Both balls will strike the ground simultaneously, but the faster ball will do so farther away from the table.
What is acceleration due to gravity ?The unit g stands for gravitational acceleration. At sea level, the standard value of g on earth's surface is 9.8 m/[tex]s^{2}[/tex]
They will strike the ground simultaneously if the table and the ground are both flat.
It is customary to divide an object's motion into a vertical component and a horizontal component. While they are on the table, neither of the balls is moving vertically. Both balls begin to accelerate downward as soon as they leave the table due to the effects of gravity. Given that both balls experience the same acceleration from gravity, they will fall at the same rate and with the same downward velocity.
Both balls will strike the ground simultaneously, but the faster ball will do so farther away from the table.
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Pls answer its for my final
The equivalent expression is (x + 2√3i) (x - 2√3i).
What is a Polynomial Equation?
The equations formed with variables, exponents and coefficients are called as polynomial equations. It can have different exponents, where the higher one is called the degree of the equation.
Given polynomial is,
x² + 12
We need to find it's equivalent expression for that see the options
Solve the option (a)
(x + 2√3i) (x - 2√3i)
Now, solve this if we get equal to x² + 12 that means that option is answer
x(x - 2√3i) + 2√3i(x - 2√3i)
x² - 2xi√3 + 2xi√3 - 2√3i * 2√3i
x² - 12 i²
we know, i² = -1
so, we get
x² + 12
We get the answer by 1st option. If you solve other options you'll get different answer.
Hence, the equivalent expression is (x + 2√3i) (x - 2√3i).
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The city council voted on a new tax. 38 council members voted in favor of the tax. The council has 76 members. What percentage of the council members voted in favor of the tax
The percentage of the council members who voted in favor of the tax is 50%.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, the council has 76 members out of which 38 members voted in favor of the tax.
The percentage amount of members who favor the tax is:
(38/76) × 100%
= 50%
Hence, the percentage of the council members who voted in favor of the tax is 50%.
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What does (5x2−14x+24)÷(x−4) equal?
I dont need explanation or anything just answer pls
The value of (5x2−14x+24)÷(x−4) is 5x + 6
How to calculate value of (5x2−14x+24)÷(x−4)?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Given ,
5x2 - 14x - 24
x - 4
5x2 multiplied by 14x, then 24.
The first term is 5x2, and 5 is its coefficient.
The coefficient of the middle term, which is -14x, is -14.
"The constant," the final term, is -24.
Step 1: Multiply the first term's coefficient by the constant 5 • -24 to get a result of -120.
Find two factors of -120 whose combined value is equivalent to the middle term's coefficient, which is -14, in step two.
-120 + 1 = -119
-60 + 2 = -58
-40 + 3 = -37
-30 + 4 = -26
-24 + 5 = -19
-20 + 6 = -14 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and 6
5x2 - 20x + 6x - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (x-4)
Add up the last 2 terms, pulling out common factors :
6 • (x-4)
Step-5 : Add up the four terms of step 4 :
(5x+6) • (x-4)
Therefore The value of (5x2−14x+24)÷(x−4) is 5x + 6
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Simplified term is 5x + 6. Simplification is the process of reducing an expression/fraction/problem to a simpler form.
What is simplification method?A mathematical expression is simplified when it is replaced with a simpler, typically shorter, equivalent statement.
Mathematical expressions are made up of different numbers and operations. To simplify them, we must first understand the rule known as the order of operations. It specifies the order in which operations must be performed when simplifying a mathematical expression.
Factoring 5x2 - 14x - 24
The first term is, 5x2 its coefficient is 5 .
The middle term is, -14x its coefficient is -14 .
The last term, "the constant", is -24
Multiply the coefficient of the first term by the constant 5 • -24 = -120
Find two factors of -120 whose sum equals the coefficient of the middle term, which is -14 .
-120 + 1 = -119
-60 + 2 = -58
-40 + 3 = -37
-30 + 4 = -26
-24 + 5 = -19
-20 + 6 = -14
Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and 6
5x2 - 20x + 6x - 24
Add up the first 2 terms, pulling out like factors :
5x • (x-4)
Add up the last 2 terms, pulling out common factors :
6 • (x-4)
Add up the four terms of step 4 :
(5x+6) • (x-4)
Which is the desired factorization
Cancel out (x-4) which appears on both sides of the fraction line.
5x + 6
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Which expression is equivalent to (ab7)4?
ab28
ab11
a5b11
a4b28
The expression that is equivalent to the given expression, (ab⁷)⁴, is a⁴b²⁸. The correct option is the last option a4b28
Writing an equivalent expressionFrom the given information, we are to determine the expression that is equivalent to the given expression
The given expression is
(ab⁷)⁴
To determine the expression that is equivalent to this expression, we will expand the given expression
Expanding the expression
(ab⁷)⁴
Applying the distributive exponent law of indices,
(a)⁴ × (b⁷)⁴
Simplifying
a⁴ × b²⁸
= a⁴b²⁸
Hence, the equivalent expression is a⁴b²⁸
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Answer:
I think it's a4b28
Step-by-step explanation:
I Need Help For This TGA
Comparing the given expression as per the solution:
(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2²
The expressions are given in the question as:
(8 + 3² - 2·6)/(7 - 1·2) and (3/4 + 1/8) + 1/8 - 2²
As per the PEMDAS rule, the required solution would be as:
⇒ (8 + 3² - 2·6)/(7 - 1·2)
⇒ (8 + 9 - 12)/(7 - 2)
⇒ (17- 12)/5
⇒ 5/5
⇒ 1
⇒ (3/4 + 1/8) + 1/8 - 2²
⇒ (6 + 1)/8 + 1/8 - 4
⇒ 7/8 + 1/8 - 4
⇒ (7 + 1)/8 - 4
⇒ 8/8 - 4
⇒ 1 - 4
⇒ -3
Here 1 > -3
Thus, comparing the given expression as per the solution:
(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2².
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Answer:Pemdas
Step-by-step explanation:Comparing the given expression as per the solution:
(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2²
The expressions are given in the question as:
(8 + 3² - 2·6)/(7 - 1·2) and (3/4 + 1/8) + 1/8 - 2²
As per the PEMDAS rule, the required solution would be as:
⇒ (8 + 3² - 2·6)/(7 - 1·2)
⇒ (8 + 9 - 12)/(7 - 2)
⇒ (17- 12)/5
⇒ 5/5
⇒ 1
⇒ (3/4 + 1/8) + 1/8 - 2²
⇒ (6 + 1)/8 + 1/8 - 4
⇒ 7/8 + 1/8 - 4
⇒ (7 + 1)/8 - 4
⇒ 8/8 - 4
⇒ 1 - 4
⇒ -3
Here 1 > -3
Thus, comparing the given expression as per the solution:
(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2².
A wire of length 15 is cut into two pieces which are then bent into the shape of a circle of radius r and a square of side s . Then the total area enclosed by the circle and square is the following function of s and r If we solve for s in terms of r , we can reexpress this area as the following function of r alone:
Thus we find that to obtain maximal area we should let r= To obtain minimal area we should let r=
Since s = (15 - 2πr ) / 4 and s > 0, the maximum r is 15/(2π). This same r will also maximize the area.
Since the length of 15 is divided between the circumference of the circle and the perimeter of the square,
2πr + 4s = 15 ⇒ s = (15 - 2πr ) / 4
A = πr2 + s2 = πr2 + [ (15 - 2πr ) / 4]2 = πr2 + (225 - 60πr + 4π2r2) / 16
A = π(1 + π/4)r2 - (15/4)πr + 225/16
dA/dr = 2π(1 + π/4)r - (15/4)π = 0 ⇒ r = (15/4)π / [2π(1 + π/4)] = 15 / (8 + 2π)
Since A(r) is concave up, it has a minimum at
r = 15 / (8 + 2π)
Since s = (15 - 2πr ) / 4 and s > 0, the maximum r is 15/(2π). This same r will also maximize the area.
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Given the following exponential function,
identify whether the change represents
growth or decay, and determine the
percentage rate of increase or decrease.
y = 970(1.042)*
The change represents growth and rate of increase is 4.2%
What is an exponential function?Exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change.
Given that, an exponential function y = 970(1.042)ˣ
When the growth rate is greater than 1, then the function represents a growth.
The general form equation is:
y(x)= a(1+r)ˣ such that r is the growth percent.
So,
1+r = 1.042
r = 0.042
r = 4.2%
Hence, the growth rate is 4.2%
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5 customers entered a store over the course of 15 minutes. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
THE CORRECT ONE GETS BRAINLIEST
Van is 12 yrs older than john. Two yrs ago. Van was twice as old as john. Find thier present age.
Answer:
John = 14 ; Van = 26
Step-by-step explanation:
V = 12 + J
V - 2 = 2(J-2)
12 + J - 2 = 2J - 4
J + 10 = 2J - 4
2J - J = 10 + 4
J = 14
V = 12 + 14
V = 26
Write as a logarithmic equation. 2^1/2= square root 2
Answer:
1
log₂√2 = ------
2
Step-by-step explanation:
I'm assuming the equation looks like this:
2¹⁽² = √2
1
log₂√2 = ------
2
I hope this helps!
help meeeeeeeeeee pleaseee
The pressure of 28 inches of mercury occurs at 6.03 miles from the eyes of the hurricane
How to determine the distance?From the question, we have the following pressure function that can be used in our computation:
f(x) = 0.48 ln(x + 2) + 27
Also from the question, we have
Pressure = 28 inches
This means that
f(x) = 28
So, we have the following equation
0.48 ln(x + 2) + 27 = 28
Subtract 27 from both sides
0.48 ln(x + 2) = 1
Divide 0.48 from both sides
ln(x + 2) = 2.083
Take the exponent of both sides
x + 2 = 8.03
So, we have
x = 6.03
Hence, the distance is 6.03 miles
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express 2/(1-(x^2)) into partial fractions
2/ ( 1 + x) ( 1 - x) is express into partial fractions.
With an example, what is a partial fraction?
The division of an algebraic fraction into smaller, "partial fractions," components is possible. Think about the algebraic fraction (3x+5) (2x2-5x-3). This formula can be broken down into its simplest form, [2/(x - 3)] - [1/(2x + 1)]. Partial fractions are the more straightforward pieces [2/(x - 3)] and [1/(2x + 1)].
The four categories of partial fractions are linear factors, degree 2 irreducible factors, repeated linear factors, and repeated irreducible degree 2 factors.
= 2/(1-(x^2))
= 2 / (1)² - (X)²
= 2/ ( 1 + x) ( 1 - x)
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Could someone help??
Answer:
C.
Step-by-step explanation:
For the first letter there are 26 choices, then, since one has been used, for the second letter there are only 25 choices left. And so on. You multiply them to get the total number of combinations.
For the digits, the initial choice is from 10 digits (0..9), which invalidates answer B.
How long will it take 15 machines to complete a task given that it takes 9 days for 5 machines to complete the same task?
Total machine days are 5 9 = 45 thus, it will take 3 days to complete the same test with 15 machines.
What are work and time?Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.
Another example of work is that if you have done your food by 1 hour it means your work duration is 1 hour so work is basically the time duration of any task which you have done.
As per the given,
5 machines take 9 days,
5 x 9 = 45 machines day
45/15 = 3 days
Hence "Total machine days are 5 9 = 45 thus, it will take 3 days to complete the same test with 15 machines".
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Which expression has the smallest value?
a
|-34|
b
|-19|
c
|11|
d
|47|
Answer:
c. |11|
Step-by-step explanation:
When it comes to absolute value, we're talking about the distance from 0. Even though 11 is greater than -19 and -34, the distance from 11 and 0 is smaller than the distance from -19 and 0 and the distance from -34 and 0.
|11-0|=11
|0-19|=19-0=19
|0-34|=34-0=34
(2x-123):3=33 ;200-8.(2x+7)=112
Answer:
x = 222:2 and x = 2
Step-by-step explanation:
(2x-123):3=33
(2x – 123):3 = 33
2x – 123 = 33.3
2x – 123 = 99
2x = 99 + 123
2x = 222
x = 222:2
x = 111
200-8.(2x+7)=112
200 – 8.(2x + 7) = 112
-8.(2x + 7) = 112 – 200
-8.(2x + 7) = -88
2x + 7 = (-88):(-8)
2x + 7 = 11
2x = 11 – 7
2x = 4
x = 4:2
x = 2
I hope my answer helps you.
The function f(x) is a cubic function and a limited table of values is provided below. Write the equation of the cubic polynomial in standard form.
The equation of the cubic polynomial is f(x) = x³ - x² -9x + 9.
What is a polynomial function?
Polynomial functions are defined for all values of x and have a finite number of roots (x-values at which the function is equal to 0). The roots of a polynomial function can be found by solving the equation f(x) = 0.
By using the given table, we can plot the points on the graph and we can draw a graph
• Fitted coefficients:
a = 9
b = -9
c = -1
d = 1
Then we can prepare the polynomial as
y = 9 - 9x - x² + x³
Now write down in the standard form, we get
f(x) = x³ - x² -9x + 9
Hence, the equation of the cubic polynomial is f(x) = x³ - x² -9x + 9.
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I literally have no idea how to do this someone help meplease
Answer:
Step-by-step explanation:
Although the answer is correct, the Step 3 is not correct.
6 Find the value of the unknowns in each of the following.
(a) 2(w 2 5 z)+3(2 x -2 -6)=4(4 7 y 3)
The required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.
Given,
To determine the value of the unknowns in the matrix,
A matrix is a collection of numbers that are arranged in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics.
Here,
[tex]2\left[\begin{array}{ccc}w&2\\5&z\end{array}\right] +3\left[\begin{array}{ccc}2&x\\-2&-6\end{array}\right] = 4\left[\begin{array}{ccc}4&7\\y&3\end{array}\right][/tex]
From the above matrix,
Equation formed,
2w + 6 = 16,
w = 5,
2z -18 = 12
z = 15
10 - 6 = 4y
y = 1
Thus, the required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.
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Help me thank y very much
Answer: 1/2
Step-by-step explanation:
Use rise over run. Up 1, over 2.
And so on. Find nice points on the graph to practice slope with!
18x=6(z-1) solve for z
Answer: z=3x+1
Step-by-step explanation:
1. Distribute 6 through the parentheses
18x=6z-6
2. Move the z variable to the left side and x variable to the right
-6z= -6-18x
3. Divide both sides by -6 in order to get z by itself
z=1+3x
4. Reorder the terms using commutative property
z=3x+1
Write the missing numbers
2. 200 300
-600 +400
_____ _____
3. 3 hours= ____minutes
_____hours= 1 day
_______months= 2 years
The missing numbers are 3 hours = 180 minutes 24 hours = 1 day
24 months = 2 years
What are numbers ?
A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them.
An arithmetic value used to indicate amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers. For instance, this is a single butterfly, and these are four.
1. 5 × x = 45
45 / 5 = x
x = 9
45 ÷ 5 = 9
2. 200 + 600 = 800
300 + 400 = 700
3. 3 hours = 180 minutes
3 * 60 minutes
24 hours = 1 day
24 months = 2 years
12 * 2 = 24
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6 people equally share 1/2 a pan of macaroni and cheesse draw a diagram to represent the situation
Share of the each person is 1/12. And the above situation can be represented in the given picture.
Fractions and diagrams:Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire.
When we cut a piece of cake from the entire thing in real life, that could be the best example for Fractions.
To represent a fraction in a diagram we choose a closed polygon like a circle, square, etc.
First, divide the polygon into the number of parts as given in the denominator and shade the number of taken parts that are given in the numerator.
Here we have
6 people equally share 1/2 a pan of macaroni and cheese
As we know 1/2 means half
By the given data, Half of the macaroni and cheese is shared by 6 people which means Half of the pan of macaroni and cheese again divided into 6 parts
=> (1/2) ÷ 6 = [tex]\frac{ \frac{1}{2} }{6}[/tex] = [tex]\frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex]
Therefore,
Share of the each person is 1/12. And the above situation can be represented in the given picture.
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The table shows the depths (relative to sea level) of several scuba divers.
What is the difference between Oscar's depth and Annabelle's depth? Write your answer as a mixed number in simplest form
Answer:(-6 5/6)
Step-by-step explanation:
-12.5=-12-1/2
-5 2/3= -5-2/3
=(-12 3/6)-(-5 4/6)
=(-6 5/6)
gimme brainlliest
Miles is renting a meeting room at a college. There is a reservation fee of $21 and an additional fee of $4 per hour. He needs to spend no more than $85. What is the possible number of hours for which Miles could rent the meeting room? Use t for the number of hours.
t ≤26.5
t<4
t ≤ 16
t<21.25
The equation represents that, Miles could rent the meeting room for t ≤ 16 hours.
What is inequality?
The word inequality means a mathematical expression in which the sides are not equal to each other. Basically, an inequality compares any two values and shows that one value is less than, greater than, or equal to the value on the other side of the equation.
The total cost for Miles to rent the meeting room for t hours is given by the equation C = 21 + 4t. We are trying to find the number of hours t for which C is equal to or less than $85.
We can solve this problem by setting up the inequality 21 + 4t ≤ 85 and solving for t.
Subtracting 21 from both sides gives us 4t ≤ 64.
Dividing both sides by 4 gives us t ≤ 16.
Thus, Miles can rent the meeting room for t hours, where t is less than or equal to 16. This means that he can rent the room for 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16 hours.
Hence, the equation represents that, Miles could rent the meeting room for t ≤ 16 hours.
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An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 8.0 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 24 engines and the mean pressure was 8.4 pounds/square inch with a standard deviation of 1.0 A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
The decision for rejecting the null hypothesis is μ = 8.4
In statistics the term hypothesis refers a tentative statement about the relationship between two or more variables.
Here we have given that engineer designed a valve that will regulate water pressure on an automobile engine and he is designed the valve such that it would produce a mean pressure of 8.0 pounds/square inch. Then it is believed that the valve performs above the specifications. Where the valve was tested on 24 engines and the mean pressure was 8.4 pounds/square inch with a standard deviation of 1.0 Here the level of significance of 0.05 will be used.
Here we have to determine the decision for rejecting the null hypothesis.
While we looking into the the given question we have identified the following values,
Standard deviation = 1.0
Mean pressure = 8.4 pounds/square
Level of significance = 0.05
Sample size = 24
According to these values the null and alternative hypothesis is written as,
H0 = μ = 8.4
Hx = μ ≠ 8.4
Therefore, H0 = μ = 8.4 is the decision for this one.
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Given that 58% of all gold dealers believe next year will be a good one to speculate
in South African gold coins, in a simple random sample of 150 dealers, what is the
probability that between 55% and 60% believe that it will be a good year to
speculate?
Tisha’s mom wants to make a smoothie using this recipe. How many cups of blueberries will she need if he uses 15 bananas?
Answer:
5 cups
Step-by-step explanation:
6bananas =2cups
6(2cups)+6(2cups)+3(1cup)= 15 bananas
5cups of blueberries
A line segment on a coordinate plane representing the
distance a bicyclist is from home has a slope of 35/2
On the line segment, x represents the time, in hours,
that the bicyclist has been riding and y represents the
bicyclist's distance, in miles, from home. The bicyclist
began his ride at home and rides his bicycle at a
constant rate. How long will it take until the bicyclist is
140 miles from home?
A. 2 hours
B. 4 hours
C. 7 hours
D. 8 hours
Time taken by the bicyclist is 8 hours.
What is slope?Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
Given slope = 35 / 2 = 17.5
Distance = 140 miles.
then time is calculated by 140 /17.5
= 8 hours
The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts the change in the vertical axis, y, with the change in the horizontal axis, x.
As x grows, there are 4 different sorts of slopes: negative, positive, zero, and undefined. The "average rate of change" can also be thought of as the slope of a line.
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How is a system of two linear inequalities in two variables similar to a system of two linear equations in two variables?
a. point of intersect
b. overlaps
c. boundary lines
d. points that are not boundary lines
which one
Answer:
q. point of intersection
Step-by-step explanation:
Both systems in two variables contains two lines that may be intersecting, parallel, or the same line.