Answer:
The independent variable is the time (variable x)
The dependent variable is the number of cars he washes (variable y)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In this problem
The relationship between the number of cars he washes and the time it takes him to wash those cars represent a a proportional variation
Let
y -----> the number of cars he washes
x -----> the time
The linear equation is [tex]y=kx[/tex]
The independent variable is the time x
The dependent variable is the number of cars he washes y
solve 4 by 216 raise to minus 2 by 3 + 1 by 256 raise to 3 by 4 + 2 by 243 raise to 1 by 5
Answer:
214....
Step-by-step explanation:
If the question is : solve 4 by 216 raise to minus 2 by 3 + 1 by 256 raise to minus 3 by 4 + 2 by 243 raise to minus 1 by 5
The given expression can be written as:
4/(216)-2/3+1/(256)-3/4+2/(243)-1/5
This expression has three terms.
Notice that the exponents are negative:
We will change the division into multiplication so that the exponents will become positive;
4*(216)^2/3+ 1*(256)^3/4+ 2*(243)^1/5
If we multiply 6 three times it will give us 6^3=6*6*6=216
If we multiply 4 four times it will give us 4^4=4*4*4*4=256
If we multiply 3 five times it will give us 3^5=3*3*3*3*3=243
So we will write it as:
=4*(6^3)^2/3+ 1(4^4)3/4 +2(3^5)^1/5
=4(6)^2+(4)^3+2(3)
=4*36+64+6
=144+64+6
=214
The answer is 214....
Which information would best fill the blanks in row 3?
1.metallic bond and low melting point
2.metallic bond and high melting point
3. covalent bond and low melting point
4.covalent bond and high melting point
Answer:
covalent bond and low melting point- 3.
Answer:
C)
Step-by-step explanation:
egdenuity 2020
Evaluate 9 ÷ 3[(18 − 6) − 22].
The expression 9 / 3[(18 - 6) - 22] evaluates to -0.3, following the order of operations: first compute the parentheses, then multiply, and finally divide.
To evaluate the expression 9 / 3[(18 - 6) - 22], we need to follow the correct order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Let's solve it step-by-step:
Next, multiply by 3. Since there are no explicit parentheses around the 3 and the expression, we interpret it as 3 times the result from step 1, 3 * (-10), which equals -30.
Finally, divide 9 by the result from step 2, 9 / -30. That gives us -0.3.
The final answer, after doing the calculations in the correct order, is -0.3.
Elisondra is eating at a restraurant with three friends. They want to choose at random who will order first. If you model the situation with the spinner, how many equal-sized sections should the spinner have?
1/4
1
3
4
ANSWER ASAP PLEASE THANK YIOU
~~ Love joshthafish
Answer:
Elisondra and her three friends add up to four people, so the spinner should have 4 equal sized sections.
Answer:
D
Step-by-step explanation:
Which is an exponential growth function f(x)=6(0.25)x
f(x)=0.25(5.25)x
Answer: Second Option
[tex]f(x)=0.25(5.25)^x[/tex]
Step-by-step explanation:
The exponential growth functions have the following form:
[tex]f(x) = a(b)^x[/tex]
Where a is the main coefficient, b is the base and x is the exponent.
For this type of functions the base b must always be greater than 1. Otherwise it would be an exponential decay function
Among the options given, the only function whose base is greater than 1 is the second option:
[tex]f(x)=0.25(5.25)^x[/tex]
Answer:
The correct answer option is B. [tex] f ( x ) = 0 . 2 5 ( 5 . 2 5 ) ^ x [/tex].
Step-by-step explanation:
If the numbers are positive along with the base of the exponent which must be greater than 1, then it an exponential growth function.
1. [tex]f(x)=6(0.25)^x[/tex]:
Here the numbers are positive but the base of the exponent is 0.25 which is less than 1 so it is not an exponential growth function.
2. [tex] f ( x ) = 0 . 2 5 ( 5 . 2 5 ) ^ x [/tex]:
Positive numbers with base of the exponent greater than 1, therefore it is an exponential growth function.
Find the measure of angle x in the figure below
Answer:
[tex]\large\boxed{x=35^o}[/tex]
Step-by-step explanation:
We have the equation:
[tex]56^o+y+51^o=180^o\\\\(56^o+51^o)+y=180^o\\\\107^o+y=180^o\qquad\text{subtract}\ 107^o\ \text{from both sides}\\\\y=73^o\\\\\text{We know: the sum of the measures of the angles of the triangle}\\\text{is equal to}\ 180^o.\\\\\text{Therefore we have the equation:}\\\\x+y+72^o=180^o\qquad\text{put the value of}\ y\\\\x+73^o+72^o=180^o\\\\x+145^o=180^o\qquad\text{subtract}\ 145^o\ \text{from both sides}\\\\x=35^o[/tex]
assume this graph is a transformation from f(t)=-6t^2 what does the term -3.7 do to the rocket’s graph? what does the value t=3.7 represent and what happens to the rocket
@jdoe0001
Answer:
Eq.
y = -6(x-3.7)^2 + 82.14
the value t = 3.7 represents the maximum amplitude of the rocket in-flight.
Step-by-step explanation:
The standard equation of the parabola is written as
ax^2 +bx +c = 0
But we can rewrite it in vertex form. (See attached picture.)
y = a(x-h)^2 + k
If we look at the question, we can see that the vertex is
(h,k) = (3.7 , 82.14)
y = -6(x-3.7)^2 + 82.14
the value t = 3.7 represents the maximum amplitude of the rocket in-flight.
Answer:
t = 3.7 represents the time at which the rocket will reach at the maximum height.
Step-by-step explanation:
In the diagram,
We have a downward parabola having vertex (3.7, 82.14),
Since, a downward parabola is maximum at its vertex,
That is, the maximum value of the graph is 82.14 at 3.7,
Here, the graph shows the path of a rocket,
That is, it shows the distance covered by the rocket in different time,
Hence, the maximum distance covered is 82.14 unit at 3.7 time.
Mrs. Gomez is a mother to 2 boys. The number of children she has is three times the number of boys she has. Her children are planning to buy her a bouquet of flowers. What is the biggest bouquet they can buy in which the ratio of pink flowers to blue flowers matches the ratio of girls to boys if the florist has 9 blue carnations and 12 pink carnations left?
a bouquet of 12 flowers, 4 pink and 8 blue
a bouquet of 14 flowers, 8 pink and 6 blue
a bouquet of 15 flowers, 6 pink and 9 blue
a bouquet of 18 flowers, 12 pink and 6 blue
Answer:
a bouquet of 18 flowers, 12 pink and 6 blue is correct.
Step-by-step explanation:
Step 1: Find the total number of children.
Number of boys = 2
Total number of children = 3 x number of boys
Total number of children = 3 x 2 = 6
Step 2: Find the ratio of girls to boys
Number of girls = total number of children - total number of boys
Number of girls = 6 - 2 = 4
Girls : Boys
4 : 2
2 : 1
Step 3: Find the ratio of pink and blue flowers
Pink : Blue = Girls : Boys = 2 : 1
Step 4: Check the statements. The ratio of Pink : Blue should be 2 : 1.
1) a bouquet of 12 flowers, 4 pink and 8 blue. Incorrect because in this statement the ratio of pink : blue is 4 : 8 = 1 : 2 instead of 2 : 1.
2) a bouquet of 14 flowers, 8 pink and 6 blue. Incorrect because in this statement the ratio of Pink : Blue 8 : 6 = 4 : 3.
3) a bouquet of 15 flowers, 6 pink and 9 blue Incorrect because in this statement the ratio of pink : blue is 6 : 9 = 2 : 3.
4) a bouquet of 18 flowers, 12 pink and 6 blue. This is correct because the ratio of pink : blue is 12 : 6 = 2 : 1.
!!
Answer:
A bouquet of 12 flowers, 4 pink and 8 blue
Step-by-step explanation:
Let
x----> the number of boys
y ---> the number of girls
z ---> the number of children
we know that
x=2 boys----> equation A
z=3x-----> z=3(2)=6 children ----> equation B
z=x+y ----> equation C
substitute the value of x and the value of z in the equation C and solve for y
6=2+y
y=6-2=4 girls
so
The ratio of girls to boys is equal to
2/4=1/2
therefore
The ratio of pink flowers to blue flowers is equal to 1/2
Let
a -----> the number of pink flowers
b -----> the number of blue flowers
so
For b=9 blue carnations -----> Find the value of a
1/2=a/b
1/2=a/9
a=4.5 pink carnations ----> It doesn't make sense (must be a integer)
For b=8 blue carnations -----> Find the value of a
1/2=a/b
1/2=a/8
a=4 pink carnations ----> It makes sense
therefore
A bouquet of 12 flowers, 4 pink and 8 blue
What is the domain and range of h(x)=(x+1)/(x^2+4x)
Answer:
h=x+1/x^3+4x^2
Step-by-step explanation:
hx^3+4hx^2=x+1
h^3+4x^2)=x+1
h(x^3+4x^2)/x^3+4x^2=x+1/x^3+4^2
h=x+1/x^3+4x^2
Answer:
hambger
Step-by-step explanation:ham de be gerf hamburger
PLEEEEEEASE HELP ME:D
Answer:
{ (1,1),(2,9),(4,8) } is the right answer. Mentioned relation has all the ordered pairs of x and y in the form of set, shown in the table.
Step-by-step explanation:
Tables can be used to describe functions. i.e. in given table two coordinates x,y used as ordered pairs and their values mentioned, the value x-coordinate comes first and than value of its corresponding y-coordinate .According to the table, if we take value of x=1 than we need to take corresponding value of y=1 written as ( 1,1 ), Similarly for if x=2, its corresponding value of 'y' will be y=3 written as ( 2,3 ) and so onThe entire table expressed in ordered pair gives set { (1,1),(2,9),(4,8) }.Answer details
Grade: Middle
Subject: Mathematics
Chapter: Representing Functions and relations
Keywords: relations, ordered pairs, tables and functions, set etc
which graph shows a negative rate of change for the interval 0 to 2 on the axis?
Answer:
the answer to your question is the fourth one listed on your multiple choice, where it shows it curving at the lowest point out of all the others , in the 4th quadrant
Which set of numbers is included in the solution set of the compound inequality?
{-7,5, 18, 24, 32}
{-9, 7, 15, 22, 26}
{16, 17, 22, 23, 24}
{18, 19, 20, 21, 22}
Answer:
It's the first set.
Step-by-step explanation:
X ≤ 18 or x > 22.
The first set is included in the solution.
Its not the second because 22 is not included.
Nor the third also because of the 22.
Nor the third because of the 19, 20, 21 and the 22.
A set is a mathematical model for a collection of items; it contains elements or members, which can be any mathematical object.
What is Compound inequality ?A compound inequality is created when two simple inequalities are combined. This article explains how to graph and solve compound equations.
How to solve?Compound inequality includes number not included in selected region given in graph hence including numbers 18,19,20,21,22
Which is option D
Hence correct option is {18,19,20,21,22}
Learn more about compound inequality
https://brainly.com/question/234674
#SPJ2
Solve for y
y-1= 5(x + 2)
[tex]\huge{\boxed{y=\bf{5x+11}}}[/tex]
Distribute the 5. [tex]y-1=5x+10[/tex]
Add 1 on each side. [tex]y=5x+11[/tex]
y−1=5(x+2)
Step 1: Add 1 to both sides.
y−1+1=5x+10+1
y=5x+11
Answer:
y=5x+11
13. MONEY During the school week, Joshua spent $3 each
day on lunch. On Tuesday, he bought a $5 ticket to the school
play and on Friday he loaned $2 to his friend. When he
checked his wallet at the end of the day Friday, he had $3
left. How much money did he start the week with?
Answer:
Joshua had $25 on Monday.
Step-by-step explanation:
We are given the following information:
Money spend on each day for lunch = $3
Number of days he attend school in a week = 5
Total money spent on lunch = [tex]3\times 5 = \$15[/tex]
Money spent on Tuesday for ticket = $5
Money spent on Friday = $2
Money left on Friday = $3
Total money in the start of week =
[tex]15 + 5 + 2 + 3 = 25[/tex]
Thus, Joshua had $25 on Monday.
I'm not exactly a geek at math and measurements is one of the things I have always messed up at.
Anyone mind helping me?
Check the picture below.
well, √180 is about 13.4, and √72 is about 8.5, clearly 2*8.5 ≠ 13.4.
Which of the following does not factor as a perfect square trinomial? A. 16a^2-72a+81 B. 169x^2+26xy+y^2 C. x^2-18x-81 D. 4x^2+4x+1
Answer:
The correct option is C.
Step-by-step explanation:
Lets solve each option one by one
A) 16a^2-72a+81
According to whole square formula:
a²-2ab+b² =(a-b)²
We have to take the square root of first and third term of each equation.
a² shows the first term = 16a^2
The square root of 16a^2 is 4a.. because 4 is the number which can be multiplied two times to give 16 and when we multiply a two times it gives us a².
b² shows the third term = 81
The perfect square of 81 is 9.
2ab shows the middle term.
2ab = 2(4a)(9) = 72a
Thus we can factor it as a perfect square trinomial:
a²-2ab+b² =(a-b)²
16a²-72a+81 =(4a-9)²
B) 169x^2+26xy+y^2
a²+2ab+b² =(a+b)²
The square root of 169x² is 13x
Square root of y² is y
The middle term 26xy =2ab= 2(13x)(y)= 26xy
Thus we can factor it as a perfect square trinomial:
a²+2ab+b² =(a+b)²
169x^2+26xy+y^2 = (13x+y)²
C) x^2-18x-81
We can not factor it as a perfect square trinomial because the third term is negative.
D) 4x^2+4x+1
a²+2ab+b² =(a+b)²
The square root of 4x² is 2x
Square root of 1 is 1
The middle term 4x=2ab=2(2x)(1)= 4x
Thus we can factor it as a perfect square trinomial:
a²+2ab+b² =(a+b)²
4x^2+4x+1 = (2x+1)²
Thus the correct option is C....
2 Points
If y = 12x - 7 were changed to y = 12x + 1, how would the graph of the new
function compare with the original?
O
A. It would be steeper.
O
B. It would be shifted down.
O
c. It would be shifted up.
O
D. It would be less steep.
The graph's y intercept would be shifted up.
Intercept of the graphThe intercept of the original point is determined as follows;
y = 12x - 7, when compared to , y = mx + c
where;
c is the intercept = -7
The intercept of the second graph is determined as follows;
y = 12x + 1
New intercept = 1
The graph's y intercept will move from -7 to +1, thus, It would be shifted up.
Learn more about intercept here: https://brainly.com/question/1884491
Final answer:
The graph of the new function y = 12x + 1 would not be steeper or less steep than the original but would be shifted up compared to the graph of y = 12x - 7.(Option C)
Explanation:
Changing the equation from y = 12x - 7 to y = 12x + 1 does not alter the slope of the line, which remains 12 in both cases. The slope of a line represents the steepness and direction of the line, and since the slope (the coefficient of x) has not changed, the steepness and direction of the line will remain the same.
The change that does occur involves the y-intercept. The original line has a y-intercept at -7, while the new equation has a y-intercept at +1. This means the entire line is shifted vertically upwards by 8 units (from -7 to +1). Therefore, the correct answer to how the graph of the new function would compare with the original is that it would be shifted up.
Which of the following correlation coefficients represents the strongest correlation?
O 0.043680937
0 -0.313535265
O-0.922107932
O 0.854423006
Answer:
Option C (-0.922107932)
Step-by-step explanation:
Correlation is a concept which explains a linear relationship between two variables. The correlation constant lies between -1 and 1. 0 lies in the center of the interval. A negative correlation means an inverse relationship, and a positive correlation means a direct relationship. 0 technically means no linear relation between the variables. Further the correlation constant lies from 0, more the strength of the relationship. This means that closer the correlation to 1, stronger the positive relationship, and closer the correlation to -1, stronger the negative relationship. It can be seen that Option C (-0.922107932) is the correlation coefficient which is the largest in terms of the magnitude. Therefore, Option C is the correct choice!!!
The Discriminant of a quadratic equationis is -6 .What types of solutions does the equation have ?
a.2 irrational solutions
b.1 real solution
c.2 complex conjugate solutions
d.2 rational solutions
Answer:
C
Step-by-step explanation:
The nature of the solutions are determined by the value of the discriminant.
Given a quadratic equation in standard form ax² + bx + c = 0 : a ≠ 0
Then the discriminant is Δ = b² - 4ac
• If b² - 4ac > 0 then 2 real and distinct solutions
• If b² - 4ac = 0 then solutions are real and equal
• If b² - 4ac < 0 then solutions are not real, 2 complex conjugate solutions
Here b² - 4ac = - 6 , hence 2 complex conjugate solutions → C
if the cost of 15 bananas is rs 84 how many bananas can be bought for rs 140?
Answer:
25 bananas.
Step-by-step explanation:
The cost of one banana = 84/15 = rs 28/5 = rs 5.60.
So the number of bananas costing rs 140
= 140 / 5.60
= 25 bananas.
Solve the following system of equations: 3x − 2y = 6 6x − 4y = 12 (0, 0) (6, 12) Infinitely many solutions No solutions
Answer:
The correct answer option is: infinitely many solutions.
Step-by-step explanation:
We are given the following system of equations:
[tex] 3 x - 2 y = 6 [/tex] --- (1)
[tex] 6 x - 4 y = 1 2 [/tex] --- (2)
Dividing equation (2) by 2 to get:
[tex] 3 x - 2 y = 6 [/tex] --- (3)
As the equation (3) is same as the equation (1), therefore the system will have infinitely many solutions.
Answer:
infinitely many solutions
Step-by-step explanation:
Note that if you multiply the first equation by 2, you get 6x - 4y = 12, which is exactly the same as the second equation. These two lines coincide, and so there are infinitely many solutions.
Find the value of the expression.
h(h + k)
for h = 4 and k = 6
Answer:
40
Step-by-step explanation:
In this question, substitute the values of h and k in the expression
Given h=4 and k=6
The expression will be;
h(h+k)
4(4+6)
solve the brackets first
4+6=10
rewrite the expression as
4(10)
open the brackets by multiplication
4×10=40
Answer:
40
Step-by-step explanation:
We must substitute the values provided to us:
[tex]h=4[/tex] and [tex]k=6[/tex]
in the expression:
[tex]h(h+k)[/tex]
we get the following:
[tex]4(4+6)[/tex]
solving the sum inside the parentheses:
[tex]4(10)[/tex]
and finally solving the multiplication
[tex]4(10)=40[/tex]
the value of the expression is 40.
What is the explicit formula for this sequence?
-7,-3, 1, 5,...
A. an = -7 + (n - 1)(-4)
B. an = 9+ (n - 1)(-4)
C. an = -7 + (n - 114
D. an= -4 + (n - 1)(-7
Answer:
[tex]a_n=-7+4(n-1)[/tex]
or
[tex]a_n=-7+(n-1)(4)[/tex]
Step-by-step explanation:
-7,-3,1,5,... is a arithmetic sequence.
Arithmetic sequences have a common difference. That is, it is going up by 4 each time.
When you see arithmetic sequence, you should think linear equation.
The point-slope form of a line is [tex]y-y_1=m(x-x_1)[/tex].
m is the common difference, the slope.
Any they are using the point at x=1 in the point slope form. So they are using (1,-7).
So let's put this into our point-slope form:
[tex]y-(-7)=4(x-1)[/tex]
[tex]y+7=4(x-1)[/tex]
Subtract 7 on both sides:
[tex]y=-7+4(x-1)[/tex]
So your answer is
[tex]a_n=-7+4(n-1)[/tex]
The explicit formula for the sequence -7, -3, 1, 5,... is an = -7 + (n - 1)(4), which corresponds to an arithmetic sequence with a common difference of 4.
The student is looking for the explicit formula for the sequence -7, -3, 1, 5,.... To find the explicit formula for a linear sequence, we look for a pattern in the increments between successive terms. In this sequence, each term increases by 4 from the previous term (-7 + 4 = -3, -3 + 4 = 1, etc.), so the common difference is 4. Using the formula for an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference, we can find the explicit formula:
an = -7 + (n - 1)(4)
Since the common difference in the question is positive and we are adding it to the first term which is negative, it is clear that choice A is the correct formula representing the given sequence:
an = -7 + (n - 1)(4)
Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 4.4% compounded daily. The annual percentage yield is (blank) %
Step-by-step answer:
APY (annual percentage yield) is the amount of interest in percent one would actually earn by investing a sum of money in a year.
It takes into account the interest rate expressed in any particular form, and the compounding period.
In the current market, most interest rates (for example, credit cards) are expressed in APR (Annual percentage rate) which is an underestimate of the actual amount to be paid, by NOT taking into account the compounding period, monthly (instead of annually) most of the time. The shorter compounding period increases the APY.
Here the APR is 4.4%. to take into account the compounding period, we divide the interest rate by 12 to give the monthly rate, 4.4%/12=0.044/12.
This rate will then be compounded 12 times to give the APY, or the future value after 12 months.
Future value = (1+0.044/12)^12 = 1.044898
Therefore the APY is 1.044898 less initial deposit, or
1.044898-1 = 0.044898, or 4.4898%, or 4.49% (rounded to 2 decimal places)
Use synthetic substitution to find g(3) and g(-6) for the function g(x)=x^5-5x^3-10x+4
Answer:
g(3)=82
g(-6)=-6632
Step-by-step explanation:
To find g(3) we are going to use synthetic division for dividing the polynomial x^5-5x^3-10x+4 by x-3.
So this means 3 goes on the outside.
Also since we are missing x^4 and x^2 term, we will need to put a 0 placeholders there.
3 | 1 0 -5 0 -10 4
| 3 9 12 36 78
|_____________________
1 3 4 12 26 82
So g(3)=82
To find g(-6) we will put -6 on the outside:
-6 | 1 0 -5 0 -10 4
| -6 36 -186 1116 -6636
--------------------------------------
1 -6 31 -186 1106 -6632
So g(-6)=-6632
At Sara's new job she spent $11.52, $6.48, $5.99, $14.00, and $9.50 on lunch the first week.
In the second week, she spent $4 more in total for the 5 lunches than the first week.
second
What is the increase in the mean for the second week compared to the first? Round the
answer to the nearest penny.
Answer:
A. 0.80
Step-by-step explanation:
First, you need to find the mean of the cost of Sara's lunches the first week. The mean is the 'average,' and to find the average, add all of your terms and divide by the amount of terms.
[tex]11.52+6.48+5.99+14+9.5\\18+5.99+14+9.5\\23.99+14+9.5\\37.99+9.5\\47.49[/tex]
Sarah's total cost for the first week was $47.49. Divide by your number of terms (5) for your average daily cost.
[tex]\frac{47.49}{5} =9.498[/tex]
This can be rounded to $9.50.
For the next week, Sara spent $4 more in total than the first week. So, add $4 to your total.
[tex]47.49+4=51.49[/tex]
Now, divide $51.49 by your number of terms (5) again to find your average for the second week.
[tex]\frac{51.49}{5} =10.298[/tex]
This can be rounded to $10.30.
Find the difference.
[tex]10.30-9.50=0.80[/tex]
Sara spent $0.80 more on average.
What is the location of the point on the number line that is 3/5 of the way from a=2 to b=17
Answer:
11
Step-by-step explanation:
The distance that a is to b is b-a=17-2=15.
The line segment from a=2 to b=17 has length 15.
We need to know what is 3/5 of 15.
3/5 of 15 means what is 3/5 times 15?
(3/5)(15)=3(3)=9
So this means we are looking to make a line segment that is 9 units from 2 which is 2 to 11.
So 11 is 3/5 the way from a=2 to b=17.
Let's check from 2 to 11 that is a length of 9 and from 2 to 17 that is a length of 15.
Is 9/15 equal to 3/5?
Yes, 9/15 can be reduced to 3/5.
PQ is the perpendicular
bisector of AB
In the construction shown, the two arcs with points P and Q have the same radius. What must be true of PO?
Answer:
PQ must bisect AB
Step-by-step explanation:
How can you estimate 33 percent of 87?
Answer:
28.71
Step-by-step explanation:
The easiest way I do this is by taking the smaller number (33) changing it to a decimal form of .33, and then multiplying it by 87 to get 28.71
Describe how to transform the graph of g(x)= ln x into the graph of f(x)= ln (3-x) -2.
Answer:
The graph of g(x) = ㏑x translated 3 units to the right and then reflected
about the y-axis and then translated 2 units down to form the graph of
f(x) = ㏑(3 - x) - 2
Step-by-step explanation:
* Lets talk about the transformation
- If the function f(x) reflected across the x-axis, then the new
function g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then the new
function g(x) = f(-x)
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* lets solve the problem
∵ Graph of g(x) = ㏑x is transformed into graph of f(x) = ㏑(3 - x) - 2
- ㏑x becomes ㏑(3 - x)
∵ ㏑(3 - x) = ㏑(-x + 3)
- Take (-) as a common factor
∴ ㏑(-x + 3) = ㏑[-(x - 3)]
∵ x changed to x - 3
∴ The function g(x) translated 3 units to the right
∵ There is (-) out the bracket (x - 3) that means we change the sign
of x then we will reflect the function about the y-axis
∴ g(x) translated 3 units to the right and then reflected about the
y-axis
∵ g(x) changed to f(x) = ㏑(3 - x) - 2
∵ We subtract 2 from g(x) after horizontal translation and reflection
about y-axis
∴ We translate g(x) 2 units down
∴ g(x) translated 3 units to the right and then reflected about the
y-axis and then translated 2 units down
* The graph of g(x) = ㏑x translated 3 units to the right and then
reflected about the y-axis and then translated 2 units down to
form the graph of f(x) = ㏑(3 - x) - 2
Answer:
c edge
Step-by-step explanation: