Using the vertex of the quadratic equation, it is found that the ball reaches it's maximum height after 2.1 seconds.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the equation is given by:
h(t) = -5t² + 21t + 120.
Meaning that the coefficients are a = -5, b = 21, c = 120.
Hence, the time at which the maximum height is reached is given by:
[tex]t_v = -\frac{b}{2a} = -\frac{21}{-10} = 2.1[/tex]
More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967
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For each decimal, find two integers closest to it. 11.6. | < 11.6< <
The decimal number 11.6 is to one decimal place, and the closest integers to 11.6 are 11 and 12
How to determine the closest integer?The decimal number is given as:
11.6
The above decimal number is between the digits 11 and 12
This means that the closest integers to 11.6 are 11 and 12
Read more about decimal at:
https://brainly.com/question/11406179
how do you find the length of a line
Answer:
You use the most important and sacred tool: ruler
Answer: By measuring with tape or ruler
Step-by-step explanation:
can anyone help pls?
[tex]7 \frac{5}{8} + 4 \frac{2}{3} [/tex]
to find:the simplest form.
solution:[tex] \frac{61}{8} + \frac{14}{3} [/tex]
[tex] = \frac{(61 \times 3) + (14 \times 8)}{8 \times 3} [/tex]
[tex] = \frac{183 + 112}{24} [/tex]
[tex] = \frac{295}{24} [/tex]
[tex] = 12 \frac{7}{24} [/tex]
hence, the correct answer is option D.
please answer this...
Step-by-step explanation:
8. Simple random sample
9. Stratified Sample
10. Convenience Sample
Just need the answer
Answer:
Step-by-step explanation: if 5/2:2/5 then 4/5 of a pint= 10/2 and you now only need 1/5 of a pint so you have to divid 5/2 by 2. that will give you 1.25 and 1.25 as a fraction is 5/4. now you need to change the fraction 10/2 so that you can add them. Equation for that is 10/2 times 2/2 that gives you 20/4 and 20/4+ 5/4=25/4 or 6 1/4(six and one fourth) of a cup
What is the percent of change from
65 to 52?
Round to the nearest percent.
Answer:
20%
Step-by-step explanation:
[tex]\frac{52-65}{65}[/tex] * 100% = -20%
Which fraction is equivalent to 4/9
A 14/19
B 2/3
C 6/11
D 8/18
Please help! Both problems are below and please make sure to answer both! Will give brainiest if possible!
Answer:
picture a is 180⁰ clockwise or counterclockwise (c)
picture b is 90⁰ counterclockwise (b)
Step-by-step explanation:
hope this helps :)
Answer:
A and B
Step-by-step explanation:
The first one is 180 clockwise…
Second picture is 90 counterwise.
I hope thi help and have a good day.
Find AC for the quadrilateral
The quadrilateral ABCD is an isosceles trapezoid, and the length of AC for the quadrilateral is 19 feet
How to determine the length of AC?The quadrilateral ABCD is an isosceles trapezoid
This means that:
Opposite sides are equalThe diagonals are also equalFrom the above highlights, we have:
AC = 7ft + 12ft
Evaluate the sum
AC = 19 ft
Hence, the length of AC for the quadrilateral is 19 feet
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Read more about quadrilaterals at:
https://brainly.com/question/5715879
Solve each equation.
a.8x=2/3
b.1 1/2=2x
c.5x=2/7
d.1/4x=5
e.1/5=2/3x
Answer:
a) x = 1/12
b) x = 3/4
c) x = 2/35
d) x = 20
e) x = 3/10
Step-by-step explanation:
a) 8x = 2/3
8x/8 = (2/3) / 8
x = 2/3 * 1/8
x = 2/24
x = 1/12
b) 1 1/2 = 2x
3/2 = 2x
(3/2) / 2 = 2x/2
3/2 * 1/2 = x
3/4 = x
x = 3/4
c) 5x = 2/7
5x/5 = (2/7) / 5
x = 2/7 * 1/5
x = 2/35
d) 1/4x = 5
1/4x * 4 = 5 * 4
x = 20
e) 1/5 = 2/3x
1/5 * 3/2 = 2/3x * 3/2
3/10 = x
x = 3/10
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What is the value of n?
Enter your answer in the box
7 cm
4 cm
8 cm
n
Answer:
n=14
Step-by-step explanation:
To find the length of the given side with length "n", we must know the relationship between the different sections when the chords cross one another.
Now, the relationship we require is that when we multiply the 2 parts of both chords together, it will be equal to the product of the two sides in the other chord. Thus;
7(8) = 4(n)
56 = 4n
14 = n
Answer number 10 please thank you
Answer:
35%
Step-by-step explanation:
Jose is wrapping a stack of 100 coins in a paper holder. Each coin is 1/8 inch thick and has a diameter of 1 inch. How many square inches of paper will Jose need to cover the stack of coins? Use 3.14 for ππ.
Answer:
10.205 inches²
Step-by-step explanation:
What is being described is essentially a cylinder (like a tin can)!Note: for this question let's assume the paper's thickness doesn't matterIf there's 100 coins, each being 1/8 inch thickThe height of the cylinder must be 100 * 1/8 = 12.5 inchesTo find the area of the bottom and top of our cylinder let's first calculate 1 side:The area of a circle = π × r²area = π × (1/8)² = π/16 inches²two circles is just double the area: 2 * π/16 = π/8Now that we know the height and the area of the top + bottomWe can now use the cylinder formula for surface areaA = 2πrh + 2πr² (notice how we've already done 2πr² with our circles!)A = 2 × π × 1/8 × 12.5 + π/8A = (13π) / 4 = (13 × 3.14) / 4 = 10.205 inches²Which of the following is the graph of f(x) = -0.5x + 3| -2?
If you mean
y=|-0.5x+3|-2The graph has been attached
If that modulus sign is typing mistake then
The yielded function is
y=-0.5x+3-2y=-0.5x+1Both graphs attached
Help asap! take your time not pushing its for my sis
Answer:
A. Whatever that is in the parenthesis should be solve first.
Answer:
A is the correct option you should always solve the bracket first if you know about BIDMAS
B- BRACKET
I- INDICES
D- DIVISION
M- MULTIPLICATION
A- ADDITION
S- SUBTRACTION
Two sides of a rectangle are (2x+5)cm and (4-x)cm. Find it's area.
Answer:
The area of the rectangle = x + 20
Step-by-step explanation:
The explanation is in the attachment
SORRY FOR MY BAD HANDWRITING
!!PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!!
use properties of logarithms to expand the logarithmic expression as much as possible.
help please!
Step-by-step explanation:
Begin by separating the division. Division in the argument of a logarithm function is equivalent to subtracting the log of the numerator and denominator:
[tex]ln( \frac{ {x}^{9} \sqrt{ {x}^{2} + 7} }{ {(x + 7)}^{7} } ) = ln( {x}^{9} \sqrt{ {x}^{2} + 7 } ) - ln(( {x + 7})^{7} )[/tex]
Multiplication under a logarithm means addition:
[tex] ln( {x}^{9}) + ln( \sqrt{ {x}^{2} + 7 }) - ln(( {x + 7})^{7} )[/tex]
Log rules say that exponents can be dragged to the front as coefficients:
[tex]9ln(x) + \frac{1}{2} ln( {x}^{2} + 7) - 7ln(x + 7)[/tex]
Diameter = 50 cm
In terms of , what is the area of the circle?
Answer:
1,962.5
Step-by-step explanation:
r=d/2
50 / 2 = 25
25 = r
A= πr²
3.14 x 25²=1,962.5
[tex]Hope[/tex] [tex]this[/tex] [tex]helps![/tex]
Solve using the square root method
Answer:
x=3 and x= -3
Step-by-step explanation:
Sorry for my handwriting I know it's not the best but I hope it helps
Answer:
x=-1.13389341903
Step-by-step explanation:
square root of 63=7.93725393319
÷-7=-1.13389341903
this should be the answer
Find the amount of time. I=$237. 90, P=$1525, r=2. 6%
Find the amount of time. __ Years
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$237.90\\ P=\textit{original amount deposited}\dotfill & \$1525\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ t=years \end{cases} \\\\\\ 237.90 = (1525)(0.026)(t)\implies \cfrac{237.90}{(1525)(0.026)}=t \implies 6=t[/tex]
A bag contains eight balls labeled 1 through 8. One ball will randomly be picked. What is the probability of picking an even number?
Answer:
Answer: 50 percent or 1/2
You and 3 friends go bowling. You bowl for 2.5 hours. You play 3 games and the total cost is $42.
Find the average rate of games per hour
Answer:
if you play 3 games and the total cost equals to 42
then just do 42 divided by 3 which is 14 so that should be your answer!
Step-by-step explanation:
im very sorry if i get it wrong im only trying to help
so i hope its correct
the slope of the line below is -3. use the coordinates of the labeled point to find a point-slope equation of the line.
Answer:
B
Step-by-step explanation:
point (5,-7) slope ( -3) form of the line would be
(Y- -7) = - 3(x-5)
y+7 = -3 (x-5)
1. Let the sample space represent all the values from 1 to 10. Let A = {1, 2, 8} and B = {2, 7}. What is the P(A ∩ B)?
A [tex]\cap[/tex] B denotes to all common elements in both A and B
Sample space=S={1,2,3,4,5,6,7,8,9,10}So
A={1,2,8}B={2,7}2 is common
Hence
A $\cap$ B={2}
Answer:
P(A ∩ B) = 1/10
Step-by-step explanation:
Given:
Sample space (S) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}A = {1, 2, 8}B = {2, 7}We can represent this information in a Venn diagram (see attachment 1).
As there are 10 equally likely outcomes (which must add up to 1), the probability of each outcome is 1/10.
Therefore, we can redraw the Venn diagram with the probabilities instead of the values (see attachment 2).
P(A ∩ B) means the probability of events A and B happening together, so it is the section of the diagram where events A and B overlap.
Therefore, P(A ∩ B) = 1/10
Which expression represents the phrase below?
8 less than the product of 6 and a number, x
A. 8 - 6x
B.6x-8
C.(6+x)-8
D.8-(6+x)
3. Which of the following points is not on the graph of y = 2x² + 3x - 10? (4,30) (6,80) (-9, 125) (-3,-1) A
Answer:
biside of A
Step-by-step explanation:
thats is the answers
PLEASE HELP I WILL GIVE BRAINLIEST I REALLY NEED IT
Given: ABCD is a trapezoid,
AD=10, BC=8,
CK- altitude of triangle ACD =30
Find: the area of ABCD
To find the area of the trapezoid we need to find the height of the trapezoid.
TrapezoidA trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.
Area of TrapezoidThe area of a trapezoid is given as half of the product of the height(altitude) of the trapezoid and the sum of the length of the parallel sides.
\rm{ Area\ of\ trapezoid = \dfrac{1} {2}\times height \times (Sum\ of the\ parallel\ Sides)
The area of the trapezoid is 54 units².
Given to us :ABCD is a trapezoid
AD=10, BC = 8,
CK is the altitude altitude
Area of ∆ACD = 30
Area of ∆ACD,In ∆ACD,
\begin{gathered}\rm { Area\ \triangle ACD = \dfrac{1}{2}\times base\times height\\\\\ \end{gathered}
Substituting the values,
30 = 1/2 * AD × CK
30 = 1/2 * 10 × CK
(30 * 2)/10 = CK
CK = 6 units
Area of Trapezoid ABCD\rm{ Area\ of\ trapezoid = \dfrac{1} {2}\times height \times (Sum\ of\ the\ parallell Sides)
Area ABCD = [tex] \frac{1}{2} \times ck \times (ad + bc)[/tex]
Area ABCD = [tex] \frac{1}{2} \times 6 \times (10 + 8)[/tex]
Area ABCD = [tex] \frac{1}{2} \times 6 \times (18)[/tex]
Area ABCD = 54 units²
Hence, the area of the trapezoid is 54 units².
x is a normally distributed variable with a mean of 32 and a standard deviation of 19 what is P(x<63)
Answer:
94.8 %
Step-by-step explanation:
mean 32 + 1.63 * SD = 63
Z-score for 1.6316 is .9484 94.8 % are < 63
A submarine traveled to St. Vincent and
back. It took four hours less time to get
there than it did to get back. The average
speed on the trip there was 15 km/h. The
average speed on the way back was 10
km/h. How many hours did the trip there
take?
Answer:
8 hrs to get there ( 12 hrs to get back)
Step-by-step explanation:
rate * time = distance distance is the same for both trips
15 km/hr * (t-4) = 10 ( t)
15t - 60 = 10 t
5t = 60
t = 12
t-4 = 8 hrs
Identify the slope and y-intercept of each of the following lines. Then graph each line.
5x - 3y = 18
Do I put the answer on the attached graph?
Answer:
Yes, but you have to write what the slope and y-intercept of the equation is as well.
Step-by-step explanation:
(Not sure if you wanted the full answer or just if you should graph it but I'm putting it here anyways :^P)
First convert the equation from standard form to slope-intercept form.
5x-3y=18 -> 5x-18-3y -> 5/3x-6=y
5/3x is the slope and 6 is the y-intercept!
Then graph the equation.
First rewrite the equation in slope intercept form
slope intercept form: y = mx + b [ where m is slope and b is y-intercept ]
[tex]\sf \rightarrow 5x - 3y = 18[/tex]
[tex]\sf \rightarrow - 3y = 18-5x[/tex]
[tex]\sf \rightarrow y = \dfrac{-5x+18}{-3}[/tex]
[tex]\sf \rightarrow y = \dfrac{-5x}{-3} + \dfrac{18}{-3}[/tex]
[tex]\sf \rightarrow y = \dfrac{5}{3}x -6[/tex]
comparing with y = mx + b, Here we can identify that the
slope: [tex]\sf \frac{5}{3}[/tex] and y-intercept: [tex]\sf -6[/tex]x-intercept: ( then y will be 0 )
[tex]\sf \hookrightarrow \dfrac{5}{3}x -6=0[/tex]
[tex]\sf \hookrightarrow \dfrac{5}{3}x=6[/tex]
[tex]\sf \hookrightarrow x=\dfrac{18}{5}[/tex]
[tex]\sf \hookrightarrow x = 3.6[/tex]
In order to graph the line
First put the x = 3.6 in the x axisSecondly put y = -6 in the y axisThen using a scale/ruler draw a straight line through this points.Graph: