[tex]\text{Given that,}\\\\f(x) = 3x +12, ~ ~ g(x) = 3x -1\\\\(f \circ g)(x)\\\\=f(g(x))\\\\=f(3x-1)\\\\=3(3x-1) +12\\\\=9x - 3 +12\\\\=9x +9\\\\=9(x+1)[/tex]
Cassidy is selling popcorn for a fundraiser sale at the price shown. he purchases a total of 150 containers of popcorn to sell. after he sells 25 containers, he will make a total profit, after his upfront costs, of $5.50 cassidy's profit, after upfront costs, can be modeled by a linear function in the form of y=mx+b.
C. Will the function be discrete or continuous? Explain.
D. Write the function that models Cassidy's profit.
E. What is the domain of the function?
F. What is Cassidy's profit or loss if he does not sell any popcorn?
G. What is cassidy's profit if he sells all the popcorn?
H. What is the range of the function?
The domain and the range of the function describes the possible profit or
loss from the sale of popcorn and the number of popcorn units.
The correct responses are;
C. The function is discreteD. The function is; y = 1.5·x - 32E. The domain is; 0 ≤ x ≤ 150F. The loss when non of the popcorn is sold is $-32G. The profit is $193H. The range is; -32 ≤ y ≤ 193Reasons:
The question parameters are;
The price of a popcorn = $1.5
Number of popcorn he purchases = 150
Total profit made = $5.50
The number of containers sold = 25
Therefore;
C. Given that the number of containers sole is countable, the function will be discrete.
D. Cost of the containers = Revenue - Profit
Which gives;
Cost of the containers = 1.5 × 25 - 5.5 = 32
The given function is therefore;
y = 1.5·x - 32
E. The domain is the 150 containers which gives;
The domain = 0 ≤ x ≤ 150
F. When no popcorn is sold, we have;
x = 0, which gives;
y = 1.5 × 0 - 32 = -32
If he does not sell any popcorn, the loss is $32
G. If all the popcorn are sold, we have;
x = 150
Therefore;
y = 1.5 × 150 - 32 = 193
The profit if all the popcorn are sold = $193
H. The range of the function are the possible y values, which is the possible profit or loss, which gives;
The range = -32 ≤ y ≤ 193
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x squared+ y squared = 2 y = 2x squared – 3 Which of the following describes the system?
Answer:
[tex]x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}}[/tex] and [tex]y=-1,\frac{1}{2}[/tex]
The ordered pair solutions are [tex](-\sqrt{\frac{7}{4}},0.5)[/tex], [tex](\sqrt{\frac{7}{4}},0.5)[/tex], [tex](-1,-1)[/tex], and [tex](1,-1)[/tex].
Step-by-step explanation:
I'm assuming the system is [tex]\left \{ {x^2+y^2=2} \atop {y=2x^2-3}} \right.[/tex]:
[tex]x^2+y^2=2[/tex]
[tex]x^2+(2x^2-3)^2=2[/tex]
[tex]x^2+(4x^4-12x^2+9)=2[/tex]
[tex]x^2+4x^4-12x^2+9=2[/tex]
[tex]4x^4-11x^2+9=2[/tex]
[tex]4x^4-11x^2+7=0[/tex]
[tex]x^4-11x^2+28=0[/tex]
[tex](x^2-7)(x^2-4)=0[/tex]
[tex](4x^2-7)(x^2-1)=0[/tex]
[tex]4x^2-7=0[/tex]
[tex]4x^2=7[/tex]
[tex]x^2=\frac{7}{4}[/tex]
[tex]x=\pm\sqrt{\frac{7}{4}}[/tex]
[tex]x^2-1=0[/tex]
[tex]x^2=1[/tex]
[tex]x=\pm1[/tex]
[tex]y=2x^2-3[/tex]
[tex]y=2(\pm\sqrt{\frac{7}{4}})^2-3[/tex]
[tex]y=2({\frac{7}{4}})-3[/tex]
[tex]y=\frac{7}{2}-3[/tex]
[tex]y=\frac{1}{2}[/tex]
[tex]y=2x^2-3[/tex]
[tex]y=2(\pm1)^2-3[/tex]
[tex]y=2(1)-3[/tex]
[tex]y=2-3[/tex]
[tex]y=-1[/tex]
Therefore, [tex]x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}}[/tex] and [tex]y=-1,\frac{1}{2}[/tex]
The ordered pair solutions are [tex](-\sqrt{\frac{7}{4}},0.5)[/tex], [tex](\sqrt{\frac{7}{4}},0.5)[/tex], [tex](-1,-1)[/tex], and [tex](1,-1)[/tex].
4. There are 20
students in a rath
class. The ratio of
boys to girls is 3:2.
a) How many boys
are in the class?
b) How many girls
are in the class?
given the equation f(x)=-2x²+4x+6 find the average rate of change from x=1 and x=2
Answer:
16
Step-by-step explanation:
1) Plug x=1 into equation
f(x) = -2(1)²+4(1)+6
f(x) = -2²+4+6
f(x) = 4+4+6
y = 14
(1,14)
2) Plug in x=2 into equation
f(x) = -2(2)²+4(2)+6
f(x) = -4²+8+6
f(x) = 16+8+6
y = 30
(2,30)
3) Use slope formula ([tex]\frac{y2-y1}{x2-x1}[/tex])
[tex]\frac{30-14}{2-1}[/tex]
[tex]\frac{16}{1}[/tex]
16
is (2×3)×4=2×(3×4) an example of associative property of multiplication?
Answer:
Yes.
Step-by-step explanation:
Associative property of multiplication is:
(A×B)×C = A×(B×C).
It says that "The way of grouping of terms doesn't change the product."
So, given example (2×3)×4=2×(3×4) is an example of associative property of multiplication.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Help please!
Solve for x
Answer:
x=5
Step-by-step explanation:
5) Write the missing numbers to find the
quotient of 782 = 17. So that 782 = 17 = 46
Answer:
quotient term: 6
dividend term: 102
Step-by-step explanation:
[tex]\dfrac{782}{17}=\dfrac{680+102}{17}=\dfrac{680}{17}+\dfrac{\boxed{102}}{17}=40 +\boxed{6} = 46[/tex]
Which of the following word phrases describe the expression y + 3?
A.three less than y
B.the sum of y and 3
C.the product of y and 3
D.three more than y
The athlete drink 16 ounces of water every two hours starting at 7:30 AM and continuing for the next 14 hours. A) how many quarts did the athlete consume? B) how many pints of water did the athlete consume?
Answer:
16x7 = 112 (16 ounces, 7 hours) 112 ounces to pints = 7 pints of water
Step-by-step explanation:
[tex] \frac{8}{20} < > = \frac{7}{13} [/tex]
Compare these factions
Answer:
<
Step-by-step explanation:
Good Question!
8/20=4/10=2/5=0.4
7/13= lcm of 5 and 13 is 75.
26/75 [<] 35/75
:)
Answer: < less than
Step-by-step explanation:
1. Find LCM of 20 and 13.
20: 20,40,60,80,100,120,140,160,180,200,220,240,260,280
13: 13, 26, 39, 52, 65, 78, 91, 104, 107, 110 ...... 234, 247, 260
The LCM is 260.
2. 20*13 = 260 13*20=260
therefore we need to multiply the numerator by those 13 and 20.
8*13 = 104 7*20 = 140
3. compare Fractions:
(104/260) < (140/260)
work out the volume of the cone giving your answer to 3 significant figures 7cm 24cm 25cm
Answer:
1231.50432021 cm³
Step-by-step explanation:
Use the formula:
[tex]\frac{1}{3} \pi r^{2} h[/tex]
And replace known values:
[tex]\frac{1}{3} \pi (7^{2})(24)[/tex]
Aaaand simplify:
[tex]\frac{1}{3}*1176 \pi[/tex]
Which gives approximately:
[tex]1231.50432021[/tex]
And don't forget to put the unit (cm³)!
Answer:
1230
Step-by-step explanation:
1/3*pi*7^2*24
1/3*pi*49*24
=1230
what is 1800/1254
[tex]1800 \div 1254[/tex]
When f(x)=4, what is the value of x?
This mapping shows a functional relationship.
Domain
Range
оо
O 2
2
4
3
-3
0
4
-1
→-1
→ 3
Check the picture below.
The value of f(x) at x=4 is 2.
What is Function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.
We have to find the value of function for x=4.
This means that from the figure we have to find the value of y when x= 4.
Now, looking into the figure we have
f(4)= 2
f(0)= -2
f(-1)= -1
f(3)= 4
So, the required value is 2.
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A girl ran to the store at a speed of 6 miles per hour, and then walked back at a speed of 4 miles per hour. If her round trip took 15 minutes, how far away is the store?
Answer:
.6 miles
Step-by-step explanation:
Answer:
0.6 miles
Step-by-step explanation:
6 × t = 4 × (15 - t)
6t = 60 - 4t
6t + 4t = 60 - 4t + 4t
10t = 60
t = 6
6 × [tex]\frac{1}{10}[/tex] = 0.6
If a cylinder has a volume of 648pi cm3( 3rd power) and a height of 8 cm, what is the radius?
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=\stackrel{cm^3}{648\pi }\\ h=8 \end{cases}\implies 648\pi =\pi r^2(8) \\\\\\ \cfrac{648\pi }{8\pi }=r^2\implies 81=r^2\implies \sqrt{81}=r\implies \boxed{9=r}[/tex]
PLS HELP PLEASSSSS IM SERIOUSLY CRYING RN
[tex]x = 23[/tex]
Step-by-step explanation:
First, we need to write the equations in their standard form, i.e., all the variables and their coefficients are to be placed on the left hand side and the plain numbers on the right hand side. The first equation is already in its standard form:
[tex]2x + 5y = 35\;\;\;\;\;(1)[/tex]
but we need to rewrite the 2nd one. So the standard form of the 2nd equation can be written as
[tex]x + 15y = -10\;\;\;\;\;(2)[/tex]
Now that the equations are in their standard forms, the next step that we need to do is to eliminate one of the variables, namely the y. To do that, we need to multiply either one of the equations so that when we add them together, the y-variable gets eliminated. Note if we multiply Eqn(1) by -3, we'll get -15y on one equation and a +15y on the other equation so that when they are added together, they cancel out. So if we do that, we get
[tex]-6x - 15y = -105\;\;\;\;\;(3)[/tex]
Adding Eqn(3) to Eqn(2), we get
[tex]-5x = -115[/tex]
or
[tex]x = \dfrac{-115}{-5} = 23[/tex]
PLZ HELP OFFERING BRAINLIEST
Find the difference. 2/5 (d-10) -2/3 (d+6)
[tex]\dfrac 25 (d-10) - \dfrac 23(d+6)\\\\\\=\dfrac{6}{15} (d-10) - \dfrac{10}{15} (d+6)\\\\\\=\dfrac{6(d-10) -10(d+6)}{15}\\\\\\=\dfrac{6d -60-10d-60}{15}\\\\\\=\dfrac{-4d-120}{15}\\\\\\=-\dfrac{4d}{15} - 8[/tex]
Help anyone?? Not that hardd
no links ! :(
Answer:
1.2
Step-by-step explanation:
First, you cancel out [tex]\frac{6}{20}[/tex] to become [tex]\frac{3}{10}[/tex]
Then that becomes [tex]-\frac{3}{10}+1.5[/tex]
Now, you convert the element to a decimal form to be [tex]-0.3+1.5[/tex]
Finally, you subtract them (because a negative plus a positive is subtraction) to get the final answer of 1.2
Hope this helps!
Johnny has a box filled with 10 black marbles and 5 purple marbles what are the odds he pulls to black marbles in a row?
Answer:
3/7
Step-by-step explanation:
The first black marble is 10/15 and the second is 9/14. Multiply them together to get 3/7 after you simplify it.
A car is traveling at 20 miles per hour during rush hour. How far does the car travel in 1 minute and 45 seconds?
Answer: 7/12 miles
Step-by-step explanation:
20mph = 20/60 miles per minute = 1/3 miles per minute
1 min 45s = 1 min + 3/4 min = 7/4 min
1/3 x 7/4 = 7/12 miles
The distance travelled by car with the given speed and time is 7/12 miles.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, a car is traveling at 20 miles per hour during rush hour.
Time =1 minute and 45 seconds
= [tex]1\frac{45}{60}=1\frac{3}{4}[/tex]
= 7/4 minutes
Now, 20 miles per minute
= 20/60 miles per minute = 1/3 miles per minute
We know that, Distance =Speed×Time
= 1/3 ×7/4
= 7/12 miles
Therefore, distance travelled by car is 7/12 miles.
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Help me please (I need write more something in order to I can submit answer)
Answer:
The answer is 4
Step-by-step explanation:
(-2.4)(10) / -3(2)
-24/-6
=4
Answer:
The answer will be 4! Hope this helps
2 with the radical of 32
I need help with this plz
Answer:Mmm
Step-by-step explanation:
I am doing the work I will thell you the answer
Yuan wrote 17 letters to friends each month for x months in a row. Write an expression to show how many total letters Yuan wrote.
The sum of 8 and a number is 9
Answer:
The sum of 8 and 1 is 9.
lol
Step-by-step explanation:
Compare the decimal by writing <,> or = on the space provided.
1). 501.019_______501.901
2). 65.561________65.651
3). 0.2134________0.03124
4). 0.500_________0.5
5). 0.004_________0.0004
•
•
•
•
•
•
•
pa answer Po please
Answer:
1. < 2. < 3. > 4. = 5. >
Step-by-step explanation:
Which of the following sequences below is a Geometric Sequence?
Select one:
a. -8, -3, 2, 7, ....
b. 1, 3, 9, 27, ....
c. 8, 4, 0, -4, ...
d. 2, 4, 6, 8, ...
B. 1, 3, 9, 27
Geometric Sequence is being multiplied by factor of 3.
You get a summer job and make a total of $5,500 throughout the summer months. The government takes out taxes from that money at a rate of 33%. How much money did you really make after taxes were taken out?
Answer:
$1650 is the answer hope it helps
if v = 6i + 3j, what is ||-10v||
The values of ||-10v|| is 51.96 units
Complex numbers are square roots of negative numbers. They are expressions that consist of both the real and imaginary axis.The general form of a complex number is expressed as z = x + iy
Given the complex number v = 6i + 3j,
10v is expressed as 10(6i + 3j)
10(6i + 3j) = 60i + 30j
Take the modulus of the complex number:
[tex]|10v|=\sqrt{60^2+30^2}\\|10v|= \sqrt{1800+900}\\|10v|= \sqrt{2700} \\|10v|=51.96units[/tex]
Hence the values of ||-10v|| is 51.96 units
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Is this relation a function?
(-1,2) (1,17) (3,-4) (1,20)