The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value). The range of a function is the set of all possible output values (y-values) that the function can produce.
When working with inequalities, the domain and range can be found by analyzing the inequality and the context of the problem.
To find the domain of an inequality function, we need to identify any restrictions or limitations on the input values (x-values) that would make the inequality invalid.
For example, if the inequality contains a denominator that cannot be equal to zero, we need to exclude those values of x from the domain.
To find the range of an inequality function, we need to identify the set of all possible output values (y-values) that would make the inequality true.
For example, if the inequality is in the form y > x, we know that all values of y that are greater than x will satisfy the inequality.
In summary, finding the domain and range of inequalities of a function involves identifying any restrictions or limitations on input values and the set of possible output values that would make the inequality true.
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I need help with this math problem, ASAP. It is in the picture, please explain how you got your answer, Thanks!
On solving the provided question we can say that the equation h(x) = 3x / x^2 +5x +7 => [tex]h(x^2) =[/tex] [tex]3x^2 / x^4 + 5x^2 + 7[/tex]
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
here,
given h(x) = 3x / x^2 +5x +7
[tex]h(x^2) =[/tex] [tex]3x^2 / x^4 + 5x^2 + 7[/tex]
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Find all the missing Angles in the triangles. Write each answer on the line provided beside the corresponding letter. Notice that angle C is in an equilateral triangle and angle D is in an isosceles triangle. Missing Angles in Triangles Name:_____________________________ Date:__________ A B D E F G H I J K L M N O P R S T A _____ B _____ C _____ D _____ E _____ F _____ G _____ H _____ I _____ J _____ K _____ L _____ M _____ N _____ O _____ P _____ R _____ S _____ T _____ C U U _____
all the missing Angles in the triangles are:
A = 60°
B = 60°
C = 60°
D = 42°
E = 35°
F = 35°
G = 55°
H = 45°
I = 45°
J = 15°
K = 15°
L = 75°
M = 120°
N = 21°
O = 69°
P = 21°
Q = 55°
R = 55°
S = 42°
T = 42°
U = 69°
What is equilateral triangle?An equilateral triangle is a triangle whose three sides are all the same length, commonly referred to as a "regular" triangle. Since all three sides of an isosceles triangle are equal, an equilateral triangle is a specific case of such an isosceles triangle.
An equilateral triangle in geometry is a triangle whose sides are all of the same length. The three angles opposing the three equal sides are equal in measure since the three sides are all equal. As a result, it is also known as an equiangular triangle since each angle is 60 degrees.
A = 60°
B = 60°
C = 60°
D = 42°
E = 35°
F = 35°
G = 55°
H = 45°
I = 45°
J = 15°
K = 15°
L = 75°
M = 120°
N = 21°
O = 69°
P = 21°
Q = 55°
R = 55°
S = 42°
T = 42°
U = 69°
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The complete question is as follows:
Ditribute to create an equivalent expreion with the fewet ymbol poible. ( 1 -2g 4h)*5
The expression is a multiplication of five times the quantity one minus two times the quantity g times the quantity h. The expression can be rewritten as (1-2g)5h, which is the same expression but with fewer symbols.
1. Simplify the expression inside the parentheses: (1-2g)
2. Multiply what is inside the parentheses by 5: (1-2g)5
3. Multiply the result by h: (1-2g)5h
This expression is a multiplication of five times the quantity one minus two times the quantity g times the quantity h. To simplify it, first we need to simplify the expression inside the parentheses. To do this, we subtract two times g from one, which gives us the result of 1-2g. We then multiply the result by 5, which gives us the result of (1-2g)5. Finally, we multiply the result by h, which gives us the final result of (1-2g)5h. This is the same expression as the original, but with fewer symbols. The result of the expression is the product of the five, the difference of one and two times g, and h.
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for each picture there is a 1/4 chance of everyone looking at the camera. how many pictures do i need to take for at least a 4/5 pprobability of everyone looking at the camera
Answer: (My view) 6.
Step-by-step explanation: Letting "n" be the number of pictures taken. The probability of no one look at the camera for n photos is of (3/4)^n.
Hence, the probability of at least one photo be the picture craven is of:
(1 - (3/4)^n), and since the likelihood of that being equal to 4/5, it's feasible to assume that (1 - (3/4)^n) = 4/5, solving for that would give:
(3/4)^n = 1/5. Notice that the proposal can also be interpreted as "The number of pictures needed such that the probability of a picture NOT including one with everyone looking at the camera is at most 1/5",
Therefore, (3/4)^n < 1/5;
To solve for that:
n = 1:
3/4 > 1/5,
n = 2:
9/16 > 1/5
n = 3
27/64 > 1/5
n = 4
81/256 > 1/5
n = 5
243/1024 > 1/5
But finally:
n = 6
729/4096 < 1/5
For at least 6 pictures she must take to have at least a 4/5 chance of having a picture in which everyone is looking at the camera.
Let p define the probability of success in a Bernoulli trial, and P define the probability Sara wants to reach "at least" and n be defined as the number of trials. Then,
= 1 - (1 - p)ⁿ ≥ P
= (1 - p)ⁿ ≤ 1 - P
= n ≥ ln(1-P)/ln(1-p)
= n ≥ ln (0.2) / ln (0.75)
=5.6
Hence for at least n=6 photos, there is at least a chance of 4/5 that everyone is looking at the camera.
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A, B, C, or D
please don't lie
picture attached
According to the information, it can be inferred that the fraction that is equivalent to the height that differentiates silver A and silver B is 1/2.
How to calculate the height difference between both floors?To calculate the difference in height between the two floors, we must identify the height of each of the floors. According to the above, we must solve the fractions, that is, do the division as shown below:
Plant A:
5/6 = 0.83Plant B:
1/3 = 0.33Subsequently, we need to identify the difference between these two results as shown below:
0.83 - 0.33 = 0.5Finally, we must identify which fractional is equal to 0.5, in this case it would be 1/2 (option D).
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Help please. Due today.
Answer:
I don't see all the answer choices, but it should be a graph with the slope of -1/2 and intersects y at -2.
Step-by-step explanation:
This equation will help you figure out what a graphed line will look like --> y=mx+b
In this equation, m represents the slope of the line, while b represents the y intercept. Since "m" is negative in the given equation, the line's slope is decreasing. Since "b" is also negative, the point the line intercepts at y will be (0,-2). I hoped this helped.
the inspector samples five cirucit boads at reuglar intervals and finds the means older quality score x for these five boards. do we expec x to be exactly 100 if the soldering process is functioning pripertly
The parameter refers to the entire population and the statistics refers to a sample, only a sample will be inspected, no, only 99.7%, a student t distribution with spread σ/√n, The mean is less variable than single observations from the population, The distribution of the mean call length x becomes approximately normal distributed.
The parameter refers to numbers that summarize the data of the entire population while; Statistics refers to the numbers that summarize the data for a subset of the population or of a sample
No, he expects 99.7% to function within three standard deviations of the mean
The distribution of the sample average will be the student t distribution curve with spread = σ/√n
The mean includes a collection of variables from the sample, hence it is less variable than single observations from the population
As per the Central Limit Theorem, the distribution of the mean call length x from large samples of calls becomes more and more approximately normal as the size of the sample approaches that of the population.
--The given question is incomplete, the complete question is
"What is the difference between parameters and statistics? 2. Does statistical process control inspect all the items produced after they are finished? 3. The inspector samples five circuit boards at regular intervals and finds the mean solder quality score of x for these five boards. Do we expect x to be exactly 100 if the soldering process is functioning properly? 4. If the quality of individual boards varies according to a normal distribution with mean µ = 100 and standard deviation σ = 4, what will be the distribution of the sample averages, x? (Recall the sample size is n = 5.) 5. In general, is the mean of several observations more or less variable than single observations from a population? Explain. 6. The distribution of call lengths to a call centre is strongly skewed. What does the Central Limit Theorem say about the distribution of the mean call length x from large samples of calls?"--
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3
a scientist adds drops of liquid to a test tube. the test tube has marks every 5 ml.
each drop contains 0.14 ml. between which two marks on the test tube will the
liquid be after the sixth drop is added? show your work.
To calculate the amount of liquid added, the scientist multiplies 6 drops by 0.14 ml, which results in 0.84 ml. Since 0.84 ml falls between 0 ml and 5 ml, it is the exact position of the liquid in the test tube.
6 × 0.14 ml = 0.84 ml
0.84 ml falls between the 0 ml and 5 ml marks on the test tube.
1. Calculate the amount of liquid added: 6 drops × 0.14 ml = 0.84 ml
2. Determine which marks the liquid will be between: 0 ml and 5 ml
3. Determine the exact position of the liquid in the test tube: 0.84 ml falls between the 0 ml and 5 ml marks on the test tube.
The scientist adds 6 drops of liquid to a test tube that has markings every 5 ml. Each drop has 0.14 ml. To calculate the amount of liquid added, the scientist multiplies 6 drops by 0.14 ml, which results in 0.84 ml. Since 0.84 ml falls between 0 ml and 5 ml, it is the exact position of the liquid in the test tube.
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Express 10.31 as a mixed number.
The mixed number would be [tex]10\frac{31}{100}[/tex].
What is a mixed number?
A mixed number is a number that is made up of a whole number and a fraction. It is a combination of a whole number and a fraction that represents a value between two whole numbers. For example, 3 1/2 is a mixed number, with 3 as the whole number and 1/2 as the fraction.
To express 10.31 as a mixed number:
The whole number part is 10.
To find the fractional part, subtract the whole number from the decimal: 0.31
To express the fractional part as a fraction, we will have to divide it by 1 and write the decimal as a fraction, in this case 0.31= 31/100
Now we can express 10.31 as a mixed number, that is 10 31/100
Hence, the mixed number would be [tex]10\frac{31}{100}[/tex].
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Mr. Lang bought a hat and a pair of gloves for each of his 12 grandchildren.
The table lists the cost of each item. Use the Distributive Property to find
the total amount of money he spent on his grandchildren.
Gloves= $6.49
Hat= $8.00
Answer:
he spent about 14 dallors and 49 cent
Solve the equation for r
(16r28)= - 4r - 7
A. Infinitely many solutions
B. No solution
с
C. 21
D. -21
The equation has B. No solution.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
here, given that,
1/4*(-16r-28)= - 4r - 7
-16r - 28 = -16r-28
this statement is not true.
so, The equation has B. No solution.
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A principal receives reports from teachers via email. the probability model describes the number of emails the principal may receive in a day. emails received 0 1 2 3 4 5 p(x) 0.05 0.15 0.35 0.25 0.15 0.05 how many emails would you expect the principal to receive each day? (2 points) 3.9 3.65 3.25 2.9 2.45
The emails would you expect the principal to receive each day is 2.45.
X = 0; P(X) = 0.05
X = 1; P(X) = 0.15
X = 2; P(X) = 0.35
X = 3; P(X) = 0.25
X = 4; P(X) = 0.15
X = 5; P(X) = 0.05
Now the number of emails should be
= 0 × 0.05 + 1 × 0.15 + 2 × 0.35 + 3 × 0.25 + 4 × 0.15 + 5 × 0.05
= 0 + 0.15 + 0.70 + 0.75 + 0.60 + 0.25
= 2.45.
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.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
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find the linearization l(x) of the function at a. f(x) = sin(x), a = π 6
The linearization of the function at a is L(x) = 1/2 + √3/2(x - π/6).
Linearization is a method of taking the gradient of a nonlinear function with respect to all variables. It is used to approximate the output of a function based on the value and slope of the function, at a given point.
The Linearization of function f(x,y) at (a,b) is L(x,y) = f(a,b) + (x−a)fx(a,b) +(y−b)fy(a,b)
Now we take a look at the given function, and the value of point a:
f(x) = sin (x)
a = π/6
Then we differentiate the function, with respect to x:
f(x) = sin (x)
f’(x) = cos (x)
We input the value of a = π/6 into the function:
y = f(π/6)
= sin (π/6)
= 1/2
f’(π/6) = cos (π/6)
= √3/2
Now we input the value of f(a) and f'(a) into the linearization formulas:
L(x) = f(a) + f'(a)(x - a)
= 1/2 + √3/2 (x - π/6)
Thus the linearization of the function at a is L(x) = 1/2 + √3/2(x - π/6).
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Rita has two coupons for a printer.
Coupon A: 15% off of a $75 printer
Coupon B: $14 rebate on a $75 printer
Choose the coupon that gives the lower price.
Then fill in the blank with the correct value.
Coupon A gives the lower price.
The price with coupon A is Sless than the price with coupon B.
O Coupon B gives the lower price.
The price with coupon B is Sless than the price with coupon A.
well, the better bargain for Rita is the bigger savings so, we know "B" gives $14 flat right off the 75 bucks, how about "A"? is the 15% more than 14 bucks?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 75}}{\left( \cfrac{15}{100} \right)75}\implies 11.25[/tex]
woopsie, no dice, so she's better off taking the $14 rebate.
Write an equation for a line given a slope of 2/3 through the pt (-6,10).
Equation for a line given a slope of 2/3 through the pt (-6,10) is y = [tex]\frac{2}{3}[/tex] x + 16.
How do I find the slope and intercept?A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the slope of the line in our equation, y = 3 x + 5, is 3.The values of the slope and y-intercept provide details on the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.Given data :
The equation of a line in point slope form is
y - y1 = m ( x - x1 )
where m represents the slope and ( x1, y1 ) a point on the line here
m = 2 / 3 and ( x1, y1 ) = ( -6, 10)
y - 10 = [tex]\frac{2}{3}[/tex] ( x - - 6 )
y - 10 = [tex]\frac{2}{3}[/tex] ( x + 6 )
y = [tex]\frac{2}{3}[/tex] ( x + 6 ) + 10
y = [tex]\frac{2}{3}[/tex] x + 16
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Problem solving
the radius of the two larger sectors is
7.8 cm
the radius of the two smaller sectors in
4.2 cm
work out the total area of the shape.
The total area of both the circles as calculated from the data given is found out to be as 246.64 cm² .
The formula to calculate the area of a circle is, (pi)r² where r = radius.
Therefore, the area of the first circle is found out to be as ,
22/ 7 x 7.8 x 7.8
=191.2 cm²
and the area of second circle will be ,
22/7 x 4.2 x 4.2
= 55.44 cm²
Therefore, the sum of the areas of the circle will be ,
191.2 + 55.44
= 246.64 cm² .
The area of a shape is known as the space occupied by it in tw dimensional space.
Every figure has a specific area and can be found by using unique formulas. The formula to calculate the area of a circle is (pi)r².
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a correlation is best expressed by . group of answer choices are built from research reviews describes the statistical relationship between two variables a collection of assertions predictions about the relationship between variables
A correlation is a statistical measure of the relationship between two variables and is expressed as a numerical value between -1 and 1.
A correlation is a measure of the relationship between two variables that is expressed as a numerical value between -1 and 1. To calculate a correlation, start by collecting data on the two variables. Then, calculate the covariance, which is the sum of the product of the differences between the two variables, divided by the number of data points. Finally, calculate the correlation by dividing the covariance by the product of the standard deviations of the two variables. The correlation can range from -1, which signifies a perfect negative correlation, to 1, which signifies a perfect positive correlation. A correlation of 0 indicates that there is no correlation between the two variables.
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How is a constant term different
than a variable term for an expression that
represents a real-world situation?
Answer:
The difference between constant and variable is that, while the first, as we have already said, remains fixed within a formula, the variable can assume different values.
Step-by-step explanation:
A constant term in an expression is a term that has a fixed value and does not change, while a variable term is a term that can take on different values. For example, in the expression 5x + 2, the 2 is a constant term because it is always 2, while x is a variable term that can take on different values.
In a real-world situation, a constant term represents a quantity that does not change. For example, if we were to write an expression to represent the cost of a product, the constant term would be the fixed cost of the product that does not change. On the other hand, a variable term represents a quantity that is subject to change. For example, in the same scenario, the variable term would represent the quantity of the product being bought, which can change.
In summary, a constant term represents a fixed value that does not change, while a variable term represents a value that is subject to change in a real-world situation.
Why is one half bigger than third?
Answer:
1/2 = 3/6 and 1/3 = 2/6
Step-by-step explanation:
we need to make the denominators the same to be able to compare
The ratio of the measures of the three angles in a triangle is 14:5:11. Find the measures of the angles.
The measures of the angles.
14x6 = 84 (angle 1) 5x6 = 30 (angle 2) 11x6 = 66 (angle 3)What are the angles in a triangle?Generally, In a space defined by Euclidean geometry, the sum of the angles of a triangle is equal to the angle that is straight.
A triangle is characterized by the presence of three angles, one at each vertex, and is defined by a set of sides that are next to one another. For a very long time, it was not known for certain whether or not there are alternative geometries for which this sum is different.
The measures of the angles in a triangle add up to 180 degrees. So, to find the measure of each angle in the triangle, we can set up the equation:
14x + 5x + 11x = 180
where
x represents the number of degrees in each angle.
Simplifying this equation, we get:
30x = 180
Dividing both sides by 30, we get:
x = 6
So, each angle in the triangle measures 6 degrees. To find the measure of each angle, we can simply multiply the ratio by 6.
14x6 = 84 (angle 1)
5x6 = 30 (angle 2)
11x6 = 66 (angle 3)
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find out if the polynomial p(×) is divisble by the goben binomial p(×)=2׳-7ײ+7×-2;×+2
Use the remainder theorem to find the remainder when the polynomial p(×) is divided the given binomial
P(×)= 2׳+4ײ+5×-1;×-3
P(×)=×59+4×49-5×39+16×29+2×19-4;×+1
Answer:
Step-by-step explanation:
yes I can help ok ok ok
The points (3, 2) and (r, -2) lie
on a line with slope -2. Find the missing coordinate r.
Answer:
r = 5
Step-by-step explanation:
calculate the slope m of the 2 given points and equate to - 2
using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 2 ) and (x₂, y₂ ) = (r, - 2 )
m = [tex]\frac{-2-2}{r-3}[/tex] = [tex]\frac{-4}{r-3}[/tex]
equating to - 2 gives
[tex]\frac{-4}{r-3}[/tex] = - 2 ( multiply both sides by r - 3 to clear the fraction )
- 4 = - 2(r - 3) ← divide both sides by - 2 )
2 = r - 3 ( add 3 to both sides )
5 = r
1. Determine the values of a and k when 299,790,000 is written in scientific notation.2. Determine the values of a and k when 0.51 is written in scientific notation.
(a) On writing 299790000 in scientific notation , the value of a is 2.9979 and value of k is 8 .
(b) On writing 0.51 in scientific notation , the value of a is 5.1 and value of k is -1 .
What is Scientific Notation ?
The general form of writing a number in scientific notation is ⇒ [tex]a\times 10^{k}[/tex] ;
Part (a) ;
the number is given to be : 299790000 ;
For writing it in scientific notation, decimal point will be placed after 2 ;
So , the scientific notation of the number is ⇒ [tex]2.9979 \times 10^{8}[/tex] ,
On comparing it with the general form of scientific notation,
we get , a = 2.9979 and k = 8 .
Part (b) ;
the number is given to be : 0.51 ;
For writing it in scientific notation, decimal point will be placed after 5 ;
So , the scientific notation of the number is ⇒ [tex]5.1 \times 10^{-1}[/tex] ,
On comparing it with general form of scientific notation,
we get , a = 5.1 and k = -1 .
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on a particular day, the petrol station has 600 customers. i how much petrol would you expect the petrol station to sell on this day? ii how many customers would you expect to buy 44 l of petrol?
i)The amount of petrol sold by the petrol station on a particular day is 21,600 L
II) Number of customers who would expect to buy 44 L of petrol is 2.28
i)The amount of petrol sold by the petrol station on a particular day can be estimated using the following equation:
Total petrol sold = Mean amount of petrol per customer x Number of customers
= 36 L x 600 customers
= 21,600 L
ii) To find the number of customers who would expect to buy 44 L of petrol, we need to find the probability of a customer buying that amount. We can use the standard normal table and the z-score formula (z = (x - mean) / std dev) to calculate the probability of a customer buying 44 liters of petrol.
z = (44 - 36) / 7 = 2.57
Using the standard normal table, we can find that the probability of a customer buying 44 liters of petrol is about 0.0038 or 0.38%.
Therefore, we can estimate that about 2.28 customers would expect to buy 44 liters of petrol on that day by multiplying the probability of buying 44 liters of petrol by the total number of customers.
Number of customers who would expect to buy 44 L of petrol = 0.38% * 600 = 2.28
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The complete question is:
The amount of petrol bought by a customer at a petrol station is normally distributed with mean 36 L and standard deviation 7 L. on a particular day, the petrol station has 600 customers. i) how much petrol would you expect the petrol station to sell on this day? ii) how many customers would you expect to buy 44 l of petrol?
Use the origin as the center of dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon. K=4
The vertices of the dilated figure is S'(-20, 4), T'(-12, 20), U'(-4, 4), V'(-12, -4)
What is transformation?Transformation is the movement of a point in the coordinate plane. Types of transformation are reflection, rotation, translation and dilation.
Dilation is the enlargement or reduction in the size of a figure by a scale factor.
Given the coordinates of polygon S(-5, 2), T(-3, 5), U(-1, 1), V(-3, -1). For a dilation with a scale factor of 4, the new coordinates are:
S'(-20, 4), T'(-12, 20), U'(-4, 4), V'(-12, -4)
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the average (arithmetic mean) of the numbers v, w, x, y, and z is j, and the average of the numbers x, y, and z is k. what is the average of v and w in terms of j and k ?
Therefore , the solution of the given problem of mean comes out to be value of the mean is 600.
What is mean?A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate: Divide by how many digits there are after adding up all the digits. the total divided by the count.
Here,
Given :The sum is 600.
The average arithmetic mean of x, y and z is 50.
=>(x + y + z)/350, sox + y + z = 150
=>4x + y + 3y+z+32
=>4x+4y+4z 4x+4y+4z4(x+y+ z) 4(x+y+2)
=> 4*150 = 600
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What is a table of a function?
The table of a function is a visual table with columns and rows that displays the function with regards to the input and output.
The relationship between an input and an output is expressed mathematically as a function. There are several ways to express a function, such as through a function table, math, graphics, or spoken language. Function machines are another name for these function tables. The output of the table is created by applying a certain rule to the input value. The rule applicable to any one input has to be consistent with the other inputs as well. There are three components: input, function, and output. It is a common practice to design function tables with one of the three components unknown and the other two acting as solving cues.
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Which of the following equations has 2 as a root
a. x² - 4x + 5 = 0
b. x² + 3x - 12 = 0
c. 2x² - 7x + 6 = 0
d. 3x² - 6x - 2 = 0
The equation that has 2 as its root is 2x² - 7x + 6 = 0 (option c)
Suppose we are given a quadratic function f(x) = ax² + bx + c, then x = q is a root if f(q) = 0.
Let's check for the given functions:
a. x² - 4x + 5 = 0
f(2) = 2² - 4(2) + 5
f(2) = 4 - 8 + 5 = 1
Since f(2) ≠ 0, hence 2 is not its root.
b. x² + 3x - 12 = 0
f(2) = 2² + 3(2) - 12
f(2) = 4 + 6 - 12 = -2
Since f(2) ≠ 0, hence 2 is not its root.
c. 2x² - 7x + 6 = 0
f(2) = 2(2)² - 7(2)+ 6
f(2) = 2(4) - 14 + 6 = 0
Hence, x = 2 is its root.
d. 3x² - 6x - 2 = 0
f(2) = 3(2)² - 6(2) - 2
f(2) = 12 - 12 - 2 = -2
Since f(2) ≠ 0, hence 2 is not its root.
Hence, the correct option is 2x² - 7x + 6 = 0 (option c)
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Solve each equation. Be sure to check solutions. Please answer the format (x,b) from least to greatest!!
1. 3h^2+2h-16=0
2. 8q^2-10q+3=0
3. 10r^2-21r=-4r+6
4. 12k^2+15k=16k+20
PLEASE HELP QUICK!!!!!!!!!!!!
Solve the inequality:
x(2x-1)>15
The solution of the inequality is x < -15/2x.
What is the linear equation?
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.
We can start solving the inequality by first isolating x on one side of the inequality.
x(2x-1)>15
Divide both sides by x(2x-1)
1>15/(x(2x-1))
To get rid of the fraction, we can invert the inequality and multiply both sides by x(2x-1)
x(2x-1)<15
Now we can simplify the inequality by factoring the left side:
x(2x-1)<15
2x-1 < 15/x
2x < 15/x + 1
2x < (15 + x) / x
Now we can multiply both sides by x
2x*x < 15 + x
2x^2 < 15 + x
Now we can subtract x from both sides
2x^2 - x < 15
Now we can factor the left side
(x-5)(2x+3) < 0
Now we can find the solution of the inequality by finding the values of x that make the inequality true
x = 5, 2x +3 < 0
x < -15/2x
Hence, the solution of the inequality is x < -15/2x.
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