From first to last, when did the presidents serve?
Drag the presidents' names into the correct order according to when they served.

The proof that Line GH ≅ Line EH is given as follows:

Given that
∠A ≅ ∠B;

⇒ AC ≅ BC (sides opposite to equal angles)

⇒ AD + DC ≅ BF + FC (sum of congruent line segments)

⇒ Since Line AG ≅ Line EB; (Given) and

DC ≅ FC; (Given)

thus,  Line GH ≅ Line EH.

A mathematical proof is inferential reasoning for a mathematical assertion that demonstrates that the provided assumptions logically ensure the conclusion.

Other previously established claims, such as theorems, may be included in the argument; nonetheless, any proof may, in theory, be formed using just some fundamental or original hypotheses known as axioms, along with the recognized rules of inference.

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Answer:

Between 6 and 7

Step-by-step explanation:

6^2 = 6 × 6 = 36

7^2 = 7 × 7 = 49

45 is between 36 and 49

Answer:

4x^2-9x+7+\frac{x-2}{x^2+x+1}

Step-by-step explanation:

Here is a hopefully helpful answer! :)

the area of the right-angled triangle with adjacent and opposite sides of 2 units is 2 square units.

what is right-angled triangle  ?

A right-angled triangle is a type of triangle that has one angle measuring exactly 90 degrees (a right angle). This angle is formed by the intersection of two sides of the triangle, which are called the legs or catheti, and it is opposite to the longest side of the triangle, which is called the hypotenuse. The hypotenuse is always opposite the right angle.

In the given question,

The area of a right-angled triangle is given by the formula:

Area = 1/2 x base x height

where the base and height are the two perpendicular sides of the triangle.

In this case, the adjacent side and opposite side of the right-angled triangle are both 2 units.

Let's call the hypotenuse of the triangle 'c'. Then, by the Pythagorean theorem, we have:

c² = 2² + 2²

c² = 8

c = √(8) = 2.8284 (rounded to 4 decimal places)

Now, we can use the trigonometric ratios to find the base and height of the triangle. In this case, we can use the tangent ratio:

tan(theta) = opposite/adjacent

tan(theta) = 2/2

tan(theta) = 1

theta = tan⁻¹(1) = 45 degrees

Therefore, the base and height of the triangle are:

base = adjacent x tan(theta) = 2 x tan(45) = 2 x 1 = 2

height = opposite x tan(theta) = 2 x tan(45) = 2 x 1 = 2

Now we can use the area formula to find the area of the triangle:

Area = 1/2 x base x height

Area = 1/2 x 2 x 2

Area = 2 square units

Therefore, the area of the right-angled triangle with adjacent and opposite sides of 2 units is 2 square units.

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Answer:

6,435

Step-by-step explanation:

The number of different committees that can be chosen can be calculated using the combination formula, also known as "n choose k," which calculates the number of ways to choose k items from a set of n items without regard to the order.

In this case, the principal wants to assemble a committee of 7 students from a student council of 15 members. Therefore, the number of different committees that can be chosen is given by the formula:

C(15, 7) = 15! / (7! * (15-7)!)

Calculating this expression gives:

C(15, 7) = 15! / (7! * 8!)

Simplifying further:

C(15, 7) = (15 * 14 * 13 * 12 * 11 * 10 * 9) / (7 * 6 * 5 * 4 * 3 * 2 * 1)

C(15, 7) = 6435

Therefore, there are 6,435 different committees that can be chosen from the 15-member student council.

By making x the subject of the formula in this equation u = cos(0.5x)​ gives x = 2cos⁻¹(u).

In Mathematics and Geometry, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal. This ultimately implies that, an equation is composed of two (2) expressions that are connected by an equal sign.

In this exercise, you are required to make "x" the subject of the formula in the given mathematical equation by using the following steps.

By taking the arc cosine of both sides of the equation, we have the following:

u = cos(0.5x)

cos⁻¹(u) = 0.5x

By multiplying both sides of the mathematical equation by 2, we have the following:

2 × cos⁻¹(u) = 0.5x × 2

x = 2cos⁻¹(u)

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Answer:

yes we need to as it helps with math stuff later on

Step-by-step explanation:

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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The result suggests that the mean wake time might have really reduced since the values barely fall above 100 min as in before treatment with a high degree of confidence. thus , the drug is effective.

Confidence interval is written in the form as;

(Sample mean - margin of error, sample mean + margin of error)

The sample mean represent x , it is the point estimate for the population mean.

Margin of error = z × s/√n

Where s = sample standard deviation = 21.8

n = number of samples = 17

Now the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

then the degree of freedom, df for the sample.

df = n - 1 = 17 - 1 = 16

Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01

α/2 = 0.01/2 = 0.005

Therefore the area to the right of z0.005 is 0.005 and the area to the left of z0.005 is 1 - 0.005 = 0.995

the t distribution table, z = 2.921

Margin of error = 2.921 × 21.8/√17

= 15.44

The confidence interval for the mean wake time for a population with drug treatments will be; 90.3 ± 15.44

The upper limit is 90.3 + 15.44 = 105.74 mins

The lower limit is 90.3 - 15.44 = 74.86 mins

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The roots of the function F(x) = x³ + 2x² + 4x + 8 are given as follows:

B. 1 real root and 2 complex roots.

The function in this problem is defined as follows:

F(x) = x³ + 2x² + 4x + 8.

The function is of the third degree, hence the total number of zeros of the function is of 3.

From the graph, the function has only one x-intercept, which is given as follows:

x = -2.

Hence the two remaining roots are the complex roots, meaning that option B is the correct option for this problem.

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Angles in a triangle add up to 180 degrees

The value of x is 85 degrees

A triangle is a polygon which has  three sides and three vertices. It is one of the normal shapes in geometry. A triangle with vertices A, B, and C has three sides & three angles A, B, C.

here, we have,

How to determine the value of x

The total  sum of angles for a triangle is 180 degrees.

So, we have:

x + 35 + 60 = 180

Evaluate the sum

x + 95= 180

Subtract 95 from both sides

x = 85

Hence, the value of x is 85 degrees

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Full question: (SAT Prep) Find the value of x. 35° 60° X

x=?​

Answer:

x = 2

Step-by-step explanation:

8 = 6x + -2x

8 = 4x

8 = 4x

4 4

2 = x

Let’s solve the equation x^2 - 4x = 5 by factoring:

First, we’ll move all the terms to one side of the equation:

x^2 - 4x - 5 = 0

Now, we’ll factor the left side of the equation. We’re looking for two numbers that multiply to -5 and add to -4. Those numbers are -5 and 1. So we can write:

(x - 5) (x + 1) = 0

Now we’ll use the zero-product property to solve for x. This property states that if the product of two numbers is zero, then at least one of the numbers must be zero. So we have:

x - 5 = 0 or x + 1 = 0

Solving each equation separately, we find that x = 5 or x = -1.

So, the solutions to the equation x^2 - 4x = 5 are x = 5 and x = -1.

Answer:

=================

Let the numbers be x and y.

Answer: 4 hours and 24 minutes

Step-by-step explanation:

Answer:

---------------------------------------

Let the cost of the meal be x.

Adding a tip of 19%:

Answer:

Wyatt should multiply with 1.19.

Step-by-step explanation:

Forming the expression,

→ 1 + (19% of 1)

Now the required number is,

→ 1 + (19% of 1)

→ 1 + ((19/100) × 1)

→ 1 + (19/100)

→ 1 + 0.19 = 1.19

Hence, required number is 1.19.

Answer:

9x , 9x- 16/3

Step-by-step explanation:

f(g(x))=f(x+6/9)=9*(x+6/9)-6= 9x+6-6=9x

g(f(x))=g(9x-6)= 9x-6+6/9=9x-48/9

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) We have drawn the graph.

c) The maximum number of machines that can be installed is 11.

d) The maximum profit is 2,500,000.

What is inequality?

An inequality is a mathematical statement that shows the relationship between two values where one value is either greater than or less than the other value. It is represented by symbols such as >, <, ≥, or ≤. For example, if x is a variable and we want to express that x is greater than 5, the inequality would be written as x > 5.

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) To graph the region, we can plot the lines that define the inequalities and shade the area that satisfies all of them.

c) Solving the system of inequalities graphically, we find the maximum number of machines that can be installed is 11 (6 small and 5 large).

d) To find the maximum profit, we need to substitute the number of machines into the profit equation. P = 250,000X + 300,000Y. Plugging in X = 6 and Y = 5, we find the maximum profit to be 2,500,000.

Hence,

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) We have drawn the graph.

c) The maximum number of machines that can be installed is 11.

d) The maximum profit is 2,500,000.

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Answer:

m=-3

Step-by-step explanation:

the answer would be x = 14

Answer:

4.9

Step-by-step explanation:

We can use the following equation to solve

\( {5}^{2} + {x}^{2} = {7}^{2} \)

Reduce

\( {x}^{2} = 24\)

\(x = \sqrt{24} \)

or 4.9

Answer:

B

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

c ≤ 4

Interval Notation:

( − ∞ , 4]

Answer:

The first one and the last one.  A and D.

Step-by-step explanation:

A linear equation is and equation where the line is going up on a graph.  In order for that to happen, y must always be bigger than x.  The first and last chart all the way to the right is the only one that has that trait.  :)

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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The smaller of two similar balloons has a diameter of 10 inches. If it takes 12 (same sized) breaths to blow up the smaller balloon and 40.5 to blow up the larger, what is the diameter of the larger balloon?​

we have that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube.

so

Find the scale factor

ratio volumes=40.5/12=3.375

3.375=(scale factor)^3

scale factor=1.5

To find out the diameter of the larger balloon multiply the scale factor by the diameter of the smaller balloon

so

1.5*(10)=15 inches

Considering the given proportion, the value of \(\frac{a}{a - b}\) is:

C) 2

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The proportion between a and b is given by:

a/b = 2.

Then:

a = 2b.

The expression is:

\(\frac{a}{a - b} = \frac{2b}{2b - b} = \frac{2b}{b} = 2\)

Hence option C is correct.

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9514 1404 393

Answer:

  34.88 feet

Step-by-step explanation:

The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

We want to find the length of the side adjacent to the measured angle. The hypotenuse is the ladder length.

  cos(29.32°) = distance/(40 ft)

  distance = (40 ft)cos(29.32°) ≈ 34.876°

The base of the ladder is about 34.88 feet from the building.

_____

Additional comment

It extends about 19.59 feet up the side of the building.

Answer:

Let x be the number of additional outfits.

5 + x < 11

Answer:

Hold a sec I got this