Answer:
[tex]\displaystyle f(x)=-\frac{1}{24}\left(x-12\right)^2+6[/tex]
Where f(x) models the height, in inches, of the frog's leap after it had leapt x inches.
Step-by-step explanation:
We are given that a frog leaps two feet, with the highest point in the jump being six inches.
Assuming the frog starts at (0,0), we want to find a quadratic function in vertex form for the path of the jump.
First, we will convert the length of the jump to inches. Two feet is equivalent to 24 inches.
Next, since the frog started at (0, 0), in order to jump a length of 24 inches, it must have ended at (0, 24). These two points will also be our two roots: x = 0 and x = 24. We can use the factored form of a quadratic:
[tex]f(x)=a(x-p)(x-q)[/tex]
Where p and q are the roots.
Substitute in the roots:
[tex]f(x)=a(x-0)(x-24)=ax(x-24)[/tex]
Now, since the frog reached a maximum height of six inches, the y-coordinate of the function at its vertex point is 6.
Since a parabola is symmetrical along its axis of symmetry, the axis of symmetry is always halfway between the two roots.
Therefore, the x-coordinate of our vertex is:
[tex]\displaystyle x=\frac{24-0}{2}=12[/tex]
So, when x = 12, f(x) = 6. Substitute:
[tex]6=a(12)(12-24)[/tex]
Solve for a:
[tex]\displaystyle- 144a=6\Rightarrow a=-\frac{1}{24}[/tex]
Therefore, our function is:
[tex]\displaystyle f(x)=-\frac{1}{24}x(x-24)[/tex]
Now, we can place this into vertex form:
[tex]\displaystyle f(x)=a(x-h)^2+k[/tex]
Where a is the leading coefficient and (h, k) is the vertex.
Our leading coefficient is -1/24, and the vertex is (12, 6). Hence, our function is:
[tex]\displaystyle f(x)=-\frac{1}{24}\left(x-12\right)^2+6[/tex]
Where f(x) models the height, in inches, of the frog's leap after it had leapt x inches.
he number line below represents the solution to which inequality?
A.) m ÷ 4 > 1.1
B.) m ÷ 3 < 1.2
C.) 2m < 8.8
D.) 5m > 22
Answer:
i think it is a hope it helps
Step-by-step explanation:
I NEED HELP FAST! How much cardboard is needed to make the box shown
Answer:
its c
Step-by-step explanation:
I WILL GIVE BRAINLIEST!!!
Answer:
108
Step-by-step explanation:
Answer:
108 yd^2
Step-by-step explanation:
Cut the figure in half. Make a rectangle and a square.
Now u got a 6ydx6yd square.
And a 6ydx12yd rectangle.
Figure out the square 1st.
6x6=36yd^2
Now figure out the rectangle.
6x12=72yd^2
Now add them together.
72+36=108yd^2
Find the price after tax for a $940 iPhone with a NJ sales tax of 6.625%.
Answer:
$1002.27
Step-by-step explanation:
940×6.625%= $62.27
$940+$62.27= $1002.27
A machine produces wooden blocks at a constant rate. At the end of 6 minutes, it has produced 48 blocks. Which table represents the relationship between the number of minutes the machine produces wooden blocks and the number of blocks produced?
Answer:
it would be D. For every minute it is doing 8 peices
Step-by-step explanation:
PLEASE HELP THIS ASSINGMENT IS LATE
Answer:
The answer of the other person
Step-by-step explanation:
A juice factory offers its juice in both bottles and cans. A class of students on a field trip decides to compare the numbers of cases of bottled juice and canned juice that are packaged each minute. The students count the number of cases that are packaged on each assembly line over several minutes.
What is the unit rate for canned juice, in cases per minute? Explain how you found this unit rate.
Answer: 50 cases per minute
Step-by-step explanation:
1. Select one of the points on the graph. Let's use (2, 100) in this case.
2. Divide the number of cases (y) by the amount of minutes (x) This means the equation would be 100 ÷ 2.
3. Since 100 cases ÷ 2 minutes = 50 cases per minute, that means that is unit rate, which can be expressed by y = 50x or f(x) = 50x.
You spin the spinner, flip a coin, then spin the spinner again. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth.
The probability of spinning an odd number, not flipping heads, then not spinning a 6 is
__
Using it's concept, it is found that the probability of spinning an odd number, not flipping heads, then not spinning a 6 is:
[tex]p = \frac{20}{81} = 24.69\%[/tex]
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem:
There are 5 odd numbers in the spinner, out of 9, hence the probability of spinner an odd number is 5/9.The coin is fair, hence the probability of flipping tails = not heads is of 1/2.Out of the 9 numbers in the spinner, only one is six, hence the probability of not spinning a 6 is of 8/9.Then, the probability of the compound event is:
[tex]p = \frac{5}{9} \times \frac{1}{2} \times \frac{8}{9} = \frac{20}{81} = 24.69\%[/tex]
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
the question is: examine the triangle shown below. set up and equation and solve it to find the value of x. you must show your equation step by step.
Answer:
x=20 degrees
2x-7+6x+7+20=180
Step-by-step explanation:
the total degrees of a triangle is 180
Given the Following.... please help!
Answer:
The exponential equation is y = -2×(1/2)^x
Step-by-step explanation:
1) The horizontal asymptote of the function is the x axis (always nice)
2) At x=0, y=-2 (i.e, this function will be multiplied by -2 bc the exponent part will transform into one at x=0)
3) Then we need to ascertain the base of the exponential. Based on the facts that at x=1, y=-1 and the "a-value" is -2, we can set up an equation to find b:
can u give me the brainliest ?
CAN SOMEONE TELL ME THE ANSWER PLEASE????????????????????????? Worth 20 points
Answer:
12
Step-by-step explanation:
Okay, so on a grid, points Q and R are parallel to each other on the point 6, we just have to figure out how far apart they are, and to figure that out, we have to find the distance between 8 and -4 so:
8 - -4 = 8 + 4 = 12
So, the distance from point Q to point R is 12
if this is wrong please let me know
hope this helps:)
Fares has a container filled with 540 grams of tea leaves. Each morning, he uses 6 grams to make a cup of tea.
Write an expression to represent the grams of tea leaves remaining after x days.
How many grams of tea leaves will remain after 17 days? Show your work.
Answer:
Step-by-step explanation:
Quantity of tea leaves used for one morning = 6 grams
Quantity of tea leaves used for 'x' days = 6 *x = 6x grams
Quantity of tea leaves left after x days = 540 - 6x
Expression: 540 - 6x
Quantity of tea leaves remaining after 17 days = 540 - 6*17
= 540 - 102
= 438 grams
A ping pong ball (0.02 kg), bowling ball (25 kg), cotton ball (0.3 kg), wrecking ball (500 kg), and baseball (5 kg) are all moving with the same velocity. Which answer choice lists them from least kinetic energy to most kinetic energy?
A
Wrecking ball, bowling ball, baseball, ping pong ball, cotton ball
B
Cotton ball, baseball, ping pong ball, bowling ball, wrecking ball
C
Cotton ball, pin pong ball, baseball, bowling ball, wrecking ball
D
Ping pong ball, cotton ball, baseball, bowling ball, wrecking ball
Answer:
D) Ping pong ball, cotton ball, baseball, bowling ball, wrecking ball.
Step-by-step explanation:
If they are moving at the same time, the objects that have more mass have more kinetic energy.
the heaviest is the wrecking ball, and then the bowling ball, the baseball, the cotton ball, and the ping pong ball.
The only answer that follows this (in reverse) is D
Part B: Suppose both girls got a 90% on their next math quiz. Which student will see a greater increase in her overall math grade?
A.
Jocelyn, because her grade will increase to 84.
B.
Kari, because her grade will increase by 0.8 points.
C.
Jocelyn, because her grade will increase by 1 point.
D.
Kari, because her grade will increase to 85.3.
The data shows the survey results of 75 randomly selected students.
Student Travel Over Spring Break
Travel Plans
Number of Students
Not traveling
34
Traveling by plane
10
Traveling by train
6
Traveling by car
23
Traveling by bus
2
The school has 300 students total. Based on the results of the poll, how many of the school’s students should be expected to travel by plane over spring break?
A.
60
B.
50
C.
30
D.
40
Use the image to answer the question.
Which angle(s) is (are) complimentary to the 57ᵒ angle?
Select ALL that apply
Answer:
1, 3
Step-by-step explanation:
measure of angle 1 and 57° form a right angle; measure of angle 1 is equal to measure of angle 3
Answer:
1 and 3
Step-by-step explanation:
Because both equals 33 degree
and 57+33=90 degree
A circle has a diameter of 8. What is the area in terms of π?
Answer Choices:
4π
8π
16π
32π
Answer:
16π
Step-by-step explanation:
ooohhhh, that makes so much more sense, I wasn't actually supposed to substitute 3.14 for π, whoops, sorry
(Help me with my
Little sisters homework)
What is the length of each line?
Answer:
1. 5 1/4
2. 2 3/4
3. 3 3/4
Step-by-step explanation:
each small line is equal to 1/4
PLS help I’ll give brainliest i’d be so grateful
Answer:
f the equation is in the form, ax + b = c, where x is the variable, you can solve the equation as before. First “undo” the addition and subtraction, and then “undo” the multiplication and division. Solve 3y + 2 = 11. Subtract 2 from both sides of the equation to get the term with the variable by itself.
Step-by-step explanation:
Answer:
The goal in solving an equation is to get the variable by itself on one side of the equation and a number on the other side of the equation. To isolate the variable, we must reverse the operations acting on the variable. We do this by performing the inverse of each operation on both sides of the equation.
Step-by-step explanation:
A 50 ft building casts a shadow that is 120 ft long. What is the distance from the top of the building to the end of the shadow?
I need help with this please
hiya boys answer this for a chance to get a cookie
Answer:
∠4 = 102°
Step-by-step explanation:
∠4 = 180 - 78 = 102°
Answer:
The answer is 3 (112 Degrees).
Step-by-step explanation:
Search it up-
Wheres my cookie- :D
I may just lack brain cells but what does it mean by compare?
Answer:
By compare it mean to compare b and a
Step-by-step explanation:
You would say/type/write "A has five students while B Has 9" Boom easy
can someone help me please?
Answer:
sin ∠I = 12/13
Step-by-step explanation:
SOH CAH TOA
↑ sin = opposite side/hypotenuse
sin ∠I = 48/52 => sin ∠I = 12/13
Look at Question 17
Please Help me
Answer:
3063
Step-by-step explanation:
;D B
The median and mean scores for a math test are shown.
Which distribution of scores would best account for the difference in the median and mean?
Median score: 82%
Mean score: 70%
Answer:
median score
Step-by-step explanation:
In the figure, line m is parallel to line n. The measure of angle 2 is 40 degrees and the measure of angle 3 is 68 degrees. What is the measure of angle 5?
Explain how you found the answer using the relationships of angles.
Answer:
∠1 - 40°
Step-by-step explanation:
∠1 - 40°
b/c it's a right triangle and we have two angles given, 50° and 90°. Add them and subtract by 180° and get 40°.
∠2 - 140°
b/c an exterior (outside) angle is equal to the two most isolated / farthest angles added. The two most is angles are 105° and 35°, add them and get 140°.
∠3 - 40°
b/c ∠'s 1 and 3 are vertical angles meaning they're equal so since ∠1 is 40°, so is ∠3.
∠4 -
b/c ∠' s 2 and 4 are vertical angles meaning they're equal so since ∠2 is 140°, so is ∠4.
∠5 - 35°
b/c we have two angles, 105° and 40°. Add them and subtract by 180° and get 35°.
hope that helps lol >:)
Simplify the expression using positive exponents.
5^9 ⋅ 5^3
Answer:
244140625 or 5^12
Step-by-step explanation:
When it comes to multiplication, you add exponents IF the base (the 5 at the bottom is called base) is the same answer. for example: 1^16 x 1^9, since the exponents are the same you just add the exponents (16 & 9) which is 25 or 1^25
Dividing is the same as multiplying except your subtracting with the examples, adding and subtracting is simplifying and solving, for example
14^2 + 13^3
14 * 14 = 196
13*13*13 =2,197
196+2,197 = 2,393
Same thing for subtraction
13^3 - 14^2
2,197 - 196 = 2,001
Hope this helps
~R3V0
Jessica rented 1 video game and 3 movies for a total of $11.50.
• The video game cost $4.75 to rent.
• The movies cost the same amount each to rent.
What amount, in dollars, did Jessica pay to rent each movie?
what is the volume of this container? 20 cm 15 cm 10 cm 15 cm 20 cm 10 cm
Answer:
6,000cm3
Step-by-step explanation:
10×20×15 = 3,000
3,000×2= 6,000
Answer:
Step-by-step explanation: Multiply all the numbers and the answer you get is the volume.9,000,000