The percentage discount is 58%
How to calculate the percentage discount ?The old price is $50
The new price is $21
The percentage discount can be calculated as follows
old price-new price/old price × 100
= 50-21/50 × 100
= 29/50 × 100
= 0.58 × 100
= 58
Hence the percentage discount is 58%
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Are collinearity and betweenness of points maintained under rotation? Explain.
Yes , Are collinearity and betweenness of points maintained under rotation.
A rotation is a transformation that maintains congruence of the original figure and its image.
What does "collinearity" mean?
Collinearity is the statistical term for the correlation of predictor variables (or independent variables) in a regression model to represent a linear connection. They are unable to independently estimate the value of the dependent variable when predictor variables in the same regression model are coupled.What is an example of collinearity?
We have perfect multicollinearity if there is a precise linear relationship between two or more independent variables. Incorrect use of dummy variables (falling into the dummy variable trap), repeating the same information (weight in pounds and weight in kilograms), etc.Learn more about collinearity
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The population of Austin, Texas, is 9.64 × 10 . The population of the
state of Texas is 30 times that of Austin. What is the approximate
population of Texas?
A. 2.9 × 10
B. 2.9 × 10
C. 2.9 × 10
D. 2.9 × 10
The population of Texas will be 2.9 × 10³.
How to calculate the value?Population of Austin, Texas = 9.64 × 10.
The population of the state of Texas is 30 times that of Austin.
Therefore the population of Texas will be:
= 30 × 9.64 × 10
= 2900
= 2.9 × 10³
Therefore, the population of Texas will be 2.9 × 10³.
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What is three x plus five x
f(x) = 3x + 10
g(x) = x - 2
Find f(g(x))
Answer:
f(g(x)) = 3x + 4
Step-by-step explanation:
to find f(g(x)) substitute x = g(x) into f(x)
f(g(x))
= f(x - 2)
= 3(x - 2) + 10
= 3x - 6 + 10
= 3x + 4
Answer:
[tex]f\left[g(x)\right]=3x + 4[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=3x+10\\g(x)=x-2\end{cases}[/tex]
Function composition is an operation that takes two functions and produces a third function.
The given composite function f[g(x)] means to substitute the function g(x) in place of the x in function f(x):
[tex]\begin{aligned}f\left[g(x)\right] & = f(x-2)\\& = 3(x-2)+10\\& = 3x-6+10\\& = 3x+4\end{aligned}[/tex]
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Simplify 3x^3 * 7y^2 * 4x * 5y ^3 using the rules of exponents
Using the rule of exponents, the expression is 12x^4 × 35y^5
What are the rules of exponents?The rules of exponents are given as:
Product of powers rule — When they are like bases, add the powersQuotient of powers rule — When they are like bases dividing, subtract the powersPower of powers rule — Multiply the powers together when a power is raised by another exponent.Given the expression;
3x^3 * 7y^2 * 4x * 5y ^3
collect the like bases
3x³ × 4x × 7y² × 5y³
Add the powers
12x^3 + 1 × 35^ 2 + 3
We then have;
12x^4 × 35y^5
Thus, using the rule of exponents, the expression is 12x^4 × 35y^5
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Is 43/21 a rational, irrational, integer,whole or natural number
Answer: an integer rational number
Step-by-step explanation:it's not a natural or a whole number, but it as integer as well as it repeats
Simplify by combining like terms. -(2x + y) -2(-x-y)
The Simplified expression for -(2x + y) -2(-x-y) is y.
Like terms in an algebraic expression is defined as those terms that have same variable and that variable has the same power .
Algebraic Operation is only possible with Like terms .
For Example ; 3x , 9x are like terms .
According to the given Algebraic expression
= -(2x + y) -2(-x-y)
= -2x-y+2x+2y
Combining like terms together
We get ,
= (-2x+2x)+(2y-y)
= 0+y
=y
Therefore , the Simplified expression for -(2x + y) -2(-x-y) is y.
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3 Let ³ - 4x² - 7x + 10 = 0 be a polynomial equation. a) Find all potential rational solution(s) using the Rational Root Theorem. Separate multiple solutions with commas if necessary. b) Find all the distinct, actual rational solution(s). Separate multiple solutions with commas if necessary. If no solutions exist, enter None.
The solution of the third degree polynomilal x³ - 4x² - 7x + 10 = 0 will be ( x - 5 )(x + 2 )( x - 1 ).
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given equation is x³ - 4x² - 7x + 10 = 0. The equation will be solved as,
x³ - 4x² - 7x + 10 = 0
x³ - 3x² - 10x - x² + 3x + 10 = 0
( x² - 3x - 10) ( x - 1 ) = 0
( x² -5x + 2x - 10 ) ( x- 1) = 0
( x - 5 )( x + 2 )( x - 1 ) = 0
Therefore, the solution of the third degree polynomilal x³ - 4x² - 7x + 10 = 0 will be ( x - 5 )(x + 2 )( x - 1 ).
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Determine whether each sequence is arithmetic. If so, identify the common difference. 97,86,75,64, ...........
The given sequence is arithmetic progression AP. The common difference is found to be (-11).
What is the sequence called arithmetic progression AP?Arithmetic Progression (AP) is a number sequence in which the difference between two numerical order is a constant value. Arithmetic Sequence is another name for it.
We would then come across some key terms in AP, that are denoted as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)Some formula use in AP are-
The AP could also be expressed in concepts of common distinctions, as shown below; a, a + d, a + 2d, a + 3d, a + 4d, ………. ,a + (n – 1) dThe terms used in this progression for a given series are the first term, this same common difference, and the nth term. If a1, a2, a3,................, an is an AP, then the common difference " d " can be calculated as; d = a2 – a1 = a3 – a2 = ……. = an – an – 1.The formula for determining the n-th term of an AP is as follows: an = a + (n − 1) × dIf the first term, common difference, and total terms are known for an AP, the sum of the initial n terms can be calculated. The arithmetic progression sum formula is given below: Sn = n/2[2a + (n − 1) × d]Now as per the given question;
The given sequence is 97,86,75,64, ...........
Let the first term is'a₁' = 97.
Let 'a₂' = 86 is the second term.
Let the third term is 'a₃' = 75.
Let the fourth term be 'a₄' = 64.
As we know, in the AP, the difference between two consecutive terms is equal and therefore is referred to as the common difference.
d = a₂ - a₁
Substitute the values;
d = 86 - 97 = -11 ........(equation 1)
Now consider other pair;
d = a₃ - a₂
d = 75 - 86 = -11 .......(equation 2)
Put the values;
Thus, both the two equation are equal. It means the common difference is same that is (d = -11).
Therefore, the stated sequence is found to be in AP and the value of the common difference is found to be (d = -11).
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What is 36/-4+2(10-8)
Answer:
36/-4+2(10-8)
36/-4+2(2)
-9+2(2)
-9(4)
-36
Step-by-step explanation:
Evaluate each expression for a=3 and b=-5 . 2 a+b
Evaluating the expression 2a + b for a = 3 and b = -5 is equal to -1.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
To evaluate an expression or an equation means to substitute a value to the variable and perform the arithmetic operations included.
Given the expression 2a + b, substitute the value of the variable a and the value of variable b.
2(3) + (-5)
Performing the arithmetic operations, we can have the value of the expression.
2(3) + (-5)
= 6 - 5
= 1
Hence, the expression 2a + b when a = 3 and b = -5 is equal to -1.
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plss help ASAP i rly need this
The answer is -0.5.
The source is from calculator soup.
what is f(2)= for the piecewise?
Answer:
Piece wise
Step-by-step explanation:
Piecewise function definition A piecewise function is a function that is defined by different formulas or functions for each given interval. Its also in the name: piece. The function is defined by pieces of functions for each part of the domain.
Which are equivalent ratios to 6:13?
Check all that are true
12:39
42:78
18:39
18:26
12:26
Answer:
are these time stamps
Step-by-step explanation:
let me know
|-x+3>2 How do I solve this ?
Answer: x<1 or x>5
Step-by-step explanation:
|-x+3|>2
-x+3>2
-x+3-3>2-3
-x>-1
x<1
-x+3<-2
-x+3-3<-2-3
-x<-5
x>5
x<1 or x>5
Which angles are complementary to each other?
Answer:
3 and 2
Step-by-step explanation:
complementary means they add up to 90 degrees. Angle 3 and 2 equal 90 degrees,
ls 1.0227 a rational number Explain
How can -6 be expressed as the sum of its integer and fractional parts?
The sum of its integer and fractional parts is (-6) + (-1/3).
What are fractions?Fractions are numerical values that represent a subset of a larger whole. A fraction is a portion or section of a whole quantity, which can be any number, a specific value, or a thing.
What Are Mixed Fractions, exactly?A mixed fraction is made up of both a whole number and a fraction. If 8 is a whole number and 1/2 is a fraction, the result is a mixed fraction.
The given expression is -6 1/3.
The integral part is -6, and the fractional part is 1/3.
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The correct question is: " How can - 6 1/3 be expressed as the sum of its integer and fractional parts? "
Simplify this::::::::::::
Answer: A
Step-by-step explanation:
can you use the multiplication property of inequality to solve 8m>-1/10?can you use the division of property to solve -9/2 >3/2?explain your reasoning
HELP ME
The simplification of the given inequalities gives;
1) m > -1/80
2) x < -1/3
How to use Algebraic Properties of Equality?
1) The multiplicative property of inequality states that both sides of an inequality can be multiplied or divided by the same number and an equivalent inequality can be formed.
Thus, applying that to 8m > -1/10, gives;
Multiply both sides by 1/8 to get;
8m * 1/8 > -1/10 * 1/8
m > -1/80
2) The division property of equality states that if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal.
Thus, applying that to -9/2x > 3/2 gives;
Divide both sides by -9/2 to get;
x < -1/3
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Find the slope of the line through each pair of points. (2,7) and (-3,11)
The slope of line passing through points (2,7) and (-3,11) is -4/5.
What is the slope of line?Slope of a Line
The slope of a line is defined as the increase divided by the run, or as the ratio of the rise to the run. It describes the slope of the line in the coordinate plane. Calculating the slope of a line and determining the slope between two different points are similar activities.
The following formula is used to determine slope:
The slope of the line between two points is given by y2 - y1 / x2 - x1.
Given points are -
(2,7) and (-3,11)
Slope of the line is -
= 11 - 7 / -3 -2
= 4 / -5
So the slope of the line is -4/5
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Help Please
Tickets for a school event were $1.75 for students and $3.75 for parents. If a total of 62tickets were sold for $178.50, how many student and parent tickets were sold? There were ____ student tickets sold and ____ parent tickets sold.
Answer:
There were 27 student tickets sold and 35 parent tickets sold.
Step-by-step explanation:
So first, we have to set up our equations!
s + p = 62 (s is the # of student tickets sold; p is the # of parent tickets sold; 62 is the total # of tickets sold)
1.75s + 3.75p = 178.50 (1.75s is the price for student tickets multiplied by the number of student tickets; 3.75p is the price for parent tickets multiplied by the number of parent tickets; 178.50 is the total amount of money)
Now! We are going to use elimination to solve for the variables, first for "s". To do this, we are going to multiply the first equation by -3.75!
-3.75 (s + p = 62)
-3.75s - 3.75 p = -232.50
+ 1.75s + 3.75p = 178.50
-2s = -54
s = 27
Next! We have to solve for "p" by multiplying the first equation by -1.75!
-1.75 (s + p = 62)
-1.75s - 1.75 p = -108.50
+ 1.75s + 3.75p = 178.50
2p = 70
p = 35
Lastly, we know that there were 27 student tickets sold, and 35 parent tickets sold.
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
PLEASE HURRY THIS IS TIMED!!! I WILL CHOOSE BRAINLIEST!!!
Step-by-step explanation:
A=M
B=N
E=P
AB=MB
BE=NP
AE=MP
I don't know about the blanks sorry
a. Write four terms of a sequence of numbers that you can describe both recursively and explicitly.
In explicit representation, a sequence is represented in terms of the first term while in recursive representation, a sequence is represented in terms of the previous term.
What are Recursive Formulas?
A recursive formula refers to a formula that defines each term of a sequence using the preceding term(s). The recursive formulas define the following parameters:
The first term of the sequence.The pattern rule to get any term from its previous term.What are Explicit Formulas?
Explicit formulas are always used to represent any term of the sequence, without writing the other terms of the sequence. The meaning of "explicit" is direct, something that can be directly found without knowing the other terms of sequence. The explicit formula helps to easily find any terms of the sequence, without knowing its previous term.
Eg, the sequence: 2, 4, 6, 8, 10, . . .
Explicit Representation An = 2 + 2(n - 1)
Recursive representation f(n) = 2 + f(n - 1)
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Determine whether the following are mutually exclusive. Explain.
choosing a quadrilateral that is a square and a quadrilateral that is a rectangle
A quadrilateral can be both a square and a rectangle, or a rectangle but not a square, because squares are rectangles but rectangles are not always squares. They do not conflict with one another.
What is termed quadrilateral?
A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.What types of quadrilaterals are examples?
A closed, two-dimensional figure with four sides, four angles, and four vertices is called a quadrilateral. Square, rectangle, and trapezium are a few examples of quadrilaterals.
The two events are mutually exclusive if they cannot occur at the same time.
A quadrilateral can be both a square and a rectangle, or a rectangle but not a square, because squares are rectangles but rectangles are not always squares.
They do not conflict with one another.
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help with the question in the image below
Answer:
Step-by-step explanation:
e
Activity
Brayden, Howard, and Vincent are on the football team. During a game, Brayden gains 1 less than 5 times the average number of yards gained per play during the game. Howard runs for 1 more than 5 times the average number of yards gained per play during the game. Vincent runs for 5 more than 4 times the average number of yards gained per play during the game.
Question:
Is it possible that all three players gained the same number of yards? Explain your response.
Answer:
The equation for Brayden and Howard gaining the same number of yards has no solution. So, they could not have gained the same number of yards. Because Brayden and Howard could not have gained the same number of yards, all three could not have gained the same number of yards.
Step-by-step explanation:
(This is straight from Edmentum)
Select the correct answer.
A triangle with vertices at A(0, 0), B(0, 4), and C(6, 0) is dilated to yield a triangle with vertices at A10, 0), B(0, 10), and C115, 0). The origin is the
center of dilation. What is the scale factor of the dilation?
OA. 1.5
OB. 2
OC. 2.5
D. 3
Reset
Next
the scale of dilation is 2.5 for the triangle ABC.
We are given the coordinates of triangle ABC as:
A(0, 0), B(0, 4), and C(6, 0)
Coordinates of dilated triangle A'B'C' is:
A' (10, 0), B'(0, 10), and C' (15, 0).
The scale of dilation can be calculated as:
k · ( 0, 0 ) = ( 0 , 0 )
k · ( 0 , 4 ) = ( 0 , 10 )
k · ( 6, 0 ) = ( 15, 0 )
k = 15 / 6 = 10 / 4 = 2.5
The scale of dilation is 2.5 for the triangle.
Therefore, the scale of dilation is 2.5 for the triangle ABC.
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Write the letter of the property, definition, or postulate that justifies each statement.
11. If m/ABC = 90°, then ZABC is a right angle.
12. If m23+ m24 = 180°, then 23 and 24 are
supplementary angles.
13. If m/PQR = m/RST, then ZPQR = ZRST
14. If 21 and 22 form a right angle, then 21 and 22
are complementary angles.
15. If ZX and Y are supplementary and ZX and Z
are supplementary, then 2Y = LZ
16. If ZJ and ZK are vertical angles, then ZJ = ZK
A. Definition of Congruence
B. Definition of Angle Bisector
C. Definition of Complementary Z's
D. Definition of Supplementary Z's
E. Definition of Perpendicular
F. Definition of a Right Angle
G. Angle Addition Postulate
H. Vertical Angles Theorem
I. Complement Theorem
J. Linear Pair (Supplement) Theorem
K. Congruent Complements Theorem
L. Congruent Supplements Theorem
17. If ZPQR and ZSTU are complementary angles, then mZPQR+ m2STU = 90°.
18. If 25 and 26 form a linear, then 25 and 26 are supplementary angles.
Answer:
Step-by-step explanation:
do i set them equal to each other since they are opposite from one another? or do i set it equal to 180? Can someone help? thanks !
Answer:
Step-by-step explanation:
Okay so this is fun, let's lable the angle just under 72, but still on the right side B. now, side b is corresponding or equal to (2y+48). So you set them to equal 180 because it makes a straight line....
(2y+48) + 72 = 180
2y + 48 + 72 = 180
2y + 120 = 180
2y = 180 - 120
2y = 60
y = 60/2
y = 30
plug this back in and ...
2(30)+48 =
(60+48) =
108
No we'll use 108 + 72 to make sure that the y is correct and....
108 + 72 = 180 so.. CORRECT! :)
