A linear transformation T : Rn → Rm is completely determined by its effect on columns of the n × n identity matrix
T/F

Any value inside an absolute value in a problem or equation indicates that the value is always positive.

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Answer:

a

Step-by-step explanation:

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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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.

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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Answer:

[tex]\boxed{384}[/tex]

Step-by-step explanation:

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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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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rotation then reflection.

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The image of A After a reflection in y=x followed by a reflection in x=−3. is (0. 7).

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).

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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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.

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

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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,

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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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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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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.

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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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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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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The bar represent 120 bars The histogram shows information about 480 cars.

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Answer:

I believe the answer is 180°

The measure of each interior angle of the polygon is 156°.

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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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

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 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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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

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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The time interval that saw Dylan maintain the fastest average speed was B. between hour 1 and hour 2.

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:

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.

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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Answer:

Step-by-step explanation:

The value of x in the equation 8 (x - 3) + 7 = 2x (4 - 17) is x = 1/2.

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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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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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 :

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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(x,, y,) is a point on the line in the point-slope formula, and m is the slope.

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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The scatter plot for the given data (See full and correct details attached) is appended accordingly.

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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