Example of an undecidable problem is given by the problems in the system created by computer viruses.
What is decidable and undecidable problems?According to the computability theory, the problems that needs either yes or no answer, but it is not possible by any computer programming languages to create exact answer then this computational problem is termed as undecidable problems.
A decidable problem is a decision problem in the computer system that can be solved by an algorithm correctly.
When is a problem said to be decidable or undecidable?
whenever we find a problem for which there is no algorithm available for solve and we are also unable to create any program that can solve the problem exactly in finite time are declared as undecidable problems.
If we find a problem that ask yes or no question about some input and there is programming language available for responding correctly then this particular problem is declared as decidable.
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13. Which situation can be represented bya true proportion?
A car used 3 gallons of gas to drive 72 miles on a highway and used 4 gallons of gas to drive 72 mileš town.
A store charged $20 for 2 shirts and charged $25 for 3 shirts.
A signal light flashed yellow 7 times in 28 seconds and flashed red 5 times in 35 seconds.
An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.
The example of a proportion, is An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.
What is a proportion?The term proportionality describes any relationship that is always in the same ratio.
Given are some statements,
a) A car used 3 gallons of gas to drive 72 miles on a highway and used 4 gallons of gas to drive 72 miles in a town.
Solution:- In this case, we see, a car is using 3 and 4 gallons of gas for driving in a highway and in a town for 72 miles respectively.
Since, the distance is same and quantity of gases is different therefore, this can not be represented as a proportion.
b) A store charged $20 for 2 shirts and charged $25 for 3 shirts.
Solution:- In this, let's first find the unit prices for each,
for $20 there are 2 shirts, therefore, for 1 shirt it will be $10, and for 3 shirts it costs $25, therefore, for 1 shirt it will cost $8.3
Since, unit price for both is not equal, therefore, this can not be represented as a proportion.
c) A signal light flashed yellow 7 times in 28 seconds and flashed red 5 times in 35 seconds.
Solution:- As in 2nd option, will here also find unit rate, since, yellow light is flashing 7 times in 28 seconds, therefore, in 4 seconds it will be flashed for 1 time, similarly, red light is flashing 5 times in 35 seconds, therefore, in 7 seconds it will be flashed for 1 time,
Since, both unit rates are not equal, therefore, this can not be represented as a proportion.
d) An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.
Solution:- Again we will find unit rate, since, the alarm is beeping 7 times in 6 seconds, therefore, it will beep for 1 time in 6/7 seconds, similarly, it is beeping 14 times in 12 seconds, so for 1 time it will beep in 12/14 = 6/7 seconds.
Here, we see that, both the unit rates are equal, therefore, this is an example of a proportion.
Hence, the last option is the correct example.
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The age of people waiting in line for a movie are given. Use the data to make a frequency table with intervals.
12, 27, 15, 31, 6, 45, 65, 55, 10, 49, 6, 8
The frequency table for the given data is shown above.
What is is frequency table?A table drawn up to show the distribution of the frequency of occurrence of a given characteristic according to some specified set of class intervals.
Given is the age of people waiting in line for a movie as -
12, 27, 15, 31, 6, 45, 65, 55, 10, 49, 6, 8
Arrange the data in ascending order -
6, 6, 8, 10, 12, 15, 27, 31, 45, 49, 55, 65
INTERVALS FREQUENCY
0 - 10 4
11 - 20 2
21 - 30 1
31 - 40 1
41 - 50 2
51 - 60 1
61 - 70 1
Therefore, the frequency table for the given data is shown above.
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What’s the gcf of 18 and 36
Answer: 18
Step-by-step explanation:
18*1=18
18*2=36
The four-digit numeral $3AA1$ is divisible by $9$. What digit does $A$ represent?
When a four-digit number is divisible by nine and is written as 3AA1, the digit A stands for 7.
Properties of 9-divisible numbersA number is itself divisible by nine if the total of its digits is also divisible by nine.
Multiples in mathematics are the outcomes of multiplying an integer by a certain number. a multiple of 9 is a number that divides by nine without remainder.
By utilizing the aforementioned attribute, we can
1 + 3 + 4 + 5 = 9, 18, or 27.
4 +2A = 9, OR 18, OR 27
calculating based on sum equal to 18
2A = 18 - 4
2A = 14
A = 7
therefore 3771 is the number
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Before beginning a unit of frog anatomy, a seventh grade biology teacher gives each of the 24 students in the class a pretest to assess their knowledge of frog anatomy. The teacher wants to compare the effectiveness of an instructional program in which students physically dissect frogs with the effectiveness of a different program in which students use computer software that only simulates the dissection of a frog. After completing one of the two programs, students will be given a posttest to assess their knowledge of frog anatomy. The teacher will then analyze the changes in the test scores (score on posttest minus score on pretest). a) Describe a method for assigning the 24 students to two groups of equal size that allows for a statistically valid comparison of the two instructional programs. b) Suppose the teacher decided to allow the students in the class to select which instructional program on frog anatomy (physical dissection or computer simulation) they prefer to take, and 11 students choose actual dissection and 13 students choose computer simulation. How might that self-selection process jeopardize a statistically valid comparison of the changes in the test scores (score on posttest minus score on pretest) for the two instructional programs? Provide a specific example to support your answer.
The following method for assigning the 24 students to two equal-sized groups allows for a statistical valid comparison of the two instructional programmes.
What is instructional program?An instructional programme is a course of study that requires the completion of a specified number of course credits from a prescribed group of courses and results in a formal award.
A) Each student will be given a unique random number generated by a random number generator on a calculator, statistical software, or a random number table. The assigned numbers will be listed in ascending order. Students with the lowest 12 numbers on the ordered list will be assigned to the instructional programme that requires physically dissecting frogs.
Students with the highest 12 numbers will receive an instructional programme that simulates frog dissection using computer software.
B) By not randomizing and allowing students to self-select, there is the possibility of changes in the differences between pre test and post test scores for a specific group due to the characteristics of students who choose a particular instructional method, rather than the instructional method itself.
For example, suppose frog-loving students already know a lot about frog anatomy; these students would be less likely to show a large difference between pre and post test scores. Assume that the frog-loving students prefer the computer simulation method (perhaps because they do not like the notion of dissecting the frogs they love).
The possible low change in pre- and post-test scores for the computer simulation group could then be attributed to the students' prior knowledge of frog anatomy, rather than to the instructional method itself. Because the students entering the frog dissection group have lower pre-test scores (less prior knowledge), they are more likely to show greater improvement between pre-test and post-test scores.
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Two radar stations 4.3 miles apart are tracking an airplane. The straight-line distance between
Station A and the plane is 9.6 miles. The straight-line distance between Station B and the plane is 8.6
miles. What is the angle of elevation from Station A to the plane? Round the distance to the nearest
degree.
9.6 ml
Ad
4.3 mi
8.6 mi
B
Therefore , the solution to the given problem of trigonometry comes out to be angle of elevation : 62.3°.
What is trigonometry?The area of mathematics called trigonometry examines the correlation between triangle length l. The field first came into existence in the Classical world, presumably in the third-century BC, as a result of the integration of geometry with astronomy studies. Precise approaches mathematics deals with certain trigonometric equations and possible uses of them in calculations. There are six common trigonometric functions in trigonometry. They are known by their respective names and abbreviations sine, trigonometry, tangent, secant, etc. cosecant (csc). The studies of triangle aspects, particularly those right triangles, is known as trigonometry. However, studying geometry entails learning about all polygons' characteristics.
Here,
given :
An aircraft is being followed by two radar stations, which are 4.3 miles apart.
Station A is 9.6 miles away from the plane in a straight line.
Thus,
To find the angle of elevation from station A to plane :
Using Trigonometric ratios:
=> Sin A = 8.5 / 9.6
=> Sin A = 85/96
=> A = [tex]Sin^{-1}[/tex](85/96 )
=> A = 62.302840124651483 °
=> A = 62.3°
Therefore , the solution to the given problem of trigonometry comes out to be angle of elevation : 62.3°.
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What is an unsolvable equation?
1. The Riemann Hypothesis Equation
In triangle abc, i the circumcenter bc i equal to 72cm d i equal to 15cm find the radiu of the circumcircle
In triangle abc, i the circumcenter bc i equal to 72cm d i equal to 15cm then the radiu of the circumcircle is 39
A chord is the line segment joining two points of the circumference of a circle as shown in the image attached.
If the chord is passing through the center of the circle then it will become diameter which means the diameter is the longest possible chord inside a circle.
A chord is always within the circumference because it is inside the circle.
Whats the definition of a circumference?
a line that goes around or encloses a circle. : the outer boundary of a figure or area. 3. : the distance around something. the circumference of the earth at the equator.
since ABC is an equilateral triangle
therefore SD bisects BC
BD= BC/2
BD= 36
IN Triangle ABC
since angle BDS = 90 degree
Therefore
BS = 39
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Let x represent the number of laptops. Let y represent the number of smartphones.
Sully earns $80 by selling a laptop and $60 by selling a smartphone. He wants to make a profit of at least $6,800. Write an inequality to model the amount Sully earns by selling laptops and smartphones
Therefore , As a result, 80x + 60y ≥ 6800 is the answer to the inequality problem given.
What is inequality?Both formulae and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,≥,≤, or.<
Here,
Let the quantity of sold laptops, x
y —- the quantity of sold smartphones
The fact that to solve this problem we use inequality help
The problem's underlying inequity is equal to
=> 80x + 60y ≥6800
Therefore , As a result, 80x + 60y ≥ 6800 is the answer to the inequality problem given.
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6x + 2y = 25.92 4x + 3y = 33.93 Solve for x and y
Answer:
y = -3x + 12.96
y = [tex]\frac{-4}{3}[/tex] x + 11.31
Step-by-step explanation:
6x + 2y = 25.92 Subtract 6x from both sides
2y = -6x + 25.92 Divide all the way through by 2
y = -3x + 12.96
4x + 3y = 33.93 Subtract 4x from both sides
3y = -4x + 33.93 Divide all the way through by 3
y = [tex]\frac{-4}{3}[/tex] x + 11.31
helpppppp
math math math math
Answer: 35
Step-by-step explanation:
So first you plug 5 into the equation which is:
10(5)-15
which is 50-15
50-15 is 35
Answer:
35
Step-by-step explanation:
plug 5 in for x and u will get 35
33
Problem 2
m, p, and z represent the lengths of the three sides of this right triangle.
m
i
Z
Р
Select all the equations that represent the relationship between m, p, and z.
Therefore , the solution of the given problem of equation comes out to bem² + p² =z².
Equation: What is it?The Latin word equ has the meaning of equivalent. Many of the English language's changeable terms, including adequate, temperate, and equality, contain Latin roots in their base words. The Latin root word equ enters our lexicon rather easily because both sides of an equation are, by essence, "equal" to one another.
Here,
Given : a triangle of m,p,z of length of right triangle :
By using Pythagoras theorem :
The relationship comes out to be :
=> m² + p² =z²
Thus , relationship between m , p and z is m² + p² =z² as per Pythagoras theorem.
Therefore , the solution of the given problem of equation comes out to be m² + p² =z².
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Because milk tea is flourishing in their town, Mathilda decided to sell Wintermelon milk tea (WMT) powder at Php 1 per gram and Okinawa milk tea (OMT) powder at Php 2 per gram. To increase her profit, she plans to mix the two milk tea powders. How much OMT should she mix with 300 grams of WMT so that she can sell the resulting mixture at Php 1.80 per gram?
So, Mathilda should mix 600 grams of OMT with 300 grams of WMT to sell the resulting mixture at Php 1.80 per gram.
Define the unitary method.The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.
The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.
What is a unit?A unit is a quantity with a fixed magnitude that is used to gauge the sizes of other quantities that behave similarly.
The terms millimeter (mm), centimeter (cm), meter (m), and kilometer (km) are used to describe length (km). The weight is measured in kilograms (kg) and grams (g). Milliliter (ml) and liter are used to measure volume (L).
Let x be the amount of OMT powder in grams. We know that the total amount of powder in the mixture is x + 300 grams since Mathilda is mixing x grams of OMT with 300 grams of WMT.
(x * Php 2 + 300 * Php 1) / (x + 300) = Php 1.80
Solving for x, we can get the amount of OMT powder in grams:
x = (300 * Php 1.80 - 300 * Php 1) / (Php 2 - Php 1.80) = 300 * (Php 1.80 - Php 1) / (Php 2 - Php 1.80) = 600
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Evaluate. 10+7⋅3+4 my answer are either 224,50,55,and,40
Answer:
55
Step-by-step explanation:
Using the regression line, or line of best fit, predict the resale value of an 8-year-old car with an original cost of $15,000.a.The 8-year-old car could be worth approximately $2000.b.The 8-year-old car could be worth approximately $5000.c.The 8-year-old car could be worth approximately $3000.d.The 8-year-old car could be worth approximately $4500.
The 8-year-old car could be worth approximately $3000.
The graphs that show the association between two variables in a data collection are called scatter plots. It displays data points either on a Cartesian system or a two-dimensional plane.
The X-axis is used to represent the independent variable or characteristic, while the Y-axis is used to plot the dependent variable. These diagrams or graphs are frequently used to describe these plots.
In the graph attached below, we can see that when the age of the car is 8 years, the resale value of the car is between points 40 and 20.
Thus, The 8-year-old car could be worth approximately $3000.
(Refer to the image attached for the complete question and graph)
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A solution of 60 quarts of sugar and water is 20% sugar. How much water must be added to make a solution that is 5% sugar
On solving the provided question we can say that by equation 180 water must be added to make a solution that is 5% sugar
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here, the equation is -
1200=300+5x
900 = 5x
x=180
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Find the lengths of the diagonals of rectangle WXYZ.
WY= 16x + 2-
XZ=36x-6
The length of each diagonal is
units.
Therefore , the solution of the given problem of equation comes out to be each diagonal measures 8.4 units in length..
Define equation.An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.
Here,
Given: 16x + 2 = 36x - 6 8 = 20x x = 8/20, simplifying to 2/5, or 0.4
You would set the two equations equal to one another and find x because a rectangle's diagonals are congruent.
Re-enter the value of x into a single of the equations.
=>16(0.4) + 2
=>6.4 + 2
=>8.4
To make sure, confirm with the other diagonal.
=>36(0.4) - 6
=>14.4 - 6
=>8.4
Each diagonal measures 8.4 units in length..
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can you help me please
Answer:
help u with what
Step-by-step explanation:
if the chosen significance level is α = 0.05, then ____________________________________________. A) there is a 5% probability of rejecting a true null hypothesis
B) there is a 5% probability of accepting a true null hypothesis
C) there is a 5% probability of rejecting a false null hypothesis
D) there is a 5% probability of accepting a false null hypothesis
C) there is a 5% probability of rejecting a false null hypothesis
Simply put, probability is the likelihood that something will occur.
When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Testing hypotheses is a crucial component of empirical research and evidence-based medicine. A well-developed hypothesis is only half the solution to the research problem. Working understanding of fundamental statistical principles is preferred for this, as well as subject-specific knowledge gleaned through a thorough survey of the literature.
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You know that 4 movie tickets in Virginia plus 5 movie tickets in Maryland cost $77. You also know that 8 movie tickets in Virginia plus 3 movie tickets in Maryland cost $91. How much does a ticket in Virginia cost?
The cost of one ticket in Virginia is $8
What is a system of linear equations?A System of Linear Equations is when we have two or more linear equations working together.
Given that, 4 movie tickets in Virginia plus 5 movie tickets in Maryland cost $77, Also know that 8 movie tickets in Virginia plus 3 movie tickets in Maryland cost $91.
To find the cost of a ticket in Virginia we will establish a system of linear equations and then solve them,
Let V represents the cost in Virginia that of in Maryland be M
Therefore,
4v+5m = 77.......(i)
8v+3m = 91........(ii)
Multiplying the equation eq(i) by 2 and subtracting eq(ii) from eq(i) [Elimination]
(8v+10m = 154) - (8v+3m = 91)
7m = 63
m = 9
Put m = 9 in eq(i)
4v+5(9) = 77
4v = 77-45
4v = 32
v = 8
Hence, Each ticket in Virginia and Maryland costs $8 and $9 respectively.
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Sugar cookies make up 38% of all sales for a local baker's cookie sales. If the baker sold 133 sugar cookies, how many total cookies did the baker sell?
The total number of cookies baker sold in all are 350 cookies.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, sugar cookies make up 38% of all sales for a local baker's cookie sales.
Let the total number of cookies be x.
Now, 38% of x=133
38/100 ×x=133
x=13300/38
x=350
Therefore, the total number of cookies baker sold in all are 350 cookies.
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Solve for x in the equation 2^(2x-1)x[1/8]^(1-x)=4^(3x+1)
Answer: x=-6
Step-by-step explanation:
[tex]\displaystyle\\2^{2x-1}*(\frac{1}{8} )^{1-x}=4^{3x+1}\\\\2^{2x-1}*8^{(-1)(1-x)}=(2^2)^{3x+1}\\\\2^{2x-1}*(2^3)^{x-1}=2^{2*(3x+1)}\\\\2^{2x-1}*2^{3*(x-1)}=2^{6x+2}\\\\2^{2x-1}*2^{3x-3}=2^{6x+2}\\\\2^{2x-1+3x-3}=2^{6x+2}\\\\2^{5x-4}=2^{6x+2}\\\\Hence,\\\\5x-4=6x+2\\\\5x-4-2=6x+2-2\\\\5x-6=6x\\\\5x-6-5x=6x-5x\\\\-6=x\\\\Thus,\ x=-6[/tex]
Answer:
Step-by-step explanation:
We have:
2^(2x-1) x [1/8]^(1-x) = 4^(3x+1)
2^(2x-1) x [1/2³]^(1-x) = 2²^(3x+1)
2^(2x-1) x 2^-3+3x = 2^6x+2
2^5x-4 = 2^6x+2
on comparing both sides we get :
5x-4 = 6x +2
x = -6
find the number that makes the ratio equivalent to 1:8
Answer:
2:16
Step-by-step explanation:
maybe i don't know im not smart but that is the ratio equalivent i guess i have to make this 20 words long soooo
Answer:
To find the number that makes the ratio equivalent to 1:8, we need to set up the ratio as a fraction and solve for the missing value.
The ratio 1:8 can be written as the fraction 1/8. In this case, the missing value is the numerator (1) and the known value is the denominator (8). To solve for the missing value, we can multiply both the numerator and denominator by the same value.
For example, if we multiply both the numerator and denominator by 2, we have:
1/8 = (12)/(82) = 2/16
If we multiply both the numerator and denominator by 4, we have:
1/8 = (14)/(84) = 4/32
If we multiply both the numerator and denominator by 5, we have:
1/8 = (15)/(85) = 5/40
In each of these cases, the ratio is still equivalent to 1:8, but the missing value (the numerator) is different. In general, we can multiply the numerator and denominator by any value to find the missing number that makes the ratio equivalent to 1:8.
For example, if we multiply both the numerator and denominator by 10, we have:
1/8 = (110)/(810) = 10/80
In this case, the missing value (the numerator) is 10, which makes the ratio equivalent to 1:8.
Step-by-step explanation:
Which one of the following solids can produce this two dimensional shape when sliced vertically
The solid that can produce the given two-dimensional shape when sliced vertically is option 2.
What is vertical alignment?When we examine anything vertically, we see it from top to bottom. When something is standing, it is referred to as the alignment.
What is horizontal alignment?When we examine objects horizontally, we do it from left to right. When anything is in the sleeping posture, it is known as the alignment.
The given shape is a rectangle. When the rectangular prism is sliced in a vertical manner the solid will represent the given shape that is a rectangle.
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A chef that manages two restaurants buys seven bags of rice and six bags of flour.
Restaurant A receives four bags of rice and two bags of flour for a total cost of
$78. Restaurant B receives three bags of rice and four bags of flour for a total
cost of $71.50. What is the cost of each bag of rice and each bag of flour?
Answer:
- A bag of rice is $16.9
- A bag of flour is $5.20
Step-by-step explanation:
Let R and F stand for the price of a bag of Rice and Flour, respectively.
We can use the information provided to set an equation that will predict the total cost for that restaurant, given the quantities of rice and flour received (Restaurants A and B)
A) 4R + 2F = 78 [4 bags of rice and 2 bags of flour, when multiplied by the prices per bag, R and F, will result in a total cost of $78.
B) 3R + 4F = 71.5 [Now it is 3 bags of rice and 4 of flour, for a total cost of $71.50
We have 2 equations and 2 unknowns. We can use substitution to find the answers. Take one of the equations and reorganize it to isolate one of the variables (R or F). We'll take the equation for A and isolate F
---
A) 4R + 2F = 78
2F = 78-4R [subtract 4R from both sides]
F = 39-2R [divide both sides by 2]
We've isolated F, and we can use this definition of F in the second equation:
===
B) 3R + 4F = 71.5
3R + 4(39 - 2R) = 71.5 [Use the definition of F derived above. In this manner, we have legally eliminated one of the two variables. (Sneaky, effective, and fun)]
3R + 156 - 8R = 71.5 [Multiply, combine like terms, and simplify]
-5R = -84.5 [Isolate R]
R = $16.9 A bag of rice costs $16.9
Now use the price of rice (R=$16.9) in one of the equations. Since the rearranged equation we used above is already conveniently written for F, we'll use it:
F = 39 - 2R
F = 39 - 2(16.9)
F = 39 - 33.8
F = $5.20 A bag of flour costs $5.20
===
CHECK:
Do these two prices satisfy both equations we first formulated?
Restaurant A: 4R + 2F = 78?
4(16.9) + 2(5.20) = 78 YES
Restaurant B: 3R + 4F = 71.5?
3(16.9) + 4(5.20) = 71.5 YES
These are the correct answers.
L) simplify
cos²x - sin²x
Answer:
cos(2x)
Step-by-step explanation:
To simplify the expression cos²x - sin²x, we can use the identity cos²x - sin²x = cos(2x).
This identity can be derived by using the double angle formula for cosine:
cos(2x) = cos(x + x) = cos(x)cos(x) - sin(x)sin(x) = cos²x - sin²x
Therefore, the expression cos²x - sin²x can be simplified to cos(2x).
Find the equation of the linear function represented by the table below in slope-intercept form.
y = 3x+4 ← equation of linear function.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
Here, we have,
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = y_2-y_1/x_2-x_1
with (x₁, y₁ ) = (- 3, - 5) and (x₂, y₂ ) = (1, 7) ← 2 ordered pairs from the table
m = 7+5/1+3
=12/4
= 3 ,
So, y = 3x + c ← is the partial equation
To find c substitute any ordered pair from the table into the partial equation
Using (1, 7 ), we get,
7= 3 + c
⇒ c = 7-3
= 4
Hence, y = 3x+4 ← equation of linear function
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23
Luke invested £4000 in a savings account for 3 years.
Compound interest was paid at a rate of 1. 8% each year.
Alexa also invested £4000 in a savings account for 3 years.
Simple interest was paid at a rate of 1. 8% each year.
Luke got more interest than Alexa in total over the 3 years.
How much more?
You must show all your working.
The amount luke made more than alexa is $3.91 .
What is simple interest ?
simple interest can be defined as the ratio of product of principal amount , rate and time and 100.
Luke investment,
This is compound interest so the future value formula will be used:
= Amount * ( 1 + rate) ^ no. of years
= 4,000 * ( 1 + 1.8%)³
= $4,219.91
Alexa investment:
Simple interest is calculated with the formula:
= Amount * ( 1 + rate * time)
= 4,000 * ( 1 + 1.8% * 3)
= $4,216
Amount Luke made more than Alexa:
= 4,219.91 - 4,216
= $3.91
Hence , The amount luke made more than alexa is $3.91 .
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At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $\$3.15$. Mary orders a bagel and a muffin, which comes out to $\$3.30$. Mary orders a piece of toast, two bagels, and three muffins, which comes out to $\$9.15$. How many cents does one bagel cost
On solving the question, by linear equation One bagel is 100*1.55 = 155 cents in dollars.
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept.
A toast costs = x dollars.
A bagel costs = y dollars.
A muffin costs = z dollars.
It costs $3.15 for two pieces of toast and a bagel.
As a result, 2x + y = 3.15. To get the price of a bagel, we express x as a function of y,
2x = 3.15 —Y
x = -o.5y+ 1.575
It costs $3.30 for a bagel and a muffin.
Since x and z are functions of y,
—0.5y + 1.575 + + 3(3.3 — y) 9.15
—0.5y + 1.575 +2y + 9.9—3y = 9.15
—1.5y + 11.475 = 9.15
1.5y = 2.325
2.325
Y = 1.55
One bagel is 100*1.55 = 155 cents in dollars.
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What grade is 2 step equations?
Teaching two step equations is a standard that needs to be taught in both 7th and 8th grade middle school PreAlgebra Math.
What is a 2 step equation?Two step equations are algebraic equations that can be solved in exactly two steps and gives the final answer of the variable in two steps. Generally two step equations are of the form ax + b = 0 where a and b are real numbers.
How do we solve 2-steps equation?A two-step equation is an equation that requires two steps to solve. We must eliminate any constant that is on the same side as the variable first. To solve first use the inverse operations to isolate the variable by itself. We can do only one operation in single step.
Now
we solve two steps equation in grade 7th and 8th.It is very easy to understand.
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