Johnny rode his bicycle down a hill. It took him 15 seconds to ride from the top of the hill to the bottom of the hill. The equation h = -3t + 45 models his height, h, in feet, above the bottom of the hill as a function of the time, t, in seconds, after he started riding down the hill. Part A: What is the average rate of change in Johnny’s height? Part B: What is the height of the hill? Part C: How long will it take Johnny to travel 1/3 of the distance down the hill?
From the height function, we get that:
a) The average rate of change is of -3 feet per second.
b) The height of the hill is of 45 feet.
c) It will take Johnny 5 seconds to travel 1/3 of the distance down the hill.
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The height, after t seconds, is given by:
[tex]h(t) = -3t + 45[/tex]
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The height of the hill is [tex]h(t)[/tex] when [tex]t = 0[/tex], thus [tex]h(0) = -3(0) + 45 = 45[/tex]. 45 feet, which means that the the answer for option B is 45 feet.-------------------------------
Item a:
The initial height is of 45 feet, at [tex]t = 0[/tex] seconds.The final height is of 0 feet, at [tex]t = 15[/tex] seconds.Thus, the average rate of change is given by:[tex]A = \frac{0 - 45}{15 - 0} = -\frac{45}{15} = -3[/tex]
The average rate of change is of -3 feet per second.
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Item c:
One-third of the distance of 45 feet is [tex]\frac{1}{3}45 = 15[/tex] feet, thus, we have to find the time at which he is at 30 feet, that is, t for which [tex]h(t) = 30[/tex][tex]h(t) = -3t + 45[/tex]
[tex]30 = -3t + 45[/tex]
[tex]3t = 15[/tex]
[tex]t = \frac{15}{3}[/tex]
[tex]t = 5[/tex]
It will take Johnny 5 seconds to travel 1/3 of the distance down the hill.
A similar problem is given at https://brainly.com/question/20732437
please help me answer this question quickly
Answer:
A and D is true.
(see how to solve in pic)
Please answer my question and explain it.
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Work Shown:
4 1/2 = 4 + 1/2 = 4 + 0.5 = 4.5
In short, 4 1/2 cups is the same as 4.5 cups
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1 cup = 8 fluid ounces
4.5*(1 cup) = 4.5*(8 fluid ounces) ....... multiply both sides by 4.5
4.5 cups = 36 fluid ounces
Answer:
D
Step-by-step explanation:
Find the sum of the counting numbers from 1 to 25 inclusive. In other words, if S = 1 + 2 + 3 + ... + 24 + 25, find the value of S.
Answer:
325
Step-by-step explanation:
You must have heard about Arithmetic Progressions (AP)
Arithmetic progressions are a series of numbers such that every successive number is the sum of a constant number and the previous number.
Our very own counting numbers form AP
For example :-
2 = 1 + 1
3 = 2 + 1
4 = 3 + 1
The number in bold (1) is that constant number which is added to a number to form its successive number.
To find the sum of series forming AP, we use the formula :-
[tex]sum = \frac{n}{2} \{ a + a _{n} \} [/tex]
here,
n is the number of termsa is the first number of the series an is the last number of the seriesSo we'll use all this information to find the sum of continuous numbers from 1 to 25 where 1 is the first term(a) and 25 is the last(an).
and n is 25
[tex]S = \frac{25}{2}\{ 1 +25\} [/tex]
[tex] = \frac{25 \times 26}{2} [/tex]
[tex] = 25 \times 13[/tex]
[tex] = 325[/tex]
So, the value of S comes out to be 325.
Answer:
s= 325
Step by step explanation:
Add all numbers 1 to 25 to get 325.
Find the missing numbers.
Answer:
Step-by-step explanation:
1÷4 / 6÷1 = 1÷4 × 1÷6 = 1/(4×6)
A 1400-seat theater sells two types of tickets for a concert. Premium seats sell for $30 each and regular seats sell for $20 each. At one event $33,950 was collected in ticket sales with 10 seats left unsold. How many of each type of ticket was sold?
Answer:
x = 638
y = 1190 - 638 = 552
Step-by-step explanation:
Let x = premium seats
let y = regular seats
x + y = 1190 (ten were not sold
30x + 20y = 30180 (amount collected
now multiply the first equation by 20 and subtract
20x + 20y = 23800
30x + 20y = 30180
-10x = -6380
x = 638
y = 1190 - 638 = 552
check it by multipying x and y by their price to see if you come up with the correct amount
Hope this helps
The 1,450 students at Classical Academy were surveyed about their use of text messaging. How many students said they text 0-50 times a day?
Answer:25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
The table below shows the number of cruise ships in a harbor on various days.
(table pic attached)
a. Write an expression for the total number of cruise ships in the harbor on Monday and Tuesday.
b. Write an expression for the total number of cruise ships in the harbor on all 5 days.
NEED HELP PLEASE- ANSWER BOTH TASKS, WILL MARK BRAINLIEST
Task 1 - Nonlinear Systems of Equations
Create a system of equations that includes one linear equation and one quadratic equation.
-
Part 1. Show all work in solving your system of equations algebraically.
-
Part 2. Graph your system of equations and show the solution graphically to verify your solution.
-
Task 2 - Polynomial Identities
Part 1. Pick a two-digit number greater than 25. Rewrite your two-digit number as a difference of two numbers. Show how to use the identity (x − y)2 = x2 − 2xy + y2 to square your number without using a calculator.
-
Part 2. Choose two values, a and b, each between 8 and 15. Show how to use the identity a3 + b3 = (a + b)(a2 − ab + b2) to calculate the sum of the cubes of your numbers without using a calculator.
-
Answer:
f(x)5.79(3)^2 for task 1
Step-by-step explanation:
Answer:
Step-by-step explanation:
Task 1:
Non linear systems of equations:
x + y = 1 -------------------(I) {Linear equation}
y = 1 - x
y = x² - 5 ---------------(II) {Quadratic equation}
Substitute y =1 - x in equation (II)
(II) --> 1 -x = x² -5
Add 'x' to both sides
1 = x² + x - 5
0 = x² + x - 5 - 1 {Subtract 1 from both sides}
x² + x - 6 = 0
x² + 3x - 2x - 6 = 0 {Rewrite the middle term}
x( x + 3) - 2(x + 3) = 0
(x + 3)(x - 2) = 0
x + 3 = 0 ; x - 2 = 0
x = - 3 ; x = 2
When x = - 3 , y = 1 -(-3 )
= 1 + 3
y = 4
When x = 2 ; y = 1 - 2 = -1
Solution of the equations: (-3,4) & ( 2,-1)
Task 2:
Part 1: x = 40 ; y = 30
(x - y)² = x² - 2xy + y²
(40 - 30)² = 40² - 2*40*30 + 30²
= 1600 - 2400 + 900
= 2500 - 2400
= 100
Part 2:
a = 10 , b = 11
a³ + b³ = (a + b)(a² - ab +b²)
(10)³ + (11)³ = (10 +11)(10² -10*11 + 11² )
= 21* (100 - 110 + 121)
= 21 * ( 221 - 110)
= 21 * 111
= 2331
If 8 apples can make 3 pies, then how many pies can you make with 24 apples?
A: 64
B: 24
C: 11
D: 9
E: 6
Please help me fast! I will give brainly
This is the question,
YOU BE THE TEACHER Your friend says that because of the order of operations, the expressions are equivalent. Is your friend correct?
10-(5x2)+7 or 10-5x2+7
Yes or No
And Explain the answer
Answer:
He's correct.
Step-by-step explanation:
As long as there is no change in sign of the variables.
a woodworker makes 238 wooden bowls a month. At the rate, how many bowls will he make in 12 months?
Answer:
2856
Step-by-step explanation:
if you multiply 238 by 12
you will get the ans
Answer: 2856
Step-by-step explanation:
A woodworker makes 238 bowls in a month: this is the unit rate. To find how many bowls will be produced by the woodworker in 12 months, multiply the unit rate by 12.
math problem for highschool
Answer:
297 units squared
Step-by-step explanation:
You just have to break the squares down and compare them to the other sides of the squares. For example, F is a 4 by 4 square and B is a 5 by 5 square, to find the dimensions of square E, you would just subtract 5 by 4. By looking at the side relationships of the squares, you can easily find the dimensions of each one.
A - 9 by 9
B - 5 by 5
C - 6 by 6
D - 7 by 7
E - 1 by 1
F - 4 by 4
G - 8 by 8
H - 5 by 5
Multiply and add to get 297
Answer:
297 units squared
Step-by-step explanation:
simplify 6^x+2-6^x/7*6^x
step by step.
Answer:
[tex]{ \tt{ = \frac{ {6}^{x} +( 2 - {6}^{x}) }{7. {6}^{x} } }} \\ { \tt{ = \frac{ {6}^{x} (1 + 2 - 1)}{7. {6}^{x} } }} \\ = { \tt{ \frac{2}{7} }}[/tex]
i dont understand this
Answer:
you should use pythagorus theoram
h square=b square plus p square
Choose 3 of the following to write using a single, positive exponent: 2^-7, 3^-23, 11^-8, 4^-9, 2^-32, 8^-3. pls, hurry don't have much time! Ill give brainliest!!!
Answer:
1,3 and the last one
Step-by-step explanation:
Final Exam 7/28/21
Score: 20/24 20/27 answered
Progress saved Done
6 VO
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Question 2
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B0/1 pt 53 19 Details
Find a degree 3 polynomial having zeros - 3, 4 and 7 and the coefficient of 23 equal 1.
The polynomial is
Question Help: Video
Submit Question
Answer:
x^3-8x^2-5x+84
Step-by-step explanation:
The polynomial can be found by expanding (x+3)(x-4)(x-7)=x^3-8x^2-5x+84
after a gymnastic competition, the coaches reviewed all the gymnasts scores to identify areas for improvement. a missed landing on an aerial cartwheel deducts 2 points from the score. the coaches found that aerial cartwheels were missed 5 times across the competition. how did these missed landings affect the scores overall
Answer: The missed points will subtract 10 from the total score.
Step-by-step explanation:
A missed landing subtracts 2 points.
If they miss the landings 5 times, you know have a problem of 5x2.
5x2=10
Therefore, The points will subtract 10 from the total score.
a single piece of sod is typically rectangular in shape and measures 46 cm wide and 1.5 m long. Assuming that you can cut the sod, how many pieces of sod would be required to cover the following lawn?
The question is incomplete
Answer:
could you add more information?
Step-by-step explanation:
what is the equation of the blue line?
Answer: y = 3x + 2
Step-by-step explanation:
[tex]\dfrac{x-x_{1} }{x_{2} -x_{1} } =\dfrac{y-y_{1} }{y_{2} -y_{1} }\\[/tex]
Let's choose two arbitrary points on the graph.
For example, let these be points with coordinates (1, 5) and (2, 8).
Substitute the coordinates of these points into the above formula and derive the equation of a straight line.
[tex]\dfrac{x-1}{2-1} =\dfrac{y-5}{8-5}\\\\\dfrac{x-1}{1} =\dfrac{y-5}{3}\\\\3(x-1)=y-5\\3x-3=y-5\\y=3x-3+5\\y=3x+2[/tex]
e) A and B are the subsets of a universal set U. If n (A) = 63, n (B) =72.
n (AUB) ,= 115, n (AUB) = 20, find
(i) n (U)
(ii) n(u)
(iii) n (Anb)
(iv) n (only A)
Also illustrate the above information in Venn-diagram.
sorry, there are two (AUB), I think one should be n(AnB) and i.e n(AnB)=20.Right?
Mr. Baldwin is packing the shipping box with ring boxes that are cubes with an edge length of 2/3 inches. if he completely fills the shipping box, how many ring boxes can he ship?
Answer:
I’m sorry but is this all the information given? Because this is incomplete.
Step-by-step explanation:
There has to be some other directions or inage attached (if there was supposed to be attached, i dont see it)
This should include the dimensions of the shipping box.
Find the coordinates of the intersection of the diagonals of parallelogram GHJK with vertices G(−4, 5), H(3, 5), J(2, −1), and K(−5, −1).
Answer: 1,2.4
i'm not sure thoo
Step-by-step explanation: :3
The coordinates of the intersections of the diagonal of parallelogram GHJK will be ( -1, 2 ).
What is parallelogram?A parallelogram is a quadrilateral having four sides and the two opposite sides are equal and parallel to each other.
Given that:-
The coordinates the intersection of the diagonals of parallelogram GHJK with vertices G(−4, 5), H(3, 5), J(2, −1), and K(−5, −1).The intersection point will be the midpoint between the points G and J or points K and H.
The coordinates of the points H and K are ( 3,5) and K ( -5,-1). So the midpoint will be calculated as:-
Midpoint = [tex]\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}[/tex]
Midpoint = [tex]\dfrac{-5+3}{2},\dfrac{5-1}{2}[/tex]
Midpoint = [tex]-\dfrac{2}{2},\dfrac{4}{2}[/tex]
Midpoint = (-1,2)
Therefore the coordinates of the intersections of the diagonal of parallelogram GHJK will be ( -1, 2 ).
To know more about parallelogram follow
https://brainly.com/question/970600
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In training for a swim meet, Tom swam 1000 meters in 2/3 hour. His swimming partner, Carl, swam 1/2 of his distance in 1/3 hour.
Answer:
1. 25 meters per hour
2. 500 meters
3. 25 meters per hour
4. the same speed as
Step-by-step explanation:
I didn't know the options for 4 so hopefully this is correct :)
What is the initial value of the function represented by this graph?
1
5
6
7
Answer:
the inital value is one.
Step-by-step explanation:
So basically, the initial value is just the value of y when x is zero. In this case, its 1 this point on the graph where x=0 is also known as the y intercept. Hope that helped.
HELP ME PLEASE
SJSJSJJSJSJSJSJ
Answer:
24.12-9.8=24.32
Step-by-step explanation:
hope this helps, sorry I'm bad at explaining, but just trust me it is this im 100% positive.
Answer: 24.32
Step-by-step explanation:
34.12 - 09.80
hope this helps
The graph shows the depth, y, in meters, of a shark from the surface of an ocean for a certain amount of time, x, in minutes:
Part A: Describe how you can use similar triangles to explain why the slope of the graph between points A and B is the same as the slope of the graph between points A and C. (4 points)
Part B: What are the initial value and slope of the graph, and what do they represent? (6 points)
Answer:
you can count the lines from point a to point b on the Y (rise) axis then on the X (run) axis. put the rise over the run as a fraction (rise)/(run to find slope. it will form a triangle.
Step-by-step explanation:
Please help me! I will give brainly!
Question,
Three pumpkins are catapulted at a contest. How much farther does Pumpkin C travel than Pumpkin A?
• Pumpkin A travels 0.61 mile.
• Pumpkin B travels 0.28 mile farther than Pumpkin A.
• Pumpkin B travels 0.06 mile farther than Pumpkin C.
How many Mile ____
============================================================
Explanation:
A = 0.61 is given to us
Pumpkin B travels 0.28 of a mile further than A does, so,
B = A+0.28 = 0.61+0.28 = 0.89
Pumpkin B travels 0.89 of a mile.
---------------------
Pumpkin C travels 0.06 of a mile more than B does, which means,
C = B + 0.06
C = 0.89 + 0.06
C = 0.95
Pumpkin C travels 0.95 of a mile.
---------------------
The last thing to do is to subtract the values of C and A
C - A = 0.95 - 0.61 = 0.34
Pumpkin C travels 0.34 of a mile further compared to pumpkin A.
---------------------
Side note: if you want to convert from miles to feet, then multiply by 5280.
For instance, 0.61 miles = 0.61*5280 = 3,220.8 feet.
See the picture to solve the question 1Question=10 points
Answer:
1.5x+2.75y+33
Step-by-step explanation:
Call x: the hour of dogs keeping
y: the hour of wolves keeping
The total charge for dogs keeping: 19+ 1.5x
The total charge for wolves keeping: 14+2.75y
Total cost (19+ 1.5x)+(14+2.75y)= 1.5x+2.75y+33
What is the solution to the following system of equations: 2x + 3y = 5 AND 5x = 5y -25
Answer:
point form (-2,3)
Equation form
x=-2, y=3
Step-by-step explanation:
solve for the first variable in one of the equation, then substitute the result into the other equation.
Answer:
(-2,3)
Step-by-step explanation:
5x=5y-25
x=y-5 divide both sides by 5
use substitution.
2(y-5)+3y=5
2y-10+3y=5 distribute the parenthesis
5y-10=5 combine like terms
5y=15 add 10 to both sides
y=3 divide both sides by 5 to get y alone
5x=5(3)-25 replace y with 3, the value we found above
5x=15-25 multiply 5 and 3
5x=-10 subtract 25 from 15
x=-2 divide both sides by 5 to get x alone
