Given:
Consider the height of the rocket, in feet after x seconds of launch is
[tex]y=-16x^2+152x+74[/tex]
To find:
The time at which the rocket will reach its max, to the nearest 100th of a second.
Solution:
We have,
[tex]y=-16x^2+152x+74[/tex]
It is a quadratic polynomial with negative leading coefficient. So, it is a downward parabola.
Vertex of a downward parabola is the point of maxima.
To find the time at which the rocket will reach its max, we need to find the x-coordinate of the vertex.
If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then the vertex is
[tex]Vertex=\left(-\dfrac{b}{2a},f\left(-\dfrac{b}{2a}\right)\right)[/tex]
Here, [tex]a=-16,b=152,c=74[/tex].
So,
[tex]-\dfrac{b}{2a}=-\dfrac{152}{2(-16)}[/tex]
[tex]-\dfrac{b}{2a}=-\dfrac{152}{-32}[/tex]
[tex]-\dfrac{b}{2a}=4.75[/tex]
So, x-coordinate of the vertex is 4.75.
Therefore, the rocket will reach its max at 4.75 second.
triangle D E F with what scale factor?
When did Beethoven start to go deaf?
If he couldn’t hear, how did he write/compose music?
How did Beethoven’s deafness change the music that he wrote, as compared to the music written before he went deaf?
Did Beethoven continue to perform & conduct even when he was deaf? (Explain.)
Please list at least three musical differences between the 2 Videos, without saying that they play different instruments:
1. A bike shop rents each of its bikes for $6.50 per hour. They also charge a
$10.50 insurance fee for each rental.
What's the total cost, y of renting an bike for x hours.
Y = _?___ + __?__
Answer:
y=6.50x+10.50
Step-by-step explanation:
Answer: 17
Step-by-step explanation:
please help this is due in a few minutes
Answer:
a. 8m
b. 7cm
Step-by-step explanation:
a. Area of a square is s², where s is the side length.
To find s:
s² = 64
s = √64
s = ±8
length cannot be negative, hence it is positive 8
b. Perimeter of a square is 4s = P, where P is the perimeter and s is the side length.
4s = 28
s = 7
idk idk.. help please
Answer:
c = √58
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
Because we have a right triangle, we can use the Pythagorean Theorem to help us solve for missing side lengths:
7² + 3² = c²
49 + 9 = c²
58 = c²
c = √58
Answer: c = √58
Step-by-step explanation:
WILL GIVE YOU BRAINLIST
Ashley is putting together a square bulletin board for her new room. The area of the bulletin board is 196cm^2 . What is the length of each side of the bulletin board? shape is square
Answer:
14
Step-by-step explanation:
Area of square is side times side. So, find the square root of 196.
Answer: The answer is 14
Step-by-step explanation: If you sqaure root 196 you will get 14
Twice a number plus four equals six
Step-by-step explanation:
Let say the unknown number we dont know is x
2x+4=6
2x=6-4
2x=2
x=2/2
x=1
So the unknown number is 1
Select the correct answer from the drop-down menu.
The product of five rational numbers is positive. At most____of these rational numbers can be negative.
A.2 B.3 C.4 D.5
Answer:
4
Step-by-step explanation:
Could anyone prove this question correct... pls... I will mark branliest for step by step solution.
Answer:
C
Step-by-step explanation:
the answer is 15. hope this helps
A number x is no less than -8.
Answer:
i think it's
x is greater than or equal to -8
Step-by-step explanation:
$6.89 per pound for salmon OR $3.50 for 8 ounces (half a pound) of salmon
Answer: 6.89 per pound (assuming you meant which is the better deal)
Step-by-step explanation:
There are 16 ounces in a pound so you can multiply, 3.5 x 2 (since it is 3.5 for 8 ounces) to get 7. Therefore $6.89 for a pound is cheaper.
-0.5-(-.8)+0.8+(-.5)
Answer:
your answer is -1
Step-by-step explanation:
Help me pleaseee thank you In advance please explain to me too so i know what to do next time :)
Alan says that two lines in the coordinate plane are perpendicular if and only if the slopes of the lines are m and 1m. Identify and correct two errors in Alan’s statement.
Answer:
First, two lines are perpendicular if one has slope m, and the other has slope -1/m (Not 1m as Alan says)
That is the first error of Alan.
Now, there is another error.
If m = 0, then -1/m tends to minus infinity (in this case we would have a vertical line).
But we can not really divide by zero, so we should state that:
m can not be zero, if a line is horizontal, the perpendicular line must be vertical.
A box of baseball cards is $25.00 with %15 off. What is the sale price of the box of cards? In other words, how much is it after
take the discount off)
Answer:
21.25
Step-by-step explanation:
you would multiply 25 by 0.15 to get the percent being taken off then subtract that from your original price
The cost y (in dollars) of renting a segway for x hours is y=30x+25. Find the initial fee and the cost per hour.
Given:
The cost y (in dollars) of renting a segway for x hours is
[tex]y=30x+25[/tex]
To find:
The initial fee and the cost per hour.
Solution:
We have,
[tex]y=30x+25[/tex] ...(i)
The slope intercept form of a linear equation is
[tex]y=mx+b[/tex] ...(ii)
where, m is slope is b is y-intercept or initial value.
From (i) and (ii), we get
[tex]m=30,b=25[/tex]
The value of m is 30, so the slope is 30. It means cost per hour is $30.
The value of b is 25, so y-intercept is 25. It means the initial fee is $25.
Find the greatest common factor of 7 and 7.
Grace swam a mile in 21 minutes. Jill swam a mile in 19.47 minutes. How
much faster did Jill swim than Grace?
Answer:
1.53
Step-by-step explanation:
because 21 minus 19.47= 1.53
Answer:
1 minute and 13 seconds
Step-by-step explanation:
x2 - 14x + 47 = 0
man how df you do dis
Answer:
-2.9375
Step-by-step explanation:
2x-14x+47=0
16x+47=0
16x=-47
x=-2.9375
Answer:
x=7+√ 2 or x=7-√ 2
Step-by-step explanation:
x^2-14x+47=0
Completing the square,
x^2-14x+49-2=0
x^2-14x+49=2
x^2-7x-7x+49=2
x(x-7)-7(x-7)=2
(x-7)^2=2
x-7=√ 2 or x-7=-√ 2
x=7+√ 2 or x=7-√ 2
The graph of a system of linear equations is shown.
What is the solution of the system?
A. (3,-2)
B. (-2.5,3.5)
C. (3.5,-2.5)
D. (4,-2)
Lisa says 12 3 = 9 Kay says 12 3 = 4 Who is correct? Why?
If three quarters of a number decreased by twenty is equal to eighty two, what is that number?
A number is :
[tex]x[/tex]
_________________________________
Three quarters of it means :
[tex] \frac{3}{4}x \\ [/tex]
_________________________________
Decrease by 20 means :
[tex] \frac{3}{4}x - 20 \\ [/tex]
_________________________________
Equals to 82 means :
[tex] \frac{3}{4}x - 20 = 82 \\ [/tex]
_________________________________
What is that number ?
x asked so we must solve the above equation for x.
Let's do it....
[tex] \frac{3}{4}x - 20 = 82 \\ [/tex]
Plus sides 20
[tex] \frac{3}{4}x = 82 + 20 \\ [/tex]
[tex] \frac{3}{4}x = 102 \\ [/tex]
Multiply sides by 4
[tex]3x = 102 \times 4[/tex]
Divided sides by 3
[tex]x = \frac{102 \times 4}{3} \\ [/tex]
[tex]x = \frac{102}{3} \times 4 \\ [/tex]
Simplify
[tex]x = 34 \times 4[/tex]
[tex]x = 136[/tex]
So that number is 136 .
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
A postal carrier delivers mail to 20 mailboxes on one side of a long street. Beginning with the first mailbox, the carrrier takes 5 seconds to sort and put the mail in each mailbox, and the mailboxes are 100 feet apart. How fast (in feet per second) must the carrier walk in order to complete delivery to all 20 mailboxes in 10 minutes? Answer in decimal form as a.b (for example, 9.7).
Answer:
3.8 seconds
Step-by-step explanation:
Time taken to sort the mail is [tex]5[/tex] seconds
Let time taken to go from one mailbox to the next be [tex]x[/tex]
Distance between the mailboxes is [tex]100[/tex] ft
So, sorting the mail for one mailbox and going to the next will be done in [tex](5+x)[/tex] seconds
This will happen 19 times and 5 seconds will be needed to sort the mail for the last mail box. The carrier will have to deliver to all the 20 mailboxes in 10 minutes. So, the total time taken will be
[tex]19(5+x)+5=10\times 60\\\Rightarrow 19(5+x)=595\\\Rightarrow 5+x=\dfrac{595}{19}\\\Rightarrow x=\dfrac{595}{19}-5\\\Rightarrow x=\dfrac{500}{19}\ \text{s}[/tex]
Time taken to go from one mailbox to the other is [tex]\dfrac{500}{19}\ \text{s}[/tex]
Speed is given by
[tex]v=\dfrac{100}{\dfrac{500}{19}}\\\Rightarrow v=3.8\ \text{ft/s}[/tex]
The speed at which the carrier has to move from one mailbox to the next is 3.8 seconds.
What's the least common denominator you could use to subtract 1/3 and 1/4
Which of the following values are solutions to the inequality −6≤1+3x?
7
11. Which question can be answered using the expression
1?
4
8
A
7
Dave fills
8
gallons of punch are in the container?
of a container that holds gallon of punch. How many
(В)
of a container that holds gallon of punch. How many
4
8
gallons of punch are in the container?
7
8
gallon?
How many gallon servings are in
in gallon?
D
How many
7
8
gallon servings are in
Somebody please helppp me!
Answer:
angle 2 is 94 degrees and angle 3 is 94 degrees
Step-by-step explanation:
4x-26=3x+4
4x=3x+30
x=30
they are vertical angles meaning they are equal
what 1 2/7 divided by 5 1/7
Answer:
0.25 as a decimal and 1/4 as a fraction
Hope this helps :)
Answer: 1/4
Step-by-step explanation:
(Not really sure how to explain it, but there's the answer.)
What transformations occur for the following equation? *
y = 8(x - 1)3 + 7
Answer:
☆<¤HOPE IT WILL HELP you 》>☆
y=(8x-8)3+7
y=24x-24+7
y=24x-17
17=24x
17/24=x
SO == x-17/24 y= 17
Alexander is a stockbroker. He earns 11% commission each week. Last week, he sold $5,400 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011?
Answer: 594 and 30888
Step-by-step explanation:
5400 x 0.11 = 594
594 dollars in commission of one week
52 weeks in a year
52 x 594 = 30888 dollars made in 2011
594 dollars in commission of one week.
$30888 he make in commission in 2011.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Stocks sold= $5400
Commission each week = 11%
So, Commission on Stocks sold
= 5400 x 0.11
= 594
Thus, 594 dollars in commission of one week.
As, 1 Year = 52 weeks
So, He can make in 2011 = 52 x 594 = $30888
Learn more about Unitary Method here:
https://brainly.com/question/22056199
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