The examples and solutions to the functions are illustrated below based on the information given.
How to illustrate the functions?1st example: The cost of a bag of rice is $100 and subsequent bags cost $95. Illustrate. the function to calculate the cost for p bags of rice.
The function will be:
C = 100 + (95 × p)
C = 100 + 95p
2nd example: The cost of a pen is $5. Find the cost of s pens.
The function will be:
C = 5 × p
C = 5p
3rd example: Calculate the total amount for m tickets if each ticket is $20.
The function will be;
C = 20 × m
C = 20m
4th example: Bon bought g mangoes at $2 each and d oranges at $3.40 each. Calculate the total cost.
C = (2 × g) + (3.40 × d)
C = 2g + 3.4d
5th example: The average age of k number of boys is 7. Find their total age.
The function will be:
a = (7 × k)
a = 7k
Learn more about functions on:
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Question 1: Akira sells lemonade at 50 cents a glass. Let m be the amount of money they make in total for g glasses. Akira only has enough lemonade for 20 glasses.
A) Write a function m(g) to represent the total money (in dollars) they make from lemonade sales.
B) What is the domain of the function? Why?
Answer:
A) m(g) = 0.5g
This is since she makes 0.5 dollars per glass
B) The domain is [tex]0 \leq g \leq 20[/tex] where g is an integer. This is since it's impossible to make less than 0 glasses and they cannot make more than 20.
Question 2: Danyon sells CD's at $20 per CD. He has only 15 CD's left.
A) Write a function m(c) to represent the total money he makes from selling c CD's.
B) What is the domain of the function? Why?
Answer:
A) m(c) = 20c, as he makes 20 dollars per CD.
B) The domain is [tex]0 \leq c \leq 15[/tex] where c is an integer, as he can't make less than 0 CD's, and he has only 15 left.
Question 3: A factory is capable of making 60 units per hour. The factory can only run for 24 hours before cool down, and 150 units have already been made.
A) Write a function u(h) to represent the number of units after h hours.
B) What is the domain of the function? Why?
Answer:
A) u(h) = 60h + 150 as it makes 60 units per hour and 150 are already made.
B) The domain is [tex]0 \leq h \leq 24[/tex] as the factory can't run for negative hours and has to cool down after 24 hours.
Question 4: Alazne sells sunglasses at $7 per pair. She has only 30 left before she needs to re-stock.
A) Write a function m(s) which calculates the amount of money she makes after selling s sunglasses.
B) What is the domain of the function? Why?
Answer:
A) m(s) = 7s, as she gets $7 per pair of sunglasses
B) [tex]0 \leq s \leq 30[/tex] where s is an integer, one cannot have a fraction of a pair and she only has 30. She also cannot sell negative sunglasses.
Question 5: Lincoln works at a burger joint in the summer. He makes $3 from every burger he makes. He already has $22 saved. He cannot make more than 10 burgers a day.
A) Write a function m(b) which calculates how much money he gets after making b burgers.
B) What is an appropriate domain for this function?
Answer:
A) m(b) = 3b + 22, as he already has 22 dollars and makes 3 more for every burger.
B) [tex]0\leq b\leq10[/tex], where b is an integer. This is since he cannot make a fraction of a burger, negative burgers, or more than 10 burgers.
James has 838 feet of rope. There are 17 teams of hikers. If James gives an equal amount of rope to each team, how much rope will each team receive?
Answer:
838 ÷ 17 = 49.29 feet each
Step-by-step explanation:
divide the total rope by number of hikers equals amount of rope each hiker will receive.
The diagram shows two right-angled triangles. PQR and QST are straight lines. It is given that sin x = [tex]\frac{15}{17}[/tex] . Find the value of cos y.
Step-by-step explanation:
[tex] \sin(x) = \frac{15}{17} = \frac{23 + c}{34} \\ 34 \times 15 = 17(23 + c) \\ 510 = 391 + 17c \\ 17c = 119 \\ c = 7[/tex]
[tex] \sin (y) = \frac{7}{25} \\ y = 16.26 \\ \cos(16.26) = \frac{ \alpha }{25} \\ 0.96 = \frac{ \alpha }{25} \\ \alpha = 24 [/tex]
[tex] \cos(y) = \frac{24}{25} [/tex]
Mr. Alvarez makes a walkway of 3 cement slabs.He uses 14 cubic feet of cement to make the walkway.Each square slab has a volume of 4 cubic feet
Answer:
I suppose that you want to see how we can find the volume of each individual slab with the given information, the procedure is as follows.
The walkway has 3 cement slabs,
He uses a total amount of 14 cubic feet to make the complete walkway.
This means that the 3 cement slabs together have a total volume of 14 ft^3
To find the volume of each slab, we need to find the quotient between the total volume and the total number of slabs, then we get:
Volume of each slab = (14 ft^3)/3 = 4 ft^3
This means that each cement slab has a volume of 4 ft^3.
Answer:
6 ft^3
Step-by-step explanation:
Rodrigo practiced playing the guitar 15 1/3 hours over the past 3 weeks.
He practiced for 5 1/4 hours during the first week and 5 2/3 hours during the second week.
How much time did Rodrigo spend practicing during the third week? Use the numbers and symbols to select the equation that represents the problem. Then solve the equation. Symbols may be used more than once or not at all.
15 1/3, 5 1/4, 5 2/3, x, =, and +.
The equation that represents the problem is
a. 15 1/3 = x - 5 1/4 - 5 2/3
b. x = 15 1/3 + 5 1/4 + 5 2/3
c. x + 15 1/3 = 5 1/4 + 5 2/3
d. 15 1/3 = 5 1/4 + 5 2/3 + x
Answer: d. 15 1/3 = 5 1/4 + 5 2/3 + x
Step-by-step explanation:
15 1/3 (total) = 5 1/4 (first week) +5 2/3 (second week) +x (third week)
When you add the amount of time Rodrigo practiced each week, you get the total amount of time he practiced
The slope is 2.92, which shows a positive relationship because it is a positive number. The
longer a person’s hair, the more it will cost to get the hair highlighted. This makes sense, as
more product is required to highlight more hair.
You buy 5 candy bars for $2.00. Find the cost of 18 candy bars? First
write a proportion to find the unit rate(price per one candy bar). Then use
the unit rate to to find the cost of 18 candy bars?
Answer- $7.50
Step-by-step explanation: edg
Which of the following correctly describes the product below?
A.
irrational
B.
rational
C.
a combination of both rational and irrational
D.
neither rational nor irrational
Answer:
C is the answer your looking for
convert 5.70 lbs to grams and explain please help
Answer:
2585.48.
Step-by-step explanation:
The formula to convert pounds to grams is to approximately multiply 5.70 by 454, which is equal to 2585.48.
3.
Which equation best describes the graph?
A. y = 2x + 3
B. y = 1/2x + 3
C. y = 1/2x – 3
D. y = 2x – 3
Answer:
Its C
Step-by-step explanation:
The y starts at negative 3 and it is going up by 1 and over 2
Hope this Helped
Answer:
C. y = 1/2x - 3
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope:
1
2
y-intercept:
(
0
,
−
3
)
x
y
0
−
3
6
0
Consider the polynomial function h(x) = x^6 - 3x^5 - 17x^3
What is the end behavior of the graph of h?
Choose 1 answer:
PLEASE HELP
Answer: As x -> positive infinity, h(x) -> positive infinity, and as x -> negative infinity, h(x) -> positive infinity
Step-by-step explanation:
Khan Academy!! Hope this helps :)
???
[tex]( \frac{ {2x}^{3} }{ {8y}^{ - 4} }) ^{ - 3} [/tex]
Answer:
I'm not sure
Step-by-step explanation:
Sorry
Find the discriminant of x2-6x -10 = 0, and determine the number of real solutions of the equation.
Answer:
76
2 real solutions
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Standard Form: ax² + bx + c = 0
Discriminant: b² - 4ac
Positive - 2 solutions Equal to 0 - 1 solution Negative - No solutions/ImaginaryStep-by-step explanation:
Step 1: Define
x² - 6x - 10 = 0
Step 2: Identify Variables
Compare quadratic.
x² - 6x - 10 = 0 ↔ ax² + bx + c = 0
a = 1, b = -6, c = -10
Step 3: Find Discriminant
Substitute in variables [Discriminant]: (-6)² - 4(1)(-10)[Discriminant] Evaluate exponents: 36 - 4(1)(-10)[Discriminant] Multiply: 36 + 40[Discriminant] Add: 76This tells us that our quadratic has 2 real solutions.
Which of the following are properties of the circumcenter of a triangle? Check
all that apply.
A. The circumcenter is at the intersection of the perpendicular
bisectors of the triangle's sides.
B. The circumcenter of an obtuse triangle is always outside it.
M C. The circumcenter is equidistant from each vertex of the triangle.
D. The circumcenter is equidistant from each side of the triangle.
Answer: A. The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides.
C. The circumcenter is equidistant fromeach vertex of the triangle.
D. The circumcenter is equidistant from each side of the triangle.
Step-by-step explanation:
The properties of the circumcenter of a triangle from the options given include:
• The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides.
• The circumcenter is equidistant fromeach vertex of the triangle.
• The circumcenter is equidistant from each side of the triangle.
Option B is wrong as the circumcenter of an obtuse triangle is not always outside it. For the circumcenter, there is intersection of all the three lines and it's not important that they should always be outside.
Question 6 (2 points)
The parabola is in intercept form.
y=(x+1)(x+7)
The vertex is
Blank 1:
Blank 2:
Answer:
Blank 1: (-7,0)
Blank 2: (-1,0)
Step-by-step explanation:
Plug x=0 into the equation and solve the resulting equation y=7 for y
Plug y=0 into the equation and solve the resulting equation 0=(x+1)(x+7) for x
Whats 8 2.5% of 75?Write your answer as a decimal.
Television is measured by the diagonal. A 55-inch tv has an actual diagonal length of 54.8 inches. Its height is 27 inch Mr.Schlagers entertainment center is 49 inches wide will the tv fit the entertainment center?
Answer:
47.68 inches
Step-by-step explanation:
As seen in the diagram attached below we can see that the tv is a rectangle. We are given the diagonal and the height which means we have to find the length. Since the tv diagonal forms a right triangle we can use the Pythagorean theorem to solve for the length. This theorem would be the following.
[tex]a^{2} + b^{2} = c^{2}[/tex]
where a and b are the sides of the triangle and c is the diagonal.
[tex]27^{2} + b^{2} = 54.8^{2}[/tex]
[tex]729 + b^{2} = 3,003.04[/tex]
[tex]b^{2} = 2,274.04[/tex]
[tex]b = 47.68[/tex]
Finally, we can see that the length of the TV is 47.68 inches
What are the coordinates of the image after a dilation
with the center at the origin and a scale factor of 2?
(0, 0) (10, 0) (10,4) (0, 4)
(-2.2) (8, 2) (8.-2) (-2,-2)
(1, 1) (6, 1) (6, 3) (1, 3)
(0, 0) (0, 2) (5.0) (5,2)
Explanation:
The scale factor 2 means we multiply the coordinates of every original point by 2. A point like (-1,1) moves to (-2,2) after doing so
As another example, (4,1) moves to (8,2) after multiplying both coordinates by 2.
Given the following parallelogram: Solve for x.
7x + 70
16x - 20
Answer:
x=10
Step-by-step explanation:
7x+70=16x-20
70=9x-20
9x=90
x=10
please help me with this
Answer: B
Step-by-step explanation:
PLZZ HELP ME IM DOING A TEST RNNNN.
Answer:
5(x)+5(y)=10
10(x)+2(y)=12
Step-by-step explanation:
i just got done with that same thing
(2, 0); y > x – 5
y < 2x + 1
Y <-X + 3
tell whether the ordered pair is a solution of the system of linear inequalities
Answer:
ang hirap pag aralan mo po muna
help please I cant figure this put
Answer:
C
Step-by-step explanation:
Because the circle is not shaded in, it doesn't count the number it's on:
So it would be a < or >.
Because this is on a number line and the shaded part goes to the left, it will be < because it points to the left.
The non-shaded circle is on 4, so your answer, x, will be:
x < 4
But the answer choices don't have this, meaning you have to simplify all of them.
The first one is:
x + 9 < 5
x < -4
x - 5 < 9
x < 14
x + 5 < 9
x < 4
x - 9 < 5
x < 14
So it would be C.
what's [2+(2x3)]x5.
x * 5 * 25 * 4 ÷ 5, if x = 813 simplified form please
Answer:
81,300
Step-by-step explanation:
2/3n+1/2=3/4 I need this fast pls
Answer:
n = ⅜
Step-by-step explanation:
Answer: n = 1/6
Step-by-step explanation:
2/3n + 1/2 = 3/4
-1/2 -1/2
2/3n = 1/4
multiply both sides by 2/3
n = 1/4 *2/3
n = 2/12
reduce
n = 1/6
In ΔTUV, t = 410 cm, ∠U=27° and ∠V=78°. Find the length of v, to the nearest 10th of a centimeter.=
Answer: 415.2
Step-by-step explanation:
These two figures are the image and pre-image of a
dilation.
Find the value of x.
4 m
6 m
4 m
6 m
8 m
9 m
6 m
Answer:
4m i think it sounds about right
Answer: the answer is 9m or D
Step-by-step explanation:
Solve for x and show work need help just stuck on this one ☝
Answer:
X=11
Step-by-step explanation:
6 x 11 is 66, after adding 2 its 68. They are equal because they are vertical angles :)
Answer:
11
Step-by-step explanation:
I did:
68 - 2= 66
66 divided by 11= 6
To check my work I did:
6 * 11= 66
66 + 2= 68
Hope this helps!
Sara says, "If you subtract 17 from my number and multiply the difference by - 2,
the result is - 22." What is Sara's number?
Answer: 28
28 - 17 = 11
11 * -2 = -22
The width A rectangle is 3 cm less then its length. The perimeter of the rectangle is 30 CM. Find The length and width of the rectangle
w = l - 3
w = 9 - 3
w = 6
//
l = 9
w = 6
//
p = 2(9) + 2(6)
p = 30