Using the form of a quadratic equation f(x) = ax^2 + bx + c, we can derive an equation for each of three given points (10,20,30 kph and their corresponding costs). Solving these simultaneously we would get the particular equation representing the situation. We could then apply this to calculate costs at various speeds including checking if it is possible to spend only 10 cents/km, determining an optimal speed range for a 13 cents/km cost, and finding the optimal speed and cost per km.
Explanation:To write a particular function that represents this scenario, we can set up three equations using the general form of a quadratic equation, which is f(x) = ax^2 + bx + c. In this case, our x-values are the speeds (10, 20, and 30 kph) and our f(x) values are the corresponding costs (28, 21, and 16 cents/km).
Substitute these values into the equation f(x) = ax^2 + bx + c, we get three equations:
100a + 10b + c = 28
400a + 20b + c = 21
900a + 30b + c = 16
By solving the system of equations, we could find the values of a, b and c. Then we would substitute the speed into the function to calculate the cost at 150 kph, and to find the speed range for a cost of 13 cents/km and check if it is possible to spend only 10 cents/km. Finally, the optimal speed and cost per km would be represented by the minimum point of the function, which in the case of a parabola occurs at x = -b/2a.
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What is the line of symmetry for the parabola whose equation is y = x2 + 10x + 25? x = -10 x = -5 x = 5
Answer:
[tex]y=x^2 + 10x + 25\\\\y=(x+5)^2[/tex]
Used the identity, [tex](a+b)^2=a^2+2ab+b^2[/tex]
The given parabola is of the form , [tex](x+a)^2=y[/tex], having vertex at ,which can be obtained by
x+a=0
x= -a
(-a,0).
So, vertex of the given parabola is , at (-5,0).
The Meaning of term line of symmetry,is that line which divides the parabola in two equal halves.
Drawing the parabola,and finding the line of symmetry,which can be obtained by drawing a line parallel to y axis, passing through (-5,0).
So, the equation of line is : x= -5
Which algebraic expression represents the phrase “the quotient of negative eight and the sum of a number and three”?
The 12 members in Dante's hiking club shared 176 ounces of trail mix equally. How many ounces of trail mix did each member get?
I need help! Really struggling with understanding how to do this
A bamboo shoot is 20 inches tall at day 0 and grows 24 inches each day. which function(s) shown below can be used to determine height, f(n), of the bamboo after n days?
I. f(n)=24n+20
II. f(n)=24n+20(n-1)
III. f(n)=f(n-1)+24 where f(0)=20
Answer:
The correct answer is option I
Step-by-step explanation:
Initial height of bamboo [tex]= 20 in\\[/tex]
Height of bamboo grows by [tex]24 in \\[/tex] every day
Let "n" be the number of days
So the height of bamboo after "n" days is
[tex]f(n) = 20 + 24n\\[/tex]
Thus, the correct answer is option I
23. A glass box shaped like a rectangular prism has width 7 inches, length 9 inches, and height 12 inches. It is being shipped in a larger box with width 10 inches, length 10 inches, and height 15 inches. The space between the glass box and the shipping box will be filled with Styrofoam peanuts. How many cubic inches of space will contain Styrofoam peanuts? Show all work.
Provide a possible situation that the graph shown could represent
1. Use an inequality symbol (<, >, ≥, =) to compare −26 ____ 54
The Side-Angle-Side Similarity Postulate states “If the measures of 2 sides of a triangle are proportional to the measures of 2 corresponding sides of another triangle and the angles between them are congruent, then the triangles are congruent”?
TRUE or FALSE
Could someone please give me the answer? The subject is math and its Pre- Algebra
Use two variables k and total to write a for loop to compute the sum of the squares of the first 50 counting numbers, and store this value in total. thus, your code should put 1*1 2*2 3*3 ... 49*49 50*50 into total. use no variables other than k and total.
An advertisement on a billboard measures 22 ft long and 8 ft high. If the ad is transferred to the side of a bus and is 30 in. Long, how tall is the new ad, to the nearest inch
the new ad is 10 ft and 11 inches tall, to the nearest inch.
What is Scale?The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary throughout a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult. This change makes the idea of size significant in two different ways.
Given, An advertisement on a billboard measures 22 ft long and 8 ft high. If the ad is transferred to the side of a bus and is 30 ft. Long.
when the advertisement is 22 ft long then the height is 8 ft.
So,
When the advertisement is 1 ft long then the height is = 8/22 ft.
the advertisement is 1 ft long then the height is = 4/11 ft.
thus,
the advertisement is 30 ft long then the height is = 4/11 * 30 ft.
the advertisement is 30 ft long then the height is = 120/11 ft.
the advertisement is 30 ft long then the height is = 10 ft 11 inches.
Therefore, When the advertisement is 30 ft long then the height is 10 ft 11 inches.
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Given f(x)=3x^2+10x−8 and g(x)=3x^2−2x .
What is (fg)(x)
Answer:
[tex]\frac{x+4}{x} \hspace{8}where\hspace{8}x\neq0,\frac{2}{3}[/tex]
Step-by-step explanation:
The division between functions is defined as:
[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)} ,\hspace{10}g(x)\neq0[/tex]
So:
[tex](\frac{f}{g} )(x)=\frac{3x^2+10x-8}{3x^2-2x}\\ \\Factor\hspace{3}x\hspace{3}out\hspace{3}the\hspace{3}denominator\\\\(\frac{f}{g} )(x)=\frac{3x^2+10x-8}{x(3x-2)}\\\\Factor\hspace{3}the\hspace{3}numerator\\\\(\frac{f}{g} )(x)=\frac{4(3x-2)+x(3x-2)}{x(3x-2)}\\\\Factor\hspace{3}3x-2\hspace{3}from\hspace{3}the\hspace{3}numerator\\\\(\frac{f}{g} )(x)=\frac{(3x-2)(x+4)}{x(3x-2)}=\frac{x+4}{x}[/tex]
Since [tex]g(x) \neq0[/tex] , let's find its roots:
[tex]3x^2-2x=0\\\\Factor\\\\x(3x-2)=0\\\\Split\hspace{3}into\hspace{3}two\hspace{3}equations:\\\\(1):x=0\\(2):3x-2=0[/tex]
For (2)
[tex]3x=2\rightarrow x=\frac{2}{3}[/tex]
Therefore the roots are:
[tex]x=0,\hspace{3}x=\frac{2}{3}[/tex]
Finally the complete answer is:
[tex](\frac{f}{g})(x)= \frac{x+4}{x} \hspace{8}where\hspace{8}x\neq0,\frac{2}{3}[/tex]
We play a game where there are 50 coins in a row, we take turns taking between 1 and 5 coins however many you like. whoever takes the last coin keeps them all. how can i win everytime and does it matter if i go first
--9/8x4/3 Please help I will mark brainliest
A tourist in ireland wants to visit seven different cities. if the route is randomly selected, what is the probability that the tourist will visit the cities in alphabetical order? round your answer to five decimal places.
The probability that the tourist will visit the cities in alphabetical order is 0.00020.
There are a total of 7! ways to visit 7 different cities, but there is only one way to visit them in alphabetical order. So, the probability that the tourist will visit the cities in alphabetical order is:
1/7! = 1/5040 = 0.0002
To five decimal places, the probability is 0.00020.
Here is a step-by-step explanation of the calculation:
We can think of the route as a permutation of 7 letters, with no of the letters being identical.
The number of permutations of 7 letters is 7!.
So, the number of ways to visit the cities in alphabetical order is 1.
The probability that the tourist will visit the cities in alphabetical order is 1/7!.
Here are some additional things to consider:
The probability that the tourist will visit the cities in alphabetical order is very small, because there are many other possible routes.
The probability would be 1 if there were only one city to visit.
The probability would be 0 if there were 7 cities and the tourist had to visit them all in alphabetical order.
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What is 7200 minutes, in days? (Remember, there are 60 minutes in an hour and 24 hours in a day.)
Answer:
5 Days is the answer
Lucy wants to make different types of Cheesecake, each cheesecake uses 2/3 pound of cream cheese, she has 2 pounds of cream cheese. How many cheesecakes can she make?
Consider today's stock listings for bukkia hog farms, shown below. 52 wk high 52 wk low symbol div. close net change 212.45 106.63 bhf 18.95 140.26 8.85 today, ken sold the 116 shares of bukkia hog farms that he purchased yesterday. how much profit did ken make
Answer:
$1026.60
Step-by-step explanation:
Today's stock listing for Bukkia hog farms as shown below :
52 wk high : 212.45
52 wk low : 106.63
symbol : bhf
Div. : 18.95
close : 140.26
net change : 8.85
Since we know net change from yesterday till date is 8.85.
Ken sold shares that he purchased yesterday = 116 × 8.85 = $1026.60
Ken made profit of $1026.60
It takes Makhaya 75 minutes and 3 paper sheets to complete a writing assignment, and it takes him 15 minutes and 1 paper sheet to complete a math assignment. Makhaya is required to spend more than 300 minutes to complete assignments, and he can use at most 20 paper sheets.
Let W denote the number of writing assignments he completes and M the number of math assignments he completes.
Write an inequality that represents the condition based on the number of minutes.
Write an inequality that represents the condition based on the number of paper sheets.
Answer:
Part a) [tex]75W+15M > 300\ minutes[/tex]
Part b) [tex]3W+M \leq 20\ paper\ sheets[/tex]
Step-by-step explanation:
Let
W------> the number of writing assignments that Makhaya completes
M-----> the number of math assignments that Makhaya completes
so
case A) Based on the number of minutes
[tex]75W+15M > 300[/tex] -----> inequality that represent the situation based on the number of minutes
The solution is the shaded area between the positive values of W and M
see the attached figure N 1
case B) Based on the number of paper sheets
[tex]3W+M \leq 20[/tex]-----> inequality that represent the situation based on the number of paper sheets
The solution is the triangular shaded area between the positive values of W and M
see the attached figure N 2
Answer:
First box: 75W+15M>300
Second box: 3W+M≤ 20
Step-by-step explanation:
Did it on Khan
An inscribed angle has a measure of 48°. Determine the measure of the intercepted arc.
24°
48°
72°
96°
Fernando evaluated the expression below. What was Fernando’s error?
Answer:
C. Fernando incorrectly found the product of -2 and -5.
Step-by-step explanation:
We have been given an image, which represents work of Fernando's evaluation of an expression. We are asked to find the error in Fernando's work.
[tex]\frac{5(9-5)}{2}+(-2)(-5)+(-3)^2[/tex]
Let us evaluate our given expression using order of operations (PEMDAS).
[tex]\frac{5(4)}{2}+(-2*-5)+9[/tex]
[tex]\frac{20}{2}+10+9[/tex]
[tex]10+10+9[/tex]
[tex]29[/tex]
Since we know that product of two negative numbers is always positive, therefore, the product of negative 2 and negative 5 will be positive 10.
Therefore, Fernando incorrectly found the product of -2 and -5 and option C is the correct choice.
Consider the expression 625(5xy)^-3/ (5x)^2 y^7
Answer:
1
-----------------
5x^5y^10
Step-by-step explanation:
Which algebraic expression is equivalent to the expression below?
9(8x + 10) + 9(9 - x)
A. 63x - 171
B. 81x + 171
C. 63x + 9
D. 63x + 171
How much will it cost to mail a first-class letter that weighs 2.8 oz?
The rate is $.22 for the first ounce and $.17 for each additional
ounce or fraction of an ounce.
a. $.56
b. $5.60
c. $.53
d. $.39
Final answer:
The total cost to mail a first-class letter that weighs 2.8 oz is $0.56, which includes $0.22 for the first ounce and $0.34 for the additional weight.
Explanation:
To calculate the cost of mailing a first-class letter that weighs 2.8 oz, you need to know the initial rate for the first ounce and the rate for each additional ounce. According to the given rates, the cost for the first ounce is $0.22, and each additional ounce (or fraction thereof) costs $0.17.
Since the letter weighs 2.8 oz, you have 1.8 oz over the first ounce. Thus, you need to pay for 2 additional ounces.
The total cost = cost for first ounce + cost for additional ounces = $0.22 + 2 x $0.17 = $0.22 + $0.34 = $0.56. Therefore, the correct answer is (a) $.56.
The diagonals of a parallelogram are congruent which could be the same parallelogram ?
A - trapezoid
B - Rectangle
C - Kite
D - rhombus
Answer:
B - Rectangle
Step-by-step explanation:
The diagonals of the parallelogram are given equal.
Diagonals of a parallelogram are equal in a rectangle .
So the given figure in which diagonals are equal is called a Rectangle.
Among the given options Option B is the right answer.
In GHI, HI = IHG =3x + 4, and IGH = 2x - 24. What is HIG?
Line segment XY is tangent to circle Z at point U. If the measure of UV is 84, what is the measure of YUV. A. 42 B. 84 C. 96 D. 168
Answer:
The measure of angle YUV is equal to [tex]m<YUV=42\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we have that
[tex]arc\ UV=84\°[/tex] -----> given problem
so
[tex]m<UZV=84\°[/tex] ------> by central angle
we know that
The triangle UZV is an isosceles triangle
because
[tex]ZU=ZV=radius[/tex]
so
[tex]m<ZUV=m<ZVU[/tex] -----> bases angle of the isosceles triangle
Remember that
The sum of the internal angles of a triangle is equal to [tex]180\°[/tex]
so
[tex]m<ZUV+m<ZVU+m<UZV=180\°[/tex]
[tex]2m<ZUV+m<UZV=180\°[/tex]
substitute and solve for m<ZUV
[tex]2m<ZUV+84\°=180\°[/tex]
[tex]m<ZUV=(180\°-84\°)/2=48\°[/tex]
[tex]m<ZUV+m<YUV=90\°[/tex] ------> by complementary angles
solve for m<YUZ
[tex]48\°+m<YUV=90\°[/tex]
[tex]m<YUV=90\°-48\°=42\°[/tex]
Answer: A. 42
Step-by-step explanation: trust i got a 100% on the quiz
Which statement describes the translation of y = −one half (x − 2)2 − 2 from standard position?
Frank is constructing the circumscribed circle for △XYZ. He has already used his compass and straightedge to complete the part of the construction shown in the figure.
Which construction could be his next step?
Place the point of the compass on point Y and draw an arc intersecting the two arcs.
Place the point of the compass on point X and draw an arc intersecting the two arcs.
Place the point of the compass on point Z and draw an arc through points X and Y.
Place the point of the compass on one of the arcs and draw an arc through point X.
Answer:
Place the point of the compass on point X and draw an arc intersecting the two arcs.
Step-by step explanation:
This is to complete the angle bisector.