The answer is:
[tex]t_1=3.60s\\t_2=7.94s[/tex]
Time equal to 3.30 seconds when the arrow was going up.
Time time equal to 7.94 seconds when the arrow was going down.
Why?To solve the problem, we need to solve the quadratic equation and find the value of values of time where the height of the arrow is 420 feet.
Also, we are given some information, we need to substitute it and then use the quadratic equation.
The equation is:
[tex]h=-16t^{2}+vot\\\\-16t^{2}+vot-h=0[/tex]
Substituting the given information we have:
[tex]-16t^{2}+vot-h=0[/tex]
[tex]-16t^{2}+180\frac{ft}{s} t-420=0[/tex]
We have a quadratic equation where:
[tex]a=-16\\b=180\\c=-420[/tex]
Now, using the quadratic equation to find the value or values of "t", we have:
[tex]\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]\frac{-180+-\sqrt{180^{2}-4*-16*-420 } }{2*-16}=\frac{-180+-\sqrt{32400-26880 } }{-32}\\\\\frac{-180+-\sqrt{32400-26880}}{-32}=\frac{-180+-\sqrt{5520}}{-32} \\\\\frac{-180+-\sqrt{5520}}{-32}=\frac{-180+-(74.29)}{-32}\\\\t_1=\frac{-180+(74.29)}{-32}=3.30\\\\t_2=\frac{-180-(74.29)}{-32}=7.94[/tex]
Hence, we have two positive values of time, it means that there are two moments of time where the height of the arrow is equal to 420 feet, those times are:
[tex]t_1=3.60s\\t_2=7.94s[/tex]
Time equal to 3.30 seconds when the arrow was going up.
Time equal to 7.94 seconds when the arrow was going down.
Have a nice day!
Answer:
3.3secs, 7.9secs
Step-by-step explanation:
We are looking for the number of seconds it takes the arrow to reach a height of 420ft. We are given the projectile formula h=−16t2+v0t, where h is the height, in feet, and t is the time, in seconds. We can substitute the initial velocity v0=180 and desired height h=420 to find
420=−16t2+180t
Rewriting this quadratic equation in standard form, we have
16t2−180t+420=0
Now that the equation is in standard form, at2+bt+c=0, we can identify the coefficients a=16, b=−180, and c=420. Substituting these into the quadratic formula, we have
t=−b±b2−4ac‾‾‾‾‾‾‾‾√2a=−(−180)±(−180)2−4(16)(420)‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√2(16)=180±5520‾‾‾‾‾√32
The approximate values for t are
t=≈180+5520‾‾‾‾‾√327.9andt=≈180−5520‾‾‾‾‾√323.3
The arrow will go up and then fall down. As the arrow goes up, it will reach 420ft after approximately 3.3s. It will also pass that height on the way down at approximately 7.9s.
Triangle ABC is translated using the rule (x, y) ? (x + 1, y ? 4) to create triangle A?B?C?. If a line segment is drawn from point A to point A? and from point B to point B?, which statement would best describe the line segments drawn?
Answer:
The line segments AA' and BB' are parallel and congruent
Step-by-step explanation:
we know that
When the transformation is a translation, the figure does not change its shape or dimensions,
so
AA'=BB'=CC'
therefore
The line segments AA' and BB' are parallel and congruent
Translation involves moving a function away from its original position.
The statement that describes the line segments is:
Both lines would be parallel and congruent
The translation is given as:
[tex]\mathbf{(x,y) \to (x + 1, y - 4)}[/tex]
Translation is a rigid transformation.
This means that, the image and the pre-image would have the same measure.
So, when a line is drawn from A to A' and B to B'
The lines would be parallelThe lines would be congruentAssume the coordinates of A and B are:
[tex]\mathbf{A = (2,3) }[/tex]
[tex]\mathbf{B = (-4,6) }[/tex]
Apply transformation
[tex]\mathbf{A' = (2 + 1, 3 - 4) = (3,-1)}[/tex]
[tex]\mathbf{'B = (-4 + 1, 6 - 4) = (-3,2)}[/tex]
The distance of lines AA' and BB' is calculated using:
[tex]\mathbf{d = \sqrt{(x_2 -x_2)^2 + (y_2 - y_1)^2 }}[/tex]
So, we have:
[tex]\mathbf{AA' = \sqrt{(2 -3)^2 + (3 - -1)^2 = \sqrt{17}}}[/tex]
[tex]\mathbf{BB' = \sqrt{(-4 --3)^2 + (6 -2)^2 = \sqrt{17}}}[/tex]
Notice that:
[tex]\mathbf{BB' = AA' = \sqrt{17}}}[/tex]
Because translation is a rigid transformation, then lines AA' and BB' would also be congruent
Read more about translations at:
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Need help with a math question
Answer:
0.000032,0.00000.64
Step-by-step explanation:
For this case, it can be observed that the sequence is performed by multiplying each term by 0.2:
We have to:
[tex]0.1 * 0.2 = 0.02\\0.02 * 0.2 = 0.004\\0.004 * 0.2 = 0.0008\\0.0008 * 0.2 = 0.00016\\0.00016 * 0.2 = 0.000032\\0.000032 * 0.2 = 0.0000064[/tex]
Answer:
The next terms are:
[tex]0.000032\\0.0000064[/tex]
To solve this system of equations by elimination, what operation could be used to eliminate the y-variable and find the value of x? 2x ? 4y = 6 ?3x + 3y = 9 A) add 3 times the second equation to 4 times the first equation B) add 4 times the second equation to 3 times the first equation C) subtract 3 times the second equation from 4 times the first equation D) subtract 4 times the second equation from 3 times the first equation
Step-by-step explanation:
4y=6 (first equation)
3x+3y=9(second equation)
we know if a=a, a+x=a+x,ax=ax
now we add 3 times
4y=6(=)12y=18
now add 4 times
12x+12y=36
now we can eliminate the y and will be
12x=18
x=1,5
2x=3
In the triangles, and .
Which statement correctly compares and ?
and are the same length.
is longer than .
is shorter than .
is shorter than or the same length as .
Answer:
answer is B just got 100%
Step-by-step explanation:
I DONT WANT TO FAIL!!!! PLEASE HELP ME WITH THE CORRECT ANSWER, WILL MARK AS BRAINLIEST!!!
What is the solution to the system of linear equations? {4x+3y=543x+9y=108 Enter your answer in the boxes.
Answer:
x = -24
y = 66
Step-by-step explanation:
12x+9y = 102
12x+16y = 432
---------------------
y = 66
4x + (66*3) = 102
198-102 = -96
-96 / 4 = -24
Answer:
solution is [tex](6,10)[/tex]
Step-by-step explanation:
[tex]4x+3y=54[/tex]
[tex]3x+9y=108[/tex]
WE use elimination method to solve for x and y
Multiply the first equation by [tex]-3[/tex]
[tex]-12x-9y=-162[/tex]
[tex]3x+9y=108[/tex]
Now add both the equations, we will get
[tex]-9x=-54[/tex]
Divide by [tex]-9[/tex] on both sides
[tex]x=6[/tex]
Now we plug in the x value in first equaiton and find out y
[tex]4x+3y=54[/tex]
[tex]4(6)+3y=54[/tex]
[tex]24+3y=54[/tex], subtract 24 on both sides
[tex]3y=30[/tex]
Divide both sides by 3
[tex]y=10[/tex]
So solution is [tex](6,10)[/tex]
In order to avoid a training violation, 85% of your store's employees must complete diversity training by the end of the week. You have 142 employees at your store and 91 have currently completed the training. How many more employees must complete the training by the end of the week to avoid a training violation? 15 20 25 30 45
Multiply the number of total employees by 85%:
142 x 0.85 = 120.7, round to 121
121 total people need to complete the training.
Now subtract the number of people who already took the training:
121 - 91 = 20
20 more people need to take it.
How many solutions does the nonlinear system of equations graphed bellow have?
Answer:
Option A) 1
Step-by-step explanation:
we know that
The solution of the nonlinear system of equations is the intersection point both graphs
In this problem the intersection point is (-2,-1)
therefore
The system of equations has only one solution
Based on the model N(1154,81) describing steer weights, what are the cutoff values for
a) the highest 10% of the weights?
b) the lowest 20% of the weights?
c) the middle 40% of the weights?
Which set of boxes containing tiles with the letters A, B, C, and D meet the following conditions?
In Box 1, P(A) > P(B)
In Box 2, P(B) + P(C) + P(D) = 1
In Box 3, P(D) = 2P(C)
Answer:
your choice is correct
Step-by-step explanation:
In your selected set of boxes, ...
Box 1 has p(A) = 2/6 > p(B) = 1/6
Box 2 contains only B, C, and D.
Box 3 has P(D) = 4/6 = 2*P(C) = 2*2/6
Write your answer without using negative exponents.
(w^5)^-7
Answer:
1/(w^35)
Step-by-step explanation:
According to the rules of exponents, you need to multiply both -7 and 5 such that you get...
w^(-35)
Since you cannot have a negative exponent according to the question, you simplify by...
w^-x means that you do 1/(w^-x)
1/(w^35)
Please mark for Brainliest!! :D Thanks!!
For more questions or more information, please comment below!
In this triangle, what is the value of X?
Enter your answer, rounded to the nearest tenth, in the box.
X=
PLEASEEE HELP 12p!!! BRAINLIEST IF CORRECT!!
Answer:
The measure of angle x is [tex]26.1\°[/tex]
Step-by-step explanation:
we know that
In the right triangle of the figure, the tangent of angle x is equal to divide the opposite side to angle x by the adjacent side to angle x
so
[tex]tan(x)=\frac{26}{53}[/tex]
[tex]x=arctan(\frac{26}{53})=26.1\°[/tex]
Please help me with this last part. The other parts are fine.
These percentiles on small data sets are confusing. We have 8 data points. So the median is the average of the 4th and 5th.
The upper quartile, 75th percentile, is between the 6th and 7th data point of the 8. I calculated its index as (8-1)*.75=6.25. One definition of upper quartile has us just pick the next one up, 36 here. Another definition has us interpolate. Since 6.25 = (3/4) 6 + (1/4) 7 we take (3/4) 33 + (1/4) 36 = 33.75 as a 75th percentile. It's hard for me to choose without knowing what you were taught.
What is the surface area of the regular pyramid below
Answer:
C. 864 units²Step-by-step explanation:
We have the square in the base and four triangles on the lateral surface.
The formula of an area of a square:
[tex]A_{\square}=a^2[/tex]
a - side lenght
We have a = 16. Substitute:
[tex]A_{\square}=16^2=256[/tex]
The formula of an area of a triangle:
[tex]A_{\triangle}=\dfrac{bh}{2}[/tex]
b - base
h - height
We have b = 16 and h = 19. Substitute:
[tex]A_{\triangle}=\dfrac{(16)(19)}{2}=152[/tex]
The Surface Area:
[tex]S.A.=A_{\square}+4_{\triangle}[/tex]
Substitute:
[tex]S.A.=256+4(152)=256+608=864[/tex]
Answer: it C. 864 units²
Step-by-step explanation: I just did it
Jace has consumed 1,500 calories so far today. He has also burned off 400 calories at the gym. He would like to keep his daily calorie total to 1,900 calories per day. How many calories does he have left to consume for the day? Is 1,100 a viable solution to this problem?
===================================
Yes; 1,100 is less than 1,500.
No; 1,100 is more than the 400 he burned off at the gym.
No; 1,100 will cause him to exceed 1,900.
Yes; 1,100 is less than 1,900
Answer:
No, it will cause him to exceed 1900.
Step-by-step explanation:
1,500 - 400 = 1,100 (his total after the gym)
1,100 + 1,100 exceeds 1,900. He wants to keep his total below 1,900, so this is not a viable solution.
Answer:
No; 1,100 will cause him to exceed 1,900.
Step-by-step explanation:
The rationale for this problem is basic.
Jace established a diet restricted to 1900kcal.
If he started 1500kcal and burned 400kcal in the gym, Jane's partial jump is 1100 calories.
Thus, it can still eat the total of 1900-100 = 800kcal.
Any value over 800kcal will exceed the tax threshold and will disrupt Jane's results.
please Simplify 3^2x3^3
Answer:
[tex]243[/tex]
Step-by-step explanation:
[tex]3^2*3^3 = 9 * 27[/tex]
[tex]9 * 27 = 243[/tex]
Answer:
243
Step-by-step explanation:
[tex]3^2*3^3[/tex]
To solve your equation, employ the use of PEMDAS.
According to PEMDAS, exponents come before multiplication, so we can simply the 3 squared and the 3 cubed first.
3 squared is the same as 3 x 3, which is 9.
3 cubed is the same as 3 x 3 x 3, which is 27.
Thus, our new equation is
[tex]9*27[/tex]
Simply do the multiplication and you have your simplified answer.
[tex]9*27=243[/tex]
please help asap will mark brainlest
Answer: -79, 21, 46, 80
Step-by-step explanation:
-79, 21, 46, 80
79 is a negative number making it the smallest. After -79 just order the numbers in the consecutive order of how you count.
Hope this helped!
~Just a girl in love with Shawn Mendes
7. The number +10 can be used to indicate a
A. 10-degree rise in temperature.
B. decrease in salary of $10.
C. withdrawal of $10.
D. loss of 10 pounds.
Hello There!
The number +10 can be used to indicate a 10-degree rise in temperature.
This is because this is an increase. All of the other options are a decrease meaning that there going down from where they were originally.
PLEASE HELP ASAP I WILL MARK BRAINLIEST!! If measures 65°, what is the measure of WZ?
Answer:
180-65=115
Step-by-step explanation:
Straight line always measures 180 degrees, take 180 and subtract 65 thats your answer.
Answer:
115 dude
Step-by-step explanation:
you just substract 65 with 180 and then you get 115
A pizza restaurant charges for each pizza and adds a delivery fee. The cost (c), in dollars, to have any number of pizzas (p) delivered to a home is described by the equation c = 11p + 5.
Each pizza costs $5 and the delivery fee is $11
The cost of 11 pizzas is $16
Each pizza costs $11 and the delivery fee is $5
The cost of 5 pizzas is $11
Answer:
Each pizza costs $11 and the delivery fee is $5
Step-by-step explanation:
We assume you want an interpretation of the equation.
The total cost of an order is the sum of any fixed cost (such as a delivery fee) and the variable cost.
Here, the variable cost is the cost of some number of pizzas. It is proportional to the number of pizzas. In the equation, it is represented by 11p, where p is the number of pizzas. The cost of each pizza must be $11, since the cost of p pizzas is 11p.
The equation's two parts are a fixed cost of $5 and a variable cost of $11 per pizza. The best description is ...
Each pizza costs $11 and the delivery fee is $5
The cost (c) to have any number of pizzas (p) delivered is calculated using the equation c = 11p + 5. This implies that each pizza costs $11 and the delivery fee is $5.
Explanation:The question involves the concept of linear equations in mathematics. In this particular case, the equation is c = 11p + 5. This equation denotes the cost (c) of pizzas delivered where each pizza prices ($11 each) is multiplied by the number of pizzas (p) and then added to the delivery fee ($5). Therefore, the third option, 'Each pizza costs $11 and the delivery fee is $5' is the correct interpretation of the equation.
To find out the cost of any number of pizzas, you would substitute that number in for 'p' in the equation. For instance, the cost of 5 pizzas would be calculated as 5 * $11 + $5 = $60.
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Identify the form of the equation and two characteristics(example: slope, y--intercept,or point) of the function's graph.
1. y = –7x + 2
2. y + 2 = 2/3(x – 5)
Answer:
1) graphical linear equation form (slope = -7, y-intercept = 2)
2) Standard linear form (slope = 2/3, y-intercept = -4/3)
Step-by-step explanation:
1) A graphical equation is always in the form of y = mx + c where y is the subject.
slope is the value before x which is -7
Y-intercept is where a line meets y axis so the value of x is 0. Y-intercept is 2.
y = -7x + 2
y= -7 (0) + 2 = 2
2) A standard form is where y is not the subject.
Step 1: Convert it into graphical equation form y = mx + c to identify the slope and y-intercept.
y + 2 = 2/3(x – 5)
y + 2 = 2/3x - 10/3
y = 2/3x - 10/3 -2
y= 2/3x - 4/3
slope is the value before x which is 2/3
Y-intercept is where a line meets y axis so the value of x is 0. Y-intercept is -4/3.
y= 2/3x - 4/3
y = 2/3 (0) - 4/3
y = -4/3
!!
Which of the following equations is of the parabola whose vertex is at (2, 3), axis of symmetry parallel to the y-axis and p = 4?
A.)y-3 = 1/16 (x-2)^2
B.)y+3 = -1/16 (x+2)^2
C.)x-2 = 1/16 (y-3)^2
Answer:
option A.) y-3 = 1/16 (x-2)^2
Step-by-step explanation:
we know that
If the axis of symmetry is parallel to the y-axis, then we have a vertical parabola
The equation of a vertical parabola is equal to
[tex]4p(y-k)=(x-h)^{2}[/tex]
where
(h,k) is the vertex
In this problem we have
(h,k)=(2,3)
p=4
substitute
[tex]4(4)(y-3)=4(4)(x-2)^{2}[/tex]
[tex]16(y-3)=(x-2)^{2}[/tex]
[tex](y-3)=(1/16)(x-2)^{2}[/tex]
Answer:
option A.) y-3 = 1/16 (x-2)^2
Step-by-step explanation:
Which is an example of SRS (simple random sample)? a. Putting all the names of the 50 elementary students sitting in the auditorium into a large fishbowl and pulling out only 10 names b. Calling households at random with the area code 312; after completing the survey with the homeowner, surveying others living in the same home c. Stopping every thirteenth person who leaves the local hardware store with a bag, showing they purchased an item d. Listing in alphabetical order the 100 players in the league, then beginning at the top of the list and calling players until you have spoken to 10 players
Answer:
a. Putting all the names of the 50 elementary students sitting in the auditorium into a large fishbowl and pulling out only 10 names
Step-by-step explanation:
When one does simple random sampling picture it like a lottery. (This is actually a good example) It is a type of smapling that is done where a smaller portion of the whole population is chosen to participate in the research. It is called random because everyone in the population has an equal chance to be selected. Although the other examples are random sampling as well, they are more systematic than simple.
Answer:
A
Step-by-step explanation:
The peroson above is correct
The results of a common standardized test used in psychology research is designed so that the population mean is 135 and the standard deviation is 30. A subject earns a score of 198. What is the z-score for this raw score?
z-score=
Answer:
2.1
Step-by-step explanation:
Mean+z score(Standard deviation)=raw score
Let the z score be z
135+z(30)=198
30z=63
z=2.1
The z-score is a measure of how many standard deviations a score is from the mean. In this case, where the test was designed with a mean of 135 and a standard deviation of 30, a score of 198 results in a z-score of 2.1.
Explanation:The z-score represents how many standard deviations an element is from the population mean. In this particular case, the results of a standardized test designed with a population mean of 135 and a standard deviation of 30 are given. A subject has a test score of 198.
To calculate the z-score, you use the formula: z = (X - μ) / σ. Where X is the score, μ is the mean, and σ is the standard deviation.
Substitute the given values into the formula:
z = (198 - 135) / 30
z = 2.1
So a test score of 198 would yield a z-score of 2.1.
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Can mutually exclusive events have an intersection of events? Explain your answer
Answer:
no
Step-by-step explanation:
exclusive pertains to one, hence the phrase, exclusive.
Mutually exclusive events or disjoint events are two events that don’t have anything in common. Nothing in common means NO INTERSECTION.
Answer: No!
Determine whether the given value is a statistic or a parameter. Upper A survey found that 54 % of all respondents go to school. Choose the correct answer below. A. The value is a statistic because it is a numerical measurement describing some characteristic of a population. B. The value is a statistic because it is a numerical measurement describing some characteristic of a sample. C. The value is a parameter because it is a numerical measurement describing some characteristic of a population. D. The value is a parameter because it is a numerical measurement describing some characteristic of a sample.
Answer:
5 but its probaly not right bc im just looking for pointsStep-by-step explanation:
Solve for x. -3 + 8x - 5 = -8 A. -2 B. -1 C. - 3 4 D. 0
Answer:
D
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
-3+5
-8+8x=-8
divide both sides by 8
x=0
In a recent year,there were approximately 45 million moviegoers in a certain country, of these about 4/5 were ages 24-34. Find the approximate number of people ages 24-34 who attended the movies in that year.
Answer:
36 million
Step-by-step explanation:
(4/5)×(45 million) = (4/5×45) million = 36 million
Approximately 36 million people aged 24 to 34 attended movies that year.
Answer: 36 million.
Step-by-step explanation:
Hi, to answer this question we simply have to multiply the total number of moviegoers (45 million) 4/5 (moviegoers between ages 24-34 )
Mathematically speaking:
45m x 4/5 =45 x 4/5= 36 million
it can also be solved like this:
45,000,000 x 4/5 = 36,000,000
The approximate number of people ages 24-34 who attended the movies in that year were 36 million.
The two functions below are used to represent the height of a rocket above the ground after it is launched. Which rocket reaches a greater distance above the ground at its maximum height? Rocket A: y = -6x 2 + 96x Rocket B: y = -4x 2 + 80x Rocket reaches a maximum height that is greater than the maximum height of Rocket
Answer:
Rocket B reaches a maximum height that is greater than the maximum height of Rocket A.
Step-by-step explanation:
A graph quickly shows the answer to this question.
__
In vertex form, the equation for Rocket A is ...
y = -6(x² -16x +8²) +6(8²)
y = -6(x -8)² +384 . . . . . . . . . maximum height is 384 feet
__
The corresponding equation for Rocket B is ...
y = -4(x² -20x +10²) +4(10²)
y = -4(x -10)² +400 . . . . . . . . maximum height is 400 feet
Rocket B reaches a maximum height greater than that of Rocket A.
Rocket B reaches a maximum height that is greater than the maximum height of Rocket A.
If it takes Tom 15 minutes to eat a burger and then 5 minutes to eat a portion of fries, how many burgers and portions of fries would he be able to eat in one hour?
Tom could eat 4 burgers and 12 portions of fries.
Answer:
3
Step-by-step explanation:
15 minutes for one burger and another 5 for one portion of fries. If he has to eat a portion of fries after each burger that's 20 minutes. An hour is only 60 minutes allowing only enough time to eat 3 burgers and portions of fries. Simply because 60 divided by 20 is 3.
Need help with a math question PLEASE HELP
Answer:
57%
Step-by-step explanation:
From the table you can state that:
the total number of students is 10,730the number of students receiving Finincial Aid is 6,101Use the definition of the probability
[tex]Pr=\dfrac{\text{The number of favorable outcomes}}{\text{The number of all possible outcomes}}[/tex]
So,
the number of favorable outcomes = 6,101the number of all possible outcomes = 10,730Hence, the probability is
[tex]Pr=\dfrac{6,101}{10,730}\approx 0.5685\approx 57\%[/tex]