Ricky has the number of stamps in the number of 15 stamps.
According to the question, the given parameters can be used to form the expression by using simplification method and the parameters are as follows:
Stamps for Ana: 8
Stamps for Ricky and Ana: 23
Given equation: 23 = r + 8
The equation formed by the simplification method is: r + a = 23
Solving above two equations, we get a = 8 stamps and r = 15 stamps.
Hence, Ricky has the number of stamps in the number of 15 stamps.
What is simplification?
The word simplification is the procedure in which complicated expression can be written in a simpler form to make the calculation easy. This method is used to calculated the answers for the unknown quantity.
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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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ls 1.0227 a rational number Explain
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.
PLEASE HELP!!
Find the x- and y- intercepts of the function.
(A) x-intercept: (-2,0)
y-intercept: none
(B) x-intercept: (-6,0),(6,0)
y-intercept: (0,-2)
(C) x-intercept: none
y-intercept: none
(D) x-intercept: none
y-intercept: (0,-2)
I think it’s C
Basically you are correct its C , ut go with your gut!
|-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
Refer to ®R .
Is -VU a radius? Explain.
The chord of a circle is defined as the line segment connecting any two points on its circumference.
VU is not a radius it is a chord.
What is a chord in a circle?The chord of a circle is defined as the line segment connecting any two points on its circumference. It should be noted that the diameter of a circle is the longest chord passing through its center.
A circle chord is a straight line with both ends on a circular arc. A secant line, or simply secant, is the infinite line extension of a chord. A chord is a segment of a line that connects two points on a curve, such as an ellipse.
A radius is a segment with ends at the center and circumference of a circle. VU, on the other hand, is a chord because it has both endpoints on the circle.
Therefore, VU is not a radius it is a chord.
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If 4(x+2)-2(x-10)=0 , what is the value of x ?
The value of x is -14.
Rewriting the equation mentioned in question to solve for the value of x -
4(x + 2) -2 (x - 10) = 0
Performing multiplication with brackets on Left Hand Side of the equation
4x + 8 - 2x + 20 = 0
Performing addition and subtraction on Left Hand Side of the equation
2x + 28 = 0
Shifting 28 to other side of equation
2x = - 28
Shifting 2 to other side of equation as denominator
x = - 28/2
Performing division to find the value of x
x = -14
Hence, the value of x is -14.
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A student has 30 minutes to complete an exam. There are 9 multiple choice questions worth 3 points each. There are also 3 short answer questions worth 5 points each. It takes about 2 minutes to answer a multiple choice question and about 6 minutes to complete a short answer question. How many multiple choice questions and short answer questions should the student answer to maximize his score in the time remaining (Use x = multiple choice; y = short answer.)
Answer:
9 multiple choice questions and 2 short answer questions
===========================================================
Explanation:
x = number of multiple choice
y = number of short answers
The statement "It takes about 2 minutes to answer a multiple choice question and about 6 minutes to complete a short answer question" means it takes 2x+6y minutes to answer x multiple choice and y short answer questions. We want this total to be 30 minutes or less.
Therefore, [tex]2x+6y \le 30[/tex] is one constraint.
---------------
Another constraint is that [tex]0 \le x \le 9[/tex] since the most multiple choice questions you can answer is 9.
Because there are 3 short answer questions, this means another constraint is [tex]0 \le y \le 3[/tex]
---------------
The list of constraints is:
[tex]\begin{cases}2x+6y \le 30\\0 \le x \le 9\\0 \le y \le 3\\\end{cases}[/tex]
If you were to graph and shade these regions on the xy grid, then you should get a pentagon with the following corner points
A = (0, 0)
B = (0, 3)
C = (6, 3)
D = (9, 2)
E = (9, 0)
We'll plug the coordinates of each vertex into the objective function P(x,y) = 3x+5y which will compute the number of points total after answering x multiple choice and y short answer questions. This computes the maximum points possible.
Plug in the coordinates of point A to get P(0,0) = 0
Repeat for point B to get P(0,3) = 15
Now move onto point C to get P(6,3) = 33
Then point D is P(9,2) = 37 and point E gets us P(9,0) = 27
---------------
Summary:
P(0,0) = 0
P(0,3) = 15
P(6,3) = 33
P(9,2) = 37
P(9,0) = 27
We see that x = 9 and y = 2 produce the largest P(x,y) value of 37
Therefore, you should answer 9 multiple choice questions and 2 short answer questions. This will yield 37 points if you were to get all of those questions correct. In other words, the most points possible are 37 when given 30 minutes.
---------------
Side note:
If you had unlimited time, then the most points possible are 9*3+3*5 = 27+15 = 42 which is the total number of points on the exam.
Getting a 37 out of 42 is a grade of about 37/42 = 0.881 = 88.1%
The maximum score is achieved at the corner point (9, 0), where the student answers 9 multiple-choice questions and 0 short-answer questions. The score at this point is 27, which is the maximum score the student can achieve in the given time.
To maximize the student's score in the given 30 minutes, we need to create an objective function and constraints based on the time available and the number of questions.
Let:
x = Number of multiple-choice questions to answer
y = Number of short-answer questions to answer
Objective Function (Score):
The score can be calculated as the sum of points obtained from multiple-choice questions and short-answer questions:
Score (S) = 3x (for multiple-choice questions) + 5y (for short-answer questions)
Constraints:
1. Time Constraint: The total time taken to answer all the questions should not exceed 30 minutes:
Time for multiple-choice questions + Time for short-answer questions ≤ 30
2. Number of Questions Constraint: The student can't answer more questions than available:
Number of multiple-choice questions (x) ≤ 9 (total number of multiple-choice questions available)
Number of short-answer questions (y) ≤ 3 (total number of short-answer questions available)
Now, let's consider the time taken to answer each type of question:
- Time for multiple-choice questions: 2 minutes per question
- Time for short-answer questions: 6 minutes per question
Based on the above information, the time constraint can be written as an equation: 2x + 6y ≤ 30
Now, we need to maximize the score (S) by selecting the values of x and y that satisfy the above constraints. This is a linear programming problem that can be solved using various optimization techniques, such as the graphical method, simplex method, or linear programming software.
Since this is a simple problem with a small number of variables and constraints, we can use the graphical method to find the maximum score. We will graph the feasible region defined by the constraints and find the corner points of the feasible region. Then, we will calculate the score (S) at each corner point and select the one with the highest score.
The feasible region will be bounded by the lines:
2x + 6y ≤ 30 (Time constraint)
x ≤ 9 (Number of multiple-choice questions constraint)
y ≤ 3 (Number of short-answer questions constraint)
The corner points of the feasible region are the intersection points of these lines.
Now, calculate the score (S) at each corner point:
For (0, 0): S = 3(0) + 5(0) = 0
For (0, 3): S = 3(0) + 5(3) = 15
For (9, 0): S = 3(9) + 5(0) = 27
The maximum score is achieved at the corner point (9, 0), where the student answers 9 multiple-choice questions and 0 short-answer questions. The score at this point is 27, which is the maximum score the student can achieve in the given time.
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Please help me with this question.
Part (a)
We need to consider
[tex]x=\frac{1}{k\pi}, k \in \mathbb{Z}[/tex]
[tex]f\left(\frac{1}{k\pi} \right)=\tan (k\pi)
[/tex]
tan(x) has a period of pi, so this is equal to tan(0)=0.
Part (b)
We need to consider
[tex]x=\frac{4}{(4n+1)\pi}, n \in \mathbb{Z} \\ \\ f \left(\frac{4}{(4n+1)\pi} \right)=\tan \left(\frac{(4n+1)\pi}{4} \right) \\ \\ =\tan \left(\pi n+\frac{\pi}{4} \right) \\ \\ =1[/tex]
Part (c)
We see that 1/x approaches infinity, and hence the limit does not exist.
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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10x-2=102 cry about it
Answer:
Step-by-step explanation:
add 2 to both sides,
10x-2=102
+2 +2
now it is 10x=104
now divide 10 from both sides.
10x/10=104/10
x=10.4
help with the question in the image below
Answer:
Step-by-step explanation:
e
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
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:
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,
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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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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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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please help me! i’m stuck on this problem :((
Answer: x=18
Step-by-step explanation:
2x+8x=180 ==> angles CDE(8x) and ABC(2x) are opposite supplementary angles meaning that they add up to 180 degrees.
10x=180
10x/10=180/10
x=180/10
x=18
Simplify this::::::::::::
Answer: A
Step-by-step explanation:
plss help ASAP i rly need this
The answer is -0.5.
The source is from calculator soup.
What is the relationship between a and b
Answer:
B. Vertical angles.
look at the image attached.
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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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
How many widgets does Widget INC. have to sell to break even?
Answer:
300 widgets
Step-by-step explanation:
Each time the widgets sold goes up by 100, the profits goes up by 400. This shows a ratio/slope of 4 if we were to graph this. To find out when they break even you need to subtract $400 from the first row to get to zero and the equivalent amount of widgets. If each widget is $4 then subtract 100 from 400 to get 300 widgets
well, we know the table has linear relationship, so let's use it to get the Profit function then, to get the equation of any straight line, we simply need two points off of it, so let's use those two points in the picture below.
[tex](\stackrel{x_1}{500}~,~\stackrel{y_1}{800})\qquad (\stackrel{x_2}{700}~,~\stackrel{y_2}{1600}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1600}-\stackrel{y1}{800}}}{\underset{run} {\underset{x_2}{700}-\underset{x_1}{500}}} \implies \cfrac{1600 -800}{700 -500} \implies \cfrac{ 800 }{ 200 }\implies 4[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{800}=\stackrel{m}{4}(x-\stackrel{x_1}{500}) \\\\\\ y-800=4x-2000\implies y=4x-1200[/tex]
how many bucks will they lose by selling "0" items?
well, let's find out by setting x = 0.
[tex]\stackrel{profit}{y}=4(0)-1200\implies y=-1200~\hfill \stackrel{\textit{they'd be losing}}{\text{\LARGE 1200}}[/tex]
how many will they need to sell to break-even?
well, to break-even that means no loses, no profits but no loses either, so-called breaking-even, you simply sell enough to cover costs, at that point the profit = y = 0, so
[tex]\stackrel{profit}{0}=4x-1200\implies 1200=4x\implies \cfrac{1200}{4}=x\implies \text{\LARGE 300}=x[/tex]
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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Suppose B is the midpoint of -AC. Use the given information to find the missing measure. A B=10 s+2, A C=40, s= ?
Value of s is 1.8.
The midpoint of a line is a point that bisects the line into equal parts. It is equidistant from both end points of the line.
As B is the midpoint of AC,
2AB = AC
∴ 2(10s + 2) = 40
∴ 20s + 4 = 40
∴ 20s = 36
∴ x = 1.8.
Now, AB = 10s + 2
Substituting the value of s,
∴ AB = 10(1.8) + 2
∴ AB = 20 units
Thus, the value of s is 1.8 and the length of AB is 20 units.
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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
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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A video game displays 168 frames in 6 seconds on Penelope's computer. What is the rate in frames per second?
Step-by-step explanation:
If theres 168 frames in six seconds, to find out how many there are per second, we simply need to divide 168 by 6. This equals 28. If you know how many there are for 6, and you want to find out how many for 1, you know you're dividing 6 by 6. So you have to do the same to the amount of frames.
