The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.
How to derive a quadratic function for the height of a ball
Quadratic functions are polynomials of grade 2 of the form y = a · t² + b · t + c, where t and y are the time and the height of the ball, in seconds and feet, respectively. To determine the value of the three coefficients we need to know three different points of the form (t, y).
If we know that (t₁, y₁) = (0 s, 0 ft), (t₂, y₂) = (1 s, 16 ft) and (t₃, y₃) = (3 s, 0 ft), then the quadratic function is:
a · 0² + b · 0 + c = 0 (1)
a · 1² + b · 1 + c = 16 (2)
a · 3² + b · 3 + c = 0 (3)
The solution to this system is a = - 8, b = 24, c = 0.
The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.
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how to find the length of sides using pythagorean theorem
Answer:
Pythagorean theorem is mainly used for finding the length of the third side of a right angled triangle if the lengths of other two sides are known.
For this, it is more useful if the theorem is stated in terms of the length of the sides of the triangle.
Consider a right angled triangle with sides of lengths p,b and h, where p,b and h are the lengths of perpendicular,base and hypotenuse respectively.
Draw squares on each of these sides.These squares have areas p²,b² and h².
For any right angled triangle with sides of length p,b and h;
[tex] \: \: \: \: \: \: \: {h}^{2} = {p}^{2} + {b}^{2} ....................(i)[/tex]
[tex] \therefore \: h = \sqrt{ {p}^{2} + {b}^{2} } [/tex]
From (i); p²=h²-b²
[tex] \therefore \: p = \sqrt{ {h}^{2} - {b}^{2} } [/tex]
Similarly,
[tex]b = \sqrt{ {h}^{2} - {p}^{2} } [/tex]
Step-by-step explanation:
[tex] \blue{ \frak{seolle_{aphr.odite} }}[/tex]
Multiple Choice Is the quadrilateral a parallelogram? If so, select the reason. W Z A) One angle is supplementary to both consecutive angles B) Not enough info or not a parallelogram C) Both diagonals bisect each other D) Both pairs of opposite angles are congruent E) Both pairs of opposite sides are congruent Skip Question 1 of 13 Submit
Answer: Both diagonals bisect each other.
Which of the following theorems verifies that AKML AOPQ?
The theorem that verifies that the two right angled triangles are similar is HA.
What are similar triangle?Two triangles are said to be similar if the ratio of their corresponding sides and the corresponding angles are equal.
Analysis:
From the diagrams KL = OQ ( hypotenuse)
∠L is equal to ∠Q which are acute.
so the two triangles are similar in hypotenuse and acute angle which is the HA theorem.
In conclusion, the HA theorem verifies that the two triangles are similar.
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Which polynomial is represented by the algebra tiles?
O x²-x-4
O x²-x+4
O 3x² -5x + 8
O
3x²-5x-8
Answer:
3x^2-5x+8 is the answers for the question
Step-by-step explanation:
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Question 7(Multiple Choice Worth 1 points)
(02.02 MC)
You are riding the bus to school and you realize it is taking longer because of all the stops you are making. The time it takes to get to school, measured in minutes, is modeled using the function gox)=x²-3x²
number of stops the bus makes if the bus makes 2 stops after you board, how long does it take you to get to school?
01 minute
03 minutes
07 minutes
O11 minutes
4x-5, where x is the
F
The time taken for the person to get to school based on the equation will be 7 minutes.
How to calculate the time?From the information given, the equation is given as:
g(x) = x⁴ - 3x² + 4x - 5
Then, we'll put 2 as x. This will be:
= 2⁴ + 3(2)² + 4(2) - 5
= 16 - 12 + 8 - 5
= 7
Therefore, the time taken for the person to get to school based on the equation will be 7 minutes.
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Simplify 5^-4/5^3 (help please asap)
Answer:
Rewrite 5[tex] {5}^{2?} [/tex]as[tex] {5} -^{4?} \times {5}^{7?} [/tex]Cancel out 5-4 both numerator and denominator[tex] \frac{1}{5 {}^{?7} ?} [/tex]calculate 5 to the power of 7 and get 78125[tex] \frac{1}{78125} [/tex]is equal to 0.0000128Answer:
=5^(-4)*5^(-3)
=5^(-7)
=1/5^(7)
Step-by-step explanation:
i took the denominator and multiplied it to the numerator
when powers of the same base are multiplying we add the exponents, so I added the -3 to -4 and got -7 which gives me 5^(-7) which is 1/5^(7)
Which of these is a correct expansion of (4x-2)(2x² + 3)?
OA. 4x 2x2 + (-2) 2x²+2x².3+(-2) 3
OB. 4x 2x² + 4x
3+2·2x²+2.3
OC. 4x 2x² + 4x 3+ (-2) 2x² + (-2) 3
HEY JUST WANTED TO GIVE THE AWNSER ITS C
The correct expansion of (4x-2)(2x² + 3) is 4x 2x² + 4x 3+ (-2) 2x² + (-2) 3.
The correct option is (C).
What is expression?An expression is a set of terms combined using the operations +, – , x or ,/.
Given expression: (4x-2)(2x² + 3)
= 4x (2x² + 3) -2 (2x² + 3)
= 4x* 2x² + 4x * 3- 2* 2x² - 2*3
= 4x* 2x² + 4x *3+ (-2) *2x² + (-2)* 3
Hence, the correct expansion is 4x 2x² + 4x 3+ (-2) 2x² + (-2) 3.
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Which of the following matches a quadrilateral with the listed characteristics
below?
1. Figure has 4 right angles
2. Figure has 4 congruent sides
3. Both pairs of opposite sides parallel
A. Rectangle
B. Parallelogram
C. Trapezoid
D. Square
The quadrilateral that matches the characteristics is a square.
What is a quadrilateral?A quadrilateral is a 2 dimensional figure with 4 sides. Example of quadrilaterals are rectangle, rhombuses, square, parallelograms and many more.
Therefore, the quadrilateral that matches the characteristics is a square.
Properties of a square
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Which of the following are properties of the incenter of a triangle? Check all
that apply.
A. The incenter is equidistant from each side of the triangle.
B. The incenter of a triangle is always inside it.
C. The incenter is where all of the bisectors of the angles of the
triangle meet.
D. The incenter of an obtuse triangle lies on the outside of the
triangle.
The incenter of a triangle is the point at which the triangle's three internal angle bisectors connect. The correct options are A, B, and, C.
What is the incenter of a triangle?The incenter of a triangle is the point at which the triangle's three internal angle bisectors connect. In other words, it is the point at which the internal angle bisectors of the triangle intersect.
The properties that are true about the incenter of a triangle are:
A. The incenter is equidistant from each side of the triangle.
B. The incenter of a triangle is always inside it.
C. The incenter is where all of the bisectors of the angles of the triangle meet.
Hence, the correct options are A, B, and, C.
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In triangle ABC, AP is an angle bisector of angle BAC. What is the length of PC? Round you answer to the nearest whole number.
A) 6
B) 7
C) 8
D) 9
The length of PC is 6
Sure hope this helps you :D
Answer:
D
Step-by-step explanation:
the angle bisector divides the opposite side into segments that are proportional to the other 2 sides.
note that BP = 16 - PC , then
[tex]\frac{BP}{PC}[/tex] = [tex]\frac{AB}{AC}[/tex] ( substitute values )
[tex]\frac{16-PC}{PC}[/tex] = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex] ( cross- multiply )
4 PC = 5(16 - PC) ← distribute parenthesis
4 PC = 80 - 5 PC ( add 5 PC to both sides )
9 PC = 80 ( divide both sides by 9 )
PC = 8.888... ≈ 9 ( to the nearest whole number )
7. Write an equation, in slope-intercept form, that has slope of -4 and y-intercept of -2.
Thank you
factorize 12f-42 thank you
18 cm
12 cm. Find the surface area of the cylinder
Answer
720π cm²
Step-by-step explanation:
Surface area of cylinder
A=2πr(s+r)
for r=12cm, s=18cm
A= 2π×12(12+18)
=24π×30
=720π
Find the first five terms of the sequence for which:
a₁ =1/3 and d = 1/2
(Write your answers as fractions)
Criangle has side lengths measuring 2x + 2 ft, x + 3 ft,
dn ft.
11 12
13 14 15
Which expression represents the possible values of n,
in feet? Express your answer in simplest terms.
x-1
n = 3x + 5
n=x-1
3x+5
PLEASE ANSWER ASAP!!
Use completing the square to rewrite the function in vertex form. f(x) = x² + 4x - 7
○ f(x) = (x+2)² - 11
Of(x) = (x-7)² +4
○ ƒ(x) = (x+2)² – 3
○ f(x) = (x − 2)² – 7
Answer: Choice A
f(x) = (x + 2)^2 - 11
=========================================================
Work Shown:
y = x^2 + 4x - 7
y+7 = x^2 + 4x
y+7+4 = x^2 + 4x + 4
y+11 = x^2 + 4x + 4
y+11 = (x + 2)^2
y = (x + 2)^2 - 11
f(x) = (x + 2)^2 - 11
In the third step, I added 4 to both sides to complete the square for the x^2+4x portion. Notice that (x+2)^2 = x^2+4x+4. So I added 4 to fill in the missing piece needed to complete the square.
Put another way the '4' added to both sides is because we first divided the x coefficient 4 in half to get 4/2 = 2. Then you square it to get 2^2 = 4.
--------------------
Alternative Method (optional)
y = x^2 + 4x - 7 is in the form of y = ax^2+bx+c
where: a = 1, b = 4, c = -7
Plug those a,b values into the formula below
h = -b/(2a)
h = -4/(2(1))
h = -2
This is the x coordinate of the vertex.
Use it to find the y coordinate of the vertex.
y = x^2 + 4x - 7
y = (-2)^2 + 4(-2) - 7
y = -11
The vertex is located at (h,k) = (-2,-11)
We have the template y = a(x-h)^2 + k update to y = (x + 2)^2 - 11 after plugging in a = 1, h = -2, and k = -11.
select all possible answers below - see picture for question & model
Translate by directed line segment AD
Rotate 180 degrees around point C, translate by directed line segment CE
and reflect across segment EF.
Rotate 180 degrees around point E
Translate by directed line segment AE and reflect across AC
Translate by directed line segment CE and rotate 90 degrees counterclockwise
around point E
Reflect across segment AB, rotate clockwise by angle BFE using center F
then reflect across segment. EF
The sequence of Transformation that could take figure 1 to figure 2 is; Translate by direct Line segment AD.
How to carry out transformations?
In the given graph, we can notice that figure 1 is exactly the same as figure two just that they are at different coordinates.
Now, to map figure 1 to figure two, what needs to be done is called translation. This is because In translation transformation, all the points in the object are moved in a straight line in the same direction.
Thus, the correct answer will be to translate by directed line segment AD.
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Please help with this question!
Hi Student!
Looking at this problem, it's fairly simple and just asks us to determine whether x = 1 is a solution to the expression that was provided. The first step that we must take to solving this is to plug in the value 1 for each of the places that we have x. Then we simplify and look at the final expression and if it evaluates to true than x = 1 is a solution to the expression.
Plug in the values
[tex]x^3 + 3 \ge 8 - 4[/tex][tex](1)^3 + 3 \ge 8 - 4[/tex]Simplify both sides
[tex]1 + 3 \ge 8 - 4[/tex][tex]4 \ge 4[/tex]Looking at the final expression that is shown, we can see that it states that 4 is greater than or equal to 4 which evaluates to true since 4 is equal to 4. Therefore, x = 1 would be considered a solution of the expression that was provided in this problem.
(Image: Start Fraction x over 4 End Fraction) + 2 = –2
If the linear equation with one variable is x / 4 + 2 = –2. Then the value of x will be negative 16.
What is simplification?Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The equation is given below.
x / 4 + 2 = –2
Solving for x, we have
x / 4 + 2 = –2
x / 4 = – 2 – 2
x / 4 = – 4
x = – 4 × 4
x = – 16
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PLEASE ANSWER FAST URGENT!!!! (BRAINLIEST WILL BE GIVEN)
Answer:
1 - 135
2 - 45
3 - 45
4 - 135
5 - 135
6 - 45
7 - 45
8 - 135
In the figure below, what is the value of xº?
Answer:
62 degree
Step-by-step explanation:
A triangle has 180 degree
180 - (43 + 75) = 62
Find The reciprocal for
2/5
6/13
21/80
Answer:
5/2 13/6 80/21
Step-by-step explanation:
the reciprocal is just flipping the fraction over, if they asked you to simplify its
4 1/2, 2 1/6, and 3 4/5
) The height h(t) in feet of a model rocket above the ground t seconds after
lift-off is given by h(t) = −t
2 +30t, for 0 ≤ t ≤ 30. When does the rocket reach its
maximum height above the ground? What is its maximum height?
After 15 seconds rocket reaches to maximum height is 225 units.
What is Differentiation?Differentiation means the rate of change of one quantity with respect to another. The speed is calculated as the rate of change of distance with respect to time.
Here, the given equation of height
h(t) = -t² + 30t
y = -t² + 30t
Now, on differentiating both side with respect to t, we get
dy/dt = -2t + 30
put dy/dt = 0, we get
0 = -2t + 30
2t = 30
t = 15
Now, at t = 15 sec. rocket reach at its maximum height.
maximum height at t = 15 sec is
h(15) = -(15)² + 30(15)
h(15) = -225 + 450
h(15) = 225
Thus, after 15 seconds rocket reaches to maximum height is 225 units.
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What is the value of 3-(-2)?
Answer:
5
Step-by-step explanation:
2 negatives will make a positive so 3-(-2) is equal to 3+2 and the answer is 5.
hope it helps
please help! needs to be submitted in 15 minutes
6 / 2 = 3
Every 3 feet of shadow would be 1 foot of height of the tower.
171 feet/ 3 = 57
Answer: The tower is 57 feet tall.
Given: Line CD bisects angle ACB, angle 1 is congruent to angle 2.
Prove: Triangle CDA is congruent to triangle CDB
Proving that Triangle CDA is congruent to triangle CDB below:
SSA ( angle one is equal to angle two and also side CD is on both side so it is equal, finally side BD is equal to AD because the line was bisected Meaning of congruent triangleCongruent triangles can be defined as triangles that have the same size and shape.
A congruent triangle, corresponding angles are equal also the corresponding sides are equal.
In conclusion, the proof that Triangle CDA is congruent to triangle CDB is given above
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Which relation describes the graph?
The relation that describes the graph {(-1, 3), (-2, 1), (-3, -3), (-4, -5)}
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The coordinates of given graph:
(-1, 3)(-2, 1)(-3, -3)(-4, 5)Hence, the relation is {(-1, 3), (-2, 1), (-3, -3), (-4, 5)}.
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Express 17 as a ratio of 68
Answer:
is it 1:4 or am I missing something
Step-by-step explanation:
A con is tossed 400 times what is the standard deviation
Answer:
deviation is 10
this will help you
Is (3,9) a solution to the equation y = 2x + 3 given the scholar's work shown below?
Answer:
Yes because 2(3) + 3 equals 9
Step-by-step explanation:
He correctly substituted x=3 into the equation and y=9. When working out both sides, he saw that both sides were equal to each other, so (3,9) is a solution!