the function h(t)=-4.9t^2+19t+1.5 describes the height in meters of a basketball t seconds after it has been thrown vertically into the air.what is the maximum height of the basketball? round your answer to the nearest tenth
Answers
we have
h(t)=-4.9t^2+19t+1.5
This function represent a vertical parabola open downward
The vertex represent a maximum
using a graphing tool
see the attached figure
please wait a minute
The vertex is the point (1.94, 19.92)
therefore
the maximum height of the basketball is 19.9 meters
Related Questions
Find the equation for the line that passes through the point (-4,-3) and that is perpendicular to the line with the equation y=3/4x-1
Answers
Given,
The coordinate that lie on the line is (-4, -3).
The equation of line is y = 3/4x-1.
The standard equation of line is,
[tex]y=mx+c[/tex]Here, m is the slope of the line.
On comparing, the slope of the line y = 3/4x-1 with the standard equation of line then m = 3/4.
The relation of two perpendicular line is,
[tex]\begin{gathered} m_1\times m_2=-1_{} \\ \frac{3}{4}\times m_2=-1 \\ m_2=\frac{-4}{3} \end{gathered}[/tex]The equation of line passing through the point (-4,-3) and perpendicular to line y = 3/4x-1 is,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=\frac{-4}{3}(x-(-4)) \\ y+3=\frac{-4}{3}(x+4) \\ 3y+9=-4x-16 \\ 3y=-4x-25 \\ y=\frac{-4x-25}{3} \end{gathered}[/tex]Hence, the equation of line perpendicular to y = 3/4x-1 is y = (-4x-25)/3.
calculate the female's BMI. Round your answer to one decimal place.
Answers
For the 17 year old female with:
Weight: 145 lbs
Height: 5'4''→64 inches
[tex]BMI=\frac{703w}{h^2}[/tex]w= weight (pounds)
h= height (inches)
Replace the given values in the formula to determine the girl's BMI
[tex]\text{BMI}=\frac{703\cdot145}{(64)^2}=24.89[/tex]The girl's BMI is 24.89
A helthy weight is considered to be w
consider functions h and k h(x) = 5x^2-1k(x) = square root 5x+1
Answers
Given:
[tex]h(x)=5x^2-1\text{ and }k(x)=\sqrt{5x+1}[/tex]Required:
We need to find the function h(k(x)) and k(h(x)).
Explanation:
[tex]Substitute\text{ }h(x)=5x^2-1\text{ in }k(h(x))\text{ to find }k(h(x)).[/tex][tex]k\lparen h(x))=k(5x^2-1)[/tex][tex]Repalce\text{ }x=5x^2-1\text{ in }k(x)=\sqrt{5x+1}\text{ and substitute in }k\lparen h(x))=k(5x^2-1).[/tex][tex]k\lparen h(x))=\sqrt{5\left(5x^2-1\right)+1}[/tex][tex]=\sqrt{5\times5x^2-5\times1+1}[/tex][tex]=\sqrt{25x^2-5+1}[/tex][tex]=\sqrt{25x^2-4}[/tex][tex]=\sqrt{5^2x^2-2^2}[/tex][tex]k(h(x))=\sqrt{(5x)^2-2^2}[/tex][tex]Substitute\text{ }k(x)=\sqrt{5x+1}\text{ in }h(k(x))\text{ to find }h(k(x)).[/tex][tex]h(k(x))=h(\sqrt{5x+1})[/tex][tex]Repalce\text{ }x=\sqrt{5x+1}\text{ in }k(x)=5x^2-1\text{ and substitute in h}\lparen k(x))=h(\sqrt{5x+1}).[/tex][tex]h(k(x))=5(\sqrt{5x+1})^2-1[/tex][tex]h(k(x))=5(5x+1)-1[/tex][tex]h(k(x))=5\times5x+5\times1-1[/tex][tex]h(k(x))=25x+5-1[/tex][tex]h(k(x))=25x+4[/tex][tex]h(k(x))=5^2x+2^2[/tex]We get
[tex]k(h(x))=\sqrt{(5x)^2-2^2}[/tex]and
[tex]h(k(x))=5^2x+2^2[/tex]We know that
[tex]\sqrt{(5x)^2-2^2}\ne5^2x+2^2[/tex][tex]k(h(x))\ne h(k(x))[/tex][tex]Recall\text{ that if }k(h(x))=h(k(x))\text{ then h and k are inverse functions.}[/tex]Final answer:
[tex]For\text{ x}\ge0,\text{ the value of h\lparen k\lparen x\rparen\rparen is not equal to the value of k\lparen h\lparen x\rparen\rparen.}[/tex][tex]For\text{ x}\ge0,\text{ functions h and k are not inverse functions,}[/tex]Some the quadratic equation by completing the square.x^2+4x-11=0First choose the appropriate form and fill in the blanks with the correct numbers. Then solve the equation. If there’s more than one solution separate them with commas.
Answers
By completing the square, we have:
[tex]\begin{gathered} x^2+4x=11 \\ x^2+4x+2^2=11+2^2 \\ (x+2)^2=11+4 \\ (x+2)^2=15 \end{gathered}[/tex]Take the square root of both sides
[tex]\begin{gathered} (x+2)=\pm\sqrt[]{15} \\ x=+\sqrt[]{15}-2\text{ OR x= -}\sqrt[]{15}-2 \\ x=3.8729-2\text{ OR -3.8729-2} \\ x=1.873\text{ OR -5.873} \end{gathered}[/tex]what is a quadrilateral with 4 congruent sides and 4 right angles called?
Answers
what is a quadrilateral with 4 congruent sides and 4 right angles called .......................
a Parallelogram with four congruent sides and four right angles.
8 singles, 10 fives, 2 twenties, and 3 hundred dollar bills are all placed in a hat. If a player is to reach into the hat and randomly choose one bill, what is the fair price to play this game?
Answers
The total number of bills are 23.
The probability to get single = 8/23
The probability to get five = 10/23
The probability to get twenty = 2/23
The probability to get a hundred = 3/23
So, the fair price to play this game is calculated below:
[tex]\begin{gathered} \text{fair price}=1\times\frac{8}{23}+5\times\frac{10}{23}+20\times\frac{2}{23}+100\times\frac{3}{23} \\ =\frac{8}{23}+\frac{50}{23}+\frac{40}{23}+\frac{300}{23} \\ =\frac{8+50+40+300}{23} \\ =\frac{398}{23} \\ =17.30 \end{gathered}[/tex]Thus, the fair price to play this game is $17.30
Evaluate the expression 25 – 14 +3.
Answers
ANSWER
14
EXPLANATION
We want to evaluate the expression given:
25 - 14 + 3
First, let us evaluate the subtraction (25 - 14). We are left with:
11 + 3
Now, evaluate:
14
That is the answer
What is the approximate area of the circle? Use 3.141 for pi and do not round your answer.
Answers
The radius of the circle is 2 units and the value of pi is 3.141.
Hence the area of the circle is given by:
[tex]\begin{gathered} A=\pi\times r^2 \\ A=3.141\times2^2 \\ A=12.564 \end{gathered}[/tex]Hence the area is 12.564 square units.
A rectangular garden is 42ft wide and 72 ft long.A blueprint is created using a scale of 1in:6ft.Find the length and width of the blueprints and do not include units in yours answers.A. Identify the length on the blueprint.B. Identify the width on the blueprint.
Answers
EXPLANATION
As we already know, scale factor is the number by wich all the components of an object are multiplied in order to create a proportional enlargement or reduction.
First, we need to turn 6ft into inches units in order to have same magnitudes.
1 ft = 12 inches
So, the relationship is now 1in: 12 in
Scale factor = blueprint size / garden size
Isolating the blueprint size:
BluePrint size = Scale Factor * Garden Size
So, replacing terms:
----> The width will be 42* 1/12 = 3.5
----> The length will be 72 * 1/12 = 6
Answers:
A. The length of the blueprint is 6
B. The width of the blueprint is 3.5
Which inequality represents the phrase, the quotient of w and four is at least 3.
Answers
The inequality that represents the phrase is:
[tex]\frac{w}{4}\ge3[/tex]Hello, what I guess I might want to understand is where to plug in the certain numbers/variables I am given. thank you
Answers
Solution
The given equation to get the accumulated amount is
[tex]\begin{gathered} A=Pe^{rt} \\ \text{Where r = rate = 10\%}=\frac{10}{100}=\text{ 0}.1 \\ t\text{ = time in years} \\ P\text{= Amount invested}=\text{ \$6000} \\ A=\text{ Accumulated amount = 2 }\times6000\text{ = \$12000 } \end{gathered}[/tex]Therefore, by substituting in these values, t will be given as
[tex]\begin{gathered} 12000\text{ = 6000}\times e^{0.1\times t} \\ \frac{12000}{6000}=e^{0.1t} \\ 2=e^{0.1t} \\ \ln \text{ 2 = 0.1t} \\ 0.6931471806=0.1t \\ t\text{ =}\frac{0.6931471806}{0.1} \\ t\text{ = }6.931471806 \\ t\approx6.9\text{ years to 1 decimal place} \end{gathered}[/tex]t approximately = 6.9 years to 1 decimal place.
If one sticker is 10 cents and Lia wants 64 stickers how much money does she have to pay?
Answers
Solve this problem using a rule of three
1 stick ------------------------ 10 cents
64 stickers ------------------ x
x = (64 x 10) / 1
x = 640 / 1
x = 640 cents
Lia needs to pay 640 cents
1 dollar ----------------- 100 cents
x ---------------- 640 cents
x = (640 x 1) / 100
x = 640/100
x = 6.4 dollars
Lia needs to pay $6.4 dollars
Kylee manages a small theme park and she has been analyzing the attendance data. Kylee finds that the number of visitors increases exponentially as the temperature increases, and this situation is represented by the function f(x) = 4x. Kylee also finds a linear equation that models the number of people who leave the park early depending on the change in temperature, and it is represented by g(x) = −x + 5. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents.
Answers
Thus, the solution is (1,4) and that represents the number in which the number of visitors incoming when the temperature is increasing matches the number of visitors leaving early when the temperature is decreasing.
1) The solution to both functions is that point that is located at the intersection of the curve and the line.
2) So, let's solve this system of equations:
[tex]\begin{gathered} \begin{matrix}y=4^x\end{matrix} \\ y=-x+5 \\ \end{gathered}[/tex]Note that we can apply the Substitution Method:
[tex]\begin{gathered} 4^x=-x+5 \\ \ln4^x=\ln_(-x+5) \\ x\ln(4)=\ln_(-x+5) \\ x=\frac{\ln(-x+5)}{\ln(4)} \\ \frac{\ln \left(-x+5\right)}{\ln \left(4\right)}=x \\ \frac{\ln \left(-x+5\right)}{\ln \left(4\right)}\ln \left(4\right)=x\ln \left(4\right) \\ \ln \left(-x+5\right)=x\ln \left(4\right) \\ \ln \left(-x+5\right)=2\ln \left(2\right)x \\ e^{\ln \left(-x+5\right)}=e^{2\ln \left(2\right)x} \\ -x+5=4^x \\ -(1)+5=4^1 \\ 4=4 \\ x=1 \end{gathered}[/tex]With the quantity of x=1 we can plug it into the second formula:
3)
[tex]\begin{gathered} y=-x+5 \\ y=-1+5 \\ y=4 \end{gathered}[/tex]4) Thus, the solution is (1,4) and that represents the number in which the number of visitors incoming when the temperature is increasing matches the number of visitors leaving.
Which expression represents the relationship between the step number n and the total number of small squares in the pattern? A Step 1 Step 2 Step 3 n²-n n2-1 n²+n n²+1
Answers
We can see in the sequence is :
[tex]0,3,8[/tex]That is a squar of side 1 minus one square so the solution will be:
[tex]n^2-1[/tex]and we can replace the first 3 steps to be sure of the answe so:
[tex]\begin{gathered} 1\to1^2-1=0 \\ 2\to2^2-1=3 \\ 3\to3^2-1=8 \end{gathered}[/tex]what are the x and y intercepts of the linear function given by the equation 2x+5y=-10
Answers
In order to find the x-intercept of the function, you need to evaluate the function for y = 0, so:
[tex]\begin{gathered} 2x+5y=-10 \\ y=0 \\ 2x+5(0)=-10 \\ 2x=-10 \\ x=-\frac{10}{2} \\ x=-5 \end{gathered}[/tex]So, the x-intercept is x = -5
In order to find the y-intercept of the function, you need to evaluate the function for x = 0, so:
[tex]\begin{gathered} 2x+5y=-10 \\ x=0 \\ 2(0)+5y=-10 \\ 5y=-10 \\ y=-\frac{10}{5} \\ y=-2 \end{gathered}[/tex]Therefore, the y-intercept is y = -2
Find the modulo class to which the number belongs for the indicated modulo system.14, modulo 2
Answers
Given:
Given the number 14.
Required: Modulo class where 14 belogs
Explanation:
For the case of mod 2, there are 2 modulo classes, from 0 to 1, equivalent to the remainder when a number 'n' is divided by 2.
14 is divisible by 2. So, the remainder of 14 divided by 2 gives 0. Hence 14 belongs to the modulo class [0].
Final Answer: 14 belongs to the modulo class of 0.
Can I get help with B? I just need to find the standard deviation
Answers
Given the set of data:
11, 7, 14, 2, 8, 13, 3, 6, 10, 3, 8, 4, 8, 4, 7
Let's find the standard deviation.
To find the standard deviation, apply the formula:
[tex]s=\frac{\sqrt{\Sigma(x-\mu)^2}}{n-1}[/tex]Where:
x is the data
u is the mean
n is the number of data = 15
To find the mean, we have:
[tex]\begin{gathered} mean=\frac{11+7+14+2+8+13+3+6+10+3+8+4+8+4+7}{15} \\ \\ mean=\frac{108}{15} \\ \\ mean=7.2 \end{gathered}[/tex]Hence, to find the standard deviation, we have:
[tex]\begin{gathered} s=\sqrt{\frac{(11-7.2)^2+(7-7.2)^2+(14-7.2)^2+(2-7.2)^2+(8-7.2)^2+(13-7.2)^2+(3-7.2)^2+(6-7.2)^2+(10-7.2)^2+(3-7.2)^2+(8-7.2)^2+(4-7.2)^2+(8-7.2)^2+(4-7.2)^2+(7-7.2)^2}{15-1}} \\ \\ s=\sqrt{\frac{188.4}{14}} \\ \\ s=\sqrt{13.457} \\ \\ s=3.7 \end{gathered}[/tex]Therefore, the standard deviation is 3.7
xzANSWER:
3.7
after a raise Alex salary increased from 30000 anually to 31590 find the percent
Answers
intial value = 30,000
final value = 31,590
30,00 ( 1 + x) = 31,590
Solve for x ( increase in decimal form)
30,000+ 30,000x = 31,590
30,000x = 31,590-30,000
30,000x =1,590
x= 1,590/30,000
x= 0.053
Multiply by 100
0.053 x 100= 5.3%
Solve the inequality. −2x+3>x−18 Enter the exact answer in interval notation.
Answers
Step 1
Given;
[tex]-2x+3>x-18[/tex]Required; To solve the inequality
Step 2
Bring like terms together
[tex]-2x-x>-18-3[/tex]Step 3
Simplify
[tex]-3x>-21[/tex]Step 4
Multiply both sides by -1
[tex]-3x(-1)<-21(-1)_{}[/tex]Step 5
Simplify
[tex]3x<21[/tex]Step 6
Divide by 3 and get the answer
[tex]\begin{gathered} \frac{3x}{3}<\frac{21}{3} \\ x<7 \\ In\text{ in}terval\text{ notation;} \\ (-\infty,7) \end{gathered}[/tex]Hence, the exact answer in interval notation is;
(-∞,7)
Line k has an equation of y = x + - 2/7. Line L includes the point (7,-2) and is perpendicular to
line k. What is the equation of line L? Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answers
Answer:
y = -x+5
Step-by-step explanation:
y-(-2) = -1(x-7)
y+2 = -x + 7
y = -x + 7-2
y = -x + 5
A bank offers a CD that pays a simple interest rate of 2.5%. How much must you put in this CD now in order to have $4,000 for a home-entertainmentcenter in 2 years.
Answers
The formula to calculate Simple Interest is given as
[tex]I=\frac{\text{PRT}}{100}[/tex]The question provides the following parameters:
[tex]\begin{gathered} R=2.5 \\ T=2 \end{gathered}[/tex]If the amount to be had now is $4000, which is inclusive of the interest to be had over the period, this means that
[tex]P+I=4000[/tex]If we substitute the value for I, we have a new equation, such that
[tex]\begin{gathered} P+\frac{\text{PRT}}{100}=4000 \\ \therefore \\ P(1+\frac{RT}{100})=4000 \end{gathered}[/tex]Substituting the values into the equation, we can solve for P as
[tex]\begin{gathered} P(1+\frac{2.5\times2}{100})=4000_{} \\ P(1+0.05)=4000 \\ 1.05P=4000 \\ P=\frac{4000}{1.05} \\ P=3809.52 \end{gathered}[/tex]The answer is $3,809.52
how many hours would it take for sally and steve?
Answers
Answer:
It would take 2.7 hours
Explanation:
To know how many hours they take together, we need to add the inverse of the time that they take to paint, so
[tex]\frac{1}{8}+\frac{1}{4}=\frac{8+4}{8(4)}=\frac{12}{32}=0.375[/tex]Because Sally takes 8 hours and Steve takes 4 hours to paint the room. Finally, we need to find the inverse of 0.375, so
[tex]\frac{1}{0.375}=2.7\text{ hours}[/tex]So, they would take 2.7 hours to paint the room.
the sum of z and 24 is equal to 116
Answers
Given that the sum of z and 24 equals 116, we can represent this statement as follows
We can then proceed to solve the equation by following the steps below:
[tex]z+24=116[/tex]Step 1: subtract 24 from both sides
[tex]z+24-24=116-24[/tex]Step 2: simplify the expression
[tex]z=92[/tex]Thus the value of Z = 92
select three values for x that makes the inequality true
Answers
Explanation:
We would insert the values of x in the inequality. If the result is true, then the value of x makes it true
-5x + 3 > -17
if x = -3
-5(-3) + 3 > -17
15 + 3 > -17
18 > -17 (true)
if x = -2
-5(-2) + 3 > -17
10 + 3 > -17
13 > -17 (true)
if x = 0
-5(0) + 3 > -17
0 + 3 > -17
3 > -17 ( true)
if x = 4
-5(-3) + 3 > -17
You survey 100 people in your school and ask them if they feel your school has adequate parking.
Only 30% of the sample feels the school has enough parking. If you have 728 students total in your school, how many would you expect out of all the student body that felt there was enough parking?
Answers
Answer:
218 students feel there is enough parking.
Step-by-step explanation:
First, we convert 30% into a decimal by moving the decimal point over twice to get 0.30. Then, we set up this equation:
0.30 x 728 = 218.4
Now, you can't have a fraction of a person, so we round to the nearest whole number to get 218 students.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 6 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Add (c + 3) + ( + 6) Add and Subtract polynomials
Answers
The given polynomial expression is
(c + 3) + (c + 6)
By opening the brackets, we have
c + 3 + c + 6
By collecting like terms, we have
c + c + 3 + 6
2c + 9
The final answer is 2c + 9
2m + 7 =9 solution please
Answers
Hello, I need some assistance with this homework question please for precalculusHW 23
Answers
ANSWER
slope = 1
EXPLANATION
Given:
Points (1, 2) and (8, 9).
Desired Outcome:
Slope of the line
Applying the slope formula
[tex]slope\text{ = }\frac{y_2\text{ - y}_1}{x_2\text{ - x}_1}[/tex]where:
y2 = 9,
y1 = 2
x2 = 8 and
x1 = 1
Substituting the values
[tex]\begin{gathered} slope\text{ = }\frac{9\text{ - 2}}{8\text{ - 1}} \\ slope\text{ = }\frac{7}{7} \\ slope\text{ = 1} \end{gathered}[/tex]Hence, the slope of the line containing the points (1, 2) and (8, 9) is 1.
at what price should an office equipment sales representative sell computers purchased at the cost of 19,985 and of the mark on rate is 35%?
Answers
To determine the selling price we need to add %35 to the purchased prise; that is:
[tex]19985+0.35(19985)=26979.75[/tex]Therefore the seling price should be $26,979.75
Enter an equation in point-slope form for the line.Slope is -8 and (1,4) is on the line.The equation of the line in point slope form is:
Answers
y - 4 = -8 ( x - 1)
Explanations:The point slope form of the equation of a line is given as:
y - y₁ = m (x - x₁)
Where m represents the slope of the line
(x₁, y₁) are the coordinates of the point
Slope is -8 and (1,4) is on the line
m = -8
x₁ = 1
y₁ = 4
Substituting these into the equation:
y - y₁ = m (x - x₁)
y - 4 = -8 ( x - 1)