False.A linear transformation T : Rn → Rm is not completely determined by its effect on the columns of the n × n identity matrix.
The columns of the identity matrix represent the standard basis vectors in Rn, which are the vectors with all components equal to zero except for one component that is equal to one. The effect of a linear transformation on the standard basis vectors provides some information about how the transformation affects certain directions in the input space, but it does not fully characterize the transformation.
To see why this statement is false, let's consider an example. Suppose we have a linear transformation T : R2 → R2. The identity matrix in this case is a 2 × 2 matrix with the columns [1 0] and [0 1]. The effect of T on the first column [1 0] could be any vector in R2, let's say T([1 0]) = [a b]. Similarly, the effect of T on the second column [0 1] could be another vector in R2, let's say T([0 1]) = [c d].
Now, we have the information about the effect of T on the columns of the identity matrix, which is T([1 0]) = [a b] and T([0 1]) = [c d]. However, this information alone is not sufficient to uniquely determine the linear transformation T. There could be infinitely many linear transformations that satisfy these conditions. For example, we could have T([x y]) = [ax + cy, bx + dy], where a, b, c, and d are arbitrary real numbers.
In this example, we can see that the effect of the linear transformation on the columns of the identity matrix only gives us partial information about T, but it does not fully determine the transformation. The linear transformation can have different effects on vectors that are not in the standard basis. In general, a linear transformation T maps every vector in the input space Rn to a corresponding vector in the output space Rm, and its behavior on the standard basis vectors alone does not capture the complete transformation.
Therefore, we can conclude that a linear transformation T : Rn → Rm is not completely determined by its effect on the columns of the n × n identity matrix. Additional information about the transformation's behavior on other vectors or basis sets is needed to fully determine the transformation.
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From the set {8, 19, 25}, use substitution to determine which value of x makes the inequality true
x = 19 and x = 25 make the inequality true.
What is inequality?
In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.
To use substitution to determine which value of x makes the inequality true, we can substitute each value from the set {8, 19, 25} into the inequality and see if it makes the inequality true or false.
For example, if the inequality is x < 10, we can substitute 8, 19 and 25 into the inequality to see which one makes it true:
8 < 10 is true
19 < 10 is false
25 < 10 is false
So, we can see that only 8 makes the inequality true. Therefore, x = 8 makes the inequality true.
If the inequality is x > 10, we can substitute 8, 19 and 25 into the inequality to see which one makes it true:
8 > 10 is false
19 > 10 is true
25 > 10 is true
Hence, x = 19 and x = 25 make the inequality true.
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Which explains why the commutative property of addition does not work for subtraction?
The commutative property of addition states that the order of the numbers being added does not affect the result. For example, the sum of 2 + 3 is the same as the sum of 3 + 2, which is 5.
The commutative property of addition does not work for subtraction because subtraction is not commutative. In subtraction, the order of the numbers being subtracted does affect the result. For example, the difference of 3 - 2 is 1, but the difference of 2 - 3 is -1.
The reason for this is that subtraction is the inverse operation of addition and the inverse operation of a commutative operation is not always commutative. In addition, subtraction is not commutative because when we subtract the smaller number from the larger number, we get a positive result but when we subtract the larger number from the smaller number we get a negative result.
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The histogram shows information about the
speed of cars as they pass a checkpoint.
The scale on the frequency density axis
is missing.
Speed of cars
Frequency density
15 20
25
30 35
Speed (mph)
40
45
50
The histogram shows information about
480 cars.
a) How many cars does the first bar represent? (4)
b) Cars with a speed greater than 40 mph are
over the speed limit. Use the histogram to
estimate the number of cars that are over
the speed limit.
+
(2)
+
Total marks: 6
The bar represent 120 bars The histogram shows information about 480 cars.
How many cars does the first bar represent?15 to 30 on x axis has , 24 on y axis (30 - 15) * 24 = 36030 to 35 on x axis has , 33 on y axis (35 - 30) * 33 = 16535 to 50 on x axis has , 5 on y axis (50 - 35) * 5= 75360 + 165 + 75 = 600 600 = 4801 = 480/600360 = 360 x 480/600 = 288first bar represent = 288 CarsA histogram is an approximate representation of the distribution of numerical data. The term was first introduced by Karl Pearson.A histogram is used for continuous data, where the bins represent ranges of data, while a bar chart is a plot of categorical variables.To learn more about first bar represent refers to:
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Problems 1- 14, use the rules of differentiation to find the derivative of the function. 1. y = 14; 2. y=x^9+3 tan x; 3. y = 1/x^4-4cos x
1 . y'=0 is the derivative of the function y = 14.
2. y' = 9[tex]x^8[/tex]+3[tex]sec^2x[/tex] is the derivative of the function y= [tex]x^9[/tex]+3tanx
3. y' = [tex]\frac{-4}{x^5}[/tex] + 4sinx is the derivative of the function y = [tex]\frac{1}{x^4}[/tex] - 4cos x
1 . The derivative of a constant is always zero.
A constant function is a function whose value does not depend on the input value.
So y = 4 is a constant function, its derivative is always zero.
So the derivative of y=4 is 0
2. The differentiation of [tex]x^9[/tex]+3tanx is 9[tex]x^8[/tex]+3[tex]sec^2x[/tex]
The power rule states that the derivative of x^n (where n is a constant) is nx^(n-1). So the derivative of x^9 is 9x^8.
The derivative of tanx is [tex]sec^2x[/tex].
And the derivative of 3tanx is 3[tex]sec^2x[/tex]
So, [tex]x^9[/tex]+3tanx is differentiated as9[tex]x^8[/tex]+3[tex]sec^2x[/tex]
3. The derivative of y = [tex]\frac{1}{x^4}[/tex] - 4cos x can be found using the power rule and the chain rule.
The power rule states that the derivative of x^n (where n is a constant) is nx^(n-1). In this case, [tex]\frac{1}{x^4}[/tex] can be rewritten as [tex]\frac{1}{x^4}[/tex] and the derivative would be -4 [tex]\frac{1}{x^5}[/tex]
The chain rule states that the derivative of (f(g(x)) is f'(g(x))*g'(x). In this case, the inner function is -4cos x, the derivative of cos x is -sin x and the outer function is , [tex]\frac{1}{x^4}[/tex] the derivative of that is -4 [tex]\frac{1}{x^5}[/tex]. So the derivative of -4cos x is -4(-sin x)
So the final derivative of y = [tex]\frac{1}{x^4}[/tex] - 4cos x is [tex]\frac{-4}{x^5}[/tex] + 4sinx
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Find the values of x and y.
y°
40°
x°
(x,, y,) is a point on the line in the point-slope formula, and m is the slope.
How should slope m be written?When you know the slope of the line to be investigated and the point supplied is also the y intercept, you may utilize the slope intercept formula y = mx + b. (0, b). The y value of the y intercept point is represented by b in the formula.
The equation of a line can be written in several different formats:
Standard form
Ax+ By = C
A, B, and C must be real numbers and A and B cannot both be zero.
Slope-intercept form
Y = MX + b
M is the slope and b is the y-intercept.
Point-slope form
y-y₁ = m(x-x1)
In the point-slope formula, (x,, y,) is a point on the line and m is the slope.
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Rahul bought a weater and aved r20 when a dicount of 25% wa given. What wa the price of the weater before the dicount ?
The price of a sweater bought by Rahul before the discount is Rs. 80.
Let us assume the price of the sweater before the discount to be x.
Given that,
The money saved by Rahul will be equal to the discount given for the sweater.
Therefore, we can say that Rs. 20 will be equal to 25% of the price of the sweater before the discount.
The equation we would obtain from the language above would be,
25% of x = 20
Solving this equation further, we can see that,
=> 25% of x = 20
=> 25* 1/100 * x = 20
=> x/4 = 20
=> x = 80
As we assumed x to be the price of the sweater before the discount,
So, the price of a sweater bought by Rahul before the discount is Rs. 80.
Complete question: Rahul bought a sweater and saved Rs. 20 when a discount of 25% was given. What was the price of the sweater before the discount?
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Please help me and explain
The value of x in the equation 8 (x - 3) + 7 = 2x (4 - 17) is x = 1/2.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side
The given equation is,
8 (x - 3) + 7 = 2x (4 - 17)
Distributive property : p (q + r) = p q + p r
Applying the property here,
8x - (8 × 3) + 7 = 2x × (-13)
8x - 24 + 7= -26x
8x - 17 = -26x
8x + 26x = 17
34x = 17
x = 17/34
x = 1/2
The mistake of Lin happened in the second step where 4 - 17 = -13 but she wrote 13.
Hence the value of x is 1/2 not -1/2 as the solution of Lin.
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i need help this is due at 12:10
Answer:
I believe the answer is 180°
Jon has to choose which variable to solve for in order to be able to do the problem below in the most efficient manner.
6 x + 3 y = 27. 5 x + 2 y = 21.
Which variable should he choose so that he can use substitution to solve the system?
Jon should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
Jon should solve for x in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.
Jon should solve for y in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
Jon should solve for x in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.
Jon should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient of y.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Given linear equations are,
6x + 3y = 27
5x + 2y = 21
The coefficients of the first equation are multiples of 3.
Hence dividing throughout the first equation by the common factor 3, coefficient of y will be eliminated.
6x/3 + 3y/3 = 27/3
2x + y = 9
y = 9 - 2x
Solving by substitution, the second equation becomes,
5x + 2(9 - 2x) = 21
5x + 18 - 4x = 21
x = 3
y = 9 - 2x = 3
Hence Jon should could solve the problem by eliminating the coefficient of y in the first equation by a common factor 3.
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How do you find the value of n in exponents?
We can find the value of n in exponents through various rules based on the given equation.
If x is any real number and n is a positive integer, then [tex]x^n[/tex] is equivalent to repeated multiplication.
We can also write [tex]x^n[/tex] in the following way:
[tex]x^n[/tex] = x * x * x * x * x *...... * x (n times)
This can be referred to as "n raised to the power of x," "n to the power of n," or just "n." In this case, n is the exponent or power, and x is the base.
We may infer a few fundamental guidelines for exponentiation from this concept. There are various methods of finding the exponent based on various rules, namely,
Product ruleQuotient rulePower of a powerPower of a productPower of onePower of ZeroPower of negative oneChange the sign of exponentsFractional exponentsRead more about exponents from:
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To find the value of n in exponents, you can use the property that a^n * a^m = a^(n+m)
For example, if you have the expression (2^3)^n, you can use the property above to find the value of n by dividing both sides by 2^3, so (2^3)^n / 2^3 = 1^n. Now you can see that n = 1.
Another way to find the value of n in exponents is to use logarithms. The logarithm base "a" of a^n is n. Therefore, if you know the value of a^n, you can find the value of n by taking the logarithm base "a" of a^n.
For example, if a^n = 8 and a=2, then n = log2(8) = 3.
In summary, there are a couple of ways to find the value of n in exponents, but the most common way is to use the property of exponents or logarithms.
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K
Find the measures of an interior angle and an exterior angle of a regular 15-gon.
The measure of an interior angle is
The measure of each interior angle of the polygon is 156°.
What is the interior angle of polygon?In a regular polygon, all interior angles are equal. The interior angle of a polygon = sum of interior angles and the number of sides is the formula for determining the size of an interior angle. A polygon's exterior angles add up to 360°.
Given that the number of sides of the polygon is 15. The sum of the interior angles of the polygon is calculated by the formula:-
Sum = ( n - 2 ) x 180
Sum = ( 15 - 2 ) x 180
Sum = 2340
The measure of each angle is calculated as:-
Angle = 2340 / 15
Angle = 156°
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Can somebody help me on this one please I am so confused don’t know none of this stuff
rotation then reflection.
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Is 1 1 2 3 5 8 an arithmetic sequence?
No, 1 1 2 3 5 8 is not an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a constant to the previous term.
Thus, the difference between successive terms is the same. In the given sequence, the difference between terms 1 and 2 is 0, between terms 2 and 3 is 1, between terms 3 and 5 is 2, and between terms 5 and 8 is 3. Therefore, the difference between successive terms is not the same and hence, 1 1 2 3 5 8 is not an arithmetic sequence.
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Ruben measured how many minutes he meditated each night and the number of hours he slept. Plot the data in a scatter plot.
Meditation (minutes) 444 888 101010 444 181818 444
Sleep (hours) 4.54.54, point, 5 9.59.59, point, 5 8.58.58, point, 5 666 101010 777
The scatter plot for the given data (See full and correct details attached) is appended accordingly.
What is a scatter plot?A scatter plot is a collection of dots drawn on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the amount, if any, of correlation between the values of observed quantities or events (called variables).
Scatter plots aid in the visual representation of correlations between economic factors such as employment and production, inflation and retail sales, and taxes and economic growth.
As you can see there is a slight positive correlation between the number of hours meditated and the numberr of hours slept.
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please help me with this problem:
the base of a rectangle is 9/4 of the height and the perimeter is 104 dm. Calculate the perimeter of the square equivalent to four times the rectangle
Answer:
[tex]\boxed{384}[/tex]
Step-by-step explanation:
Let B be the base of the rectangle and H the heightWe are givenGraph the image of A(7, −6)
after a reflection in y=x
followed by a reflection in x=−3.
The image of A After a reflection in y=x followed by a reflection in x=−3. is (0. 7).
What is a reflection?There are two ways of reflection.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
A = (7, -6)
Reflection rules over y = x.
(x, y) → (y, x)
So,
(7, -6) = (-6, 7)
Now,
Reflection in x = -3
Reflection rules over the y-axis.
(x, y) → (-x, y)
So,
x = -3
There are 3 units between -3 and -6.
So,
3 + 3 = 6 units will be added during reflection over y = -3
i.e
3 units on the left side of y = -3
3 units on the right side of y = -3
So,
(-6, 7) = (-6 + 6, 7) = (0, 7)
Thus,
The image of A is (0. 7).
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The reflection of image of point in y = x is (-6, 7),
and reflection in x = −3 is (-13, -6).
What are transformations?The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation.
Given a point A(7, −6)
A. a reflection in y = x
Flipping is the term for reflection. A reflection is the shape's mirror image. The line of reflection is the path taken by an image when it reflects.
reflection in y = x
x changed to y and y changed to x
x = -6 and y = 7
coordinates are A'(-6, 7)
B. a reflection in x = −3.
let the coordinates be (a, b)
reflection in x = k
image coordinates will be A" (2k - a, b)
here a = 7, k = -3, and b = -6
2k - a = 2(-3) - 7
2k - a = -13
image coordinates will be A"(-13, -6)
Hence the coordinates are A'(-6, 7),
and reflection in x = -3,
coordinates aere A"(-13, -6).
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Can someone help me with these pls
The speed of spin of carousel is 0.286 miles/minutes. The The speed at which something moves in a specific direction is known as its velocity. as the speed of a car driving north on a highway or the speed at which a rocket takes off.
Which math is speed?based on the distance traveled in a given amount of time. These cars can travel at speeds of more than 150 kilometers per hour (km/h). Meters per second (m/s) is the fundamental unit of speed in the metric system.
Given,
distance spinned=2 miles
time taken=7min
speed=distance/time
speed=2/7=0.286 miles/minute
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What is the exponential of 10?
The term "exponential of 10" means the numbers in which the base is 10 and the exponent is an integer.
The Exponential of 10 or the "powers of 10" means when the number 10 is multiplied a certain number of times, then the product is expressed using exponents.
These numbers which are written as the exponents are exponents of 10.
For example : 10² , 10³ represents different exponents of 10 .
In general form of the exponent of 10 or power of 10 is represented as 10ⁿ .
For Example : 10 to the exponent of 5 can be written as 10⁵, and
it's value is calculates as :
⇒ [tex]10^{5}=10\times\ 10 \times 10\times 10\times 10[/tex]
⇒[tex]10^{5}= 100000[/tex] .
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Look at the picture
Answer:
1/15
Step-by-step explanation:
dividend=1/3
divisor=5
since
Dividend ÷ Divisor = Quotient.
1/3 ÷5 = 1/15
Therefore, quotient = 1/15
Contruct an iocele right-angled Triangle 'XYZ' in which angle Y=90° and two ide are 5cm each
Isosceles right angled triangle XYZ is constructed with the given measure of ∠Y =90° , YX = 5cm and YZ = 5cm each using steps of construction.
Constructed diagram is attached.
As given in the question,
Given measurement to construct a isosceles right angled triangle are:
Measure of ∠Y =90°
Measure of side length
YX = 5cm and YZ = 5cm
Constructed diagram is attached.
Step of construction :
Draw a ray.Take point Y on it and draw an arc of any measure.Take the measure more than half of the radius of the drawn arc.Take each end point as centre and draw an arc on the upper half plane of the ray.Draw ray perpendicular through point Y in the upper half plane.Now take measure of 5cm and point Y as centre and cut an arc on each of the ray.Name the point as 'X' and 'Z'.Join XZ .Isosceles right angled triangle is constructed with the given measurement.Therefore, construction of isosceles right angled triangle is done as per the above steps of construction.
The above question is incomplete, the complete question is :
Construct an isosceles right-angled Triangle 'XYZ' in which angle Y=90° and two side are 5cm each.
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Is the residual always 0?
The residual square sum may equal 0. Your model will fit your data more closely if the residual sum of squares is small; conversely, if the residual sum of squares is large, your model will match your data less closely. A value of 0 indicates that your model fits the data perfectly.
What Exactly Is Residual Value?
The estimated value of an asset that is fixed at the end of its useful life or lease term is its residual value, which is often referred to as salvage value. In lease agreements, the residual value is one of the lessor's main methodologies for calculating the lessee's periodic lease payments.
A good residual value is what?
Check out the Car Lease Ratings section of our Lease Kit for a complete list of high-residual vehicle brands and models.
A car is probably not a good lease deal if the lease-end residual value is less than 50% of the MSRP (for a 36-month lease). 55% to 65% of MSRP would be a nice residual.
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The average time taken to complete a test follows normal probability distribution with a mean of 70 minutes and a standard deviation of 25 minutes. The probability of a randomly selected student completing the test in 45 minutes or less is approximately equal to %. The probability of a randomly selected student completing the test in 95 minutes is %.
The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 70, \sigma = 25[/tex]
The probability of 45 minutes of less is the p-value of Z when X = 45, hence:
Z = (45 - 70)/25
Z = -1
Z = -1 has a p-value of 0.16 (rounding).
As for the probability of an exact time, such as 95 minutes, is of 0%, as the normal distribution is continuous.
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how to know if a piecewise function is a function
Answer:
Step-by-step explanation:
Twelve less the product of two numbers, ‘a’ and ‘b’. what does it mean.
Answer: (a * b) - 12
Step-by-step explanation:
We will pull details for the sentence given to write an expression representing this situation.
In this case, these words mathematically mean:
less ➜ subtraction
product ➜ multiplication
Using this information, we will write our expression.
(a * b) - 12
Is rotation congruent or similar?
Answer:
a
Step-by-step explanation:
during which time interval did dylan maintain the fastest average speed
The time interval that saw Dylan maintain the fastest average speed was B. between hour 1 and hour 2.
Where did Dylan maintain the fastest speed ?Dylan maintained the fastest speed at the interval that saw him cover more distance in a shorter amount of time. You can find the speed at these intervals by using the speed formula of distance divided by time.
Speed between hour 0 and 1 :
= 25 miles / 1 hour
= 25 miles per hour
Speed between hour 1 and 2 :
= ( 75 - 25 ) / 1
= 50 miles per hour
Speed between hour 3 and 5 :
= ( 125 - 75 ) / 2
= 25 miles per hour
The fastest speed was therefore between hour 1 and 2.
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Options for this question are:
between hour 0 and hour 1between hour 1 and hour 2between hour 2 and hour 3between hour 3 and hour 5Is x³ an exponential function?
Yes, x³ is an exponential function. An exponential function is a function in which the variable (x) is in the exponent.
The general form of an exponential function is f(x) = a^x, where a is the base and x is the exponent. In the case of x³, the variable (x) is in the exponent. x³ represents x raised to the power of 3, where x is the base and 3 is the exponent.
Exponential functions are often used to model growth and decay in a variety of natural phenomena, such as population growth, radioactive decay, and compound interest. Understanding exponential functions is important for solving mathematical problems, especially in algebra, calculus, and applied fields such as physics and engineering.
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What is called absolute number?
Any value inside an absolute value in a problem or equation indicates that the value is always positive.
What is called an absolute number?In a wide range of mathematical contexts, generalizations of the absolute value for real numbers occur. Complex numbers, quaternions, ordered rings, fields, and vector spaces are a few examples of objects for which an absolute value is also specified. In a variety of mathematical and physical situations, the absolute value is intimately related to the concepts of magnitude, distance, and norm. Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line. A number can never have a negative absolute value. View some illustrations. 5 is 5 in its entirety.Any value inside an absolute value in a problem or equation indicates that the value is always positive. Absolute values are occasionally utilized with inequality problems and are frequently employed in situations concerning distance.To learn more about absolute number refer to:
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Two rectangles are similar.
Rectangle 1: W = 12 in, P = 34 in
Rectangle 2: W = 14 in, P = ?
Provide an answer accurate to the nearest hundredth.
The answer accurate to the nearest hundredth is 38.5
How to find the nearest hundredth?
To find the nearest hundredth of a number, you can round it to the nearest hundredth. To do this, you need to look at the third digit after the decimal point.
If the digit is less than 5, you can round down.If the digit is greater than or equal to 5, you can round up.Regarding the rectangles, since the two rectangles are similar, we know that the ratio of their corresponding sides are equal.
W1/W2 = P1/P2 = k (where k is the proportionality constant)
So, P2 = (P1 * W2)/W1 = (34 * 14)/12 = 38.5
Hence, The answer accurate to the nearest hundredth is 38.5
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Consider the function g(x)=2[tex]x^{2}[/tex]-x
When g(x) is divided by x+1 the quotient is [tex]\frac{g(x)}{x+1}[/tex] = 2x-3+ [tex]\frac{k}{x+1}[/tex]
What is the value k?
The value of the constant k in the equation of the division of g(x) by (x + 1); [tex]\frac{g(x)}{x + 1} = 2\cdot x - 3 + \frac{k}{x + 1}[/tex] obtained by the long division of g(x) = 2·x² - x by (x + 1) is 3.
What is the method for the long division of a polynomial?The method or algorithm of finding the long division of a polynomial, p(x) known as the dividend, by a divisor, g(x) makes use of the equation;
p(x) = q(x) × g(x) + r(x)
Where;
q(x) = The quotient
r(x) = The remainder from the division;
The specified equation; [tex]\frac{g(x)}{x + 1} = 2\cdot x - 3+\frac{k}{x+1}[/tex], indicates that the remainder, r(x) = k.
The value of k in the specified equation, can be found by dividing the function g(x) = 2·x² - x, by (x + 1) as follows;
The expression obtained when g(x) is divided by (x + 1) using long division, is presented as follows;
[tex]{}[/tex] 2·x - 3
(x + 1) |2·x² - x
[tex]{}[/tex] 2·x² + 2·x
[tex]{}[/tex] -3·x
[tex]{}[/tex] [tex]{}[/tex] -3·x - 3
[tex]{}[/tex] [tex]{}[/tex] 3
The remainder obtained from the long division of 2·x² - x by (x + 1) is; 3
The result of the long division of 2·x² - x by (x + 1) is therefore;
[tex]\frac{g(x)}{x+1} =2\cdot x - 3 + \frac{3}{x + 1}[/tex]
Comparison of the equation; g(x)/(x + 1) = 2·x - 3 + k/(x + 1) and the equation; g(x)/(x + 1) = 2·x - 3 + 3/(x + 1), indicates that the value of k is 3
Learn more about the long division of polynomials here: https://brainly.com/question/28925622
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