Answer:
Part 1) [tex]f(x)=-5(x-10)(x+2)[/tex]
Part 2) After 10 seconds.
Step-by-step explanation:
We have the function:
[tex]f(x)=-5x^2+40x+100[/tex]
Where f(x) represents the height x seconds after it is released into the air.
Part 1)
First, let's distribute a -5 out of the function:
[tex]f(x)=-5(x^2-8x-20)[/tex]
Now, let's factor. We want to pick two number that multiplies to -20 and adds to -8.
We can use -10 and 2. So:
[tex]f(x)=-5(x^2+2x-10x-20)[/tex]
Factor:
[tex]\begin{aligned}f(x)&=-5(x^2+2x-10x-20) \\ f(x)&=-5(x(x+2)-10(x+2)) \\ f(x)&=-5(x-10)(x+2) \end{aligned}[/tex]
Hence, our factored form is:
[tex]f(x)=-5(x-10)(x+2)[/tex]
Part 2)
We want to find after how many seconds does it take for the projectile to reach the ground.
If it reaches the ground, the height above the ground, f(x), will be 0.
So, we can set f(x) equal to 0 and solve for x. Instead of using the original equation, we can use the factored form. So:
[tex]0=-5(x-10)(x+2)[/tex]
Zero Product Property:
[tex]x-10=0\text{ or } x+2=0[/tex]
Solve for x:
[tex]x=10 \text{ or } x=-2[/tex]
Since x measures time, -2 does not make sense in this context.
Therefore, our solution is x=10.
So, after 10 seconds, the projectile will hit the ground.
WILL GIVE BRAINLIEST NEED DONE ASAP
Write an equation in standard form of the line that passes through the given point
and has the given slope.
1. (2,-4), m= 2/3
2. (5, -3); m = 2
3. (6,0); m = 3/4
4. (-1, 2); m = 7
5. (-3,-5)m= 1/3
6. (4,0); m = -5
Answer:
y=2/3x-16/3
Step-by-step explanation:
ok ill show you how to do one question since the rest will take too long so what you do is
equation is y=mx+b right
so you have slope and these points (2,-4) and m=2/3
y=2/3x +b right
now all you do is sub in x and y which are ur given points
-4=2/3 (2) +b
now you solve for b
-4 = 4/3 + b
-4-4/3 = b
-12/3 - 4/3 = b
-16/3=b so therefore
y=2/3x-16/3
Do imaginary numbers follow the rules of algebra?
Answer:
no
Step-by-step explanation:
I need help ill giv3 brainlyness
Answer:
i think the answer if (-9,-3)
Step-by-step explanation:
Tell me if i got it right so i can see where i made a mistake IF i got it wrong
could someone help me with this ? i need to find m
the three angles of a triangle always add up to 180 degrees.
So, add the three angles together!
2x - 12 + 2x + 17 + 9x - 7 = 180
Group the similar numbers together.
13x -2 = 180
13x = 182
x = 14
Plug x in to 2x + 17
14*2 + 17 = 45
mX = 45 degrees
Answer:
m∠X = 45°
Step-by-step explanation:
All angles in a triangle add up to 180°
2x - 12 + 2x + 17 + 9x - 7 = 180
13x = 180 - 17 + 12 + 7
13x = 182
x = 14°
m∠X = 2x + 17
sub x = 14° into m∠X
2(14) + 17
m∠X = 45°
What is the equation of the line that passes through the point (-6,3) and has a slope of -2/3
Answer:
The answer is y=-2/3x-1
Step-by-step explanation:
y-y=m(x-x1)
y-3=-2/3(x-(-6))
y-3=-2/3x-4
+3 +3
y=-2/3x-1
if 6 litres of petrol cover's 60km , how many litres of petrol will a car need to cover 50km
Answer:
5 litres
Step-by-step explanation:
60 ÷ 10 = 6
50 ÷ 10 = 5
So 5 litres of petro
I hope this helped, please mark Brainliest, thank you!
2(x2 + 6) – 3 vy when x = 3 and y = 64.
Answer:
73
Step-by-step explanation:
you would do distributive property we know x= 3 so on the inside would be 32 now since we are doing distributive property you multiply 32x2 and 6x2
then you add them together and after you subtract 3 from 76 which = 73
A cook has 11.64 pints of olive oil before the dinner service. There were 5.2 pints of olive oil used during the dinner service. What amount of olive oil is left after the dinner service, with the correct number of significant digits?
A. 6.44 pints
B. 16.84 pints
C. 6.4 pints
D. 17 pints
Answer:
c
Step-by-step explanation:
a truck weighs 9,000 pounds. a repair shop sends a tow truck that can pull 5 tons.can the tow truck tow the truck? explain.
If you have 6 pieces of plywood
that are 4'x8', how many total
1xl pieces can you get out if
you use all of them?
Answer:192
Step-by-step explanation:
Calculate the area l*w or s*s
Divide the two areas to get the number of 1*1 from 1 plywood then multiply by their number which is 6 here
4*8=32/1=32*6=192
Nothing but slope.................
Answer:
1. 1
2. 3
3. 4
Step-by-step explanation:
Question
Help me -.8+ 2X = .3 - x
Step-by-step explanation:
2x+x=.3+.8
3x= 1.1/:3
x=0.366
Answer:
x = -2.566667
Step-by-step explanation:
simplify both sides
8 + 2x = 0.3 - x
8 + 2x = 0.3 + - x
2x + 8 = - x + 0.3
add x to both sides
2x + 8 + x = - x + 0.3 + x
3x + 8 = 0.3
subtract 8 from both sides
3x + 8 - 8 = 0.3 - 8
3x = -7.7
divie both sides by 3
3x/3 = -7.7/3
x = -2.566667
due 7:59 am est. Faith is saving up to buy a new bicycle. She already has $40 and can save an additional $6 per week using money from her after school job. How much total money would Faith have after 8 weeks of saving? Also, write an expression that represents the amount of money Faith would have saved in w weeks.
Answer:
After 8 weeks, Faith would have $88. money saved = 40+6w
Answer:
$88 saved in 8 weeks
Step-by-step explanation:
Part 1:
You would first set up the equation 40 + (6 x 8) = t. T would be the total money saved. You would then do 6 times 8 first, as they're in parenthesis. You would get 48. You now have 40 + 48 = t. You would now add like terms, and you would get 88 = t. You would save $88 in 8 weeks.
Part 2:
40 + 6w = t
w would represent the number of weeks, t would represent the total number of money saved.
what is the answer to (x+3)^2 +(y-6)^2
Answer:
1the answer is 1! hope this helps.
The answer is x^2+ y^2-27
8. If b(x) = -2(x-50), what is the value of
b(20)? Request
5.
For each equation, determine if x = 2 is a solution. Explain or show your reasoning.
a.
-2(x – 4) = 4
b.
26
= 13
C.
-3.8x = -7.4
4(x - 1) – 3(x - 2) = -8
d.
x=2 is a solution of equations -2(x – 4) = 4 and 26/x=13
What is Equation?Two or more expressions with an Equal sign is called as Equation.
-2(x-4)=4
-2(2-4)=4
4=4
Hence, x=2 is the solution
26/x=13
Now x=2
26/2=13
13=13
Hence, x=2 is the solution
-3.8x=-7.4
Now x=2
-3.8×2=-7.4
-7.6=-7.4
x=2 is not a solution of -3.8×2=-7.4
4(x - 1) – 3(x - 2) = -8
4(2-1)-3(2-2)=-8
4=-8
x=2 is not a solution of -3.8×2=-7.4
Hence, x=2 is a solution of equations -2(x – 4) = 4 and 26/x=13
To learn more on Equation:
https://brainly.com/question/10413253
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Mr. Chang's class has 28 students, 7 of whom are girls. Which equation shows how to determine the number of girls in
Mr. Chang's class?
o 28-4-49
0 28 x 7 - 16
017-28 - 11
o 1-28-
Answer:
Girls in Mr. Chang's class: 28 - 21 ; # girl students = # total students - # boy students ; 7 girl students.
Boys in Mr. Chang's class: 28 - 7 ; # boy students = # total students - girl students ; 21 boy students.
The amount of money that Jacob earns based on the number of hours he works is shown in the table. Find the constant of proportionality.
Answer:
Y=7.5x
Step-by-step explanation:
8-5=3 and 60-37.5 is 22.5 divide 22.5 by 3 and you get 7.5 which is the rate that he earns an hour
the length of a rectangle is 8 units greater than its width . find the dimensions when its area is 105 square units.
I hope this helps ;)
Find the distance between the two points in simplest radical form.
(1,8)(6,-4)
A recent survey by the alumni of a major university indicated that the average salary of 10,000 of its 300,000 graduates was $125,000. What is the Population?
Answer:
The population is the total number of the universities graduates i.e [tex]N = 300,000[/tex]
Step-by-step explanation:
From the question we are told that
The number of students that are consider is n = 10,000
The total number of graduates is [tex]N = 300,000[/tex]
The mean is [tex]\= x = \$125 , 000[/tex]
Here the population is The total number of graduates with value [tex]N = 300,000[/tex], this is because a population is the pool from with a sample is drawn and in this case the pool is [tex]N = 300,000[/tex] while the sample with is drawn is n = 10,000
is y=x/4 a proportional relationship
Answer:
yes
Step-by-step explanation:
The function f(x) = x/4 represents a proportional relationship.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. A straight line represents a proportional relationship. Mathematically -
y = mx + b
(y - b)/x = m [m is constant]
or
y = mx
m = y/x [m is constant]
Given is the following function -
y = x/4
We have -
f(x) = x/4
Now, we know a straight line represents a proportional relationship. The general form of equation representing the proportional relationship is -
y = mx
where - [m] is constant
y = x/4
y = (1/4)x
On comparing, we get -
m = 1/4
Hence, the function f(x) = x/4 represents a proportional relationship.
Therefore, the function f(x) = x/4 represents a proportional relationship.
To solve more questions on proportional relationship, visit the link below-
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Can someone help explain how I get the answer for this? S=R-rR solve for R
Answer:
s/(1-r)=R
Step-by-step explanation:
S=R-rR
S=R(1-r)
s/(1-r)=R
Use the graph below to answer the question. Quadrilateral PQRS will be rotated 90° clockwise about the origin resulting in quadrilateral P'Q'R'S'. Which statement is true
Answer: it’s D
Step-by-step explanation:
HELP NOW 15 Points!!!!!!!
Which expression is not equivalent to the other three?
2x + 2+ 2x + 3x – 8
4 + 7x – 2
–2 + 5x + 2x – 4
8x – x – 6
Answer:
4+7x-2
Step-by-step explanation:
i dont know how nit is the anwser put i got it right
Witch fraction is not in simplest form 5/15 or 5/12
Select all the expressions that can be used to find the price of a $400 telescope after a 32% markup. A)400 • 0.32 B) 400 • 3.2 C)400 • 1.32 D)400 + 400(0.32) E)400 • 400(1.32)
Answer:
(D) 400 + 400(0.32)
Step-by-step explanation:
We need to find the price of a $400 telescope after a 32% markup.
32% markup means increase in the cost of telescope by 32%. It can be calculated as follows :
[tex]P=400+32\% \ of\ 400\\\\=400+\dfrac{32}{100}\times 400\\\\=400+0.32(400)[/tex]
Hence, the correct expression is option (d).
Answer:
(D) 400 + 400(0.32)
Step-by-step explanation:
We need to find the price of a $400 telescope after a 32% markup.
32% markup means increase in the cost of telescope by 32%. It can be calculated as follows :
Step-by-step explanation:
what is the input value other than -7 for which h(x)=3
Answer:jrntker,fgv;rmjhnopgykjpftg.l/;[]ref
Step-by-step explanation:
wem,yk6iotfkmmkgjjjkdlmeruijtnmgjhudjmv n
Jake has $100 dollars in his wallet. He spends $15 at Tastee Sub and $10 at Wawa. As he is walking home, Jake finds a $20 bill on the ground. Then Brandon comes along and borrows $40 from jake. That night jake decided to do some chores at home and earns $35. How much does jake end up with at the end of the day
Answer: $75
Step-by-step explanation:
PLS HELP!!!!!!!!!!!!!