Using the vertex of the quadratic equation, it is found that the stone reaches a maximum height of 221.0625 ft after 3.5625 s.
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, considering initial velocity of v(0) = 114 and an initial height of h(0) = 18, the equation is:
h(t) = -16t² + 114t + 18.
Which is a quadratic equation with coefficients a = -16, b = 114, c = 18.
Hence:
[tex]x_v = -\frac{114}{2(-16)} = 3.5625[/tex]
[tex]y_v = -\frac{114^2 - 4(-16)(18)}{4(-16)} = 221.0625[/tex]
Hence, the stone reaches a maximum height of 221.0625 ft after 3.5625 s.
More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967
given : PK and PL - tangent
KM perpendicular KP
angle KML = 50°
Solve - angle KPL
Please help me with how to solve this, thanks!
Answer:
∠KPL = 80°
Step-by-step explanation:
As KM is perpendicular to KP, this means that KM is the diameter of the circle, as the tangent of a circle is always perpendicular to the radius.
The angle at the circumference in a semicircle is always a right angle. So if KM is the diameter then ΔKLM is a right triangle with ∠KLM = 90°
The sum of the interior angles of a triangle is 180°.
Therefore, ∠KLM + ∠KML + ∠LKM = 180°
As ∠KLM = 90° and ∠KML = 50°
⇒ 90° + 50° + ∠LKM = 180°
⇒ ∠LKM = 40°
As ∠PKM = 90° then
⇒ ∠PKL = 90 - ∠LKM
= 90 - 40
= 50°
Tangents from a common point to a circle are always equal in length, so as PK and PL are tangents from point P, then PK = PL
Therefore, ΔLPK is an isoceles triangle and so its base angles ∠PKL and ∠PLK will be equal.
Since ∠PKL = 50° then ∠PLK = 50°
Again, as the sum of interior angles of a triangle is 180°:
⇒ ∠KPL + ∠PKL + ∠PLK = 180°
⇒ ∠KPL + 50° + 50° = 180°
⇒ ∠KPL = 80°
KellyConnect
Cameron Moore
Customer: "I just purchased 9 products from you at $44.00 each. I just realized my
company offers a 20% discount on all of your products. Can you tell me what my new
total should be?"
Answer:
$316.8
Step-by-step explanation:
9 x 44 = 396
396 × 0.80 = $316.8
or
396 * 0.20 = 79.2
396 - 79.2 = $316.8
Use the equation below to find c, if a=43 and b= 53.
C= = 180-a-5
Answer:
180-a-5
180-43-5
180-48
180-48=132
c=132
without solving what can you tell about the solution to this equation?
Answer:
A
Step-by-step explanation:
B could be any number, and given that there is no sum, you cannot possibly determine what number B is.
Answer:
A
Step-by-step explanation:
An infinite solution has both sides equal.
In question 1, the left part is equal to the right part
Joshua spends 25 minutes of each day reading. He reads d days a week. Let m represent the number total minutes of reading a week. Write an equation to represent the situation. help I didn't study for math class and I have a test
Answer:
25 x D = Y
Step-by-step explanation:
Example: Say he reads for three days a week.
25 x 3 = 75
or 6 days
25 x 6 = 150
or 4
25 x 4 = 100
Expand the logarithmic expression log3(2xy3z5). Question 9 options: A) 2(log3x + 3log3y + 5log3z) B) log32x + log3y3 + log3z5 C) log32 + log3x + 3log3y − 5log3z D) log32 + log3x + 3log3y + 5log3z
Answer: D
Step-by-step explanation:
[tex]\log _{3}\left(2 x y^{3} z^{5}\right) \\ =\log _{3} 2+\log _{3} x+\log _{3} y^{3}+\log _{3} z^{5}[/tex]
[tex]\left(\because \log _{c}(a \cdot b)=\log _{c} a+\log _{c} b\right)[/tex]
[tex]=\log _{3} 2+\log _{3} x+3 \log _{3} y+5 \log _{3}z \rightarrow \left(\because \log _{c} a^{b}=b \log _{c} a\right)[/tex]
Therefore, Option D is the correct answer
What is the value of 5^3i^9
Answer:
5^(3)i^(9)= five cubes times i to the power of 9=125i
Step-by-step explanation:
Raise 5 to the power of 3
rewrite i9 as (i^4)2^i
so, you get 125((i^4)^2i)
i^4=1
125(1^2i)
125i
if z=-1-v3i and 26 = a +bi, then a =
and =
Find the area of the figure.
A: 24.5 ft²
B: 44 ft²
C: 49 ft²
D: 14.8 ft²
Answer:
49ft²
Step-by-step explanation:
A=bh
A=bh=9.8·5=49
Solve the system of equations.
5x−4y=−10
y=2x−5
Answer:
x = 10
y = 15
Step-by-step explanation:
5x − 4y = −10 ⇒ ( 1 )
y = 2x − 5 ⇒ ( 2 )
Let us find the value of x.
For that, we can replace y with ( 2x - 5 ).
Let us take equation 1.
5x − 4y = −10
5x - 4 ( 2x − 5 ) = -10
5x - 8x + 20 = -10
-3x = -20 - 10
-3x = - 30
Divide both sides by ( -3 ).
x = 10
And now let us find the value of y.
Let us take equation 2.
y = 2x − 5
y = 2 × 10 - 5
y = 20 - 5
y = 15
Answer:
X=10
Step-by-step explanation:
5x-4y=-10.....1
y=2x-5......2
sub 2 into 1
5x-4(2x-5)=-10
5x-8x+20=-10
5x-8x=-10-20
-3x=-30
x=10
sub x=10 into 2
y=2(10)-5
y=20-5
y=15
I need this answer fast please factorise the following 16gh2 – 8hi + 24h =
Answer: 8h(2gh - i + 3)
Step-by-step explanation:
factorise 8 out as 8 is a comon factor of 16, 8 and 24
factorise h out together with 8 because all of them have h
The Diameter of the medal is 6cm , thickness is 0,035cm determine the radius of the medal
A clothing manufacturer has the marginal revenue function MR(x)=30-0.2x, 0 ≤ x ≤ 100 (in dollars per suit), where x is the number of suits sold each week. Then the total revenue from selling 60 suits is $
Based on the marginal revenue function for the clothing manufacturer, the total revenue from selling 60 suits is $1,440.
What is the total revenue from selling the suits?
The marginal revenue function of 30 - 0.2x is the differentiated revenue function.
Performing an integration will therefore give us the revenue function as:
= 30x - 0.1x²
Now that we have the revenue function and know that x = 60 suits, the revenue is:
= (30 x 60) - (0.1 x 60²)
= 1,800 - 360
= $1,440
Find out more on the revenue function at https://brainly.com/question/19755858.
Consider the sequence below:
5, 8, 13, 20, 29 …
What is the 10th term of the sequence?
Its counting by odd numbers
3, 5, 7, 9, 11, 13, 15, 17, 19, 21
5,8,13,20,29,40,53,68,85,104,125
Answer:
40,53,68,85,104,125,148, 173, 200, 229
If prices increase at a monthly rate of 0.1%, by what percentage do they increase in a year?
Answer:
Step-by-step explanation:
Since the prices increase at a monthly rate of 0.1% per month. To find the percentage do they increase a year, we need to convert 0.1% to a decimal.
So here how we do it. We put 0.1 percent on the numerator because it a small number which is what we want over 100 like this:
[tex]\frac{0.1}{100}[/tex]
Now when plugging this into your calculator you get:
0.001
.So what do we do with this number?
We now times it by 12 like this:
0.001 x 12 which gives us:
0.012
So we can convert this back to a percentage by moving the decimal by 2 places to the right which gives us 1.2%.
Another way we could of done this without doing the long way to figure it out is by multiplying 0.1 times 12 which still gives us 1.2%
evaluate F (-1) where f (x) is the piece wise function graphed below
Check the picture below.
ithout graphing, determine the number of solutions to the system of equations.
2x−10y=−2
y=x/5−1
Select the correct answer below:
no solution
one solution
infinitely many solutions
Answer:
No solution
Step-by-step explanation:
(I am going to use substitution)
2x−10y=−2
y=x/5−1
(Substitute the y into the other problem)
2x - 10 (x/5 -1) = -2
2x - 2x + 10 = -2
10 = -2
No solution
Hope this helps :)
A runner's journal shows the number of miles run each day for a week:
Sunday: 1 miles
Monday: 4 miles
Tuesday: 7 miles
Wednesday : 10 miles
Thursday: 13 miles
Friday: 16 miles
Saturday:
Based on the arithmetic sequence how many miles are planned for Saturday?
The number of miles planned on Saturday is 19 milea
What is an arithmetic sequence?This means the sequence where the difference between one term and the next term is a constant.
In this case, the following information are illustrated:
Sunday: 1 miles
Monday: 4 miles
Tuesday: 7 miles
Wednesday : 10 miles
Thursday: 13 miles
Friday: 16 miles
As we can see there's a difference of three between them. This can be seen as:
= 4 miles - 1 mile
= 3 miles
Therefore, the number planned on Saturday will be:
= Friday + 3 miles
= 16 miles + 3 miles
= 19 miles
Learn more about sequence on;
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#SPJ1
The set of ordered pairs below is a relation. {(1, 5), (0, 2), (-1, -1), (-2, -4)} What is the range of the relation?
Answer:
{ - 4, - 1, 2, 5 }
Step-by-step explanation:
the range is the values of y from the ordered pairs in the relation
range = { - 4, - 1, 2, 5 }
convert y = -0.5(x + 4)^2 - 2 standard form
Answer:
I think the answer is: y = 0.5x^2 + 4x + 6, <3
Step-by-step explanation:
please help i will give brainliest
Answer:
[D] 1/14
Step-by-step explanation:
Given that:
What is the probability of picking an orange marble and flipping tails?
Solution:
First let see how many orange marbles are there:
As we can see there is 1 orange marble out of 7 total. The probability of picking an orange marble is 1/7.
Now let see how many side a coin have:
As we can see the probability of flipping tails is 1/2 because 1 side is tails out of 2 sides total.
Now multiply both together:
(1/7)× (1/2) = (1×1)/(7×2) = 1/14
This represents the probability of getting an orange marble and flipping tails.
In additionally 1/14 can't be simplify anymore.
Kavinsky
Answer:
[D] 1/14
Step-by-step explanation:
Knowing that there are 5 purple marbles, 1 brown marble, 1 orange marble. Since, on the given question all we need to know is the total marbles and the orange marbles.
Which the probability is 1/7
Now for the coin.
Knowing that there are two sides on a coin
Heads and tails (1/2)
Which is only 1/2 also known as 50% probability.
Now multiply straight across:
1/2 × 1/7
⇒ 1 × 1 = 1
⇒ 2 × 7 = 14
Thus, the answer is 1/14
can't be farther simplify.
[RevyBreeze]
what number is 90% of 140?
126
Step-by-step explanation:A percentage is a proportion of some whole number. There are 2 ways to find percentages. Firstly, you can multiply by a decimal, or you can use a shortcut.
Multiplying with Decimals
You can always rewrite percentages as decimals. To do this move the decimal point 2 digits to the left. This means that 90% becomes 0.90. Then multiply this decimal by the whole number to find the correct percentage.
0.90 * 140 = 126Shortcut
Because 90% is a multiple of 10%, we can use a shortcut. First off, find 10% of 140. To find 10% of any number, move the decimal 1 digit to the left. This means 10% of 140 is 14.0. Next, 90% is 10% less than 100%. So, subtract 10% from 140 to find 90%.
140 - 14 = 126Answer:
126
Step-by-step explanation:
We need to find 90% of 140.
90% is the same as 0.9 or 9/10.
140 can be written as 14 x 10.
Multiply 14 x 10 with 9/10.
⇒ 14 x 10 x 9/10
[The 10 and 1/10 cancel out by cross multiplication]
⇒ 14 x 9
⇒ 126
An arithmetic series contains 14 numbers. The first number is 12. The last number is 38. What is the sum of the series?
312
350
494
700
Answer: The answer is B:350
Step-by-step explanation:
edge
Answer:
B
Step-by-step explanation:
Got it right
30x³ + 10x²
Help me please
*basically you write the function in its simplest term where you cannot
simplify it further
So:
[tex]30x^3+10x^2 = 10(3x^3+x^2) = 10x^2(3x+1)[/tex]
Answer: [tex]30x^3+10x^2[/tex] when factorized ⇒ [tex]10x^2(3x+1)[/tex]
Hope that helps!
A cardboard box, which has the shape of a parallelepiped, has the following sizes: 35 cm by 27 cm
(rectangular base). The height of the box is - 27 cm. Calculate the volume of the box.
Answer:
25,515
Step-by-step explanation:
35 x 27 x 27
945 x 27
25,515
Cooper's family is going to relax at the beach all day! In preparation, Cooper made s sandwiches for them to eat when they get hungry. Cooper put 3 slices of turkey and 3 slices of ham on each sandwich.
Pick all the expressions that represent how many slices of meat Cooper used on the sandwiches.
help i need help i mark branliest
Answer:
48°
Step-by-step explanation:
Vertically opposite angles are equal. Angle 7 is vertically opposite to angle 5.
Answer:
The measure of angle 7 is 48 degrees
Step-by-step explanation:
Angle 5 and 7 are opposite angles. Opposite angles are congruent.
Solve the equation. \dfrac34 =m+\dfrac14 4 3 =m+ 4 1 start fraction, 3, divided by, 4, end fraction, equals, m, plus, start fraction, 1, divided by, 4, end fraction m=m=m, equals
Answer:
[tex]\boxed{\dfrac{1}{2} = m}[/tex]
Step-by-step explanation:
Given equation:
[tex]\dfrac{3}{4} = m + \dfrac{1}{4}[/tex]
Step-1: Subtract 1/4 both sides
[tex]\dfrac{3}{4} = m + \dfrac{1}{4}[/tex]
[tex]\dfrac{3}{4} - \dfrac{1}{4} = m[/tex]
[tex]\dfrac{2}{4} = \boxed{\dfrac{1}{2} = m}[/tex]
Callie runs 30 minutes a day. She has already run 90 minutes this week. How many days will it take her to run at least 240 minutes?
Which fraction represents the decimal 0.8888...?
StartFraction 80 Over 99 EndFraction
StartFraction 1,111 Over 1,250 EndFraction
Eight-ninths
Nine-eighths
Answer:
8/9
Step-by-step explanation:
A fraction that has denominator factors of 2 or 5 (only) will be finite in length. It will not be a repeating decimal fraction. This eliminates choices B and D.
The number of 9s in the denominator of a repeating decimal fraction will be equal to the number of repeating digits. The fraction 0.8888... has one repeating digit (8), so it can be written as 8/9.
_____
Additional comment
The fraction 80/99 will be the 2-digit repeating decimal 0.808080...
The fraction 1111/1250 evaluates to 0.8888, a 4-digit decimal fraction that does not repeat.
__
A fraction such as 0.142857...(6-digit repeat) can be written as ...
124857/999999 . . . . denominator has 6 nines
This fraction reduces to 1/7.
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[tex] \color {blue} \rule {1pt} {100000pt} [/tex]