Stuart and Francisco designed a black rocket and a white rocket during an aerospace class. Both rockets were launched after class. During the launch, Stuart and Francisco recorded data of their rockets trajectories. Stuart modeled the black rockets distance from the ground, in feet, x seconds after it was launched with the graph. Francisco modeled the white rockets distance from the ground, in feet, x seconds after it was launched with the function g(x)= -16x^2 + 50x +7 . Both wanted to know what the greatest distance was from the ground for each rocket. Stuart obtained that his rockets greatest distance from the ground was [Drop down 1] while Francisco obtained a greatest distance of [Drop down 2].
Answers
We will see that for Stuart the maximum height is 30ft, and for Francisco it is 46.0625 ft
How to get the greatest distance from the ground?In the case of Stuart it is simple, as we have a graph, we just need to see the largest y-value on the graph. We can see that it is y = 30, then for Stuart, the largest distance from the ground is 30ft.
In the case of Francisco, we need to find the maximum of:
g(x)= -16x^2 + 50x +7
Notice that this is a quadratic of negative leading coefficient, so the maximum is at the vertex.
x = -50/(2*-16) = 25/16
Evaluating the function in 25/16 we get:
g(25/16) = -16*(25/16)^2 + 50*(25/16) +7 = 46.0625 ft
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Related Questions
The adults and children in a neighborhood attended a party. There were 18 children.
There were w fewer children than adults. How many people were there at the party?
Answers
There was a total of w + 36 people at the party.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given, The adults and children in a neighborhood attended a party. There were 18 children.
Let "x" be the number of Persons in the party
Since,
There were w fewer children than adults.
thus,
Number of Adults in the party = w + 18
x = w + 18
Total number of people at party = x + 18
Total number of people at party = w + 18 + 18
Total number of people at party = w + 36
Therefore, there were w + 36 people at the party.
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Help help help math math
Answers
Answer:
(-16, -4)
Step-by-step explanation:
4x - 13y = -12
x = 2y - 8
Substitute for x:
4(2y - 8) - 13y = -12
8y - 32 - 13y = -12
-5y - 32 = -12
-5y = 20
y = -4
Solve for x:
4x - 13(-4) = -12
4x + 52 = -12
4x = -64
x = -16
Solution to this system: (-16, -4)
I hope this helps!
Answer:
there are two methods
1. graphical method
2. elimination method
3. substitution method
Police use the formula: v = √ 20 L to estimate the speed of a car, v , in miles per hour, based on the length, L , in feet, of its skid marks when suddenly braking on a dry, asphalt road. At the scene of an accident, a police officer measures a car's skid marks to be 109 feet long. Approximately how fast was the car traveling? Round your answer to the nearest tenth (one decimal place) of a unit.
Answer: The car was traveling at approximately ____________ miles per hour.
Answers
Answer:
46.7 mph
Step-by-step explanation:
The speed can be found by substituting the measured skid length for the variable in the formula.
v = √(20L)
v = √(20×109) = √2180 ≈ 46.7
The car was traveling at approximately 46.7 miles per hour.
Is a 779 a good MI score
Answers
Answer:
yes
explanation:
Your score falls within the range of scores, from 740 to 799, that is considered Very Good. A 779 FICO Score is above the average credit score. Consumers in this range may qualify for better interest rates from lenders.
Cual es el resultado de la división 636
entre 3
Answers
Answer:
its gonna be 212 fam
Step-by-step explanation:
3+8+(87÷4)=(12345676×3825829){=dheg
Answers
Answer:
Read the explanation
Step-by-step explanation:
look at the photo
a cyclist travels 108m in 12 seconds.what is her speed in km/h
Answers
Step-by-step explanation:
=108÷12
=9m/s
=9x0.001x1/3600
=2.5x10^6km/h
Can you find the missing side length?
Answers
Step-by-step explanation:
you need to calculate all the sides that are given to get the other side
It seems like they have shown you how to calculate so give it a try
3. For each triangle, find the length of the labeled side.
Answers
Answer:
see explanation for detailed analysis
I WILL MARK YOU THE BRAINLIEST LINKS WILL BE REPORTED AND DELETED !
What is the values of 9p5 ?
A: 45
B: 126
C: 3024
D: 15,120
Answers
Answer:
The correct answer is D:-15,120
[tex]^{n}P_{r}=\dfrac{n!}{(n-r)!}\\\\\implies ^{9}P_5 = \dfrac{9!}{(9-5)!} =\dfrac{9!}{4!} = 15120[/tex]
The answer is D.
Choose the correct graph of the function y=√x+1.
Answers
Answer:
[A}
Step-by-step explanation:
Graph using the end point and a few selected points.
x y
0 1
1 2
2 2.41
Graph also below:
Find y intercept
[tex]\\ \rm\rightarrowtail y=\sqrt{x}+1[/tex]
[tex]\\ \rm\rightarrowtail y=0+1=1[/tex]
y intercept=(0,1)Option A
find m<DAC= x in circle O given that m<BOA= 66° and m<DB= 20°. (The figure is not drawn to scale.)
Answers
Answer:
66+20+x=180(sum of angle in a triangle)
x=180-(66+20)
x=180-86
x=94
A company interviewed 21 applicants for a recent opening. Of these applicants, 7 wore blue and 6 wore white, while 5 applicants wore both blue and white. What is the number of applicants who wore neither blue nor white?
Answers
Answer:
3 participants
Step-by-step explanation:
7 + 6 + 5 = 18
21 - 18 = 3 participants
What is the factorization of the trinomial below?
x^3 - 12x^2 + 35x
A. (x - 7)(x + 5)
B. x(x - 7)(x - 5)
C. (x^2 - 7)(x + 5)
D. x(x - 7)(x + 5)
Answers
The square root of the cube of 4 is equal to
3 or 4 or 16 or 8 or 2
Answers
Answer:
Step-by-step explanation: 1.587401052
Answer:
8
Step-by-step explanation:
this means
[tex] \sqrt{ {4}^{3} } [/tex]
4³ = 4×4×4 = 64
the square root of 64 is 8.
For each value of u, determine whether it is a solution to
- 57 = 5u - 7
2, 3, 10, 0
Answers
Answer:2 is a solution 3 is not 0 is not 10 is and also to determine the solution you can get calculator soup to help you Hope this helps bye
Find the area of sector RST Enter your answer in terms of a fraction of it and rounded to the nearest
hundredth.
Answers
Fort nite battle pass is 8 dollars
A kite with diagonals is shown. It has side lengths of 13, 13, 37, and 37. The length from the left point to the middle point is 12, and the distance from the right point to the middle point is 12.
The figure is a kite. What is the length of the kite’s longer diagonal?
5 units
35 units
40 units
48 units
Answers
Step-by-step explanation:
we have to solve 2 right-angled triangles via Pythagoras
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle).
one triangle is 37, 12 and the longer part of the long diagonal.
the second triangle is 13, 12 and the shorter part of the long diagonal.
the whole diagonal is then the sum of both parts.
37² = 12² + longer part²
1369 = 144 + longer part²
longer part² = 1225
longer part = 35
13² = 12² + short part²
169 = 144 + short part²
25 = short part²
short part = 5
so, the total diagonal is 35 + 5 = 40 units.
The length of the longer diagonal obtained using Pythagorean theorem is 40 units
What is the Pythagorean theorem?The Pythagorean theorem is a fundamental geometric relationship that states that the square of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the other two sides (the legs). Mathematically, we get
c² = a² + b²
Where a and b are the lengths of the legs and c is the length of the hypotenuse side of the right triangle.
The diagonals of a kite are perpendicular to each other
The diagonal that is bisected in a kite is the shorter diagonal
The lengths from the left point to the middle and the distance from the right point to the middle are both 12, which indicates that the diagonal from left to right of the kite is bisected, which is the shorter diagonal. Therefore;
The length of the shorter diagonal is; 12 + 12 = 24
Therefore, the longer diagonal forms two right triangles to the left and two right triangles to the right
The hypotenuse length of the right triangles are 37 and 13, while the leg common to both right triangles on each side is half the length of the shorter diagonal, or 12
The Pythagorean theorem indicates that we get;
Length of the longer diagonal = √(13² - 12²) + √(37² - 12²) = 40
The length of the longer diagonal is 40 units
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Westford Lake was originally blue because it only had 810 algae plants. Then towns and farms cropped up by the lake. This caused 9,772 more algae plants to grow, which turned the lake green. How many algae plants are now in Westford Lake?
Answers
Answer:
10,582 algae plants
Step-by-step explanation:
10,582 algae plants. You have to add 810 and 9,772 to get 10,582 algae plants.
Special Right Triangles
Isosceles Right Triangle
30-60-90 Triangle
help 1-12 please
Answers
Step-by-step explanation:
remember, the sum of all angles in a triangle is always 180°.
1.
since it is a right-angled triangle, and one of the leg angles is 45°, then the other leg angle is also 45°.
which makes this an isoceles triangle.
so, the second leg is 6 too.
the baseline (Hypotenuse) is then per Pythagoras
baseline² = 6² + 6² = 36 + 36 = 72 or 2×36
baseline = sqrt(72) = 6×sqrt(2)
2.
this is then a 30-60-90 triangle.
the left leg (a) is then 2a/2 = 10/2 = 5.
and the bottom leg is 5×sqrt(3).
3.
isoceles triangle.
so, left and right legs (a) are both 3 (from the 3×sqrt(2)).
4.
30-60-90 triangle
upper leg is then 6×sqrt(3).
the baseline is 2 times the left leg : 2×6 = 12
5.
isoceles triangle
both legs are 2 (from the 2×sqrt(2)).
6.
30-60-90 triangle
left leg is 4 (from the 4×sqrt(3)).
the baseline is 2×4 = 8.
7.
isoceles triangle.
6 = a×sqrt(2)
a (both legs) = 6/sqrt(2)
8.
30-60-90 triangle
9 = a×sqrt(3)
a (left leg) = 9/sqrt(3)
baseline = 2a = 2×9/sqrt(3) = 18/sqrt(3)
9.
due to the equal leg angles this is an isoceles triangle.
4 = a×sqrt(2)
a (both legs) = 4/sqrt(2)
10.
30-60-90 triangle
the bottom leg (a) = 2a/2 = 6/2 = 3
the left leg is then 3×sqrt(3)
11.
isoceles triangle
left leg is also 5.
baseline is 5×sqrt(2)
12.
30-60-90 triangle
12 = a×sqrt(3)
a (left leg) = 12/sqrt(3)
the baseline is then 2a = 2×12/sqrt(3) = 24/sqrt(3)
The formula for finding the
change in CPL is [(new-old)/old]
for different baskets of goods
and services. What is the
change in the CPL if the new
price for transportation
services is $100 and the old
price was $80?
A. 25%
B. 15%
C. 10%
Answers
Answer:
25%
Step-by-step explanation:
100-80=20
20/80Ⅹ100=25%
What is the slope-intercept equation for this line?
y = [?]x+ []
Answers
Answer:
y=3x+1
Step-by-step explanation:
What is the range of this data set? 64°, 72°, 74°, 68°, 70°, 68°, 68°, 75°, and 44°
Answers
Answer:
31
Step-by-step explanation:
First put your numbers in order
44 , 64 , 68 , 68 , 68 , 70 , 72 , 74 ,
Then subtract the Highest and Lowest numbers by each other
75 - 44 = 31
Select the correct answer from each drop-down menu.
On the day the link was emailed, trailer
Two days after the link was emailed, trailer
Four days after the link was emailed, trailer
had the most views.
had the most views.
had the most views.
Answers
Answer:
k
[tex]2xyy15 { { \div - \\ \sqrt[ {x. - - {?}^{?} }^{2} ]{?} }^{2} }^{2} [/tex]
Answer:
On the day the link was emailed, trailer
A
had the most views.
Two days after the link was emailed, trailer
A
had the most views.
Four days after the link was emailed, trailer
B
had the most views.
Step-by-step explanation:
The total number of views on the day the email was sent, two days later, and four days later are represented by the values of the functions when x = 0, 2, and 4.
Substitute these values into the equation:
Find these values in the table:
Apply the described rule:
So, on the day the link was emailed, trailer A had the most views.
Two days after the link was emailed, trailer A had the most views.
Four days after the link was emailed, trailer B had the most views.
What is the length of the triangular prism shown? 25 cm
15 cm
9 cm
25 cm
12 cm the answers are A.86 B.1008 C.1350 D.1080
Answers
To calculate surface area of an object you must calculate the area of each shape land then add them all together.
Answer:
Total Surface Area = 1008 cm^2
Step-by-step explanation:
2 X 1/2 X (12 X 9) (Surface area of the two triangles) (Area of triangle = 1/2 Base X Height)
+ 25 X 15 (Slanted Surface)
+ 25 X 9 (Back Rectangle)
+ 25 X 12 (Bottom Rectangle)
= 1008
here is it not sure if you will spot it
Answers
i dont understand your question
Answer:
[tex]f(x)=-5x^2+20x[/tex]
8.75 m
Step-by-step explanation:
Given ordered pairs: (0, 0) (1, 16) (2, 20) (3, 15.5) (4, 0)
From inspection, we can see that the difference in the x-values is constant (they increase by 1 each time), yet the difference in the y-values is not constant. Therefore, the relation is not linear.
As the y-values increase from 0 to 20 and then decrease back to 0, the curve is likely to be a parabola opening downwards.
The x-intercepts are at x = 0 and x = 4, so this suggests that the axis of symmetry is x = 2, and so the vertex is (2, 20).
Creating an equation using the x-intercepts:
[tex]f(x)=a(x-0)(x-4)[/tex] where [tex]a[/tex] is some constant
[tex]\implies f(x)=ax(x-4)[/tex]
[tex]\implies f(x)=ax^2-4ax[/tex]
Creating an equation using the vertex form:
[tex]f(x)=a(x-2)^2+20[/tex]
[tex]\implies f(x)=ax^2-4ax+4a+20[/tex]
Equating constants to determine a:
[tex]4a+20=0 \implies a=-5[/tex]
Therefore, equation of best fit: [tex]f(x)=-5x^2+20x[/tex]
When x = 0.5:
[tex]\implies f(0.5)=-5(0.5)^2+20(0.5)[/tex]
[tex]=-1.25+10[/tex]
[tex]=8.75[/tex]
Therefore, an estimate for the height of the rocket 0.5 s after it's launched is 8.75 m
Help pls
Question 1 Part A (3 points): What is the greatest common factor (GCF) of the polynomial:
18x3 + 6x2y - 9x2 - 3xy
Answers
Answer:
I think the answer is 3x
Step-by-step explanation:
If i am wrong please correct me
The correct answer is 3x
What is greatest common factor?The greatest common factor is the largest factor among all the numbers in the equation.
So, the equation is [tex]18x^{3}+6x^{2} y-9x^{2} -3xy[/tex]
We need to find the GCF from the given equation
[tex]3x(6x^{2} +2xy-3x-y)[/tex]
Hence, here we are getting the common factor as 3x
which the largest common factor in the given equation.
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Please help i really dont like iready and im really confused. thank you!
Answers
Answer:
15 inches cubed
Step-by-step explanation:
length 2 1/2 in
width 1 1/2 in
height 4 in
V= = l x w x h
V = 2 1/2 x 1 1/2 x 4
60/4 = 15
arrange in descending order
Answers
Answer:
7 / 16, 3 / 7, 1 / 5
Step-by-step explanation:
1 / 5 = 0.2
3 / 7 = 0.428
7 / 16 = 0.4375
In descending order,
0.4375, 0.428, 0.2
Hence the answer is 7 / 16, 3 / 7, 1 / 5
7/16,3/7.1/5
Step-by-step explanation:
1/5 = 0.2
3/7= 0.428
7/16 = 0.4375
In descending order,
0.4375, 0.428. 0.2
how do I not know 4th grade math I really am 0iq
Answers
Just multiply 20 times the amount of a certain fabric used to make 1 toy
For example
Cristian uses 3/8 sheet of red to make one toy so multiply 3/8 by 20 and you get 7.5 but since you are calculating the number of full sheets they need you will round up to 8 sheets of red fabric
Answer:
C) 8 sheets of red and 13 sheets of yellow felt
Step-by-step explanation:
Red felt
Red felt needed for 1 toy = 3/8 sheet
⇒ Red felt needed for 20 toys = 20 × 3/8 sheets
[tex]\sf \implies 20 \times \dfrac38=\dfrac{20}{1}\times \dfrac38=\dfrac{20 \times 3}{1 \times 8}=\dfrac{60}{8}=7\frac12[/tex]
Therefore, 8 complete sheets of red felt are needed.
Yellow felt
Yellow felt needed for 1 toy = 5/8 sheet
⇒ Yellow felt needed for 20 toys = 20 × 5/8 sheets
[tex]\sf \implies 20 \times \dfrac58=\dfrac{20}{1}\times \dfrac58=\dfrac{20 \times 5}{1 \times 8}=\dfrac{100}{8}=12\frac12[/tex]
Therefore, 13 complete sheets of yellow felt are needed.