The ideal way to find the intercepts of an equation with the "x" and "y" axes is to evaluate both values when the image is 0, as described below:
First let's define equation
What are equations?An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.
Equations can be graphed, just like a function.
Now that we know what an equation is and its structure, let's explain it with an example.
Let the equation
2y = 4x + 2, determine its intersections with the axes "x" and "y".
First, we clear:
y = (4x + 2)/2
y = 2x + 1
Now we equal y = 0 and find intersection with the x-axis0 = 2x + 1
2x = -1
x = -1/2
we equal x = 0 and find cut with the y-axisy = 2(0) + 1
y = 1
As we can see, to find the intercepts, we only have to evaluate the equation when y = 0 and when x = 0.
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How do you check the function is continuous or discontinuous?
A function is continuous if it is defined for all values of the independent variable and there are no breaks, jumps, or gaps in its graph. In other words, a function is continuous if you can draw its graph without lifting your pen from the paper.
To check whether a function is continuous at a particular point, you can use the following methods:
The two-part definition of continuity: A function is continuous at a point if the following two conditions are met:
The limit of the function as it approaches the point from the left and the right exists and is equal to the function's value at that point.
The function is defined at the point.
The Epsilon-Delta definition of continuity: A function is continuous at a point if, for every epsilon (a small positive number) there exists a delta (also a small positive number) such that, for all points x within delta units of the point in question, the function's value at x is within epsilon units of the function's value at the point.
The graph of the function: You can also check the continuity of a function by looking at its graph. If the graph is a continuous curve with no breaks or jumps, then the function is continuous. If the graph has breaks or jumps, then the function is discontinuous.
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The Epsilon-Delta definition of continuity states that a function is continuous at a point if there is an epsilon (a small positive number) and a delta (also a small positive number) such that the value of the function at x is within epsilon units of the value of the function at the point for all points x within delta units of the point in question.
The function's graph: Additionally, you can examine a function's graph to see whether it is continuous. The function is continuous if the graph displays a continuous curve without any interruptions or leaps. The function is discontinuous if the graph has breaks or jumps.
Which of the following equations represents a proportional relationship? A. x=2.9 B. x+y=2.9 C. y=2.5/x D. y/x=2.5
The equation that represents a proportional relationship is y/X = 2.5. That is option D.
What is proportional relationship?A proportional relationship is the type of relationship that exist when between two variables which can be represented as y and x where a constant of proportionality exists between the two variables as k.
The relationship between these two variables can either be directly proportional or indirectly proportional.
The relationship that exists between X and y is a direct proportional relationship with a constant of proportionality of 2.5.
y = 2.5 X
= y/X = 2.5. Where 2.5 is the constant.
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boulder is flung out of the top of a 3,000 m tall volcano. The bouIders height, y, in meters, is a function of the horizontal distance it travels, x, in meters. The slope of the line representing the volcano's hillside is -5/3 At what height above the ground will the boulder strike the hillside?
Using the linear function y = -5/3x + 3000, the boulder will touch the ground at 1800m
Linear FunctionA linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
A model of a linear function is given as y = mx + c
where m is the slope or rate of change of the function and c is the constant value or y - intercept
In this function;
The slope is - 5/3 and the constant is 3000
m = -5/3c = 3000The linear function can be written as
y = -5/3x + 3000
The height at which the boulder will strike the ground, the value of y = 0
0 = -5/3x + 3000
5/3x = 3000
x = 1800
The point is at 1800m
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How do you find the value of X and Y in a given figure?
The value of angle x is 70° and angle y is 60° in the given figure with exterior angle = 120°
From the given figure, we know that the Exterior angle = 120°
To find the values of x and y we will follow the following steps.
We know that the sum of interior opposite angles is equal to the exterior angle of the triangle.
The exterior angle of the triangle=120°
The interior angles are x and 50°
50° + x = 120°
x = 120°- 50°
x = 70°
Also, we know that the sum of the y and the exterior angle is 180° because they are forming a linear pair.
Hence we have,
y + 120° = 180°
y = 180° - 120°
y = 60°
Therefore, the value of angle x is 70° and angle y is 60°.
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Which is a graph of y 3x − 1?
The graph of y=3x-1 will be a straight line that does not passes through origin.
What is straight line?A line is a geometry object that extends on both sides and is defined by zero width. Simply put, a straight line is a line devoid of bends. A straight line is one that has no curves and continues to infinity on both sides.
Write standard form of straight line.ax+by=c is the standard form of straight line.
A straight line serves as the visual representation of a linear function's graph.
The given function is as follows:
y=3x-1
A linear function looks like this:
y=mx+c
Where:
m=3: the slope
c=-1: the y-intercept
So given function has a different y-intercept than 0.
So, the resulting graph o does not cross through the origin.
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Find the indicated z-scores shown in the graph The graph is bell shaped, both ends are shaded. The number on the right is 0.0322 and the number on the left is 0.0322. The z-scores are (____,_____) use comma to seperate answers as needed. Round to two decimal places as needed
The z-scores are (-1.85, 1.85)
What is Z- score?An illustration of a standardised score is the z-score. A z-score calculates how far a data point deviates from the distribution's mean by standard deviation.
If a Z-score is 0, it indicates that the data point's score is identical to the mean score
Given:
If we look at the z score table we will get the value of z- score.
The value 0.0322 lies in horizontal row 1.8 and column 0.05.
Then, for left value 0.0322 is -1.85
and, for right value 0.0322 is 1.85.
Hence, the z-scores are (-1.85, 1.85)
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How do you find the domain of A?
Take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the domain of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.
What is a domain?The collection of all potential inputs for a function is its domain.
For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
The set of numbers x for which a function is defined in a valid manner is known as the domain of the function.
A function's domain is referred to as a closed interval if it is specified across the interval a ≤ x ≤ b.
So, to find the domain of a, consider the function y = f(x), which has the independent variable x and the dependent variable y.
A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
Therefore, take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the domain of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.
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What is * in a math problem?
Answer:
it means multiply like the × symbol
Step-by-step explanation:
The senior class is collecting orders for graduation, So far, 54% have ordered their yearbook, 58% have ordered their gown and 15% have ordered their gown but not their yearbook. Find that probability that a randomly selected senior...
1. has ordered both a gown and a yearbook.
2. has ordered a yearbook or a gown.
3. has ordered neither a yearbook nor a gown.
4. has ordered a yearbook but not a gown.
Answer:
1. has ordered both a gown and a yearbook: 54%
2. has ordered a yearbook or a gown: 58% + 54% = 112%
3. has ordered neither a yearbook nor a gown: 100% - (58% + 54%) = 88%
4. has ordered a yearbook but not a gown: 54% - 15% = 39%
Step-by-step explanation:
What is the value of b2 4ac for the following equation 2x2 2x 1 0 4120?
The value of b2 - 4ac for the equation 2x2 + 2x - 1 = 0 is 12.
The equation 2x2 + 2x - 1 = 0 can be written in the form ax2 + bx + c = 0, where a = 2, b = 2 and c = -1. The formula for calculating b2 - 4ac for this equation is
[tex]b2 - 4ac = (b2) - (4)(a)(c)= (2)2 - (4)(2)(-1)= 4 - (-8)= 12[/tex]
Therefore, the value of b2 - 4ac for the equation 2x2 + 2x - 1 = 0 is 12.
To calculate this value, the formula first finds the value of b2, which is the square of the coefficient of the x-term (2). Then it multiplies the coefficient of the x2-term (2) by the constant term (-1), and multiplies the result by 4. Finally, it subtracts the result of this multiplication from the value of b2.
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simplify 2√12+3√48-75
To simplify this expression, we can start by simplifying the square roots:
2√12 + 3√48 - 75
= 2√(12) + 3√(48) - 75
= 2√(43) + 3√(412) - 75
= 2√4 * √3 + 3√4 * √12 - 75
= 2 * √3 + 3 * √12 - 75
We can then combine like terms:
= 2 * √3 + 3 * √12 - 75
= (2 * √3 + 3 * √12) - 75
= 5 * √12 - 75
Finally, we can simplify the expression to get our final answer:
= 5 * √12 - 75
= 5 * 2√3 - 75
= 10√3 - 75
= -75 + 10√3
= -75 + 10√3
So the simplified expression is -75 + 10√3.
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Multiple choice math. Make sure you are correct tho!
Answer: The answer is option 1
Step-by-step explanation
The given equation is [tex](p^{2} r^{3} /pr^{4} )^{2}[/tex]
[tex](p^{2} r^{3} /pr^{4})^{2}[/tex] = [tex]p^{4} r^{6} /p^{2}r^{8}[/tex] (the given equation whole square is applied)
[tex]p^{4} r^{6} /p^{2} r^{8}[/tex] = [tex]p^{2} /r^{2}[/tex] (the p and r are canceled out )
Therefore the correct answer is [tex]p^{2} /r^{2}[/tex]
How can you determine if the two angles are congruent by AAS A?
By using the the application of ASA we can determine the two angles are congruent by AAS.
AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.
AAS congruence can be proved in easy steps.
Suppose we have two triangles ABC and DEF, where,
Diagram attaches at the end of the solution.
∠B = ∠E [Corresponding angles]
∠C = ∠F [Corresponding angles]
AC = DF [Adjacent sides]
By angle sum property of triangle, we know that;
∠A + ∠B + ∠C = 180 ………(1)
∠D + ∠E + ∠F = 180 ……….(2)
From equation 1 and 2 we can say;
∠A + ∠B + ∠C = ∠D + ∠E + ∠F
∠A + ∠E + ∠F = ∠D + ∠E + ∠F [Since, ∠B = ∠E and ∠C = ∠F] ∠A = ∠D
Hence, in triangle ABC and DEF,
∠A = ∠D
AC = DF
∠C = ∠F
Hence, by ASA congruency, (AAS: the application of ASA)
Δ ABC ≅ Δ DEF
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23.From the following information, prepare trading account for the year ended 31st March, 2013 Cash purchases Rs. 4,50,000; credit purchases Rs. 27,00,000; returns inward Rs. 60,000; cash sales Rs. 4,80,000; credit sales Rs. 33,00,000; returns outward Rs. 30,000; freight inwards Rs. 9,000; carriage inwards Rs. 9,000; wages and salaries Rs. 12,000; opening stock Rs. 4,50,000; closing stock Rs. 2,64,000 but its market value is Rs.2,52,000
The table showing trading account is given below
What is a trading account for a year?he trading account gives details of total sales, total purchases and direct expenses relating to purchase and sales. Trading account format for the year contains Particulars, Amount, Dr., Cr., Purchases, Sales, etc.
Given here,
Particulars Amount
Cash purchases Rs.4,50,000
Credit purchases Rs.27,00,000
Returns inwards Rs.60,000
Cash sales Rs.4,80,000
credit sales Rs.33,00,000
Returns outward Rs.30,000
freight inwards Rs.9000
carriage inwards Rs.9000
Wages and salaries Rs.12000
Opening stock Rs. 4,50,000
closing stock Rs. 2,64,000
Market value Rs.2,52,000
Hence the trading account for the year ended 31st March, 2013 is given above
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Olivia is going on a 490 mile journey. So far, she has travelled 1% of her journey. How many miles has she travelled
Answer:
4.9 miles
Step-by-step explanation:
(.01)(490)=4.9
A water pail in your backyard has a small hole in it. You notice that it has drained a total of 2.5 liters in 4 days. What is the average change in water volume each day?
The average change in water volume is (answer here)iter(s) per day.
The average change in the volume of water per day is obtained as 0.625 litres.
What is the rate change of volume?The rate change of volume is the change of volume with respect to time.
For instantaneous change the derivative of the expression of volume can be taken.
The average change in the volume of water can be obtained as follows,
Average change = Volume of water ÷ Number of days
= 2.5 ÷ 4 = 0.625
Hence, the average change in water volume is given as 0.625 liters per day.
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The probability that a person has immunity to a particular disease is 0.8. Find the mean number who have immunity in samples of size 17
The mean number who have immunity in samples of size 17 is 13.6
What is a Mean number?Sample Size =17
Immunity to a Particular disease=0.8
=17*0.8
=13.6
The average of the numbers is the mean. Calculating is simple: add up all the numbers, then divide by the total amount of numbers. To put it another way, it is the total divided by the number. In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value.It is a statistical idea with significant financial implications. The idea is applied in a number of financial areas, such as business appraisal and portfolio management, although not exclusively.To learn more about Mean refer to:
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Explain how to find the circumference of the circle with a radius of 4 inches
The circumference of the circle with a radius of 4 inches is 8π inches.
What is the circumference of a circle?The circumference is the perimeter of a circle or ellipse in geometry. That is, the circumference would be the circle's arc length if it were opened up and straightened out to a line segment. In general, the perimeter is the length of the curve around any closed figure.
Given that the radius of the circle is 4 inches. The circumference of the circle will be calculated by the formula,
Circumference = 2πr
Circumference = 2 x π x 4
Circumference = 8π inches
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What is the slope of the line 5x 3y 15?
-a/b=-5/3 is the slope of the line 5x 3y 15
for
ax+by=c
the slope is -a/b
the slope of paralell lines are the same
find slope
5x+3y=15
-a/b=-5/3
paralell as same slope
the slopes are:
L1: slope 3
L2: slope -3
L3: slope -1/3
So now multiply the slopes of each pair of lines:
L1 and L2: 3 * (-3) = - 9 => No, they are not perpendicular
L2 and L3: (-3) * (-1/3) = 1 => No, they are not perpendicular
L1 and L3: (3) * (-1/3) = -1 => Yes, they are penpendicular.
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Tommy and zach are tarting out at the ame poition tommy run north at 5 mile per hour and zach tart to
run eat 2 hour later at the rate of 8 mile per hour how long until tommy and zach are 16 mile apart round to the nearet tenth if neceary
Tommy and Zach will be 16 miles apart after 2.90 hours.
Let the time taken for Tommy and Zach to run until they are 16 miles apart be t hours.
Tommy runs North at a speed of 5 miles per hour.
Therefore, the distance covered by Tommy in t hours is 5 multiplied by t hours:
=5t miles
Zach runs East at a speed of 8 miles per hour.
Zach started running 2 hours later so that he would run for (t - 2) hours.
Distance covered by Zach in (t - 2) hours running at a speed of 8 miles per hour :
=8(t - 2) miles
Since they are now 16 miles apart, Pythagoras's theorem, a²+ b² = c², is applied.
[8(t - 2)]²+ (5t)² = 16²
64(t - 2)² + 25t² = 256
64(t² + 4 - 4t) + 25t² = 256
64t² + 256 - 256t + 25t² = 256
89t² -256t + 256 - 256 = 0
89t² - 256t = 0
t( 89t - 256) = 0
(89t - 256) = 0
9t = 256
= 256÷9
t = 2.90 hours
Therefore, for 2.90 hours, Zach and Tommy will be 16 miles apart.
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What is the function of f and G?
Answer:
f(x) and G(x)
Step-by-step explanation:
When you want to write a function of something, you can write it as the letter followed by "(x)"
One card is drawn (hkv-fhyp-che) from a well-shuffled deck of 52 cards. Calculate the probability that the card will
(i) be an ace,
(ii) not be an ace.
The probability of getting an ace from a well-shuffled deck of 52 cards is 1/13 and the probability of not getting an ace is 12/13
We can calculate the probability by the following method:
Total number of cards in a pack of cards= 52
Number of ace cards in a pack of cards= 4
Probability of an event= Number of possibilities of that event / Total number of possibilities
(i) If drawing an ace card is considered an event, suppose E, then:
P(E)= Number of ace cards/ Total number of cards
= 4/52
(ii) Probability of any event other than E= 1- Probability of the event E=
If the drawing of a non-ace card is considered an event, suppose E', then
P(E')= 1- the probability of drawing an ace card
= 1- P(E)
= 1-1/13
= (13-1)/ 13
= 12/13
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determine the 2.5th percentile of the normal distribution with a mean of 72.5 and a standard deviation of 15 as a decimal rounded to the nearest tenth.
Answer:
43.1
Step-by-step explanation:
2.5 % = .025 look for this value on the z-score table to find this corresponds to z = - 1.96 Standard Deviations
72.5 - 1.96 * 15 = 43.1
for a ride on a rental scooter, bob paid an fee to start the scooter plus cents per minute of the ride. the total bill for bob's ride was . for how many minutes did bob ride the scooter?
The total cost for Bob's ride is C = x + m and no. of minutes of the ride is
m = C - x.
What is a numerical expression?A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.
Given, A ride on a rental scooter, bob paid a fee to start the scooter plus cents per minute of the ride.
Let, 'x' be the fee in cents to start the scooter and 'm' be the no. of minutes of riding.
Therefore, The total bill(C) for Bob's ride is,
C = x + m.
The no. of minutes Bob ride the scooter is simply,
m = C - x.
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Cuánto es?
35
— –1
10
Answer:
145
Step-by-step explanation:
Cuánto es means what is the answer
35 - (-110)
Two negative signs equal a positive sign
35 + 110 = 145
How do you find a prime number?
A prime number is a positive integer greater than one that has no positive integer divisors other than one and itself. To find if a number is prime or not, if a number is divide by any other positive number other than 1 and itself it is not a prime number.
What is a prime number?A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.
What is whole number?Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.
8 is not a prime number because 8 is divided by 2 and 4 other than 1 and itself.
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How do you factor x3 y3?
The factor of x³y³ is x.x.x.y.y.y or x²xy²y.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
x³y³
This can be factorized as,
x.x.x.y.y.y
or
x²xy²y
Thus,
The factor is x.x.x.y.y.y or x²xy²y.
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What is the median of 35 27 51 31 28 19 33?
Answer:
31
Step-by-step explanation:
What is the median of 35 27 51 31 28 19 33?
Median: center most value when values are arranged in numerical order so:
19 , 27 , 28 , 31 , 33 , 35 , 51
Marie buys a kite priced at $27. If the sales tax is 10%, how much tax
will Marie pay?
Answer: $2.70
Step-by-step explanation:
10% = 0.1
Take 27 times 0.1 = $2.70
A ditributor of computer oftware want to obtain ome cutomer feedback concerning it newet package. Three thouand cutomer have purchaed the package. Aume that 600 of thee cutomer are diatified with the product. Twenty cutomer are randomly ampled and quetioned about the package. Let X denote the number of diatified cutomer ampled. (a) Find the denity for X. (b) Find E[X] and Var X. (c) Set up the calculation needed to find P[X ? 3]. (d) Ue the binomial table to approximate P[X ? 3]
(a) The distribution of X is binomial with parameters n = 20 and p = 600/3000 = 1/5 since we are randomly selecting 20 clients without replacement and interested in the proportion of happy consumers. Given below is the probability density function for this binomial distribution.
f(x) is equal to (n pick x) * p * x * (1-p) (n-x)
Where p and 1-p are the probability of success and failure, respectively, and n pick x is the binomial coefficient, which is equal to n!/(x! * (n-x)!).
(b) The formula for the anticipated value of X, or E[X], is
E[X] = np = 20 * (1/5) = 4
Var X, the variance of X, is defined as follows:
Var X = np(1-p) = 20*1/5*4/5=3.2
(c) The cumulative distribution function of the binomial distribution's formula can be used to get P[X >= 3]:
Sum(i=3 to n) f for P[X >= 3] (i)
Summarizing from I = 3 to 20 and substituting the values from the density function, we obtain:
Sum(i=3 to 20) = P[X >= 3] [(20 pick I (1/5)*i*4/5*(20-i)]
(d) We must determine the value of the cumulative distribution function at x = 3, which is equivalent to the likelihood of receiving three or fewer successes out of 20 trials, in order to approximate P[X >= 3] using the binomial table. By using n = 20 and p = 1/5 to calculate the value of the cumulative distribution function at x = 3 in the binomial table, it is possible to determine this probability. P[X >= 3]'s estimated value is 0.586.
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