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
40 POINTS!!!
All integers are either odd or even. Conceptually, an integer is odd if it has a remainder of 1 when dividing by 2. And an integer is even if it has a remainder of 0 when dividing by 2.
But when proving something rigorously, mathematicians use more precise definitions, like these: an integer is odd if it can be written in the form 2k + 1, where k is some integer. An integer is even if it can be written in the form 2k, where k is some integer. For example, 13 is odd because 13 can be written as 2(6) + 1.
With these definitions, use complete sentences to explain why zero is an even number.
Answer:
[tex] = > 2k + 1 \\ when \: k = 0 \\ 2(0) + 1 \\ = 1 \\ \therefore \: zero \: is \: odd \\ \\ = > 2k \\ when \: k = 0 \\ 2(0) \\ = 0 \\ \therefore \: zero \: is \: not \: even \: because \: when \: divided \: by \: 2 \: \: remainder \: is \: zero[/tex]
An artist made a 54-inch-tall statue of a former president. If the president was 6 feet tall, what scale did the artist use?
Answer:
[tex]1\text{ inch}=\frac{1}{9}\text{ foot}[/tex]
Step-by-step explanation:
To get a scale of inches to feet, divide both 54 and 6 by 54:
[tex]54\:\text{inches}=6\:\text{feet},\\\implies 1\:\text{inch}=\frac{6}{54}\:\text{ft}\implies \boxed{1\:\text{inch}=\frac{1}{9}\:\text{foot}}[/tex]
Find the circumference for the circle. use 3.14 for pi
A. 25.12 m.
B. 12.56 m.
C. 7.14 m.
D. 50.24 m.
Answer: 50.24
Step-by-step explanation:
=3.14x4 squared
=3.14x16
=50.24
Please help me with this geometry question and show work
(3) 8
Step-by-step explanation:
Note that ∆ADE is similar to ∆ABC. As such, the ratios of their legs are equal. Also note that AD = AB + BD.
BC/AB = DE/AD
BC/10 = 12/(10 + 5) = 12/15 = 4/5
or
BC = 10(4/5) = 8
Please help??? An explanation would help too and the answers
the first, (f+g)(x) is f(x) + g(x)
calculating it like:
x² + 7x + (8 -x²)
= x² + 7x + 8 -x²
= 7x + 8
you just writ it down as a calculation and calculate it. i hope that helps understanding the concept/basic idea. please let me know wich ones you need more help with.
edit1: the domain is the range of possibilities wich x we can plug into the new equation
Describe the relationship between ∠2 and ∠8
Answer:
Alternate Interior Angles
Step-by-step explanation:
Angles can be corresponding; alternate or same side; or interior or exterior. The angles 2 and 8 are on opposite sides of the transversal; this means that they must be alternate angles. Additionally, they are both within the parallel lines, so they are interior. Alternate interior angles are always congruent. Therefore, their measurements must be equal.
Answer:
They are alternate interior angles
Step-by-step explanation:
<2 and <8 are inside the parallel lines and on opposite sides of the transversal
They are alternate interior angles
CAN SOMEONE HELP ME ASAP????
Find the gradient of the line 2y = -10x + 1
Answer:
Gradient = -5
Step-by-step explanation:
The gradient of a line is the slope of the line.
The standard form of the line equation is y = mx + b
where m is the slope ( or gradient) b is the y - intercept.
Given :
2y = -10x + 1
[tex]y = -\frac{10}{2} x + \frac{1}{2}\\\\y = -5x + \frac{1}{2}\\\\Therefore , \ gradient \ is \ -5[/tex]
The gradient of the line whose equation is 2y=-10x+1 is -5.
What is gradient?Gradient could be a measure of how steep a slope or a line is.
How to calculate the gradient of the line?The equation of the road is 2y=-10x+1
y=-5x+1/2
Therefore the gradient of the line is that the coefficient of x which is -5.
Hence the gradient of the line is -5.
Learn more about gradient at https://brainly.com/question/23016580
#SPJ2
Use the Pythagorean theorem to find the missing length in the right triangle
Answer:
Hi, there your answer is 25
Step-by-step explanation:
Here's the Pythagorean Theorem formula [tex]a^{2} +b^{2}=c^{2}[/tex]
[tex]7^{2}+24^{2}[/tex]=[tex]c^{2}[/tex]
49+576=[tex]c^{2}[/tex]
625=[tex]c^{2}[/tex]
[tex]\sqrt{625}=c^{2}[/tex]
[tex]25=c[/tex]
Hope this helps :)
PLZ HELP ANY GUESS WOULD HELP
Answer:
1st onne I believe I couldd be wrong but thats what I got
Step-by-step explanation:
Find the product of (2x-3)(x-1)
Answer:
Step-by-step explanation:
[tex](2x -3)(x-1) = 2x(x-1) -3(x-1)[/tex]
[tex]=2x^2 -2x -3x +3\\= 2x^2 - 5x + 3[/tex]
Find the missing side
Answer:
x = 71.5 in
Step-by-step explanation:
Remember the SOHCAHTOA rule
Soh...
Sine = Opposite / Hypotenuse
...cah...
Cosine = Adjacent / Hypotenuse
...toa
Tangent = Opposite / Adjacent
In this case, we use: CAH.
cos(52) = 44/x
x = 44/cos(52)
x = 71.5 inches
someone please help
Answer:
sqrt(106) =c
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
5^2 +9^2 = c^2
25+81 = c^2
106 = c^2
Taking the square root of each side
sqrt(106)= sqrt(c^2)
sqrt(106) =c
Answer:
Length of missing side is 10.44/ √106.
Step-by-step explanation:
Here we have
A right triangle with
1st side = a = 5
2nd sidd = b = 9
and , we need to find 3rd side of triangle
let the 3rd side be x.
Using Pythagoras theorem
a ² + b ² = c ²
( 5 ) ² + ( 9 ) ² = ( c)²
25 + 81 = ( c) ²
106 = ( c) ²
Taking square root of each side
√106 = √ c ²
√106 = c
10.44 = c
So, missing side if triangle is 10.44 /√106.
Find Sin/Cos/Tan and Csc/Sec/Cot of A.
Answer:
Sin A = 5/13,
Cos A = 12/13,
tan A = 5/12
CSC A = 13/5
Sec A = 13/12
Cot A = 12/5
What is the value of x in the triangle?
Round your final answer to the
nearest hundredth
Given:
In a right angle triangle,
Hypotenuse = 25 cm
Base = x
Angle between base and hypotenuse = 18 degrees.
To find:
The value of x.
Solution:
In a right angle triangle,
[tex]\cos \theta =\dfrac{Base}{Hypotenuse}[/tex]
In the given right triangle,
[tex]\cos (18^\circ) =\dfrac{x}{25}[/tex]
[tex]\cos (18^\circ) \times 25=x[/tex]
[tex]0.9510565 \times 25=x[/tex]
[tex]23.7764125=x[/tex]
Round the answer to the nearest hundredth (two decimal).
[tex]x=23.78[/tex]
Therefore, the value of x is about 23.78 cm.
Lines J and k intersect at point Q and h is a straight line. What is the value of X ?
Answer:
Step-by-step explanation:
Angles on a straight line add up to 180 so 180-135 equals 45. Vertically opposite angles are equal so the second angle inside the triangle equals 100. Henceforth, we can solve this equation:
x +45+100 = 180 (angles in triangle add up to 180)
x+145=180
x=35
Vertically opposite angles are equal so x will become 35.
Hope this helps!
The figure below is a square. Find the length of side x in simplest radical form with a
rational denominator.
VT
Answer:
x = [tex]\sqrt{14}[/tex]
Step-by-step explanation:
[tex]\sqrt{7}[/tex] / sin(45) = x / sin(90) (Cause its a square, the edges are 90 degrees)
[tex]\sqrt{14}[/tex] = x / 1
x = [tex]\sqrt{14}[/tex]
You want to estimate the number of students in your school who support extra funding for the history club. You survey every ninth student who enters the
school.
Determine whether the sample is based or unbiased
Answer:
unbiased
Step-by-step explanation:
it would be biased if you lets say survey the history club kids
What is the constant of proportionality in the equation y=\dfrac{5}{9}xy= 9 5 xy, equals, start fraction, 5, divided by, 9, end fraction, x? constant of proportionality ==equals
Answer:
5/9
Step-by-step explanation:
If a variable y is directly proportional to x, then;
y = kx where;
k is the constant of proportionality
Given the expression y = 5/9 x
On comparing with the general formula;
kx = 5/9 x
k = 5/9
Hence the constant of proportionality of the expression is 5/9
Answer:
5/9
Step-by-step explanation:
i tried it on khan and its right trust me
What’s the measure of POQ?
Answer: 70 degrees 35 times 2
Please help me.....................
Answer:16500
Step-by-step explanation:
That is, for every 100 people, there are 26 people aged between 11 and 20. So 63500 will have 16500 people aged 20.
what is 200x149 who can answer that for me i need help on this my teacher said i cant use couculater
Answer:
29,800
Step-by-step explanation:
that will be 149 x 2 which equals 298
149
×2 Multiply 9 × 2 = 18
------ Keep the 8 carry the 1 multiply 4 by 2 then add 1 finally multiply 2 by 1
298
Then add two zeros at the end since we're multiplying a number with two zeros. (This method only works for numbers that end with zeros)
Final answer: 29800
work out the average speed of 40 km in 2.5 hours
Answer:
19.20
Step-by-step explanation: used
a calc
Use the sum of cubes identity to write this polynomial expression in factored form:
8x3 + 27.
Answer:
[tex] {8x}^{3} + 27 \\ = {8x}^{3} + {3}^{3} \\ let : 8x \: be \: a \\ : 3 \: be \: b \\ = > {a}^{3} + {b}^{3} : \\ {(a + b)}^{3} = (a + b)( {a}^{2} + 2ab + {b}^{2} ) \\ {(a + b)}^{3} = ( {a}^{3} + 3{a}^{2} b + 3a {b}^{2} + {b}^{3} ) \\ ( {a}^{3} + {b}^{3} ) = {(a + b)}^{3} - 3ab(a + b) \\ \therefore( {8x}^{3} + 27) = {(8x + 3)}^{3} - 72(8x + 3)[/tex]
Left parenthesis 5 plus 2 square root of 6 right parenthesis squared = a plus b square root of 6 then the value of a and b are
Answer:
The values of [tex]a[/tex] and [tex]b[/tex] are [tex]33[/tex] and [tex]\frac{20\sqrt{3}}{3}[/tex], respectively.
Step-by-step explanation:
The statement is equivalent to the following mathematic expression:
[tex]\left(5 + 2\sqrt{2})^{2} = a + b\cdot \sqrt{6}[/tex] (1)
By definition of the perfect square trinomial:
[tex]25 + 20\cdot \sqrt{2} + 8 = a + b\cdot \sqrt{6}[/tex]
[tex]33 + 20\sqrt{2} = a + b\cdot \sqrt{6}[/tex]
And by direct comparison we have the following system:
[tex]a = 33[/tex] (2)
[tex]b\cdot \sqrt{6} = 20\sqrt{2}[/tex] (3)
By (3), we solve for [tex]b[/tex]:
[tex]b = \frac{20}{\sqrt{3}}[/tex]
[tex]b = \frac{20\sqrt{3}}{3}[/tex]
The values of [tex]a[/tex] and [tex]b[/tex] are [tex]33[/tex] and [tex]\frac{20\sqrt{3}}{3}[/tex], respectively.
what is the answer? can someone help
Answer: Choice B
Explanation: The rule you use is [tex]\sqrt{m*n} = \sqrt{m}*\sqrt{n}[/tex]
Answer:
Step-by-step explanation:
A: is not the answer. The answer is √144 which is 12
B: is correct. You can do it this way, by breaking the 9 and 16 apart.
C: I don't know exactly what the logic of 36 is, but it is not the right answer.
D: I can't explain why the choice would be division. It is multiplication of some sort. D is incorrect.
Part A
Whose scatter plot matches the data, and what is wrong with the incorrect scatter plot?
Answer: hello your question has some missing data attached below is the missing data
answer:
The second scatter plot
Step-by-step explanation:
The scatter plot that matched the data is the second scatter plot while the first scatter plot wrongly represents the data because values of the Iron not present in the data is also represented in the scatter plot and also some values present in the data table is also missing in the First scatter plot
Answer:
Hello, I am currently doing the same assignment and the brothers scatter plot would be wrong.
Step-by-step explanation:
If you do not believe me then check and see how the table says the iron used were 2, 3, 4, 5, 6, 7, 8, and 9 but in the brothers scatter plot it is shown to have the irons down as 1, 2, 3, 4, 5, 6, 7, and 8.
(in other words the other person who answered is correct)
Please help me I put 100 points for anyone who helps me
Answer:
a)
The discount id 40%, so the function is:
d = 0.4pb)
p = 100 ⇒ d = 40p = 200 ⇒ d = 80p = 300 ⇒ d = 120p = 400 ⇒ d = 160p = 500 ⇒ d = 200The graph is attached
c)
p = $85 ⇒ d = 0.4*$85 = $34Sale price is:
CP = p - d = $85 - $34 = $51Answer:
please give me some thanks please good morning
can you guys help me fill the right angle measures
Answer:
3 = 20
5 = 20
8= 160
Step-by-step explanation:
angle 2 and 3 are on the same line, so 180 - 160 is 20 degrees
rule of alternate interior angles: angle 5 is equal to 3
rule of alternate exterior angles: angle 8 is equal to 2
PLEASE HELP ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPp
Answer:
M1=44 M2=136 M3=44 M4=136
Step-by-step explanation:
M3= 44 so M1=44 due to opposite angles being equal
then if two of the angles add to 88
360-88= 272
divide 272 by 2 as M2 and M4 are equal
272/2=136
Answer:
m∠1 = 44°
m∠2 = 136°
m∠4 = 136°
Step-by-step explanation:
m∠1 explanation:
I got it from m∠3 since they're both congruent
m∠2 explanation:
Since we already have the measure of 3 and 1, we can easily add both of the measures (44 + 44 = 88°) then subtract it from 360° (total) = 272°
Then since both measures (2 and 4) are congruent (measuring the exact same length and angle) we can divide 272° ÷ 2 = 136°
m∠4 explanation:
I got it from m∠2 since they're both congruent
A telephone technician charges $45.00
per hour plus a $50.00 service charge.
Your father's firm hires him to hook up
his company's phone system.
Here is the cost function used to
represent this situation in terms of the
number of hours worked:
c(h) = 45h + 50
Find the total charges if it takes the telephone 4.5 hours to complete the task
