The height of the bullet after 3 second is 640m
What is motion under gravity?Motion under gravity refers to the movement of an object whose vertical motion is affected by the presence of gravity. The force that attracts objects downwards is gravity. In fact, gravity works towards the centre of the Earth.
When an object is thrown up, the height of the object is calculated as h = v²/2g
where v is the velocity and g is the acceleration due to gravity.
v = -16t²+ 256(t)
when t = 3s
v = -16( 3)²+ 256
v = -144+256
v = 112m/s
therefore the height attained by the bullet =
h = 112²/2×9.8
h = 640m
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the population of tree frogs in increasing by a rate of 35% every year. the population started with 6 tree frogs. how many tree frogs will there be in 8 years? brainly
The population growth rate can be calculated using the equation x = x₀ (1+r)ⁿ. The population after 8 years will be 66 frogs.
The population growth is the increase in population after the specified number of years. Lets look into the data which is given.
The initial population is 6 tree frogs.
Population growth percent = 35%
Rate of growth, r = 35/100 = .35
The population growth is calculated using the equation, x = x₀ (1+r)ⁿ
x₀ is initial population
r is the rate
n is the number of years.
x = 6 (1+r)⁸ = 66.19
So the population of frog after 8 years will be 66.
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Find the slope of the line passing through the points of -2,8 and 4,8
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{0}{4 +2} \implies \cfrac{ 0 }{ 6 } \implies \text{\LARGE 0}[/tex]
what is the sum in the simpelest form
4 1/2 + 1 3/5
uppose that each member of the executive board also has a specified office: one member of the executive board is the president, another is the vice president, a third is the secretary, and the last one the treasurer. how many different executive boards can there be?
After solving, total 360 different executive boards can there be.
In the specified office have one member of the executive board is the president, another is the vice president, a third is the secretary, and the last one the treasurer.
So there are total 6 members.
The total number of members in executive board = 4
So, the ways of selecting different executive boards = [tex]^{6}P_{4}[/tex]
The ways of selecting different executive boards = [tex]\frac{6!}{(6-4)!}[/tex]
The ways of selecting different executive boards = [tex]\frac{6!}{2!}[/tex]
The ways of selecting different executive boards = [tex]\frac{6\times5\times4\times3\times2!}{2!}[/tex]
The ways of selecting different executive boards = 6 × 5 × 4 × 3
The ways of selecting different executive boards = 360
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To learn more about
The complete question is:
From a committee of 6 members, suppose that each member of the executive board also has a specified office: one member of the executive board is the president, another is the vice president, a third is the secretary, and the last one the treasurer. How many different executive boards can there be?
Which of the following lines is parallel to y = 1/5x + 4
5 y - x = 6
y + 5 x = 4
5 y - 2 x = 15
The line that is parallel to y = 1/5x + 4, is A. 5 y - x = 6.
What are parallel lines ?Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. No matter how far we extend a parallel line, it will never meet another parallel line.
As mentioned parallel lines will have the same slope so the line that is parallel to y = 1/5x + 4 would have the same slope of 1 / 5.
Converting the first option to slope intercept form gives:
5 y - x = 6
5 y = 6 + x
y = 6 / 5 + x / 5
y = 1.2 + 1 / 5 x
This slope is the same as y = 1/5x + 4 so they are parallel.
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Jim weighed 225 pounds. After dieting and exercising, he lost 16% of his weight. How many pounds does Jim now weigh?
Please answer quick I need the help
New weight = 225 x (1 - (16 / 100)) = 225 x 0.84 = 189 pounds.
So, after dieting and exercising, Jim now weighs 189 pounds.
Answer: 189 pounds
Step-by-step explanation:
If he lost 16% of his weight, Jim is now 84% of his original weight.
84% = 0.84
225 x 0.84
189 pounds
What is the scale factor from Figure A to Figure B?
The scale factor of figure A to fig B is 1 : 4
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
Figure A is the small triangle and figure B is the small triangle.
The ratio of the corresponding lengths of the triangles must give thesame value.
scale factor = original length/ new length
scale factor = 14/56 = 1/4 = 1 : 4
also , 16/64 = 1/4 = 1:4
7/28 = 1/4 = 1:4
therefore since the ratio of all the sides are equal, the scale factor of figure A to fig B is 1:4
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Write the slope-intercept form of the equation of the line. ( Question is Attached.)
Assist me,
Thanks!
The factors of 42 are shown below. Which of them are not prime?
1
2 3 6
7 14 21 42
Answer:2 and 3
Step-by-step explanation:
When y varies directly as x and x = 2 when y = 6.
What is the value of x when y = 10
Answer: its 15
Step-by-step explanation:
Please help
find the area of the irregular shape. Round to the nearest tenth
The area of the irregular figure is 65.12 cm².
What is the area of the irregular shape?
We know that a shape is said to be irregular if the shape does not fit into any of the known patterns of shape that we have. In this case, we have a kind of shape that is made up of the rectangle and the semi circle.
We know that we can be able to obtain that area of the rectangle by the use of the formula;
A = l * w
A = area
l = length
w = width
We then have;
A = 8 cm * 5 cm
= 40 cm^2
For the semi circle;
A = (π r²)/2
A = (3.14 (4²))/2 = (3.14*16)/2 = 50.24/2 = 25.12cm²
Total area of the figure = 40 cm² + 25.12 cm² = 65.12 cm²
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Any help appreciated
Answer:
Step-by-step explanation:
A parabola has vertex (2,3) and contains the point (0,0). Write and equation for this parabola
The equation of the parabola with a vertex (2,3) and contains the point (0,0) is: y = -3/4(x - 2)² + 3
How to write the equation of parabolaParabolic equitation or Quadratic equation with a vertex (2,3) and contains the point (0,0) is written using the vertex form of the equation which is:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The vertex
v (h, k) = (2, 3)
h = 2
k = 3
substitution of the values into the equation gives
y = a(x - 2)² + 3
considering the parabola passed the point (0, 0)
y = a(x - 2)² + 3
0 = a(0 - 2)² + 3
-3 = a(4)
a = -3/4
substituting for a
y = -3/4(x - 2)² + 3
hence the required equation is y = -3/4(x - 2)² + 3
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ii. (2 points) you put the coin back, take another, and flip it 4 times. it lands t, h, h, h. how likely is the coin to be type h50?
If the coin is tossed four times , then the probability of getting exactly two heads and two tails is 3/8 .
the number of outcomes in tossing a coin is = 2 = {H , T} ;
the number of outcomes in tossing the coin four times is = 2⁴ = 16 ;
we have to find the probability of getting exactly 2 heads and 2 tails :
So , the required outcomes will be = {HHTT, HTHT, HTTH, THHT, THTH , TTHH} ;
the number of favorable outcomes is = 6 ;
the probability is = 6/16 = 3/8 .
Therefore , the required probability is 3/8 .
The given question is incomplete , the complete question is
If a coin is tossed 4 times, what is the probability of getting exactly two heads and two tails ?
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Enter the range of values for x:
2x - 4
10
45°
60°
[?]
Enter
The range of the values of x is 7<x<2.
In the given quadrilateral we can see that 2 of its sides are equal and the diagonal of the quadrilateral divides the quadrilateral into 2 triangles.
we can label the diagonal as "b" and the equal sides as "a".
when we apply the cosine law on the upper triangle, we get,
(2x-4)² = a² + b² - 2abcos45°
=(2x-4)² = a² + b² - 2ab×1/√2
=(2x-4)² = a² + b² - √2ab
Similarly, applying the cosine law on the lower triangle,
10² = a² + b² - 2abcos60°
= 10² = a² + b² - 2ab×1/2
= 10² = a² + b² - ab
we can clearly see from the above 2 equations formed by applying cosine law to the triangles that,
(2x-4)²<10²
2x-4<10
2x<14
x<7
and we know that 2x-4 has to be positive So,
2x-4>0
2x>4
x>2
combining these inequalities we get,
7<x<2
which gives the range, where x will belong
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Answer:
Step-by-step explanation:
The answer that thay already gave is backwards its actully 2<x<7 in acellus
the question is on the picture
The length of the line segment is given by the distance equation
D = 7.2 units
What is the distance of a line between 2 points?The distance of a line between 2 points is always positive and given by the formula
Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )
The distance between A and B is D , and the distance D is
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Given data ,
Let the distance of the line segment between two points be D
Now , the equation will be
Let the first point be represented as P ( 1 , 6 )
Let the second point be represented as Q ( 7 , 2 )
Now , distance between P and Q is D , and the distance D is
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
D = √ ( 1 - 7 )² + ( 6 - 2 )²
On simplifying the equation , we get
D = √ ( -6 )² + ( 4 )²
D = √ ( 36 + 16 )
D = √ 52
D = 7.2 units
Hence , the distance is 7.2 units
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A traffic light at a certain intersection is green 55% of the time, yellow 10% of the time, and red 35% of the time. A car approaches this intersection once each day. Let Y denote the number of days up to and including the third day on which a red light is encountered. Assume that each day represents an independent trial.
Find P(Y=7)
Find the mean of Y
Find the Variance of Y
The probability of the car encountering it's first red light on the third day, i.e., P(Y = 3) will be 0.1479
According to the question,
we have to calculate the probability of the car encountering it's first red light on the third day, i.e., P(Y = 3)
Here,
Probability of encountering a Red light = 0.35, since traffic light at the intersection is red 35% of the time.
And Y is the number of days that pass up to and including the first time the car encounters a red light, i.e.,
The distribution here is a geometric one, where
P(Y = 3)
= P(Not red light in initial 2 lights) x P(red light in third light)
= [(1 - 0.35)² X 0.35]
= 0.1479
so, the probability of the car encountering it's first red light on the third day, i.e., P(Y = 3) will be 0.1479.
Note:
mean and variance of this question is not possible to find out.
the complete question ends till the probability to find the first red light on the third day.
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Zac and lynn are each traveling on a tri so far ac has traveled 123. 75 miles in 2. 25 hours. Lynn leaves half an hour after Zar=c so far she has traveled 105 milwa in 1. 75 hours assume Zac an Lynn travel at a constant rate
The solution of the system of linear equations is :-
x = 6 hours .
y = 330 miles.
Now, According to the question:
Let x be the number of hours that have elapsed since Zac started traveling .
Let y be the number of miles traveled .
We know that,
Speed = Distance / Time.
so,
Speed of Zac = D / T = 123.75 / 2.25 = 55 miles / hour.
Speed of Lynn = D / T = 105 / 1.75 = 60 miles / hour.
then, Distance travelled by Zac in x hours = S * T
y = 55 × x
y = 55x miles
and, Distance travelled by Lynn in (x - 0.5) hours = S * T
y = 60 × (x - 0.5)
y = 60x - 30
Therefore, a system of linear equations that represents the distance each of them has traveled since Zac left on his trip are :-
y = 55x ----------- Eqn.(1)
y = 60x - 30 ------------- Eqn.(2)
Now, putting value of Eqn.(1) in Eqn.(2) , we get,
55x = 60x - 30
60x - 55x = 30
5x = 30
x = 6 hours.
Putting value of x in Eqn.(1),
y = 55 * 6
y = 330 miles.
Hence, the solution of the system of linear equations is :-
x = 6 hours .
y = 330 miles.
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how to simplify, 8(-6x-4)
Answer: -48x-32
Step-by-step explanation:
A regular pentagon is such that is vertices Lie
circumference of a circle of radius
on
the
4.5cm. find the length of aside of the
pentagon to the nearest mm.
Answer: The length of a side of a regular pentagon can be found using the formula, side = 2r * sin(π/5), where r is the radius of the circle that the pentagon is inscribed in. Using this formula, the length of a side of the pentagon is approximately 4.08 cm or 40.8 mm (rounded to the nearest mm).
Molly's teacher got six boxes of pencils each box contains P pencils he use 16 pencils in the first month of school write an expression that represents the given situation
Answer:
The expression that represents the given situation is 6P - 16.
Step-by-step explanation:
The teacher got six boxes of pencils, and each box contains P pencils. Since the teacher used 16 pencils in the first month of school, the total number of pencils left after the first month can be represented by the expression 6P - 16.
This expression means that the teacher started with 6 boxes of pencils, each containing P pencils, for a total of 6P pencils. But since the teacher used 16 pencils in the first month, the total number of pencils left after the first month is 6P - 16.
Factor.
5x + 25
7m +42
a -ounce bottle of fresh water is . a -ounce bottle of spring water is . which statement about the unit prices is true?
The true statements about the unit prices :
spring water has a lower unit price of $0.11/ounce and fresh water has a lower unit price of $0.12/ounce
The correct answer: option (A) and option (C)
We use the unitary method in order to determine the unit price.
Here, 16-ounce bottle of spring water is $1.76. A 20-ounce bottle of fresh water is $2.40
Let us assume that the unit price of spring water be 'm' and the unit price of freshwater be 'n'.
By unitary method the unit price of spring water would be,
m = 1.76/16
m = 0.11
This means, 1 ounce bottle of spring water is $0.11
And the unit price of freshwater be:
n = 2.40 / 20
n = 0.12
i.e., the unit price of freshwater is $0.12
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The complete question is:
A 16-ounce bottle of spring water is $1.76. A 20-ounce bottle of fresh water is $2.40. which statement about the unit prices is true?
A)spring water has a lower unit price of $0.11/ounce
B) spring water has a lower unit price of $0.12/ounce
C)fresh water has a lower unit price of $0.12/ounce
D)fresh water has a lower unit price of $0.11/ounce
The sides of a triangle are measured at a = 4, b = 5 and c = 6. What is the length of Median A?
The length of median A is 11.7.
What is centroid and median of a triangle and its coordinates?The point of intersection of a triangle's medians is its centroid (the lines joining each vertex with the midpoint of the opposite side).
If the triangle has its vertices as (x_1, y_1), (x_2, y_2) , \: (x_3, y_3), then the coordinates of the centroid of that triangle is given by:
[tex](x,y) = \left( \dfrac{x_1 + x_2 + x_3}{3} + \dfrac{y_1 + y_2 + y_3}{3} \right)[/tex]
Given;
The sides of triangle
a = 4, b = 5 and c = 6
The median of triangle =½√(2b2+2c2-a2).
=(2*5*5+2*6*6-4*4)
=(50+72-16)
=[tex]\sqrt{138}[/tex]
=11.7
Therefore, the median of triangle will be 11.7
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Find the sum of -3x+9 and 7x2-2x+1
The sum of the given expressions -3x + 9 and 7x^2 - 2x + 1 is
= 7x^2 - 5x +10
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given expressions are ,
-3x + 9 and 7x^2 - 2x + 1
So,
The sum of the expressions could be
= -3x+9 + 7x^2 - 2x + 1
= 7x^2 -3x-2x + 9+1
=7x^2 - 5x +9+ 1
= 7x^2 - 5x +10
Hence, The sum of the given expressions -3x + 9 and 7x^2 - 2x + 1 is
= 7x^2 - 5x +10
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A line is perpendicular to y = −1/3x + 7
and intersects the point (4,2).
What is the equation of this
perpendicular line?
y = [?]x + [ ]
Hint: Use the Point-Slope Form: y - y₁ = m(x - X1)
Then write the equation in slope-intercept form.
A line that is perpendicular to the line y = -1/3x + 7 has a slope that is the negative reciprocal of -1/3 which is 3.
We know that the line intersects the point (4,2), so we can use this point and the slope to write the equation of the line in point-slope form:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through, m is the slope, and y and x are the coordinates of any point on the line.
So the equation of the line that is perpendicular to y = −1/3x + 7 and intersects the point (4,2) is:
y - 2 = 3(x - 4)
Simplifying this, we get
y = 3x - 2
To convert this to the slope-intercept form we can rewrite it as
y = 3x + b
Therefore, the equation of the line that is perpendicular to y = −1/3x + 7 and intersects the point (4,2) is y = 3x - 2
For the following right triangle, find the side length x. Round your answer yo the nearest hundredth
Answer:
14.87
Step-by-step explanation:
Pythagorean Thereom
c²= a²+b²
10²+11²=c²
100+121=c²
221=c²
c=14.866...
c=14.87
Evaluate : 2 (x-4) + 3x - x^2 for x = 3.
A. 6
B.- 6
C. 2
D. -2
Answer: -2
Step-by-step explanation:I'am in a rush right now sorry
Three players scored a total of 70 points during a basketball game. Jan
scored twice as many points as Tritt and ten points fewer than Sarah. Let x
represent the number of points that Jan scored. Which equation could be
used to solve for the number of points that Jan scored in the game?
Ox+(0.5x)+(x+10) = 70
O 0.5x+(x+10) = 70
O 3x = 70
Ox+(x+10)+2x = 70
The equation that can be used to solve for the number of points that Jan scored in the game is:
x + 2x + (x-10) = 70
Given that Jan scored twice as many points as Tritt, we can use the equation
2x = Tritt.
Given that Jan scored ten points fewer than Sarah, we can use the equation
x = Sarah - 10.
Also, we know that the total number of points scored by all three players is 70, so we can use the equation:
x + Tritt + Sarah = 70
If we replace Tritt with 2x and Sarah with x-10, we get:
x + 2x + (x-10) = 70
So the equation that can be used to solve for the number of points that Jan scored in the game is:
3x -10 = 70
We get x = 30, which means Jan scored 30 points in the game.
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Leila just put 14.11 gallons of fuel into her car. There were 1.9 gallons in the car to begin with. How much fuel is in Leila's car now?
Answer:
16.01 gallons of fuel.
Step-by-step explanation:
So we already know that there were initially 1.9 gallons. We have to add 14.11 gallons of fuel to the starting amount.
14.11 + 1.9 = 16.01 gallons
I hope this was able to help you :D
To find out how much fuel is in Leila's car now, we need to add the amount of fuel she just put in to the amount that was already in the car.
Leila put 14.11 gallons of fuel in the car and there were 1.9 gallons in the car to begin with.
So, 14.11 gallons + 1.9 gallons = 16.01 gallons
This is the correct answer because 14.11 gallons is the fuel Leila put into her car and 1.9 gallons is the fuel that was already in the car. Adding these two values together gives the total amount of fuel in the car now, which is 16.01 gallons.