Answer:
The maximum height the rocket reaches is 16.
Step-by-step explanation:
You know that a model rocket is launched in the air and the quadratic function is modeled by the equation y = -16*x² + 32*x where x is measuring time and y is the height of the model rocket.
A quadratic function or function of the second degree is a polynomial function defined by:
y= a*x² + b*x + c
A quadratic function has a maximum or a minimum and the vertex formula is used to get the highest or lowest value of the function. When a> 0, the vertex of the parabola is at the bottom of it, being a minimum (that is, the parabola opens "upward"), and when a <0 the vertex is at the top , being a maximum (that is, the parable opens "downward").
The value of the vertex on the x-axis can be calculated with the expression [tex]x=\frac{-b}{2*a}[/tex]
The value of the vertex on the y axis must be obtained by substituting the value of the vertex on the x axis in the function y= a*x² + b*x + c
In this case, a= -16, b=32 and c=0. Since a<0 the vertex will indicate the maximum of the function.
The value of the vertex on the x-axis is [tex]x=\frac{-32}{2*(-16)}=1[/tex]
The value of the vertex on the y axis is:
y = -16*1² + 32*1
Solving:
y= -16*1 +32
y= -16 +32
y=16
The maximum height the rocket reaches is 16.
Could someone help me I’m almost done please please
y=4
Step-by-step explanation:
cube root 64
please help
write the fraction as a decimal
Answer:
it's 7 divided by 10
transfer the 0 up and make it 0.7
what is the slope of the line?? PLZ help
Find the coordinates of the midpoint of the segment with the endpoints M(-5,9) and N(-2,7).
Answer:
(-3.5 , 8)
Step-by-step explanation:
midpoint (x , y)
x = (-5 + -2) / 2 = -7/2 = -3.5
y = (9 + 7) / 2 = 16/2 = 8
Which expression does the graphic represent? 8 positive tiles. 1 tile is crossed out. 7 minus 1 7 minus (negative 1) 8 minus 1 8 minus (negative 1)
Answer:
7-(-1)
Step-by-step explanation:
Answer: Ur answer is B
Step-by-step explanation:
A number c divided by 9 is less than or equal to -23 .
Answer:
c [tex]\leq[/tex] -207
Step-by-step explanation:
Create an inequality and solve for c:
[tex]\frac{c}{9}[/tex] [tex]\leq[/tex] -23
Multiply by 9 on each side:
c [tex]\leq[/tex] -207 is the answer
Write the slope-intercept form of the equation of each line.
Answer:
1) positive 2)negative 3)negative
Step-by-step explanation:
i hope thats what your asking
Simplify the expression below:
3(4 x + 2y)
Answer:
12x+6y
Step-by-step explanation:
Thomas drew a line of best fit for the scatter plot as shown. Enter an equation for the line of best fit in slope-intercept form. The line of best fit equation in slope-intercept form is y =
Answer:
Equation of line best fits the scatter plot is y = [tex]-\frac{30}{7} x + 108[/tex]
Step-by-step explanation:
Let the equation of line be y = mx + c
where m = slope of line and c is the intercept on y -axis
from the graph intercept on y-axis is 108
and the slope of line is given by m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] where ([tex]x_2,y_2[/tex]) and ([tex]x_1,y_1[/tex]) is the points on line
let, points be (4,96) and (18,36)
on calculating this m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = [tex]-\frac{30}{7}[/tex]
Therefore equation of line best fits the scatter plot is y = [tex]-\frac{30}{7} x + 108[/tex]
1 over 8 + c = 4 over 5 whats x?
Find the value of x.
Answer:
x = 132°
Step-by-step explanation:
sum of total exterior angles = 360°
x + 147° + 81° = 360°
x + 228° = 360°
x = 360° - 228°
x = 132°
if p=3+2√2 find the values of p+1/p
Answer: 1,71572875
Step-by-step explanation: (4+2rad2)/3+2rad2
Answer:
6
Step-by-step explanation:
1/p = 1/(3 + 2sqrt2)
Multiplying by the conjugate (which you should pretty much always do to simplify), we get
(3-2sqrt2)/((3+2srqt)(3-2sqrt2))
which is
(3-2sqrt2)/(9-8) = 3-2sqrt2.
Therefore p + 1/p = 3+2sqrt2 + 3 - 2sqrt2 = 6
A mass of 50 g decreased by 17%. What is the new
mass?
Answer:
8.5g
Step-by-step explanation:
the mass decreased by 17%,so the decrease in mass 17% of 50g.17% of 50 = 0.17 × 50 =8.5 the mass decreased by 8.5g
The mass is decreased by [tex]8.5g[/tex].
What is the percentage?
A percentage is a number or ratio expressed as a fraction of [tex]100[/tex]. It is often denoted using the percent sign, "%".
Here given that,
A mass of [tex]50[/tex] g decreased by [tex]17[/tex] %.
So, in the mass [tex]17[/tex] % of [tex]50g[/tex] and of [tex]50g[/tex] is [tex]17[/tex] % is of the form:-
[tex]50=0.17[/tex] ×[tex]50=8.5[/tex]
Hence, the mass is decreased by [tex]8.5g[/tex].
To know more about the percentage
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you saved $250.00 to spend over the summer. You decide to budget $25.00 to spend a week. Define the variable and write a function that represents this situation
Answer:
200
Step-by-step explanation:
Order these Quadratic Functions from the narrowest to widest listed as 1,2,3,4
Answer:
From narrowest to widest:
1) [tex]8\cdot x^{2} + 2\cdot x +5[/tex]
2) [tex]5\cdot x^{2}-1[/tex]
3) [tex]2\cdot x^{2}+4[/tex]
4) [tex]\frac{2}{5}\cdot x^{2}+3\cdot x -5[/tex]
Step-by-step explanation:
The "width" of the quadratic function is determined by the value of the coefficient associated by the monomial of highest grade, with respect to the primitive of the quadratic function, represented by [tex]y = x^{2}[/tex], whose ruling coefficient is 1. If the ruling coefficient of the quadratic function is greater than one, then the curve becomes narrower at the same time that the coefficient increases. Otherwise, if the ruling coefficient of the quadratic function is greater than zero and less than 1, then the curve becomes wider at the same time that the coefficient approximates to zero.
Based on this considerations, we proceed to list the quadratic functions from the narrowest to widest:
1) [tex]8\cdot x^{2} + 2\cdot x +5[/tex]
2) [tex]5\cdot x^{2}-1[/tex]
3) [tex]2\cdot x^{2}+4[/tex]
4) [tex]\frac{2}{5}\cdot x^{2}+3\cdot x -5[/tex]
Lastly, we include a graphic with all polynomials (tagged as 1, 2, 3, 4) in comparison primitive function (tagged as 0).
First and second place in a contest use a ratio to share a cash prize. When first place pays $100, second place pays $60. How much does first place pay when second place pays $36?
Answer:
100/60×36
=$60 is what the first one will pay
=
Step-by-step explanation:
PLEASE SHOW FULL SOLUTIONS!!!!!! WILL MARK BRAINLIEST TO THE BEST ANSWER!!! THANK YOU AND GOD BLESS...
9514 1404 393
Answer:
x = 60y = 50Step-by-step explanation:
The linear pair at G totals 180°, so we have ...
x + 2x = 180
3x = 180 . . . . . collect terms
x = 180/3 . . . divide by 3
x = 60
__
The total of angles in the triangle is 180°, so ...
x + y + 70 = 180
60 + y + 70 = 180 . . . . substitute for x
y = 180 -130 . . . . . . . . . subtract 130
y = 50
1. 7p - 6pc + 3c - 2 Number of terms: Coefficients: Constant terms:
Step-by-step explanation:
Given:
7p - 6pc + 3c - 2
Find:
Number of terms
Coefficients
Constant terms
Computation:
Number of terms = 4
Coefficients = (7, -6, 3)
Constant terms = -2
10) Determine which of the following are functions. 11) What are the domain and range of the following relation?
Answer:
10) The first 2 on the left are functions and the one on the top right is a function, but the bottom right is not.
11) Domain = (2, 8, -1, 0) Range = (5, -2, 4, 5)
Solve for p. p/8 + 12 = 36
9514 1404 393
Answer:
p = 192
Step-by-step explanation:
p/8 +12 = 36 . . . . . given
p/8 = 24 . . . . . . . . .subtract 12
p = 8·24 . . . . . . . . .multiply by 8
p = 192
wait can sm1 like pls help me i have a d in this class
In a two-digit number, the unit's digit is 2 more than that of the ten's digit. The sum of the digits is 27 less than the number. Find the product of the digits of the number
Answer:
15 is the product of the digits of the number
Step-by-step explanation:
Let the two digit number be xy
Unit digit is 2 more than ten’s digit
y - x = 2 ••••••(i)
Secondly;
x + y = (10x + y) - 27 •••••(ii)
From i, y = x + 2
Put this into ii
x + x + 2 = 10x + x + 2 - 27
2x + 2 = 11x - 25
11x - 2x = 25 + 2
9x = 27
x = 27/9
x = 3
From above;
y = x + 2
y = 3 + 2 = 5
The product of the numbers xy will be 5 * 3 = 15
In the previous election 6,400 people voted. What is the percent decrease in actual voters?
A 8.6%
B. 11.4%
C 12.5%
D. 14.3%
Answer:
14.3%
Step-by-step explanation:
6400-5600=800
800/6400×100=14.3
Answer:
14.3
Step-by-step explanation:
4(46+2b= 3(b-11
what is the answers
Answer:
4(4b+3)+2b=3(b-11)16b+12+2b=3b-3318b+12=3b-3318b-3b=-33-1215b=-45b=-45/15b=-3Which of the following is an example of a unit rate?
a. John earns $15 for mowing three lawns
b. Kelly types 90 words per minute
c. Indra earns two detentions every two weeks
d. Three bags of chips cost $3.75
Answer:
I think it's b or c because a unit rate is a ratio which the two terms are in different units
1) Name the triangle.
scalene and acute
() isosceles and acute
() isosceles and right
()) scalene and right
Answer:
Isosceles and right triangle
What is 42653 rounded to the nearest ten
Answer: 42650
Step-by-step explanation:
The tens place is behind the ones place.
The number in the tens place in 42653 is 5.
So to round to the nearest tens you have to change three to 0 because if the number in the ones place is 5 or more, then the number in the tens place would be 1 higher than it used to be while the number in the ones place turns to 0.
However if the number in the ones place is less than 5, then that's the only thing that changes, the ones place would change into a '0.'
Hope that helped!
42650 is the value of the 426563 when rounded to the nearest ten.
What is place value?The value a digit in a number represents based on where it is in the number is known as place value.
Given, the number 42653 which is rounded to the nearest ten value needs to find. Since,
The one's place is in front of the tens place. In the number 42653, the tens place value is 5. The number three must be changed to 0 in order to round to the next tens because, if the number in the one's place is 5 or greater, the number in the ten's place would be 1 higher than it was previously while the number in the one's place would become 0. The one's place would change to a "0" if the number in the one's place is less than 5, but that is all that changes.
Therefore, When rounded to the nearest ten, 42650 represents the value of 426563.
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Triangle ABC is shown. DE is a straight line with D on AC and E on BC AB = 46m, EC = 18m, CD = 29m and ED = 20m. Calculate the length AD.
Answer:
37.7m
Step-by-step explanation:
Triangle ABC is shown. DE is a straight line with D on AC and E on BC AB = 46m, EC = 18m, CD = 29m and ED = 20m. Calculate the length AD.
We solve using Similarity Theorem
BA/AC =BD/DC
46/AD+29 = 20/29
Cross Multiply
46 × 29 =20 (AD + 29)
1334 = 20AD + 580
20AD = 1334 - 580
20AD = 754
AD = 754/20
AD = 37.7m
Nick divides 527 baseball cards evenly into 17 stacks. How many baseball cards are in each stack?
This is division btw.
Answer:
Its 31
Step-by-step explanation:
Just Use A Calculator
HELP PLZ
Solve each proportion for the variable
Answer:
x = -1
Step-by-step explanation:
4/12 can be simplified to 1/3
1 x+2
--- = --------------
3 2x+5
Using cross products
1 ( 2x+5) = 3 (x+2)
Distribute
2x+5 = 3x+6
Subtract 2x from each side
2x+5-2x = 3x+6-2x
5 = x+6
Subtract 6 from each side
5-6 = x+6-6
-1 =x
Answer:
Step-by-step explanation:
Key skills: Proportions, One variable equations, Multiplication, Distribution Property
1) The best approach to this problem is with cross multiplication.
Cross multiplication is where we multiply the numerator of one fraction with the denominator of the other fraction, and the denominator of one fraction with the numerator of the other fraction.
2) Here we would do: 4(2x+5) and 12(x+2)
3) Since this is a proportion --> 4(2x+5) = 12(x+2)
4) Now, we use distribution property to expand both.
4(2x+5) --> 8x+ 20 12(x+2) --> 12x+24
5) With simplifying we can solve for x:
8x+20=12x+24 We then move the 12x to the left side, and the 20 to the right side: 8x-12x=24-20Now we combine like terms: -4x=4Then we divide by -4 on both sides to solve for x. x=-1If you plug in x=-1 back into the equation: 4/12= 1/3
4/12 does equal 1/3 so x= -1 is the right answer.
Hope you have a nice day and understood this problem explanation!! :D