RESUELVE USANDO LAS PROPIEDADES DE LA POTENCIA
PLISSSSSSSSS CON PROCEDIMIENTOOOOOOO
Answers
Answer:
Tenemos dos propiedades de la potencia en este caso:
Para un numero real A:
[tex]A^0 = 1[/tex]
[tex](A^n)^m = A^{n*m}[/tex]
En este caso nuestra ecuación es:
[tex][ [(\frac{0.1234}{-3.2098})^4]^3]^0[/tex]
usando la segunda propiedad, podemos reescribir como:
[tex][ [(\frac{0.1234}{-3.2098})^4]^3]^0 = (\frac{0.1234}{-3.2098})^{4*3*0} = (\frac{0.1234}{-3.2098})^0[/tex]
Y acá tenemos un numero real a la potencia 0, sabemos que esto es igual a 1, entonces:
[tex](\frac{0.1234}{-3.2098})^0 = 1[/tex]
Related Questions
Find the area of
1.Table
Length = 123cm
Width = 82cm
Height = 76cm
2.Living room
Length = 422cm
Width = 278cm
Height = 253cm
3. Door
Length = 87cm
Width = 2.3cm
Height = 208cm
Answers
Answer:
1. 766,536cm^3
2. 29,680,948cm^3
3. 41,620.8cm^3
Step-by-step explanation:
1. 123×82 = 10,086 10,086×76 = 766,536
2. 422×278 = 117,316 117,316×253 = 29,680,948
3. 87×2.3 = 200.1 200.1×208 = 41,620.8
Hope this helps! :)
Which complex number does not lie on the line segment plotted on the graph?
Answers
Answer:
Notice that for 3 out of the 4 numbers, there is a relationship between the x and the y coordinate of the number; for 3+i, -2i, -2-4i we have that the real part is larger by 2 from the imaginary part. Thus, the points are on the same line in the imaginary plane; they satisfy x=y+2 or Re{z}=Im{z}+2. However, 2-4i does not satisfy this equation since 2 is not equal to -4+2. Hence, this point does not belong to the line that the other 3 points define.
Step-by-step explanation:
Help me please with this maths question thank you
Answers
Answer:
Step-by-step explanation:
A)
The opposite sides of a rectangle are equal. The width make this obvious because both of them are x.
B)
The lengths are not so obvious, but it is never the less true. The two sides are obvious and they are therefore true.
4x + 1 = 2x + 12 Subtract 1 from both sides.
- 1 -1
4x = 2x + 11 Subtract 2x from both sides
-2x -2x
2x = 11 Divide by 2
x = 11/2
x = 5.5
C)
P = L + L + w + w
P = 4(5.5) + 1 + 2(5.5) + 12 + 5.5 + 5.5
P = 22 + 1 + 11 + 12 + 11
P = 23 + 23 + 11
P = 57
What is the GCF of 1683t, 4085, and 68t??
O 4
O 483t
O 8
O 8837
Answers
Answer:I’m pretty sure ( not 100% thou ) the awnser would be A) 4
Consider random samples of size 1200 from a population with proportion 0.65 . Find the standard error of the distribution of sample proportions. Round your answer for the standard error to three decimal places.
Answers
Answer:
The standard error of the distribution of sample proportions is of 0.014.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Consider random samples of size 1200 from a population with proportion 0.65 .
This means that [tex]n = 1200, p = 0.65[/tex]
Find the standard error of the distribution of sample proportions.
This is s. So
[tex]s = \sqrt{\frac{0.65*0.35}{1200}} = 0.014[/tex]
The standard error of the distribution of sample proportions is of 0.014.
Which problem has a greater (bigger) answer? Solve both, choose the one that has the bigger answer and explain (1-2 sentences) how you found your
answer.
1) (2 + 3) (5 + 5)
2)2 + 3 x 5 + 5 =
Answers
= 10 + 15 + 10 + 15 =
= 50
2) 5 • 10 =
= 50
Help and explain explain !!!!!!!!!!
Answers
Answer:
[tex]x=-1\text{ or }x=11[/tex]
Step-by-step explanation:
For [tex]a=|b|[/tex], we have two cases:
[tex]\begin{cases}a=b,\\a=-b\end{cases}[/tex]
Therefore, for [tex]18=|15-3x|[/tex], we have the following cases:
[tex]\begin{cases}18=15-3x,\\18=-(15-3x)\end{cases}[/tex]
Solving, we have:
[tex]\begin{cases}18=15-3x, -3x=3, x=\boxed{-1},\\18=-(15-3x), 18=-15+3x, 33=3x, x=\boxed{11}\end{cases}[/tex].
Therefore,
[tex]\implies \boxed{x=-1\text{ or }x=11}[/tex]
As part of a classic experiment on mutations, 10 aliquots of identical size were taken from the same cul-ture of the bacterium E. coli. For each aliquot, the number of bacteria resistant to a certain virus was determined. The results were as follows:
14 15 13 21 15
14 26 16 20 13
Construct a frequency distribution of these days and display it as a histogram.
Determine the mean and the median of the dad and mark their locations on the histogram.
Answers
Answer:
a. See the attached excel file for the frequency distribution table, and the attached photo for the histogram.
b. We have:
Mean = 16.7
Median = 15
Note: See the attached photo for the locations of Mean and Median on the histogram.
Step-by-step explanation:
a. Construct a frequency distribution of these days and display it as a histogram.
Note: See the attached excel file for the frequency distribution table, and the attached photo for the histogram.
b. Determine the mean and the median of the dad and mark their locations on the histogram.
From the attached excel file, we have:
Total of F = 10
Total of FX = 167
Therefore, we have:
Mean = 167 / 10 = 16.7
Median is the middle number after arranged the data in ascending or descending order. Using the ascending order, we have:
13 13 14 14 15 15 16 20 21 26
Since 15 and 15 are in the middle, their average are the median which is calculated as follows:
Median = (15 + 15) / 2 = 15
Note: See the attached photo for the locations of Mean and Median on the histogram.
ABCD is a square of side 12 cm. It is formed from two rectangles AEGD and
EBCG. H is a point on AD and F is a point on BC.
Find the area of EFGH.
Answers
Answer:72 [tex]cm^{2}[/tex]
Solution 1:
Step 1: Find EF use Pythagorean theorem
[tex]EF^{2} = EB^{2} + BF^{2}[/tex]
[tex]EF^{2} = 6^{2} + 6^{2}[/tex]
EF = [tex]\sqrt{6^{2} + 6^{2} }[/tex] = 6[tex]\sqrt{2}[/tex] cm
Step 2: The area of EFGH = [tex]EF^{2}[/tex]= [tex](6\sqrt{2} )^{2}[/tex] = 72
Solution 2: See that the area of EFGH is equal [tex]\frac{1}{2}[/tex] the area of ABCD
The area of ABCD = 12x12 = 144
Thus, the area of EFGH = 144: 2 = 72:)
Have a nice day!
Cenntura was having fun playing poker she needed the next two cards out to be heart so she could make a flesh five cards of the same suit there are 10 cards left on the deck and three our hearts what is the probability that two cards doubt to Seterra without replacement will both be hearts answer choices are in percentage for format rounded to the nearest whole number
Answers
Answer:
7% probability that the next 2 cards are hearts.
Step-by-step explanation:
Cards are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
10 cards, which means that [tex]N = 10[/tex]
3 are hearts, which means that [tex]k = 3[/tex]
Probability that the next 2 cards are hearts:
This is P(X = 2) when n = 2. So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,10,2,3) = \frac{C_{3,2}*C_{7,0}}{C_{10,2}} = 0.0667[/tex]
0.0667*100% = 6.67%
Rounded to the nearest whole number, 7% probability that the next 2 cards are hearts.
An urn contains 2 small pink balls, 7 small purple balls, and 6 small white balls.
Three balls are selected, one after the other, without replacement.
Find the probability that all three balls are purple
Express your answer as a decimal, rounded to the nearest hundredth.
Answers
Answer:
The probability is P = 0.08
Step-by-step explanation:
We have:
2 pink balls
7 purple balls
6 white balls
So the total number of balls is just:
2 + 7 + 6 = 15
We want to find the probability of randomly picking 3 purple balls (without replacement).
For the first pick:
Here all the balls have the same probability of being drawn from the urn, so the probability of getting a purple one is equal to the quotient between the number of purple balls (7) and the total number of balls (15)
p₁ = 7/15
Second:
Same as before, notice that because the balls are not replaced, now there are 6 purple balls in the urn, and a total of 14 balls, so in this case the probability is:
p₂ = 6/14
third:
Same as before, this time there are 5 purple balls in the urn and 13 balls in total, so here the probability is:
p₃ = 5/13
The joint probability (the probability of these 3 events happening) is equal to the product between the individual probabilities, so we have:
P = p₁*p₂*p₃ = (7/15)*(6/14)*(5/13) = 0.08
Select the correct answer. What is the range of the function shown on the graph above?
A. -8
B.-2y <-7
C. -7 Sy < -2
D. -9
Answers
Answer: The answer would be D
Step-by-step explanation:
If you have 3/8 of one pie, what does the denominator tells you ?
Answers
Step-by-step explanation:
There was originally 8 pieces of pie.
Answer:
if you have 3/8 of one pie, the denominator tells you that the pie was divided into 8 piece.
Uma lâmpada de incandescência traz os seguintes dados inscritos no seu bulbo. U= 220 V e P = 100 W. Conhecendo as relações U = R. i e P = U. i , pode-se afirmar que o valor da resistência R da lâmpada durante o funcionamento é, em omhs:
Answers
Answer:
The resistance is 484 ohm.
Step-by-step explanation:
An incandescent lamp has the following data inscribed on its bulb. U= 220 V and P = 100 W. Knowing the relations U = R. i and P = U. i , it can be stated that the value of the resistance R of the lamp during operation is, in omhs:
P = 100 W
V = 220 V
Let the current is I.
P = V I
100 = 220 I
I = 0.45 A
Now,
V = I R
220 = 0.45 x R
R = 484 ohm
The resistance is 484 ohm.
Last week at the business where you work, you sold 120 items. The business paid $1 per item and sold them for $3 each. What profit did the business make from selling the 120 items?
Answers
Answer:
240
Step-by-step explanation:
minus how much u sold them and how much it cost to make
3-1=2
times 2 and 120
2(120)
240
The greatest common factor of 45a^2b^3 and 18a^4b
Answers
Answer:
9a²b
Step-by-step explanation:
Hi there!
We need to find the greatest common factor out of 45a²b³ and 18[tex]a^{4}[/tex]b
We can split apart the monomials to make it easier
45a²b³ is 45*a²b³
18[tex]a^{4}[/tex]b is 18*[tex]a^{4}[/tex]b
First, let's find the GCF out of 45 and 18 (the number coefficients)
we can find all of the multiples of the 2 numbers:
45 is made up of 9 and 5
9 is made up of 3 and 3
so 3*3*5 is 45
18 is made up of 2 and 9
9 is made up of 3 and 3
so 2*3*3 is 18
3*3 is in both 45 and 18, so 9 is the GCF out of 45 and 18
Now let's find the GCF out of a²b³ and [tex]a^{4}[/tex]b
a²b³ made up of a² and b³
so a²b³ is a*a*b*b*b
[tex]a^{4}[/tex]b is made up of [tex]a^{4}[/tex] and b
so [tex]a^{4}[/tex]b is a*a*a*a*b
a*a*b is in both a²b³ and [tex]a^{4}[/tex]b, so the GCF out of a²b³ and [tex]a^{4}[/tex]b is a²b
Now multiply 9 and a²b together, as they are only the GCF of the parts of the monomials
9*a²b=9a²b
there's the greatest common factor of the 2 monomials
Hope this helps!
You are certain to get a heart, diamond, club, or spade when selecting cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Answers
Answer:
The probability of this event is represented by a value of 1.
Step-by-step explanation:
Probability of a certain event:
The probability of an event that is considered to be certain, that is, guaranteed to happen, is 100% = 1.
You are certain to get a heart, diamond, club, or spade when selecting cards from a shuffled deck.
This means that the probability of this event is represented by a value of 1.
Zero is not a real number True or
False
Answers
I NEED HELP FAST!!!!!!
Answers
Answer:
6.
Step-by-step explanation:
.
Answer:
[tex]C)\:8[/tex]
8 units tiles must be added
--------------------------------------
~HOPE IT HELPS~
~HAVE A GREAT DAY!!~
10=−4x+3x^2 solve
please help!
Answers
Answer:
-1.28 AND 2.61
Step-by-step explanation:
[tex]10= -4x+3x^2\\ 3x^2 -4x - 10 = 0\\\\[/tex]
use quadratic formula
x = [tex]\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex] x = [tex]\frac{-b-\sqrt{b^{2} -4ac} }{2a}[/tex]
Solution/X-Intercepts: -1.28 AND 2.61
If $3000 is invested at 3% interest, find the value of the investment at the end of 7 years if the interest is compounded as follows. (Round your answers to the nearest cent.)
(i) annually
(ii) semiannually
(iii) monthly
(iv) weekly
(v) daily
(vi) continuously
Answers
Answer:
annualy=$3689.62
semiannually=$3695.27
monthly=$3700.06
weekly=$3700.81
daily=$3701.00
Continuously=$3701.03
Step-by-step explanation:
Given:
P=3000
r=3%
t=7 years
Formula used:
Where,
A represents Accumulated amount
P represents (or) invested amount
r represents interest rate
t represents time in years
n represents accumulated or compounded number of times per year
Solution:
(i)annually
n=1 time per year
[tex]A=3000[1+\frac{0.03}{1} ]^1^(^7^)\\ =3000(1.03)^7\\ =3689.621596\\[/tex]
On approximating the values,
A=$3689.62
(ii)semiannually
n=2 times per year
[tex]A=3000[1+\frac{0.03}{2}^{2(4)} ]\\ =3000[1+0.815]^14\\ =3695.267192[/tex]
On approximating the values,
A=$3695.27
(iii)monthly
n=12 times per year
[tex]A=3000[1+\frac{0.03}{12}^{12(7)} \\ =3000[1+0.0025]^84\\ =3700.0644[/tex]
On approximating,
A=$3700.06
(iv) weekly
n=52 times per year
[tex]A=3000[1+\frac{0.03}{52}]^3^6 \\ =3000(1.23360336)\\ =3700.81003[/tex]
On approximating,
A=$3700.81
(v) daily
n=365 time per year
[tex]A=3000[1+\frac{0.03}{365}]^{365(7)} \\ =3000[1.000082192]^{2555}\\ =3701.002234[/tex]
On approximating the values,
A=$3701.00
(vi) Continuously
[tex]A=Pe^r^t\\ =3000e^{\frac{0.03}{1}(7) }\\ =3000e^{0.21} \\ =3000(1.23367806)\\ =3701.03418\\[/tex]
On approximating the value,
A=$3701.03
Suppose that a survey was taken and it showed that 18% of online shoppers in the United States would prefer to do business only with large well-known retailers. If 2700 online shoppers were surveyed, how many are willing to do business with any size retailers?
Answers
Step-by-step explanation:
You can conclude that 82% of all shoppers will do business with any retailer of any size aslong as they are on the internet.
82% of 2700 = 0.82 * 2700 =2214
which makes the other responder correct.
1. Find the Perimeter AND Area of the figure
below.
2 ft
5 ft
2 ft
5 ft
Answers
Answer:
A = 16 ft^2
P = 20 ft
Step-by-step explanation:
P = perimeter
A = area
STEP 1: divide the shape into rectangles
Rectangle 1: 2ft*3ft
Rectangle 2: 2ft*5ft
STEP 2: Find the area of each rectangle
Equation for area of a rectangle = bh
Rectangle 1: b = 2, h = 3
Rectangle 2: b = 2, h = 5
(2 * 3) + (2 * 5)
6 + 10
16 ft^2
Now, we have to find the perimeter
STEP 1: Find the unknown side lengths.
To find the lengths of the sides not labeled, you have to use the lengths of the sides we already know.
The length of one parallel side is 5, and the length of another parallel side is 2. The length of the unknown side starts at the same place as the top of the side length that is 5, and ends at the top of the side length that is 2. This means that we have to subtract 2 from 5 in order to find the unknown side length.
STEP 2: Add up all the side lengths
P = 2 + 5 + 5 + 2 + 3 + 3
P = 20 ft
Don't forget to label your answers!!
I hope this made sense, it's is a little hard to explain in simple terms without being able to draw, but I hope it helped.
Select the line segment.
Answers
Answer:
i think you need to attach a fine for us to do so?
Step-by-step explanation:
Answer:
I can't tell you without the problem
19. The sum of a number m and a number n, multiplied by ninety-one 20. Forty-one times the difference when six is subtracted from a num- bera 21. A number r divided by the difference between eighty-three and ten 22. The total of a number p and twelve, divided by eighteen 23. The product of a number c and three more than the sum of nine and twelve 24. The sum of a number y and ten, divided by the difference when a number x is decreased by five. I need to convert all of them into expressions. PLEASE HELP.
Answers
Answer:
Step-by-step explanation:
19.
The numbers are m and n
Sum of m and n = m + n
Sum is multiplied by 91 = 91 x ( m + n )
20.
Let the number be = m
Six subtracted from the number = m - 6
41 times the difference = 41 x ( m - 6)
21.
Let the number be = r
Difference between 83 and 10 = 83 - 10 = 73
[tex]The \ number\ divided \ by\ the \ difference \ = \frac{r}{73}[/tex]
22.
Total of p and 23 = p + 12
[tex]Total \ divided \ by \ 18 = \frac{p + 12 }{18}[/tex]
23.
The product of c and 3 = 3c
Sum of 9 and 12 = 21
Product is more than Sum = 3c + 21
24.
Sum of y and 10 = y + 10
Number x decreased by 5 = x - 5
[tex]Sum \ divided \ by \ difference = \frac{ y + 10 }{x - 5}[/tex]
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 310.
(a) Find an expression for the number of bacteria after
hours.
(b) Find the number of bacteria after 3 hours.
(c) Find the rate of growth after 3 hours.
(d) When will the population reach 10,000?
Answers
Answer:
a) The expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].
b) There are 2975 bacteria after 3 hours.
c) The rate of growth after 3 hours is about 3365.3 bacteria per hour.
d) A population of 10,000 will be reached after 4.072 hours.
Step-by-step explanation:
a) The population growth of the bacteria culture is described by this ordinary differential equation:
[tex]\frac{dP}{dt} = k\cdot P[/tex] (1)
Where:
[tex]k[/tex] - Rate of proportionality, in [tex]\frac{1}{h}[/tex].
[tex]P[/tex] - Population of the bacteria culture, no unit.
[tex]t[/tex] - Time, in hours.
The solution of this differential equation is:
[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex] (2)
Where:
[tex]P_{o}[/tex] - Initial population, no unit.
[tex]P(t)[/tex] - Current population, no unit.
If we know that [tex]P_{o} = 100[/tex], [tex]t = 1\,h[/tex] and [tex]P(t) = 310[/tex], then the rate of proportionality is:
[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex]
[tex]\frac{P(t)}{P_{o}} = e^{k\cdot t}[/tex]
[tex]k\cdot t = \ln \frac{P(t)}{P_{o}}[/tex]
[tex]k = \frac{1}{t}\cdot \ln \frac{P(t)}{P_{o}}[/tex]
[tex]k = \frac{1}{1}\cdot \ln \frac{310}{100}[/tex]
[tex]k\approx 1.131\,\frac{1}{h}[/tex]
Hence, the expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].
b) If we know that [tex]t = 3\,h[/tex], then the number of bacteria is:
[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]
[tex]P(3) = 100\cdot e^{1.131\cdot (3)}[/tex]
[tex]P(3) \approx 2975.508[/tex]
There are 2975 bacteria after 3 hours.
c) The rate of growth of the population is represented by (1):
[tex]\frac{dP}{dt} = k\cdot P[/tex]
If we know that [tex]k\approx 1.131\,\frac{1}{h}[/tex] and [tex]P \approx 2975.508[/tex], then the rate of growth after 3 hours:
[tex]\frac{dP}{dt} = \left(1.131\,\frac{1}{h} \right)\cdot (2975.508)[/tex]
[tex]\frac{dP}{dt} = 3365.3\,\frac{1}{h}[/tex]
The rate of growth after 3 hours is about 3365.3 bacteria per hour.
d) If we know that [tex]P(t) = 10000[/tex], then the time associated with the size of the bacteria culture is:
[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]
[tex]10000 = 100\cdot e^{1.131\cdot t}[/tex]
[tex]100 = e^{1.131\cdot t}[/tex]
[tex]\ln 100 = 1.131\cdot t[/tex]
[tex]t = \frac{\ln 100}{1.131}[/tex]
[tex]t \approx 4.072\,h[/tex]
A population of 10,000 will be reached after 4.072 hours.
Step 1: For each circle (A-G) in the table below, use the given information to determine the missing
information. Include supporting work showing and explaining how you found the missing information.
Circle
Center
Radius
Equation
A
(x - 9)2 + (y - 12)2 = 64
B
(-1,-17)
5
С
(-9,13)
9n
D
x2 + (0 - 1)2 = 36
E
x2 + y2 – 26x = -160
F
*2 + y2 + 22x +12y = -93
G
x2 + y2 – 10x+12y = -52
Answers
Answer:
I don't really understand the question
Step-by-step explanation:
c
what is the value of -2x²y³ when ×=2 and y=4?
Answers
Answer:
1024
Step-by-step explanation:
Given :-
x = 2 y = 4Value of -2x²y³
2x³ y³2 * (2)³ * (4)³2 * 8 * 64 1024Answer:
254
Step-by-step explanation:
^ <- this is the square sign
-2x^y^3
x=2
y=4
put x values in to x place and y value in to y place.
-2(2)^2(4)^3
Find the squares and - it with 2
-2(4)(64)
2-256=254
:. the value of -2x^2y^3 =254
That the answer.
Hope this is what you asked.
What is the standard form equation of the quadratic function shown in this graph?
Answers
Answer:
A is the equation in standard form
Step-by-step explanation:
If f(x) =4x2 - 8x - 20 and g(x) = 2x + a, find the value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).
Answers
Answer:
The possible values are a = -2.5 or a = 4.5.
Step-by-step explanation:
Composite function:
The composite function of f(x) and g(x) is given by:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this case:
[tex]f(x) = 4x^2 - 8x - 20[/tex]
[tex]g(x) = 2x + a[/tex]
So
[tex](f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20[/tex]
Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).
This means that when [tex]x = 0, f(g(x)) = 25[/tex]. So
[tex]4a^2 - 8a - 20 = 25[/tex]
[tex]4a^2 - 8a - 45 = 0[/tex]
Solving a quadratic equation, by Bhaskara:
[tex]\Delta = (-8)^2 - 4(4)(-45) = 784[/tex]
[tex]x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5[/tex]
[tex]x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5[/tex]
The possible values are a = -2.5 or a = 4.5.
