An object is thrown in the air with an initial velocity of 5 m/sec from a height of 9 m. The following equation models the height of the object in meters after t seconds. How many seconds does it take for the object to hit the ground?
Answers
Check the picture below.
[tex]~~~~~~\textit{initial velocity in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&5\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&9\\ \qquad \textit{of the object}\\ h=\textit{object's height}\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-4.9t^2+5t+9\implies \stackrel{h(t)}{0}=-4.9t^2+5t+9 \implies 4.9t^2-5t-9=0[/tex]
since we don't get any neat integer values from it hmmm let's plug that in the quadratic formula to see what we get as h(t) = 0.
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{4.9}t^2\stackrel{\stackrel{b}{\downarrow }}{-5}t\stackrel{\stackrel{c}{\downarrow }}{-9}=0 \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ t= \cfrac{ - (-5) \pm \sqrt { (-5)^2 -4(4.9)(-9)}}{2(4.9)}\implies t=\cfrac{5\pm\sqrt{25+176.4}}{9.8} \\\\\\ t=\cfrac{5\pm \sqrt{201.4}}{9.8}\implies t\approx \begin{cases} 1.96~~\checkmark\\ -0.94 \end{cases}[/tex]
notice, we do not use the negative value for "t", since the seconds cannot be less than 0.
Related Questions
It took Jaytree 38 seconds to rip about half a DVD.
About what is Jaytree's "ripping rate” in DVDs per
minute?
Answers
Answer:1
Step-by-step explanation:
Which of the following is a way that anorexia nervosa is different from bulimia nervosa?.
Answers
One key difference between anorexia nervosa and bulimia is the type of nocive relationship patients with these disorders have with food.
What do anorexia nervosa and bulimia have in common?These two are eating disorders, which means they are diseases that involve nocive or abnormal relationships with food.
What makes these disorders different?Anorexia nervosa patients avoid eating, while bulimia patients eat but use purges such as induced vomit to avoid gaining weight.Patients from anorexia nervosa often have a low weight, while a patient from bulimia can still have a normal weight.Binge eating is common in bulimia but not in anorexia nervosa.Learn more about anorexia in: https://brainly.com/question/2681827
A salt-water tank needs to contain 5 gallons of water for each 1-inch fish. If lan has a 30-gallon tank, predict how many inch-long fish he can have. S
Answers
Answer:
6in
Step-by-step explanation:
Let's organize what we know.
- 5gal/1in
- 30gal tank
Since we need to find the inches of the fish he can have, we can set up a proportion like this:
5/1=30/x
We can cross multiply.
5x=1(30)
Simplify: 1*30=30
5x=30
Now we can isolate the variable.
5x=30
/5 /5
x=6
The material Santiago will use to build the ramp cost $2.20 per square foot. Find the total cost of materials for the ramp? All sides are; 21.7, 20, 12 for perimeter and 8.5 for the height.
Answers
Answer:Santiago is playing a game on his computer and is designing a ramp that bikers will jump off to land in a foam pit. His designs are shown below. Use the designs to answer each question. RAMP FOAM PIT 24 ft 21.7 ft 8.5 ft 12 ft 99 wa 20 ft 1. What is the total surface area of the ramp? 2. Santiago wants the lateral surfaces of the ramp to be painted red. How many square feet of the ramp will be painted red? 3. The material Santiago will use to build the tamp costs $2.20 per square foot. What will the total cost of building the ramp be? 4. The foam pit is a rectangular prism, but the top of the pit will be open. What is the total surface area of the foam pit? 5. The lateral surfaces of the foam pit will be lined with extra padding. How many square feet will be lined with extra padding? 6. The total cost of materials to build the foam pit is $1,285.20. What is the cost of materials per square foot? 7. Santiago's total budget for the materials to build the ramp and the foam pit is $3,000. With his current design, will be he over budget or under budget, and by how much?
Step-by-step explanation:
Santiago is playing a game on his computer and is designing a ramp that bikers will jump off to land in a foam pit. His designs are shown below. Use the designs to answer each question. RAMP FOAM PIT 24 ft 21.7 ft 8.5 ft 12 ft 99 wa 20 ft 1. What is the total surface area of the ramp? 2. Santiago wants the lateral surfaces of the ramp to be painted red. How many square feet of the ramp will be painted red? 3. The material Santiago will use to build the tamp costs $2.20 per square foot. What will the total cost of building the ramp be? 4. The foam pit is a rectangular prism, but the top of the pit will be open. What is the total surface area of the foam pit? 5. The lateral surfaces of the foam pit will be lined with extra padding. How many square feet will be lined with extra padding? 6. The total cost of materials to build the foam pit is $1,285.20. What is the cost of materials per square foot? 7. Santiago's total budget for the materials to build the ramp and the foam pit is $3,000. With his current design, will be he over budget or under budget, and by how much?
*) 3. Write the equation in slope-intercept form of the line that passes through the points (5, 4) and (-1, 6). I
Answers
Answer:
3y = -x + 17
Step-by-step explanation:
Equation of a line is in the form:
y = mx + c
where m is slope and c is intercept
Mathematically;
slope m = (y2-y1)/(x2-x1)
= (6-4)/(-1-5) = 2/-6 = -1/3
So the equation is now;
y = -x/3 + c
Multiply through by 3
3y = -x + 3c
To get c substitute the value of a point say (5,4)
x = 5 and y = 4
3(4) = -5 + 3c
12 = -5 + 3c
12+ 5 = 3c
3c = 17
c = 17/3
So the equation is
y = -x/3 + 17/3
and that is
3y = -x + 17
Kayla buys a shirt for 18. 9 she pays with a $10 bill homw much change should she reseive
Answers
Answer:
none
Step-by-step explanation:
Kayla is buying an $18.90 shirt for $10, she is underpaying $8.90.
Therefore, she needs to pay another $8.90 to pay for the full price of the shirt.
Unless there was a discount on the shirt, this answer makes the most sense to me.
1.6 is what percent of 5?
Answers
Answer:
32%
Step-by-step explanation:
For which values of c does the quadratic equation x^2-2x +c=0 have
One root equal to zero and one negative root
Answers
Answer:
There is no values of c that makes it true
Step-by-step explanation:
The roots of the quadratic equation x² – 2x + c = 0 are 0 and –2. Then the value of c is zero.
What is a quadratic equation?It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
For which values of c does the quadratic equation
x² – 2x + c = 0 ...1
The one root is equal to zero and one negative root.
Let negative a be the one root.
x = 0, –a
Then we have factorized the equation,
(x)(x + a) = 0
On solving, we have
x² + ax = 0 ...2
In comparing equation 2 with equation 1, we have
a = –2 and c = 0
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
Select from the drop-down menus to correctly complete the statement.
This polygon has
Choose...
sides, so it is a
Choose...
This polygon has
Choose...
3
4
5
6
sides, so it is a
triangle
quadrilateral
pentagon
hexagon
Answers
Answer:
6 sides, hexagon
Step-by-step explanation:
If you count the sides you see there are 6, and 6 sided figures are hexagons.
If the equation is further simplified, which equation for a parabola does it become? x2 = 4py x2 = 2y2 2p2 y2 = 4px y2 = 4py.
Answers
The equation for a parabola does become [tex]\rm x^2=4py[/tex].
What is parabola?A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.
Given
The derivation for the equation of a parabola with a vertex at the oriin.
The equation of the parabola can be written as;
[tex]\rm (x)^2 + (y - p)^2 = (0)2 + (y + p)2\\\\x^2 + y^2 - 2py + p^2 = y^2 + 2py + p^2\\\\ x^2= 2py+2py\\ \rm \\x^2=4py[/tex]
Hence, the equation for a parabola does become [tex]\rm x^2=4py[/tex].
To know more about parabola click the link given below.
https://brainly.com/question/3719015
Nellie has a bankruptcy on her credit report and therefore pays higher interest rates on her current loans. she took out a car loan for $45,000 payable for 6 years at an interest rate of 15%. if she had not applied for bankruptcy, she would have been able to take out the loan at a rate of 6%. approximately how much more in interest over the life of the loan does nellie have to pay? a. $68,510.16 b. $53,696.16 c. $32,206.32 d. $14,814.00 please select the best answer from the choices provided a b c d
Answers
The amount more in interest over the life of the loan which Nellie have to pay is $14814.
What is bankruptcy?
Bankruptcy is the procedure by which the people who are unable to pay the debts to creditors, may get relief from some or all the debts.
Nellie has a bankruptcy on her credit report and therefore pays higher interest rates on her current loans.
Nellie took out a car loan for $45,000 payable for 6 years at an interest rate of 15%. Thus, the interest is,
[tex]I=\dfrac{45000\times6\times15}{100}\\I=40500[/tex]
If she had not applied for bankruptcy, she would have been able to take out the loan at a rate of 6%. In this case, the interest paid would be,
[tex]I=\dfrac{45000\times6\times6}{100}\\I=16200[/tex]
The difference between the interest paid would be,
[tex]I=40500-16200\\I=24300[/tex]
Hence, the amount more in interest over the life of the loan which Nellie have to pay is $14814.
Learn more about the bankruptcy here;
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A real estate agent is trying to find the average credit score of some of her clients. She compiled the scores in the table below. What is the mean credit score in this group? (Round to the nearest whole point, if applicable. ) 787 615 550 674 784 773 620 720 704 a. 668 b. 784 c. 692 d. 704 Please select the best answer from the choices provided A B C D.
Answers
Answer:
Step-by-step explanation:
First Add the scores.
Score Total = 787 + 615 + 550 + 674 + 784+ 773 + 620 + 720 + 704
Score Total = 6227
Now divide by the number of members of the sum.
Number of members = 9
The average score = Total Score / number of members
The average score = 6227 / 9 = 691.9
The average score = 692 which is C
3xsquared - 3x -1 = x + 1
Answers
Answer:
x = 2 + √10
-------------
3
x = 2 - √10
------------
3
Step-by-step explanation:
3x² - 3x - 1 = x + 1
-x - 1 -x - 1
3x² - 4x - 2 = 0
-b +/- √b² - 4ac -(-4) +/- √(-4)² - 4(3)(-2) 4 +/- √16 + 24
------------------ = ---------------- = -----------------
2a 2(3) 6
4+/-√40 4 + √ 4 × 10 4 +2√10 2 + √10
------------ = ------------- = ------------ = ------------
6 6 6 3
4 - √ 4 × 10 4 - 2√ 10 2 - √10
---------------- = ----------------- = ---------------
6 6 3
I hope this helps!
Use the similar triangles on the coordinate plane to determine the equation for the given line. Y = three-fourths x y = four-thirds x y = 4x 3 y = 3x 4.
Answers
The equation of the line plotted in the graph with the similar triangles on the coordinate plane is y equal to three-fourths x.
Symbolically, it can be written as,
[tex]y=\dfrac{3}{4}x[/tex]
What is the equation of line?The equation of the line is the way of representation of a line in the equation form.
The equitation of the lines represents the line by the set of points on which the line lies or passes through in the coordinate system.
[tex]y=mx+c[/tex]
Here, (m) is the slope of the line and (c) is the y intercept.
The similar triangles on the coordinate plane to determine the equation for the given line. The line and the triangle is graphed in the image attached below.
The line passes from origin point (0,0). The coordinate points on the line say P are (4,3) as shown in the image. Thus, for this the slope of the line can be given as,
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\m=\dfrac{3-0}{4-0}\\m=\dfrac{3}{4}[/tex]
The equation of the line for 3/4 slope is,
[tex]y=\dfrac{3}{4}x[/tex]
Hence, the equation of the line plotted in the graph with the similar triangles on the coordinate plane is,
[tex]y=\dfrac{3}{4}x[/tex]
Learn more about the equation of line here;
https://brainly.com/question/13763238
Answer:
Its A. :]
(Edge 2022)
Anna, Irina, Avel, and Vlad are going on a road trip. The following table shows an incomplete probability model for who will be driving during any given kilometer.
Person Probability
Anna \dfrac18
8
1
start fraction, 1, divided by, 8, end fraction
Irina \dfrac38
8
3
start fraction, 3, divided by, 8, end fraction
Avel ??question mark
Vlad \dfrac18
8
1
start fraction, 1, divided by, 8, end fraction
What is the probability that Avel will be driving during any given kilometer?
Choose 1 answer:
Answers
Answer:
The answer is 3/8.
Step-by-step explanation:
I watched it on khan academy. im just unsure how to explain it. Lol but im 100% sure it is 3/8. Have a nice day hope this helped! :3
There are two jars once I contains two red gumballs three green gumballs and one yellow gumball. The other jar contains two blue balloons in three purple balloons. Jeff randomly draws one gumball and then one balloon what is the probability will get one red gumball and one blue balloon
Answers
Answer:
P(1 red gumball and 1 blue balloon) =[tex]\frac{2}{15}[/tex]
Step-by-step explanation:
There are two jars.
One jar has 2 red, 3 green and 1 yellow gumball.So, there are 2+3+1=6 gumballs.
Another jar has 2 blue and 3 purple balloons. Totally there are 2+3=5 balloons.
So,
Probability of drawing 1 red gumball from jar 1 =[tex]\frac{2}{6}[/tex]
Probability of drawing 1 blue balloon =[tex]\frac{2}{5}[/tex]
So, P( 1 red gumball, 1 blue balloon)= [tex]\frac{2}{6} *\frac{2}{5} =\frac{2}{15}[/tex]
Distributive property
[tex]6(2x + y) + 2y - 12x[/tex]
How can I simplify this expression and justify it
Answers
Answer:
8y
Step-by-step explanation:
=(6)(2x)+(6)(y)+2y+−12x
=12x+6y+2y+−12x
Combine Like Terms:
=12x+6y+2y+−12x
=(12x+−12x)+(6y+2y)
=8y
Answer:
8y
Step-by-step explanation:
6(2x+y) comes first 12x+6y then you take 2y and add it from 6y giving you 8y and that gives you the most simplified answer 12x and -12x cancel each other out
it says leave ur answer as radicals in simplist form pls help!!! marking brainliest
Answers
Answer:the one near 45 is 5 and the straight line is 4
Step-by-step explanation:
it says solve for x pls help i’m marking brainliest!!!!
Answers
Answer:
x= 9
Step-by-step explanation:
i got 9 by subtracting 54-45 and got 9 therefore x=9
Complete the table below. Show all your work. ILL PUT YOU AS BRAINLIEST PLSSS
Answers
Answer:
See below.
Step-by-step explanation:
y=2x+3
-----
y=2(-2)+3
y=-4+3
y=-1
y=2(-1)+3
y=-2+3
y=1
y=2(0)+3
y=0+3
y=3
y=2(1)+3
y=2+3
y=5
y=2(2)+3
y=4+3
y=7
-hope it helps
Are Lines DE and GH Congruent?
Answers
Answer:
No
Step-by-step explanation:
This time I did the work on paper lol
vivi is a drummer for a band. she burns 756 calories while drumming for 3 hours. she burns the same number of calories each hour how many calories does vivi burn per hour
Answers
Answer:
252 cph
Step-by-step explanation:
756 divide by 3 is 252
Answer:252
Step-by-step explanation:
Completing the Square
ALGEBRA
Please solve this! Giving Brainliest
Answers
Answer:
Step-by-step explanation:
1: x^2 + 6x = - 7
2: x^2 + 6x + (6/2)^2 = -7 + (6/2)^2
2: x^2 + 6x + 9 = - 7 + 9 This might be a 2
2: x^2 + 6x + 9 = 2
3: (x + 3)^2 = 2
4: √(x + 3)^2 = √2
5: x + 3 = +/- √2
6: x = -3 +/- √2
solve 2x^2+x-6=0
1. {-3/2, 2}
2. {}
3. {-2, 3/2}
Answers
Answer:
3. {-2, 3/2}
Step-by-step explanation:
[tex]\mathrm{Solve\;with\;the\;quadratic\;formula}[/tex]
[tex]x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot \:2\left(-6\right)}}{2\cdot \:2}[/tex]
[tex]\sqrt{a^1-4*2(-6)=7}[/tex]
[tex]x_{1,\:2}=\frac{-1\pm \:7}{2\cdot \:2}[/tex]
[tex]\mathrm{Separate\:the\:solutions}[/tex]
[tex]x_1=\frac{-1+7}{2\cdot \:2},\:x_2=\frac{-1-7}{2\cdot \:2}[/tex]
[tex]x=\frac{-1+7}{2*2}:\frac{3}{2}[/tex]
[tex]x=\frac{-1+7}{2*2}:-2[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]
[tex]x=\frac{3}{2},\:x=-2[/tex]
~Learn with Lenvy~
Answer:
Step-by-step explanation:
answer- {-2, 3/2}
steps are in the image.
Anyone can figure this out
Answers
Answer:
... there's nothing there. you forgot to attach something i believe
Step-by-step explanation:
( -6p - 8 ) - ( 2p - 6 ) plz :)
Answers
Answer:
-8p-14
Step-by-step explanation:
HELP WILL GIVE BRAINLIEST!!!!
Answers
Answer:
- 1/9
Step-by-step explanation:
- ( 3 ^ -5) ( 3 ^3)
We know that a^ b* a^c = a^ ( b+c)
- ( 3^(-5+3))
-( 3 ^ (-2))
We know that a^ -b = 1/a^b
- ( 1/ 3^2)
- 1/9
Answer:
- 1/9
Step-by-step explanation:
stop deleting my answer Brainly :) its right
The equation 5x − 8y = 20 expresses a linear relationship between x and y. The point (15, 7) is either on the graph of this line, above it, or below it. Which? How do you know?
Answers
Answer:
Below
Step-by-step explanation:
5 (15) - 8 (7)= 20
75-56=20
19=20
19<20
Find the equation in slope-intercept form of a line through (2, 4) with slope 0. Oy=2 Ox=2 Oy=4 0 x = 4
Answers
answer in fraction: 14 7/27
Answers
Answer:
385/27
Step-by-step explanation: