A toy rocket was shot into the air. The graph below represents the height over the time of the rocket. Which of the following are true? Select all that apply.
A. The rocket was launched from a platform 4.9 feet above the ground
B. The rocket reached a maximum height of 59 feet
C. It took the rocket 3.5 seconds to reach its maximum height
D. The rocket landed after 34 seconds
E. The equation that represents the rocket’s height over time has two solutions
Answers
The correct statements are:
- B. The rocket reached a maximum height of 59 feet.
- C. It took the rocket 3.5 seconds to reach its maximum height.
- E. The equation that represents the rocket’s height over time has two solutions.
To determine which statements about the rocket's flight are true, analyze the given graph.
1. Statement B: The rocket reached a maximum height of 59 feet.
- This statement is true. The highest point on the graph is marked as (3.5, 59), indicating that the maximum height of the rocket was 59 feet.
2. Statement C: It took the rocket 3.5 seconds to reach its maximum height.
- This statement is true. The coordinates (3.5, 59) show that the rocket reached its maximum height at 3.5 seconds.
3. Statement E: The equation that represents the rocket’s height over time has two solutions.
- This statement is true. The parabolic path of the rocket implies a quadratic equation. A quadratic equation typically has two solutions, which correspond to the times when the rocket is at ground level (height = 0). From the graph, we see the rocket starts at (0, 0) and lands at (6.9, 0), confirming two solutions.
Verifying the incorrect statements:
1. Statement A: The rocket was launched from a platform 4.9 feet above the ground.
- This statement is false. The graph shows that the rocket was launched from the origin point (0, 0), meaning it was launched from ground level, not 4.9 feet above the ground.
2. Statement D: The rocket landed after 34 seconds.
- This statement is false. The graph indicates the rocket landed at 6.9 seconds, not 34 seconds.
The correct options are:
A. The rocket was launched from a platform 4.9 feet above the ground.
B. The rocket reached a maximum height of 59 feet.
C. It took the rocket 3.5 seconds to reach its maximum height.
D. The rocket landed after 34 seconds.
E. The equation that represents the rocket's height over time has two solutions.
To determine the validity of each statement, we must analyze the graph of the rocket's height over time. Here is the logical reasoning behind each option:
A. The rocket was launched from a platform 4.9 feet above the ground.
This statement is true if the graph's vertical intercept (the height at time zero) is 4.9 feet. The vertical intercept is the starting height of the rocket before it is launched.
B. The rocket reached a maximum height of 59 feet.
This statement is true if the graph reaches a maximum value of 59 feet at some point in time. This would be the peak of the graph, where the height is greatest.
C. It took the rocket 3.5 seconds to reach its maximum height.
This statement is true if the time at which the graph reaches its maximum height is 3.5 seconds. This is the horizontal coordinate of the peak of the graph.
D. The rocket landed after 34 seconds.
This statement is true if the graph returns to the horizontal axis (height of zero) at 34 seconds. This would indicate that the rocket has returned to the ground.
E. The equation that represents the rocket's height over time has two solutions.
This statement is true if the graph intersects the horizontal axis at two distinct points. The first intersection represents the launch point (time zero), and the second intersection represents the landing point. The fact that there are two intersections implies that the equation has two solutions.
Related Questions
A store owner buys a total of 4,000 items for two different products. For shipping costs, it is $0.10 per item of product A and $0.04 per item of product B. If the total shipping cost is $352, which system of equations can be used to determine how much of product A and product B the store owner bought?
Answers
0.1x + 0.04y = 352
Product A represents x and product B represents y. The first equation is the total number of items the store owner buys. The second equation is cost per item for both products. The above system of equations can be used to determine how much product A and product B the store owner bought.
which numbers have exactly 2 factors
Answers
3 is 1 and 3
I really need the answer I’ve been stuck on this all day
Answers
Those are the steps on how to answer your problem
there was a warning of volcano eruption in Kilauea in Hawaii. from September 7th to September 8th 2014, the flow advanced about 3/8 kilometers towards the edge of highway 130. the distance (in kilimeters) between the edge of the lava flow and the highway 130 can be given by the function f(t)=6-3/8t where t is the number of days since September 9, 2014. what is the input variables? What are the units of the input variable?
Answers
When you are given an equation, there is an input and an output. In this case, you put in the number of days and the output is the distance between the lava and the road.
If you make a chart of the inputs and outputs, you will see that the lava is getting closer to the road.
The constant of proportionality between the circumference and _______ of a circle is equal to π which means that for any given circle, the length around the circle _______ by its diameter is a little over _______ , or more exactly π
Blank 1: Diameter or radius
Blank 2: Divided or multiplied
Blank 3: 4, 3, or 5
PLEASE ANSWER ASAP
Answers
blank 2 =multiplied
blank 3=3.
Hope this helped!
Sorry couldn't answer faster i didn't see this question.
Mark me as brainliest Please!!!
Plz help please thanks so much
Answers
1/2(120)
60
He needs to paint 60 sq ft.
The measures of the angles of triangle ABC are angle a 48 degrees angle B 6x - 28 angle C 2x what is the value of x
Answers
48 + 6x - 28 + 2x = 180
8x + 20 = 180
8x = 160
x = 20
Please help asap!
Two angles are supplementary. If one angle measures 43 degrees, what is the measure of the second angle?
A. 47 degrees
B. 57 degrees
C. 137 degrees
D. 147 degrees
Answers
Answer:
147
Step-by-step explanation:
Explain how to write a word problem to match the inequality d < 120. Demonstrate with an example.
Answers
You could accomplish this with a budget, like
D is how much money you plan to spend, but you only have 120 dollars
Something like that
Answer:
So the Variable D has to be less than 120, which means the problem has to state that a certain number cannot be bigger than 120.
Step-by-step explanation:
helppppppppppppp meeeeeeeeeeeeeeeee
Answers
X = -10
-10y = -90
Y= 9
For this case what you should do is see the intersections with each of the axes and then join the ordered pairs.
We have then:
For the x axis:
y = 0
Substituting in the equation:
9x-10 (0) = - 90
9x-0 = -90
x = -10
For the y axis:
x = 0
Substituting in the equation:
9 (0) -10y = -90
0-10y = -90
y = 90/10
y = 9
We graph the ordered pairs:
(x1, y1) = (- 10, 0)
(x2, y2) = (0, 9)
Answer:
See attached graph.
r+3.2=6.1
What is the value of r? Show work
Answers
The answer is 2.9.
Reason:
Solve this two ways:
1. You could be just regularly solving the question but subtracting 6.1 to 3.2.
6.1-3.2=2.9
2. Or you could be solving variable.
Subtract 3.2 on both sides:
6.1-3.2=2.9
r=2.9
If you need anymore help feel free to ask me!
Hope this helps!
~Nonportrit
Brainliest pts pls
Which expression is equivalent to the expression below? Select all that apply. –25(15 – 20d + 5c) A. –30 + 40d – 10c B. –6 + 8d – 2c C. –2c + 8d – 6 D. 6 – 8d + 2c
Answers
The equivalent expressions are [tex]-6+8d-2c[/tex] and [tex]-2c+8d-6[/tex]. So, the correct options are B and C.
Given:
The given expression is:
[tex]-\dfrac{2}{5}(15-20d+5c)[/tex]
To find:
The equivalent expressions.
Explanation:
We have,
[tex]-\dfrac{2}{5}(15-20d+5c)[/tex]
Using the distributive property, we get
[tex]=-\dfrac{2}{5}(15)-\dfrac{2}{5}(-20d)-\dfrac{2}{5}(5c)[/tex]
[tex]=-6+8d-2c[/tex]
It can be rewritten as:
[tex]=-2c+8d-6[/tex]
The equivalent expressions are [tex]-6+8d-2c[/tex] and [tex]-2c+8d-6[/tex]. Therefore, the correct options are B and C.
Learn more:
https://brainly.com/question/7627111
Upon applying the distributive property, the given expression, –25(15 – 20d + 5c), simplifies to –375 + 500d – 125c. None of the options provided match this expression, making the correct answer 'None of the above'.
Explanation:The student is asked to find an expression equivalent to –25(15 – 20d + 5c). To do this, we will apply the distributive property to multiply –25 by each term inside the brackets. This gives us:
–25 × 15 = –375–25 × (–20d) = 500d–25 × 5c = –125cCombining these we get the expression –375 + 500d – 125c. When we look at the options provided, none are equivalent to the expression we derived. Therefore, the correct answer is:
None of the aboveLearn more about Equivalent Expression here:https://brainly.com/question/34140345
#SPJ3
Kim and her 5 friends hiked over a three day weekend hey hiked the same distance each day how many miles did they hike per day?
Answers
Answer:
3
Step-by-step explanation:
Jasmine has a piece of ceramic tile that is shaped as a parallelogram. What is the area of this parallelogram?
96 in²
288 in²
352 in²
384 in²
Answers
⓶ Now that we know that the formula to calculate the area of a parallelogram is :
A = b × h
You need to find the numbers to replace the base and the height in the formula!
We already know that the height is : 12 in.
So we are left with a formula looking like this :
A = b × 12 in.
⓷ Now we need to find the base! To do so, you need to add the height of the rectangle (which is 8 in.) to the height of one of the triangle (which is 16 in.) :
8 in. + 16 in. = b
↓
8 in. + 16 in. = 24 in.
↓
24 in. = b
So we are left with a formula looking like this:
A = 24 in. × 12 in.
⓸ All there’s left to do now, is calculate the area of the parallelogram using the formula :
A = 24 in. × 12 in.
↓
24 in. × 12 in. = 288 in.²
↓
A = 288 in.²
So your final answer is : the area of this parallelogram is ↠ 288 in.²
I really hope this helped, if there’s anything just let me know! ☻
288 would be your Answer hope this helps
what is this plzz need help for math homework it is very hard
Answers
For the total length of the five rods in terms of a is L = 15a.
The formula for the Total Length of Five Rods
Certainly! To find a formula for the total length (L) of the five rods in terms of a, let's denote the lengths of the rods as a, 2a, 3a, 4a, and 5a (since there are five rods, each consecutive rod has a length that is one unit greater than the previous rod). So, the lengths of the rods are:
First rod: a
Second rod: 2a
Third rod: 3a
Fourth rod: 4a
Fifth rod: 5a
Now, to find the total length (L), add up the lengths of all the rods:
L = a + 2a + 3a + 4a + 5a
Combine like terms:
L = (1 + 2 + 3 + 4 + 5) · a
The sum of the first n natural numbers is given by the formula n(n + 1)/2, so in this case:
L = 5 · 6/2 · a
Simplify the expression:
L = 15a
So, the formula for the total length L in terms of a is L = 15a.
The complete question is:
Here are five straight rods.
All measurements are in centimeters.
The total length of the five rods is L" " cm.
Find a formula for L in terms of a.
Write your formula as simply as possible.
A person sold 100 shares of stock at a loss of 40%. If the selling price for the 100 shares was 3000 which of the following comes closest to what was paid for the stock
Answers
purchase price = $3000/0.60 = $5000
This system has one solution. y=x2−3x+7y=3x−2 What is the y-coordinate of the solution? Enter your answer in the box.
Answers
y = 7
Explanation:
The first given equation is:
y = x² - 3x + 7 ...........> equation I
The second given equation is:
y = 3x - 2 ..............> equation II
Substitute with equation I in equation II and solve for x as follows:
y = 3x - 2
x² - 3x + 7 = 3x - 2
x² - 3x + 7 - 3x + 2 = 0
x² - 6x + 9 = 0
(x-3)² = 0
This means that:
x = 3
Now, substitute with the value of x in equation II to get the y as follows:
y = 3x - 2
y = 3(3) - 2
y = 7
Hope this helps :)
Median; 1.5
Median; 3
Mean; 1.5
Mean; 3
Answers
If it was symmetrical, you would do Man/Mean Absolute Deviation
Answer:
the median is the number in the middle the mean is the sum of all numbers and divided
Step-by-step explanation:
mean 1,2,3,4,5,6
1+2+3+4+5+6=21
21/6= 3.5 <- mean
Median 1,2,3,4,5,6
2,3,4,5
3,4
median 3.5
Tamara has 12 pencils. There are three red pencils and p other pencils. Write an equation to represent this situation.
Answers
HELPP ME PLZZZZ
Which of the four images was formed by a reflection of the letter T?
A
B
C
D
Answers
The answer is not A because T would be flipped, the answer is not D because T can not be reflected in that area without translations, and the answer is not B because T cannot (once again) be reflected in such locations without translations, Therefore, that leaves us with our best bet being the answer C.
PLEASE HELP ASAP!!!!!!!!!!!
A number cube with six sides numbered 1 through 6 is rolled. The probability of rolling a 5 is 16. What is the probability of not rolling a 5? Enter your answer as a fraction, in simplest form, in the box.
Answers
Which means the probability of not rolling it is the opposite - 5/6
How many triangles exist with the given side lengths?
12 in, 15 in, 18 in
A.
No triangle exists with the given side lengths.
B.
More than one unique triangle exists with the given side lengths.
C.
Exactly one unique triangle exists with the given side lengths.
Answers
Write and solve a real-world problem that represents the following one-variable inequality. Then solve the inequality, showing all steps.
200 + 0.75x ≤100 + 2.50x
Answers
so, 300+0.75x ≤ 2.5x
300 ≤ 3.25x
then divide
x ≤ 299 and 1/13
what is 64/25 as a mixed number?
Answers
jamal purchased a boat for 7/10 of the asking price of $18,950. He had to pay 6.5% sales tax. What was the amount of Jamal's bill?
Answers
Since Jamal is only paying for 7/10 of the asking price, we can multiply it by 0.7.
0.7 x 18950 = 13265
Now, we have to add on the tax, so we should multiply the new amount by 1.065.
13265 x 1.065 = 14127.23
Jamal's bill will be $14,127.23
Good luck,
MrEQ
ILL GIVE BRAINLIEST PLEASE ORDER THESE LEAST TO GREATEST
Answers
0.125 being the least and 2.5% being the greatest
Ascending Order: 0.125, 2.5, 1/4 ( Least to Greatest.).
Descending Order: 1/4, 2.5, 0.125 ( Greatest to Least.).
Hope this helps.
There are 6 brown, 5 blue, and 2 orange marbles in a hat. What is the probability of picking two orange marbles in a row without returning the marbles back to the hat? (Write your answer as a fraction.)
Answers
Sarah is blowing up spherical balloons for her brother's birthday party. One of the balloons has a radius of 3 inches. Round to the nearest tenth.
Suppose Sarah can inflate the balloon at a rate of 200 cubic inches per minute. How long will it take her to inflate the balloon?
Answers
[volume of a sphere]=(4/3)*pi*r³
for r= 3 in
calculate the volume of one balloon
balloons=(4/3)*pi*r³-------> (4/3)*pi*3³----------> 113.04 in³
if the rate is 200 in³ --------------------> 1 minute
113.04 in³------------------------> X
X=113.04/200------------> 0.5652
the answer is 0.6 minutes
Final answer:
Sarah will take approximately 0.6 minutes or 34 seconds to inflate a spherical balloon with a radius of 3 inches at a rate of 200 cubic inches per minute, after calculating the volume of the balloon and dividing by the rate.
Explanation:
How long will it take Sarah to inflate a spherical balloon with a radius of 3 inches at a rate of 200 cubic inches per minute?
To solve this problem, we first need to calculate the volume of the spherical balloon using the formula for the volume of a sphere, which is [tex]V = \(\frac{4}{3}\)\pi r^3[/tex], where r is the radius of the sphere. In this case, the radius is 3 inches. Plugging the values into the formula, we get:
[tex]V = \(\frac{4}{3}\)\pi (3)^3 = \(\frac{4}{3}\)\pi (27) = 36\pi cubic inches[/tex]
Now, given that Sarah can inflate the balloon at a rate of 200 cubic inches per minute, we can calculate the time it takes to inflate the balloon by dividing the total volume by the rate:
[tex]Time = \(\frac{Volume}{Rate}\) = \(\frac{36\pi}{200}\) minutes[/tex]
Using the approximation \(\pi = 3.14\), this results in:
[tex]Time = \(\frac{36 \times 3.14}{200}\) = \(\frac{113.04}{200}\) ≈ 0.565 minutes[/tex] or about 33.9 seconds, rounded to the nearest tenth.
Therefore, it will take Sarah approximately 0.6 minutes or 34 seconds to inflate the balloon.
Enter a recursive rule for the geometric sequence. 10, −80, 640, −5120, ...
a(1)=
a(n)=
Answers
[tex]a_1=10 \\a_{n}=a_{n-1} \times (-8)[/tex]
This is because the first term, a₁, is 10. A recursive rule is dependent upon the term before it (a(n-1)) and the common ratio. The common ratio, or the number that each term is multiplied by, is -8.
Answer:
The value is:
a(1)=10 and a(n)=(-8)×a(n-1)
Step-by-step explanation:
We are given a sequence as:
10, -80 , 640 , -5120 ,.........
since by looking at the sequence we could see that it is a geometric progression (G.P.) with common ratio -8.
Also a(1) denotes the first term of the sequence and a(n) denotes the nth term of the sequence.
a(1)=10
Also a(n)=(-8)×a(n-1)
since a(1)=10
a(2)=(-8)×10=-80
a(3)=(-8)×(-80)=640
a(4)=(-8)×640=-5120
and so on.
Hence the answer is:
a(1)=10 and a(n)=(-8)×a(n-1)
Solve for d.
13d + 4 = 43
A.3
B.13
C.39
D.None of the above
Answers
Because 43-4=39
39/13=3