Answer:
Final potential energy = 24 Joule
The velocity with which object must be thrown = [tex]4 \sqrt{10}[/tex] m/s
Step-by-step explanation:
Given:
Mass of object, m = 0.30 Kg
Height of object, h = 8 m
Acceleration due to gravity, g = 10 [tex]ms^{-2}[/tex]
a) Formula for Potential Energy:
[tex]E_p =mgh[/tex]
Where m is the mass of object
g is acceleration due to gravity and
h is the height of object
Putting the values of m, g and h
[tex]E_p = 0.3 \times 10 \times 8\\\Rightarrow E_p =24 J[/tex]
b) Formula for initial and final velocity:
[tex]v^{2} =u^{2} +2gh[/tex]
where v is the final velocity
u is the initial velocity with which the object is thrown
g is acceleration due to gravity and
h is the height obtained by object
here v = 0 at the height 8 m because it will come to rest at the point it attains the maximum height.
h = 8m
g = -10 [tex]ms^{-2}[/tex] (negative because the object's velocity is decreasing)
Putting the values to find 'u':
[tex]0^{2} =u^{2} +2 \times -10 \times 8\\\Rightarrow u^{2} = 160\\\Rightarrow u = 4 \sqrt{10}\ m/s[/tex]
Find the slope of the line that passes through the points (-1, -2) and (-9, -2)
Answer:
0
Step-by-step explanation:
Ok use the equation: (Y2 - Y1) / (X2 - X1)
((-2) - (-2)) / ((-9)-(-1))
0/ -8
we know that 0 divided by any number is 0
so slope = 0
which number produces an irrational number when multiplied bby 1/2
Which table represents the graph of a logarithmic function in the form y=log3x when b>1?
Answer:
The satisfied table of the given function[tex]y = log_{b} (x)[/tex]
x 1/8 1/4 1/2 1 2
y -3 -2 -1 0 1
Step-by-step explanation:
Explanation :-
Given logarithmic function [tex]y = log_{b} (x)[/tex] if b >1
Given first table
i)
put x = [tex]\frac{1}{8}[/tex] given b > 1 so we can choose b = 2
[tex]y = log_{2} (\frac{1}{8} )[/tex]
[tex]y = log_{2} (2^{-3} )[/tex]
we will apply logarithmic formula
log x ⁿ = n log (x)
[tex]y = log_{2} (2^{-3} ) = -3 log_{2} (2) = -3 (1) = -3[/tex]
y = -3
ii)
put x = [tex]\frac{1}{4}[/tex] given b > 1 so we can choose b = 2
[tex]y = log_{2} (\frac{1}{4} )[/tex]
[tex]y = log_{2} (2^{-2} )[/tex]
we will apply logarithmic formula
log x ⁿ = n log (x)
[tex]y = log_{2} (2^{-2} ) = -2 log_{2} (2) = -2 (1) = -2[/tex]
y = -2
iii)
put x = [tex]\frac{1}{2}[/tex] given b > 1 so we can choose b = 2
[tex]y = log_{2} (\frac{1}{2} )[/tex]
[tex]y = log_{2} (2^{-1} )[/tex]
we will apply logarithmic formula
log x ⁿ = n log (x)
[tex]y = log_{2} (2^{-1} ) = -1 log_{2} (2) = - (1) = -1[/tex]
y = -1
iv)
put x = 1 given b > 1 so we can choose b = 2
[tex]y = log_{2} (1 )[/tex] = 0
y = 0
v)
put x = [tex]2[/tex] given b > 1 so we can choose b = 2
[tex]y = log_{2} (2 )[/tex]
y = 1
Final answer:-
The satisfied table of the given function
x 1/8 1/4 1/2 1 2
y -3 -2 -1 0 1
The first option is correct because that table of values represents the graph of a logarithmic function in the form [tex]y=\log_b x,b>1[/tex].
Given:
The lograrithmic function form is [tex]y=\log_b x,b>1[/tex].
To find:
The table of values that represents the graph of a logarithmic function in the form [tex]y=\log_b x,b>1[/tex].
Explanation:
It is given that [tex]b>1[/tex]. Let [tex]b=2[/tex], then
[tex]y=\log_2 x[/tex] ...(i)
Substitute [tex]x=\dfrac{1}{8}[/tex] in (i), we get
[tex]y=\log_2 \dfrac{1}{8}[/tex]
[tex]y=\log_2 \dfrac{1}{2^3}[/tex]
[tex]y=\log_2 2^{-3}[/tex]
[tex]y=-3[/tex]
Substitute [tex]x=\dfrac{1}{4}[/tex] in (i), we get
[tex]y=\log_2 \dfrac{1}{4}[/tex]
[tex]y=\log_2 \dfrac{1}{2^2}[/tex]
[tex]y=\log_2 2^{-2}[/tex]
[tex]y=-2[/tex]
Substitute [tex]x=\dfrac{1}{2}[/tex] in (i), we get
[tex]y=\log_2 \dfrac{1}{2}[/tex]
[tex]y=\log_2 2^{-1}[/tex]
[tex]y=-1[/tex]
Substitute [tex]x=1[/tex] in (i), we get
[tex]y=\log_2 1[/tex]
[tex]y=0[/tex]
Substitute [tex]x=2[/tex] in (i), we get
[tex]y=\log_2 2[/tex]
[tex]y=1[/tex]
The table of values is:
[tex]x[/tex] [tex]y[/tex]
[tex]\dfrac{1}{8}[/tex] [tex]-3[/tex]
[tex]\dfrac{1}{4}[/tex] [tex]-2[/tex]
[tex]\dfrac{1}{2}[/tex] [tex]-1[/tex]
[tex]1[/tex] [tex]0[/tex]
[tex]2[/tex] [tex]1[/tex]
Therefore, the first option is correct.
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Find the sum of ( 1- 1/n) + (1 - 2/n) + ( 1 - 3/n)...upto n terms
Answer:
(n-1) / 2
Step-by-step explanation:
We have that the sum has the form of:
Sn = n / 2 [2 * a + (n-1) * d]
we compute the terms of a and d
a = 1 - 1 / n
a = (n - 1) / n
, that is, the first term, in the case d is the subtraction between the second and the first term, thus:
d = 1 - 2 / n - (1 - 1 / n)
d = 1 - 2 / n - 1 + 1 / n
d = - 1 / n
now if replacing these values:
Sn = n / 2 * [2 * (n - 1) / n + (n-1) * (- 1 / n)
Sn = n / 2 * [2 * (n-1) - (n-1)] / n
Sn = 1/2 * (n-1)
Therefore, the value of that sum is (n-1) / 2
Can someone please do the probability please
Answer:
47/73
Step-by-step explanation:
There are 73 people who like tea. 47 are women, 26 are men. This means that the probabili that the person chosen is a women is 47 out of the 73.
When Jonathan bought 12 peaches and pears, at $1.50 per peach and
at $1.60 per pear, the total price was $18.50.
How many peaches and pears did he buy, respectively?
Fill in the blanks provided and solve for the answer.
One number is 9 more than another number. The sum of the numbers is 25. What is one of the numbers?
Answer:
16? maybe
Step-by-step explanation:
i justed counted from 9 to 25,l
Answer:
8 or 17
Step-by-step explanation:
The system of equations for this is:
x = 9 + y
x + y = 25
Find the value of y by plugging the first equation into the second.
9 + y + y = 25
9 + 2y = 25
2y = 16
y = 8
One of the numbers is 8.
OR
Find the value of x by plugging the value of y into one o the equations.
x = 9 + 8
x = 17
or
x + 8 = 25
x = 17
One of the numbers is 17.
the function f is defined by f(x) = 3x-7/8.
(1) Evaluate f(-2) and f(2 5/6).
(2) final the value of x for which f(x)=5
Answer:
-55/8, 61/8, x=47/24
Step-by-step explanation:
not sure if you meant f(25/6) or f(2 5/6), I just assumed it was the second one
but basically just sub in the value into the eqn given
If AB = 3x + 5, BC = 2x + 8, and AC = 88, what is the value of x?
Answer:
x = 15
Step-by-step explanation:
AB + BC = AB
3x+5 + 2x+8 = 88
Combine like terms
5x +13 = 88
Subtract 13 from each side
5x+13-13 = 88-13
5x = 75
Divide each side by 5
5x/5 = 75/5
x = 15
Answer:
15
Step-by-step explanation:
AB + BC = AB
3x + 5 + 2x + 8 = 88
5x + 13 = 88
5x = 88 - 13
= 75/5
= 15
Hope this helps!
1. Evan drove 308 km in the same time that Meghan drove 329 km. If Meghan drove
on average 6 km/h faster than Evan, calculate her average speed and the time taken
for the journey.
Answer:
Her average speed is 94 km/h
Time taken is 3.5 hours
Step-by-step explanation:
Let Evan’s average speed be x km/h.
now since Meghan drove faster, according to the question, we can say her average speed would be x + 6 km/h
Mathematically, time = distance/speed
so; since time is the same; we have
308/x = 329/(x + 6)
cross multiply
329(x) = 308(x + 6)
329x = 308x + 1848
329x-308x = 1848
21x = 1848
x = 1848/21
x = 88 km/h
Meghan average speed = x + 6 = 88 + 6 = 94 km/h
Time taken would be 329/94 = 3.5 hours
Which of the following is a ray shown in the drawing?
Answer:
So to get the answer we need to find both of the rays. So first we need to find the end points for the horizontal one. That would be D and E for the horizontal. Those are points, do the same for the diagonal one. AC would be it. AC and DE would be the answer
Please answer correctly !!!!!! Will mark brainliest answer !!!!!!!!!
Answer:
(x+2)²+1
Step-by-step explanation:
because the graph we know that gx is (x+2)²+1
According to survey records, 75.4% of women aged 20-24 have never been married. In a random sample of 25 young women aged 20-24, find the mean, variance and standard deviation for the number who are or who have been married.
Answer:
mean = 6.15
variance = 4.637
standard deviation = 2.15
Step-by-step explanation:
It is given that 75.4% of women aged 20-24 have never been married.
We are interested in finding the mean, variance and standard deviation for the number who are or who have been married.
So the percentile of women who have been married is given by
[tex]p = 1 - 0.754 \\\\ p = 0.246 \\\\q = 1 - p \\\\q = 1 - 0.246 \\\\q = 0.754[/tex]
The mean is given by
[tex]mean = n\times p[/tex]
Where n is the sample size
[tex]mean = 25\times 0.246 \\\\mean = 6.15[/tex]
Therefore, the mean is 6.15
The variance is given by
[tex]variance = n \times p \times q \\\\variance = 25 \times 0.246 \times 0.754 \\\\variance = 4.637[/tex]
Therefore, the variance is 4.637
The standard deviation is given by
[tex]standard \: deviation = \sqrt{variance} \\\\standard \: deviation = \sqrt{4.637} \\\\standard \: deviation = 2.15[/tex]
Therefore, the standard deviation is 2.15
What are the solutions of the system 7x + 3y = -3 and y = -2x? (-1, 0) and (0, -1) (-8, 3) and (3, -8) (-1, 0) and (-8, 3) (0, -1) and (3, -8)
The solution of the system of equation can be solved by using substitution method. Therefore, the solutions of the system 7x + 3y = -3 and y = -2x is (-3, 6)
How to find solution to the system of equation
7x + 3y = - 3
y = - 2x
Substitute the value of y in equation(i)
Therefore,
7x + 3(- 2x) = -3
7x - 6x = -3
x = -3
Let's find y by substituting the value of x in equation(ii)
y = -2x
y = -2(-3)
y = 6
Therefore, the solution set of the equation is (-3, 6)
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When multiplying two negative integers, what is the sign of the product?
positive
negative
zero
one
Mark this and return
Save and Exit
y Next
Sul
Answer:
positive
Step-by-step explanation:
negative and negative = positive
positive and positive = positive
positive and negative = negative
negative and positive = negative
hope u got what u needed
Answer:
The correct answer is positive
Step-by-step explanation:
Negitive x Negitive = Positive
Positive x Positive = Positive
Negitive x Postive = Negitive
Positive x Negitive = Negitive
This should help you for next time you have a question like this.
I hope this helps.
Which of the following is an equation of a line parallel to the equation y=4x+1?
−12 − (−25) + 8
plzz helpp im not sure is it 21??
Answer:
21
Step-by-step explanation:
−12 − (−25) + 8
Subtracting a negative is like adding
-12 +25+8
First do -12 +25 25-12 = 13 Replace in the equation
13+8
21
Answer:
Yes, the answer is
[tex]21[/tex]
Step-by-step explanation:
we know that,
[tex]( - ) \times ( - ) = ( + )[/tex]
Now let's solve the problem,
[tex] - 12 - ( - 25) + 8 \\ - 12 + 25 + 8 \\ = 21[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Add the polynomials.
(4x + 11) + (12x + 2)
a
16x + 13
b
12x + 9
С
25x + 16
d. 19x + 13
Answer:
[tex](4x + 11) + (12x + 2) =(4x + 12x) + (2 + 11) = 16x + 13[/tex]
Step-by-step explanation:
Answer = a. 16x+13
You and a friend are trying to find a flag hidden in the woods. Your friend is standing
75 feet away from you. When facing each other, the angle from you to the flag is 720 and the angle from your friend to the flag is 53°. Is there enough information to locate
the flag?
Answer: Yes there is
Step-by-step explanation:
look bro your trying to get a total of 180 degrees
you already got 72 and 53 degrees
so add the two numbers and then subtract it from 180 degrees
thats 180 degrees minus 125 degrees
your missing point is 55 degrees
Mary is also a civil engineer, and she is building a triangular community garden. She knows two angles in the triangular garden, diagramed below. A triangle has angle measures 92 degrees, 27 degrees, and a degrees. The exterior angle to a degrees is b degrees. What are the measures of interior angle a and exterior angle b? a = ° b = °
Answer:
A= 61
B=119
Step by step:
a; interior angle
180-(27+92)
=180(119)
=61
b; exterior angle
180-61
=119
Answer: 61 and 119
Step-by-step explanation:
Math help please! What are the possible solutions to this system?
Answer:
x < 6.5
y < -1.5
Step-by-step explanation:
y > x - 8
Therefore x < y + 8
y < 5 - x
Therefore x < 5 - y
2x < 13
x < 6.5
6.5 < 5 - y
y < -1.5
Alberto sanded a wooden floor with his electric sander at a constant rate. Suppose
1
3
he sanded 40 square feet of floor in hours. How large an area would he have
5
sanded in 1 hour?
John is selling tickets to an event. Attendees can either buy a general admission ticket, x, or a VIP ticket, y. The general admission tickets are $55 in the VIP tickets are $70. If he knows he sold a total of 25 tickets and made $1480 how many of each type did he sell?
Answer:
Step-by-step explanation:
55x + 70y = 1480
x + y = 25
55x + 70y = 1480
-55x -55y = -1375
15y = 105
y = 7 VIP tickets sold
x + 7 = 25
x = 18 general admission tickets
(18,7)
which function below is the inverse of f(x)= 7x-1/2
Answer: [tex]f^{-1}(x)=\frac{x}{7}+\frac{1}{14}[/tex]
Step-by-step explanation:
If we have y=7x-1/2, the inverse is where we solve for x instead of y.
We can isolate x to get 7x=y+1/2, then divide by 7 to get x=y/7+1/14.
Therefore, [tex]f^{-1}(x)=\frac{x}{7}+\frac{1}{14}[/tex].
Hope that helped,
-sirswagger21
please help me, with full explanation!!!!
Answer:
9.54 cm
Step-by-step explanation:
In triangle ABD, AD is the hypotenuse (longest side)
We know that according to Pythagoras theorem,
a^2+b^2=c^2
In the figure, c (10cm) and a (5cm) is given. So,
(5)^2 + b^2 = 100
25+b^2 = 100
b^2 = 75
So b is √75 = 8.66
Therefore BD is 8.66 cm
Now even BDC is a triangle
In it, the hypotenuse is missing but we know the value of other sides
so, in Pythagorean theorem,
a=4 (CD)
b=8.66 (BD)
c=x
Therefore,
(4)^2 + (8.66)^2 = x^2
16+74.99= x^2
x^2 = 90.99
x= 9.54 cm
Hope this helps!
The double number lines show the ratio of minutes to days. How many minutes are in 2 days
Answer:
2880 minutes are in two days
The formula for the area of a triangle is , where b is the length of the base and h is the height.
Find the height of a triangle that has an area of 30 square units and a base measuring 12 units.
3 units
5 units
8 units
9 units
Answer:
5 units
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
30 = 1/2 (12)h
Multiply
30 = 6h
Divide each side by 6
30/6 = 6h/6
5 = h
Answer:
5 units
Step-by-step explanation:
Next time please supply the formula, which was apparently given in this question:
A = (1/2)(base)(height)
Here, A = 30 units^2 = (1/2)(12 units)(height), or
30 units^2 = (6 units)(height)
Solving for (height), we get
30 units^2
(height) = ------------------ = 5 units
6 units
The height is 5 units
Classify the following triangle. Check all that apply.
Answer:
Right, Scalene (D and E)
Step-by-step explanation:
One side of the triangle contains a right angle, therefore it is a right triangle
the three sides are all different lengths from each other, making it scalene
Answer:
D. Right
E. Scalene
Step-by-step explanation:
Definitions
Acute: A triangle whose angle measure are all acute angles.
Equilateral: A triangle with all the same side lengths and angle measures.
Obtuse: A triangle with one obtuse angle and two acute angles.
Right: A triangle who has a right angle and two acute angles.
Scalene: A triangle whose sides are all different lengths
Isosceles: A triangle who has 2 sides the same length and the other different.
Our triangle fits the descriptions of the right triangle and scalene triangle.
In the diagram above, <1 = 135º.
Find the measure of <3.
Answer:
The measurement of ∠3 is 135°
Step-by-step explanation:
In the problem, we are given a measurement. The measurement of ∠1 is 135°. We are asked to find the measurement of ∠3.
∠1 and ∠3 are corresponding angles. This means that they will have the same measurements.
So, if m∠1 is 135° then the m∠3 is also 135°
Answer:
m∠=135°
Step-by-step explanation:
These lines are parallel lines, which is indicated by the two arrows towards the right of the lines.
Since these lines are parallel, corresponding angles, such as ∠1 and ∠3 can exist.
Corresponding angles are congruent, which means they have the same measure.
∠1 and ∠3 are corresponding angles, therefore
∠1=∠3
We know that the measure of ∠1 is 135 degrees. Therefore, ∠3 will also have a measure of 135 degrees.
135=∠3
The measure of ∠3 is 135 degrees.
In △XYZ, m∠X = 27° and m∠Y = 48°. Which gives the sides of the triangle in order from shortest to longest?
Answer:
z, y and x
Step-by-step explanation:
Now, to answer this question, what we must know is that the side facing the largest angle is the largest while the side facing the smallest is the smallest.
What i’m saying in essence is that the bigger the angle faced, the larger the side.
Now since we have 3 angles in a triangle that adds up to 180
we have 27 and 48 already, the third side would be 180-27-48 = 105
So which side faces which angle?
Let’s have a diagrammatic representation of the said triangle.
Check this in the attachment please
The longest side is thus z, followed by y and lastly x
The measure of the angle from shortest to longest will be ∠z, ∠y, and ∠x.
What is angle measurement?An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).
Given data;
m∠X = 27°
m∠Y = 48°
The sum of the angle of the triangle is 180°
m∠X+m∠Y+m∠Z = 180°
27° +48° + m∠Z = 180°
m∠Z = 105°
The order of the angle measurement;
m∠Z > m∠Y > m∠X
Hence, the measure of the angle from shortest to longest will be ∠z, ∠y, and ∠x.
To learn more about the angle measurement, refer to the link;
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