Using translation concepts, it is found that the function that would meet Daniel's needs is:
g(x) = -cf(x) - b, c > 1, b > 0
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent function is f(x).
The transformations are as follows:
Vertical stretch, hence the function has to be multiplied by a constant c that is greater than 1, that is, [tex]g(x) = cf(x), c > 1[/tex].Reflection over the x-axis, hence the function is multiplied by -1, that is, [tex]g(x) = -cf(x), c > 1[/tex].Shift down, hence a constant b is subtracted from the graph, that is, [tex]g(x) = -cf(x) - b, c > 1, b > 0[/tex].You can learn more about translation concepts at https://brainly.com/question/21197885
80 POINTS
Gavin is moving into a new apartment that has a kitchen with an area of 50 square feet. If the area of the kitchen is 10 square feet more than the area of the bedroom, what is the area of the bedroom?
Complete the steps below to find the area of Gavin’s bedroom.
Part A
Let the variable b represent the area of the bedroom. Write an equation in terms of b to represent Gavin’s situation.
Part B
What is the first step in solving the equation you wrote in part A? Explain.
Part C
Rewrite the equation from part A to complete the first step.
Part D
What is the second step in solving the equation you wrote in part A? Explain.
Part E
Rewrite the equation from part C to complete the second step.
Part F
Recall the method that the video showed to solve Gavin’s word problem. The video showed how we can use numerical expressions (with the help of a diagram) to arrive at a solution.
Compare the expression method from the video with the equation method that uses the variable b. Do both methods use the same sequence of operations?
Part G
What does your answer to part F imply? Explain.
Answer:
40
Step-by-step explanation:
A. 50 - 10 = b
B. Finding the equivalence is the first step
C. b = 40
D. Subtracting 10 from 50
E. Already did b = 40
F. Yes, they both work the same way.
G. you have choices to make to get the right answer.
Karl has 200 coins in a jar. Nickles make up 10% of the coins in the jar, pennies make up 60% of the coins in the jar. All the coins in the jar are pennies, nickles, or dimes.
1) How many of the coins are nickles?
2) How many of the coins are dimes?
3) If Karl removes 100 pennies from the jar, then what percent of the remaining coins in the jar would be pennies?
PLEASEEEE HELP ASAP!!!!!!!!!!!! IT WOULD MAKE MY LIFE!!!
Answer:
We know that there are 200 coins
10 percent of the coins in the jar are nickels.
60 percent of the jar are pennies.
So how many nickels, dimes, and pennies.
Let’s break this down.
So 200 coins and 60 percent are pennies.
so lets find pennies first, so remeber percent means “out of a hundred” so 60 percent is really 60/100 or 0.6. Multiply 0.6 by 200 and you’d get 120 pennies.
120 pennies
Now 10 percent fo the coins in the jar are nickels. Same thing, 10 percent is basically 10/100 or 0.1. 0.1 * 200 is 20.
(1) 20 nickels
Now we know that there are 120 pennies and 20 nickels. The remaining is 60 coins left which has to be dimes.
2) 60 dimes.
Now if Karl removes 100 pennies, what would the percentage be. Now there were 120 pennies. So 120-100= 20. There’d be 20 pennies left.
We have to find the percentage but remember its 100 coins gone too so.
200-100=100
So it’s asking what percent of 100 is 20. Which should be pretty simple to look at (only in this situation or any other easily definable benchmarks).
3) 20 percent are pennies.
Hope it helped?
*brainly is appreciated*
4(3y-9) can be written as ?
Hey there!
4(3y - 9)
DISTRIBUTE 4 WITHIN the PARENTHESES
= 4(3y) + 4(-9)
= 12y - 36
Therefore, your answer is: 12y - 36
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
[tex]4(3y - 9) = (4 \times 3y) - (4 \times 9) [/tex]
[tex]= 12y - 36[/tex]
How to solve:
3*9^(2n) = (3^(n +1))^3
Answer:
3
Step-by-step explanation:
3*9^(2n) = (3^(n +1))^3
= 3×9^0^3
= 3×9^0
= 3×1
= 3
What are the steps to (5xy^3)^2(xy)^4?
Answer:
25x^6 y^10
Step-by-step explanation:
Simply: (5xy^3)^2: 25x^2 y^6
25x^2 y^6 (xy)^4
Apply exponent rule: (a * b)^n = a^n b^n
(xy)^4 = x^4 y^4
25x^2 y^6 x^4 y^4
Simply: x^2 x^4: y^10
25x^6 y^6 y^4
Simply: y^6 y^4: y^10
25x^6 y^10
Can anyone help please
Answer: Money is the reason we exist.
Step-by-step explanation:
I reallyyyy need help on this!!!! Can someone Help out??
Answer:
(4,5)
Step-by-step explanation:
To begin, we'll solve for y in the first equation.
-y = 3 - 2x
y = 2x - 3
Then, plug this in for y in the second equation.
9x - 6(2x-3) = 6
9x - 12x + 18 = 6
-3x = -12
x = -12/-3
x = 4
Then, you just plug your x value into one of the equations and solve for y. Personally, I think it's easiest to plug it into y = 2x - 3
y = 2(4) - 3
y = 8 - 3
y = 5
[tex]\bold{\huge{\purple{\underline{ Solution }}}}[/tex]
[tex]\bold{\underline{ Given:-}}[/tex]
We have given two equations that is 2x - y = 3 and 9x - 6y = 6[tex]\bold{\underline{ Let's \: Begin :-}}[/tex]
[tex]\sf{ 2x - y = 3 ...eq( 1 )}[/tex]
[tex]\sf{ 9x - 6y = 6 ...eq( 2 )}[/tex]
Solving eq( 1 ) :-
[tex]\sf{ 2x - y = 3 }[/tex]
[tex]\sf{ x = 3 + y/2 ...eq(3 )}[/tex]
Subsitute eq( 3 ) in eq( 2) :-
[tex]\sf{ 9(3 + y/2) - 6y = 6}[/tex]
[tex]\sf{ 27 + 9y/2 - 6y = 6}[/tex]
[tex]\sf{ 27 + 9y - 12y/2= 6}[/tex]
[tex]\sf{ 27 + - 3y = 6 × 2 }[/tex]
[tex]\sf{ - 3y = 12 - 27 }[/tex]
[tex]\sf{ - 3y = - 15 }[/tex]
[tex]\sf{ y = -15/-3}[/tex]
[tex]\sf{ y = 5 }[/tex]
[tex]\sf{\red {Thus, \: the\: value\: of \:y \: is\: 5 }}[/tex]
Now, Subsitute value of x in eq( 3) :-
[tex]\sf{ x = 3 + 5/2 }[/tex]
[tex]\sf{ x = 8/2 }[/tex]
[tex]\sf{ x = 4}[/tex]
[tex]\sf{\pink{Hence , \: the\: value\: of\:x\:and \:y \: is\: 4 \: and \: 5 .}}[/tex]
An isosceles triangle has side lengths of 16, an altitude of x, and a base of 2x. Find the length of the base.
Answer:
Step-by-step explanation:
Since the altitude of an isosceles triangle drawn from its vertex angle bisects the base, we can use the pythagorean theorem to say that:
16^2 = x^2 + x^2
256 = 2x^2
128=x^2
x = 8sqrt2.
so the base has a length of 16sqrt2.
Help!!! ASAP!!!!
Please help me!!!
No wrong answers!!!
Answer:
*
Step-by-step explanation:
Pattern A: is adding 2 dots each time
Pattern B: is going up 1,2,3,4 (adding that amount each time)
Pattern C: Times by 3 each time
please answer this math question with a clear explanation, thank you in advance to whoever does
I think the answer is B
To find this out, I used the process of Elimation.
It can't be A, because it is greater than 1.414...
It cant be C, because that's just the number 1
it can't be D, because that's less than 1.414...
So, the answer is B
Hope you find this useful!
Answer:
√4/2
Step-by-step explanation:
The square root of 2 has the approximate value 1.41421356
Tiana is 25 years old. She lives with a roommate and a dog. She has worked at a fancy restaurant for 6 months. She works 40 hours per week and makes $2.13 per hour. She usually serves 45 tables per week. The average bill at the restaurant is $130 per table, and she typically receives a 20% tip. How much does she make in a typical week?
Answer:
$1,255.5 dollars per week
Step-by-step explanation:
40Hr * $2.13 = $85.2 per week from hours alone
$130 * 0.20 = $26 tip per table
$26 * 45 tables = $1,170 in tips
$85.2 + $1,170 = $1,255.2 per typical week
help pls i beg you
with steps
Answer:
b) 1990659
Step-by-step explanation:
b) 9*9*9*9=6561, 12*12*12=1728, 8*8*8*8=4096 / 12*12=729, 2*2*2*2*2=32. 6561*1728*4096/729*32=1990656
I will mark brainliest!!!! help me please
Answer:
4n√(3n) +3√n -√(3n)
Step-by-step explanation:
The expression can be simplified, but terms cannot be combined.
[tex]\sqrt{48n^3}+\sqrt{9n}-\sqrt{3n}=\sqrt{(4n)^2(3n)}+\sqrt{3^2n}-\sqrt{3n}\\\\=\boxed{4n\sqrt{3n}+3\sqrt{n}-\sqrt{3n}}[/tex]
complete the table of values when x+2y equals 7
Answer:
x=7-2y
Step-by-step explanation:
Help me awnser these questions please
Answer: y=x-1
General equation of linear function: [tex]y=mx+b[/tex]
A(-1;0); x=-1, y=0
B(0;-1); x=0, y=-1
Let's solve the system of equations
[tex]\displaystyle\\\left \{ {{0=-1m+b} \atop {-1=0x+b}} \right. =>b=-1=>0=-m-1;m=-1[/tex]
Multiply & simplify: (3x - 2)^2
Mungkin Gini Kali Ya Kak
(3) × 2(2)
Answer:
9x² - 12x + 4
Step-by-step explanation:
(3x - 2)²
= (3x - 2)(3x - 2)
Each term in the second factor is multiplied by each term in the first factor , that is
3x(3x - 2) - 2(3x - 2) ← distribute parenthesis
= 9x² - 6x - 6x + 4 ← collect like terms
= 9x² - 12x + 4
What is the volume in cubic cm of this cone????
Answer:
113.04 cm³
Step-by-step explanation:
Volume = [tex]\frac{\pi r^2h}{3}[/tex]
Solve:
[tex]\frac{\pi3^2(12)}{3}[/tex][tex]\frac{\pi(9)(12)}{3}[/tex][tex]\frac{108\pi}{3}[/tex][tex]36\pi\\[/tex][tex]36(3.14)[/tex][tex]113.04[/tex]-Chetan K
18) Mr. Smith travels 280 miles in 4 hours.
How far can he go in 6.5 hours?
Answer:
here's your answer hope it helps you
Step-by-step explanation:
distance= speed*time
speed=70 miles per hour(280 in 4 hrs so divide)
time= 6.5 hour
distance=70×6.5 miles
distance=455.0 miles
Find the value of x. PLS HELP ASAP
Answer:
[tex] \sqrt{212} [/tex]
Step-by-step explanation:
[tex]( {2 \sqrt{5} })^{2} - {2}^{2} \\( 4 \times 5) - 4 \\ 20 - 4 \\ 16 \\ \sqrt{16 } = 4 \\ \\ {4}^{2} + {14}^{2} \\ 16 + 196 = 212 \\ \sqrt{212} [/tex]
i bought 16 cupcakes and then last week i bought 9 keep the pattern going
PLEASE I WILL GIVE BRAINLY
Answer:
25
Step-by-step explanation:
Signs of trig functions:
Answer:
Step-by-step explanation:
Each one of the trig functions is plus in two quadrants.
The sin(theta) is plus in 2
The Tan(theta) is plus in 3
The cos(theta) is plus in 4
Rule: if the trig function is not plus, then it is minus.
So if Tan (theta) is minus it means theta is in quad 2 or quad 4
So in this case theta is either in quad 2 or quad 4.
The sin is plus, that means that theta is in quad 2.
I need help, please pick the answers many that there the equivalent of 4(x + 1) + 7(x + 3)?
Answer:
B and C
Step-by-step explanation:
4(x+1) + 7(x+3)
4x + 4 + 7x + 21 <-- Choice B
11x + 25 <-- Choice C
SOMEONE PLS TELL ME HOW TO SOLVE THIS AND HOW TO GET THE ANSWERS STEP BY STEP
Answer:
Down Below
Step-by-step explanation:
Exponent Rules:
[tex]a^x * a^b = a^{a + b}, \frac{1}{a^{|x+b|}}[/tex][tex]\frac{a^x}{a^b} = a^{x - b}[/tex][tex](a^x)^b = a^{xb}[/tex]Given these rules,
[tex]3^9 * 3^4 = 3^{13}[/tex][tex]3^4 * 3^{-9} = \frac{1}{3^5}[/tex][tex]\frac{3^9}{3^5} = 3^{9 - 4} = 3^5[/tex][tex](3^9)^4 = 3^{36}[/tex]-Chetan K
Determine the total annual UIF contributions that will be paid by Mrs Chauke
The unemployment insurance fund (UIF) is simply a short-term relief that's given to employees when they're unemployed.
What is an unemployment insurance fund?Your information is incomplete. Therefore, an overview of the unemployment insurance fund will be given
The unemployment insurance fund is a short-term relief that's given to employees when they're unemployed. It is also given when they're unable to work due to maternity, adoption, illness, etc.
The unemployment insurance fund (UIF) is calculated as 2% of an employee's remuneration that is split evenly between the employee and the employer,
Learn more about insurance on:
brainly.com/question/25855858
4/7 and 3/10 with same denomiator
Answer:
4/7 = 40/70
3/10 = 21/70
Step-by-step explanation:
can someone please help me?
Answer:
2. x = 3
3. x = 10 and y =2
Step-by-step explanation:
2.
From inspection, we can see that EF = 10 and KL = 5
Therefore the ratio KL : EF = 5 : 10 = 5/10 = 1/2
This means that the side measures of ΔJKL are 1/2 the corresponding side measures of ΔGEF
Therefore, if GF = 22, then JL = 22 ÷ 2 = 11
So: 2x + 5 = 11
⇒ 2x = 11 - 5 = 6
⇒ x = 6 ÷ 2 = 3
x = 3
3.
From inspection, we can see that DF = 12 and HJ = 9
Therefore the ratio DF : HJ = 12 : 9 = 12/9 = 4/3
This means that the side measures of ΔDEF are 4/3 times the corresponding side measures of ΔHGJ
Therefore, if HG = 6, then DE = 6 x 4/3 = 8
So: 2y + 4 = 8
⇒ 2y = 8 - 4 = 4
⇒ y = 4 ÷ 2 = 2
y = 2
Similarly, if GJ = 24, then EF = 24 x 4/3 = 32
So: 4x - 8 = 32
⇒ 4x = 32 + 8 = 40
⇒ x = 40 ÷ 4 = 10
x = 10
Is (4,2) a solution to this system of equations?
y = -x + 6
y = 2x - 4
Answer:
No
Step-by-step explanation:
substitute the x- coordinate of the point into both equations and if the value obtained is equal to the y- coordinate then the point is a solution.
y = - 4 + 6 = 2 ← true
y = 2(4) - 4 = 8 - 4 = 4 ≠ 2 ← false
Thus the point is not a solution to the system
Which statement about f(x) and its translation, g(x), is true? The domain of g(x) is {x | x > 6}, and the domain of f(x) is {x | x > 0}. The domain of g(x) is {y | y > 0}, and the domain of f(x) is {y | y > 6}. The asymptote of g(x) is the asymptote of f(x) shifted six units down. The asymptote of g(x) is the asymptote of f(x) shifted six units up.
The correct statement about f(x) is the asymptote of g(x) is the asymptote of f(x) shifted six units up.
The given functions are;
F(x) = 7x
g(x) = 7x + 6
Parent functionA parent function is the simplest function that still satisfies the definition of a certain type of function.
We can see that 6 has been added to the function f(x) to get the function g(x).
We know that when we add some constant 'c' in the function then the function gets shifted upward by 'c' units.
Therefore, we will get g(x), when we will shift f(x) upward by 6 units.
Both functions are linear functions hence, the asymptote of g(x) is the asymptote of f(x) shifted six units up.
Hence, the correct statement about f(x) is the asymptote of g(x) is the asymptote of f(x) shifted six units up.
To know more about the parent function click the link given below.
https://brainly.com/question/18599661
Answer:
d The asymptote of g(x) is the asymptote of f(x) shifted six units up.
Step-by-step explanation:
There are 150 adults and 225 children at a zoo. If the zoo makes a total of $5100 from the
entrance fees, and the cost of an adult and a child to attend is $31 dollars, how much does it cost each
for a parent and a child?
Answer:
It costs $25 for a parent and $6 for a child
Step-by-step explanation:
Let x be the cost it takes for an adult to enter, and y be the cost it takes for a child to enter then...
x+y=31
150x+225y=5100
We can write the first equation in terms of x by subtracting y from both sides...
x=31-y
Now, we can solve the system of equations by substitution (substitute 31-y for x)...
150(31-y)+225y=5100
Distribute the 150 to the terms inside of the parentheses
150(31)-150(y)+225y=5100
4650-150y+225y=5100
Combine like terms
4650+75y=5100
Subtract 4650 from both sides
75y=450
Divide both sides by 75
y=6
Plug 6 back in for y to solve for x:
x=31-y=31-6=25
It costs $25 for a parent and $6 for a child
18
N
h
30°
450
W
y
27
972
93
18
Answer:
12. 5
11.
10
10
15. 7
14. 11
2
=
16
16
18. 3
+
11
17
3
4
co
loo
8
Step-by-step explanation:
12. 5
11.
10
10
15. 7
14. 11