MATHEMATICS COLLEGE

(2x - y + 3) (2x - y - 3)using identities

Answers

Answer 1

Answer:

Step-by-step explanation:

(2x-y+3)(2x-y-3)=

4x²-2xy-6x-2xy+y²+3y+6x-3y-9=

4x²-4xy+y²-9=

(2x-y)²-9

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In which quadrant of the coordinate plane is the point (−4,1) located

Answers

Answer:

Quadrant II

Step-by-step explanation:

Below will be a picture provided to show you which quadrants are in a coordinate grid.

To graph (-4, 1) we will start at the origin, go 4 units to the left and 1 unit up.

As you can see in the image, it will be plotted in quadrant 2.

Best of Luck!

Answer:

quadrant II or 2

Step-by-step explanation:

I'm not sure if your teacher wants in Roman Numerals or not.

in quadrant II/2 x is negative (on the left side of the y-axis) and y is positive (above the x-axis)

Tasia’s bank account balance was -$25.64. She deposited a check into her bank account and her new balance is $152.29. How much was the check that Tasia deposited into her account?

Answers

Answer:

$177.93

Step-by-step explanation:

Answer:

The check is 177.93$

Step-by-step explanation:

I did 25.64+152.29= 177.93

U can check it by doing -25.64+177.93

Find the surface area and volume of a rectangular solid with length 10, width 7, height 12surface area______square inches
volume_____cubic inches

Answers

Answer:

Surface area is =548

Volume = 840 in³

Step-by-step explanation:

l × w, l × w, w × h, w × h, l × h, l × h

70 + 70 + 84 + 84 + 120 + 120 = 548

l × w × h = 840

The volume of a sphere is 5000 pi m^3 what’s the surface area of the sphere

Answers

Volume of sphere is given by:
V=4/3πr³
the radius of the sphere will therefore be given by:
5000π=4/3πr³
solving for r we get:
r³=3750
hence
r=15.54 m
the area will therefore be:
A=4πr²
A=4π(15.54)²A=965.49π m²

Answer:

3,033.11 m²

Step-by-step explanation:

V=3/4πr³

5,000π= 4/3 πr³

5,000= 4/3 r³

3/4 x 5,000 = r³

3,750 = r³

r = 15.536

SA = 4πr²

SA = 4π(15.536)²

SA = 3,033.11 m²

Use the method of variation of parameters to find a particular solution of the given differential equation. Then check your answer by using the method of undetermined coefficients.y'' − y' − 2y = 5e−t

Answers

Answer:

y = C₂ e²ᵗ + e⁻ᵗ [C₁ - (5t/3)]

Step-by-step explanation:

y" - y' - 2y = 5e⁻ᵗ

The total solution of this differential equation will be a sum of its complimentary and particular solutions.

y = y꜀ + yₚ

The complimentary or homogenous solution is a solution of

y" - y' - 2y = 0

y꜀ = Ay₁ + By₂

Solving this part in the attached image, we obtain

y₁ = e⁻ᵗ and y₂ = e²ᵗ

The particular solution can be obtained using the method of variation of parameters and the method of undetermined coefficients.

The method of variation of parameters is used and explained in the page 1, 2 and page 3 of the attached images.

The method of undetermined coefficients is then used to check if the solution obtained is correct.

With y = C₂ e²ᵗ + e⁻ᵗ [C₁ - (5t/3)],

y' and y'' were obtained and put in the equation, and the answer obtained was 5e⁻ᵗ.

So, Proved!

y = C₂ e²ᵗ + e⁻ᵗ [C₁ - (5t/3)]

Hope this helps!!!

Some parts of California are particularly earthquake- prone. Suppose that in one metropolitan area, 25% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random; let X denote the number among the four who have earthquake insurance. a. Find the probability distribution of X. [Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with proba bility (.25)(.75)(.25)(.25) and associated X value 3. There are 15 other outcomes.] b. Draw the corresponding probability histogram. c. What is the most likely value for X

Answers

Answer:

a. Binomial random variable (n=4, p=0.25)

b. Attached.

c. X=1

Step-by-step explanation:

This can be modeled as a binomial random variable, with parameters n=4 (size of the sample) and p=0.25 (proportion of homeowners that are insured against earthquake damage).

a. The probability that X=k homeowners, from the sample of 4, have eartquake insurance is:

$P(x=k) = \dbinom{n}{k} p^(k)(1-p)^(n-k)\n\n\nP(x=k) = \dbinom{4}{k} 0.25^(0)\cdot0.75^(4)$

The sample space for X is {0,1,2,3,4}

The associated probabilties are:

$P(x=0) = \dbinom{4}{0} p^(0)(1-p)^(4)=1*1*0.3164=0.3164\n\n\nP(x=1) = \dbinom{4}{1} p^(1)(1-p)^(3)=4*0.25*0.4219=0.4219\n\n\nP(x=2) = \dbinom{4}{2} p^(2)(1-p)^(2)=6*0.0625*0.5625=0.2109\n\n\nP(x=3) = \dbinom{4}{3} p^(3)(1-p)^(1)=4*0.0156*0.75=0.0469\n\n\nP(x=4) = \dbinom{4}{4} p^(4)(1-p)^(0)=1*0.0039*1=0.0039\n\n\n$