Let p(x) = a1x^2 + b1x +c1 and q(x) = a2x^2 + b2x + c2 be polynomials in P2. Define an inner product in P2 as follows {p,q} = 5a1a2 + 4b1b2 + 3c1c2.
Given p(x) =5x^2 + (-1)x + (-3) and q(x) = 2x^2 + (4)x +(-3). Evaluate the following expressions
1. p(x) - q(x) = 3x^2 - 5x
2. {p - q, p-q} = 145
3. llp-qll = sqrt({p-q,p-q}) = sqrt(145)

For part 1, I know the answer and how to get it.
For part 2, I know the answer but I'm not sure how to get to it

Answer:

x = -1, 1

Step-by-step explanation:

The function h(x) is given below:

[tex]\displaystyle{h(x)=\dfrac{x-9}{x^2-1}}[/tex]

The denominator must not equal to 0. Therefore,

[tex]\displaystyle{x^2-1\neq 0}[/tex]

Solve the inequality; factor the expression:

[tex]\displaystyle{(x-1)(x+1) \neq 0}[/tex]

Hence,

[tex]\displaystyle{x \neq 1,-1}[/tex]

Therefore, x = -1, 1 both are not in the domain of h.

To solve this problem, we can set up a system of equations based on the given information.

Let's assume the amount of money Ralph Chase will receive through the short-term note is represented by "x" and the amount through the long-term note is represented by "y".

According to the problem, the total amount Ralph plans to sell the property for is $145,000. Therefore, we have the equation:

[tex]\displaystyle x+y=145000[/tex] ...(1)

Now let's consider the interest paid annually. The interest paid on the short-term note at 10% is calculated as [tex]\displaystyle 0.10x[/tex], and the interest paid on the long-term note at 8% is [tex]\displaystyle 0.08y[/tex]. The total annual interest paid is given as $13,100. Therefore, we have the equation:

[tex]\displaystyle 0.10x+0.08y=13100[/tex] ...(2)

We now have a system of two equations (1) and (2). We can solve this system to find the values of "x" and "y".

Multiplying equation (2) by 100 to eliminate decimals, we get:

[tex]\displaystyle 10x+8y=1310000[/tex] ...(3)

Now we can solve equations (1) and (3) simultaneously using any method such as substitution or elimination.

Multiplying equation (1) by 10, we get:

[tex]\displaystyle 10x+10y=1450000[/tex] ...(4)

Subtracting equation (3) from equation (4), we can eliminate "x" and solve for "y":

[tex]\displaystyle 2y=140000[/tex]

Dividing both sides by 2, we find:

[tex]\displaystyle y=70000[/tex]

Now substituting the value of "y" back into equation (1), we can solve for "x":

[tex]\displaystyle x+70000=145000[/tex]

Subtracting 70000 from both sides, we have:

[tex]\displaystyle x=75000[/tex]

Therefore, the amount of money Ralph Chase will receive through the short-term note is 75,000 and through the long-term note is $70,000.

Answer:

arc LKF = 208°

Step-by-step explanation:

the angle FLX between the tangent and the secant is half the measure of the intercepted arc LKF , then intercepted arc is twice angle FLX , so

arc LKF = 2 × 104° = 208°

Answer:

Step-by-step explanation:

Let's revisit the equation and the solution using the values x = -4, 0, and 5.

The given equation is: 5 + x - 12 = x - 7

Let's go through the steps again to solve it:

5 + x - 12 = x - 7

Combine like terms:

x - 7 = x - 7

Now, subtract x from both sides:

x - x - 7 = x - x - 7

Simplify:

-7 = -7

The equation simplifies to -7 = -7, which is true.

Now, let's use the values x = -4, 0, and 5 to verify the solution.

For x = -4:

5 + (-4) - 12 = (-4) - 7

-11 = -11

The equation is satisfied for x = -4.

For x = 0:

5 + 0 - 12 = 0 - 7

-7 = -7

The equation is satisfied for x = 0.

For x = 5:

5 + 5 - 12 = 5 - 7

-2 = -2

The equation is satisfied for x = 5.

Therefore, the solution x = 0 is correct, and it satisfies the equation for the given values. My earlier statement that x = -4 and x = 5 do not satisfy the equation was incorrect. I apologize for the confusion caused.

You will need to purchase approximately 1/42 of a tube, which is less than a full tube. In practical terms, you would need to purchase at least one tube to meet your requirement of 42 ounces of capsaicin arthritis rub.

To determine the number of tubes of capsaicin arthritis rub you will need to purchase, we can divide the total required quantity by the quantity in each tube.

Given that the cost of capsaicin arthritis rub is $21 and you need to buy 42 ounces, we need to find out how many ounces are in each tube.

Let's assume that each tube contains x ounces of capsaicin arthritis rub.

Now we can set up a proportion to solve for x:

42 ounces / x tubes = 1 tube / x ounces

Cross-multiplying gives us:

42x = 1 * x

Simplifying the equation:

42x = x

Dividing both sides of the equation by x (since x cannot be zero):

42 = 1

Since this equation is not true, it means that there is an error in our assumption. We need to revise our assumption.

Let's assume that each tube contains 1 ounce of capsaicin arthritis rub.

Now we can set up a new proportion:

42 ounces / x tubes = 1 tube / 1 ounce

Cross-multiplying gives us:

42x = 1 * 1

Simplifying the equation:

42x = 1

Dividing both sides of the equation by 42:

x = 1/42

As a result, you will need to buy less than a full tube—roughly 1/42 of a tube. In order to get the 42 ounces of capsaicin arthritis rub you need, you would essentially need to buy at least one tube.

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Answer:

B)  There are two solutions, but only one is viable.

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}A=w^2+4w\\A=4w+45\end{cases}[/tex]

To solve the system of equations, substitute the first equation into the second equation:

[tex]w^2+4w=4w+45[/tex]

Solve for w using algebraic operations:

[tex]\begin{aligned}w^2+4w&=4w+45\\w^2+4w-4w&=4w+45-4w\\w^2&=45\\\sqrt{w^2}&=\sqrt{45}\\w&=\pm \sqrt{45}\\w &\approx \pm 6.71\; \sf cm\end{aligned}[/tex]

Therefore, there are two solutions to the given system of equations.

However, as length cannot be negative, the only viable solution is w ≈ 6.71 cm.

Answer:

Jana is likely trying to solve option B:

"A person can afford a $290-per-month loan payment. If he is being offered a 4-year loan with an APR of 0.6%, compounded monthly, what is the most money that he can borrow?"

Step-by-step explanation:

Option B is the correct choice because it aligns with the values entered by Jana into the TVM Solver. Jana set the loan term (N) to 48, which represents 48 months (4 years). The APR value of 0.6% also matches what Jana inputted.

By selecting option B, Jana is attempting to find out the maximum amount of money she can borrow given that she can afford a $290-per-month loan payment and is offered a 4-year loan with an APR of 0.6%, compounded monthly.

This calculation will help Jana determine the loan amount that corresponds to her desired monthly payment and the given loan terms.

Answer: it contains 12 containers

Step-by-step explanation: i dont know  what the answer is but i know what i can help you with all you have to do is round the answer.

Answer:

When p, the probability of success, is zero in a binomial distribution, the probability of getting exactly k successes in n trials is also zero for all values of k except when k is zero (i.e., when there are no successes).

So, in the case of (0.3)^0, the result would be 1, because any number raised to the power of 0 is equal to 1. Therefore, the probability of getting zero successes in a binomial distribution when the probability of success is 0.3 is 1.

Answer: 88.94

Step-by-step explanation:

First, l found what was 8.125 out of 110 which is 8.94

then added 8.125 and 8.94 which got 118.94

But Angela gave the retailer an $30 coupon so l subtracted 30 from 118.94 which got me 88.94

The calculated value of x to the nearest degree is 56

From the question, we have the following parameters that can be used in our computation:

The triangle

The value of x can be caluclated using the following cosine rule

So, we have

cos(x) = 5/9

Evaluate the quotient

cos(x) = 0.5556

Take the arc cos of both sides

x = 56

Hence, the value of x to the nearest degree is 56

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Step-by-step explanation:

Perimeter =  pi * diameter

  radius = 1  1/3  yard   then diameter =  2  2/3 yd

perimter = pi *  2 2/3   yds = 8.38 yds

(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).

In 2011 the assets are about $669.6 billion

(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).

In 2016 the assets are about $931.5 billion.

(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).

In 2019 the assets are about $1135.4 billion.

Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:

[tex]A(x)=324e^{0.066x}[/tex]

where:

For the year 2011, the cost (in billions of dollars) is given by;

x = (2011 - 2007) + 7

x = 4 + 7

x = 11 years.

Next, we would substitute 11 for x in the exponential function:

[tex]A(11)=324e^{0.066 \times 11}[/tex]

A(11) = $669.6 billions.

Part b.

For the year 2016, the cost (in billions of dollars) is given by;

x = (2016 - 2007) + 7

x = 9 + 7

x = 16 years.

Next, we would substitute 16 for x in the exponential function:

[tex]A(16)=324e^{0.066 \times 16}[/tex]

A(16) = $931.5 billions.

Part c.

For the year 2019, the cost (in billions of dollars) is given by;

x = (2019 - 2007) + 7

x = 12 + 7

x = 19 years.

Next, we would substitute 19 for x in the exponential function:

[tex]A(19)=324e^{0.066 \times 19}[/tex]

A(19) = $1135.4 billions.

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Answer:

a)

[tex] \frac{1}{( - 7)^{4} } [/tex]

Answer:

[tex](-7)^-^4=\frac{1}{(-7)^4}[/tex]

Step-by-step explanation:

The user aswati already wrote the correct answer, but I wanted to help explain why their answer is correct so that you'll understand.

According to the negative exponent rule, when a base (let's call it m) is raised to a negative exponent (let's call it n), we rewrite it as a fraction where the numerator is 1 and the denominator is the base raised to the same exponent turned positive.

Thus, the negative exponent rule is given as:

[tex]b^-^n=\frac{1}{b^n}[/tex]

Thus, [tex](-7)^-^4[/tex] becomes [tex]\frac{1}{(-7)^4}[/tex]

Answer:

D, g(x) = 1/4 x^2

Step-by-step explanation:

You can try plugging in the x and y values into each equation. The answer to this would be D, where if you plug in 2 as the x value, you get 1/4 * 4 which equals 1. This also makes sense because 2x would have a narrower curve while 1/2x would have a wider curve.

The perimeter of the rectangle is 140 inches.

Let's denote the width of the rectangle as w. According to the given information, the length of the rectangle is six times its width, so we can express the length as 6w.

The area of a rectangle is given by the formula A = length × width. Substituting the values we have:

A = (6w) × w

600 = 6w^2

To solve for w, we divide both sides of the equation by 6:

w^2 = 100

Taking the square root of both sides:

w = ±10

Since width cannot be negative in this context, we discard the negative value and consider the positive value, w = 10.

Now that we have the width, we can find the length of the rectangle:

Length = 6w = 6 × 10 = 60

The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values:

P = 2(60 + 10)

P = 2(70)

P = 140

Therefore, the perimeter of the rectangle is 140 inches.

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Step-by-step explanation:

a linear relationship or function is described in general as

y = f(x) = ax + b

Because the variable term has the variable x only with the exponent 1, this makes this a straight line - hence the name "linear".

here f(x) is P(x) :

P(x) = ax + b

now we are using both given points (ordered pairs) to calculate a and b :

20 = a×170 + b

2820 = a×220 + b

to eliminate first one variable we subtract equation 1 from equation 2 :

2800 = a×50

a = 2800/50 = 280/5 = 56

now, we use that in any of the 2 original equations to get b :

20 = 56×170 + b

b = 20 - 56×170 = 20 - 9520 = -9500

so,

P(x) = 56x - 9500

The angle m∠MHU between the intersection of the secant line HM and tangent line HU is equal to 54°

To calculate for the angle between the intersection of a secant and a tangent we need to know the measure of the intercepted arc, and then divide it by 2 to get the angle.

If the measure of the arc HM is given to be equal to 108°, then the measure of angle MHU is calculated as:

angle MHU = 108°/2

m∠MHU = 54°

Therefore, the angle m∠MHU between the intersection of the secant line HM and tangent line HU is equal to 54°

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Answer:

Area of triangle = (1/2)(12²) = (1/2)(144) = 72

Area of circle = π(12²) = 144π

P(point falls in triangle) = 72/(144π)

= 1/(2π)

= about .16

= about 15.92%

Answer:

The number is 16

Step-by-step explanation:

This follows a multiplication rule,

4 times 1 = 4

4 times 2 = 8

4 times 3 = 12

4 times 4 = 16

So, the number is 16

The value of 12 remains 12.

The value of X cannot be determined without additional information.

The value of 25° remains 25°.

To find the values of the variables in the given information, we have:

12: This is a given value and does not require calculation. Therefore, the value of 12 remains as it is.

X: Without additional information or an equation to solve, we cannot determine the value of X. It could represent any unknown quantity or variable, and its specific value would depend on the context or problem being solved.

25°: This is an angle measure in degrees. The value of 25° remains as it is.

To summarize:

The value of 12 remains 12.

The value of X cannot be determined without additional information.

The value of 25° remains 25°.

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The domain of f(x) is (0, +∞), and the range is (0, +∞). The graph of the function will have a vertical asymptote at x = 0 and will continuously increase as x approaches positive infinity.

To graph the given logarithmic function f(x) based on the table, we can use the information provided. The table presents pairs of values (x, y), where x represents the input and y represents the output of the function.

From the table, we can observe that the input values (x) are positive and non-zero. This indicates that the domain of the function is x > 0, meaning x is greater than zero. In interval notation, the domain would be written as (0, +∞).

Looking at the output values (y) in the table, we see that they are all positive. This suggests that the range of the function is y > 0, meaning y is greater than zero. In interval notation, the range would be expressed as (0, +∞).

Graphically, the function f(x) is logarithmic and will have a vertical asymptote at x = 0. As x approaches positive infinity, the function increases without bound. The graph starts at y = 125 when x = 1, and it intersects the y-axis at y = 5 when x = 1.5. The graph of the function will resemble a curve that approaches but never touches the x-axis.

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The speed of the plane is equal to 120 mph.

In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using miles per hour (mph).

Mathematically, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Time = distance/speed

Let the variable s represent the speed of the plane in miles per hour. Therefore, an equation that models the situation can be written as follows;

240/s = 80/s - 80

80s = 240s - 19200

19200 = 160s

s = 19200/160

s = 120 mph.

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Based on the provided data sets, it can be observed that both Data Set K and Data Set L have identical values. Therefore, their centers and spreads are also identical.

The center of a data set can be measured using various statistical measures such as the mean, median, or mode. Since the data sets have the same values, all these measures will yield the same result for both sets.

In this case, the center of Data Set K is equal to the center of Data Set L.

Similarly, the spread of a data set refers to the measure of variability or dispersion within the data. Common measures of spread include the range, variance, and standard deviation.

However, since the data sets are exactly the same, all these measures will yield identical results for both sets. Thus, the spread of Data Set K is the same as the spread of Data Set L.

In summary, both the center and the spread of Data Set K are the same as those of Data Set L. Therefore, there is no difference between the two data sets in terms of their central tendency or variability.

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Answer: [tex](-\infty, 0) \cup (0, \infty)[/tex]

Step-by-step explanation:

The graph of [tex]\frac{\sin x}{x}[/tex] is continuous for all real [tex]x[/tex] except [tex]x=0[/tex], and multiplying this by [tex]1/3[/tex] does not change this.

The correct answer choice is: A. The system has exactly one solution. The solution is (11, 7).

The correct answer choice is: A. all three countries had the same population of 7 thousand in the year 2011.

Based on the information provided above, the population (y) in the year (x) of the countries listed are approximated by the following system of equations:

-x + 20y = 129

-x + 10y = 59

y = 7

where:

By solving the system of equations simultaneously, we have the following solution:

-x + 20(7) = 129

x = 140 - 129

x = 11

-x + 10(7) = 59

x = 70 - 59

x = 11

Therefore, the system of equations has only one solution (11, 7).

For the year when the population are all the same for three countries, we have:

x = 2010 + (11 - 10)

x = 2011

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