Answer:
Please find attached sketch of the path of the ball, having plot area and plot points, created with MS Excel
Step-by-step explanation:
Question;
The equation representing the path of the ball obtained from a similar question posted online are;
h₁ = -4·(t + 1)·(t - 5), h₂ = -4·(t - 2)² + 36, h₃ = -4··t² + 16·t + 20
The above equations represent the same path
The equation, h₁ = -4·(t + 1)·(t - 5), gives the roots of the height function, h(t), used in determining the height of the ball after time t
At (t + 1) = 0 (t = -1) or at (t - 5) = 0 (t = 5), the ball is at ground level
The ball reaches the ground, is at ground level at t = 1, and at t = 5 seconds after being tossed, where h(t) = 0
The equation of the path of the ball in vertex form, y = a·(x - 2)² + k, is h₂ = -4·(t - 2)² + 36, where, by comparison, we have;
The vertex of the ball = The maximum height reached by the ball = (h, k) = (2, 36)
The coefficient of the quadratic term, t², is negative, therefore, the shape of the parabola is upside down, ∩, shape
The sketch of the path of the ball created with MS Excel, used in plotting the vertex, the initial value and the root points of the parabola, through which the ball passes and joining of the points with a 'smooth' curve is attached
The 12th term of the arithmetic sequence is 10.5. The 18th term of this sequence is 13.5. Find the common difference and the first term.
let the n'th term be called x, and the value of the term y,
then there is a function y=a*x + b
that will give us all term we want.
this formula is also used for straight lines.
we just need a and b. we already got two data points. we can just plug the known x/y pairs into the formula
10.5 = a*12 + b
13.5 = a*18 + b
now lets manipulate these lines.
multiply the first line by 3 and the second line by 2
31.5 = a*36 + 3b
27 = a*36 + 2b
subtract the second line from the first line
4.5 = b
yey, we now know b, let's plus b into either line from above, I'll go with the first one, looks easier.
10.5 = a*12 + 4.5
6 = a*12
0.5 = a
now y=a*x + b can be filled with a and b
y = 0.5 * x + 4.5
for x=1 (the first term) it's f(1)=5
each step is 0.5, hence the common difference.
2and way:(13.5-10.5)/(18-12)
= 3 / 6
= 0.5
we got the comment difference by looking at the full difference over 6 steps and divined by these 6 steps.
from step 12 to step one it's 11 steps down
10.5 - 0.5*11
= 10.5 - 5.5
= 5
okay I admit... 2and way to do it might be faster and more intuitive... :D
Find the FACTORS of
36
Answer:
factors of 36 are 1,2,3,4,6,9,12,18,and 36
3(t-3)=5(2t+1) solve the following linear equations
Step-by-step explanation:
3(t-3)=5(2t-1)
= 3t-9=10t-5
= 3t-10t = -5+9
= -7t = 4
= -t = 4/7
= - 4/7 Answer
hope it helps
Can some one help me answer this
7. √9
√9 is a rational number because √9 = 3 = 3/1.
8. No, there is no integer between -6 and -7.
9. π
π is an irrational number
Help. ME. confused!
this is geometry. hi i need help pls.
Answer:
Step-by-step explanation:
Answer:
B is the answer
Step-by-step explanation:
A net is a two-dimensional pattern that can be folded to form a three-dimensional surface. T/F
Answer: True
Explanation:
Consider a 3D cardboard box that you can unfold. It would unfold into a 2D net that you can then re-fold back into its 3D form. The 2D net is useful to help visualize and calculate the surface area. The surface area is simply the total area of all the external faces.
Write an expression in simplified form for the area of each rectangle. Width: 11 Length: 3x+2
Answer:
33x+22
Step-by-step explanation:
The area of a rectangle is
A = l*w where l is the length and w is the width
A = 11(3x+2)
Distribute
= 33x+22
Area of rectangle = Length * Width
Length is 3x+2Width is 11⇛Area = 11(3x+2)
⇛Area = 33x + 22
abc or d please help me!
Answer:
A
Step-by-step explanation:
Cuz that’s the only graph that goes with the statement.
on this graph it’s saying the cost of 3 hair accessories is $10.
X = 3
Y = 10
Consider the following points. (−4, −1) and (4, 2) Let Y'O' be the image of YO after a reflection across line . Suppose that ′ is located at (1, 4) and ′ is located at (−2, −4). Which of the following is true about line ?
The line was reflected about the line y = -x.
-----------------------------------------
This question is solved using reflection concepts.
There are various kinds of reflections, 90º clockwise about the origin, 90º counterclockwise, among other, and each of them has a rule.
-----------------------------------------
In this question:
Point (-4,-1) became (1,4).Point (4,2) became (-2,-4).From this, we have the following rule: (x,y) -> (-y,-x)
Checking the rules, it can be said that the line was reflected about the line y = -x.
A similar question can be found at https://brainly.com/question/16130908
The figure is not drawn to scale.
Answer:
93°, 89°, 93°
Step-by-step explanation:
∠1 and ∠4 are supplementary angles:
m∠1 + m∠4 = 180°; m∠1 = 93°
∠2 and ∠4 are vertical angles:
m∠2 = m∠4 = 87°
∠3 and ∠4 are supplementary angles:
m∠3 + m∠4 = 180°; m∠3 = 93°
a man is now 9 times as old as his daughter. in four years time he'll be five times as old as his daughter. what are their present ages
Answer: The father is 36 right now and the son is 4
Step-by-step explanation: 9x4 is 36 and 36/9=4.
Find a 2-digit number smaller than 50, the sum of whose digits does not change after being multiplied by a number greater than 1
The only 2-digit number that is lesser than 50 and the sum of its digits remain unaffected despite being multiplied by a number < 1 would be '18.'
To prove, we will look at some situations:
If we add up the two digits of 18. We get,
[tex]1 + 8 = 9[/tex]
And we multiply 18 by 2 which is greater than 1. We get,
[tex]18[/tex] × [tex]2 = 36[/tex]
The sum remains the same i.e. [tex]3 + 6 = 9[/tex]
Similarly,
If 18 is multiplied to 3(greater than 1), the sum of the two digits comprising the number still remains the same;
[tex]18[/tex] × [tex]3 = 54[/tex]
where (5 + 4 = 9)
Once more,
Even if 18 is multiplied to 4 or 5(greater than 1), the sum of its digits will still be 9.
[tex]18[/tex] × [tex]4 = 72[/tex]
[tex](7 + 2 = 9)[/tex]
[tex]18[/tex] × [tex]5 = 90[/tex]
[tex](9 + 0 = 9)[/tex]
Thus, 18 is the answer.
Learn more about 'numbers' here: brainly.com/question/1624562
In the PQRS triangle PQ=QR, QR side extended to S Show that PQ+RS=QS. -S Q R
pls explain too
Answer:
Step-by-step explanation:
from the picture:
QP = QR
and
QR = RS
so
PQ + RS = QS
Please help out explanation need it
Answer:
156m^2
Step-by-step explanation:
I dont know what you mean by "each figure," but if you need the surface area for the rectangular prism, then the answer is 156, because the top square has a surface area of 3*6, then it equals 18, and the bottom square is the same, so it is also 18, 18*2=36
The 4 rectangle on the side are all the same, and they are all 10x3 which is 30, so 30*4 because there are 4 rectangles, equals 120.
120+36=156. The surface area of the rectangle is 156m^2
Triangle LMN is dilated by a scale factor of 2/3 to form triangle L’M’N. Side NL measures 48. What is the measure of side N’L’?
find the area of the right triangle
Answer:
the area of right angle is 1.5×2.5=3.75
Answer:
1.5 units^2
Step-by-step explanation:
If we say that the missing side is x, we can use the pythatgorean theorem to find it.
1.5^2 + x^2 = 2.5^2 => 2.25 + x^2 = 6.25 => x^2 = 4 => x=2
The area of a triangle is hieght * base * 1/2 => 1.5 * 2 * 1/2 = 1.5
What is the range for the following
numbers?
5, 1, 12, 3, 4, 2, 10
Answer:
11
Step-by-step explanation:
Find the range by calculating the difference between the smallest and largest numbers in a set.
The smallest number is 1, and the largest number is 12.
Find the difference:
12 - 1
= 11
So, the range is 11.
Answer:
11
Step-by-step explanation:
1,2,,3,4,5,10,12
Range is lowest value subtracted from highest value so: 12 -1 = 11
answered by g a u t h m a t h
Mrs. Santos is buying binders for the students in her class. She determined that 15 binders would cost $22.50.
Cost of Binders
On a coordinate plane, a graph titled Cost of Binders has number of binders on the x-axis and total cost in dollars on the y-axis. The line goes through points (0, 0) and (15, 22.5).
If all of the binders cost the same amount, which statement is true?
It will cost $12 for 18 binders.
It will cost $20 for 30 binders.
It will cost $42 for 28 binders.
It will cost $48 for 48 binders.
Answer:
It will cost $42 for 28 binders
Step-by-step explanation:
We know that 15 binders = 22.50 dollars . We need to find the cost of 18, 30, 28, and 48 binders to figure out if they match up with the statements. One way to do this is to find the cost for one binder, and then multiply that by the number of binders to find the cost for a certain number of binders. For example, if one binder costs 2 dollars, five binders would cost 2 * 5 = 10 dollars.
To figure out how much one binder costs, we can use the division property of equality to divide both sides of our equation (15 binders = 22.50 dollars) by 15. We divide by 15 because anything divided by itself is equal to 1, and that would make it 1 binder = something dollars.
Applying this, we get
(15 binders)/15 = (22.5 dollars)/15
1 binder = 1.5 dollars
For 18 binders, this would cost 1.5 * 18 = 27 dollars. We know this because we add 1.5 dollars for each binder.
For 30 binders, this would cost 30*15=45 dollars
For 28 binders, this would cost 1.5 * 28 = 42 dollars
For 48 binders, this would cost 1.5*48 = 72 dollars
The only one that matches up is 28 binders for 42 dollars
Answer:
$42 for 28 binders.
Step-by-step explanation:
B
Factories (x+2y)^3+(x-2y)^3
With full explanation
Answer:
[tex]\boxed{=2x(x^2+6y^2)}[/tex]
Step-by-step explanation:
Remember:
[tex](a+b)(a-b)=a^2-b^2\\\\a^3+b^3=(a+b)(a^2-ab+b^2)\\\\\\(x+2y)^3+(x-2y)^3\\\\=(x+2y+x-2y)((x+2y)^2-(x+2y)(x-2y)+(x-2y)^2)\\\\=2x(x^2+4xy+4y^2-(x^2-4y^2)+x^2-4xy+4y^2)\\\\=2x(x^2+6y^2)\\[/tex]
indentify the explicit function for the sequence in the table
Answer:
Option B
a(n) = 8 + (n-1) • 6
Answered by GAUTHMATH
What is the surface area of a cylinder with base radius 4 and height 7?
Answer:
To find the surface area of a cylinder you need a specific formula.
The formula to finding the surface area is
[tex]A=2\pi rh+2\pi r^2[/tex]
2 x pi x 7 + 2 x pi x 4 squared
144.513262065 would be the specific answer.
Solve for ggg.
-3+5+6g=11-3g−3+5+6g=11−3g
Answer:
-3 + 5 + 6 g = 11 - 3 g - 3 + 5 + 6 g = 11 - 3 g
6 g + 2 = 3 g + 13 = 11 - 3 g
{g = 11/3, g = 1, g = -1/3}
{3 g = 11, g = 1, 3 g + 1 = 0}
{3 g + 13 = 2 (3 g + 1), 11 - 3 g = 2 (3 g + 1), 11 - 3 g = 3 g + 13}
Which statement explains the type of function that is represented by the equation
y=x2 + 9?
23. What are the roots of the quadratic equation seen below?
f(x) = x? - 16x + 60
(A) x = 6, 10
(B) x =-6, 10
(C) x =- 10, 6
(D) x =- 10,- 6
Find the value of the expression x3−y3+x2+y2+3 by substituting x=−2 and y=1.
[tex]\\ \sf\dashrightarrow x^3-y^3+x^2+y^2+3[/tex]
[tex]\\ \sf\dashrightarrow (-2)^3-(1)^3+(-2)^2+(1)^2+3[/tex]
[tex]\\ \sf\dashrightarrow -8-1+4+1+3[/tex]
[tex]\\ \sf\dashrightarrow -9+8[/tex]
[tex]\\ \sf\dashrightarrow -1[/tex]
Answer: -1
Concept:
Here, we need to understand the idea of evaluation.
When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.
Solve:
Given information
x = -2
y = 1
Given expression
x³ - y³ + x² + y² + 3
Substitute values into the expression
=(-2)³ - (1)³ + (-2)² + (1)² + 3
Simplify exponents
=-8 - 1 + 4 + 1 + 3
Simplify by simple operation (addition/subtraction)
=-9 + 4 + 1 + 3
=-5 + 1 + 3
=-4 + 3
=[tex]\boxed {-1}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The teacher's helper was putting cookies onto plates. He put 1 cookie on the first plate, 4 cookies on the second plate, 16 cookies on the third plate, and 64 cookies on the fourth plate. What kind of sequence is this?
Answer:
Geometric sequence
Step-by-step explanation:
A geometric sequence involves each number after the first one being multiplied by a specific number, called the common ratio.
This situation is a geometric sequence, where the common ratio is 4.
For example, there are 4 cookies on the second plate, 16 on the third, and 64 on the fourth. To get each number, the previous number is multiplied by 4.
So, this is a geometric sequence.
If he placed one cookie on the first dish, four on the second, sixteen on the third, and sixty-four on the fourth. A geometric sequence is a type of sequence.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity,
It is given that the educator placed one cookie on the first dish, four cookies on the second, sixteen cookies on the third, and sixty-four cookies on the fourth.
Each number following the first in a geometric sequence is multiplied by a particular number, known as the common ratio. The common ratio in this situation, which is a geometric sequence, is 4.
The second dish, for instance, has four cookies, the third, sixteen, and the fourth, sixty-four. Each number is obtained by multiplying the preceding number by four.
Thus, if he placed one cookie on the first dish, four on the second, sixteen on the third, and sixty-four on the fourth. A geometric sequence is a type of sequence.
Learn more about the sequence here:
brainly.com/question/21961097
#SPJ2
working alone, aliyah can dig a 10ft by 10 ft hole is 6 hours. one day her friend eugene helped her and it only took 3.75 hours. how long would it take eugene to do it alone? disclaimer: the answer is 11.95 hours, but i keep getting 10. please use the 1/x+1/y=1/z strategy
Answer:
I think the answer is 10 hours
the 11.95 seems wrong
Step-by-step explanation:
[tex]\frac{1}{6} + \frac{1}{y} = \frac{1}{3.75}[/tex]
multiply by 22.5 y
3.75 y + 22.5 = 6y
y = 10
please help, will give brainliest!!!
Answer:
≈ 0.19
Step-by-step explanation:
So first, we find the probability of getting 1 yellow marble (the formula is the number of amount of type over the total number of items), which is:
10/(6+10+5+1)
= 10/22
= 5/11.
So getting a yellow marble on the first try is 5/11 likeliness.
Now, for the second one, we do the same except that you are NOT putting it back into the bag, which means we have to subtract the yellow marble you already took AND ALSO ONE FROM THE TOTAL AMOUNT OF YELLOW MARBLES.
To find the probability of getting the second marble, our equation is:
9/(6+9+5+1)
= 9/21
= 3/7.
Lastly, to find the probability of getting them both consecutively, we multiply the two results.
5/11 * 3/7
= 15/77
≈ 0.19
I hope this helped! :D
Find the distance on the number line between 14.3 and 4.1.
[tex]\\ \sf\longmapsto 14.3-4.1[/tex]
[tex]\\ \sf\longmapsto \dfrac{143}{10}-\dfrac{41}{10}[/tex]
[tex]\\ \sf\longmapsto \dfrac{143-41}{10}[/tex]
[tex]\\ \sf\longmapsto \dfrac{102}{10}[/tex]
[tex]\\ \sf\longmapsto 10.2[/tex]
