[tex]\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}[/tex]
[tex]\bf ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\[/tex]
[tex]\bf \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]
now, with that template in mind, let's take a look
[tex]\bf \begin{cases} f(x)=&2^x\\ g(x)=&f(x+k)\\ & f(x-5)\\ &2^{x-5} \end{cases}~\hspace{10em}g(x)=2^{\stackrel{A}{1}(\stackrel{B}{1}x\stackrel{C}{-5})}+\stackrel{D}{0} \\\\\\ \textit{horizontal shift by }\cfrac{C}{B}\implies \cfrac{-5}{1}\implies -5\qquad \qquad \textit{ of 5 units to the right}[/tex]
The graph of g(x) is shifted horizontally 5 units to the right of the graph of f(x).
The correct option is (b).
What is a Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
As per the given data:
We are given 2 functions, and we have to find out the shift in the graph.
f(x) = 2^x
g(x) = f(x+k)
When the value of k = -5 we have to find out the shift in the graph of g(x).
For finding out the shift in the graph of g(x):
g(x) = f(x+k)
By substituting the given value of f(x) = 2^x and k = -5:
g(x) = 2^(x-5)
When y = f(x) is changed to y = f(x - 5) the graph of f(x) shifts 5 units to the right horizontally.
Similarly, for g(x) = 2^(x-5) the graph will shift by 5 units to the right.
Hence, The graph of g(x) is shifted horizontally 5 units to the right of the graph of f(x).
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Ollie has $400 balance on her credit card.She pays $60 a month on the card.Does this situation have a positive or negative rate of change?explain
Answer:
It has a negative rate of change.
Step-by-step explanation:
She is losing money so the rate of change is negative
perform all the steps to evaluate this expression. (6^7)(3^3)/(6^6)(3^4) What is the value of the expression?
To evaluate the expression (6^7)(3^3)/(6^6)(3^4), simplify each term, resulting in 6^10 / 6^10, which equals 1.
Explanation:To evaluate the expression (6^7)(3^3)/(6^6)(3^4), we can simplify each term first. The numerator can be simplified as (6^7)(3^3) = 6^(7+3) = 6^10. The denominator can be simplified as (6^6)(3^4) = 6^(6+4) = 6^10. Therefore, the expression simplifies to 6^10 / 6^10, which is equal to 1. So the value of the expression is 1.
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The sum of an integer n and four is equal to the difference of ten and two.What is the value of n?
Answer:
n=4
Step-by-step explanation:
Attachment has my work.
Tickets cost $36 each. this is 60% of the cost of the regular price what is the cost of the regular price?
Answer:
$60
Step-by-step explanation:
regular price=x
60% of x = 36
60/100 * x= 36
x=36/0.6
x=60
PLEASE HELP! all you need to do is drag the things in the correct order....
Answer:
16*j+4
16+8*4
16+32
48
Step-by-step explanation:
A survey of 120 middle schools showed that 30% have a foreign language program. How many schools have a foreign language program?
Equation:
Solution:
Answer:
36
Step-by-step explanation:
Equation: Schools with foreign language program = 0.30(120 middle schools).
Solution: " = 36
36 of these 120 middle schools have a foreign language program.
Answer:
36 schools have a foreign language program
Step-by-step explanation:
Equation: 30/100 *120=x
Solution: 3600/100=x
36=x
Brian works 24 hours this week. His earns 9.25 per hour. He pays $37.50 in payroll tax. He deposits half of his pay after taxes in his savings account. He deposits the other half of his pay after taxes in his checking account. How much money is deposited into each account?
Answer:
$92.25
Step-by-step explanation:
Begin with 24 hours times $9.25 an hour.
Get $222.
Subtract $37.50.
Get $184.5.
Divide this by 2.
Get $92.25 as your final answer
Brian will deposit $92.25 into both his savings account and his checking account after calculating his net pay by subtracting payroll taxes from his gross earnings and dividing the remainder by two.
To calculate how much money is deposited into Brian's savings and checking accounts, we need to follow these steps:
First, calculate Brian's gross pay by multiplying his hourly wage by the number of hours he worked.Deduct the payroll taxes from the gross pay to find out the net pay.Divide the net pay by two to determine how much goes into each account.Let's do the math:
Brian's gross pay = 24 hours x $9.25/hour = $222Brian's net pay after taxes = $222 - $37.50 = $184.50Money deposited into each account = $184.50 / 2 = $92.25So, Brian will deposit $92.25 into his savings account and another $92.25 into his checking account.
a tree is 8ft tall and grows 8 inches each year. In how many years will the tree reach a height of 30 feet?
A.27
B.33
C.45
D.52
Answer:
B
Step-by-step explanation:
30 ft = 360 in
8 ft = 64 in
360 in - 64 in = 296 in
296 / 8 = 33
It will take approximately 32.84 years for the tree to reach a height of 30 feet.
To determine the number of years it will take for the tree to reach a height of 30 feet, let's break down the growth process step by step.
Initially, the tree is 8 feet tall.
The tree grows 8 inches (0.67 feet) each year.
Let's assume it takes "x" years for the tree to reach a height of 30 feet.
So, the height of the tree after "x" years can be represented by the following equation:
Height after x years = Initial height + (Growth rate * x)
In this case, the initial height is 8 feet, and the growth rate is 0.67 feet (8 inches).
Height after x years = 8 + (0.67 * x)
Now, we need to solve for "x" when the height reaches 30 feet:
30 = 8 + (0.67 * x)
Subtract 8 from both sides of the equation:
22 = 0.67 * x
To isolate "x," divide both sides by 0.67:
x = 22 / 0.67
Now, calculate "x":
x ≈ 32.84 years
So, the Answer: B. 33 years
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Which of the following would be appropriate to measure in centimeters?
the length of a paperclip
the yearly increase in a child's height
the width of a swimming pool
the distance between Philadelphia and New York City
the height of a standard ceiling
Answer:
Centimeter is a small measuring unit, usually used to measure small things like the length of a pencil.
Let us check all the options:
1. the length of a paperclip - yes it can be measured in cm. Like a standard paperclip is 3.5 cm long.
2. the yearly increase in a child's height - Yes it can be measured in cm.
3. the width of a swimming pool - No, it can be measured in feet or meters.
4. the distance between Philadelphia and New York City - No, it can be measured in km or miles.
5. the height of a standard ceiling - No, it can be measured in feet.
Which measurement correctly completes the statement 627 L=? mL A. 6.27 B. 627,000 C. 62,700 627,000,000? Pls help I’ll give you brainliest!
Final answer:
To convert liters to milliliters, multiply the number of liters by 1000. Therefore, 627 liters is equal to 627,000 milliliters.
Explanation:
To correctly complete the statement 627 L = ? mL, we need to convert liters to milliliters. Since there are 1000 milliliters (mL) in 1 liter, we multiply the number of liters by 1000 to find the number in milliliters.
Thus, the conversion is:
627 L × 1000 = 627,000 mL
Therefore, the statement 627 L = 627,000 mL is correct.
please help me the photo is my queston
Answer:
i think it would be 30
Step-by-step explanation:
The $120 repair bill included $36 for parts and rest for labor. What percent of the bill was for labor?
Answer:
30%
Step-by-step explanation:
70% of the $120 repair bill was for labor, calculated by subtracting the cost of parts from the total bill and then finding the percentage of the remaining labor cost.
Explanation:The question is asking what percent of a $120 repair bill was for labor if $36 was for parts. Since the total bill is $120, the cost for labor is the total bill minus the cost for parts, which is $120 - $36 = $84 for labor. Now, to find the percentage of the bill that was for labor, you use the formula (part/whole) × 100, which in this case is ($84/$120) × 100 = 70%. Therefore, 70 percent of the bill was for labor.
what is the axis of symetry given f(x)=x^2+4x-19
Answer:
x = -2
Step-by-step explanation:
The formula for the axis of symmetry is;
x = -b/2a
In this case;
b = 4 , a = 1
Therefore;
x = -4/2(1)
= -2
Thus; the axis of symmetry is x = -2
Answer:
x = -2 is the axis of symmetry.
Step-by-step explanation:
We have given the function:
f(x)=x²+4x-19
We have to find the axis of symmetry.
We know that the formula for axis of symmetry is:
x = -b /2a
In this equation, b = 4 , a = 1
Putting these values we get,
x = -4/2(1)
x = -4/2
x = -2
x = -2 is the axis of symmetry of this function.
The Johnson family drove 52 miles on 4 gallons of gasoline. Which of the following equations can be used to find how far they can travel on a full tank of 15 gallons?
Answer:
y = 13x
Step-by-step explanation:
First we need to take the number miles the Johnson family drove and divide it to the number of gallons of gasoline used to find how many miles per gallon
Miles per gallon = 52/4
Miles per gallon = 13
Now that we know how many miles per gallon, let's make an equation to find how much they can travel on a full tank of 15 gallons.
Let y = number of miles traveled
Let x = number of gallons
y = 13x
Now let's see how much they can travel in 15 gallons.
y = 13x
y = 13(15)
y = 195 miles
So the Johnson family can drive 195 miles on a full tank of 15 gallons of gasoline.
Uno de los triángulos agudos de un triángulo rectángulo mide 18° más que el otro. ¿Cuánto mide cada ángulo del triángulo?
Do u want me to translate it or what???
solve the following system of equations below 4x+y=16 2x+3y=-2
x = 5
y = -4
steps:4x + y = 16
multiply 2nd equation by 2
4x + 6y = -4
subtract equations
0 -5y = 20
-5y = 20
y = 20 ÷ -5
y = -4
substitute y = -4 to find the value of x
4x + (-4) = 16
4x - 4 = 16
4x = 20
x = 5
Please help me
Determine the value of base b if (152)b = 0x6A. Please show all steps.
Answer:
The value of b is, 8
Step-by-step explanation:
To determine the value of b:
Given:
[tex](152)_b = 0x6A[/tex] ....[1]
Since, 0x6A represents the hexadecimal form.
To convert this hexadecimal form into decimal form:
[tex](6A)_{16}= (6 \times 16^1)+(A \times 16^0)=(6 \times 16)+(10 \times 1) =96+10 = 106[/tex]
⇒[tex]0x6A=106[/tex](decimal form)
Now we have to convert this decimal form into octal
8 | 106
8 | 13 | 2
| 1 | 5
1
Then, the octal form we get, [tex](152)_8[/tex]
Substitute this in [1] we have;
[tex](152)_b = (152)_8[/tex]
On comparing both sides we have;
b = 8
Therefore, the value of b is, 8
What is the area of this figure?
you would take 264+77+150=491in2
The answer is 491in squared
Calculate the slope:
rise: 37
run: 63
Answer:
.587
Step-by-step explanation:
Slope is rise over run.
rise/run=37/63=.587
Solve the system of equations y=8x+15 and y=x+57
Answer:
x=6, y=63
Step-by-step explanation:
since both equal y, they equal each other-
8x+15=x+57
7x=42
x=6
then to solve for y-
y=(6)+57
y=63
The solution to the system of equations y = 8x + 15 and y = x + 57 is found via substitution, yielding x = 6 and y = 63 as the answer.
To solve the system of equations y = 8x + 15 and y = x + 57, we can use the method of substitution or elimination. However, since both equations are already solved for y ,, the most straightforward approach is substitution, implying that 8x + 15 = x + 57. To find the value of x, we subtract x from both sides and subtract 15 from both sides, yielding 7x = 42. Dividing both sides by 7, we find that x = 6. Substituting x = 6 into either of the original equations, for instance, y = 8(6) + 15, gives us y = 63. Therefore, the solution to the system of equations is x = 6 and y = 63.
Is the sequence geometric ? -48,96,-192,384...
Answer:
yes
Step-by-step explanation:
If the sequence is geometric then the common ratio r between consecutive terms will be equal.
[tex]\frac{96}{-48}[/tex] = - 2
[tex]\frac{-192}{96}[/tex] = - 2
[tex]\frac{384}{-192}[/tex] = - 2
The common ratio between terms = - 2
Hence the sequence is geometric
A point represents a _____.
Answer:
A point represents a place/location.
Step-by-step explanation:
A point is used to locate a place in a map. It has no length, width and height.
The point is an undefined term. We use the point as undefined term and using the point we define line, line segment, angle and so on.
So a pointed represented location in a xy-coordinate plane.
pls help ✨ , im struggling , show work too pls (I WILL GIVE OUT BRAINLIEST)
Answer:
First shape : 204cm^2
Second shape : 57in^2
Step-by-step explanation:
For the first shape :
The front and back triangles are 3 * 8 / 2 which gives us 12 on each side.
The side rectangles are 5 * 10 which is 50 on each side.
The bottom rectangle is 10 * 8 which is 80.
Add them all up and you get 204.
For the second shape :
The triangles are all congruent and the area is 3 * 8 / 2, so we get 12 on each side.
Then the bottom square is 3^2, which is 9.
Add them all up together and you get 57.
An auditorium has three levels. Level 1 seats 3,577 people, Level 2 seats 5,214 people, and Level 3 seats 5,879 people. How many seats are in all three levels combined? A. 8,991 B. 14,670 C. 14,970 D. 14,370
Answer:
14,670
Step-by-step explanation:
3,577 + 5,214 + 5,879 =14,670. Hope this helps! ☺
What is the definition of transformation
Answer:
IN MATHS,TRANSFORMATION is a process by which one figure, expression, or function is converted into another one of similar value.
IN PHYSICS ,TRANSFORMATION is the induced or spontaneous change of one element into another by a nuclear process.
IN BIOLOGY,TRANSFORMATION is the genetic alteration of a cell by introduction of extraneous DNA, especially by a plasma.
Final answer:
In Biology, transformation involves the uptake of external DNA by a cell, leading to changes in its morphology and physiology. This process is commonly observed in bacteria, such as Streptococcus pneumoniae. It can result in the conversion of a non-virulent strain into a virulent one.
Explanation:
Transformation in Biology refers to the process in which external DNA is taken up by a cell, resulting in a change in its morphology and physiology. This genetic change through gene transfer is commonly observed in prokaryotes, such as bacteria. For example, in the case of Streptococcus pneumoniae, the bacterium that causes pneumonia, transformation can lead to the conversion of a non-virulent strain (rough) into a virulent one (smooth).
factor 2x^2 + 7x+3
a: (2x+2)(x+1)
b:(2x+3)(x+1)
c:(2x+1)(x+3)
Split the second term in 2x^2 + 7x + 3 into two terms
2x^2 + 6x + x + 3
Factor out the common terms in the first two terms, then in the last two terms;
2x(x + 3) + (x + 3)
Factor out the common term x + 3
= c: (2x + 1)(x + 3)
I need help with this problem for math. 15 points!
I think it's 75 if wanting to add up to 180
HELP ASAP :
A movie theater calculates its revenue using the equation R=4.85t, where R is revenue in dollars and t is the number of tickets sold. What is the revenue if 88 tickets are sold?
1) $426.80
2) $88.00
3) $426.08
4) $18.14
4.85×88=$426.80.
1) $426.80 is the answer
what adds to 0 and miltiplies to -49?
what is the value of x? (2x-2) (3x-52)
Answer:
x = 54
Step-by-step explanation:
2x + 2 = 3x - 52
-2x -2x
2 = x - 52
2+52 = x-52 +52
54 = x