In Exercises \( 1-8, W \) is a subset of \( R^{2} \) consisting of vectors of the form \[ \mathbf{x}=\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right] \] In each case determine whether \( W \)

To find the composite functions, we simply substitute one function into the other.

For example, f[g(x)] means we substitute g(x) into f(x) wherever there is an x. So, f[g(x)] = 3(g(x)) + 4 = 3(2x^2 − 5x − 9) + 4 = 6x^2 − 15x − 23.Similarly, we can find the other composite functions: g[f(x)] = 2(f(x))^2 − 5(f(x)) − 9 = 2(3x+4)^2 − 5(3x+4) − 9 = 18x^2 + 7x - 7f[f(x)] = 3(f(x)) + 4 = 3(3x+4) + 4 = 9x + 16

For the last part, f/g means we divide f(x) by g(x):f/g = (3x+4)/(2x^2−5x−9)The domain of this function is all real numbers except for the values of x that make the denominator equal to zero.

To find these values, we set the denominator equal to zero and solve for x:2x^2−5x−9 = 0(2x+3)(x-3) = 0x = -3/2, 3 So the domain of f/g is (-∞, -3/2) ∪ (-3/2, 3) ∪ (3, ∞) in interval notation.

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Answer:

First we would shrink by a factor of 3

Then translate 6 units on the x axis

Then reflect across x=6

Hence, the total surface area of the rectangular prism is 736 in².

A 3D object's surface area is calculated as the total of all of its faces. For instance, if we wanted to figure out how much paint we would need to paint a cube, we would use the cube's surface area.

To calculate the total surface area of the rectangular prism, we need to find the area of each of its six faces and add them together.

The area of the top and bottom faces, which are identical, is:

Length x Breadth = 16 in x 8 in = 128 in².

The area of the front and back faces, which are also identical, is:

Height x Breadth = 10 in x 8 in = 80 in².

The area of the left and right faces, which are also identical, is:

Height x Length = 10 in x 16 in = 160 in².

Therefore, the total surface area of the rectangular prism is:

2(Length x Breadth) + 2(Height x Breadth) + 2(Height x Length)

= 2(16 in x 8 in) + 2(10 in x 8 in) + 2(10 in x 16 in)

= 256 in² + 160 in² + 320 in²

= 736 in²

Hence, the total surface area of the rectangular prism is 736 in².

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The library in Georgetown has 35 tables, 5 of which are hexagons and 30 of which are octagons.

An octagon is a two-dimensional shape with eight sides and eight angles. It is a regular polygon, meaning that all of its sides and angles are equal. Octagons are often seen in everyday life, such as in stop signs, tiling, and in some types of architectural structures.

In order to answer this question, we must first solve a simple equation. We know that the total number of tables in the room is 35, and we know that each hexagonal table seats six people, while each octagonal table seats eight people. Therefore, we can set up an equation to represent the total number of people being seated at all of the tables: 6x + 8y = 236, where x is the number of hexagonal tables and y is the number of octagonal tables.

By solving this equation, we can determine that x = 5 and y = 30. This means that there are 5 hexagonal tables and 30 octagonal tables in the room. Therefore, the library in Georgetown has 35 tables, 5 of which are hexagons and 30 of which are octagons.

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Javier is saving $460 per month for the first two months, and $257.5 per month for the first four months.

What is equation of a straight line?

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

After 2 months, Javier has saved a total of $920. Therefore, we can write the following equation:

2m = 920

Simplifying this equation, we get:

m = 460

This means that Javier is saving $460 each month.

After 4 months, Javier has saved a total of $1030. Using the same logic as before, we can write:

4m = 1030

Simplifying this equation, we get:

m = 257.5

This means that Javier is saving $257.5 each month.

To model the relationship between the amount of money Javier has saved and the number of months he has saved for, we can use the equation of a straight line:

y = mx + b

where y is the amount of money saved, x is the number of months, m is the monthly savings rate, and b is the starting amount saved.

Using the values we found earlier, we can write two equations:

y = 460x + b (for the first two months)

y = 257.5x + b (for the first four months)

To find the value of b, we can substitute the values of x and y for one of the points:

920 = 460(2) + b

Simplifying, we get:

b = 0

So the final equation that models the relationship between the amount of money Javier has saved and the number of months he has saved for is:

y = 460x (for the first two months)

y = 257.5x (for the first four months)

This means that Javier is saving $460 per month for the first two months, and $257.5 per month for the first four months.

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Answer:

24,000 grams

Step-by-step explanation:

<3

The possible rational roots of f(x) are ±1, ±2, ±4, ±8, ±1/2, and ±1/4.

The Rational Root Theorem states that if a polynomial [tex]f(x) = anxn + an-1xn-1 + ... + a1x + a0[/tex] has a rational root, then it must be of the form p/q, where p is a factor of the constant term a0 and q is a factor of the leading coefficient an.

For the given polynomial [tex]f(x) = -x + 14x3 - 18x2 - 4x5 - 26x4 + 8[/tex], the constant term is 8 and the leading coefficient is -4.

The factors of 8 are ±1, ±2, ±4, and ±8. The factors of -4 are ±1, ±2, and ±4.

Therefore, the possible rational roots of f(x) are:

p/q = ±1/1, ±2/1, ±4/1, ±8/1, ±1/2, ±2/2, ±4/2, ±8/2, ±1/4, ±2/4, ±4/4, ±8/4

Simplifying gives us the possible rational roots:

±1, ±2, ±4, ±8, ±1/2, ±4/2, ±8/2, ±1/4, ±2/4, ±8/4

Simplifying further gives us the final list of possible rational roots:

±1, ±2, ±4, ±8, ±1/2, ±2, ±4, ±1/4, ±1/2, ±2

Removing duplicates, the final list of possible rational roots is:

±1, ±2, ±4, ±8, ±1/2, ±1/4

Therefore, the possible rational roots of f(x) are ±1, ±2, ±4, ±8, ±1/2, and ±1/4.

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Micah can use the <div> tag.

What is Tag?

A tag is given as the label that has been attached to someone or something in order to add identification to the particular thing. The tag in the HTML or any other language has been used for the conversion of the HTML document into web pages. The tags are braced in the < >.

Micah can use the <div> tag to divide a block of content on a web page and set it apart with different formatting.

The <div> tag is a container tag that is used to group and separate HTML elements on a web page.

Micah can give the <div> tag a class or an ID attribute and use CSS to apply different formatting to the content within that tag.

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The height of the white board for the given aspect ratio is found as 36 in.

Aspect ratio of a white board = 16:9 .

Width = 64 in

Let the height be 'h'.

So, using proportions.

16/9 = 64/h

h = 64*9 /16

h = 36

Thus, the height of the white board for the given aspect ratio is found as 36 in.

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Answer:

[tex]x=\frac{3}{2} - i\frac{\sqrt{7}}{2}[/tex]

[tex]x=\frac{3}{2} + i\frac{\sqrt{7}}{2}[/tex]

Step-by-step explanation:

We can use the quadratic formula to solve the equation:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -3, and c = 4. Substituting these values into the formula, we get:

x = (3 ± sqrt((-3)^2 - 4(1)(4))) / 2(1)

x = (3 ± sqrt(9 - 16)) / 2

x = (3 ± sqrt(-7)) / 2

Since the square root of a negative number is not a real number, the solutions to the quadratic equation are complex numbers. Therefore, the answer is:

[tex]x=\frac{3}{2}+i\frac{\sqrt{7} }{2}[/tex]

[tex]x=\frac{3}{2} - i\frac{\sqrt{7}}{2}[/tex]

The probability of transitioning from the UU state to the UD state, which is 0.2

a) The state transition diagram for this Discrete time Markov chain can be represented as follows:
``
      0.8        0.2
   UU -------> UU <------- UD
   ^            |          ^
   |            |          |
   |            |          |
   |            V          |
   |          0.4        0.5
   |         DD <------- DU
   |          ^          |
   |          |          |
   |          |          |
   |          |          V
   |         0.35       0.5
   |-------- DD <------- DD
      0.2        0.65
```

Where UU represents the state where the stock price went up for the last two days, UD represents the state where the stock price went up today but not yesterday, DU represents the state where the stock price went up yesterday but not today, and DD represents the state where the stock price went down in the last two days.

b) The transition matrix for this Discrete time Markov chain can be represented as follows:

```
      | UU   UD   DU   DD |
      |-------------------|
  UU  | 0.8  0.2  0.0  0.0 |
  UD  | 0.0  0.0  0.6  0.4 |
  DU  | 0.0  0.5  0.0  0.5 |
  DD  | 0.2  0.0  0.0  0.8 |
```

Where the rows represent the current state and the columns represent the next state. Each entry in the matrix represents the probability of transitioning from the current state to the next state. For example, the entry in the first row and second column represents the probability of transitioning from the UU state to the UD state, which is 0.2.

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Answer:

8 + 2x = 30

Step-by-step explanation:

The sides of the triangle add up to the perimeter:

7 + x + x + 1 = 30

Simplify by combining like terms:

8 + 2x = 30

Answer:-3

Step-by-step explanation:its just -9 + b/3 = -3 not even hard

60Answer: it would be 60

Step-by-step explanation:

it’s going up and down by 10

Yes, f(x) and g(x) are inverse functions.

An inverse function is a function that "undoes" the original function. In other words, if we plug the output of the original function into the inverse function, we will get the original input back.

To determine if two functions are inverses of each other, we can use the following steps:

1. Plug the first function into the second function, replacing x with f(x). In this case, we will plug f(x) = 3x - 4 into g(x) = 4 - 3x:

g(f(x)) = 4 - 3(3x - 4)

2. Simplify the expression:

g(f(x)) = 4 - 9x + 12

g(f(x)) = 16 - 9x

3. Now plug the second function into the first function, replacing x with g(x):

f(g(x)) = 3(4 - 3x) - 4

4. Simplify the expression:

f(g(x)) = 12 - 9x - 4

f(g(x)) = 8 - 9x

5. If the two simplified expressions are equal to each other, then the functions are inverses of each other. In this case, g(f(x)) = 16 - 9x and f(g(x)) = 8 - 9x are not equal to each other, so the functions are not inverses of each other.

However, if we rearrange the equation for g(x) to solve for x, we get:

g(x) = 4 - 3x

3x = 4 - g(x)

x = (4 - g(x))/3

This is the same as the equation for f(x), but with g(x) in place of x. Therefore, f(x) and g(x) are inverse functions.

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The distance traveled by the bullet is 1000 feet.

The distance traveled by the bullet can be calculated by multiplying its speed by the time it takes to hit the target:

Distance = Speed x Time

Substituting the given values, we get:

[tex]Distance = 510^6 feet/hour * 210^{-4} hours[/tex]

Simplifying this expression, we get:

Distance = 1000 feet

Therefore, the bullet has traveled 1000 feet before striking the target.

In summary, the distance traveled by the bullet can be calculated by multiplying its speed by the time it takes to hit the target. In this case, the distance traveled is 1000 feet.

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Answer:

x = 40°

Step-by-step explanation:

given Δ ABD is isosceles with AB = AD

then the base angles are congruent , that is

∠ ABD = ∠ ADB = 25°

given ABC is a straight line then the 3 angles on it sum to 180° , that is

∠ ABD + x + 115° = 180°

25° + x + 115° = 180°

x + 140° = 180° ( subtract 140° from both sides )

x = 40°

Felix needs to sell more hats and/or T-shirts in order to raise enough money to pay for his summer camp registration.

This situation's inequality system is as follows:

h + t ≥ 32 (Felix hopes to sell a total of at least 32 hats and t-shirts)

(Felix needs to raise at least $288.) 8h + 12t = 288

The second inequality can be rearranged as follows:

2h + 3t ≥ 72

The graph with the lines h + t = 32 solid and the region above it shaded, and 2h + 3t = 72 dashed and the region above it shaded, is the one that depicts the system of inequalities with the solution region shaded in. The offered image's option D corresponds to this graph.

We may change h = 28 and t = 5 into the inequality to see if selling 28 hats and 5 T-shirts is enough to pay for Felix's summer camp registration:

h + t ≥ 32\s28 + 5 ≥ 32\s33 ≥ 32 (Because this inequality is real, at least 32 hats and t-shirts were sold.)

8h + 12t ≥ 288\s8(28) + 12(5) ≥ 288\s224 + 60 ≥ 288\s284 ≥ 288 (Because this imbalance is untrue, Felix's summer camp registration costs cannot be covered by selling 28 caps and 5 T-shirts.)

Felix must therefore sell more hats and/or T-shirts to raise enough cash to cover the cost of his summer camp registration.

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The coefficient of variation (CV) of a distribution is the ratio of the standard deviation to the arithmetic mean. Therefore, in this case the CV is:CV = (1.456/44.5) x 100 = 3.27

The correct answer is therefore B: 3.27
The coefficient of variation (CV) is a measure of relative variability. It is the ratio of the standard deviation to the mean (average) of a distribution. The formula for calculating the coefficient of variation is:
CV = (standard deviation / mean) × 100

In this case, the standard deviation is 1.456 and the mean is 44.5. Plugging these values into the formula gives:
CV = (1.456 / 44.5) × 100
CV = 0.0327 × 100
V = 3.27

Therefore, the correct answer is b. 3.27. The coefficient of variation of this distribution is 3.27.

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Both statements are false because the sum of two angles does not equal the sum of their cosines or sines.

Statement 53 is false. This is because the sum of two angles does not equal the sum of their cosines. The correct equation for the sum of two angles in terms of their cosines is:

\( \cos \left(30^{\circ}+60^{\circ}\right)=\cos 30^{\circ} \cos 60^{\circ} - \sin 30^{\circ} \sin 60^{\circ} \)

Using this equation, we can calculate the correct value of the cosine of the sum of the two angles:

\( \cos \left(30^{\circ}+60^{\circ}\right)=\cos 30^{\circ} \cos 60^{\circ} - \sin 30^{\circ} \sin 60^{\circ} \)
\( \cos 90^{\circ}=\frac{\sqrt{3}}{2} \cdot \frac{1}{2} - \frac{1}{2} \cdot \frac{\sqrt{3}}{2} \)
\( \cos 90^{\circ}=0 \)

Statement 54 is also false. This is because the sum of two angles does not equal the sum of their sines. The correct equation for the sum of two angles in terms of their sines is:

\( \sin \left(30^{\circ}+60^{\circ}\right)=\sin 30^{\circ} \cos 60^{\circ} + \cos 30^{\circ} \sin 60^{\circ} \)

Using this equation, we can calculate the correct value of the sine of the sum of the two angles:

\( \sin \left(30^{\circ}+60^{\circ}\right)=\sin 30^{\circ} \cos 60^{\circ} + \cos 30^{\circ} \sin 60^{\circ} \)
\( \sin 90^{\circ}=\frac{1}{2} \cdot \frac{1}{2} + \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2} \)
\( \sin 90^{\circ}=1 \)

In conclusion, both statements are false because the sum of two angles does not equal the sum of their cosines or sines. The correct equations for the sum of two angles in terms of their cosines and sines are shown above.

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Answer:

The discount is 15% of the cost of the meal before the discount, so the discounted cost is:

Discounted cost = $78.97 - 0.15($78.97) = $67.12

Now we need to calculate the tip on the cost before the discount. The tip is 20% of the cost before the discount, so the tip amount is:

Tip = 0.20($78.97) = $15.79

Adding the discounted cost and the tip, we get the total cost of the meal:

Total cost = $67.12 + $15.79 = $82.91

Therefore, the total cost of the meal, including the discount and tip, is $82.91.

the above question, we may state that Hence, the surface area rectangular prism has a surface area of 148 square centimeters.

An object's surface area is a measure of how much space it takes up overall. The entire amount of space around a three-dimensional form is its surface area. The total surface area of a three-dimensional form is referred to as its surface area. By summing the areas of each face, one may get the surface area of a cuboid with six rectangular faces. Instead, you may identify the box's dimensions using the following formula: Surface (SA) equals 2lh, 2lw, and 2hw. The total amount of space occupied by the surface of a three-dimensional form is measured as surface area.

Shown above is a rectangular prism. We may apply the formula: to determine the surface area.

2lw + 2lh + 2wh = Surface Area

where the prism's length, breadth, and height are indicated by l, w, and h, respectively.

As we look at the image, we can see that it is 6 cm long, 4 cm wide, and 5 cm tall. These values can be used as substitutes in the formula:

Surface Area = (2,6,4,2,6,5,2) (5)

Area of Surface = 48 + 60 + 40

Area of Surface = 148

Hence, the rectangular prism has a surface area of 148 square centimeters.

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Answer:

It depends on what's given in the problem.

Step-by-step explanation:

There's a few ways to find the hypotenuse of a triangle, but we must have something given to us.

A Few Methods (Most Common to Least Common):

The Pythagorean Theorem. 2 legs of a right triangle are given. You should add the 2 legs together to find the hypotenuse.

[tex]a^2 + b^2 = c^2[/tex]

Sine, or Cosine. This is only used when there's a given angle, and/or at least one given side.

[tex]Sin \ (\theta) = \frac{opposite}{hypotenuse}[/tex]

[tex]Cosin \ (\theta)=\frac{adjacent}{hypotenuse}[/tex]

Rare, but possibly we need to find the area of the triangle. There needs to be at least 1 angle given.

This is the formula we need to find the Hypotenuse:

[tex]Area = \frac{1}{2} \times h^2 (hyp.) \times sin (angle) \times cos(angle)[/tex]

This is a lot to learn. Let me know if you have any questions.

The final simplified expression is: [tex]6x^(2) - 22x + 9[/tex]

To simplify the given expression, we need to combine like terms. This means that we need to add or subtract terms that have the same variable and exponent.

The given expression is: [tex]12x^(2)+9-8x-6x^(2)-14x[/tex]

First, let's combine the terms with the same variable and exponent:

[tex]12x^(2) - 6x^(2) = 6x^(2)[/tex]

[tex]-8x - 14x = -22x[/tex]

Now, let's substitute these simplified terms back into the expression:

[tex]6x^(2) + 9 - 22x[/tex]

This is the simplified expression. There are no more like terms to combine, so we cannot simplify it further.

The final simplified expression is: [tex]6x^(2) - 22x + 9[/tex]

Answer: [tex]6x^(2) - 22x + 9[/tex]

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Answer:

h is 19.5

Step-by-step explanation:

8.5 is 11 less than h

8.5 = h - 11

Add 11 to both sides

19.5 = h

Answer: The correct response is "Interest rates vary between lenders and can drastically change the monthly payment."

The interest rate is one of the most important things to consider when shopping around for loans because it determines the cost of borrowing money. Different lenders offer different interest rates, and even a small difference in interest rates can have a big impact on the total cost of the loan. A higher interest rate will result in a higher monthly payment, and a longer repayment period, which can make the loan more expensive overall. Therefore, it is important to shop around and compare interest rates from different lenders to find the best deal.

Step-by-step explanation:

Simplify both sides of the equation using algebraic methods and see if they are equal or not equal.

What is Linear Equation?

A linear equation is a mathematical equation that represents a straight line on a graph. It is an equation in which the highest power of the variable is one. A general linear equation can be represented as y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

Linear equations can be solved algebraically using techniques like substitution or elimination, and they can be used to model real-world situations involving linear relationships.

If an equation is true for all values of x, then it is called an identity. To check if an equation is an identity, we can simplify both sides of the equation using algebraic methods and see if they are equal. If they are, then the equation is an identity.

On the other hand, if an equation is true for no values of x, then it is a contradiction. In this case, we can also simplify both sides of the equation using algebraic methods and see if they are not equal. If they are not, then the equation is a contradiction.

If neither of these cases applies, then the equation may be true for some values of x but not for others.

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Answer: I need to woo

Step-by-step explanation: your exciting boy come find me