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.
Please help me solve this problem
Select the step in the solution that FIRST shows an error.
Step 1: 4x – 10 = 10
Step 2: 4x = 20
Step 3: 4x = 5
Step 4: X = 1.25
Step 1
Step 2
Step 3
Step 4
Answer:Step 3
Step-by-step explanation:
PLEASE HELP ASAP!!!
OK SO I SOLVED ALL OF THIS: It costs a company $20 per box to make pocket-sized stuffed animals. The company also has a fixed manufacturing cost of $2300. The owners are trying to calculate their cost for making boxes of animals. --Function Rule: c(x) = 20b + 2300.
BUT I NEED HELP WITH THIS!!! Use your function rule to find out how many boxes of stuffed animals can the company manufacture for $5000? SHOW WORK.
basically just show the work to find out what "b" would have to be in order for the
answer to be $5,000 i would appreciate it so much :) please help this is due today :(
Answer:
The company can manufacture 135 boxes of stuffed animals for $5000
Step-by-step explanation:
To find b, substitute $5000 for c(x), so
5000 = 20b + 2300Then subtract 2300 from both sides of the equation, so
5000 (-2300) = 20b + 2300 (-2300)2700 = 20bFinally divide both sides of the equation by 20, so
2700/20 = 20b/20135 = bTo check your answer substitute 135 in as b...
c(x) = 20(135) + 2300c(x) = 5000FOR A TEST!! HELP! Complete the similarity ratio for the similar triangles.
Answer:
add them up
Step-by-step explanation:
add 8 10 10 and 80 25 20
Judy has 2 3/4 bags of rock that she wants to use in her yard. Each bad will cover 310.2 sq ft. How many square feet will Judy be able to cover if she used all the bags of rocks? Round up your answer to the neatest tenth place.
Answer:
853.1 sq ft
Step-by-step explanation:
Total bags of rock = 2 3/4
Each bag will cover 310.2 sq ft
How many square feet will Judy be able to cover if she used all the bags of rocks?
Total Square feet covered = number of bags of rock × area covered by each bag
= 2 3/4 × 310.2 sq ft
= 11/4 × 310.2 sq ft
= 853.05 sq ft
To the nearest tenth
= 853.1 sq ft
CAN YOU PLEASE HELP ME CORRECT ANSWER GETS BRAINLIST !
Answer:
25
Step-by-step explanation:
7^2+24^2=625 the sqr root of 625 is 25
Answer:
Answer is 25
Step-by-step explanation:
[tex]24x^{2} +7x^{2} =25x^{2}[/tex]
What addition statement does this show?
A. 10 + 3 = 13
B. 10 + (–3) = 7
C. –10 + 3 = –7
D. –10 + (–3) = –13
please answer as soon as you can!<3
Answer:
I think the answer is A sorry if I am wrong
Step-by-step explanation:
Answer:
The answer is b
Step-by-step explanation:
10 + (-3) = 7
two intersecting lines cannot be both parallel to the same line ?
True or false
Answer:
true it is true two inter
What is the solution to the system of equations?
y= 1/3x-10
2x + y = 4
34756Step-by-step explanation:
Which figure has the largest shaded region?
Answer:
is A
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Both the others have 3/4 shaded c has less
Ms. Pitt went to dinner with her family. The bill came to $55 left a 20% tip. How much money did Ms. Pitt spend in all?
The average of your 3 quiz grades is 17 points. Two of your quiz grades are 14 points and 19 points. Write and solve an equation to find the score of your third quiz.
Answer:
The equation would be 14+19+x=51, and the 3rd quiz score would be 18.
Step-by-step explanation:
To get to the average, you have to add all the quiz scores and divide by the number of quizzes. If you work backwards, you can multiply the average by the number of quiz scores, which is 51. Then you subtract the known test scores, and you get your answer.
Noah pays $7.65 for a cappuccino on days he's running late to work. One week, he was late on Monday, Wednesday, and Friday. How much did he spend (in $) on cappuccinos that week? $
Answer:
Amount Noah spent on cappuccino for that week = $22.95
Step-by-step explanation:
Noah pays $7.65 for a cappuccino on days he's running late to work
Cost of cappuccino per day = $7.65
One week, he was late on Monday, Wednesday, and Friday.
That is 3 days in a week
How much did he spend (in $) on cappuccinos that week? $
Amount Noah spent on cappuccino = cost of cappuccino per day × 3 days
= $7.65 × 3
= $22.95
Amount spent on cappuccino for that week = $22.95
Albie's total income is $695.25 in a week
where his sales are $2870. If he earns a
commission of 7.5% of his sales, what is
his retainer? can you tell me how to work it out aswell please
Answer:
Step-by-step explanation:
7.5/100= .075
$580000 x .075 = $43,500 commission
Markus receives dollar bills from his grandfather for one week. On the first day he received $1; on the second day he received $2, on the third day he received $4, and on the fourth day he received $8. If this continues, how much money will Markus have in total by the end of the week?
(Don't forget your units.)
Answer:
$127
Step-by-step explanation:
1+2+4+8+16+32+64=127
The second the is doble the first day, the third day is double the second day, the fourth day is double the third day, keep on continuing the patern.
Answer: Markus will receive $64 dollars at the end of the week.
Step-by-step explanation: 1*2=2 2*2=4 4*2=8 8*2=16 16*2=32
32*2=64
Anthony says that the expression abc has three terms because it uses three different variables. Critique Anthony's reasoning and explain whether he is correct.
Answer:
Anthony's reasoning is incorrect
Step-by-step explanation:
The expression abc is not made up of three terms because it is just an entity. For the expression to be called a three term expression, each of the variables must be separated using mathematical signs. For example, the expression a + b + c can be referred to as three terms because each variables are separated by a plus sign. In this case they are different entity.
From the above explanation, we can conclude that Anthon's reasoning is incorrect. The expression abc is just one term not three terms.
Deon has $600 in his saving account
•He spends $15 per month on Netflix
•He spends $5 per month in Hulu
If he does not make any more purchases, select all of the months that he can continue to have the subscription before he goes into debt.
Answer:
30 months total
Step-by-step explanation:
15+5=20
600÷20=30
PROBLEM I WITHOUT A CALCULATOR)
1. A room is warming up such that the temperature rise, in degrees Fahrenheit, is proportional
to the time the room has been heating. After 4 minutes, the room temperature rose 12 °F.
(a) What is the constant of proportionnlit for the
Please help
Answer:
12 minutes I think question kinda confusing
Can u guys PLEASE ANSWER THIS QUESTION ASAP URGENTLY
Find the equation of the parabola in general form
Answer:
x^2-4x+3
Step-by-step explanation:
Since the zeroes of the quadratic are 1 and 3, we can set up an equation in factored form:
(x-1)(x-3)
=x^2-4x+3
We can further check that this is the right answer by evaluating it at the vertex:
(2)^2-4*2+3=-1
Since that corresponds to the graph, the answer is x^2-4x+3
Please help asap
25m^2+30m-30m-36
Answer:
(5m+6) (5m-6)
Step-by-step explanation:
That's how you factor it since +30 and -30 cancel out
An element's identity is determined by the number of
Answer:
number of protons
Step-by-step explanation:
The identity of an element is determined by the number of protons. One cannot alter the number of protons without altering the identity of the element. By adding a proton, the atomic number increases by one and the element identity changes. Number of neutrons can be altered to create isotopes.
Is 5.1 times 10 to the power of 9 a scientific notation?
Answer:
yes
Step-by-step explanation:
hope it helps
it will be written as 5.1×10^9
Answer:
yes
Step-by-step explanation:
A number in scientific notation consists of the product of a number from 1 to under 10 and an integer power of 10.
5.1 is a number from 1 to under 10.
10^9 is an integer power of 10.
Therefore, 5.1 * 10^9 is a number written in scientific notation.
0.409 +0.681
can you add this with the repeating decimals?
Answer:
Yes, you can and the answer would be 1.09.
Step-by-step explanation:
Vanessa wanted to buy chocolate online. The Chocolatier A offers 2 pounds of chocolate for
$32.50, while the Chocolatier B offers 2 pounds of the same chocolate for $35.00. Which
company is offering the lowest price per pound?
Both companies have the same price
Chocolatier B
Chocolatier A
Answer:
Chocolatier A has the lower price.
Step-by-step explanation:
32.50 < 35
:( can sum1 please help me I got 15min till its due and well my grades are due in 5 and I'm really suck at this question
Answer:
14 is the answer your welcome
Two shapes with equal perimeter are pictured below.
What is the measure, in units, of CD¯¯¯¯¯¯¯¯?
Answer:
Measure of CD = 17 units
Step-by-step explanation:
Perimeter of a polygon = Sum of measures of all sides of the polygon
Perimeter of the given rectangle = 2(length + width)
= 2[(x + 3) + (2x - 1)]
= 2(3x + 2) units
Perimeter of triangle EFG = EF + FG + GE
= (x - 7) + (4x - 8) + (3x + 1)
= (8x - 14)
= 2(4x - 7) units
Since, perimeters of both the figures are equal,
2(3x + 2) = 2(4x - 7)
3x + 2 = 4x - 7
4x - 3x = 7 + 2
x = 9
Measure of CD = (2x - 1)
= 2(9) - 1
= 17 units
If km and np are parallel lines and m
Answer:
60 degrees
Step-by-step explanation:
WILL GIVE BRAINLIEST. Will report if answer is absurd What is the trademark of a linear table?
Answer:
You can tell if a table is linear by looking at how X and Y change. If, as X increases by 1, Y increases by a constant rate, then a table is linear. You can find the constant rate by finding the first difference.
Step-by-step explanation:
Hope this helps!
find the value of 1/2×3/5 +1/2×2/5 by using suitable property.
please answer this friends
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{5}[/tex] + [tex]\frac{1}{2}[/tex] × [tex]\frac{2}{5}[/tex] ( perform multiplication before addition )
= [tex]\frac{3}{10}[/tex] + [tex]\frac{2}{10}[/tex]
= [tex]\frac{5}{10}[/tex] ( divide numerator/ denominator by 5 to simplify )
= [tex]\frac{1}{2}[/tex]
Answer:
0.5
Step-by-step explanation:
first put the given below:
1/2 × 3/5 + 1/2 × 2/5 = 0
second take the first and second for the first answer to make the whole answer:
((1/2 × 3)/5) = 0
( 1/2 ) × 3 = 1.5
1.5/5 = 0.3
FIRST SOLVATION ( ANSWER ): 0.3
third , after we take the first solvation the second is we need to compute the remaining given or number:
((1/2 × 2)/5) = 0
( 1/2 ) × 2 = 1
1/5 = 0.2
SECOND SOLVATION ( ANSWER ): 0.2
and the last but not the list , the last is add the first solvation and second solvation and you will see what is the answer:
0.3 + 0.2 = 0.5
FINAL ANSWER: 0.5
Dennis is getting balloons for his grandfather's birthday party. He wants each balloon string to be 9 feet long. At the party store, string is sold by the yard. If Dennis wants to get 69 balloons, how many yards of string will he need?
Answer:
207
Step-by-step explanation:
9ft=3yrds
3x69=207