A frog leaps 2 feet. The highest point in the jump is 6 inches. Assume the frog starts at (0, 0). Write a quadratic function in vertex form for the path of the jump. Specify the units you use.
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.
Here is an expression 3.2 evaluate the expression when t is 4 middle school math
Answer: Answer: C. 3.2 × 10^4
Step-by-step explanation: for this case the multiplication of the values with exponent are summed, as the exponent are the 6 and -3
6 - 3 = 3
this will be the exponent of the common value which is the 10.
after you only need to multiply 8 and 4 by separate the
8 * 4 = 32.
then we only need to place the values one by one
32 × 10^3
3 is the result of the sum of the exponent.
10 is the common value.
32 is the result of the product.
if we add another zero to the multiplication we get 3.2 and exponent finish with one more zero, then we get this result
3.2 × 10^4
because of that the C is the correct answer, keep in mind that the other answers do not apply correctly the rule of the exponent, because the rest of answer give us wrong answer with final result of the exponent.
plz help if you can do all that would be great the one that starts with a -3 and then 0 its done
Answer:
so in the first box next to -3 it would be -8
the next box would be 1
and the last one would be 7
then the other table the first box would be 1
then the second would be -2
and the last would be -6
and I hope you know how to graph
Is this a function? explain
Answer:
Yes this is a function.
Step-by-step explanation:
This graph is a function because it passes the vertical line test. The vertical line test ensures that no x value has more than one y value. You can take a pencil, hold it vertically, and move it horizontally across your paper to test whether or not the graph contains multiple y values for a single x value. If it passes this test, then the graph is indeed a function.
∠y =
plzz help due today!!
Answer:
y = 60
Step-by-step explanation:
All triangle angles add up to 180 so:
y + y + y = 180
3y = 180
y = 60
Answer:
y=60
Step-by-step explanation:
this is something to remember
when the angles of a triangle are all the same, they are 60°
A cone has a volume of 263.76 cubic yards and a height of 7 yards. What is its radius?
Use a ~ 3.14 and round your answer to the nearest hundredth.
Answer:
6
Step-by-step explanation:
Can anyone help me with this please? It's the system of equations and I'm stuck...
PLZ NO LINKS!!!!
A rectangle has sides that are 10 m, 10m, 5m, and 5 m. What is the rectangle’s length?
5m
20 m
10 m
30 m
The way the question is worded is a little confusing.
I think I would say 10m. It could be 5m, but usually they list length first, then width. The perimeter, the whole distance around the outside, is 30 m (10 + 10 + 5 +5)
The length of the rectangle will be 10 m.
What is a rectangle?A rectangle is a two-dimensional shape (2D shape) in which the opposite sides are parallel and equal to each other and all four angles are right angles.
Given that, a rectangle has sides that are 10 m, 10 m, 5 m, and 5 m.
We need to find the length of the rectangle,
We have the dimensions 5 m x 10 m,
Lengths in a rectangle tells that how much the rectangle is long and the width tells how much the width tells about the breadth of the rectangle,
So, we can say that,
Length = 10 m
Width = 5 m
Hence, the length of the rectangle is 10 m.
Learn more about rectangle click;
https://brainly.com/question/29123947
#SPJ2
please please please pleaseee help
Answer:
D.
Step-by-step explanation:
As you can see, there is a total of 8 slices, and 5 are shaded. So, you know that it is 5/8. As you can also see, there is 5 of these. So, you would have 5/8 5 times, or:
5/8 x 5
Hope this helps!
pls help me i dont know how to do this
Answer:
follow the steps
Step-by-step explanation:
HELLLPP PLEASE! Thank you!!
A radio disc jockey has 8 songs on this upcoming hour's playlist: 4 are rock songs, 2 are reggae songs, and 2 are country songs. The disc jockey randomly chooses the first song and the second is a reggae song? Write your answer as a fraction in simplest form.
Answer:
16/32
Step-by-step explanation:
Multiply 5,5,5,5 4 times which gives me 625
72 times 3=216+7=223
The slope of the equation is y=-6-2
34+81=115
C decreased over 5 years should company use
124 c
D rotation 90 degrees counterclockwise followed by reflection across the x-axis
C 8cm,15cm,40cm
B A’(16,32),(48,32),(64,80)
how which one is it
Answer:
Confusion
Step-by-step explanation:
what the heck are you asking?
Answer:
b
Step-by-step explanation:
please help thank you
Answer:
[tex]\frac{7}{22}[/tex], the total sum of the money is
Step-by-step explanation:
1- [tex]\frac{5}{11}[/tex]= [tex]\frac{6}{11}[/tex]
[tex]\frac{6}{11}[/tex]*[tex]\frac{7}{12}[/tex]= [tex]\frac{7}{22}[/tex]
x* [tex]\frac{7}{22}[/tex]= 4500
4500/[tex]\frac{7}{22}[/tex]= about 14142.85
this is what I got out.
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
Two sides of a triangular tile measure 4 inches and 6 inches. The length of the third side is either 7 inches or 10 inches. Which lengthis the correct length for the third side?
A.) 7in
B.) 10in
PLEASE HELP WILL GIVE BRAINLIEST
Which statement is true?
Answer:
c ???
Step-by-step explanation:
NO LINKS ACTUAL ANSWERS
What is the area of the figure below?
40 mm 2
88 mm 2
80 mm 2
96 mm 2
Answer:
the area of the figure below is 56mm
Answer:
88 mm 2
Step-by-step explanation:
The small top recatngle has an area of 16 and the large bottom one has an area of 72. Add them together and you get 88 mm 2.
Several students in Ashton’s class were randomly selected and asked how many text messages they sent yesterday. Their answers were 1, 0, 10, 7, 13, 2, 9, 15, 0, 3.
Find the range for these data.
Answer:
Hello Love!
All range is in math Is the highest number subtracted by the smallest number so our equation is 15 - 0 = 15
so 15 is our range!
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
While walking to the gym, Marie decides to play a game using a her lucky fair
six-sided die (which she carries with her all the time). Tossing an even number would
indicate walking forward that many steps and, likewise, tossing an odd number would
mean walking backwards that many steps (i.e. if she tosses a 3, she walks backward 3
steps). If the probability that after 2 rolls of the die, she is further away from the gym
that she was at the beginning of the game, can be represented as m/n
for m and n being relatively prime positive integers, find m^2 + n^2 ?
Answer:
i think that every time she rolls the dice, she is further away from the gym
Step-by-step explanation:
Which is a coefficient in the expression (3 x 5 ) + 4x
Answer:
4
Step-by-step explanation:
the coefficient is the number next to the variable. In this case, the variable is x so the number right next to x is the coefficient
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
Maya uses blue and orange fabric to make identical wall decorations. The graph below shows the relationship between the amounts of blue and orange fabrics used.
Answer: 3/7
Step-by-step explanation:
im not sure but i thinks its 3/7
4x − 30 = ≤12 solve the inequality.
Answer:
4x − 30 = ≤12
Step-by-step explanation:
4x − 30 = ≤12
+30 on both sides
4x≤42
divided by 4 on both sides
x≤10.5
someone help please and no bias answers
Answer:
C, 8.5
Step-by-step explanation:
The area of a rectangular prism is Length times Width times Height. If the volume of the tank (which is a rectangular prism) is 1360, then the L x W x H is 1360. The area of the base of the tank is determined by multiplying the Length and the Width together, so that means that L x W = 160.
Our first equation
L x W x H = 1360
Our second equation
L x W = 160
We see that 1360 divided by 160 gets us the height of the prism.
1360 / 160 = 8.5, so the answer is C
Which solid figure does this net represent?
A) cone
B) square pyramid
C) rectangular prism
D) triangular pyramid
Answer:
rectangular prism
Step-by-step explanation:
Explain how you can use a number line to find the sum of -8.3 + 10.5
Answer:
don't search link
Step-by-step explanation:
Find the perimeter of the figure. Round your answer to the nearest hundredth.
Answer:
40.56 in.
Step-by-step explanation:
8 × 3.14 × 1/2 = 12.56 (perimeter for the half circle)
12.56 + 10 + 8 + 10 = 40.56
Answer:
Perimeter = 40.56 inches
Explanation:
The perimeter of a shape is all side lengths added up, so, we know there are sides with the lengths 10 inches, 10 inches, 8 inches, and a semicircle.
To find the perimeter of a semicircle, the formula is
C = πd/2, circumference equals pi times diameter divided by 2 OR C = πr, circumference equals pi times radius.
The diameter is 8, so, filling out the formula, it's
C = 3.14 x 8 /2
C = 25.13/2
C = 12.56
So, adding all the sides up, it's 10 in. + 10 in. + 8 in. + 12.56 in.
Therefore, the answer/perimeter/circumference is 40.56 inches.
This is my second answer so far, I hope it helped!