Why is f called a linear function?

Answer:

I dont know the answer but maybe this page can help, it even gives you the explanation or the steps.

Explanation:

symbolab.com

The matrix that has A₁ and A₂ as eigenvalues is determined by substituting the values of A₁ and A₂ into the matrix equation. The resulting matrix will have A₁ and A₂ as its eigenvalues.

To find the matrix with A₁ and A₂ as eigenvalues, we substitute these values into the general matrix equation for eigenvalues. Let's assume the matrix we're looking for is a 2x2 matrix:

[[a, b],

[c, d]]

For a matrix to have eigenvalues A₁ and A₂, it must satisfy the equation:

|A - λI| = 0

Where A is the matrix, λ is the eigenvalue, and I is the identity matrix. Substituting A₁ and A₂ into this equation, we get:

|[[a, b], [c, d]] - A₁ * [[1, 0], [0, 1]]| = 0

|[[a, b], [c, d]] - A₂ * [[1, 0], [0, 1]]| = 0

Simplifying these equations, we have:

|[[a - A₁, b], [c, d - A₁]]| = 0

|[[a - A₂, b], [c, d - A₂]]| = 0

The resulting matrices can be used to determine the values of a, b, c, and d that satisfy these equations. Thus, the matrix with A₁ and A₂ as eigenvalues can be constructed.

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Answer:

19n+9u=7500 and 4u-n

Step-by-step explanation:

The value x in the secant line using the Intersecting btheorem is 19.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one  of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the image;

External line segement of the first secant line = 8

First sectant line segment = ( x + 8 )

External line segement of the second secant line = 9

First sectant line segment = ( 15 + 9 )

Using the Intersecting secants theorem:

8 ×  ( x + 8 ) = 9 × ( 15 + 9 )

Solve for x:

8x + 64 = 135 + 81

8x + 64 = 216

8x = 216 - 64

8x = 152

x = 152/8

x = 19

Therefore, the value of x is 19.

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Answer:

3 hours :)

Step-by-step explanation:

5 km x 3 = 15km

also i hope you can catch up on ur work :)

(A - B) u (A n B) = A is proved using several properties from Theorem 6.2.2. of Set Identities.

To prove (A - B) u (A n B) = A algebraically, we can use the following steps:

(A - B) u (A n B) // Given

[(A n B) U (A - B)] // Definition of union

[(B n A) U (A - B)] // Commutative law of intersection

[(B U (A - B)) n (A U (A n B))] // Distributive law of union over intersection

[(B U (A n B)') n (A U B)] // Complement law of intersection and De Morgan's law

[(B U (A - B)) n (A U B)] // Complement law of A n B

[(B U (A n B)') n (A U B)] // Definition of A - B

[(B U (A n B)') n (B U A')] // De Morgan's law

[(B n (B U A')) U ((A n B)'' n (B U A'))] // Distributive law of intersection over union

[(B n U) U (Ø n (B U A'))] // Complement law of B U A' and B n (B U A')

B U Ø // Identity law of intersection and complement law of B U A'

B // Identity law of union

Therefore, (A - B) u (A n B) = A is proved. We used several properties from Theorem 6.2.2, including the commutative law of intersection, distributive law of union over intersection, complement law of intersection, De Morgan's law, complement law of A n B, definition of A - B, distributive law of intersection over union, complement law of B U A', and identity law of intersection and union.

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Answer:(4,-25)

Step-by-step explanation:

Answer:

it is b :) on edge

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

took the test

Answer:

4/3π(0.973r³)

Step-by-step explanation:

Volume of a sphere = 4/3πr³

Given the radius of dodge ball rd = r

radius of tennis ball rt = 0.3r

Taking their difference

Volume difference  = 4/3πrd³ - 4/3πrt³

Volume difference  = 4/3π(r)³ - 4/3π(0.3r)³

Volume difference  = 4/3π(r³ - 0.027r³)

Volume difference = 4/3π(0.973r³)

Hence the differmce in volume is  4/3π(0.973r³)

Given

Equation

x tea chart __, 0, 2, __

y tea chart 0,__, __, 3

Procedure

y = 0

12x = 16

x = 16/12

x = 4/3

x = 0

-8y = 16

y = 16/-8

y = -2

x = 2

12(2) - 8y = 16

24 - 8y = 16

-8y = 16-24

-8y = -8

y = 1

y = 3

12x - 8(3) = 16

12x - 24 = 16

12x = 16+24

12x = 40

x = 40/12

x = 20/6

x tea chart 4/3, 0, 2, 20/6

y tea chart 0, -2, 1, 3

Answer:

I think it's 5 bc hypothetically speaking

The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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The measure of following values for the given circle is:

Sector AE = (2/3)π square units

Sector AB = (10/9)π square units

Sector ECB = (1/3)π square units

Angle BOC = 160 degrees

In geometry, a circle is a two-dimensional shape that is defined as the set of all points in a plane that are equidistant from a given point called the center. The distance from the center to any point on the circle is called the radius of the circle.

Here,

Sector AE:

The central angle of 60 degrees represents one-sixth (60/360) of the circle, so the sector AE has an area of one-sixth of the total area of the circle. The area of the circle is πr² = 4π square units, so the area of sector AE is:

(1/6) x 4π = (2/3)π square units

Sector AB:

The central angle of 50 degrees represents 5/18 (50/360) of the circle, so the sector AB has an area of 5/18 of the total area of the circle. The area of the circle is πr² = 4π square units, so the area of sector AB is:

(5/18) x 4π = (10/9)π square units

Sector ECB:

Since angles EOC and BOC are complementary (they add up to 90 degrees), the central angles they subtend are also complementary. Therefore, the central angle of sector ECB is 90 - 60 = 30 degrees. This represents one-twelfth (30/360) of the circle, so the sector ECB has an area of one-twelfth of the total area of the circle. The area of the circle is πr² = 4π square units, so the area of sector ECB is:

(1/12) x 4π = (1/3)π square units

Angle BOC:

Since angles AOB and COE are both right angles (as they subtend diameters of the circle), we know that angle AOC is 90 degrees. Therefore, angle BOC is:

360 - 90 - 60 - 50 = 160 degrees

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Answer:

x= 113

y= 67

z= 49

Step-by-step explanation:

a triangle equals to 180° so lets start with the triangle that has two given degrees

28 + 39 + x = 180 solve

x = 113

no we can find y by using x + y = 180 since it's a straight line

we know the value of x so 113 + y = 180. solve.

y= 67

now do the same thing we did from the start since we have two given degrees on the other triangle.

67 + 64 + z = 180

z= 49

To solve the given differential equations using the method of undetermined coefficients, we need to find a particular solution that satisfies the non-homogeneous equation. So, the general solution is given by: (a) y = y_h + y_p = Ce^(4x) + (-x - 4xe^(-2x) + 8x^2 - 1)e^(-2x) + 8x - 1, (b) y = y_h + y_p = Ce^x + (-x + 22.21e^x)

Let's solve each equation separately:

(a) y' - 4y = 16xe^(-2x) + 8x + 4

Step 1: Solve the associated homogeneous equation:

The homogeneous equation is y' - 4y = 0, which has the solution y_h = Ce^(4x), where C is a constant.

Step 2: Track down a specific non-homogeneous equation solution:

Since the non-homogeneous term contains terms like xe^(-2x) and x, we assume a particular solution of the form:

y_p = (A + Bx)e^(-2x) + Cx + D

Differentiating y_p, we have:

y'_p = (-2A + B - 2Bx)e^(-2x) + C

Substituting y_p and y'_p into the original equation, we get:

(-2A + B - 2Bx)e^(-2x) + C - 4((A + Bx)e^(-2x) + Cx + D) = 16xe^(-2x) + 8x + 4

Matching coefficients of like terms on both sides, we get:

-2A + B - 4A - 4D = 0 (coefficients of e^(-2x))

-2B - 4C = 16x (coefficients of xe^(-2x))

-2A + C = 8x (coefficients of x)

-4D = 4 (constant term)\

Solving these equations, we find A = -1, B = -4, C = 8, and D = -1.

Therefore, the particular solution is:

y_p = (-x - 4xe^(-2x) + 8x^2 - 1)e^(-2x) + 8x - 1

The general solution is given by:

y = y_h + y_p = Ce^(4x) + (-x - 4xe^(-2x) + 8x^2 - 1)e^(-2x) + 8x - 1

(b) y' - y = (2x + xe^2) + 22,21

Step 1: Solve the associated homogeneous equation:

The homogeneous equation is y' - y = 0, which has the solution y_h = Ce^x, where C is a constant.

Step 2: Track down a specific non-homogeneous equation solution:

Since the non-homogeneous term contains terms like 2x, xe^2, and 22.21, we assume a particular solution of the form:

y_p = Ax + B + Cx^2 + De^x

Differentiating y_p, we have:

y'_p = A + C + 2Cx + De^x

Substituting y_p and y'_p into the original equation, we get:

(A + C + 2Cx + De^x) - (Ax + B + Cx^2 + De^x) = (2x + xe^2) + 22.21

Matching coefficients of like terms on both sides, we get:

A - Ax = 2x + xe^2 (coefficients of x)

C - Cx^2 = 0 (coefficients of x^2)

C + D = 22.21 (constant term)

According to the first equation, A = -1.

From the second equation, we have C = 0.

Substituting A = -1 and C = 0 into the third equation, we get D = 22.21.

Therefore, the particular solution is:

y_p = -x + 22.21e^x

The general solution is given by:

y = y_h + y_p = Ce^x + (-x + 22.21e^x)

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The approximate change in demand when the price is increased from $3.00 per pound to $3.20 per pound is approximately -49.6 pounds.

The demand function is given by D = 1000 - 40x², where x represents the price per pound.

First, let's calculate the demand at the initial price of $3.00 per pound:

D_initial = 1000 - 40(3²)

D_initial = 1000 - 40(9)

D_initial = 1000 - 360

D_initial = 640

Now, let's calculate the demand at the increased price of $3.20 per pound:

D_final = 1000 - 40(3.2²)

D_final = 1000 - 40(10.24)

D_final = 1000 - 409.6

D_final = 590.4

The approximate change in demand is given by:

Change in demand = D_final - D_initial

Change in demand = 590.4 - 640

Change in demand ≈ -49.6

Note that the negative sign indicates a decrease in demand.

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Using the given exponential function,

The rate of the disease spreading is approx. 140 peoples per day affected.

let P be the number of people's that are contacting a new disease.

given exponential function about the new disease modeled by population is

P(t) = 3725/(1 +1.72 e⁻⁰·⁵²ᵗ) ---(1)

where t is time measured in days

we want to calculate the rate of diseases spreading on day 4 i.e t = 4

putting the value t = 4 in above formula, we get

P(t=4) = 3725/(1 + 1.72 e⁻⁽⁰·⁵²⁾⁴)

=> P( t= 4) = 3725 / (1 + 1.72× e⁻⁰·²⁸)

=> P(t=4) = 3725/(1 + 1.72× 0.124)

=> P(t = 4) = 3725/(1+ 0.2148)

=> P(t=4) = 3725/1.2148

=> P(t = 4) = 3066.14

Hence, after 4 days of diseases spread , total 3066 people's are affected from it .

rate of diseases spreading per day is equal to (3725-3066)/4 = 659/4 = 139.75

so, rate of spreding diseases is 139.75 ~ 140 peoples per day .

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Answer:

????

Step-by-step explanation:

The number of hours he works is missing???

The annual interest rate with continuous compounding is 3.6171%.

To solve this problem, we can use the formula for compound interest:

\(A = P(1 + r/n)^(nt)\)
Where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.

a. Quarterly compounding:
We know that P = $11,000, A = $14,000, n = 4 (quarterly compounding), and t = 6 years. Substituting these values into the formula, we get:

$14,000 = $\(11,000(1 + r/4)^(4*6)\)
\(1.2727 = (1 + r/4)^24\)
Taking the 24th root of both sides, we get:
1 + r/4 = 1.03636
r/4 = 0.03636
r = 0.14545
r = 3.636%

Therefore, the annual interest rate with quarterly compounding is 3.636%.

b. Continuous compounding:
We can use the formula\(A = Pe^(rt),\) where e is the mathematical constant approximately equal to 2.71828. Substituting the given values, we get:

$14,000 = $\(11,000e^(r*6)\)
\(e^(r*6) = 1.2727\)

Taking the natural logarithm of both sides, we get:
r*6 = ln(1.2727)
r = ln(1.2727)/6
r = 0.03617
r = 3.6171%

Therefore, The annual interest rate with continuous compounding is 3.6171%.

The correct answers are:
a. = 3.636% (rounded to three decimal places)
b. = 3.6171% (rounded to four decimal places)

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Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Bc

Probability of rolling at least one 3 is option E. 2/5.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

Given that, a fair four-sided die and a fair five-sided die are rolled together.

Probability of rolling at least one 3 means that 3 is rolled in any one of the die or both dice.

Sample space of rolling 3 are {(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (1, 3), (2, 3), (4, 3)}

There are 8 chances of getting at least one 3 in any of the die.

Total number of outcomes = 4 × 5 = 20

Probability of getting at least one 3 = 8/20 = 2/5

Hence the required probability is 2/5.

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       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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Answer:

C(1,4) , A(-2,-3), R (3,2)

Step-by-step explanation:

the formula thing for rotating 180° about the origin is (x,y) -> (-x,-y)

this doesn't mean make the number negative, but make it the opposite if that makes sense

e.g. F(2,-4) -> F(-2,4)

The pH of the 0.500 M acetic acid solution is approximately 2.52 (option a).

To find the pH of a solution of acetic acid, we need to consider its acid dissociation constant, Ka. Acetic acid (CH3COOH) is a weak acid, and its dissociation in water can be represented by the equation:

CH3COOH ⇌ CH3COO- + H+

The Ka expression for acetic acid is:

Ka = [CH3COO-][H+] / [CH3COOH]

Given that Ka = 1.8×10^(-5) for acetic acid, we can set up an equation using the concentration of acetic acid ([CH3COOH]) and the concentration of the acetate ion ([CH3COO-]):

1.8×10^(-5) = [CH3COO-][H+] / [CH3COOH]

Since we are given a 0.500 M solution of acetic acid, we can assume that the concentration of acetic acid is 0.500 M initially.

1.8×10^(-5) = [CH3COO-][H+] / 0.500

To solve for [H+], we need to make an assumption that the dissociation of acetic acid is negligible compared to its initial concentration (0.500 M). This assumption is valid because acetic acid is a weak acid.

Therefore, we can approximate [CH3COO-] as x and [H+] as x.

1.8×10^(-5) = (x)(x) / 0.500

Rearranging the equation:

x^2 = 1.8×10^(-5) * 0.500

x^2 = 9.0×10^(-6)

Taking the square root of both sides:

x ≈ 3.0×10^(-3)

Since x represents [H+], the concentration of H+ ions in the solution is approximately 3.0×10^(-3) M.

To find the pH, we use the formula:

pH = -log[H+]

pH = -log(3.0×10^(-3))

pH ≈ 2.52

Therefore, the pH of the 0.500 M acetic acid solution is approximately 2.52 (option a).

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Answer: x=<4

Step-by-step explanation:

Answer:

2 days

Step-by-step explanation:

there is still 1/5 of his crops that need to be harvested. to see how many days that will take divide that amount and see how many 1/10 fit into it. 1/10+ 1/10 = 2/10 which is also 1/5 so it will take 2 days.

The number of chocolates remaining in the box after Chase birthday can be represented by the equation 18 - 4t = 6

Number if chocolates in the box = 18

Number of nights = 4

Remaining chocolates in the box = 6

Based on the information given, the number of chocolates remaining in the box after Chase birthday can be represented by the equation 18 - 4t = 6.

To get the number of chocolates that he takes each night will be:

18 - 4t = 6

Collect like terms

4t = 18 - 6

4t = 12

t = 12/4

t = 3

He takes 3 chocolates every night.

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Answer:

In the form y=mx+c it is y=-10/7x-45/7

Step-by-step explanation:

We use the formula y-y1=m(x-x1) where m is the slope given by (y2-y1)/(x2-x1)

m=-5-5/-1-(-8)

m=-10/7(plug it into the formula and simplify)

y-5=-10/7(x-(-8)

y-5=-10/7(x+8){multiply through by 7}

7y-35=-10(x+8)

7y-35=-10x-80 (make y the subject)

7y=-10x-80+35

7y=-10x-45(divide through by 7)

y=-10/7x-45/7