Which equation is equivalent to 2x + 3y = 12?
The area of a rectangle is x^2 - 6x - 7 with a width of x - 7. What is the lenght?
[tex] {x}^{2} - 6x - 7 = (x - 7)(x + 1) \\ [/tex]
[tex]width = (x - 7)[/tex]
So
[tex]length = (x + 1)[/tex]
Just it...
So we're done.
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Determine whether the statements are True or False. Justify your answer with an explanation.
If f(x) = x + 1 and g(x) = 6x, then (f ○ g)(x) = (g ○ f)(x).
If you are given two functions f(x) and g(x), you can calculate (f ○ g)(x) if and only if the range of g is a subset of the domain of f.
Problem 1
Answer: False---------------------------------
Explanation:
The notation (f o g)(x) means f( g(x) ). Here g(x) is the inner function.
So,
f(x) = x+1
f( g(x) ) = g(x) + 1 .... replace every x with g(x)
f( g(x) ) = 6x+1 ... plug in g(x) = 6x
(f o g)(x) = 6x+1
Now let's flip things around
g(x) = 6x
g( f(x) ) = 6*( f(x) ) .... replace every x with f(x)
g( f(x) ) = 6(x+1) .... plug in f(x) = x+1
g( f(x) ) = 6x+6
(g o f)(x) = 6x+6
This shows that (f o g)(x) = (g o f)(x) is a false equation for the given f(x) and g(x) functions.
===============================================
Problem 2
Answer: True---------------------------------
Explanation:
Let's say that g(x) produced a number that wasn't in the domain of f(x). This would mean that f( g(x) ) would be undefined.
For example, let
f(x) = 1/(x+2)
g(x) = -2
The g(x) function will always produce the output -2 regardless of what the input x is. Feeding that -2 output into f(x) leads to 1/(x+2) = 1/(-2+2) = 1/0 which is undefined.
So it's important that the outputs of g(x) line up with the domain of f(x). Outputs of g(x) must be valid inputs of f(x).
The given statement is false.
What is composite function ?Composite function is a combination of two or more than two functions combined by mathematical operation of addition,subtraction,multiplication and division.Where output of one function is input to the other function.
According to the given question two functions are given f(x) and g(x) and and we have to compose in different order and see if they are same or not.
Given, f(x) = x + 1 and g(x) = 6x
So, (fog)(x) is, output of g(x) is the input of f(x) which is
f(6x) = (6x) + 1
f(6x) = 6x + 1.
Now, (gof)(x) is, output of f(x) is now input of g(x) which is
g(x+1) = 6(x+1)
g(x+1) = 6x + 6.
Thus we can see fog(x) ≠ gof(x).
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y=ax2+bx+c standard form
Answer:
y=3x^2+12x+13
a=3
b=12
c=13
Step-by-step explanation:
If Jeremy is feeding his Chihuahua 1/2 cup of dog food but uses 1/10 of a cup, how many scoops will he need to feed his dog?
Answer: 5
Step-by-step explanation:
The question is asking how many tenths are in one half. You need to divide one half by one tenth. To divide fractions you need to invert and multiply.
1/2 ÷ 1/10
Step 1: Invert and multiply
1/2 × 10/1 = 10/2
Step 2: Simplify
10/2 = 5
Solve the equation.
m2 = 43
Is that 2m=43 or m^2=43??
If 2m=43 then...
m=43/2
m=21.5
If m^2=43 then...
m=√43
Answer:m=21.5
Step-by-step explanation:
Does 1 2 and 5 make a right triangle
Answer:
Yes.
Step-by-step explanation:
If the catetes are 5 and 12, then the hypotenuse is 13, and it is a special right triangle.
A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.M. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.2 gallons. What is the average rate of flow of the gasoline into the gas tank?
Answer:
2.55gallons.minStep-by-step explanation:
given that the initial time before pumping is 3:40 p.M.
after pumping the time reads 3:44, hence he use 4 min to fill his tank
time taken=4 min
also given is that had pumped 10.2 gallons
the capacity of tank= 10.2gallon
Then the average rate of pump is
average rate= capacity of tank/time taken
average rate= 10.2/4min
average rate=2.55gallons.min
Bijou Museum sells 75% of its tickets for the regular price of $14. The remaining discount tickets are sold for the price of $10. Variable cost per guest is $2 for both groups, and fixed costs total $66,000 per month. What are the number of regular-price guests and discount guests at the breakeven point?
Answer:
Regular price guests = 3300
Discount price guests = 1100
Step-by-step explanation:
Breakeven point is the point where total revenue and total cost are equal.
Now, we know total cost is $66,000 per month.
Now, we are told that the museum sells 75% of its tickets for the regular price of $14.
If the total number of tickets is x. It means the number of regular tickets guests is 75%x = 0.75x
We are told that variable cost per guest in each group is $2. This means that total revenue from regular tickets guest is;
14(0.75x) + 2(0.75x) = 12x
Now, the remaining tickets are discount tickets sold for $10.
It means number of discount tickets guests = 0.25x
Total revenue from discount tickets =
10(0.25x) + 2(0.25x) = 3x
Thus, at break even point, we have;
12x + 3x = 66000
15x = 66000
x = 66000/15
x = 4400
Thus;
Regular price guests = 0.75 × 4400 = 3300
Discount price guests = 0.25 × 4400 = 1100
A gym's membership in 2012 was 9,300. The current membership is 2,800. Which expression can be used to find the
percent of change?
Answer:
Find the difference between the two, divide by the years, and should get the percent of change
Step-by-step explanation:
The change in percentage is 69.89%.
Given that, a gym's membership in 2012 was $9,300.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
The current membership is $2,800.
We know that, the percentage change = (New value - Original value)/Original value × 100
Now, the percentage change = (9300-2800)/9300 × 100
= 6500/9300 × 100
= 0.6989 × 100
= 69.89%
Therefore, the change in percentage is 69.89%.
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can anyone answer this?
Answer:
it is J
Step-by-step explanation:
.
A baker is making cakes for a party. She uses 2 1/4 cups of flour for each cake. If she has 11 cups of flour, how many cakes can she make?
PLZ HELP It’s due soon
Answer:
30
Step-by-step explanation:
Answer:
Oh thats easy its $30
Step-by-step explanation:
so for 2 icecreams it costs $6
so if u divide them it would become 1 icecream for $3 so
10 times 3 will be $30
1. Find f(3) for
the function
below.
f(x) = 4^x
Answer:
64
Step-by-step explanation:
f(x) = 4^x,
When x = 3,
=> f(3) = 4^3
= 4 * 4 * 4
= 64
Answer:
f(3) = 64
Step-by-step explanation:
To evaluate f(3), substitute x = 3 into f(x) , that is
f(3) = 4³ = 64
Relationship B has a greater rate than Relationship A. This graph represents Relationship A.
Which equations could represent Relationship B?
Select each correct answer.
A.y = 1.4x
B.y=12x
C.y = 2.2x
D.y = 3x
Alex has twice as much money as Jennifer. Jennifer has $6 less than Shannon. Together they have $54. How much money does each have?
Answer:
Alex has twice as much money as Jennifer.
a = 2j
Jennifer has $6 less than Shannon.
j = s-6
j+6 = s
All together the three friends have $54.
a + j + s = 54
Replace a and s
2j + j + (j+6) = 54
4j = 54 - 6
4j = 48
j = 48/4
j = 12
Jennifer has $12
Alex= 2*12 = $24
Shannon = 24+12+s = 54
= 36+s = 54
s = 18
Shannon has $18
Log2 x + log2 (6-x)=3 solve for x algebraically
Answer:
The solution is x = 2 and x = 4
Step-by-step explanation:
Let us revise some rules in logarithmic function:
[tex]log_{a}(x)+log_{a}(y)=log_{a}(xy)[/tex]The logarithmic function is the inverse of the exponential function [tex]log_{b}(c)=a[/tex] is the inverse of [tex]b^{a}=c[/tex]Let us solve the question
∵ [tex]log_{2}(x)+log_{2}(6-x)=3[/tex]
→ By using the first rule above
∴ [tex]log_{2}(x)(6-x)=3[/tex]
→ Multiply x by (6 - x)
∵ x(6 - x) = x(6) - x(x) = 6x - x²
∴ [tex]log_{2}(6x-x^{2})=3[/tex]
→ Change the logarithmic function to exponential function using
the second rule above
∴ [tex]2^{3}=(6x-x^{2})[/tex]
∵ 2³ = 8
∴ 8 = 6x - x²
→ Add x² to both sides
∴ x² + 8 = 6x
→ Subtract 6x from both sides
∴ x² - 6x + 8 = 0
→ Factorize it into 2 brackets
∴ (x - 2)(x - 4) = 0
→ Equate each factor by 0 to find the values of x
∵ x - 2 = 0
→ Add 2 to both sides
∴ x = 2
∵ x - 4 = 0
→ Add 4 to both sides
∴ x = 4
∴ The values of x are 2 and 4
∴ The solution of the equation is x = 2 and x = 4
Which is not a pair of congruent angles in the diagram below?
angles BCD and BAD
angles ABD and BDC
angles BDA and DBC
angles ABD and BAD
:)
Answer:
angles ABD and BAD
Answer:
angles ABD and BAD
Step-by-step explanation:
The graph below represents the total shipping cost of x items for four different companies.
Shipping Charges
A graph has number of items on the x-axis and shipping cost in dollars on the y-axis. Line W goes through points (0, 5) and (2, 13). Line U goes through (0, 12) and (3, 16). Line Y goes through (0, 10) and (2, 12). Line Z goes through (0, 0) and (2, 4).
Which list places the companies in order from the steepest slope to the least steep slope?
W, Z, U, Y
U, Y, W, Z
W, Z, Y, U
U, Y, Z, W
Answer:
Steepest to most gentle: W, Z, U, Y
Step-by-step explanation:
Answer: WZUY
Step-by-step explanation: On Edgenuity!!!!!!!!!!!
is the line liner?
someone help i need this to pass
Answer:
yes
Step-by-step explanation:
A motorist drives at a constant rate of 60 kph. If his destination is 240 kilometers away from his
starting point, how many hours will it take him to reach the destination? Write a rule that best describes
the problem and draw its graph using any method.
Answer:
4 hours
Step-by-step explanation:
240/60=4
The rule that best describes the problem is time = 240/60.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, A motorist drives at a constant rate of 60 kph and his destination is 240 kilometers away from his starting point.
We know, Distance = time×speed.
time = distance/speed.
time = 240/60.
time = 4 hours.
speed×time = distance.
60t = 240.
60x = 240. (x = t).
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A piece of cable 1/2 cm long weighs 25 grams. What will a 1 1/2cm length of the same cable weigh?
Answer:
75 grams
Step-by-step explanation:
1/2 cm = 25 grams
(1 1/2) /( 1/2) = 3 times as much
1 1/2 cm = 3 x 25 75 grams
On a coordinate plane, a triangle has points D (negative 2.5, 5), E (0, negative 1), and F (negative 5, negative 1).
What is the y-coordinate of point D after a translation of (x, y) → (x + 6, y – 4)?
D′(3.5,___ )
Answer:
D = (3.5,1)
Step-by-step explanation:
(-2.5,5) is given
you must do (x+6,y-4)
x y
(-2.5,5)
-2.5+6=3.5
x=3.5
5-4=1
y=1
(3.5,1)
Answer:
(3.5, 1)
Step-by-step explanation:
edg 2021
A grocery delivery service has 22 members. Each member pays monthly dues of $12.80
on the first day of the month,9 members paid
their dues. The remaining members paid
their dues on the third day of the month. How much
money was
collected in dues on the
(third days of the month?
A.115.20
B.232
C.166.40
D.131.84
Answer:
C
Step-by-step explanation:
If 9 members paid on the first day, this means they did not pay on the third day
The remaining people (everyone but the 9) paid on the third day
Therefore we must subtract to find out how many members paid on the third day
22 - 9 = 13
Each of the 13 members paid $12.80 which means we must multiply
13 × 12.80 = 166.40
In total, the grocery store collected $166.40 on the third day of the month
combine like terms to create an equivalent expression 6(1/2 w - 3/4)
11/12 times 7 equals what in a fraction
Answer: 77/12
Step-by-step explanation:
1) 11/12 * 7 = (11*7)/12 = 77/12
BD = 8 and AB = 4 Find AD
Answer:
AD is 12
Step-by-step explanation:
Answer:
AD=12
Step-by-step explanation:
AB=4
BD=8
AD=AB+BD
AD=4+8
AD=12
Hope this helps :)
Please help me ffuufgigjgjfufjdjfjckcmdhsndjf
Answer:
1/16
Step-by-step explanation:
I usually provide explanations, but I'm pretty sure you need an answer fast. Tell me if you need an explanation!
Answer:
1/16
Step-by-step explanation:
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rationalise the denominator 20 over root 2
Answer:
see explanation
Step-by-step explanation:
Given
[tex]\frac{20}{\sqrt{2} }[/tex]
To rationalise the denominator multiply the numerator and denominator by [tex]\sqrt{2}[/tex], that is
[tex]\frac{20(\sqrt{2}) }{\sqrt{2}(\sqrt{2}) }[/tex]
= [tex]\frac{20\sqrt{2} }{2}[/tex]
= 10[tex]\sqrt{2}[/tex]
What is the slope of the linear function y= - 5/3 - x
Answer:
The slope-intercept form is y=mx+b y = m x + b , where m is the slope and b is the y-intercept. Using the slope-intercept form, the slope is 3 .
Step-by-step explanation:
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