Equation that passes through the points (5,5) and (5,-8)

Answer:

(a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^(n-1) b^1 + C(n, 2)a^(n-2) b^2 + ... + C(n, n-1)a^1 b^(n-1) + C(n, n)a^0 b^n

The binomial expansion of (2x - 3y)^5 is:

32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5

The binomial expansion of the given expression is 32x⁵+240x⁴y+720x³y²+1080x²y³+810xy⁴+243y⁵.

The given expression is (2x-3y)⁵.

In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial.

(2x)⁵+⁵c₁(2x)⁴(3y)¹+⁵C₂(2x)³(3y)²+⁵C₃(2x)²(3y)³+⁵C₄(2x)(3y)⁴+⁵C₅(3y)⁵

= 32x⁵+5(16x⁴)(3y)+10.(8x³)(9y²)+10(4x²)(27y³)+5(2x)(81y⁴)+243y⁵

= 32x⁵+240x⁴y+720x³y²+1080x²y³+810xy⁴+243y⁵

Therefore, the binomial expansion of the given expression is 32x⁵+240x⁴y+720x³y²+1080x²y³+810xy⁴+243y⁵.

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To multiply a square root by a square root and a whole number, you can use the distributive property of multiplication

Given data ,

Let the numbers be represented by the expression A

Now , the value of A is

A = √2 × 3√5

First, you can simplify each square root:

√2 = 1.4142 (rounded to 4 decimal places)

3√5 = 5.1962 (rounded to 4 decimal places)

Next, you can multiply the two simplified square roots and the whole number:

√2 × 3√5 = 1.4142 × 5.1962 × 3

= 22.3607 × 3

= 67.0821

Hence , the expression is A = √2 × 3√5 = 67.0821

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Answer:

32 ways

Step-by-step explanation:

Since there are 8 red chalks and 4 white chalks.

Then number of ways to select exactly 2 red chalks is; 8C2 = 28 ways

Number of ways to select exactly 1 white chalk is; 4C1 = 4 ways

Total number of ways = 28 + 4 = 32 ways

Answer:

step 2

Step-by-step explanation:

Erin's mistake is in step 2 it should be 8*2 first and 16* 5 which equals to 86

The unit cost of pears is $1.50 per pound.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Cost for 1/3 lb of pears = $0.50

Since, 1 lb = 1 pound

Implies that,

Cost of 1/3 pounds of pears = $0.50

To find the cost of one pound of pears,

Use ratio property,

1/3 pound costs = 0.50

1 pound costs = 0.50 x 3 = $1.50

The cost of one pound of pear is $1,.50.

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Answer:

4 ft

Step-by-step explanation:

You need to divide that 200 ft among those 50 sections to get what amount of feet goes into each section.

The probability of drawing a seven and then a four when randomly drawing two cards without replacement is 0.0045 or approximately 0.45%.

The probability of drawing a seven and then a four when randomly drawing two cards without replacement can be calculated using the following steps:

First, we need to determine the total number of possible outcomes when drawing two cards from a standard deck of 52 cards without replacement. This can be found using the combination formula:

C(52,2) = 52! / (2! * (52-2)!) = 1,326

Next, we need to determine the number of favorable outcomes where we draw a seven and then a four.

There are four sevens and four fours in a deck of 52 cards, so the probability of drawing a seven on the first draw is 4/52. Since we are not replacing the card, there are now 51 cards left in the deck, and three of them are fours. Therefore, the probability of drawing a four on the second draw is 3/51.

The probability of drawing a seven and then a four is the product of the probabilities of drawing a seven on the first draw and a four on the second draw:

P(seven and then four) = (4/52) * (3/51) = 0.0045 or approximately 0.45%.

Therefore, the probability of drawing a seven and then a four when without replacement is 0.0045 or approximately 0.45%.

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Using a calculator, it is found that the approximate slope of the line of best fit for the data is of -4.54762.

The slope is found inserting the points (x,y) in a calculator. In this problem, the points are as follows:

(1, 36), (2,34), (3,30), (4,31), (5,23), (6,16), (7,11), (8,5).

Hence, using the calculator, the slope is of -4.54762.

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The answer is : Biff gets angry at the idea that Linda can hear Willy when he talks to himself because he doesn't want her to see the truth about Willy's mental state.

This is an important plot point in Arthur Miller's play, Death of a Salesman. Why does Biff get angry at the idea that Linda can hear Willy when he talks to himself? Biff gets angry at the idea that Linda can hear Willy when he talks to himself because he doesn't want her to see the truth about Willy's mental state.

What is Death of a Salesman?

Death of a Salesman is a play written by Arthur Miller in 1949 that tells the story of Willy Loman, an aging salesman who is struggling to come to terms with his declining success and his own sense of failure. The play is widely regarded as one of the most important American plays of the 20th century and has been adapted into numerous films and stage productions over the years.

Who is Biff in Death of a Salesman?

Biff is one of the main characters in Death of a Salesman. He is the son of Willy Loman and Linda Loman and is portrayed as a complex character who is struggling to come to terms with his own sense of failure and disillusionment. Biff is an important character in the play because he is the only character who is able to see through his father's delusions and confront him with the truth about his life and his failures.

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Answer:

-300 because of the negative sign attached to the 4

(a) Continuity of f at x=0 is to be determined.  

Definition: A function is said to be continuous at a point c in its domain if its limit at that point exists and is equal to the value of the function at that point.  

Let's evaluate the limit of f(x) as x approaches 0 from the right side:

limf(x) as x → 0+ = limsinc(x) as x → 0+

= lim sin(x) / x as x → 0+

= 1.  

Now, let's evaluate the limit of f(x) as x approaches 0 from the left side:

limf(x) as x → 0-

= limsinc(x) as x → 0-

= lim sin(x) / x as x → 0-

= 1.  

Since the limits of f(x) as x approaches 0 from both sides exist and are equal to f(0), therefore f is continuous at x=0.  

Answer: Yes, f is continuous at x=0.

(b) Differentiability of f at x=0 is to be determined.  

Definition: A function is said to be differentiable at a point c in its domain if its limit at that point exists and is finite.

 Let's evaluate the limit of f'(x) as x approaches 0:

\(limf'(x) as x → 0 = lim (d/dx[sinc(x)]) as x → 0\)

= limcos(x)/x - sin(x)/(x^2) as x → 0

= 0 - 1/0^2 = -∞.  

Since the limit of f'(x) as x approaches 0 is not finite, therefore f is not differentiable at x=0.

 Answer: No, f is not differentiable at x=0.

\(limcos(x)/x - sin(x)/(x^2) as x → 0\)

(c) Roots of f are to be determined.  

Definition: A root of a function is any point c in its domain at which f(c)=0.

 f(x)=sinc(x)=sin(x)/x=0 when sin(x)=0.  sin(x)=0 for x=nπ

where n is an integer.

Therefore, f has roots at x=nπ,

where n is an integer.

Each root has a multiplicity of 1 because the derivative of sinc(x) is never equal to 0.

Answer: f has roots at x=nπ,

where n is an integer, and each root has a multiplicity of 1.

(d) The supremum and maximum of f and the number of relative extrema are to be determined.

Definition: The supremum of a function f is the least upper bound of the range of f.

The maximum of a function f is the largest value of f on its domain.

The range of f is [-1,1].  

Therefore, sup f=1 and max f=1.  

The function sinc(x) is continuous, symmetric about the y-axis, and has zeros at the odd multiples of π.  

The relative maxima occur at the even multiples of π, and the relative minima occur at the odd multiples of π.  

The value of the function at each relative extremum is -1.  

Let c be an even integer, so that x=cπ is a relative extremum.

Then f(cπ)=sinc(cπ)=(-1)^c/(cπ).

By the definition of absolute value,

\(f(cπ)|=|-1^c/(cπ)|=1/(cπ)=√(1/(c^2π^2))\).  

Therefore, \(f(cπ)|=-1√(1+c^2π^2).\)

Answer: sup f=1, max f=1, there are infinite relative extrema, and f(cπ)|=-1√(1+c^2π^2) for any even integer c.

(e) An infinite product is to be evaluated.

Formula:

p\(i(n=1 to ∞) (1+(z/n))^-1\) =\(e^(γz)/z pi(n=1 to ∞) (1+(n^2/a^2))^-1\)

= \(a/π pi(n=1 to ∞) (1+(na)^-2\))  = a/π sin(πa).  

Let a=1/√2 and z=1.  

Then,

11 1 1 1 11 1 1 11 + + 22 2 2 2 2 2 22  = \((1+(1/1))^-1(1+(1/2))^-1(1+(1/3))^-1(1+(1/4))^-1\)...  = 1/(1+1/2) * 2/(2+1/3) * 3/(3+1/4) * 4/(4+1/5)...  

= 2/3 * 3/4 * 4/5 * 5/6 *...  

= [3/(2+1)] * [4/(3+1)] * [5/(4+1)] * [6/(5+1)] *...

= [3/2 * 4/3 * 5/4 * 6/5 *...] / [1+1/2+1/3+1/4+...]  

= 3/2 * πsin(π/2) / \(e^γ\)

= 3/2 * π^2 / \(e^γ\).  

Answer: 11 1 1 1 11 1 1 11 + + 22 2 2 2 2 2 22  = 3/2 * \(π^2 / e^γ\).

(g) The limit of x/sin(x) as x approaches 0 and the derivative of sin(x) with respect to x when x is a measure of an angle in degrees are to be determined.

 Formula:\(lim x→0 sin(x)/x\) = 1.  

Let y be a measure of an angle in degrees.  

Then x=yπ/180.  

Formula: d/dy(sin(yπ/180)) = (π/180)cos(yπ/180).  

Answer: \(lim x→0 x/sin(x)\) = 1 and d/dy(sin(yπ/180)) = (π/180)cos(yπ/180).

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Answer:

Step-by-step explanation:

Slope is rise over run.

For example, 2 is equivalent to 2/2 so you find the graph that has a point at (2, 2).

Hope this helps :D

.7 * 295.99 = original price

.7 * 295.99 = 207.193 = $207.19

Answer:

a=12

Step-by-step explanation:

12-6=6

Answer:

2x+y=3

-2x -2x

y=-2x+3 would be your slope intercept form (y=mx+b)

Answer:

(-7,-3)

Step-by-step explanation:

step one) solve one equation for x.

y=-3x

-3x/-3=y/-3

x=(-y/3)

step two) plug in x for the other original problem.

y=x-4

y=(-y/3)-4

step three) solve for y.

y=(-y/3)-4

y+4=(-y/3)-4+4

3*(y+4)=(-y/3)*3

3y+12=-y

(3y+12)-3y=-y-3y

12/-4=-4y/-4

y=-3

step four) plug in -3 for y and solve for x.

y=x-4

-3=x+4

-3-4=x+4-4

-7=x

I am in algebra two so you can trust my answer. if you need more help lmk in the comments. happy holidays and stay safe!

The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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Answer: 5^6

Step-by-step explanation:

First, you have to simplify the numbers so that all of them share the same base. For this problem, the base for all of these numbers would be 5. So now the equation looks like this:

5^2 * 5^1 * 5^3

Next we have to turn all of these numbers into one. Whenever you multiply the numbers, all you have to do is add the exponents together. So now it will look like this:

5^(2+1+3)

Add the numbers up and you get your answer.

5^6

Step-by-step explanation:

An easy way is to first make a rectangle.

put 5x^2 in the bottom left

put -4 in the top right.

also, make a diamond. for the sum it will be -19x, for the product it will be -4*5x^2 which equals -20x^2

solve the diamond then put those answers in the missing squares.

hope this helps :)

Write the Python expressions for the following mathematical expressions: (1 + x) * (1 + y) * (1 + z), x + y²  + z⁴   , and xyz * (1 + x)³   .

The given mathematical expressions can be written as Python expressions as follows:

In Python, the `**` operator represents exponentiation, so `y**2` denotes y squared and `z**4` denotes z to the power of 4.

The multiplication operator `*` is used for multiplication, and the addition operator `+` is used for addition.

Parentheses `()` are used to group operations and ensure the correct order of evaluation.

These Python expressions can be used to calculate the respective mathematical expressions for given values of x, y, and z.

The expressions follow the mathematical operations and precedence rules, allowing for accurate computation in Python.

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A. The y-intercept is at the point (0, 0).

B.  The zeros are x = 0 or x = ±√5

C.

A) The y-intercept of this graph is the point where x = 0.

When  x = 0, the value of y

= 0^4 - 5*0^2

= 0.

Therefore, the y-intercept is at the point (0, 0).

B) The x-intercepts/roots of the function are the values of x that make y = 0.

To find these values, we need to set y = 0 and solve for x:

x⁴ - 5x² = 0

x⁴ = 5x²

x² = x⁴/5

x = ±√(x⁴/5)

We can simplify this expression by factoring x² out of both sides:

x²(x² - 5) = 0

x² = 0 or x² - 5 = 0

x = 0 or x = ±√5

hence the x-intercepts are at x = 0 and x = ±√5.

C) The end behavior of this function refers to how the graph of the function approaches the x-axis as x approaches positive infinity and negative infinity.

x → ∞ f(x) → ∞

x → -∞ f(x) → -∞

D) The graph is attached

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Answer:

wait what do you need help with

Step-by-step explanation:

Answer:

post another question and i will answer it

Step-by-step explanation:

where your question

Functions (c) L(1) = C1 + AC and (d) L(1) = C°1 are linear operators on R^n, while functions (a), (b), and (e) do not satisfy the properties of linearity and therefore are not linear operators.

a) L(A) = 1 - 1: This function is not a linear operator because it does not preserve scalar multiplication. Multiplying A by a scalar c would yield L(cA) = c - c, which is not equal to cL(A) = c(1 - 1) = 0.

b) L(A) = 1 + 17: Similar to the previous case, this function is not linear since it fails to preserve scalar multiplication. Multiplying A by a scalar c would result in L(cA) = c + 17, which is not equal to cL(A) = c(1 + 17) = c + 17c.

c) L(1) = C1 + AC: This function is a linear operator since it satisfies both the preservation of addition and scalar multiplication properties. Adding matrices A and B and multiplying the result by scalar c will yield L(A + B) = C(1) + AC + C(1) + BC = L(A) + L(B), and L(cA) = C(1) + cAC = cL(A).

d) L(1) = C°1: This function is a linear operator since it satisfies the properties of linearity. Addition and scalar multiplication are preserved, and L(cA) = C(0)1 = c(C(0)1) = cL(A).

e) L(1) = 1?C: This function is not a linear operator as it does not preserve scalar multiplication. Multiplying A by a scalar c would give L(cA) = 1?(cC), which is not equal to cL(A) = c(1?C).

In summary, functions (c) L(1) = C1 + AC and (d) L(1) = C°1 are linear operators on R^n, while functions (a), (b), and (e) do not satisfy the properties of linearity and therefore are not linear operators.

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Dividing two polynomials may produce another polynomial only when the divisor has a lower degree than the dividend. Otherwise, it will generally result in a rational function.

No, dividing two polynomials may not result in another polynomial. It can produce a rational function.

A polynomial is an algebraic expression consisting of terms with non-negative integer exponents. When two polynomials are divided, the result is not always a polynomial.

If the degree of the polynomial being divided (dividend) is higher than the degree of the polynomial dividing (divisor), then the result can be a polynomial with a lower degree. However, if the degree of the divisor is equal to or greater than the degree of the dividend, the result will generally be a rational function, which is a ratio of two polynomials.

A rational function has the form P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) is not equal to zero. The division can introduce terms with negative or fractional exponents, making the result a rational function rather than a polynomial.

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Answer:

27 miles

Step-by-step explanation:

Find the linear equation which is y = 3x

y = 3(9)

y = 27

Answer:

27 miles is the answer

Step-by-step explanation:

x | y

4 |12

5 | 15

6 |18

7 |21

8 | 24

9 |27

 x is increasing by 1 and y by 3 so  by this way 27 is the answer

Answer:

7 degrees colder

Step-by-step explanation:

15 degrees - 8 degrees = 7 degrees

The average value of the function g(x) = e^(sin(x))cos(x) on the interval [0,π/2] is approximately 0.896.

To find the average value of g(x), we need to compute the definite integral of g(x) over the interval [0,π/2] and divide by the length of the interval. That is, gave = (1/(π/2 - 0)) ∫(0 to π/2) e^(sin(x))cos(x) dx

Using integration by parts, we can evaluate the integral to obtain gave = (2/π) (e - 1) Numerically, this is approximately 0.896, rounded to three decimal places. Therefore, the average value of g(x) on the interval [0,π/2] is approximately 0.896.

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Answer:

37

Step-by-step explanation:

i just know

Answer: 7%

(Hope this is right.)

Step-by-step explanation:

Let's solve this using the information we have and an equation.

Shane: $32,000 - (Given)

Theresa: 18,000+14x, if x=1,160 - (Given)

---------------------------------------------------------------

Step two: (Theresa) 14(1,160) =16,240 (Algebra)

Step three: (Theresa) 18,000+16,240=34,240 (Algebra, given.) - cost of Theresa's car.

---------------------------------------------------------------

Finally,

They're asking for how much more she paid for her car as a percentage of what Shane paid.

34,240-32,000=2,240 and

2,240/32,000=0.07

0.07x100=7

Answer 7% more than what Shane paid.

False. To calculate a percent increase, the portion is not the missing element. The portion refers to the initial or original value, while the missing element is the final or increased value.

The formula for calculating a percent increase is:

Percent Increase = (Final Value - Initial Value) / Initial Value * 100

In this formula, the initial value is the portion that represents the starting or original value. The final value is the missing element, as it represents the increased or final value after the increase.

By subtracting the initial value from the final value, we obtain the difference between the two. Dividing this difference by the initial value gives us the relative increase as a decimal or fraction. Multiplying by 100 converts it into a percentage, representing the percent increase.

Therefore, the portion in calculating a percent increase is the known value or initial value, while the missing element is the final value that we are trying to determine or find.

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