What is the magnitude of the size change of the figures formed by these matrices?
[3 -2 1] [6 -4 2]
4 1 -1 8 2-2 ...?

To approximate functions near zero using the linear approximation (1+x)^k ≈ 1 + kx, we find an approximation for each given function.

To approximate the function f(x) for values of x near zero using the linear approximation (1+x)^k ≈ 1 + kx, we need to find an approximation for each given function:

a.) f(x) = (1-x)^8 ≈ 1 - 8x

b.) f(x) = -8/(1-x) ≈ -8x

c.) f(x) = 1/(sqrt(1+x)) ≈ 1 - 0.5x

d.) f(x) = sqrt(4+x^2) ≈ 2 + x^2/4

e.) f(x) = (6+3x)^(1/3) ≈ 2 + x/3

Answer:

Irrational

Step-by-step explanation:

A rational number can be expressed as a ratio of two integers , p and q of the form \[\frac{p}{q}\]

So following are examples of rational numbers:

On the other hand , any number which cannot be expressed in this form is called an irrational number. For example:

The probability that you missed your friend’s call is 1/6

The range is given as:

Range = 3:00 P.M. and 5:00 P.M.

The number of minutes in the range is:

Total = 120 minutes

At 3:20 that you notice the phone is off the hook, the number of minutes missed is:

Time missed = 20 minutes

The probability is then calculated as:

P = 20/120

Evaluate

P = 1/6

Hence, the probability that you missed your friend’s call is 1/6

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[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{6 \dfrac{19}{25}}[/tex]

[tex]\mathsf{= \dfrac{6\times25 + 19}{25}}[/tex]

[tex]\mathsf{= \dfrac{150 + 19}{25}}[/tex]

[tex]\mathsf{= \dfrac{169}{25}}[/tex]

[tex]\mathsf{= 169 \div 25}[/tex]

[tex]\mathsf{= 6.76}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{6.76}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

Among the options given, B. 45 is not a perfect square because no integer squared equals 45.

The question is asking us to identify which number among the given options is not a perfect square. A perfect square is a number that can be expressed as the product of an integer with itself. Here are the given options with explanations:

Therefore, the number that is not a perfect square in the options provided is B. 45.

Answer:

[tex]m{\angle}D=60^{\circ}[/tex]

Step-by-step explanation:

From the given figure, it can be seen that [tex]m{\angle}A=60^{\circ}[/tex], [tex]m{\angle}B=60^{\circ}[/tex], thus

From ΔABD, using the angle sum property, we have

[tex]m{\angle}A+m{\angle}B+m{\angle}D=180^{\circ}[/tex]

⇒[tex]60^{\circ}+60^{\circ}+m{\angle}D=180^{\circ}[/tex]

⇒[tex]120^{\circ}+m{\angle}D=180^{\circ}[/tex]

⇒[tex]m{\angle}D=180^{\circ}-120^{circ}[/tex]

⇒[tex]m{\angle}D=60^{\circ}[/tex]

therefore, the measure of [tex]{\angle}ADB[/tex] is [tex]60^{\circ}[/tex].

Hence, ΔABD is an equilateral triangle.

Answer:

i took the test

Step-by-step explanation:

The value of integral is  2 * arc sin((x - 2) / 2) + (x - 2) * √(4 - (x - 2)²) / 2 + C.

To solve the integral ∫ √(4x - x²) dx, follow these steps:

Complete the Square: Rewrite the quadratic expression under the square root. Start with: 4x - x²

Rearrange it to the standard quadratic form: -x² + 4x. To complete the square, factor out the negative sign: (x² - 4x)

Next, complete the square inside the parentheses:

x² - 4x = (x - 2)² - 4

So, we get:

(x² - 4x) = - [(x - 2)² - 4] = 4 - (x - 2)²

Therefore:

√(4x - x²) = √(4 - (x - 2)²)

Substitute Variables: Let u = x - 2. Then, du = dx, and the integral becomes:

∫ √(4 - u²) du

Apply the Trigonometric Substitution: Use the trigonometric substitution u = 2 sin θ. Then du = 2 cos θ dθ. Substitute these into the integral:

∫ √(4 - (2 sin θ)²) * 2 cos θ dθ

= ∫ √(4 - 4 sin² θ) * 2 cos θ dθ

= ∫ √(4 (1 - sin² θ)) * 2 cos θ dθ

= ∫ 2 cos θ * 2 cos θ dθ

= ∫ 4 cos² θ dθ

Use Trigonometric Identity: Apply the double-angle identity cos² θ = (1 + cos 2θ) / 2:

∫ 4 cos² θ dθ

= ∫ 4 * (1 + cos 2θ) / 2 dθ

= ∫ (4 + 4 cos 2θ) / 2 dθ

= ∫ (2 + 2 cos 2θ) dθ

Integrate each term:

∫ 2 dθ + ∫ 2 cos 2θ dθ = 2θ + sin 2θ + C

Back-substitute: Replace θ with the original variable x. Recall u = 2 sin θ, so θ = arcsin(u / 2). Since u = x - 2, substitute back:

θ = arcsin((x - 2) / 2)

Therefore:

2 * arcsin((x - 2) / 2) + sin(2 * arcsin((x - 2) / 2)) + C

Using the identity sin(2θ) = 2 sin θ cos θ:

sin(2 * arcsin((x - 2) / 2))

= 2 * (x - 2) / 2 * √(1 - ((x - 2) / 2)²)

= (x - 2) * √(4 - (x - 2)²) / 2

Answer: The simplified form will be

[tex]\frac{1}{(x+3)(x+4)}[/tex]

Step-by-step explanation:

Since we have given that

[tex]\frac{x+1}{x^2+x-6}\div \frac{x^2+5x+4}{x-2}[/tex]

We need to simplify the above expression, we get that

[tex]\frac{x+1}{x^2+x-6}\div \frac{x^2+5x+4}{x-2}\\\\=\frac{x+1}{x^2+x-6}\times \frac{x-2}{x^2+5x+4}\\[/tex]

Now, we first factorize the quadratic equation:

[tex]x^2+x-6\\\\=x^2+3x-2x-6\\\\=x(x+3)-2(x-3)\\\\=(x+3)(x-2)[/tex]

Similarly,

[tex]x^2+5x+4\\\\=x^2+4x+x+4\\\\=x(x+4)+1(x+4)\\\\=(x+4)(x+1)[/tex]

So, it will become

[tex]\frac{x+1}{x^2+x-6}\times \frac{x-2}{x^2+5x+4}\\\\=\frac{x+1}{(x+3)(x-2)}\times \frac{x-2}{(x+4)(x+1)}\\\\=\frac{1}{(x+3)(x+4)}[/tex]

Hence, the simplified form will be

[tex]\frac{1}{(x+3)(x+4)}[/tex]

The total simple interest earned on a $3000 CD over 30 months with an annual interest rate of 5.5% is $412.50 and the balance at maturity is $3412.50.

To calculate the total amount of simple interest earned on a certificate of deposit (CD) we use the formula I = Prt, where I is interest, P is the principal amount (initial amount of money), r is the annual interest rate (in decimal form), and t is the time in years. For the given 30-month CD purchased for $3000 with an annual simple interest rate of 5.5%, we first convert 30 months to years by dividing by 12 (30 / 12 = 2.5 years).

Using the formula: I = $3000 × 0.055 × 2.5 = $412.50. Therefore, the total interest earned is $412.50.

To calculate the balance at maturity, we add the total interest to the principal: Balance = Principal + Interest = $3000 + $412.50 = $3412.50.

5.27 can be converted to a mixed number 5 27/100, where 5 is the whole number and 27/100 is the decimal part expressed as a fraction, without reducing to lowest terms.

To convert the decimal number 5.27 to a proper fraction or a mixed number, we first recognize that .27 is the decimal part of 5.27. We can write .27 as a fraction by considering it as 27 hundredths, which is 27/100. Therefore, we have the whole number 5 and the fraction 27/100. Combining these, we get the mixed number 5 27/100. Since we are instructed not to reduce to lowest terms, the mixed number remains as is.

Answer:

The evaluation is [tex]f(-2)=-4[/tex]

Step-by-step explanation:

We were given an explicit function of x, wich has the form

[tex]f(x)=x^2+4x[/tex]

The problem ask to evaluate f(-2), this means to put the value x=-2 into the function, so

[tex]f(-2)=(-2)^2+4(-2)=4-8=-4[/tex]

Therefore, the answer is

[tex]f(-2)=-4[/tex]

The final result is 73 divided by 8 equals 9, with a remainder of 9.

When you divide 73 by 8, use long division to find the quotient and remainder.

1. Write the dividend (73) and the divisor (8) as shown:

                                             8 | 73

2. Start dividing:  Since 8 is larger than 7, we move to the next digit.

3. Bring down the next digit (3) to the right of the remainder:

                                                  8 | 73 | 8

                                                     - 64

                                                     _____

                                                          9

4. The remainder is 9.

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