Answer:
Kerry's ball stays longer in the air than Marias ball by an extra 0.582 seconds
Step-by-step explanation:
The equation that models the height, h, in feet of object thrown modeled as a time function is given as follows;
h(t) = -16t² + v₀·t + h₀
Where;
v₀ = The velocity upwards (vertical velocity)
h₀ = The initial height of the object in feet
The given parameters are;
The initial height from which Maria throws a ball = 6 feet
The initial vertical velocity with which Maria throws the ball = 40 feet per second
The initial height from which Kerry throws a ball = 5 feet
The initial vertical velocity with which Kerry throws the ball = 50 feet per second
For Maria, from the equation for the height of the object, we have;
h(t) = -16t² + v₀·t + h₀
Where for Maria, we have;
h₀ = 6 feet
v₀ = 40 ft/s
Substituting gives;
h(t) = -16 × t² + 40 × t + 6 = -16·t² + 40·t + 6
h(t) = -16·t² + 40·t + 6
The time it takes for the ball to go up and come back down again is given by the value of t, when h = 0 (ground level) as follows;
0 = -16·t² + 40·t + 6
16·t² - 40·t - 6 = 0
From the quadratic formula, we have
[tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]
[tex]t = \dfrac{40\pm \sqrt{(-40)^{2}-4\times 16 \times (-6)}}{2\times 16} = \dfrac{40 \pm 8 \times \sqrt{31} }{32} = \dfrac{5}{4} \pm \dfrac{\sqrt{31} }{4}[/tex]
t ≈ 2.64 s or -0.14 s
Therefore, the time the ball spends in the air ≈ 2.64 s
For Kerry, we have;
h₀ = 5 feet
v₀ = 50 ft/s
Substituting gives;
h(t) = -16 × t² + 50 × t + 5 = -16·t² + 50·t + 5
h(t) = -16·t² + 50·t + 5
Which gives;
16·t² - 50·t - 5 = 0
From the quadratic formula, we have
[tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]
[tex]t = \dfrac{50\pm \sqrt{(-50)^{2}-4\times 16 \times (-5)}}{2\times 16} = \dfrac{50 \pm 2 \times \sqrt{705} }{32} = \dfrac{25}{16} \pm \dfrac{\sqrt{705} }{16}[/tex]
t ≈ 3.222 s or -0.097 s
he time the ball spends in the air ≈ 3.222 s
Therefore, Kerry's ball that spends approximately 3.222 seconds stays longer in the air than Maria's ball that spends approximately 2.64 seconds in the air.
The difference in the two time duration is 3.222 - 2.64 = 0.582
Kerry's ball stays longer in the air than Marias ball by an extra 0.582 seconds.
find the missing side length. and how do i set up to solve?
Answer:
its 6 because the lines show they are parellel so it has to be equal to 18 and 12 plus 6 is 18
Step-by-step explanation:
and ice cream factory makes 240 quarts of ice cream in 2 hours. how many quarts could be made in 36 hours? What was that rate per day?
Answer:
Step-by-step explanation:
So first I divided 240 by 2 to get the hourly rate, which is 120. Then i multiplied 120 times 36 and got 4,320 quarts in 36 hours. The daily rate is 2,880, I got that by multiplying 120 by 24 because there are 24 hours in a day.
-7q + 12r = 3q - 4r what dose r equal
Answer:
r = 5y/8
Step-by-step explanation:
isolate the variable by dividing each side by factors that contain the variable.
I WILL MARK BRAINLIEST!!!!!!!!!
Determine whether the table below represents a linear function. Explain your reasoning.
Answer:
It is not
Step-by-step explanation:
It is not because this is an exponential function
y=x^2
1^2=1
2^2=4
3^2=9
4^2=16
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Chase and his little brother made up a game using coins. They flip the coins towards a cup and receive points for every one that makes it in. Chase starts with 19 points, and his little brother starts with 27 points. Chase gets 3 points for every successful shot, and his brother, since he is younger, gets 1 point for each successful shot. Eventually, the brothers will have a tied score in the game. How many points will they both have? How many additional shots will each brother have made? Chase and his brother will both have a score of by making shots.
Answer:
Chase and his brother will both have a score of 31 points by making 4 successful shots.
Step-by-step explanation:
Given that initially Chase has 19 points and his brother has 27 points.
In one successful flip, Chase get 3 points and in one successful flip, his little brother get 3 points
Assuming that both have the same score after n number successful flip of the coin.
So, points earned by Chase in n successful flip [tex]= 3\times n =3n[/tex]
and points earned by his little brother in n successful flip [tex]= 1\times n=n[/tex].
Total points of Chase [tex]= 19+3n\cdots(i)[/tex]
Total points of his little brother [tex]= 27 + n\cdots(ii)[/tex]
As the brothers have tied scores in the game, that means both have the same score, so from equations (i) and (ii), we have
[tex]19+3n = 27 + n \\\\\Rightarrow 3n-n = 27-19 \\\\\Rightarrow 2n=8 \\\\\Rightarrow n=8/2=4[/tex]
So, after n successful throw, both have the same score.
Hence, each brother made 4 additional successful shots.
Now, put n=4 inequation (i) or (ii) to get the total points, i.e
Total points of each brother [tex]= 19+ 3\times 4 = 31.[/tex]
Hence, each brother has 31 points.
How do I solve this?
-6x-1+5x^2 = 8x^2
Thanks
Answer:
[tex]\displaystyle x=\frac{-3+\sqrt{6}}{3}\text{ and } x=\frac{-3-\sqrt{6}}{3}[/tex]
Or, by approximating:
[tex]x\approx-0.1835\text{ or } x\approx -1.8165[/tex]
Step-by-step explanation:
Let’s convert this to standard form. We have:
[tex]-6x-1+5x^2=8x^2[/tex]
Subtract 5x² from both sides:
[tex]-6x-1=3x^2[/tex]
And add 6x and 1 to both sides:
[tex]0=3x^2+6x+1[/tex]
This is not factorable. So, we will need to use the quadratic formula.
The quadratic formula for a quadratic in standard form is given by:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}}[/tex]
In this case, a=3; b=6, and c=1.
Substitute appropriately:
[tex]\displaystyle x=\frac{-6\pm\sqrt{6^2-4(3)(1)}}{2(3)}[/tex]
Simplify:
[tex]\displaystyle x=\frac{-6\pm\sqrt{24}}{6}[/tex]
We can simplify the square root:
[tex]\sqrt{24}=\sqrt{4}\cdot\sqrt{6}=2\sqrt{6}[/tex]
Hence:
[tex]\displaystyle x=\frac{-6\pm2\sqrt{4}}{6}[/tex]
Simplify:
[tex]\displaystyle x=\frac{-3\pm\sqrt{6}}{3}[/tex]
Hence, we will have two solutions:
[tex]\displaystyle x=\frac{-3+\sqrt{6}}{3}\text{ and } x=\frac{-3-\sqrt{6}}{3}[/tex]
Approximating them, we can see that our solutions are approximately:
[tex]x\approx-0.1835\text{ or } x\approx -1.8165[/tex]
PLEASEEE HELPPPPPPPP JSBSJSBDSB
Answer:
-11
Step-by-step explanation:
Please hurry I need this fast.
Answer:
Option 3
Step-by-step explanation:
The two triangles are proved congruent to each other so CPCTC proves that the angles are also congruent.
A taxi driver had 27 fares to and from the airport last Monday. The price for a ride to the airport is $14, and the price for a ride from the airport is $7. The driver collected a total of $294 for the day. Let x represent the number of trips to the airport and y represent the number of trips from the airport. Write the ordered pair (x,y) that represents the solution in this situation.
Answer:
(15, 12)
Step-by-step explanation:
Let's generate two systems of equations that fit this scenario.
Number of trips to the airport = x
Number of trips from the airport = y
Total number of trips to and from the airport = 27
Thus:
[tex] x + y = 27 [/tex] => equation 1.
Total price for trips to the Airport = 14*x = 14x
Total price of trips from the airport = 7*y = 7y
Total collected for the day = $294
Thus:
[tex] 14x + 7y = 294 [/tex] => equation 2.
Multiply equation 1 by 7, and multiply equation 2 by 1 to make both equations equivalent.
7 × [tex] x + y = 27 [/tex]
1 × [tex] 14x + 7y = 294 [/tex]
Thus:
[tex] 7x + 7y = 189 [/tex] => equation 3
[tex] 14x + 7y = 294 [/tex] => equation 4
Subtract equation 4 from equation 3
-7x = -105
Divide both sides by -7
x = 15
Substitute x = 15 in equation 1
[tex] x + y = 27 [/tex]
[tex] 15 + y = 27 [/tex]
Subtract both sides by 15
[tex] y = 27 - 15 [/tex]
[tex] y = 12 [/tex]
The ordered pair would be (15, 12)
plz help meeeee asap
Jonah’s family is ordering dinner. Each adult meal costs $8.50, each kid meal costs $6.75, and
each drink costs $1.75. There are a adults and k kids in the family. If everyone orders a meal and
a drink, which expression can be used to express the total cost of the meal?
A 8.50a + 6.75k + 1.75
B a(8.50 + 1.75) + 6.75k
C (a + k)(8.50 + 6.75 + 1.75)
D 8.50a + 6.75k + 1.75(a + k)
Answer:
D
Step-by-step explanation:
WILL GIVE BRAINLIEST,
WORTH 10 POINTS
ANSWER ASAP ⚠️⚠️⚠️⚠️⚠️⚠️
hiiiiiiiiiiiiiiiiiii
Enter an equation in standard form of the line.
(4,-9) and (2, -3) are on the line.(10 points)
Answer:
((7
Step-by-step explanation:
how many arrangements are there of the letters in the word: CHAPTERS
Answer: 40320 ways
Step-by-step explanation:
From the question, we are informed that we should the number of arrangements that are in the letters in the word: CHAPTERS.
First, we should note that there are 8 letters in the word CHAPTERS, therefore the number of ways that the word can be arranged is 8! which simply means:
8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 40320 ways
Select ALL of the terms below that make the following statement true.
Every rectangle is a ___________.
A. parallelogram
B. square
C. quadrilateral
D. rhombus
Answer:
quadrilateral
Step-by-step explanation:
A rafter makes an angle of 22.5° with the roof joist, as shown
How tall is the board supporting the middle of the roof?
Answer:
≈ 5 ft
Step-by-step explanation:
Using the tangent ratio in the right triangle.
let the height of the board be h , then
tan22.5° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{12}[/tex] ( multiply both sides by 12 )
12 × tan22.5° = h , then
h ≈ 5 ft ( to the nearest whole number )
A plumber is connecting pipes in the shape of a triangle. Which of the following pipe lengths could form a triangle?
15,6,5
13,12,5
40,20,10
19,16,2
Answer: 13,12,5
Step-by-step explanation:
According to the triangles inequality : The sum of any two sides of a triangle must be greater than the third.
since [tex]6+5 =11 \ngtr 15[/tex]
[tex]20+10=30\ngtr40\\\\ 16+2=18\ngtr19[/tex]
Only pipe lengths with measure 13,12,5 can form triangle as
13+12 >5
12+5>13
13+5>12
Hence, the correct option is 13,12,5.
Need help ASAP!!!!!!
Answer:
Step-by-step explanation:
1) (x+2)(x+2)=-x-2
[tex]x^{2}[/tex] +2x +2x +4+=-x-2
[tex]x^{2}[/tex]+4x+4+x+2
[tex]x^{2}[/tex]+5x+6
2) [tex]x^{2}[/tex] +4x +12 -16x +24=0
[tex]x^{2}[/tex] -12x+36=0
3) (x-4)(x+1)
x=4 and/or x=-1
4) (x-5)(x-6)
x=5 and/or x=6
5) (x-7)(x+2)
x=7 and/or x=-2
6) [tex]x^{2}[/tex]+3x-10=0
(x-5)(x+2)
x=5 and/or x=2
7) [tex]x^{2}[/tex]+x-20
(x-5)(x+4)
x=5 and/or x=-4
Hello, I don’t understand this equation and the steps to do it so could you help me out?
Circumference= C=(pie)d
Solve for d in the equation.
Answer:
c is circumference which is equal to 3.14 multiplied by d
Step-by-step explanation:
what is 0.4 rounded? is it possible to turn it into another pair of decimal numbers or can I only change it to a whole number?
Answer:
Im a little confused on what your asking but for 0.4 as a decimal is 0.4,for a fraction 0.4 is 2/5 and for a percent 0.4 is 40%
Step-by-step explanation:
I hope this helps!!
Point A is at (3, 2.5) and point B is at (3, 1.4) on a coordinate grid. The distance between the two points is . Input numbers and decimal point only, such as 5.8.
Answer: 2.5-1.4=1.1 your welcome
Answer:
1.1
Explanation:
If you subtract 2.5 by 1.4, you get 1.1
I'VE SAVED THE DAY MARK ME THE BRAINLIEST
toby has $13 to buy t-shirts for his bowling team. Each t-shirt costs $4. How many t-shirts can he buy?
Answer:
3
Step-by-step explanation:
13 ÷ 4 = 3.25
but you wont by .25 of a shirt so he can only buy 3 shirts
15. Mr. Taylor rides his moped down the country road in front of his house. His wife and their two sons ride bicycles in the opposite direction on the same road. If they leave at the same time and Mr. Taylor travels 24 mi/hr while Mrs. Taylor and the boys travel 8 mi/hr, how much time will pass before they are 24 mi apart?
Answer:
b67
Step-by-step explanation:
Johan is buying 3 tickets for each of 2 movies. Each ticket costs $11.75. How much money will Johan spend?
Answer:
Johan spends $70.50.
Step-by-step explanation:
3 * 2 * 11.75 = 70.50
trigonometry ratio of multiple angles
Answer:
See Attached
Step-by-step explanation:
See Attached for proof of RHS = LHS
HELP PLS MY MOM IS GONNA BE MADDDD
5/8 ÷ 1/4
5/8 • 4/1
5/2
Answer:
2.5 If I am right
Step-by-step explanation:
5/8 divided by 1/4= 2.5
I think
Please Help ASAP!!!!!
Answer:
3.05 ft
Step-by-step explanation:
24 Which expression 18 a factor of 81.x2 – 25?
Answer:
[F]Step-by-step explanation:
9x-5 is a factor of [tex]81x^{2} -25[/tex]
On a coordinate plane, a triangle with side length of 5 has points (negative 4, 1), (0, 4), (4, 1). A triangle with a side length of x has points (negative 2, negative 1), (0, negative 2), (2, negative 1).
The smaller triangle is the image of the bigger triangle after a sequence of transformations. What is the value of x?
x =
units
Answer:
X=2.5
Step-by-step explanation:
On Edge