How many feet do you travel going 40 mph?

Given that the two matrices A and B are square matrices of order 3 and 2 respectively and, 2A⁻¹B = B - 4I. To show that A - 2I is invertible, we need to prove that det(A - 2I) ≠ 0.The equation given can be written as:2A⁻¹B = B - 4I2A⁻¹B + 4I = B2(A⁻¹B + 2I) = B

Here, B can be replaced by 2(A⁻¹B + 2I) which gives:B = 2(A⁻¹B + 2I)Now, the equation can be written as:A⁻¹B = ½(B - 4I)Now, we have two matrices, A and B, where A is a square matrix of order 3 and B is a square matrix of order 2.Given, 2A⁻¹B = B - 4I2(A⁻¹B) + 4I = BSubstituting ½(B - 4I) for A⁻¹B,

we get:2 * ½(B - 4I)A = ½(B - 4I)A = ¼(B - 4I)We know that A is a square matrix of order 3 and A - 2I is invertible, i.e. (A - 2I)⁻¹ exists. Let's assume that det(A - 2I) = 0, which means (A - 2I)⁻¹ does not exist.Therefore, det(A - 2I) ≠ 0 and (A - 2I)⁻¹ exists. So, A - 2I is invertible and the proof is complete.

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Given matrices A and B are square matrices of orders 3 and 2 respectively and 2A^−1B = B - 4I, we have to show that A - 2I is invertible.

Now, if (2A^−1 - I) is invertible, then we can write it as(2A^−1 - I)^-1 = 1/2 A(B)^-1If we multiply both sides of the equation with B, we get: B (2A^−1 - I) (1/2 A(B)^-1) = -2I(B)^-1By distributive property, it becomes:

B [(2A^-1 × 1/2A(B)^-1) - (I × 1/2A(B)^-1)] = -2I(B)^-1Let us simplify\(2A^-1 × 1/2A(B)^-1 = BB(B)^-1 =\) I, so the equation becomes:

B (I - 1/2(B)^-1) = -2I(B)^-1Or, B [I - 1/2(B)^-1] = -2I(B)^-1Thus, (I - 1/2(B)^-1) is invertible. Thus, the matrices 2A^−1 - I and I - 1/2(B)^-1 are invertible.

As the product of two invertible matrices is also invertible, the matrix B (2A^−1 - I) (1/2 A(B)^-1) is invertible.

Now, A - 2I = (1/2)A [2A^−1 × B - 2I]Thus, we get:

A - 2I = (1/2)A [B (2A^−1 - I) (1/2 A(B)^-1) - 2I]Now, we know that the product of invertible matrices is invertible.

So,\(B (2A^−1 - I) (1/2 A(B)^-1\)) is invertible. And so, \((B (2A^−1 - I) (1/2 A(B)^-1) - 2I)\)is also invertible. Finally, (1/2)A [B (2A^−1 - I) (1/2 A(B)^-1) - 2I] is invertible.So, A - 2I is invertible. Hence, this is the required proof and we have shown that A - 2I is invertible.

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The examples of SAS congruence postulates are

The SAS is stands for Side-Angle-Side congruence postulate which states that triangles are congruent if two sides and an included angle of a triangle are congruent with two sides and an included angle of a second triangle. Note that we need to include the angle between the two sides.

Example 1 : Let's say you have one triangle, ∆ABC with side lengths 5 and 10 and the angle included between those two sides is 30 degrees. If you have a second triangle, ∆DEF that also has side lengths 5 and 10 with a 30 degree angle in between, then by the SAS Postulate ∆ABC is similar to ∆DEF.

Example 2 : Point C is the midpoint of BF

so, AC = CE

Statement Reason

AC = CE C is mid point so, it

divides equal parts .

BC = CF C is mid-point

∠ACB =∠ECF Opposite angles

Thus, by the Side Angle Side postulate, the triangles are congruent i.e,∆ABC ≅ ∆CEF

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Answer:

Chord 12 cm long subtends an angle of 40 degrees at the center of a circle.

θ= 40° = 0.698 rad

Let R be the radius of circle.

Chord Length = 2Rsin(θ/2)

12=2R sin (0.698 /2)

R= 17.54

Ans: Radius of circle = 17.54 cm

The system of equations for this problem is defined as follows:

From the first equation, we have that:

y = 21 - 3x.

The second equation is given as follows:

2x + 2y = 24.

Simplifying the equation, we have that:

x + y = 12.

Replacing the first equation, we have that the value of x is obtained as follows:

x + 21 - 3x = 12

2x = 9

x = 4.5.

Then the value of y is of:

4.5 + y = 12

y = 7.5.

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Answer:

In the system of equations, x represents the weight in ounces of each bar of soup.

In the system of equations, y represents the weight in ounces of each bottle of lotion.

The ordered pair that is a solution to the system of equations is given as follows: (4.5, 7.5).

Step-by-step explanation:

Answer:

B. y - 2 = 1/3(x - 3)

Answer:

B.

Explanation:

If you actually do the math you get B

The exact value of cosine function at cos 120° is -1/2.

We can use the double-angle identity for cosine to find the exact value of cos 120°. The double-angle identity states that cos 2θ = 2 cos² θ - 1.

In this case, we want to find cos 120°. We can rewrite 120° as 2 * 60°. So, using the double-angle identity, we have:

cos 120° = cos(2 * 60°)

= 2 * cos² 60° - 1

Now, we know that cos 60° = 1/2. Substituting this value into the equation, we get:

cos 120° = 2 * (1/2)² - 1

= 2 * (1/4) - 1

= 1/2 - 1

= -1/2

Therefore, the exact value of cos 120° is -1/2

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Answer:

It's B, because thats where the two points cross

Step-by-step explanation:

Answer:

i think the answer is B.4

Answer:

If I understand this right, the answer is $48.00

Step-by-step explanation:

If they pay $1.50 three times a month just times $1.50 by 12 because there are 12 days in a month, then you get 16, then you times 16 by 3 and you get 48.

(I hope this is right lol)

Answer:

$54.00

Step-by-step explanation:

3 transactions × $1.50 per transaction = $4.50 per month

$4.50 × 12 months in a year = $54.00

Chillee sold consulting services on account to customer RST for $4,000, terms 1/10, n/30.The journal entry would be: Debit: Account Receivable $3,880Debit: Sales Discount $120Credit: Sales $4,000.

Explanation: To record the sale transaction, the company will debit account receivable to record the amount which is due from the customer. RST has a 10-day period to make the payment so the company will record a discount of $120 as sales discount. The discount was calculated using the formula: Discount = Total sale x discount rate Discount = $4,000 x 1%Discount = $40Discount as a percentage of sale = $40/$4,000 = 1%.Therefore, Sales discount is debited with $120.Credit sales with $4,000.The balance of Account Receivable should be $3,880 (4,000-120), so it will be debited with $3,880.

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Answer:

Step-by-step explanation:

It's no wonder that no one wanted to answer this...it was really mind-boggling!

If Jones can paint a car in 8 hours, then he gets 1/8 of the job done in 1 hour. If Smith can paint the car in 6 hours, then he gets 1/6 of the job done in 1 hour. We need to find out how long it would take them to get the whole job done if they work together. Even though we are asked to find out how long it will take Smith to finish when Jones ditches him, we have to start here first. The work equation for that problem is

\(\frac{1}{8}+\frac{1}{6}=\frac{1}{x}\). The LCD is 24x, so mutliplying everything by 24x gives us the new equation

3x + 4x = 24 and

7x = 24 so

x = 3.428571429 hours. Working together they get 100% of the job done in 3.428571429 hours. Therefore, if 100% of the job is done in 3.428571429 hours, we can use that to find the percentage they get done working together for 1 hour:

\(\frac{percent}{hours}: \frac{100}{3.428571429}=\frac{x}{1}\) Cross multiply to get

100% = (3.428571429)x% and divide to get

\(x=29\frac{1}{6}\)% of the job gets done in 1 hour when they work together. But they work 2 hours together, so that means that in 2 hours, right when Jones leaves, \(58\frac{1}{3}\) % of the car is done, leaving Smith with \(41\frac{2}{3}\) % to finish on his own.

We go back to the beginning where we determined that Smith can finish 1/6 of the car alone in 1 hour, so he gets \(16\frac{2}{3}\) % done per hour on his own.

If he can finish 16.66666% of the car in an hour on his own, we can use ratios to find out how long it will take him to finish the remaining 41.6666% on his own.

\(\frac{percent}{hours}:\frac{16.6666}{1}=\frac{41.6666}{x}\) Cross multiply to get

16.6666x = 41.6666 so

x = 2.5

It will take Smith 2.5 hours to finish the job after Jones leaves.

True.

Given the statement 'If the distance from 0 to x on a number line is greater than 5, then -5+x is positive' is True.

For the given question,

The distance from 0 to x on a number line is greater than 5

We write the above statement in mathematical expression form as,

⇒ |x - 0| > 5

⇒ |x| > 5

⇒ x > 5  

We need to determine the value of an expression -5 + x

From (1),

⇒ x > 5  

Subtract -5 from both sides,

⇒ -5 + x = -5 + 5

⇒ -5 + x > 0

From the above expression, we observe that the value of the expression is always greater than 1.

This means the value of an expression -5 + x is positive.

Therefore, the given statement 'If the distance from 0 to x on a number line is greater than 5, then -5+x is positive' is True.

In mathematics, a number line can be described as a figure that symbolizes numbers on a consecutive line. The digits on a number line are positioned successively with equal spacing along its length. It can be infinitely expanded in any direction and is often depicted horizontally.

Absolute value is the distance between a digit and zero on a number line. Since the space is forever positive, the absolute value will always be positive.

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Answer:

8 in.

Step-by-step explanation:

Perimeter of a rectangle, P = 2(L + W)

Value of P = 46.

Length is 7 inches less than the width.  This translates to L = W - 7

Substitute L = W - 7 into the perimeter equation, you get

46 = 2(W - 7 + W)

46 = 2(2W - 7)

46 = 4W - 14

4W = 60

W = 60 / 4 = 15 in

L = W - 7 = 15 - 7 = 8 in

The width and length of the rectangle in inches are 17 and 10 respectively.

Perimeter is the sum of the lengths of all the sides of a given plane figure.

According to the given question the length of a rectangle is 7 inches less than its width.

Assuming the width of the rectangle is x inches.

∴ From the given data length of the rectangle is ( x - 7) inches.

Given perimeter is 54 inches.

We know perimeter of a rectangle is 2( length + breadth).

∴ 2{ x + ( x - 7) } = 54.

  2 { 2x - 7 } = 54

  4x - 14 = 54

  4x = 54 + 14

  4x = 68

    x = 17.

So, the width of the rectangle is 17 inches and length of the rectangle is (17 - 7) inches which is 10 inches.

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Answer:

The doing would be x

Step-by-step explanation:

since you are calculating domain for a specific value it would be the corresponding g(x) value which is the domain

Answer:

x- intercept = 2, y- intercept = - \(\frac{8}{7}\)

Step-by-step explanation:

To find the x- intercept, let y = 0 in the equation and solve for x

4x - 7(0) = 8 , that is

4x = 8 ( divide both sides by 2 )

x = 2 ← x- intercept

To find the y- intercept , let x = 0 in the equation and solve for y

4(0) - 7y = 8, that is

- 7y = 8 ( divide both sides by - 7 )

y = - \(\frac{8}{7}\) ← y- intercept

The cost of the apples is 2.9 dollars.

The cost of the bananas is 5.7 dollars.

The total cost is 6 dollars, each apple cost $1.50 each banana cost $.30 and there’s two more bananas then apples.

Therefore,

let

x = number of apples

y = 2x

where

Therefore, using equations,

1.5(x) + y(0.30) = 6

Hence,

where

y = 2x

1.5(x) + 2x(0.30) = 6

1.5x + 0.6x = 6

2.1x = 6

divide both sides by 2.1

x = 6 / 2.1

x = 2.9 dollars

y = 2(2.9) = 5.7 dollars

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Answer:

( 1, - 3.5 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) the midpoint is

( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )

Here (x₁, y₁ ) = C (9, 2) and (x₂, y₂ ) = D (- 7, - 9 )

midpoint = ( \(\frac{9-7}{2}\) , \(\frac{2-9}{2}\) ) = ( \(\frac{2}{2}\), \(\frac{-7}{2}\) ) = (1, - 3.5 )

A lottery has 3 possible outcomes, they are -20, 0, and 20. The probability of each outcome is 0.2, 0.5, and 0.3, respectively. Compute the expected value of the lottery, variance, and the standard deviation of the lotteryExpected Value:

The expected value of the lottery is:

E(x) = ∑[x*P(x)]Where x is each possible outcome, and P(x) is the probability of that outcome.

E(x) = -20(0.2) + 0(0.5) + 20(0.3) E(x) = -4 + 0 + 6 E(x) = 2So, the expected value of the lottery is 2. Variance:The variance of a lottery is:

σ² = ∑[x - E(x)]²P(x)Where x is each possible outcome, P(x) is the probability of that outcome, and E(x) is the expected value of the lottery.

σ² = (-20 - 2)²(0.2) + (0 - 2)²(0.5) + (20 - 2)²(0.3) σ² = 22.4

So, the variance of the lottery is 22.4.

Standard Deviation:

The standard deviation of a lottery is the square root of the variance. σ = √22.4 σ ≈ 4.73So, the standard deviation of the lottery is approximately 4.73.

b) Given the start-up job offer lottery, one payoff (I1) is RM110,000, the other payoff (I2) is RM5,000. The probability of each payoff is 0.50, and the expected value is RM55,000. The utility function is given by U(I) = √I. The equation is:pU(I1) + (1-p)U(I2) = U(EV - RP)

Where U(I) is the utility of income I, p is the probability of the high payoff, I1 is the high payoff, I2 is the low payoff, EV is the expected value of the lottery, and RP is the risk premium.

Substituting the given values, we have:0.5√110000 + 0.5√5000 = √(55000 - RP)Simplifying, we get:

550√2 ≈ √(55000 - RP)Squaring both sides, we get:302500 = 55000 - RPRP ≈ RM29500So, the risk premium is approximately RM29500.

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The  system of 2 linear equations in two variables x, y, which form parallel lines are 2x + 3y = 7 and 2x + 3y = 10, the row reduction process has revealed that the system is inconsistent, and there is no common solution to the equations.

To create a system of parallel lines, we can take two linear equations with the same slope but different y-intercepts. For example, let's take the following two equations:

2x + 3y = 7

2x + 3y = 10

Both equations have the same slope of -2/3 but different y-intercepts. To visualize this, we can rewrite the equations in slope-intercept form:

y = (-2/3)x + 7/3

y = (-2/3)x + 10/3

These equations represent lines with the same slope but different y-intercepts, and they are parallel.

To row reduce the system, we can represent the equations in an augmented matrix form:

[2 3 | 7]

[2 3 | 10]

To row reduce, we can subtract the first row from the second row, as shown below:

[2 3 | 7]

[0 0 | 3]

The resulting system represents a line with no solution, as 0x + 0y = 3 is a contradiction.

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Answer:

She payed $29.60

Step-by-step explanation:

Expression: 12.36•2+1.98/2+3.49+.40

To solve this expression, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). However, in this expression, there are no parentheses or exponents, so we can start by performing the multiplication and division, and then the addition:

12.36•2 + 1.98/2 + 3.49

= 24.72 + 0.99 + 3.49+.40 (performing multiplication and division)

= 29.6 (adding the results)Therefore, the final result of the expression 12.36•2+1.98/2+3.49+.40 is 29.6.

Answer: $30

Step-by-step explanation:

2 packages of Chicken = $12.36 x 2 = $24.72

1/2 pound of broccoli = 1/2 x $1.98 = $0.99

1 Gallon of milk = 1 x $3.49 = $3.49

Add all of these together along with the extra $0.80

$24.72 + $0.99 + $3.49 + $0.80 = $30

Here you go!

Answer:

B

Step-by-step explanation:

Answer: $11,942.29

Step-by-step explanation:

Let the value after 9 years be y

y = 22400 (0.9325)^9

y = 11,942.29

Answer:

$5 is the answer.......

Answer:

one box cost is $5

Step-by-step explanation:

$25 - $5 = $20 - this is the cos of four cereal boxes

$20 / 4 = $5 each box cost

Answer:

x=88° a=+3 b=4a-3

Step-by-step explanation:

as triangles ADE and BCE are congruent by sss axiom

so correponding angles are equal

i.e<AED = <BEC

and <DAE =90-60

=30°

so

62°+x+30°=180°

therefore x=88°

The absolute error in approximating a quantity using the nth-order Taylor polynomial centered at 0 for the function f(x) = ln(1 + x) can be estimated using the remainder term. The remainder term for a Taylor polynomial provides an upper bound on the absolute error.

The nth-order Taylor polynomial for f(x) = ln(1 + x) centered at 0 is given by\(Pn(x) = x - (x^2)/2 + (x^3)/3 - ... + (-1)^(n-1) * (x^n)/n.\)The remainder term Rn(x) is defined as Rn(x) = f(x) - Pn(x), and it represents the difference between the actual function value and the value approximated by the polynomial.

To estimate the absolute error, we can use the remainder term. For example, if we want to estimate the absolute error for approximating f(0.5), we can evaluate the remainder term at x = 0.5. By calculating Rn(0.5), we can obtain an upper bound on the absolute error. The larger the value of n, the more accurate the approximation and the smaller the absolute error.

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Answer: 4/9 ≅ 0.4444444 = four ninths. ... Then simplify the result to the lowest terms or a mixed number.

Answer:

see explanation

Step-by-step explanation:

(a + b)(a - b)

Each term in the second factor is multiplied by each term in the first factor, that is

a(a - b) + b(a - b) ← distribute parenthesis

= a² - ab + ab - b² ← collect like terms

= a² - b²

This is a standard algebraic identity, called the difference of squares

Answer:

i believe C

Step-by-step explanation:

Answer:

Each neighbor will get 12 candles so in total, 60 candles will be sold.

Step-by-step explanation:

An equation of the plane through the origin and parallel to the plane 3x - y + 3z = 4 is 3x - y + 3z = 0.

To find an equation of the plane through the origin and parallel to the plane 3x - y + 3z = 4, we can use the fact that parallel planes have the same normal vector.

Step 1: Find the normal vector of the given plane.
The normal vector of a plane with equation Ax + By + Cz = D is . So, in this case, the normal vector of the given plane is <3, -1, 3>.

Step 2: Use the normal vector to find the equation of the parallel plane.
Since the parallel plane has the same normal vector, the equation of the parallel plane passing through the origin is of the form 3x - y + 3z = 0.

Therefore, an equation of the plane through the origin and parallel to the plane 3x - y + 3z = 4 is 3x - y + 3z = 0.

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