Answer:
6 seconds after launch.
Step-by-step explanation:
You should make sure there aren't odd symbols in your question when you post it.
Assuming it is just the equation -5x^2 + 20x + 60, if you graph it you can see the path of the ball. at x=0 this is the starting point It then hits the ground when it touches the x axis. So this is finding zeroes of a quadratic.
You could do this several ways; find a way to factor it, guess and check, the quadratic formula or completing the square. I will complete the square as that is what I am most used to. If you would like to see another let me know.
The first step in completing the square is making sure the x^2 has a coefficient of 1, so now it has -5 so we have to factor out -5 from the equation.
-5x^2+20x+60 = -5(x^2 - 4x - 12)
Now you only really need to focus on the factored expression, but I will continue writing everything. The next step is to find (b/2)^2 where b is the coefficient of the x term. In this case -4. so (b/2)^2 = (-4/2)^2 = 4.
Again, focusing on x^2 - 4x - 12 you want to add and subtract (b/2)^2 from that expression. since you are adding and subtracting you are not changing the value, but we can use this.
-5(x^2 - 4x - 12) = -5(x^2 - 4x - 12 + 4 - 4)
Here you want to rearrange it a bit. Originally c was the constant term, -12, now you want it to be the positive (b/2)^2, which is positive 4. also you can combine the two other constant terms. the original c and -(b/2)^2, but I will hold off for now so I don't do too much at once.
-5(x^2 - 4x - 12 + 4 - 4) = -5(x^2 - 4x + 4 - 12 - 4)
Now you focus on x^2 - 4x + 4. Hope fully you recognize this is the same as (x-2)^2. This always happens at this step of the process. also notice -2 = b/2. Using only variables here are the first steps.
ax^2 + bx + c
a(x^2 + (b/a)x + (c/a))
a(x^2 + (b/a)x + (c/a) + (b/(2a))^2 - (b/(2a)^2)
a(x^2 + (b/a)x + (b/(2a))^2 + (c/a) - (b/(2a))^2)
a((x + b/(2a))^2 + (c/a) - (b/(2a))^2)
Again, being able to make x^2 - 4x + 4 into (x-2)^2 or x^2 + (b/a)x + (b/(2a))^2 into (x + b/(2a))^2 willa lways happen. this is because if you expand (x + b/(2a))^2 you always get x^2 + (b/a)x + (b/(2a))^2.
Now I would combine the -12-4
-5(x^2 - 4x + 4 - 12 - 4) = -5((x - 2)^2 - 12 - 4) = -5((x - 2)^2 - 16)
If you redistribute the -5 you get vertex form, but I am going to stop here because I will just undo that in the next step. So this is the form you want. Finally we can find when it equals 0. So, you set this equal to 0 and use algebra to solve.
-5((x - 2)^2 - 16) = 0
Divide both sides by -5
(x-2)^2 - 16 = 0
add 16 to both sides
(x-2)^2 = 16
Take the square root of both sides, but also count botht he positive and negative version of the answer. the reason is both 2 and -2 squared get you 4.
x - 2 = +/-4
I am using +/- to indicate I am using both positive and negative 4. Now though add 2 to both sides. since you have +/- 4 you are going to get two different results. -4+2 and 4+2
x = -2 and 6.
now, the question wants times after x=0 (the start) so you only get 6. so x=6, or in other words 6 seconds after launch.
Let me know if you have any questions.
Answer:
6
Step-by-step explanation:
sorry no step by step explanation because I’m in a rush please mark me as brainliest bye have a great day !!! :D
For this problem you have to solve for m
Answer:
81
Step-by-step explanation:
RZT = 137
RZS = 56
SZT = 137 - 56 = 81
Sara was choosing songs for her "Birthday Dance Party" shuffle tonight. She wanted to choose: 3 of her 8 Beyonce songs, 4 of her 12 Justin Timberlake songs, 2 of her 5 Drake songs, and finish it off with either Micheal Jackson or the Beatle's version of Happy Birthday. How many different ways can she make her Birthday song mix?
Answer:
554400
Step-by-step explanation:
To answer this question, we use combination as we are just interested in selection rather Than arrangement.
Beyonce songs ; 3 from 8 = 8C3
Justin ; 4 from 12 = 12C4
Drake ; 2 from 5 = 5C2
Version of happy birthday = 1 from 2 = 2C1
Recall :
nCr = n! ÷ (n-r)!r!
However, the answers can also be obtained using a calculator :
8C3 * 12C4 * 5C2 * 2C1 = 554400 different mix
Please help me solve my problem!!!
Answer:
FH is the smallest angle since it is lesser than all the other ones.
I need help with this trig question
===========================================================
Work Shown:
Apply the cosine ratio to find the adjacent side AB
cos(angle) = adjacent/hypotenuse
cos(B) = AB/BC
cos(62) = AB/12
12*cos(62) = AB
AB = 12*cos(62)
AB = 5.6336587534307
AB = 5.6 cm
Make sure your calculator is in degree mode.
Figure A is a scale image of Figure B.
What is the value of x?
NO LINK. OR I WILL REPORT YOU.
Answer:
4.4
Step-by-step explanation:
x / 4 = 11 / 10
x = ( 4 x 11 ) / 10
= 44 / 10
x = 4.4
Answer:
5
Step-by-step explanation:
To measure scale factors, you have to measure how much units apart each triangle is, and apply the same length to x on figure A.
Here is the equation I used:
10-4=6
11-6=5
Both triangles are 6 units in difference.
Seventy weather balloons were sent up. Twenty-eight were found. What percent wer ound? 17
Step-by-step explanation:
let the percent of found balloons be x
given,
total number of balloons= 70
number of found balloons= 28
according to the question,
x% of 70= 28
x/100 × 70 = 28
x=40
hence 40% of the balloons were found
Can someone help me?It's urgent and thank you!
Answer:
575.71
Step-by-step explanation:
Year 1: 960 x .88 (100%-12%)=844.80
Year 2: 844.80 x .88 =743.424
Year 3: 743.424x.88=654.21
Year 4: 654.21 x .88=575.71
how do I even solve this??
Please answer thanks! Brainliest
Step-by-step explanation:
The last two answers is correct
Answer:
4
Step-by-step explanation:
The answer to T - H is negative
2/9 en numero decimal porfavor
me urge
Answer:
0.22222222222222
Step-by-step explanation:
What 75 degree + 105 degree ?
Answer:
75˚ + 105˚ = 180˚
Step-by-step explanation:
75 + 105 =
180
Hope this helps!
the ratio of blue to yellow paint when mixed to make green paint is 3:2 what percentage of the green paint is made from yellow paint
Answer:
40%
Step-by-step explanation:
3 + 2 = 5
Since 2 is the ratio of yellow paint, 2/5 x 100 = 40%
Hope this helped!
Plzz help me with this question.
Jade says that the absolute value of a number and the opposite of a number is the same thing. Is Jade correct? Use examples to help you explain.
Answer:
No, the absolute value of a number is different from the opposite.
Step-by-step explanation:
For example, the absolute value of 4 is 4.
l4l = 4
But the opposite of 4 is -4.
Absolute value is ALWAYS positive, but the opposite of a positive number is a negative number.
Peter arranges a total of 12 books on 3 shelves in the library. He puts the same
number of books on each shelf. Which picture shows the books on the shelves?
You didn't include a picture of the answer choices, but this is what the answer would look like. Pretend the different shapes represent different rows:
ΔΔΔΔ
ββββ
αααα
There are three rows. 4 Books in each row.
Select 2 answers: one for the questions A and one for the question B
Answer:
2a & 5a
Step-by-step explanation:
I don't know I guessed dont input the answers i said
Answer:
A. 0.25 inches
B. 0.125 inches
Step-by-step explanation:
A.
The smallest increment is represented by 1/4. Converting this into decimal form would make this 0.25.
Work:
1/4 = x/100
1 × 100 = 4 × x
100 = 4x
25 = x
25/100
0.25
B.
The uncertainty is what is not labeled on the ruler. We know 0.25 (1/4), 0.50 (2/4), and 0.75 (3/4) are labeled on the ruler. Out of all the options, 0.125 is not labeled. Therefore, 0.125 is the uncertainty.
Solve the system of equations -3x - 3y =18 and -4x - y = 0
Answer:
Point Form:
(2,−8)
Equation Form:
x=2 , y=−8
Step-by-step explanation:
Answer:
x=2
y=-8
Step-by-step explanation:
you could calculate it by rearranging and manipulating the equations, but this time I graphed it with desmos as two lines with an intersection
plzz help it's due today
Answer:
B
Step-by-step explanation:
Say the point below point B is point C.
AB belongs to triangle ABC.
To find hypotunuse AB, we need BC and AC so that we can use pythagorean thereom.
BC is already given --> 1.
AC is a diagonal of the rectangular prisms's base.
We already have 2 sides for the triangle that the base diagonal belong's to.
AC^2 = 4^2 + 6^2
AC^2 = 16 + 36 = 52
AC = √52
Now we have AC ad BC. We can find AB using pythagorean thereom.
AC^2 + BC^2 = AB^2
(√52)^2 + (1)^2 = AB^2
52 + 1 = AB^2
AB^2 = 53
AB = √53
option B
In the rectangle below, EI = 2x+6, FI= 5x-6, and m ZIFE = 490.
Find EG and m LIGF.
E
F
Guy
MZIG
H
G
Answer:
gyufigaruofhasidjfdskcm
Step-by-step explanation:
Consider the relation y → 4 x−1 for the domain {3, 5, 7, 9}
(a) Calculate the values for the range.
Answer:
{ 11, 19, 27, 35 }
Step-by-step explanation:
To find the range substitute each value of x from the domain into the relation
x = 3 : y → 4(3) - 1 = 12 - 1 = 11
x = 5 : y → 4(5) - 1 = 20 - 1 = 19
x = 7 : y → 4(7) - 1 = 28 - 1 = 27
x = 9 : y → 4(9) - 1 = 36 - 1 = 35
range is { 11, 19, 27, 35 }
Together, teammates Pedro and Ricky got 2679 base hits last season. Pedro had 283 more hits than Ricky. How many hits did each player have?
Pedro had base hits
Answer:
Pedro: 1481 Base hits
Ricky: 1198 Base hits
Step-by-step explanation:
First, take the total amount of base hits last season 2679, then subtract how many more Pedro has 283.
2679 - 283 = 2396 now divide the sum in half 2396 ÷ 2 = 1198 that gives you how many each player has, you're then going to add the amount that you took off to only Pedras total since he had 283 more
Pedro: 1198 + 283 = 1481
Ricky: 1198
Explain fully, please
Answer:
Step-by-step explanation:
formula of volume of cone is given so u simply substitute the values given and calculate.
Work is done for u .
Hope this helps u
Help pleaseeeeeeeeeeeeeeeeeeeeee
Answer:
i think its contrast
Step-by-step explanation:
it s sayin this awncer is equal to the other one.
There are x boys playing in the park. The number of girls in the park in equal to the square root of the number of boys. If the total number of boys and girls playing in the park is 42, find the number of boys
Suppose that your statistics professor tells you that the scores on a midterm exam were approximately
normally distributed with a mean of 78 and a standard deviation of 7. The top 15% of all scores have
been designated A’s. Your score is 89. Did you earn an A? Explain.
Answer:
YesStep-by-step explanation:
z-score representing 85% is 1.04 (from table)
Let x be the score representing the lower limit of 85%.
Use the formula to find z-scores:
z = (x - μ)/σWe have:
z = 1.04, μ = 78, σ = 7Substitute the values and solve for x:
1.04 = (x - 78)/7x - 78 = 7.28x = 85.28The lower limit of the top 15% is 85.28.
Since your score is greater than 85.28 you earned an A
We want to know what percentage of the population have college degrees. We take a sample of 100 individuals and find that 28 have college degrees. Answer the following, rounding your answers to 2 decimal places. a. What is the sample proportion? b. Find the SE. c. Construct a 95% confidence interval. d. What does this 95% confidence interval tell us about our population proportion p? (One sentence is the perfect length for an answer)
Answer:
a) p = 28/100 p = 0,28 or p = 28%
b) SE = 0,0448
c) CI 95 % = ( 0.1921 ; 0.368 )
We can support with 95 % of confidence that the proportion of people with a College degree would be found within these limits
Step-by-step explanation:
a) Sample proportion: Is the number of positive success divide by sample size
That is from 100 ( individuals) ( sample size ) it was found that 28 had College degree ( positive success)
Then p = 28/100 p = 0,28 or p = 28%
b) The standard error is
SE = (√p*q)/n
p = 0,28 then q = 1 - 0,28 q = 0,72
SE = √ (0.28)*(0.72)/100
SE = √0.002016
SE = 0,0448
c) CI = 95 % then significance level is α = 5 % α = 0.05
α/2 = 0.025
From z- table we find z(c) = 1.96
Then CI 95 % = p₀ ± z(c) * SE
CI 95 % = 0.28 ± 1.96*0.0448
CI 95 % = ( 0.28 ± 0.088 )
CI 95 % = ( 0.1921 ; 0.368 )
d) We can support with 95 % of confidence that the proportion of people with college degree would be found within these limits
Helpppp meh, 50 points and u better answer correctly!!
Answer:
yessir
Step-by-step explanation:
gimme brainliest i think its C
What is the correct value of x in the triangle
Answer: 4
Step-by-step explanation:
Using the 30°-60°-90° Triangle Theorem we know that the base side is half of the hypotenuse. That means it is half of 8 which is 4
f(x) = x^2. What is g(x)?
Answer:
Step-by-step explanation:
The standard form of the quadratic we need is
[tex]y=a(x-h)^2+k[/tex] where we have everything we need but a. That's what we will solve for.
x and y come from the coordinate given on the red graph:
x = 2 and y = 1
h and k come from the coordinates of the vertex:
(0, 0). Fill all that in and solve for a:
[tex]1=a(2-0)^2+0[/tex] and
1 = 4a so
a = 1/4 That makes our equation
[tex]y=\frac{1}{4}(x-0)^2+0[/tex] or simplified:
[tex]y=\frac{1}{4}x^2[/tex], choice B.
CAN SOMEONE PLEASE HELP ME!!!! I NEED HELP BAD