Equivalence is a relationship that exists between two statements such that if the two statements are both true or both false, then the affirmation of one and the negation of the other contradicts itself.
Equivalent generally refers to two numbers, terms, or expressions that have the same value. There are many ways to express equivalent quantities. It can be represented by bars or equal signs. "Equivalence" relies on a specific relationship called an equivalence relationship. Any two elements are said to be equivalent if there is an equivalence relation between them. Also, in mathematics, equality is different from equivalent. The same means the same in all respects, and equivalent means similar but not identical. For example, 2 is said to be equal to 2, but it is equivalent to 1 + 1.
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Tiana hare a granola bar with her brother. They each get one piece of the bar. What fraction name one part?
A fraction share that Tiana share with her brother called half part. This because the part is split into two where the first part is called first half and other called as second half.
How to name a piece that split into several part?To name a piece of an object that split into several you have to:
Determine how many part that the object splitDetermine the name the total part that created such as half for two, one third for three, quarter for four, etc. The name always following by the order of the split like the first part of quarter part called the first quarter.Learn more about fraction of a set here
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9+15/5x3 using pemdas
Answer:18
Step-by-step explanation: Using the order of operations (PEMDAS), you would first perform any calculations inside of parentheses, then exponents, then multiplication and division from left to right, and finally, addition and subtraction from left to right.
9 + 15 / 5 x 3
= 9 + 3 x 3
= 9 + 9
= 18
So the answer would be 18.
Please help me i am struggling only do the left side
Answer:
1. Y = -1/4x + 1
3. Y = 2/5x + 1
5. Y = 4/5x + 5
7. Y = -x + 5
9. Y = -5/2x - 16
Step-by-step explanation:
Find the slope using the formula
Use the slope and one of the points to find the y-intercept
Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.
Is log x increasing or decreasing function?.
log x is strictly increasing in interval (0, ∞).
In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as For x > 0 , a > 0, and a ≠1,y= loga x if and only if x = ay .Then the function is given by f(x) = loga x .The base of the logarithm is a. This can be read it as log base a of x. The most 2 common bases used in logarithmic functions are base 10 and base e
The given function is f(x)= logx.
f'(x)=derivative of f= 1/x.
clearly ,1/x>0
hence the function is strictly increasing.
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How do you find the mean and standard deviation of a discrete distribution?.
The mean and standard deviation of a discrete distribution can be found by calculating the sum of all the values in the distribution multiplied by their respective probabilities and then dividing the result by the total probability.
To calculate the standard deviation, the sum of the squares of the differences between the values and the mean has to be multiplied by the corresponding probabilities and divided by the total probability.
The square root of this outcome is then the standard deviation. The standard deviation is a measurement of the spread or dispersion of the data, whereas the mean of a discrete distribution is a measure of the central tendency of the data.
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How do you find an inequality?.
When solving an inequality:
you can add the same quantity to each side. you can subtract the same quantity from each side. you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.In arithmetic, an inequality is a relation that makes a non-equal assessment between two numbers or other mathematical expressions. it is used most usually to evaluate numbers on the range line by using their size.
In mathematics, a dating between two expressions or values that aren't identical to every other is called 'inequality. ' So, a loss of balance consequences in inequality. The three facets and three angles proportion an important relationship. In arithmetic, the term “inequality” represents the that means “not equal”. allow us to bear in mind a simple example if the expressions in the equations are not the same, we can say it is inequality.
Whilst two actual numbers or algebraic expressions are represented with symbols like <, > or ≤, ≥ they can be called an inequality. as an example, 3x<20, or 4x+y>12. which means Of The Symbols used in Inequalities: The image < manner 'less than' and ≤ means much less than or same to.
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Daniel travels 325 miles in 5 hours. How many miles did he travel in 11 hours
Answer:
Below
Step-by-step explanation:
The answer can be found by 11/5 * 325
here is how this comes about
ratios
325 is to 5 hours as 'd' is to 11 hours
325/5 = d/11 Multiply both sides by ' 11 '
11/5 * 325 = d ( the equation above )
d = 715 miles
Write the prime factorization of 21. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).
The prime factorization of the number 21 is:
21 = 3*7
How to write the prime factorization?We want to write the prime factorization of 21.
To do so, we just need to divide the number by prime numbers.
The first prime number we can try is 2, if we divide by 2 we get:
21/2 = 10.5
This is not an integer, so 2 is not a factor.
The next one is 3:
21/3 = 7
Now we can rewrite:
21 = 3*7
Where 3 and 7 are prime numbers, so that is the prime factorization.
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What number would you multiply the second equation by in order to eliminate the x term when adding to the first equation?.
For the given system of equations 4x – 9y = 7 , –2x + 3y = 4 answer of the following question are:
a. To eliminate x-terms we need to multiply 2 to the second equation and add it to the first equation.
b. To eliminate y-terms we need to multiply 3 to the second equation and add it to the first equation.
As given in the question,
For the given system of equation,
4x – 9y = 7 ___(1)
–2x + 3y = 4 ___(2)
a. To eliminate x-terms multiply by 2 to the (2) equation and add it to (1)
4x – 9y = 7
–4x + 6y = 8
-3y = 15
⇒ y = -5
b. To eliminate y-terms multiply by 3 to the (2) equation and add it to (1):
4x – 9y = 7
–6x + 9y = 12
-2x = 19
⇒x = -19/2
Therefore, for the given system of equations 4x – 9y = 7 , –2x + 3y = 4 :
a. To eliminate x-terms we need to multiply 2 to the second equation and add it to the first equation.
b. To eliminate y-terms we need to multiply 3 to the second equation and add it to the first equation.
The above question is incomplete , the complete question is:
Use this system of equations to answer the questions that follow.
4x – 9y = 7 , –2x + 3y = 4
a. What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation?
b. What number would you multiply the second equation by in order to eliminate the y-terms when adding to the first equation?
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What are the 3 arguments for the range function?.
A function argument is a value supplied to achieve the Range function's outcome. This is often alluded to as a latent variable.
This is an optional argument that determines the sequence's point of reference. The default assumption is 0.
A mathematical function includes one or much more arguments in the form of the independent variables that are specified in the definition and can also include parameters.
This is a necessary argument that determines the sequence's final chapter location.
This is an optional argument that specifies the adjustment between both sequence members. The default mode is 1.
A domain of the sum of two or multivalued argument values is considered to be the domain of a function with two or more variables.
A cyclical function's argument is angular. A hyperbolic perspective is the input of a hyper equation.
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11. Find the measure of ∢ 11.
Since 1 and 3 are vertical angles, the graphic demonstrates that m1 = 90. They have identical measurements, therefore m3 = 90. 1 and 2 are additional.
what is circle ?A circle is formed when every point in the plane that is a specific distance apart from another point does so (center). Thus, it is a curve made up of points that are separated from one another by a set distance while moving in the plane. It is also rotationally symmetric about the center at all angles. A circle is a closed, two-dimensional object where each pair of points in the plane is equally separated from the "center." A specular symmetry line is made by drawing a line through the circle. It is also rotationally symmetric about the center at all angles.
given
when measured with a protractor, points to 100°, crossing 90°. As a result, the angle has a 100° measurement.
Since 1 and 3 are vertical angles, the graphic demonstrates that m1 = 90. They have identical measurements, therefore m3 = 90. 1 and 2 are additional.
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How do you graph the equation y =- 3x?.
Equations of degree one and having two variables are known as linear equations in two variables. It is of the form, ax +by +c = 0, where a, b and c are real numbers, and both a and b not equal to zero.
Equations of the form a x +b y = 0; where a and b are real numbers, and a ,b ≠ 0, is also linear equations in two variable.
Since the solution of linear equation in two variable is a pair of numbers (x,y), we can represent the solutions in a coordinate plane.
To draw graph , we need to find some points
y =-3x
for y =-3x ,lets substitute value and check,
x=0
then y =0
x=1
then y =-3
x=2
then y =-6
x=3
then y =-9
x=-1
then y =3
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3x + 2y = 1
5x + 4y = 5
Answer:
x = -3
y = 5
Step-by-step explanation:
3x + 2y = 1
5x + 4y = 5
First, we multiply the first equation by -2
-6x -4y = -2
5x + 4y = 5
-x = 3
x = -3
Now put -3 back in for x and solve for y
3(-3) + 2y = 1
-9 + 2y = 1
2y = 10
y = 5
Let's check
3(-3) + 2(5) = 1
-9 + 10 = 1
1 = 1
So, x = -3 & y = 5 is the correct answer.
Solve the quadratic equation by the square root method and write the solutions in radical form. Simplify the solutions.
(4x+21)2=27
Answer:
8x+42=27
8x=-15
x=-1.875
Step-by-step explanation:
What is the range is called?.
The set of all the outputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outcomes of the dependent variable.
For e.g. the range of the function F is {1983, 1987, 1992, 1996}.
On the other hand, the whole set B is known as the codomain of the function.
It is the set that contains all the outputs of the function.
So, the set of real numbers is a codomain for every real-valued function. The codomain of the function F is set B.
How to Find the Range of a Function
Consider a function y = f(x).
The spread of all the y values from minimum to maximum is the range of the function.
In the given expression of y, substitute all the values of x to check whether it is positive, negative or equal to other values.
Find the minimum and maximum values for y.
Then draw a graph for the same.
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What type of function always has an inverse?.
The type of function always has an inverse is one to one.
In math function is referred as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Here we need to identify the type of the function always has an inverse.
As we all know that in each and every function has an inverse, here we have also know that but not every inverse will be a function.
Where as the inverse may fail the vertical line test.
Here we have identified that if the original function is a one-to-one function then its inverse will be a function.
Finally in a one-to-one function not only passes the vertical line test, then it also passes a horizontal line test.
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how much work is done when a 100 lb rock is lifted to a height of 3 ft?
A. The work done is 300 ft-lbs when a 100 lb rock is lifted to a height of 3 ft.
To calculate the work done, we can use the formula: Work = force x distance x cos(Ф).In this case, the force is the force of gravity acting on the rock, which can be calculated using the formula:
force = m * g
where m is the mass of the rock and g is the acceleration due to gravity (32.17 ft/s^2).
force = 100 lb * 32.17 ft/s^2 = 3,217 ft-lbs
The distance is the height to which the rock is lifted, which is 3 ft.
The angle of the rock to the vertical is 90 degrees, so cos(90) = 0.
So,
Work = force x distance x cos(theta) = 3,217 ft-lbs * 3 ft * 0 = 300 ft-lbs
So, the work done is 300 ft-lbs.
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How do you find the measure of an angle in a triangle?.
There are several ways to find the measure of an angle in a triangle, depending on the information given about the triangle and the angles. Some common methods include:
Using the angles in a triangle sum to 180 degrees: If you know the measures of two angles in a triangle, you can use the fact that the angles in a triangle sum to 180 degrees to find the measure of the third angle.
Using the Pythagorean theorem: If you have a right triangle, you can use the Pythagorean theorem to find the measure of the right angle (90 degrees)
Using the Law of Cosines: If you know the measures of two angles and the lengths of all three sides of a triangle, you can use the law of cosines to find the measure of the third angle.
Using trigonometry: If you know the lengths of two sides of a triangle and the measure of one angle, you can use trigonometry to find the measure of the other angles.
It is important to note that in order to find the measure of an angle you need to know at least one angle and the values of the sides of the triangle or two angles.
(−8x+7)(4x+2)−(−8x+7)(6x−9)
Answer: [tex]16x^2-102x+77[/tex]
Step-by-step explanation:
1) distribute
[tex](-8x+7)(4x+2)\\-32x^2-16x+28x+14\\-32x^2+12x+14[/tex]
2) distribute
[tex](-8x+7)(6x-9)\\-48x^2+72x+42x-63\\-48x^2+114x-63[/tex]
3) solve
[tex](-32x^2+12x+14)-(-48x^2+114x-63)\\(-32x^2+12x+14)+(48x^2-114x+63)\\16x^2-102x+77[/tex]
I'm unsure how to answer this question,can someone walk me through it?
Without evaluating, rewrite 3^10×37^9/9^12 as a single power with base 3
The simplified exponential expression 3^10×37^9/9^12 as a single power of 3 is given as follows:
3^70.
How to simplify the exponential expression?The exponential expression for this problem is defined as follows:
[tex]\frac{3^{10} \times (3^7)^{12}}{9^{12}}[/tex]
Applying the power of power rule, we have that:
(3^7)^12 = 3^(7 x 12) = 84.
When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, hence:
3^10 x 3^84 = 3^94.
For the denominator, we have that:
9^12 = (3²)^12 = 3^24.
When two terms with the same base and different exponents are divided, we keep the base and subtracted the exponents, hence:
3^94/3^24 = 3^(94 - 24) = 3^70.
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Write the expanded form of the expression. y(3.05x−3.75)−2.25y
Answer:
3.05yx - 6y
Step-by-step explanation:
y(3.05x−3.75)−2.25y
3.05yx -3.75y - 2.25y
3.05yx - 6y
Margo can purchase tile at a store for $0.59 per tile and rent a tile saw for $18. At another store she can borrow the tile saw for free if she buys tiles there for $1.19 per tile. How many tiles must she buy for the cost to be the same at both stores?
Answer:
30 tiles
Step-by-step explanation:
We know
First store
$0.59 per tile
Rent a tile saw for $18
Second store
1 tile = $1.19
We have the equation
0.59x + 18 = 1.19x
18 = 0.6x
x = 30 tiles
So, she must buy 30 tiles for the same cost at both stores.
Answer:
Margo must purchase 30 tiles for the cost to be the same at both stores.
Step-by-step explanation:
By analyzing the "real-world" problem, we can convert the words into two algebraic equations.
Step 1:Store 1:
"$0.59 per tile and rent a tile saw for $18."
y = 0.59x + 18
y = the price of the tiles bought
0.59 = price of one tile
x = number of tiles
18 = the fixed cost of a saw
Store 2:
"At another store, she can borrow the tile saw for free if she buys tiles there for $1.19 per tile."
In this case, the saw is free. Thus, we don't need to add a price to the equation.
y = 1.19x
y = the price of the tiles bought
1.19 = price of one tile
x = number of tiles
Step 2:Now that we have both equations, we can write down the equations that equate other. This formula will indicate that the equations would intersect at a certain point on the x and y values. Hence, this step will answer how many tiles are required for both stores to equal the same price.
[tex]0.59x+18=1.19x[/tex]
Now solve for x:
[tex]0.59x-0.59x+18=1.19x-0.59x\\\\18=0.6x\\\\\frac{18}{0.6} =\frac{0.6x}{0.6}\\\\30=x[/tex]
Margo can buy 30 tiles from both stores for the cost to be equal.
You might ask, "But what about the price?" This is where we solve for y; this variable will answer how much the tiles would cost at 30 tiles. So, we can take the answer for "x" and plug it into any of the two equations.
[tex]y=1.19x\\y=1.19(30)[/tex]
For this equation, all you have to do is multiply both numbers to get your answer.
[tex]y=35.7[/tex]
Bottom Line:Therefore, Margo can buy 30 tiles for the cost to be same at both stores at $35.70.
Find AC
A. 36
B. 60
C. 48
D. 12
Answer:
48
Step-by-step explanation:
AB+CB=AC which is 18+30 which is 48
Answer:
C. 48
Step-by-step explanation:
This distance of AC is the same as the distance between BC plus the distance between AB. In other words: AB + BC = AC
AB = 18
BC = 30
30 + 18 = AC
AC = 48
For a ride on a rental scooter, Boris paid a $8 fee to start the scooter plus $6 cents per minute of the ride. The total bill for Boris's ride was $19.58 . For how many minutes did Boris ride the scooter?
Answer:
193 minutes
Step-by-step explanation:
We know
Boris paid an $8 fee to start the scooter plus 6 cents per minute of the ride.
Let y represent the total cost and x represent the number of minutes we have the equation
y = 0.06x + 8
Now, put $19.58 in for y and solve
19.58 = 0.06x + 8
11.58 = 0.06x
x = 193 minutes
So, Boris rides the scooter for 193 minutes.
What is the nature of the roots for the given quadratic equation 5x 2 − 2x − 3 0?.
A quadratic equation has the generic form ax2 + bx + c = 0. Thus, the roots are hypothetical, meaning that they have two false roots.
What kind of thing is a root?The equation's nature of roots indicates whether it contains rational, irrational, or fictitious roots. Imaginary roots and unreal roots are synonyms.
What is a quadratic form's nature?Having just second-order terms, the quadratic form is a unique nonlinear function (either the square of a variable or the product of two variables).
2x2 - 3x + 5 = 0
a = 2 , b = -3, c = 5
b2 - 4ac = (- 3)2 - 4 (2) (5) (5)
= 9 - 40
= - 31
b2 - 4ac < 0
Therefore, the equation lacks any true roots.
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Full Question = Find the nature of the roots of the quadratic equations. If the real root exist, find them:
i) 2x2 - 3x + 5 = 0
Solve 4.8=2.4 plsssss help
[tex]\huge\text{Hey there!}[/tex]
[tex]\frak{\text{A}ssuming. . .}[/tex]
[tex]\mathsf{4.8x = 2.4}[/tex]
[tex]\frak{\mathsf{DIVIDE}\ 4.8\ to\ both\ sides}[/tex]
[tex]\mathsf{\dfrac{4.8x}{4.8} = \dfrac{2.4}{4.8}}[/tex]
[tex]\frak{\mathsf{Simplify} \ it}[/tex]
[tex]\mathsf{x = \dfrac{2.4}{4.8}}[/tex]
[tex]\mathsf{x = 0.5}[/tex]
[tex]\huge\boxed{\frak{T}}\huge\textsf{herefore your answer should be:}}[/tex]
[tex]\huge\boxed{\mathsf{x = 0.5}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
How many solutions are there to the equation xi x2 x3 x4 17 where Xi x2 x3 and x4 are nonnegative integers?.
The number of solutions to an equation x₁ + x₂ + x₃ + x₄ = 17 are 1140
Consider given equation x₁ + x₂ + x₃ + x₄ = 17,
where x₁ , x₂ , x₃ and x₄ are non-negative integers.
As we know x₁ is the number of ones before the first zero, x₂ the number of ones between the first and the second zero, x₃ the number of ones between the second and the third zero, and x₄ is the number of ones after the third zero.
This means, there is a 1-1 correspondence between the solutions and reorderings of 17 ones and 3 zeros.
So, the number of solutions to given equation would be,
n = ²⁰C₃
Using combination formula [tex]^nC_r=\frac{n!}{r!\times(n-r)!}[/tex],
²⁰C₃ = 20! / (3! × (20 - 3)!)
²⁰C₃ = 1140
So, n = 1140
The possible number of solutions = 1140
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The complete question is:
How many solutions are there to the equation x₁ + x₂ + x₃ + x₄ = 17 where x₁ , x₂ , x₃ and x₄ are nonnegative integers?.
Given triangles AABC and ADEF, if BC = EF, and AB = DE, What information do you need to prove the triangles congruent using the SAS postulate?
How is substitution used to determine if an ordered pair is the solution to a system of equations?.
Substitution is a method for solving systems of equations by substituting the values from one equation into the other. To use substitution to determine if an ordered pair is the solution to a system of equations, first solve one of the equations for either x or y.
Then substitute this value into the other equation, and solve for the other variable. If the ordered pair you obtain is also found in both equations, then it is a solution to the system.
Take the equation set as an example.
2x + y = 5
3x – y = 1
To use substitution to determine if (2, 3) is a solution to this system, first solve one of the equations for either x or y:
2x + y = 5 ⇒ y = 5 – 2x
Add this value to the other equation after that:
3x – (5 – 2x) = 1
⇒ 5x = 6
⇒ x = 6/5
Finally, substitute 6/5 back into either equation to find y:
2(6/5) + y = 5
⇒ 12/5 + y = 5
⇒ y = 10/5
⇒ y = 2
Since (6/5, 2) is found in both equations, it is a solution to the system.
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A political adviser stood at the corner of 1st Avenue and Main Street and asked every 10th person who walked past if they intended to vote in the next election. Identify the sampling method used.