Leyla drops a penny from a height of 150m. How long will it take to hit the ground? Round to the nearest tenth of a second. use the formula h(t)=-4.9t²+v₀t+h₀, where v₀ is the initial velocity and h₀ is the initial height.
It will take approximately 5.5 seconds for the penny to hit the ground.
To determine the time it takes for the penny to hit the ground, we can use the given formula for the height as a function of time:
[tex]\[ h(t) = -4.9t^2 + v_0t + h_0 \][/tex]
Given that the penny is dropped and not thrown, the initial velocity [tex]\( v_0 \)[/tex] is 0. The initial height [tex]\( h_0 \)[/tex] is 150 meters. We want to find the time [tex]\( t \)[/tex] when the height [tex]\( h(t) \)[/tex] is 0, which is when the penny hits the ground.
Plugging in the known values, we get:
[tex]\[ 0 = -4.9t^2 + 0 \cdot t + 150 \][/tex] Simplifying, we have:
[tex]\[ 4.9t^2 = 150 \][/tex]
Now, we solve for [tex]\( t \)[/tex]:
[tex]\[ t^2 = \frac{150}{4.9} \][/tex]
[tex]\[ t^2 \approx 30.612244898 \][/tex]
Taking the square root of both sides to solve for [tex]\( t \)[/tex]:
[tex]\[ t \approx \sqrt{30.612244898} \][/tex]
[tex]\[ t \approx 5.532851414 \][/tex]
Rounding to the nearest tenth of a second, we get:
[tex]\[ t \approx 5.5 \][/tex]
what is the value of x if the equation is
x+90+18.4
If one angle of a triangle measures 32 degrees and another angle measures 71 degree, what is the measure of the third angle?
Six friends each put $250 into a single account that earns 5.5% annually. The interest earned is added to the account at the end of each year. The friends want to use the money in the account to go on a vacation after four years. The friends get together after most have finished college four years later. How much money is in the account?
HURRY, PLEASE I NEED HELP!!!
the measures of the angle of,triangle, ABC are given by the expressions in the table.
angle measure
A (4x-13)
B 15
C (x+18)
what is the measure of A and C
enter your answers in the boxes
m A=___
m C=___
In a triangle we apply angle sum property of triangle, which is given by:
Sum of angles of triangle =180 degrees.
We are given three angles,
A =(4x-13)
B =15
C =(x+18)
Adding the three angles and equating it to 180,
[tex] (4x-13) +15 + (x+18) =180 [/tex]
combining like terms
[tex] 5x+20 =180 [/tex]
[tex] 5x=180-20 [/tex]
[tex] 5x =160 [/tex]
x=32
angle A = 4x-13 = 4(32)-13 = 115 degrees.
angle C = x+18 = 32 +18 = 50 degrees.
Answer : angle A is 115 degrees and Angle C is 50 degrees.
A horizontal line goes through the point (–7,10). Which statements are true about this line? Check all that apply. The slope of the line is zero. Another point on the line is (3,10). The y-intercept of the line is –7. The equation of the line is y = 10.
The statement 1,2, and 4 are true and 3 is not true below given the reason behind it.
What is a graph?The link between lines and points is described by a graph, which is a diagrammatic representation of a network.
A graph is made up of some points and the distance between two It doesn't matter how much time the lines are or where the points are located. A node is a name for each constituent in a graph.
The given statement is a line passing through ( -7, 10 ) so
Option 1 ⇒ the slope of that line will be zero because it is a horizontal line so it will be true.
Option 2 ⇒another point on this line will be (3,10) since it is a horizontal line so the y coordinate is the same and the x coordinate can vary so it is also true.
Option 3 ⇒ the y-intercept of this line will be 10 which is not true and can be confirmed by options 1 and 2.
Option 4 ⇒ the equation of the line will be y =10 which is true hence it is a horizontal line.
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Help please what is the sum?
Which equation represents a line which is parallel to the line x-8y=48 x−8y=48?
The required line is y = x/8 - 6 which is parallel to the given line x − 8y = 48.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
The slope-intercept form is y = mx+c, where the slope is m and the y-intercept is c
The equation is given in the question below as
x − 8y = 48
We have to convert the equation to slope-intercept form
x − 8y = 48
− 8y = - x + 48
Divided by -8 into both sides of the above equation,
− 8y / (− 8) = - x / (− 8) + 48 / (− 8)
y = x/8 - 6
Since the slope is the same, therefore the lines are parallel.
Therefore, the required line is y = x/8 - 6 which is parallel to the given line x − 8y = 48.
Hence, the correct answer would be an option (A).
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The question seems to be incomplete the correct question would be
Which equation represents a line which is parallel to the line x − 8y = 48?
A. y = x/8 - 6
B. y = x/2 - 8
C. y = x/6 - 4
D. y = x/4 - 2
A rectangular prism has a length of 2 1/2 centimeters, a width of 2 1/2 centimeters, and a height of 5 centimeters. Justin has a storage container for the prism that has a volume of 35 cubic centimeters. What is the difference between the volume of the prism and the volume of the storage container?
Answer:
3.75
Step-by-step explanation:
find the volume of the cylinder with the given measurement. r= 2, h= 3
Please help thank you.
Analyze the diagram to complete the statements. The m∠MXN is the m∠YZX. The m∠LZX is the m∠ZYX + m∠YXZ. The m∠MYL is 180° − m∠ZYX.
By using the picture that was provided below, you can see that
m<MXN is greater than m<YZX.
Angles m<LZX is equal to m<ZYX + m<YZX and
m<MYL is equal to 180 degrees minus M<ZYX.
I hope this helps! Have a good day
Answer:
Step-by-step explanation:
the sum of 5 consecutive odd number is 145
An object is traveling around a circle with a radius of 10 cm. If in 20 seconds a central angle of 1/3 radian is swept out, what is the linear speed of the object?
I think I've set my formula up right (v=Δ20/Δ1/3 radian), but I don't know what to do with the Δ thing. Once I know how to do that I should be able to like, actually figure it out.
A check is _____.
A.) Just like debit card
B.) A promissory note (I.O.U)
C.) Required to be paid by your bank when presented
D.) Not able to be forged
Answer:
B
Step-by-step explanation:
A check is an I.O.U. or a promissory note.
Cheryl volunteers to mow the lawn at a retirement home.She can mow 1/4 of the lawn in 3/4 of an hour .At what rate ,how many hours will it take Cheryl to mow the entire lawn
A certain species of tree grows an average of 3.1 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 600 centimeters tall.
Regard triangleTRI and the following facts:
Segment IR || Segment NA
TA= 12 cm, RA= 3 cm, NT= 18 cm, AN= 22
(a)What theorem or postulate proves Triangle ANT similar to RIT?(b)Solve for NI by using the Side-Splitting Theorem.Show all work.(c)What is the scale factor for similar triangles ANT and RIT?
(d)Calculate RI. Show your work.
(e)What is the ratio of the areas of the two triangles? Show your work.
please help me thank you.
What is the approximate value of the function at x = 0?
a) -3
b) -4
c) -5
d) -4.5
The triangles are congruent by SSS or HL. The diagram shows the sequence of three rigid transformations used to map ABC onto A"B"C". What is the sequence of the transformations? rotation, then reflection, then translation rotation, then translation, then reflection reflection, then translation, then rotation reflection, then rotation, then translation
Answer:- The sequence of the transformations for the given diagram must be reflection, then rotation, then translation.
Explanation:-
Given : Four triangles which are congruent by SSS postulate or HL theorem.
According to the given diagram , the rigid transformations are as follows
1. Reflection: ΔABC is flipped about BC to form ΔA'BC such that AC=A'C and its is already given that they are congruent thus the rigid transformation used here is reflection.
2. Rotation:- ΔA'BC is rotated about point A' at some angle to form ΔA'B'C' , and they are congruent (given). Thus the rigid transformation used here is rotation.
3.Translation:- ΔA'B'C' is translated exactly right by some factor to form ΔA"B"C" ∵ all the points have changed but as these triangles are congruent (given) then corresponding parts must be equal.Thus the rigid transformation used here is translation.
The sequence should be in the order for the given transformation as, reflection, then rotation, then translation. Thus the option D is the correct option.
How to rotate, reflect, and translation the figure?Rotation, reflection and translation is the way of transformation of an figure.
Rotation- Rotation of an object is rotating it about a fixed point without changing its shape and size.Reflection- Reflecting of an object is flipping it across a line without changing its shape and size.Translation- Translation of an object is the shifting of the object without changing its dimensions, without rotating it and without reflecting it.Given information-
In the given diagram the, triangle ABC is transformation into the three stages.
First the figure ABC is just flipped into the triangle A'BC by keeping the side BC fixed.Then the triangle A'BC is rotated around the point A' and to place of A'B'C'.Finally the figure is transact right from one place to another which is A"B"C".Hence the correct sequence of the transformations is reflection, then rotation, then translation. Thus the option D is the correct option.
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14. The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height (y), in mm, to which it grows: y = 4 + 2x. What does the y-intercept of this function represent?
A) The original height of the plant was 4 mm.
B) The original height of the plant was 2 mm.
C) The height of the plant increases by 2 mm for every hour of sunlight it receives.
D) The height of the plant increases by 4 mm for every hour of sunlight it receives.
16. The table below shows the values of y for different values of x:
x 7 8 9 10 11 12 13
y 3 5 7 9 10 13 14
The correlation coefficient for the data is 0.9976. Which statement is true about the data in the table?
A) There is a strong positive relationship between x and y.
B) There is a strong negative relationship between x and y.
C) There is a weak positive relationship between x and y.
D) There is a weak negative relationship between x and y.
10. Two groups of students were asked how far they lived from their school. The table below shows the distances in miles:
Group A (distance in miles) 1 1.5 3 3.2 2.8 1.5 1.8 2.5 2.2
Group B (distance in miles) 2 2.5 3.2 3 1.8 2.4 3 1.5 1.8
Which statement best compares the mean distances for the two groups?
A) It is equal for Group A and Group B.
B) It is greater for Group B than Group A.
C) Its value for Group A is double its value for Group B.
D) Its value for Group B is double its value for Group A
DONT ANSWER IF YOU'RE NOT 100% CERTAIN...I NEED TO PASS
Answer:
Ok so the first one, your answer will be C. The height of the plant increases by 2 mm for every hour of sunlight it receives. For the second one, It is B.There is a strong negative relationship between x and y. And the last one is B. It is greater for Group B than Group A.
Step-by-step explanation: Hopes this helps!!! :)
What is this answer?
Class 10R sat a test. The mean mark of the class was 70%. There are 30 students in class 10R, 20 of whom are boys. The mean mark for the boys in the test was 62%.Work out the mean mark for the girls.
86%
70X30=2100
20X62=1240
2100-1240 = 860
860/10=86
Answer:
Mean mark for the girls is [tex]86%[/tex].
Step-by-step explanation:
Given information:
Number of total students in the class=[tex]30[/tex]
Number of boys in the class=[tex]20[/tex]
Then, number of girls will be=[tex]30-20[/tex]=[tex]10[/tex]
The mean mark of the class=[tex]70\times30=2100[/tex]
The mean mark for the boys is [tex]62[/tex]
Then, mark for the boys[tex]=62\times20=1240[/tex]
The mark for the girls=[tex]2100-1240=860[/tex]
Then mean mark of the girls will be [tex]\frac{860}{10}=86[/tex]
Hence, mean mark for the girls is [tex]86%[/tex].
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Let f(x)=25x2−2 .
The function g(x) is a vertical stretch of f(x) by a factor of 2.
What is the equation of g(x)?
Enter your answer in the box.
g(x) =
We are given function f(x) = 25x^2 -2.
g(x) is a vertical stretch of f(x) by a factor of 2.
We know, the transformation rule
y= k f(x), vertical stretch by a factor k. For k>0.
Because function f(x) is being vertical stretched by a factor of 2. So, we need to multiply f(x) function by 2.
Therefore, g(x) = 2 f(x) = 2*(25x^2-2).
Therefore, g(x) = 2*(25x^2-2) or g(x) = 50x^2-4.
Answer:
The Given function is
f(x)= 25 x² -2
Now, a function g(x) is obtained when the function f(x) is stretched by a factor of 2.
Consider point (x,y) on f(x).When function is stretched vertically by a factor of 2 ,it means, the coordinate changes from (x,y) to (x,2 y).
Since we have to stretch the function as whole, we will multiply original function by 2.
So, g(x)= 2× [25 x² - 2] =50 x² -4
g(x)=50 x²- 4
A circular piece of glass has a radius of 2.1 meters. The glass sells for $1.70 per square meter. What is the total cost of the circular piece of glass?
$23.54
$94.16
$3.57
$11.21
simplify the expression by combining like terms. 6x - 7 + 2x + x + 2
9x - 5
8x -5
8x + 5
7x -5
Solve the equation. b + 8 = 16
B = 24
B = -24
B = 8
B = -8
Solve the equation. 6p =-84
P = -14
P = 7
P =-7
P = 14
Name the property shown. 7 + 6 = 6 + 7
Solve the equation. 15 = 5x
X = 3
X = 10
X = 14
X = 5
The second step in the process for factoring the trinomial x^2-3x-40 is to
Answer:
Second step x( x +5 ) -8 (x+ 5 ) in process of factoring .
Step-by-step explanation:
Given : Trinomial x²-3x-40 .
To find : The second step in the process for factoring .
Solution : We have x²-3x-40 .
On factoring x²+ 5x - 8x - 40 .
Taking common x from first two terms and -8 from last two terms.
x( x +5 ) -8 (x+ 5 ) .
Therefore , Second step x( x +5 ) -8 (x+ 5 ) in process of factoring .
3 out of every 5 picks are orange. If 12 picks are orange, how many picks are there in all?
Johanna’s parents give her $10 per week for lunch money. She cannot decide whether she wants to buy or pack her lunch. If a hot lunch at school cost $2, write and solve an inequality to finding the maximum number of times per week Johanna can buy her lunch