Draw the direction field for the following differential equations, then solve the differential equation. Draw your solution on top of the direction field. Does your solution follow along the arrows on your direction field? 75. y' e' Draw the directional field for the following differential equations. What can you say about the behavior of the solution? Are there equilibria? What stability do these equilibria have? 79. y = y²-1

Answer:

5 x + 4 y = 4 b

Step-by-step explanation:

You haven't specified what form you need. Here is the Standard form, but you can also calculate the Slope intercept form points and the Point-Slope form.

Find the equation of the line in standard form with the properties:

slope: m = -5/4

At least two parameters must be provided to determine a line equation:

Since the line is incompletely determined, compute the equation assuming an arbitrary y-intercept b

Substitute the slope m = -5/4 into the slope-intercept equation y = m x + b:

y = -(5 x)/4 + b

Add (5 x)/4 to both sides:

(5 x)/4 + y = b

Multiply both sides by 4:

4 ((5 x)/4 + y) = 4 b

Distribute: 4 ((5 x)/4 + y) = 5 x + 4 y:

Answer: 5 x + 4 y = 4 b

Answer:

it is an isosceles triangle

so angle c is 50°

and you know the sum of angle of the triangle is 180° so 50° is already given and angle c is also 50° then 50° +50°+b= 180°

then b= 180° -100°

b= 80°

hence angle B is 80°and

angle c is 50°.

Answer:

angle c is 50°

Step-by-step explanation:

Answer:

M = -3/2

C = 1/2

Explanation:

3 x + 2 y − 1 = 0

-> 2y = 1-3x

y=-3/2x+1/2

so M = -3/2 and C = 1/2

Answer:

2320000

Step-by-step explanation

work out the perimeter first 6+4 times 2= 20

20 time 2m high=40

40 times 58000= 2320000

A truth table with 4 rows (one for each combination) and at least 3 columns (one for R, one for B, and one for the statement itself).

The truth table for Statement 1B will have 4 lines.

To see why, we can look at the number of possible combinations of truth values for the variables involved in the statement. In this case, there are two variables: R and B. Each variable can take on one of two truth values (true or false).

So, there are 2 × 2 = 4 possible combinations of truth values for R and B. These are:

R = true, B = true

R = true, B = false

R = false, B = true

R = false, B = false

We need to evaluate the given statement for each of these combinations, which will require us to create a truth table with 4 rows (one for each combination) and at least 3 columns (one for R, one for B, and one for the statement itself).

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Complete Question

Carmen is putting together a business plan for her sandwich restaurant, Subs Away, so she can expand to another location. She wants to include some information about recent sales but only has certain information about last month's sales. She currently offers ham, turkey and vegetarian sandwiches. She sells the ham sandwiches for $10 each and the turkey sandwiches for $11.25.

Last Month's Vegetarian Sales

Total Sandwiches Sold 75

Total Income $712.50

How much does Carmen charge for the vegetarian sandwich?

Answer:

 \(X=9.5\)

Step-by-step explanation:

From the question we are told that:

Total Vegetarian Sandwiches Sold \(T_{vs}=75\)

Total Vegetarian Sandwiches Income \(T_{vi}=$712.50\)

Generally the equation for Cost of vegetarian sandwich is mathematically given by

 \(X=\frac{Total\ income\ from\ vegetarian\ sandwich}{No.\ of\ vegetarian\ sandwich\ sold}\)

 \(X=\frac{T_{vi}}{T_{vs}}\)

 \(X=\frac{712.50}{75}\)

 \(X=\$9.5\)

The integral, ∫ [ (9ˣ - eˣ )/3ˣ ] dx evaluate value is 3ˣ/ ln(3) - eˣ/3ˣ(1 - ln 3). So, the correct answer is option (c).

Integration is defined as the process of finding the area of the region under the curve. This is done by drawing as many small rectangles covering up the area and summing up all their areas. If d/dx(F(x) = f(x), then ∫ f(x) dx = F(x) + C, where C is integration constant and indefinite integrals. We have an integral, say , I = ∫ [ (9ˣ - eˣ )/3ˣ ] dx

and we have to determine its value.

I = ∫ [ (9ˣ - eˣ )/3ˣ ] dx

=> I = ∫ [ (9ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3²ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3²ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3ˣ - eˣ/3ˣ ] dx

=> I = ∫ 3ˣ dx - ∫ eˣ3⁻ˣ dx

=> I = 3ˣ/ ln(3) - eˣ/3ˣ(1 - ln 3) + C

( since, ∫aˣ dx = aˣ/ln a)

where C --> integration constant

So, the required value is 3ˣ/ln(3)-eˣ/3ˣ(1 - ln 3).

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Complete question:

Find integral ∫ [ (9ˣ - eˣ )/3ˣ ] dx .

a) 3ˣ - eˣ/(1 - ln 3) + C

b) 9ˣ/2ln3 - eˣ/(3ˣ ln 3) + C

c) 3ˣ/ln3 - eˣ/3ˣ(1 - ln 3) + C

d) 3ˣ/ln3 - eˣ/3ˣ + C

The side opposite to angle B is AC. The side adjacent to angle B is BC. The hypotenuse is segment AB.

A pair of sides are referred to as neighboring if they have a shared angle. The term "hypotenuse" refers to a right-angled triangle's longest side as compared to the base and perpendicular lengths. The right angle, the largest angle of the three angles in a right triangle, lies opposite the hypotenuse side. In essence, only the right triangle possesses the hypotenuse feature, not any other triangles.

From the figure we observe that the side opposite to angle B is AC.

The angle adjacent to angle B is BC.

The hypotenuse is segment AB.

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Answer:

(65) (64)

Step-by-step explanation:

The solutions to the quadratic equation f(x) = x² + 10x - 1 are x = -5 + √26 and x = -5 - √26

To solve the quadratic equation f(x) = x² + 10x - 1

we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For the given equation, a = 1, b = 10, and c = -1.

Substituting these values into the quadratic formula:

x = (-(10) ± √((10)² - 4(1)(-1))) / (2(1))

= (-10 ± √(100 + 4)) / 2

= (-10 ± √104) / 2

Simplifying further:

x = (-10 ± 2√26) / 2

= -5 ± √26

Therefore, the solutions to the quadratic equation f(x) = x² + 10x - 1 are:

x = -5 + √26 and x = -5 - √26

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Answer:

54

Step-by-step explanation:

The square in the middle = 36, as 6x6=36

There are 2 triangles on each side of the center square.

Since the base of the trapezoid is 12, and the base of the square is 6, that leaves 3 for the base of each triangle.

3x6=18x1/2 (As a triangle's area is b (base) x h (height) x (one half) 1/2

18x1/2 is 9.

Each triangle equals 9.

36+9+9=54

The final answer is 54

Answer:

3b/2 + 3

Step-by-step explanation:

The formula to calculate perimeter of rectangle is 2l + 2w

The length is half the width so length is 1/2 (b/2 +1), which when simplified is b/4 + 1/2

Using the formula to calculate perimeter you can substitute and calculate

p= 2l + 2w

p= 2(b/4 + 1/2) + 2(b/2 + 1)

p= 2b/4 +2/2 + 2b/2 +2

p= 1/2b + 1 + b + 2

p= 3/2b + 3

Simplified it's 3b/2 +3

Answer:

Step-by-step explanation:

By Pythagoras' Theorem, a² + b² = c².

Substituting the values of a and b, we get:

7² + 25² = c²

49 + 625 = c²

c² = 674

c ≈ 26.0 (to 1 d.p.)

Answer:

35$

Step-by-step explanation:

It will take 10 years and 11 months to payoff the balance. The total interest is $2,574.43

Answer:

i think it is proportional

Step-by-step explanation:

because because for both sides they're adding a specific number like from 5 to 8 you add 3 so for 1.5 to 2.5 your adding .5

The height of the prism whose volume is 600cm^3 is 10 cm

What is the Volume of a prism?

The total area that a prism takes up in three dimensions is known as its volume. It is defined mathematically as the result of the base's area and length.

Therefore,

Prism volume is equal to Base Area x Length.

Cubic units are the unit of measurement used to indicate a three-dimensional object's volume.

A triangular prism's volume

A triangular prism is a prism that has three rectangular sides and two triangle bases. The formula for a triangular prism's volume is as follows since the cross-section of a triangular prism is a triangle:

The volume of a Triangular Prism = (½) abh cubic units.

Where

a is a triangular prism's apothem length.

b is the triangular prism's base length.

h is a triangular prism's height.

The volume of a triangular prism is area x length

Volume = 600cm^3

base =6cm

length = 20cm

height=?

The area of the triangle is 1/2 x base x height = 3 x height

volume = area x length

volume= 3 x height x 20

600 = 60 x height

height = 10 cm

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Answer:

equilateral

Step-by-step explanation:

A shape is equilateral if all the sides are the same length. In geometry class, people learn about many shapes, such as triangles and squares. A square is equilateral, because all of its sides are the same length. ... The word equal should help you remember what equilateral means.

Answer:

An isosceles triangle has 2 sides of equal length . The dashes on the lines show they are equal in length. The angles at the base of the equal sides are equal.An equailateral triangle has 3 sides of equal length.

The Maximum Likelihood Estimator (MLE) for θ in the given probability density function is θ ^ MLE = - (1/n) * ∑(i=1 to n) ln(Yi).

To find the Maximum Likelihood Estimator (MLE) for θ in the given probability density function f(y∣θ), we maximize the likelihood function. The likelihood function is the product of the individual probabilities of observing the given data, assuming the parameter θ.

The likelihood function L(θ) is obtained by substituting the given probability density function f(y∣θ) with the observed data. Taking the logarithm of the likelihood function (ln L(θ)) simplifies the calculations.

To maximize ln L(θ), we take the derivative with respect to θ and set it equal to zero. However, in this case, we can simplify the process by directly taking the logarithm of the given probability density function f(y∣θ) and finding the θ that maximizes it.

By taking the logarithm of f(y∣θ), we get ln f(y∣θ) = ln(θ^y * (1 - θ)^(1 - y)/θ) = y * ln(θ) + (1 - y) * ln(1 - θ) - ln(θ).

Now, the MLE for θ is the value that maximizes ln L(θ), which is equivalent to maximizing ln f(y∣θ). To find this value, we differentiate ln f(y∣θ) with respect to θ and set it equal to zero.

d/dθ (ln f(y∣θ)) = (y/θ) - (1 - y)/(1 - θ) - 1/θ.

Setting the derivative equal to zero and solving for θ gives θ = y, which is the MLE for θ.

Therefore, the Maximum Likelihood Estimator (MLE) for θ in this case is θ ^ MLE = - (1/n) * ∑(i=1 to n) ln(Yi), where n is the sample size and Yi is the observed value.

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Answer: x=-3ab/2+ac

Step-by-step explanation:

Multiply to remove the fraction, then set equal to 0 and solve.

Turning of head is rooting reflex.

Reflex is defined as the action which is performed without thought. In other words, it is an unconscious behaviour or involuntary movement. Newborns have different reflexes such as rooting reflex, moro reflex, stepping reflex, tonic neck reflex and grasp reflex.

Rooting reflex acts on touch. Based on this, babies feed themself. They start sucking when the roof of their mouth is touched. Moro reflex occurs on sudden sound or movement of high intensity. Tonic neck reflex results in fencing position of baby. Grasp reflex is seen when baby closes their fingers and stepping reflex concerns legs.

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The greatest amount of gold that can be in the vault is 0 ounces.

To find the greatest amount of gold that can be in the vault, we need to determine the maximum number of 8 ounce tablets that can be stored.

If the total weight of gold and silver is 130 ounces, we can subtract the weight of the silver from the total to get the weight of gold.

Since each silver tablet weighs 5 ounces, the weight of silver can be found by dividing the total weight by 5.

130 ounces ÷ 5 ounces = 26 tablets of silver

Now, to find the maximum number of 8 ounce tablets that can be stored, we divide the weight of gold by 8.

130 ounces - (26 tablets × 5 ounces) = 130 ounces - 130 ounces = 0 ounces of gold

Therefore, the greatest amount of gold that can be in the vault is 0 ounces.

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The statement "a quadrilateral is a square if and only if it is a rectangle" made by Ruby is a true biconditional statement in mathematical terms.

A quadrilateral is a four-sided shape that can have different properties based on its sides and angles.

Ruby says that a quadrilateral is a square if and only if it is a rectangle. This statement can be written as:

(Q is a square) if and only if (Q is a rectangle)

To understand if this statement is a true biconditional statement, we need to examine the definition of a square and a rectangle and how they relate to each other.

A square is a type of quadrilateral where all four sides are equal in length and all four angles are equal (90 degrees). In other words, a square is a rectangle that has four equal sides.

A rectangle is a type of quadrilateral where all four angles are equal to 90 degrees. This means that the opposite sides are parallel and equal in length.

Based on the definitions, we can conclude that the statement "a quadrilateral is a square if and only if it is a rectangle" is a true biconditional statement.

This means that if a quadrilateral is a square, it is also a rectangle and vice versa. If a quadrilateral is not a square, it cannot be a rectangle.

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Answer:

Step-by-step explanation:

Since,

It's a rectangle so it will be formed on the coordinate which is 3units above dot(3,5) in picture where above the dot there is no point .

Answer:

The answer is six eighths

There's 8 letters in all and 6 of them are consonants (M, T, H, C, L, B)

Step-by-step explanation:

so all you have to do is take out all the vowel and count the letters that are consonant then you make that your top number than you put that over the amount of numbers in total

Answer:

x = 36

Step-by-step explanation:

f(x) = 2x + 10 is the equation in function notation given that an equation for measuring height of a balloon versus time is h=2t+10, where the variables h and t represents height and time respectively. This can be obtained by understanding what function notation is.

Here is an example of function notation and its meaning,

⇒ f(x) = x²

the name of the function is f, the input variable is x, the formula is x²

We can evaluate this function for a particular value of x

Here in the question it is given that,

We have to find the equation in function notation.

Let the name of the function be f, the input variable be x and the given formula will be 2x + 10.

Then the function notation can be written as,

f(x) = 2x + 10

Hence f(x) = 2x + 10 is the equation in function notation given that an equation for measuring height of a balloon versus time is h=2t+10, where the variables h and t represents height and time respectively.

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Answer:

So 4 sets means 10 x 4=40

40 cupcakes in all

24 x 1=24 cupacakese aten.

40-24= 16

So 16 cupcakes left which i want to eat....:)

Step-by-step explanation:

-2(7 + y)2 -8(y + 1)​

Simplify :)

−12y−36

Answer:

There should be about 612 girls

Step-by-step explanation:

350 divided by 4 = 87.5

87.5 x 7 = 612.5

round 612.5 down, which gets 612