Answers
Answer:
(a)
[tex]f(x) = \left \{ {{5x;\ 0<x\le 5} \atop {5x-5; x > 5}} \right.[/tex]
(b) Rate = 5
(c) Rate = 5
Step-by-step explanation:
Given
The attached graph
Solving (a): The piece-wise function
For the first line
Calculate the slope of the first line
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (5,25)[/tex]
So, the slope is:
[tex]m = \frac{25 - 0}{5 - 0}[/tex]
[tex]m = \frac{25}{5}[/tex]
[tex]m = 5[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Where: [tex]m = 5[/tex] and [tex](x_1,y_1) = (0,0)[/tex]
[tex]y = 5(x - 0) + 0[/tex]
[tex]y = 5(x) + 0[/tex]
[tex]y = 5x[/tex]
So, the function of the first line is:
[tex]f(x) = 5x;\ 0 < x \le 5[/tex]
For the second line
Calculate the slope of the second line
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (5,20)[/tex]
[tex](x_2,y_2) = (9,40)[/tex]
So, the slope is:
[tex]m = \frac{40 - 20}{9 - 5}[/tex]
[tex]m = \frac{20}{4}[/tex]
[tex]m = 5[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Where: [tex]m = 5[/tex] and [tex](x_1,y_1) = (5,20)[/tex]
[tex]y = 5(x - 5) + 20[/tex]
[tex]y = 5x - 25 + 20[/tex]
[tex]y = 5x -5[/tex]
So, the function of the second line is:
[tex]f(x) = 5x -5;\ x>5[/tex]
Hence, the piece-wise function is:
[tex]f(x) = \left \{ {{5x;\ 0<x\le 5} \atop {5x-5; x > 5}} \right.[/tex]
Solving (b): The rate at which customers that buy up to 5lb buy.
[tex]x = 5[/tex]
This question implies that, we determine the rate at which this customer buys.
For [tex]x = 5[/tex]
[tex]f(x) = 5x;\ 0 < x \le 5[/tex]
The slope of the above function is 5.
So, this customer buys at the rate of $5 per lb
Solving (b): The rate at which customers that buy more than 5lb buy the extra pounds above 5lb.
For [tex]x > 5[/tex]
[tex]f(x) = 5x -5;\ x>5[/tex]
Assume x = 6
[tex]f(6) = 5 * 6 - 5[/tex]
[tex]f(6) = 30 - 5[/tex]
[tex]f(6) = 25[/tex]
Express as 20 + 5
[tex]f(6) = 20 + 5 * 1[/tex]
Assume x = 7
[tex]f(7) = 5 * 7 - 5[/tex]
[tex]f(7) = 35 - 5[/tex]
[tex]f(7) = 30[/tex]
[tex]f(7) = 20 + 10[/tex]
Express 10 as 5 * 2
[tex]f(7) = 20 + 5 * 2[/tex]
So, we have:
[tex]f(6) = 20 + 5 * 1[/tex]
[tex]f(7) = 20 + 5 * 2[/tex]
This can be generalized as:
[tex]f(x) = 20 + 5(x - 5)[/tex]
For the above functions;
20 represents the amount they buy the first 5
5 represents the rate at which they buy extra pounds above 5
Hence, they buy the extra pounds at the rate of $5 per pound
Related Questions
Andrew wrote the number 186,425 on the board. In which number is the value of the digit 4
exactly 100 times the value of the digit in the number Andrew wrote?
A 681,452
B 462,017
C 246,412
D 124,655
Answers
Answer:
C
Step-by-step explanation:
The four is in the hundreds so times one hundred it'd be in the 10,000 so it is C.
The radius of a circle is 16 cm. Find its area in terms of \piπ
Answers
Answer256pi
Step-by-step explanation:
Area=pi*r^2
=pi*16^2
256pi
Arthur earned $22.50 last night delivering lunches for his family's restaurant. He puts 30% of his earnings into his savings account. he then bought a magazine for $3.95 and a CD for $11.49. of the amount earned last night, how much money does arthur have left that is not in his savings account
Answers
Answer:
$4.26
Step-by-step explanation:
40 POINTS !! 40 POINTS !!
PLEASE HELP , DONT SKIP !
NO LINKS OR FILES.
Answers
Answer: The answer is 4 pieces of chalk
Answer:
7 chalks
Step-by-step explanation:
7 crosses are above numbers that are higher than 5
PLSS help me ☝............
Answers
Answer:
New Coordinates: G'(0,4) Y'(3,3) M(3,7)
Movement: Translation 3 units up
Step-by-step explanation:
Since you're adding to the y-coordinate, your points will move up which makes this a translation
The Northwood Clock Tower measures 193 meters tall. Dante is creating a scale model of this building using the scale 75 meters : 1 meter.
To the nearest tenth of a meter, what will be the height of the scale model?
Answers
Step-by-step explanation:
Height of real/height of scale=ratio of scale
193/x=75/1
x=2.6
Hope that helps :)
A) 9)___ + 7) = 18 + 63 B) ___(12 + 9) + 36 + 27 C) 8(___+7) = 24 + 56 D) ___(5 + 8) + 20 +32
Answers
Answer:
A) 9(2+7)
B) 3(12+9
C) 8(3+7)
D)4(5+8)
Step-by-step explanation:
A)
9*(x+7) = 18+63
9*(x+7) = 81
81/9 = x+7
9 = x+7
x = 2
B)
x*(12+9) = 36+27
x*(12+9) = 63
x*21 = 63
x = 63/21
x = 3
C)
8*(x+7) = 24+56
8*(x+7) = 80
x+7 = 80/8
x+7 = 10
x = 3
D)
x*(5+8) = 20+32
x*13 = 52
x = 52/13
x = 4
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
What value of c makes x2 + 6x + c a perfect square trinomial?
3
6
9
12
Answers
9514 1404 393
Answer:
(c) 9
Step-by-step explanation:
The square of a binomial has the form ...
(x +a)² = x² +(2a)x +a²
You will note that the value of 'a' is half the coefficient of the x term (2a). The constant term is the square of the value of 'a'. This means the number you want is ...
c = (6/2)² = 9
Answer:
9
Step-by-step explanation:
Ava swam for 154 minutes during her first week of vacation. In her two weeks of vacation, she swam for a total of 357 minutes. How many more minutes did she swim for in the second week than in the first week?
Answers
Answer:
Ava swam 203 more miles
Step-by-step explanation:
357-154=203
CAN U PLZ ANSWER THIS ITS FOR A TEST
Answers
Answer:
A. 300in^2
Step-by-step explanation:
Area=LWH
15*10*2=300
The side adjacent to ∠W is …
Question 1 options:
side 34
side WU
side 90
side VW
Answers
The side adjacent to ∠W is side WU.
9514 1404 393
Answer:
(b) side WU
Step-by-step explanation:
With respect to any given acute angle in a right triangle, the sides of the triangle are called "adjacent", "opposite", or "hypotenuse".
The two sides that form angle W are WU and WV. Side WV is the longest, opposite the right angle, so it is the hypotenuse. Side WU is "adjacent" to angle W, and side UV is "opposite" angle W.
(It can help to note that the name of the opposite side UV does not contain the letter of the angle W. The name of the adjacent side WU does contain the letter of the angle.)
the length of rectangular park is 15 m longer than that of the park is 114m find it's length and breadth
Answers
Answer: Length: ≈20.5 Breadth: ≈5.5
Step-by-step explanation: x(x+15)=114, solving for x we get 5.547 and 20.547.
It is reported that 56% of a state is experiencing drought conditions. An agricultural researcher randomly selects ten farmers in the state and asks if their farms are experiencing drought. What is the expected number of farmers who have experienced drought? Find the standard deviation.
Answers
Answer:
I think your answer would be 5.6
Step-by-step explanation:
56% of 10 = 5.6
A marble is drawn at random from the bag shown below. The bag contains 3 green, 4 yellow, 5 blue, and 8 pink
marbles.
What is P(not yellow)?
A 1/5 B 2/5 C 4/5
Answers
Answer: c 4/5
Step-by-step explanation: out of 5 only four are chosen leaving us with an answer of 4/5 :D hope it helped
In a popular online role playing game, players can create detailed designs for their
character's "costumes," or appearance. Fatoumata sets up a website where players
can buy and sell these costumes online. Information about the number of people who
visited the website and the number of costumes purchased in a single day is listed
below.
126 visitors purchased no costume.
228 visitors purchased exactly one costume.
34 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase
exactly one costume as a decimal to the nearest hundredth.
Mk
Answers
Answer: 0.59
Step-by-step explanation:
The probability that the next person will purchase exactly one costume is 0.59.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Total number of visitors = 126+228+34 = 388
Total number of visitors who purchased exactly one costume = 228
The probability = 228/388 = 0.587 ≈ 0.59
Thus, the probability that the next person will purchase exactly one costume is 0.59.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ2
Someone please help me!
Answers
Answer:
x^2+y^2=25
Step-by-step explanation:
bc x-0=x and ect.
Matt is baking cookies.
He uses butter, sugar and flour in a ratio of 2 : 3 : 4
Matt uses 300 g of flour.
How much sugar does he use?
Answers
200g butter
300g flour
400g sugar
URGENT WILL GIVE BRAINLIEST!!!!
Answers
Answer:
7/10
Step-by-step explanation:
Answer:
7/10
Step-by-step explanation:
There is a total of ten numbers, and only seven of them are odd numbers (1, 3, 7, 9, 15, 19, 21)
You have a 70% chance of picking an odd number.
PLZ HELP ASAP 50 PTS (MATH) + Brainliest
1) Factor the trinomial. Show ALL work:
x2 − 5x + 6
2) Factor the polynomial using grouping. Show ALL work:
5x3-2x2+25x-10
3( Determine the missing term from the perfect square trinomial. Show ALL work.
x2 − ______+ 36
Write in factored form: ( )2
4( Choose ONE of the following polynomial and factor completely, showing ALL work.
16x2 − 81
15x2 − 35
3x2 + 21x + 36
Answers
Answer:
x+3 and x+2( 5 x + 2 ) ( x 2 + 5 )9x^2+163x2 + 21x + 36Step-by-step explanation:
x2 + 5x + 6Let us try factorizing this polynomial using splitting the middle term method.
Factoring polynomials by splitting the middle term:
We need to find two numbers ‘a’ and ‘b’ such that a + b =5 and ab = 6.
On solving this we obtain, a = 3 and b = 2
Thus, the above expression can be written as:
x2 + 5x + 6
= x2 + 3x + 2x + 6
= x(x + 3) + 2(x + 3)
= (x + 3)(x + 2)
Thus, x+3 and x+2 are the factors of the polynomial x2 + 5x + 6.
For Step 1, you just want to find all combinations of two numbers that multiply together to be 56. Make sure you take negatives into account. Those pairs of numbers are:
(p, q, p+q)
(1, 56, 57)
(-1, -56, -57)
(2, 28, 30)
(-2, -28, -30)
(4, 14, 18)
(-4, -14, -18)
(7, 8, 15)
(-7, -8, -15)
Use those pairs of numbers and their sums to fill in the three columns of your table.
STEP 2 Look down your p+q column to find the pair of numbers that add up to equal to -15. That's (p, q) = (-7, -8). STEP 3 Using the information from steps 1 and 2, you can factor the trinomial like this: x2 - 15x + 56 = (x + p)(x + q) = (x - 7)(x - 8) FOIL that back out if you'd like, to make sure the expressions are equivalent. STEP 4 Hopefully, seeing steps 1 through 3 worked out will help you with step 4. Find all the pairs of numbers that multiply together to be 36 (1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6, and all their negative equivalents), then figure out which pair has a sum of 12. That means you've found your p and q, and can factor the trinomial as (x + p)(x + q).Answer:
1) Factor the trinomial. Show ALL work:
(x-2)(x-3) steps see explanation
2) Factor the polynomial using grouping.
Group and factor out the greatest common factor (GCF), then combine.
[tex](5x-2) (x^{2} +5)[/tex]
4) Choose ONE of the following polynomial and factor completely.
15x2 − 35 = [tex]5 (3x^2-7)[/tex]
Step-by-step explanation:
x2−5x+6
The middle number is -5 and the last number is 6.
Factoring means we want something like
(x+_)(x+_)
We need two numbers that
Add together to get -5
Multiply together to get 6
Try -2 and -3:
-2+-3 = -5
-2*-3 = 6
Fill in the blanks in
(x+_)(x+_)
with -2 and -3 to get...
(x-2)(x-3)
4( Choose ONE of the following polynomial and factor completely,
15x^2-35
35 as 5*7
15 as 5*3
= 5*3x^2-5*7
How to make a triangle and 2 trapezoids out of a triangle
Answers
Answer:
Draw two lines inside the triangle.
Step-by-step explanation:
Like in the Attachment
What is the area of the triangle? 13 5 12
Answers
Answer:29
Step-by-step explanation:
One number is seven more than four times another number. If the sum of the numbers is 22, find the numbers.
Answers
Answer:
the answer is actually study and you would know
Step-by-step explanation:
Answer:
3 and 19
Step-by-step explanation:
What is the value of the expression (25-7)x2 divided by 4+2
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{(25-7)(2)}{4}+2}[/tex]
[tex]\mathsf{25-7=\bf 18}[/tex]
[tex]\mathsf{\dfrac{\bold{18}(2)}{4}+2}[/tex]
[tex]\mathsf{18(2)= \bf 36}[/tex]
[tex]\mathsf{\dfrac{\bold{36}}{4}+2}[/tex]
[tex]\mathsf{\dfrac{36}{4}=\bf 9}[/tex]
[tex]\mathsf{\bold{9}+2 }[/tex]
[tex]\bold{= 11}[/tex]
[tex]\boxed{\large\textsf{Possible answer \#1: \bf 11 }}\huge\checkmark[/tex]
[tex]\huge\text{OR....}[/tex]
[tex]\mathsf{\dfrac{(25-7)(2)}{4+2}}[/tex]
[tex]\mathsf{25-7=\bf 18}[/tex]
[tex]\mathsf{\dfrac{\bold{18}(2)}{4+2}}[/tex]
[tex]\mathsf{18(2)=\bf 36}[/tex]
[tex]\mathsf{\dfrac{\bold{36}}{4+2}}[/tex]
[tex]\mathsf{4+2= \bf 6}[/tex]
[tex]\mathsf{\dfrac{36}{\bold{6}}}[/tex]
[tex]\mathsf{\bf = 6}[/tex]
[tex]\boxed{\large\textsf{Possible answer \# 2: \bf 6}}\huge\checkmark[/tex]
[tex]\boxed{\boxed{\large\text{{Answer(s): \bf Answer \#1: 11 OR Answer \#2: 6}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Pls help ASAP. Pls and thx.
Answers
Answer:
(assuming the. values are the shaded areas)
area = x^2 + 2x +2
perimeter = 4x + 8
Step-by-step explanation:
you have all the side except the side of the 2 squares at the top.
The squares are 1 unit on each side because the area of the 2 slender rectangles on each side is x.
So the area is x^2 + x + x + 1 + 1
The perimeter is 1+x+1+1+1+x+1+1+1+x+1+x
(starting from the lower left side and walking around the perimeter clockwise)
Write and solve an equation for the following.
Four more than one-half a number is three. What is the number?
Answers
Answer:
4+ [tex]\frac{1}{2}[/tex]x = 3
Step-by-step explanation:
4 + [tex]\frac{1}{2}[/tex]x = 3 (subtract 4 from both sides)
[tex]\frac{1}{2}[/tex]x = -1 (multiply both sides by 2)
x = -2
Answer:
4+ 1/2 x = 3
Step-by-step explanation:
X =-2
what is 1000x45 how do i get the anwser
Answers
Answer:
45000
Step-by-step explanation:
put the equation like this
1000
x 45
And multiple form right to left or just take 45 and add 3 0's because anything multiplied by 1 is what number u multiplied it by
Answer:45000
Step-by-step explanation:
so you know that 10x45=450 just add 2 more zeros and thats ur answer may i be marked brainliest
Need help on em punett sqaures
Answers
Answer:
Black Fur: 100% White Fur: 0%
Step-by-step explanation:
B B
b Bb Bb (all dominant)
b Bb Bb
Black Fur: 100% White Fur: 0%
Answer:
B B
______
b | Bb | Bb |
b | Bb | Bb |
_____
Phenotype Probability (%):
Black Fur: 100%
White Fur: 0%
_____________________
Which statement is accurate for the right triangle shown below?
Ꮎ
50
1
a
47
Answers
Answer:
The statement that is accurate is csc(θ)=1.06
Step-by-step explanation:
Looking at the reference angle in this triangle, we can see that the side that is 47 units is opposite of it, the side that is 50 units is the hypotenuse, and the side that is 17 units is adjacent to it.
Because we know this, we can plug our sides into the formula for cscθ, secθ, and cotθ.
So:
cotθ=adjacent/opposite = 17/47= 0.36
cscθ=hypotenuse/opposite = 50/47=1.06
Now without even looking at the other statements, we can see that the second one is correct as cscθ=hypotenuse/opposite = 50/47=1.06
Therefore, the statement that is accurate is csc(θ)=1.06.
Gabrielle is 11 years older than Mikhail. The sum of their ages is 107. What is Mikhail's age?
Answers
Answer:
Mikhail's age is 48
Step-by-step explanation:
Answer:
107-11=96
96÷2=48
so Mikhail is 48 years old
Corinna rowed 4/5 mile on a rowing machine in 1/6 hour. What is her rowing rate in miles per hour
Answers
Answer: 8.20 miles I believe