, of each point.
For example, let's focus on point L which is at (2,-1)
x = 2 becomes x = 0.25*2 = 0.5y = -1 becomes y = 0.25*(-1) = -0.25Point L(2,-1) moves to L ' (0.5, -0.25) which will move it closer to the origin, which shrinks the image. Use this idea for the remaining points.
Note: this trick only works if the center of dilation is the origin.
6/5 pls help as fast as possible
Answers
Answer: 6 divided by 5 is 1.2
Step-by-step explanation: I used Siri lol
Answer:
1.2 in decimal form. equivalent form-12/10. i really dont know what your asking. so i hope this is what you wanted.
Step-by-step explanation:
Solve 5 - 2x < 7.
A) x < -1
B) x > -1
0x<
-12
D) x>-12
Answers
Answer:
x < - 1
Step-by-step explanation:
You have to treat it is a linear equation.
First, - 5 from both sides, resulting in -2x < 2.
Lastly, you need to find x on it's own so you have to divide by - 2.
Therefore, the answer would be x < -1.
Hope this helps :)
How do I find the excluded values? Please help I have a test tomorrow.
Answers
Answer:
what is that answer plss
HELP ASAP! TYSM IF U DO, WILL GIVE BRAINILEST!
Answers
its d becuase i used math-way
Step-by-step explanation:
b
=
4
Answer:
Option DStep-by-step explanation:
Given equation:
b - 12 = - 8Add 12 to both sides:
b - 12 + 12 = - 8 + 12b = 4Correct graph is D, where point 4 is marked
Angle wxz is congruent to angle zxy. Find the value of X
Answers
Answer:
x = 18
Step-by-step explanation:
Congruent angles have equal measures.
74° = (4x +2)°
72 = 4x . . . . . . divide by °, subtract 2
18 = x . . . . . . . divide by 4
Please look for the question in the picture.
Answers
it will be c
as
negative with negative erased together
How to perform aerial math for following:
5.1 x 3.5 X 0.5+9.4
Answers
If a triangle has a base of 6' and a height of 4' its area would be what?
A= bxh 2
A= 6x4 2
A= 12 sq. ft.
Answers
Answer:
Hello There!
According to the question,
Base=6
And
Height =4
Let's know the formula
[tex] \frac{1}{2} \times base \times height \\ so \\ \frac{1}{2} \times 6 \times 4 \\ [/tex]
simplify 2 with 6 then it will look like this
[tex] \frac{1}{1} \times3 \times 4 \\ \\ [/tex]
1 has no value so
[tex]3 \times 4 = 12 {ft}^{2} \\ [/tex]
So third option
[tex]a = 12 {ft}^{2} [/tex]
is correct.
[tex]\Large\textsf{Hope \: It \: Helped}[/tex]
Answer:
Area = 12 sq ft
Step-by-step explanation:
The formula to find the area of a triangle is
1/2 bh so we will replace the letters with their number value
1/2 (6x4)
1/2 x 24 = 12
So, 12 is your answer!
Lashonda finished a race in 5 minutes. How many seconds is this
Answers
Answer:
300 seconds
Step-by-step explanation:
There are 60 seconds in a minute. If there are 5 minutes, you have to multiply 5 by 60.
5 x 60 = 300
-hope it helps
Answer:
360 sec
Step-by-step explanation:
this is because 60sec is one mintute
so 60x5= 360
End of Semester test geometry semester a question 29
Triangle DEF is dilated with respect to the origin by a scale factor of to produce ΔD'E'F'. What is the length of side D'E'?
A.
B.
C.
D.
Answers
The resulting coordinate will be D'(2, 6), E'(4, -6), and F'(0, 10),
Let the coordinate of the triangle DF be given as D(1, 3), E(2, -3) and F(0, 5).
For instance, if the coordinate point (x, y) is dilated by a factor of k, the resulting coordinate will be (kx, ky)Note that each of the coordinates is multiplied by the scale factor.
For the coordinates D(1, 3), E(2, -3), and F(0, 5), assuming the coordinate point is dilated by a factor of 2, the resulting coordinate will be D'(2, 6), E'(4, -6), and F'(0, 10),
Learn more on dilation here: https://brainly.com/question/10253650
Note that the question is answered on a general term.
Answer:
√5
Step-by-step explanation:
I got it right on Edmentum
Hook me up with a 5 star and a thanks :)
A passenger plane flew from Texas to Frankfurt and back. The round trip is 9900 km.
return trip took 4 hours less than the trip to Frankfurt because of the 50 km/hr wind over the ocean on the return trip. Assume there was no wind on the trip to Frankfurt. Let x km/hr represent the average speed of the plane in still air.
Answers
We want to find the average speed of the plane in still air, we will get that the average speed of the plane in still air is 355.3 km/hr
So we know that the total trip is 9900km, so from Texas to Frankfurt the distance is half of that:
9900km/2 = 4950km
Now, The speed of the plane in still air is x km/hr
The speed of the air is 50 km/hr, and it flows from Frankfurt to Texas.
So in the first part of the trip, the wind blows in opposite direction to the motion of the plane, thus the speed of the plane will be:
(x - 50) km/hr
While in the return trip the wind blows in favor of the plane, in this case, the speed is:
(x + 50)km/hr
Then if the first part of the trip lasts for T hours (the second for T - 4 hours) we can write the system of equations:
(x - 50)*T = 4950
(x + 50)*(T - 4) = 4950
Where I removed the units so it is easier to read.
If we isolate T in the first equation we get:
T = 4950/(x - 50)
Now we can replace this in the other equation to get:
(x + 50)*(4950/(x - 50) - 4) = 4950
If we multiply both sides by (x - 50) we get:
(x + 50)*4950 - 4*(x + 50)*(x - 50) = 4950*(x - 50)
Now we can solve this for x:
(x + 50)*4950 - 4*(x^2 - 2500) - 4950*(x - 50) = 0
100*4950 - 4*(x^2 - 2500) = 0
495000 - 4*x^2 + 10000 = 0
505000 = 4*x^2
√(505000/4) = x = 355.3
The average speed of the plane in still air is 355.3 km/hr
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13476446
Add 8.563 and 4.8292. then times the answer by 9.183 divide it 2 times by 1.192. Add to the answer with this number after your finished: "19.323
Answers
Answer:
105.876373581
Step-by-step explanation:
8.563 + 4.8292 = 13.3922
13.3922 × 9.183 = 122.9805726
122.9805726 ÷ 1.192 = 103.171621309
103.171621309 ÷ 1.192 = 86.5533735811
86.5533735811 + 19.323 = 105.876373581
Step-by-step explanation:
8.563+4.8292=A
( A*9.183)÷1.192÷1.192=B
B+19.323=C
Is (x + 2) a factor of f(x) = x3 - 7x2 + 2X – 8? Use either the remainder theorem or the factor theorem to explain your reasoning.
Answers
[tex]\text{Given that,}\\\\f(x) = x^3 -7x^2 +2x -8\\\\\\\text{(x+2) will be a factor of f(x) if } f(-2) = 0 \\\\\\f(-2) = (-2)^3 -7(-2)^2 +2(-2) -8 = -48 \\\\\\\text{Since}~ f(-2) \neq 0, ~ (x +2) \text{is not a factor of f(x).}[/tex]
How do I multiply minted numbers? Please explain step by step to get marked as brainliest
Answers
Answer:
Step-by-step explanation:
help me plssssssssssssss
Answers
Answer:
C .......
Step-by-step explanation:
Please somebody help me with this
Answers
Answer: call 911
Step-by-step explanation: call 911
What is the value of a in this linear system?
a + b + c = 62
a - b = 12
2a + b + c = 92
O A.
14
OB.
30
OC.
18
o
c
D.
26
Answers
Answer:
Step-by-step explanation:
C
Suppose a 5-digit number is formed using the digits from 1 to 9 (without replacement). What is the probability that it will be an even number?
Answers
Answer:
First take 5 empty. Digits.The no of digits are 9 (1-9).The last no must be even so . The total no of even no’s . Are 4 (2,4,6,8)The probability of last digit is 4There are remaing 8 digits so. Place them where. U required. The probability are. 8, 7,6,5(no reputations)The final answer is 4*8*7*6*5=6720 waysAnswer:
0.444 (44.4%)
Step-by-step explanation:
All possible ending: 1,2,3,4,5,6,7,8,9 ... 9
ending with 2,4 6,8 to make even number: 4
___ ___ ___ ___ ___
even number : 8 * 7 * 6 * 5 * 4
All 5 digit without repeating: 8 * 7 * 6 * 5 * 9
possibility = (8*7*6*5*4) / (8*7*6*5*9)
= 4/9
= 0.444 (44.4%)
_______________________________________________
(4 * ₈P₄) / (9 * ₈P₄) = 4/9
correct?`````````````````````````````
Answers
Answer:
Yes
Step-by-step explanation:
Given the function f(x)=X^2- 3x, find f(-4)
Answers
-4 to the second power is 16 so it would be 16-(-12)= 28