Solve the math problem

The Pythagoras theorem is solved and the value of x of the figure is x = 12.80 units

Given data ,

Let the figure be represented as A

Now , let the line segment BC be the middle line which separates the figure into a right triangle and a rectangle

where ΔABC is a right triangle

Now , the measure of AB = 8 units

The measure of BC = 10 units

So , the measure of the hypotenuse AC = x is given by

From the Pythagoras Theorem , The hypotenuse² = base² + height²

AC = √ ( AB )² + ( BC )²

AC = √ ( 10 )² + ( 8 )²

AC = √( 100 + 64 )

AC = √164

So , the value of x = 12.80 units

Hence , the triangle is solved and x = 12.80 units

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Answer: 9/20

Step-by-step explanation:

45/100 ÷ 5/5 = 9/20

To convert 0.45 into a fraction, we can consider it as 45/100. Then to get the simplest form of the fraction, we divide both the numerator and denominator by their greatest common factor which is 5. So, the simplest form of the fraction is 9/20. Therefore Matt ate 9/20 of his birthday cake.

A system of n number of linear equations in n unknowns has an many number of solutions if the coefficients of matrix is unique. The assertion is always accurate. The given statement is always true.

From the question, the given statement is:

A system of n linear equations in n unknowns has an endless number of solutions if the matrix of coefficients is unique. The assertion is always accurate.

The given statement is always true.

Consider the system of equations Ax = b. If A is single, there is no A-inverse. As a result, there is no one approach to solve the system. Then, there are still two options:

We can't tell which condition is right only examining the matrix [A b]. There exists an endless number of solutions if [A b] is equal to A's rank.

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Answer:

Step-by-step explanation:

Q1.

Q2.

The trinomial is incorrect. It should be x² - 8x - 20.

Then the factors are:

Q3.

Sets

Union is the addition of the the elements into one set:

The answer is D 62°

Equation:

4x-2=62

Solving for x:

4x-2+2=62+2

4x=64

4x/4=64/4

x=16

Plug 16 into the equation to see if the answer is correct:

4•16-2=62

4•16=64

64-2=62°

Hope this helped!

The graduated cylinder is most precise in measuring volume.

Precision is the degree to which separate measurements agree with one another. The general rule is that you can estimate one additional digit past the measuring device's smallest division, 100-mL graduated cylinders are read to 1 decimal, and the smallest graduated cylinder will hold the entire volume.

Precision refers to the number of significant figures in a measurement. When measuring liquid volumes, it is critical to read the graduated scale from the lowest point on the curved surface of the liquid, known as the liquid meniscus.

This means that the balance provides the most accurate and detailed measurement of volume compared to the other two devices.

Hence, the graduated cylinder is most precise in measuring volume.

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

Step-by-step explanation:

x = 0

y = -4 (0) + 3

y = 3

(0,3) is a solution.

x-axis is parallel

Answer:

4500 students

Step-by-step explanation:

5000 / 100 = 50

50 x90 = 4500 :D

The solutions to the original equation on the interval [0,2) are:

0.2071, 1.4112

what is trigonometry

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

We can use the trigonometric identity:

cos(a)cos(b)sin(a)sin(b) = (1/4)sin(2a)sin(2b)

Applying this identity, we have:

cos(6x)cos(5x)sin(6x)sin(5x) = (1/4)sin(12x)sin(10x)

So, our equation becomes:

(1/4)sin(12x)sin(10x) = 1

Multiplying both sides by 4, we get:

sin(12x)sin(10x) = 4

Now, let's consider the function f(x) = sin(12x)sin(10x) - 4. We want to find the zeros of this function on the interval [0,2).

Using a graphing calculator or some analysis, we can see that the function has two zeros on this interval, one between x=0 and x=1, and another between x=1 and x=2.

Using numerical methods such as the bisection method or Newton's method, we can approximate the zeros to four decimal places:

The first zero is approximately 0.2071.

The second zero is approximately 1.4112.

Therefore, the solutions to the original equation on the interval [0,2) are:

0.2071, 1.4112.

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Answer:

Step-by-step explanation:

Answer:

 y = 2x-5

Step-by-step explanation:

Lets look for an equation in the standard form of y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

A reference line is given:  y=2x+3.  It has a slope of 2.  Parallel lines have the same slope, so the line we are looking for will also have a slope of 3.  We can therefore wrtite what we know sio far.  The new line will be:

                 y = 2x+b

Any vale of b will produce a line that is parallel to the referenc elien.  But we need a line that goes through a given point of (3,1).  By choosingf the correct value of b, we can force the line therough this point.  The easiest way to find b is to use the known point in the equiation we have thuis far, and solve for b:

y = 2x+b

1 = 2*(3)+b  for (3,1)

b = -5

The equation of a line parallel to y=2x+3 and going through point (3,1) is:

   y = 2x-5

See attached graph.

The center of the circle is located at the point (2, -1), and the radius is equal to 6 units.

The equation of the given circle is in the standard form of the circle equation, (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius. By comparing the given equation with the standard form, we can identify that the center of the circle is at the point (2, -1) since (h, k) = (2, -1). Additionally, the radius can be determined by taking the square root of the value on the right side of the equation, which in this case is 36. Hence, the radius is 6 units.

In this case, the equation (x - 2)² + (y + 1)² = 36 represents a circle with its center at the point (2, -1) and a radius of 6 units. The center of the circle is determined by the values of h and k in the standard form of the circle equation, while the radius is found by taking the square root of the value on the right side of the equation. Knowing the center and radius allows us to visualize and understand the properties of the circle, such as its position in the coordinate plane and the distance from the center to any point on the circle's circumference.

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Since, m and n are prime positive number. Therefore,

               m + n = 18 + 19 =037

The polynomial we are given is rather complicated, so we could use Rational Root Theorem to turn the given polynomial into a degree-2 polynomial. With Rational Root Theorem, x = 1, -1, 2, -2 are all possible rational roots. Upon plugging these roots into the polynomial, x = -2 and x = 1 make the polynomial equal 0 and thus, they are roots that we can factor out.

The polynomial becomes:

(x - 1)(x + 2)(x^2 + (2a - 1)x + 1)

Since we know 1 and -2 are real numbers, we only need to focus on the quadratic.

We should set the discriminant of the quadratic greater than or equal to 0.

(2a - 1)^2 - 4 ≥ 0.

This simplifies to:

a ≥ 3/2

or,

a ≤ - 1/2

This means that the interval (- 1/2 ,3/2) is the "bad" interval. The length of the interval where a can be chosen from is 38 units long, while the bad interval is 2 units long. Therefore, the "good" interval is 36 units long.

36/38 = 18/19

18+ 19 = 037

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Answer: D = 3c-5

Step-by-step explanation:

The first shape shows the input, C, the second one multiplies it by 3, next, it subtracts C by 5, leaving you with D equaling C times three, minus five.
You can simplify this equation into this:

D=3C (multiplied by 3)

Then subtract by 5
D=3C-5

By using the concept of division we can find the number of students assigned per teacher.

In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. It is one of the fundamental operations in mathematics.

Number of teachers=29

Number of students in sixth grade=406

The number of students in assigned for each teacher

=\(\frac{Total number of students}{number of teachers}\)

=\(\frac{406}{29}\)

=14

The number of students assigned per teacher is 14.

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A system having ΔG equal to zero means that the system is at equilibrium at standard conditions. This is option c. In a chemical reaction, ΔG represents the change in Gibbs free energy, which is a measure of the energy available to do work.

When ΔG is equal to zero, it indicates that the system is balanced, with the forward and reverse reactions occurring at the same rate. At equilibrium, the concentrations of reactants and products remain constant over time. For example, consider the reaction A ⇌ B. Initially, if we have more A than B, the forward reaction will be favored until equilibrium is reached. At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of A and B remain constant. In this case, ΔG is zero.

It is important to note that while a ΔG of zero indicates equilibrium, it does not provide information about whether the reaction is spontaneous or nonspontaneous. The spontaneity of a reaction is determined by the sign of ΔG. If ΔG is negative, the reaction is spontaneous, while a positive ΔG indicates a nonspontaneous reaction.

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The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

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Answer:

22cm

Step-by-step explanation:

Circumference of a circle = 2πr

π = 22/7

r = 3.5

Circumference of a circle = 2 × (22/7) × 3.5

Circumference of a circle = 22cm.

Answer:

910.5

Step-by-step explanation:

Since median is the middle number and there are two of them remaining. You take those two remaining numbers add them then you divide by two.

=1821

=1821÷2

=910.5

Answer:

925

Step-by-step explanation:

You arrange the numbers from the smallest to the largest.

856,894,899,909,912,916,923,927,943,946,958,973,975,998.

Eliminate a number from the starting point and consecutively eliminate from the last point. Do this continuously.

You will be left with 923 and 927.

Add the two numbers then divide by 2.

The two schools will have an equal number of students enrolled in 21 years (3150 + 75(21) = 2475 + 60(21)).

The solution involves applying algebraic equation to find the unknown value.

The two high schools, Lincoln High School and Desert Mountain High School, have 3150 and 2475 students enrolled, respectively. Lincoln High School is estimating a decrease in enrollment at an average of 75 students per year. Meanwhile, Desert Mountain High School is expecting an increase of 60 students per year.

At these projected rates, the schools will have an equal number of students enrolled in 21 years.

To calculate the number of years that the two schools will have an equal number of students enrolled, you can use the formula:

L + 75x = D + 60x

Where L is the initial enrollment of Lincoln High School, D is the initial enrollment of Desert Mountain High School, and x is the number of years.

Substituting the given values, we get:

3150 + 75x = 2475 + 60x

Solving for x, we get:

15x = 675

x = 45

Therefore, the two schools will have an equal number of students enrolled in 21 years (3150 + 75(21) = 2475 + 60(21)).

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Let d be the distance from the diagonals' intersection and the larger side, so the distance from this point to the smaller side is d + 4 cm. Then d is half of the rectangle's shorter side (call it x), and d + 4 cm is half of the longer side (call it y).

The perimeter of the rectangle is 56 cm, which means

2x + 2y = 56 cm

or

x + y = 28 cm

In terms of d, this becomes

2d + 2 (d + 4 cm) = 28 cm

Solve for d :

2d + 2d + 8 cm = 28 cm

4d = 20 cm

d = 5 cm

Then the sides of the rectangle have length

x = 2d = 10 cm

y = 2 (d + 4 cm) = 2 (13 cm) = 26 cm

x=1

Step-by-step explanation:

f(x)=0 is basically the x-axis. the line passes through 3 points on the x-axis, the only correct pint listed is x=1. :)

Answer:cot t = 1.875

\(sin t=\frac{-8}{17}\) but sin²t + cos²t = 1 ⇔ cos²t = 1 - sin²t

⇔cos t = \(\sqrt{1-sin^{2}t }=\sqrt{1-(\frac{-8}{17})^{2} }=|\frac{15}{17}|\)

but  t is a quadrant III angle => cos t = \(\frac{-15}{17}\)

=> cot t = \(\frac{-15}{17}:\frac{-8}{17}=\frac{15}{8}=1.875\)

Step-by-step explanation:

The disadvantage is that the coefficients of x in the four equations can only take two values, so if one of every values ​​is m, the alternative will be -1/m.

A relationship between two terms on either side of an equal sign is depicted by a straightforward equation.

Simple equations also pursue one or a mixture of the four arithmetic computations of addition, simple arithmetic, multiplication, and division.

There are three basic forms of the system of equations: point-slope form, standard form, and slope-intercept form.

So, Shannon's error:

In a rectangle, the neighboring sides are perpendicular to one other, whereas parallel runs between the opposing sides.

The slope of line segments is equal, and the slope, of a perpendicular line to some other line with a slope, m, is -1/m , thus the slopes of the axis of symmetry should be equal, which gives:

The equation should consist of two sets of linear equations with equal slopes: B. Pair y = -x + 6 and y = -x - 5

Therefore, the slopes of the other two lines are -1/-1 = 1 and the equations of the other two lines are y = x - 4 and y = x - 5 respectively.

Therefore, the disadvantage is that the coefficients of x in the four equations can only take two values, so if one of every values ​​is m, the alternative will be -1/m.

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Answer:

-24.1t^2+3

Step-by-step explanation:

Answer:

a=−1/2, 3

3Step-by-step explanation:

Answer:

A Scatter (XY) Plot has points that show the relationship between two sets of data. In this example, each dot shows one person's weight versus their height. (The data is plotted on the graph as " Cartesian (x,y) Coordinates ")

Step-by-step explanation:

hope it helps

Answer:

1/2 cm

Step-by-step explanation:

the area of the triangle is √3/4cm^2.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

Here, given that,

An equilateral triangle with side length 1 cm .

we know,

area of An equilateral triangle

=√3/4×side²

so, the area of the triangle = √3/4×1

                                            =√3/4 cm^2

hence,  the area of the triangle is √3/4cm^2.

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Answer:

i think its 12

Step-by-step explanation:

The employee's yearly salary is calculated as $37,440 using the arithmetic operations.  

The employee earns $18 per hour and works 40 hours per week. To calculate the weekly salary, we multiply the hourly wage by the number of hours worked:

Weekly salary = Hourly wage × Hours worked per week

Weekly salary = $18/hour × 40 hours/week = $720

Next, to calculate the yearly salary, we use the multiplication operation the weekly salary by the number of weeks in a year:

Yearly salary = Weekly salary × Weeks in a year

Yearly salary = $720/week × 52 weeks/year = $37,440

Therefore, the employee's yearly salary is $37,440. This calculation assumes a 40-hour work week and 52 weeks in a year. It's important to note that this calculation does not account for overtime pay or any other additional benefits or deductions that may affect the employee's total annual income.

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