What do you get if you cross a chicken with a cow?
Yes, I know how these sound.

If [tex]y=x^m[/tex] is a solution to the ODE

[tex]x^2 y'' - 7xy' + 15y = 0[/tex]

then substituting [tex]y[/tex] and its derivatives

[tex]y' = mx^{m-1} \text{ and } y'' = m(m-1)x^{m-2}[/tex]

gives

[tex]m(m-1)x^2x^{m-2} - 7mxx^{m-1} + 15x^m = 0[/tex]

[tex]m(m-1)x^{m} - 7mx^{m} + 15x^m = 0[/tex]

[tex](m(m-1) - 7m + 15)x^{m} = 0[/tex]

We ignore the trivial case of [tex]y=x^m=0[/tex]. Solve for [tex]m[/tex].

[tex]m(m-1) - 7m + 15 = 0[/tex]

[tex]m^2 - 8m + 15 = 0[/tex]

[tex](m - 3) (m - 5) = 0[/tex]

[tex]\implies \boxed{m=3} \text{ or } \boxed{m=5}[/tex]

The equation would use to determine how long he drove each way is 2x - 8 = 60.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given that Lots took one hour to drive from his apartment to Philips arena and back. the return drive took 8 minutes less than the trip to the arena.

Since the return trip took 8 minutes less, the complete equation must be written in minutes.

Here x - 8 represents the time it took to return to Philips Arena.

The total travel time, including both directions, was 60 minutes;

thus, add x and x - 8 and set them both equal to 60.

So 2x - 8 = 60

Therefore, the equation would use to determine how long he drove each way is 2x - 8 = 60.

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Answer:

Line 3

Step-by-step explanation:

Proportional relationship:

• They are straight lines that have a constant slope

• The line must pass through the origin at (0,0)

• The y intercept is zero

The only line passing through the origin at the point (0,0), is Line 3

Total assets is $20,120; total liabilities is $3,384; net worth is $16,7366; total cash inflows is $3,804; and total cash outflows is $3,920.

Total assets = Cash in checking account + Savings account balance + Current value of automobile + Household possessions + Stereo equipment + Home computer + Value of stock investment = $1,340 + $2,770 + $8,020 + $3,510 + $3,320 + $1,160 = $20,120

Total liabilities = Balance of educational loan + Credit card balance = $3,050 + $334 = $3,384

Net worth = Total assets - Total liabilities = $20,120 - $3,384 = $16,736

Cash outflows = Rent for the month + Spending for food + Telephone bill paid for month + Loan pyment + Auto insurance + Payment for electricity  + Lunches/parking at work + Donations + Clothing purchase + Restaurant spending = $1,390 + $1,110 + $85 + $143 + $321 + $189 + $204 + $139 + $223 = $3,804

Cash inflows = Monthly take-home salary = $3,920

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The probability that a hand of five cards chosen at random and without replacement from a standard 52 card deck will have a king of spades, exactly one other king, and exactly two queens = 0.000332

A deck of cards consist of 52 cards in which each 13 cards are from 4 suits: Spades, Hearts, Diamonds and Clubs.

Each suit consist of cards Ace, King, Queen, Jack and other 9 cards.

So in 52 cards there is 4 kings and 4 queens each.

Five cards are selected at random and without replacement.

Five cards from a 52 deck cards can be chosen in 52C5 ways.

A spade king can be chosen in 1C1 way. [ Since there is only one spade king]

Exactly one other king can be chosen in 3C1 ways. [Since now only 3 kings are remaining after choosing 1 spade king]

Exactly 2 queens can be chosen in 4C2 ways.

Now 4 cards are selected out of 5. The remaining 1 card is chosen out in 48C1 ways.

So the probability that the five cards chosen will have a king of spades, exactly one other king, and exactly two queens

                           = (1C1 x 3C1 x 4C2 x 48C1) /52C5 = 18/54145 =0.000332

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The height of the boat floating above the seafloor at high tide is 17.5 feet.

In this question, we have been given a boat which is anchored in the water.

At low tide, the boat is floating 20 feet above the seafloor and is a horizontal distance of 40 feet away from its anchor.

And at high tide, the boat is a horizontal distance of 35 feet away from its anchor.

We need to find the distance the boat floating above the seafloor at high tide.

Consider the following diagram.

Let the boat floating m feet above the seafloor when the boat is a horizontal distance of 35 feet away from its anchor.

Since both the triangle are similar triangles, the corresponding sides must be in proportion.

⇒ 20/40 = m/35

We need to find the value of m.

⇒ 20 × 35 = m × 40

⇒ m = 35 / 2

⇒ m = 17.5 feet

Therefore, the height of the boat floating above the seafloor at high tide is 17.5 feet.

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Answer:

B. y = -1/4x + 2

Step-by-step explanation:

The slopes of two perpendicular lines are negative reciprocals of each other. So slope is -1/4

Using m = -1/4, y =4, x = -8

y = mx + b

4 = -1/4(-8) + b

4 = 2 + b

b = 2

so y = -1/4x + 2

The solution to the given Inequality is a > 12 and the graph is as attached.

We are given the Inequality as;

8a - 30 > 66

Now, use addition property of equality to add 30 to both sides to get;

8a - 30 + 30 > 66 + 30

8a > 96

Now, use division property of equality to divide both sides by 8 to get;

8a/8 > 96/8

a > 12

The graph of this is as attached.

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Answer:

JGL, LGJ, 2

Step-by-step explanation:

Let

S = 1 + 2 + 3 + … + (n - 2) + (n - 1) + n

Reversing the order of terms, we have

S = n + (n - 1) + (n - 2) + … + 3 + 2 + 1

and we observe that terms in the same position on the right side add up to n + 1.

2S = (1 + n) + (2 + (n - 1)) + (3 + (n - 2)) + … + (n + 1)

There are n terms in the sum, so each the right side is simply n copies of n + 1, and

2S = n (n + 1)

S = n (n + 1)/2

Now,

17 + 18 + 19 + … + 41 + 42 + 43

= (1 + 2 + 3 + … + 41 + 42 + 43) - (1 + 2 + 3 + … + 14 + 15 + 16)

= (S with 43 terms) - (S with 16 terms)

= 43 (43 + 1)/2 - 16 (16 + 1)/2

= 810

hi

so the amount will be increased by  1 + 3/100 = 1.03

so multiply current balance by 1.03 and she will know balance in a year

Answer:

The answer will be

[tex] \frac{1}{4} \times \frac{1}{3} = \frac{1}{12} [/tex]

Or 12%

Answer:

cdf

Step-by-step explanation:

VV Goku uiiuuyujn. b. nnm, 1

Step-by-step explanation:

make a scale drawing of swimming pool where 1 centimeter represents 5 meters

Answer:

C

Step-by-step explanation:

153/56= 207G

Answer:

fsfdsesdfsesd 'jp

Step-by-step explanation:

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Answer:

y = 2x - 2

Step-by-step explanation:

y = 2x + 2

4 = 2(3) + c

4 = 6 + c

c = -2

y = 2x - 2

The line is parallel so slope remains same but intercept changes.

Answer:

-4/7, 1/19, 7/4

Step-by-step explanation:

-4/7 is less then zero, and the only negative number so it is first

1/19 is the second lowest

7/4 is the highest because it is the only one that is greater then 1. (simplified, 7/4= 1 3/4)

Answer:

25x^2 -9

Step-by-step explanation:

(5x+3)(5x-3)

FOIL

first  5x*5x = 25x^2

outer 5x*-3 = -15x

inner 3*5x = 15x

last = 3*-3 = -9

Add them together  25x^2 -15x+15x -9

Combine terms  25x^2 -9

Answer:

[tex] \sf25 {x}^{2} - 9[/tex]

Step-by-step explanation:

We can use Foil method to find the answer for this expression.

(5x + 3) (5x - 3)

That is:

F --> First ---> (5x)(5x)

O --> Outside ---> (5x) (-3)

I --> Inside ---> (3)(5x)

L --> Last ---> (3) (-3)

And now we have to add those terms together while combining like terms.

[tex] \sf(5x)(5x) + (5x)( - 3) + (3)(5x) + (3)( - 3) \\ \sf25 {x}^{2} - 15x + 15x - 9 \\ \sf25 {x}^{2} - 9[/tex]

The equation for the line that connects the locations is y = 2x + 5.

The slope of a line, commonly known as the gradient, is defined as the value of the steepness or direction of a line in a coordinate plane. Slope can be determined using many ways given the equation of either a line or the coordinates of points on the straight line. . The slope is defined mathematically as "climb overrun" (change in y divided by change in x).

x₁ = 1

y₁ = 7

x₂ = -3

y₂ = -1

To obtain the equation of a line, we must first determine its slope. This is computed as:

m = [y₂ - y₁ ]/[x₂ - x₁]

Substituting the value we get:

m = [(-1) - 7 )/((-3) - 1)]

  = -8/-4

   = 2

The slope of the line = 2.

The line's intercept is:

The slope is the next step toward solving for  a such equation of the line.

A typical linear equation is presented as:

y = mx + c

Let us substitute the slope and intercept values.

y = 2x + 5

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Answer: To the right

Step-by-step explanation:

The negatives on a number line are on the left side and the positives on the right.

Step-by-step explanation: educated guess

The area of the semicircle with the given diameter is 189.97 mm^2

The given parameters are

Diameter, d = 22 mm

The area of the semicircle is calculated as

A = 1/2 * pi * (d/2)^2

So, we have

A = 1/2 * 3.14 * (22/2)^2

Evaluate the expression

A = 189.97 mm^2

Hence, the area of the semicircle with the given diameter is 189.97 mm^2

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Answer: No, for example, 50/2=25, 25 isn't even

Step-by-step explanation:

Answer:

No, it's not

Step-by-step explanation:

when u divide an even number with even number,the ans maybe appear in even as well as odd number also

For e.g:

1. 36/12=3

2. 12/6=2

3. 30/6=5

4. 60/10=6

Answer:

y-intercept : 3

x-intercepts are 1 and 2

Vertex is at (2,-1)

Axis of symmetry is at x = 2

Step-by-step explanation:

See attached graph.

The equation y = x² – 4x + 3 represents a parabola

y-intercept at is at B(0,3); y-intercept is 3

x-intercept points at C(1,0) and D(3,0) so x-intercepts are 1 and 3

The vertex is the lowest point on this parabola (2-1)

Axis of symmetry is a line passing through the vertex and dividing the parabola into two equal halves. This is the vertical line x = 2

Answer:

The absolute value inequality will be |x| ≥ -2.

Step-by-step explanation:

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Step-by-step explanation:

a) 5