( a+b) ^2-a^2+b^2
kkkkkkkkkkkkkkk​

Applying the exterior angles theorem, the measure of angle GHI is: 29°.

The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

In other words, if a triangle, for example triangle GHI, has angles G, H, and I, and angle HIJ is the exterior angle formed by extending side GI through point I to point J, then the measure of angle HIJ is equal to the sum of the measures of angles IGH and GHI.

Given the following:

m<IGH = (x+16)°,

m<HIJ = (4x – 12)°,

m<GHI= (x +10)°

Therefore:

m<HIJ = m<IGH + m<GHI

Substitute:

4x - 12 = x + 16 + x + 10

4x - 12 = 2x + 26

4x - 2x = 12 + 26

2x = 38

2x/2 = 38/2

x = 19

m<GHI= (x +10)° = 19 + 10 = 29°

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Given the following 2nd-order differential equation (Cauchy-Euler equation), \(x^2y''+4xy'-4y=0\), find the general solution.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A differential equation in the form \(ax^2y''+bxy'+cy=0\) , which is a Cauchy-Euler equation, can be solved in the following manner.

Where the characteristic equation => \(am^2+(b-a)m+c=0\)

After solving for "m" the possible solutions are...

\(\bold{Real, \ Distinct \ Roots} \Rightarrow y=c_1x^{m_1}+c_2x^{m_2}\\\bold{ Repea ted \ Roots} \Rightarrow y=c_1x^{m}+c_2x^{m}ln(x)\\\bold{Complex \ Roots} \Rightarrow y=c_1x^{\alpha}cos(ln(x^\beta ))+c_2x^{\alpha}sin(ln(x^\beta )); \ m= \alpha \pm \beta i\)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

\(\Longrightarrow x^2y''+4xy'-4y=0 \ where \ a=1, \ b=4, \ and \ c=-4\)

The characteristic equation:

\(\Longrightarrow (1)m^2+(4-1)m+(-4)=0 \Longrightarrow \boxed{m^2+3m-4=0}\)

Solve for "m."

\(\Longrightarrow m^2+3m-4=0 \Longrightarrow (m-1)(m+4)=0 \Longrightarrow \boxed{m=1,-4}\)

Note that m's are distinct and real.

\(Thus, \ \boxed{y=c_1x+c_2x^{-4}} \therefore Sol.\)

Where the arbitrary constants c_1 and c_2 can be solved for given an initial condition.

The correct answer is option (e) \($y = c_1 x + c_2 x^2$\).

We can use the Cauchy-Euler equation to find the general solution of the given differential equation. The Cauchy-Euler equation is given by:

\($a_n x^n y^{(n)}+a_{n-1} x^{n-1} y^{(n-1)}+\cdots+a_1 x y^{\prime}+a_0 y=0$\)

where \($a_n, a_{n-1}, \ldots, a_1, a_0$\) are constants and \($y^{(n)}, y^{(n-1)}, \ldots, y'$\) denote the \($n$\)th, \($(n-1)$\)th, \($\ldots$\), first derivatives of y with respect to x.

In the given differential equation, we have \($a_2 = 1$\), \($a_1 = 4$\), and \($a_0 = -4$\). Therefore, the Cauchy-Euler equation becomes:

\($x^2 y^{\prime \prime}+4 x y^{\prime}-4 y=0$\)

We assume a solution of the form \($y=x^r$\). Substituting this into the differential equation, we get:

\($$x^2 r(r-1) x^{r-2}+4 x r^1 x^{r-1}-4 x^r=0$$\)

Simplifying, we get:

\($$\begin{aligned}& r(r-1)+4 r-4=0 \\& r^2+3 r-4=0 \\& (r+4)(r-1)=0\end{aligned}$$\)

So, we have two roots\($r_1 = -4$\) and \($r_2 = 1$\). Therefore, the general solution of the differential equation is:

\($y=c_1 x^{-4}+c_2 x^1$\)

Thus, the correct answer is option (e) \($y = c_1 x + c_2 x^2$\).

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Answer:

7/10

Step-by-step explanation:

140/200

the zero at the back of 140 will cancel the zero at the back of 200

2 divide 14=7

and 2 divide 20 =10

so;

140/200

=7/10

Solution

For this case we can set up the following equation:

Then the final answer for this case is:

y

Answer:

older than those found in shallower layers of sediment. This is because sedimentary rock layers form over time, with the oldest layers at the bottom and the newest layers at the top. As sedimentary rocks form, they often trap the remains of plants and animals, which then become fossils. The deeper layers have been buried for a longer period of time, so they contain older fossils. This principle is known as the law of superposition and is an important tool for dating fossils and determining the relative ages of different rock layers.

Answer: 1/7

Step-by-step explanation:

7x=1

x=1/7

We are supposed to prove that the first player has a winning strategy for the game of Chomp if the initial board is two squares wide.

Let us assume that the board is of 2 x m size.

Then by using c we will prove that the first player has a winning strategy.

Base Case: If the board is 2 x 1, then the only square left is the bottom left square, so the second player will take it and win the game.

Inductive Hypothesis: Assume that for some positive integer k, whenever we have a board with 2 x m squares, where 1 ≤ m ≤ k, the first player has a winning strategy.

Inductive Step: Now we must prove that the first player has a winning strategy for a board of size 2 x k + 1.

The first move of the first player is to chomp the cookie in the bottom row at the far right. This leaves a board of size 2 x k.

By the inductive hypothesis, the first player has a winning strategy for this board. Therefore, the second player has to make the second move.

He can either chomp a cookie in the bottom row to the left of the chomped cookie or a cookie in the top row. If he chomps a cookie in the bottom row, the first player uses the same strategy as for a board of size 2 x k. If he chomps a cookie in the top row, the first player chomps the corresponding cookie in the bottom row, leaving a board of size 2 x k. By the inductive hypothesis, the first player has a winning strategy for this board.

Therefore, the first player has a winning strategy for a board of size 2 x k + 1 whenever he starts by chomping the cookie in the bottom row at the far right.

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Answer:

-4/3

Step-by-step explanation:

-2 - 1 is -3

6-2 is 4

Answer:

obtuse

Step-by-step explanation:

Since it has an obtuse angle, it is an obtuse triangle.

Answer:

B) Obtuse

Step-by-step explanation:

This triangle is an obtuse triangle because it contains one obtuse angle, which is 126° since that is greater than 90°.

0.5328 is the probability that a patient has total cholesterol between 180 and 190

We have, Mean value, μ = 200 mg/dl

Standard deviation, σ = 20 mg/dl

Let X be the random variable that represents the total cholesterol levels in the population, then the distribution of X is given as follows:

X ~ N(μ, σ^2)Here, X ~ N(200, 20^2)

Now, the probability that a patient has total cholesterol levels between 180 and 190 i.e.,P(180 < X < 190)

Using the Z-score standardization formula,

Z = (X - μ) / σ

Z-score for X = 180,

Z₁ = (180 - 200) / 20 ⇒ -1

Z-score for X = 190,

Z₂ = (190 - 200) / 20 ⇒ -0.5

Therefore, P(180 < X < 190) = P(-1 < Z < -0.5)

Now, we can use a standard normal distribution table to find this probability:

P(-1 < Z < -0.5) = Φ(-0.5) - Φ(-1) ⇒ 0.6915 - 0.1587 = 0.5328 (rounded to 4 decimal places)

Therefore, the probability that a patient has total cholesterol levels between 180 and 190 is 0.5328 (rounded to 4 decimal places).

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The calculated value of the composite function is (f * g)(x) = sin(x)cos(x)

From the question, we have the following parameters that can be used in our computation:

f(x) = sin(x) and g(x) = cos(x)

The composite function (f * g)(x) is calculated as

(f * g)(x) = f(x) * g(x)

So, we have

(f * g)(x) = sin(x) * cos(x)

Evaluate the products

(f * g)(x) = sin(x)cos(x)

Hence, the solution is (f * g)(x) = sin(x)cos(x)

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Question

Let f(x) = sin(x) and g(x) = cos(x)

Find (f * g) directly using the definition of convolution:

\(f * g(x) = \frac{1}{2 \pi} \int_{-\pi}^{\pi} f(x-y) g(y) d y \]\)

Answer:

1. Take the number after the rise and divide it by 1.02.

2. 52/1.3

3. 135 *1.1

4. 37.40*1.45

Step-by-step explanation:

Answer:

35 pounds of tea for 80 cents.

Step-by-step explanation:

Equation::

value + value = value

80x + 60(50-x) = 74*50  

80x + 60*50 - 60x = 74*50  

20x = 14*50

x = 35 lbs (amt. of 80 cent tea to use)

50-x = 15 lbs (amt. of 60 cent tean to use)

Answer:

35 pounds of tea for 80 cents.

15 pounds of tea for 60 cents.

Step-by-step explanation:

x · 80 + y · 60 = 50 · 74

x + y = 50 · (- 60)

80x + 60y= 50 · 74

- 60x - 60y = -50 · 60

20x = 50 · (74-60) = 50 · 14

x = 50 · 14/20

35 pounds of tea for 80 cents.

y = 50 - 35 =

15 pounds of tea for 60 cents.

Answer:

−12

Step-by-step explanation:

To solve this expression, we need to use the order of operations. The order of operations is a set of rules that dictate the sequence in which operations should be performed in a mathematical expression. The order of operations is often abbreviated using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Answer:

b = 125

Step-by-step explanation:

Given a varies directly as \(\sqrt[3]{b}\) then the equation relating them is

a = k\(\sqrt[3]{b}\) ← k is the constant of variation

To find k use the condition a = 3 , b = 64 , then

3 = k\(\sqrt[3]{64}\) = 4k ( divide both sides by 4 )

\(\frac{3}{4}\) = k

a = \(\frac{3}{4}\) \(\sqrt[3]{b}\) ← equation of variation

When a = \(\frac{15}{4}\) , then

\(\frac{15}{4}\) = \(\frac{3}{4}\) \(\sqrt[3]{b}\) ( multiply both sides by 4 to clear the fractions )

15 = 3\(\sqrt[3]{b}\) ( divide both sides by 3 )

5 = \(\sqrt[3]{b}\) , then

b = 5³ = 125

The surface area of the figure is equal to 641.1 square inches.

The figure comprises of a smaller and a bigger cone, the sum of their surface area is the surface area of the figure.

Surface area of cone = πr[r + √(h² + r²)]

surface area of smaller cone = 22/7 × 6in[6in + √(8² + 6²)]

surface area of smaller cone = 301.7 square inches

Height of the bigger cone = √(12² - 6²) = 10.4in

surface area of bigger cone = 22/7 × 6in[6in + √(10.4² + 6²)]

surface area of bigger cone = 339.4 square inches

surface area of the shape = 301.7 + 339.4

surface area of the shape = 641.1 square inches.

Therefore, the surface area of the figure is equal to 641.1 square inches.

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Answer:

y = -12/(4d - 7d)

Step-by-step explanation:

Step 1: Write equation

4dy + 12 = 7dy

Step 2: Solve for y

Subtract 7dy on both sides: 4dy + 12 - 7dy = 0

Subtract 12 on both sides: 4dy - 7dy = -12

Factor out y: y(4d - 7d) = -12

Divide both sides by 4d - 7d: y = -12/(4d - 7d)

Hello! :)

First thing you do is add -7dy to both sides

4dy + 12 + -7dy = 7dy + -7dy

-3dy + 12 = 0

Next you will have to add -12 to both sides

-3dy + 12 + -12 = 0 + -12

-3dy = -12

Last thing you have to do is divide both sides by -3d

-3dy/-3d = -12/-3d

y = 4/d (ANSWER)

The measurement of angle DBC is equal to 33°, here we have to know the meaning of angle.

Angle is the measurement distance between two straight line or ray when they meet and it can also say that their one part is opening and other part is joint.

We have given that, ∠ABD = 4x, ∠DBC = 3x and measure of angle ABC is equal to 77°.

So ∠ABD + ∠DBC = ∠ ABC

⇒  4x + 3x = 77°

⇒ 7x = 77°

⇒ x = 11°

So, ∠ ABD = 4x = 4 * 11 = 44°

and, ∠DBC = 3x = 3 * 11 = 33°

Therefore, angle DBC is equal to 33°.

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Complete Question:

What is the measure of angle DBC if the measure of angle ABD is represented by 4x, the measure of angle DBC is represented by 3x and the measure of angle ABC is 77° ?

Answer:

12

Step-by-step explanation:

bruh i searched it up

Answer:

12

Step-by-step explanation:

As asked by the question, the value of K for a given equation of a line is equal to the slope of the line.

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.

A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).

The value of K for a given line is equal to the slope of the line. Since lines are generally expressed in the form of y = mx +b , where m is the slope of the line and b is the y-intercept of the line. Here , the value of K will be equal to the slope m of the line.

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Answer: x = {41,42,43...}

Step-by-step explanation:

0.25x - 4 > 6

0.25x > 6 + 4

0.25x > 10

x > 10/0.25

x > 40

The possible values of x are {41,42,43...}

Answer:

11

Step-by-step explanation:

Plug in the variable into the equation. 7+4=11

Answer:

11

Step-by-step explanation:

a is 7 so 7 + 4 = 11

this should be the answer if not i dont know. sorry

Answer:

The cylinder is better to buy because it can hold more.

Step-by-step explanation:

If the heights of a cone and a cylinder are equal, then the volume of the cylinder is three times as much as the volume of a cone. Cylinder has a greater volume.

Example:

let's say you have a container. one shaped as a cylinder and one as a cone. both of them have a height of 1. Which one do you think will hold more?

the cylinder will hold more because of its shape and volume.

I hope this helps

hang in there ;)

To solve the given linear programming (LP) problem using the graphical LP approach, we will plot the feasible region, identify the corner points, and determine the optimal solution.

Here are the steps:

Step 1: Plot the constraints:

- Plot the line 5x + y = 32, which represents the constraint 5x + y ≤ 32. To do this, find two points that lie on this line by assigning values to x and solving for y. For example, when x = 0, y = 32, and when x = 6, y = 2. Connect these points to draw the line.

- Plot the line x + 3y = 12, representing the constraint x + 3y ≥ 12. Again, find two points on this line and connect them. For instance, when x = 0, y = 4, and when x = 12, y = 0.

- Draw the lines representing x = 20 and y = 20 as vertical and horizontal lines passing through x = 20 and y = 20, respectively.

Step 2: Identify the feasible region:

- Shade the area that satisfies all the constraints. The feasible region is the intersection of the shaded regions.

Step 3: Identify the corner points:

- Find the coordinates of the corner points of the feasible region. These points are the intersections of the lines representing the constraints.

Step 4: Evaluate the objective function:

- Calculate the objective function Z = 3x + 12y for each corner point.

Step 5: Determine the optimal solution:

- Identify the corner point that gives the minimum value of the objective function Z. This point corresponds to the optimal solution of the LP problem.

Once you have completed these steps, you will have the complete solution to the LP problem using the graphical LP approach.

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Answer:

20,30

Step-by-step explanation:

multiply by the factor for each one to get  a bigger picture

Answer:

4 box: 9

5 box:4.5

6 box: 27

Step-by-step explanation:

Do 3/.5= 6 so multiply the numbers by 6

1.5•6=9

4.5•6=27

Hope this helps! ;-)

Answer:

5.6 brainlist plz

Step-by-step explanation:

Answer:

5.6

Step-by-step explanation:

Just take the negative sign out and you have your answer, because you can't have a negative answer as a absolute value.

Hope this helps!!! :D