The ^ operator in logical mathematics means the OR operation . Therefore , the statement ∧ and ∠means that a or the negation of a is joined by the or operation .
These are known as logical operations as they are based upon logic.The meaning of the term logic is reasoning which means to resonate. The reasoning may be a legal opinion or mathematical confirmation.
We apply logic on expression to check whether they are true of false . Some of the mathematical logics are a negation, conjunction, and disjunction logical operations. The symbols used for them in mathematical logic is, ‘~’ for negation ‘^’ for conjunction and ‘ v ‘ for disjunction.
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Rewrite the expression (2t+6)+7t in the simplest form show your work.
Answer:
14t²+42t
Step-by-step explanation:
So you're basically going to use distributive property.
(2t+6)+7t is the same as, (2t)7t + 6(7t).
2t(7t)= 14t² and 6(7t)= 42t.
Combine the two answers and you get 14t²+42t.
14t²+42t is the simplest form you can get to.
12. Sarah uses long division to convert
a rational number 2 to a decimal.
P
Which of the following statements
cannot be true?
A. The decimal form of P
q
terminates with a zero in the
tenths place.
B. The decimal form of P
eventually repeats.
C. The decimal form of never
terminates or repeats.
D. The decimal form ofis 0.
On solving thr provided question, by help of arithmetic progression, we got to know that a10 = 207
what is arithmetic progression?There are two approaches to define arithmetic progressions (AP): The difference between any two successive terms in an arithmetic sequence must always be equal, and it is sometimes referred to as a series in which all terms except the first are created by adding a predetermined number to the preceding term.
9,15,25..............
15-9 = 6
25-15 = 10
a4 - 25 = 14 => a4 = 39
frequently referred to as a series in which all terms save the first are formed by adding a predefined number to the preceding term since the difference between any two succeeding terms in the sequence must always be equal.
a5-39 = 18 => a5 = 57
a6-57 = 22 => a6 79
...
...
...
...
...
a10 - 169 = 38 => a10 = 207
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On a negatively skewed curve, which is true?
The answer is On a negatively skewed curve ,The mean is lower than the median, which is lower than the mode
What is Negatively skewed curve?When a distribution is negatively skewed in statistics, more values are concentrated on the right side (tail) of the distribution graph while the left tail of the distribution graph is longer.
A longer or fatter tail on the left side of the distribution is referred to as negative skew, whereas a longer or fatter tail on the right is referred to as positive skew. The direction or weight of the distribution is indicated by these two skews.
The distribution's mean, median, and mode are referred to as its central tendency. The fact that the usually skewed data's mean, median, and mode are all equal illustrates how equally distributed wealth and income are, as well as the importance of government initiatives and economic growth.Because the negative side is so weighted, the distributions have a large gap. The data, for instance, includes income distributionin negatively skewed distribution, data shows the unequal distribution, the central tendency shows as under:Mode > Median > Mean.
Examples of negatively skewed curveUniversity exams. The tests are the same, yet a small fraction of students receive zero, average, or high percentage scores, indicating a negative skewed distribution of the data.The human Life cycle ,As many people live ordinary lives, some live very short lives, and some live very long lives in terms of age, the human life cycle is another illustration of a negatively skewed distribution.What causes a negatively skewed distribution?When the long tail is on the distribution's left side, the distribution is said to be left skewed. They are also referred to as negatively skewed by statisticians. Probabilities taper off more slowly for decreasing values, which causes this circumstance.
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Write an equivalent expression by distributing the "-" sign outside the parentheses:
-(-10p - 0. 7q) – 4. 6
After distribution of the negative sing in the parenthesis, the equivalent expression is 10.7p - 4.6
The expression that is given to us is -(-10p - 0. 7q) – 4. 6.
Now, we know that the meaning of equivalent expression is the it has the same value as that of the original expression.
We have to use the "-" and distribute it over the expression to form an equivalent relation,
So, we know,
-(-10p - 0.7q) – 4.6
Here, p is a constant,
Multiplying the negative sign inside of the bracket,
= (-(-10p)-(-0.7p)-4.6
= 10p + 0.7p - 4.6
= 10.7p - 4.6
So, the equivalent expression is 10.7p - 4.6.
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BOUNDS QUESTION GCSE MATHS - A race is measured to have distance of 10.6km, correct to the next0.1km. Sam runs the race in a time of 31 minutes 46seconds, correct to the nearest second.
Sam's average speed in this race is Vkm/hour.
By considering bounds, calculate the value of Vkm to a suitable degree of accuracy. You must show your work and get reasons for your answer. [5 MARKS]
The average speed of Sam's race car is equal to 20 kilometers per hour.
How to determine the average speed of a race car
In this question we find the case of a race car being displaced in a race whose length (s) is 10.6 kilometers, a distance traveled in a time (t) of 31 minutes and 46 seconds (1906 seconds). The average speed (v), in kilometers per hour, is described by the following formula that assumes an hypothetical constant speed:
v = s / t
Where:
s - Distance, in kilometers.t - Time, in hours.First, convert time into hours:
t = (31 min) · (1 hour / 60 min) + (46 s) · (1 hour / 3600 s)
t = 0.529 h
Second, calculate the average speed:
v = (10.6 km) / (0.529 h)
v = 20.038 km / h
v = 20 km / h
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How do you find the X and y-intercept of a function?
To find the x-intercept and y-intercept of a function, one can set the x or y value equal to zero and solve for the other variable.
The x-intercept of a function is the point where the graph of the function crosses the x-axis. To find the x-intercept, one can set the y-value equal to zero and solve for the x-value. For example, if the function is y = 2x + 3, the x-intercept can be found by setting y equal to zero and solving for x. In this case, 0 = 2x + 3, which means x = -3/2. So the x-intercept of this function is (-3/2,0).
The y-intercept of a function is the point where the graph of the function crosses the y-axis. To find the y-intercept, one can set the x-value equal to zero and solve for the y-value. For example, if the function is y = 2x + 3, the y-intercept can be found by setting x equal to zero and solving for y. In this case, y = 2(0) + 3 = 3, so the y-intercept of this function is (0,3).
Knowing the x and y intercepts of a function gives an idea of where the graph will start and the behavior of the function in the x and y-axis.
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Please help me respond this
The closest estimate of x when the functions satisfy the condition f(x) = g(x) is 1.65
What is a function?
Function is a mathematical law that establishes the relationship between an independent variable and a dependent variable.
Given,
[tex]f(x) =[/tex] [tex]\log\x_{3} (2x)[/tex]
[tex]g(x) = -4x^{2} + 3x +7[/tex]
Now plotting both the graphs in Desmos, we got the result as in the below figures.
Given f(x) = g(x)
So from the graphs, we can find an intersecting point. This intersecting point is common to both f(x) and g(x)
Therefore from the graph, the closest estimate of x is 1.65.
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Is 8 15 17 are Pythagorean triples?
No, 8, 15, 17 are not Pythagorean triples.
No, 8 15 17 are not Pythagorean triples. A Pythagorean triple is a set of three positive integers a, b, and c such that a2 + b2 = c2. In other words, the sum of the squares of two integers must equal the square of the third integer.
In the case of 8 15 17, if we calculate the sum of the squares of the two smaller integers, 8 and 15, we get
[tex]8^2 + 15^2 = 64 + 225 = 289[/tex].
This does not equal the square of the third integer,
[tex]17^2 = 289,[/tex]
so 8 15 17 are not Pythagorean triples.
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Put these numbers in order from least to greatest.
-9 11/20,0.25,9/20,9 1/25, 9
Answer:
From Least to Greatest
-9, 1/25, 0.25, 9/20, 11/20, 9
Step-by-step explanation:
Answer:
-9, 0.25, 9/20, 11/20, 9, 9 1/25
Step-by-step explanation:
You can convert everything in decimals or into fractions with a common denominator. Using what you have, you then put them in order.
I converted them all into decimals, getting:
-9, 0.55, 0.25, 0.45, 9, 9.04
Then I put them in order
-9, 0.25, 9/20, 11/20, 9, 9 1/25
Why do we use log e?
log with base 10 is mainly used to simplify manual computation and it is also related to the decimal system. if we calculate the log of any variable with base 10, then an integer just greater than that calculated value gives the number of digits in that number.
likewise, log with base 2 is used in digital and computer applications where binary system prevails.
The worth of log e is around equal to 0.4342944819 where log e has a base value equal to 10.
1. The value of log e base 10 is around equal to 0.4342944819.
2. The value of log e with base e, that is, ln the e value is equal to 1.
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To the nearest pound, Tim has £8
To the nearest 50p, Sue has £4. 50
Work out the maximum possible total amount of money.
Give your answer in pounds (£).
The maximum possible total amount of money would be = 13.23 £
What is Linear Equation ?
Linear Equation can be defined as the equation in which the highest degree of the variable is one.
Given,
To the nearest pound, tim has £8
To the nearest 50p, sue has £4.50
so, to the nearest pound, tim has £8
=> 7.5 ≤ Tim has < 8.5
sue has £4.50
to the nearest 50 p
=> 4.25 ≤ Sue < 4.75
=> possible total amount of money
= 7. 5 + 4.25 ≤ Amount < 8.5 + 4.75
=> 11.75 ≤ Amount < 13.25
maximum possible total amount of money would be less than 13.25
and in term of paisa maximum < 4.75 = 4.74
and maximum less than < 8.5 = 8.49
Hence maximum possible total amount of money would be = 13.23 £
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A taste test asks people from Texas and California which pasta they prefer brand A or brand B. This table shows the results. Brand A Brand B Total 125 150 105 275 45 Texas California Total 80 90 170 60 A person is randomly selected from those tested. What is the probability that the person is from California, given that the person prefers brand A? Round your answer to two decimal places
Therefore , the solution of the given problem of probability comes out to be thus brand A is more prefer by the person as probability of B IS 0.43.
Define probability.A probability is a number that represents the likelihood that a certain event will occur. Probabilities may be expressed as percentages
range from 0% to 100% or from 0 to 1.
Here,
Given :
Which brand of pasta do Texas and California prefer
Because brand B is preferred by 45 persons in Texas, the answer would be A.
There are 105 persons that favor brand B overall.
=> 45/105
=> 15/ 35
=> 0.42857...
So ,
rounded it would be 0.43,
thus brand A is more prefer by the person
Therefore , the solution of the given problem of probability comes out to be thus brand A is more prefer by the person as probability of B IS 0.43.
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The coordinates of a triangle are: R(-4,4) S(-2,-2) T(2, 3) Brian determined A RST was a scalene triangle, but he wanted to the find the lengths of the three sides. Complete the table to determine the three side lengths of ARST. 37 38 140 141 length of RS length of ST length of TR
The length of the sides RS, ST and TR are √72, √41 and √37 in the scalene triangle RST.
The distance between any two points A(a,b) and B(c,d) in the plane is given by,
AB = √((c-a)²+(d-b)²)
Here, it is given that the points of the triangle are R(-4,4) S(-2,-2) T(2, 3).
The triangle is scalene so length of every side is different.
Now, Using the above formula,
RS = √((2+4)²+(-2-4)²)
RS = √(36+36)
RS = √72
ST = √((2+2)²+(3+2)²)
ST = √(16+25)
ST = √41
TR = √((2+4)²+(3-4)²)
TR = √(36+1)
TR = √37
So, Brian is correct, the triangle is a scalene triangle.
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NEED HELP ASAPP 100 POINTSSS
Answer:
Statement 1) Corresponding angles
Statement 2) Congruent
Statement 3) 150 degrees
Statement 4) Vertical Angles
Statement 5) Congruent
Statement 6) 150 degrees
Statement 7) Alternate exterior angles
Statement 8) Congruent
Statement 9) Alternate Interior angles are congruent
Step-by-step explanation:
Explanation:
1) I've learned this before
2) Not all Corresponding angles are obtuse
3) Corresponding angles have the same measure
4) I've learned this before
5) Vertical Angles are congruent
6) Same reason as before
7) I've learned this before
8) Alternate Interior angles are congruent
9) I've learned this before
Please mark me the brainliest! Thank you!
What is a 7th interval?
A seventh interval is a chord that consists of a triad and the notes that form the seventh chord above the root of the chord. Unless otherwise stated, "7th chord" usually means the dominant 7th chord, i.e. major triad and minor 7th chord.
The 7th interval, simply called 'September', is the pitch difference between the root note and the 7th note of the diatonic scale.
Sounding the seventh above the root of the chord as his fourth note, along with the other three notes of the dominant chord, strengthens the "suspension" inherent in the function of the dominant chord, and the expected chord Increases mitigation of return to tonic.
So instead of playing "G-B-D" (Sol-Si-Re) as the dominant "C" (Do), we play "G-B-D-F" (Sol-Si-Re-Fa).
The harmonic power of the "7th interval" is so strong that some or all of his three other notes in the chord are omitted, allowing them to be visualized in the listener's ear .
In music theory, the minor seventh is one of two intervals spanning seven staff positions. It's the smaller of two sevenths, and it's minor because it spans ten semitones. A major seventh spans 11 degrees. For example, the interval from A to G is a minor seventh. This is because the G note is ten semitones above his A, and his seven staves from A to G. Diminished 7th and increased 7th have the same number of staves, but a different number of semitones (9 and 12 respectively).
Minor sevenths are rare in melodies (especially in openings), but more common than major sevenths. The most famous example, often used in theory classes, occurs between the first two words of the phrase "There's a place for us" in the West Side Story song "Somewhere." Another well-known example occurs between his two notes at the beginning of the introduction to the music of the main theme of Star Trek: The Original Series.
Complete Question:
What is personification class 7th?
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A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly.After 11months he weighed 140 Kilograms. He gained weight at rate of 5.5 kilograms per month.
Let y represent the sumo wrestler’s weight (in kilograms)after x month.
Complete the equation for the relationship between the weight and number of months.
The equation that shows the relationship between the weight and number of months. y = 79.5 + 5.5x
What is weight ?In science and technology, the weight of an object is the force acting on an object due to gravity. Some standard textbooks define weight as a vector quantity, the gravitational force acting on an object. Others define weight as a scalar quantity, the magnitude of gravitational force. Still others define it as the size of the reaction force applied to the body by mechanisms resisting the influence of gravity: weight is a quantity measured, for example, by a spring balance.
Given that ; Total Month = 11 months
Gained weight at the rate = 5.5 kilograms per month.
Assume initial weight W,
The initial weight + total month x rate = 140
w + 11 x 5.5 = 140
w = 79.5
if y is total weight after x months
y = 79.5 + 5.5x
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How do you describe a logarithmic function?
A logarithmic function is a type of inverse function.
A logarithmic function is a type of inverse function that is commonly used in mathematics and science. It is typically written in the form of y = log base b (x), where b is the base of the logarithm, and x is the input value. The most common bases for logarithms are 10 (common logarithm) and e (natural logarithm).
The logarithmic function is the inverse of the exponential function with base b. This means that if y = log base b (x) then x = b^y
One way to describe a logarithmic function is to say that it represents the exponent to which the base number must be raised in order to produce the input value x. For example, log base 10 of 100 is 2, because 10^2 = 100.
Another way to describe a logarithmic function is to say that it is a way of expressing very large or small numbers in a more manageable form. For example, instead of expressing a number like 10^9 as 1 billion, it can be expressed as 9 using a logarithm to base 10.
It is also important to note that logarithmic function have some key characteristics such as:
The domain of a logarithmic function is x>0, since the logarithm of a non-positive number is undefined.
The range of a logarithmic function is all real numbers.
The graph of a logarithmic function has a vertical asymptote at x=0, since the logarithm of a non-positive number is undefined.
A logarithmic function is increasing over its domain and concave down.
The x-intercept of the graph is (1,0), since the logarithm of 1 is always 0.
Overall, logarithmic functions are mathematical tools that allow us to simplify the representation and manipulation of very large and small numbers, and are used in many areas of science and engineering.
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Task #2: Jack makes $32 when he sells 4 pumpkins. How many pumpkins will he have to sell to make $48? If Jack finds that he has $120 at the end of the day, how many pumpkins did he sell?
Answer:
1. 6
2. 15
Step-by-step explanation:
4 pumpkins: $32
=> 1 pumpkin = 32 : 4 = $8
- He will have to sell 48 : 8 = 6 pumpkins to make $48
- He sold: 120 : 8 = 15 pumpkins that day
What is an unsolvable problem?
As a result, it may be shown that the answer to the algorithm problem at hand is a halting problem, which is indecidable and thus impossible to solve.
Algorithm : what is it ?No matter the circumstance, algorithms are fundamentally problem solvers of expression ; they exist to identify, resolve, and frequently automate of solution to a specific problem. Algorithms are frequently introduced in area introductory textbooks by characterizing them as "a series of steps to complete a problem."
Here,
one of the most common problems that hasn't been solved is the stopping problem. It asks the following question:
Does M come to a standstill when given the input w for any Turing machine with the parameters alphabet = a, b, and any string w over
It can be shown that the halting problem cannot be resolved since it is indecisive.
As a result, it may be shown that the answer to the algorithmic problem at hand is a halting problem, which is indecidable and thus impossible to solve.
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How many triangles are there in the following figure 18 17 16 15?
There are 15 triangles in the given figure. Each of the four shapes in the figure can be divided into four triangles.
The figure contains four triangles, each with three sides. To calculate the total number of triangles in the figure, we can multiply the number of sides of each triangle by the number of triangles. Therefore, the total number of triangles in the figure is 3 x 4 = 12.
However, the figure also contains two additional triangles that are formed when three of the triangles intersect. To calculate the total number of triangles, we must add the two additional triangles to the 12 triangles we calculated earlier. Thus, the total number of triangles in the figure is 12 + 2 = 14.
Since the figure also has three more sides, it can be divided into one more triangle. Therefore, the total number of triangles in the figure is 14 + 1 = 15.
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What’s the slope of the line graphed below?
Answer:
slope = (3/2)
Step-by-step explanation:
point 1: (-1, 1); Point 2: (1, 4)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 4 - 1 3 3
----------- = ------------ = --------- = -------
x₂ - x₁ 1 - (-1) 1 + 1 2
I hope this helps!
F(1)=120,f(n)=f(n-1)+_n>_2
The value of next two terms are,
⇒ 0 and - 60
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The values are,
⇒ f (1) = 120,
⇒ f (2) = 60
And, The function is,
⇒ f (n) = f (n - 1) + ___
For n ≥ 2
Now,
Since, The values are,
⇒ f (1) = 120,
⇒ f (2) = 60
And, The recursive formula is,
⇒ f (n) = f (n - 1) + b
For n ≥ 2
Substitute n = 2;
⇒ f (2) = f (2 - 1) + b
⇒ 60 = f (1) + b
⇒ 60 = 120 + b
⇒ b = 60 - 120
⇒ b = - 60
So, The recursive formula is,
⇒ f (n) = f (n - 1) - 60
Substitute n = 3;
⇒ f (3) = f (3 - 1) - 60
⇒ f (3) = f (2) - 60
⇒ f (3) = 60 - 60
⇒ f (3) = 0
Substitute n = 4;
⇒ f (4) = f (4 - 1) - 60
⇒ f (4) = f (3) - 60
⇒ f (4) = 0 - 60
⇒ f (4) = - 60
Thus, The next two term are 0 and - 60.
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What is Y 1 on a graph?
The graph of y is a straight line parallel to the x−axis through the point (0,1)
Now, According to the question:
Let's know:
What is slope and example?
Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).
The equation is Y = 1
A straight line in slope (m) and intercept (c) form is:
y = mx + c
y is a straight line of slope 0 and y- intercept of 1
y = 0.x + 1
y = 1
Hence, the graph of y is a straight line parallel to the x−axis through the point (0,1)
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Jordann is painting her kitchen. To get the color she wants, she mixes 6 parts red paint and 2 parts yellow paint.
1) Write the ratio of parts red paint to parts yellow paint as a fraction.
2) Then, write the unit rate of red paint to yellow paint. (How many parts of red paint does she need for every 1 yellow part?)
What color do you imagine her kitchen will be?!
Answer:
1. 6:2
2.for every 1 yellow paint, she needs 3 red paints
3.an orange
Step-by-step explanation:
1. It would be 6:2 because for every 2 parts yellow she needs 6 parts red
2. Since the ratio is first 6:2, just divide it by 2 since there is 2 yellow and it's asking how much red you need for 1 yellow
what is the difference in the volumes, in cubic inches, of two spheres, one with a radius of 3 inches and the other with a radius of 5 inches.
The difference in the volumes of the sphere is 410.29 inches³.
What is the difference in the volumes?A sphere is a three dimensional circle in which each point on the circumference is equidistant from its center. The volume of a three-dimensional object is the amount of space in the object.
The formula for the volume of the sphere = 4/3πr³
Where:
π = 3.14r = radiusDifference in the volumes = volume of the larger sphere - volume of the smaller sphere
(4/3 x 5³ x 3.14) - (4/3 x 3³ x 3.14)
523.33 - 113.04 = 410.29 inches³
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Ali is collecting signatures for a petition. He currently has 520 signatures. He has 6 more weeks to collect the remaining signatures he needs. He needs a total of at least 1,000 signatures before he can submit the petition. Ali wants to collect the same number of signatures each week. Write and solve the inequality for the situation
An inequality that represents the number of signatures Ali needs to collect in each of the remaining weeks so that he will have enough signatures to submit the petition: 520 + 6m ≥ 1000
and the minimum number of signatures he needs to collect = 80
Given that Ali wants to collect the same number of signatures each week.
Assume that Ali collects m number of signatures each week.
He has 6 weeks to collect the remaining signatures he needs.
So, by unitary method in 6 weeks the number of signatures he would collect:
6 × m
He currently has 520 signatures and he needs a total of at least 1,000 signatures before he can submit the petition.
so, we get an inequality.
520 + 6m ≥ 1000
We solve above inequality.
6m ≥ 1000 - 520
m ≥ 480/6
m ≥ 80
Ali needs to collect at least 80 signatures, so that he will have enough signatures to submit the petition.
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Function rules from equations
For a given input value q, the function f outputs a value r to satisfy the following equation.
11g 4= 3r6
Write a formula for f(g) in terms of q.
f(q) =
Stuck? Review related articles/videos or use a hint.
Report a problem
On solving the provided question, we can say that - 11g +4= 3r-6 the value of this equation is -10/3
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
here,
11g +4= 3r-6
g = 0
3r = -10
r = -10/3
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A ship travels 50 km on a bearing of 27°, and then travels on a bearing of 117° for 140 km. Find the distance traveled from the starting point to the ending point
The distance traveled from the starting point to the ending point is 30.35 km.
What is a bearing?
A bearing tracks the rotation of an angle around the north line in a clockwise fashion. The line connecting the compass's centre to a location and measuring its bearing in degrees as it moves clockwise from north is known as the bearing.
The ship travels 50 km on a bearing of 27°, and then travels on a bearing of 117° for 140 km.
The x-coordinate of the final point is -
50 cos (27°) + 140 cos (117°) = -19
The y-coordinate of the final point is -
50 sin (27°) + 140 sin (117°) = 23.67
The distance from (0,0) to the final point is as follows -
d = √(-19)^2+(23.6)^2)
= √(921.27)
= 30.35 km
Therefore, the distance traveled is 30.35 km.
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Which statement is correct?
Answer:
B. ST and TK intersect at a 90 degree angle.
I know this because you can see that in between STK, there is a square in the corner indicating a 90 degree angle.
Step-by-step explanation:
Hope it helps! =D
You're working late one night and notice that the hard drive on your new computer is very active even though you aren't doing anything on the computer and it isn't connected to the Internet. What is the most likely suspect?
Answer:
The most likely suspect for the hard drive being very active even though the computer is not being used and is not connected to the Internet is malware. Malware is a type of software that is designed to cause harm to a computer system, and it can often run in the background without the user's knowledge.