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Dividing fractions

the given family of functions is the general solution of the differential equation on the indicated interval y=[tex]7/2e^{x} -7/2e^{-x}[/tex]

What is differential equation?

Equations which involves functions and its derivative is known as differential equation. these equations are highly used to model behaviour of complex system.

How to solve?

y(x) = [tex]C_{1} e^{x}+C_{2}e^{-x}[/tex]

y(0) = [tex]C_{1} +C_{2}[/tex]

0 =[tex]C_{1} +C_{2}[/tex]  --------------------------------------------------(1)

y'(x) =   [tex]C_{1}e^{x} -C_{2}e^{-x}[/tex]

y'(0) =  [tex]C_1- C_{2} }[/tex]

7 =  [tex]C_{1}-C_{2}[/tex] -------------------------------------------------(2)

From Equation 1 and 2

[tex]C_{1} +C_{2}[/tex] = 0

[tex]C_{1} -C_{2}[/tex] = 7

[tex]C_{1}[/tex] = 7/2

[tex]C_{2}[/tex] = -7/2

y=[tex]7/2e^{x} -7/2e^{-x}[/tex]

the complete question is

The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y = c1ex + c2e−x, (−∞, ∞); y'' − y = 0, y(0) = 0, y'(0) = 7

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Answer:

y = 1/4x + 1

1/4 is the slope and 1 is the y-intercept

The statements that are true in the lines of construction of the straightedge and compass construction which makes use of congruent circles, are;

Line EF is the perpendicular bisector of segment BD

Line EF is the bisector of angle BAC

Geometric figures are constructed using a compass and a straightedge, by using outlined steps or procedures.

From the diagram, given that the circumference of the circle with center B passes through the center of the circle with center D, and vice versa, we have;

Circle B is congruent to circle D

The steps to construct a perpendicular bisector to the segment BD includes;

Therefore;

The steps to construct the angle bisector of angle BAC

The angle bisector can be constructed by using the following steps

Which gives;

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The body mass index of a person 65 inches tall with a weight of 175 pounds is 29.12

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

The body mass index (BMI) is given by:

BMI = [mass in pounds / (height in inches)²] * 703

Given mass = 175 pounds, height = 65 in, hence:

BMI = [175/65²] * 703 = 29.12

BMI = 29.12

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3 x 5 x 5 x 8 x 10 = 6,000

3 x 5 = 15, 15 x 5 = 75.

8 x 10 = 80.

75 x 80 = 6,000

Use the Pythagorean theorem to solve for c using the lesser two sides.

The answer is A.

From the statement, we know that stack of 30 science flashcards has:

• 10 with insects,

• 8 with trees,

• 8 with flowers,

• 4 with birds.

The probability of selecting a tree or a flower is given by:

4/15

In linear equation, 42 units quizzes will josie have taken in total.

What is a formula for linear equations?

josie took a total = 24 quizzes

the course  =  6 weeks

quizzes will josie have taken = 24/6 = 4

after attending 10 weeks of school this quarter = 10 * 4 = 40 units

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We determine the scale factor by comparing the lengths of corresponding sides of the square.

The length of O’N’=15 and the length of the corresponding segment ON =9.
Then, we compute the scale factor:
O’N’=kON

15=9k

k=15/9=5/3.

The scale factor is k=5/3.

Answer:

60000

Step-by-step explanation:

Answer:

Step-by-step explanation:

6 × [tex]10^{4}[/tex] =

6 × 10000 =

60000

Answer: 3.215 × 10^-7

Step-by-step explanation:

The exponent is smaller than all of the others, so it's the smallest.

Answer:

6kg

Step-by-step explanation:

5 to 30 ratio

1 to 6 ratio

Answer:

30/5=6

6 kg beans for $1

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The amount of Miranda's total monthly expense is  $970.

Basically, an expense refers to any cost of operations that a company incurs to generate revenue. It also means the cost that one is required to spend on obtaining something.

In a typical firm, the common expenses include a payment to suppliers, employee wages, factory leases, equipment depreciation etc.

in the question context, the expenses are:

Total monthly expenses = $60 + $85 + $195 + $55 + $575

Total monthly expenses = $970.

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Answer:

23.8/5.6=4.25

Step-by-step explanation:

Answer:

4.25

Step-by-step explanation:

[tex] \sf \: 23.8 / 5.6 =4.25[/tex]

[tex] \sf----------------------------------[/tex]

Answer:

The farmer had to do 27 loads.

Step-by-step explanation:

Basically the easy way to do this is to grab a calculator (or the paper and pen way) and keep adding 336 until you get to 8914.

Once you add it all you will see there is a remainder of his corn left (that has not been delivered):178

Even though it isn't a full 336, the farmer would still have to make another trip.

336*26=8,736

So, adding the remainder into it's own load, we would get:

27.

Answer:

a)16777216

b)279936

c)32768

d)49

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Answer:

ok!

a) 4^9 ×4^3=4^9+3=4^12

b) 6^5 ×6^2=6^5+2=6^7

c) 8^6 ÷8=8^6-1 =8^5

d) 7^8÷7^6=7^8-6=7^2

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I answered first.

Step-by-step explanation:

It's simple!

If there is multiplication, add the powers.

If there is division, subtract the powers.

The principal amount invested by Shen in the saving bond is $9,000.

As per the given question;

The formula for simple interest is-

SI = PRT/100

Put the values;

SI = PRT/100, write the formula in the terms of P

P = 100×SI/RT

P =  100×1620 / (3×6)

On simplification;

P = 9,000

Thus, the amount invested by Shen in the saving bond is $9,000.

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The rules of exponents which can be used to solve the expression as given in the task content are; Product rule, Negative rule and Quotient rule.

It follows from the task content that the rules which can be used to correctly solve the expression as given in the task content be determined.

Since the expression given is;

10³ * 10-⁷ * 10²

We can therefore have rewrite 10-⁷ using the negative rule so that we have; 1/10⁷.

Also, the product rule can be used on; 10³ * 10² so that we have; 10⁵.

Ultimately, the quotient rule can be used on the resulting expression; 10⁵/10⁷ so that we have; 10-².

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Answer: In simplest form it would be 6 1/40

Step-by-step explanation:

[tex] \frac{241}{40} [/tex]

but in mixed number

[tex]6\frac{1}{4} [/tex]

The solution of the equation b² = 48 is b = 4√3

The equation can be solved as follows;

b² = 48

Therefore, we are to find the value of b in the equation.

The value of b comes with a square sign, so we have to remove the square to make b stand alone in the equation.

By removing the square sign we have to square root both sides.

Hence,

b² = 48

square root both sides of the equation

b² = 48

√b² = √48

Therefore,

b = √16 × 3

b = 4√3

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Answer: the function only intersects the y axis

Step-by-step explanation:

Answer:

The function only intersects the y axis.

Step-by-step explanation:

See the attached worksheet.

The value of Chrissy's height from the problem is 76

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Let x represent Chrissy's height. 55 is the difference of Chrissy's height and 21. Hence:

x - 21 = 55

x = 76

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Answer:

the answer is c

Step-by-step explanation:

1) The rule of transformation is described as; A: A rotation 90° clockwise about the origin

2) The value of x is; 2

3) The value of x is 10

4) The slope of the line is; 2

1) The rule of transformation for When the point M (h, k) is rotated through 90° clockwise about the origin, the point M (h, k) takes the image M' (k, -h). Thus, that is the rule here.

2) From the given image, we can tell that the angles 50° and 26x - 2 are corresponding angles. Thus, they are congruent and we have;

26x - 2 = 50

26x = 52

x = 2

3) From the given image, we can see that the given angles are supplementary and as such they add up to 180 degrees. Thus;

9x + 15 + 6x + 15 = 180

15x + 30 = 180

15x = 150

x = 10

4) Slope is;

m = (y2 - y1)/(x2 - x1)

m = (1 - (-3))/(1 - (-1))

m = 4/2

m = 2

5) Same question as the first one.

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Step-by-step explanation:

x(c - b) = g

divide through by (c - b)

x(c - b) = g

(c - b) (c - b)

x = g/ (c - b)

Answer : 3(x - 5)(x + 5)

example 3(x 2 - 25)

               3x2 - 75

sorry about what happened but I hope this helps have a great day

∠1 and ∠4 are supplementary angle in transversal line .

What is a transversal angle?

1) ∠6 ≅ ∠8   congruent angle.

2) ∠6 = ∠1 and ∠8 = ∠3    are Verical angles.

3) ∠1 and ∠4 are supplementary angle.

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