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Answer:

Ejercicios Resueltos  

ANGULOS  

1. Si el complemento de ángulo x es 2x, ¿Cuál es el valor de x en  

grados?  

Solución:  

2x x 90 += °

3x 90

x 90 / 3

x 30

= °

= °

= °

2. Si el suplemento del ángulo x es 5x, ¿Cuál es el valor de x?  

Solución:  

5x+x=180

6x=180

x=180 /6

x=30

°

°

°

°

3- Determínese los dos ángulos x e y, cuya suma es 90 y cuya  

diferencia es 10 .  

°

°

Solución:  

-Planteamos el sistema de ecuaciones:  

x y 90

x y 10

+= °

−= °

-Resolvemos el sistema. Mediante el método de suma y resta  

obtenemos:  

2x 100

x 100 / 2

x 50

= °

= °

= °

-Hacemos la sustitución del valor encontrado de x en la primera  

ecuación: 50 y 90

y 90 50

y 40

°+ = °

= °−

= °

°

∴La solución al problema es x 50 , y 40 =°= °

°

4. Hállense dos ángulos complementarios tales que su diferencia sea  

30° .  

Solución:  

-Planteamos el sistema de ecuaciones:  

x y 90

x y 30

+= °

−= °

-Resolvemos el sistema. Mediante el método de suma y resta  

obtenemos:  

2x 120

x 120 / 2

x 60

= °

= °

= °

-Hacemos la sustitución del valor encontrado de x en la primera  

ecuación:  

60 y 90

y 90 60

y 30

°+ = °

= °−

= °

∴La solución al problema es x 60 , y 30 = °= °

°

5. Hállense dos ángulos suplementarios tales que el uno sea 20 mayor  

que el otro.  

°

Solución:  

-Planteamos el sistema de ecuaciones:  

x y 180

x y 20

+= °

=+ °

-Resolvemos el sistema:  

(y 20 ) y 180

2y 180 20

2y 160

y 80

+ °+ =

= °− °

= °

= °

-Hacemos la sustitución del valor encontrado de y en la primera  

ecuación: x 80 180

x 180 80

x 100

+ °=

= °−

= °

°

°

∴La solución al problema es:  

x = °= ° 100 , y 180

TRIANGULOS  

1.- ¿Cuánto miden cada uno de los ángulos interiores del siguiente  

triángulo?  

Solución:  

Nota: La suma de los ángulos interiores de los triángulos es  

180° .  

((( A B C 180 ++= °

3x 5x 4x 180 ++ = °

12x 180 = °∴( ( (( A 22.5 , B 52.5 , C 30 , CBR 127.5 = ° = ° =° = °

x 15 = °

∴( ( A 45 , B 75 ,C 60 =° =°= °

°

°

°

°

°

°

2.- ¿Cuánto miden cada uno de los ángulos del siguiente triángulo?  

Solución  

a) Ángulo extendido  

( ( B CBR 180 + = Esto debido a que son ángulos suplementarios  

(B 15x 60 180 + − °=

(B 180 60 15x = °+ °−

(B 240 15x = °−

b) Suma de los ángulos interiores del triángulo  

((( A B C 180 ++=

3x (240 15x) 4x 180 + °− + =

7x (240 15x) 180 + °− =

− + °= 8x 240 180− =− 8x 160°

x 7.5 =

∴( ( (( A 22.5 , B 52.5 , C 30 , CBR 127.5 = ° = ° =° = °  

3.- Escribe la definición de bisectriz del triángulo.  

Es la semirrecta que biseca el ángulo, es decir, divide el ángulo  

en dos ángulos congruentes.  

4.- ¿Qué es la mediatriz de un triángulo?  

La mediatriz de un lado de un triángulo (y en general de un  

segmento de recta), es la recta perpendicular a ese lado en su  

punto medio.  

5.- ¿Que es la mediana de un triángulo?  

La mediana de un triángulo, es el segmento de la recta que une  

un vértice con el punto medio del lado opuesto.  

CUADRILATEROS  

1.- ¿Qué cuadrilátero tiene las dos diagonales iguales y sus lados son  

iguales dos a dos?  

Rectángulo  

2.- Si los ángulos de un cuadrilátero miden, respectivamente, 80º, 110º  

y 70º, ¿Cuánto medirá el ángulo que falta?  

100º

3.- ¿Cuál es el paralelogramo que tiene las diagonales perpendiculares?  

Rombo  

4.- ¿Cómo se llama el cuadrilátero que tiene dos lados paralelos?  

Trapecio  

5.- Encuentra el área del paralelogramo que tiene 5cm de base y 3 de  

altura  

A b*a

A 5*3

A 15

=

=

=

POLÍGONOS 1.- Cuatro ángulos interiores de un pentágono valen respectivamente  

110°, 90°, 85° y 125°. ¿Cuánto vale el quinto ángulo?  

Solución:  

Si la suma de los ángulos interiores de un polígono es:  

180°*(n-2)=180°*(5-2) = 540°, a lo que le se le resta los  

valores de los ángulos que se dieron, consecuentemente, el  

quinto ángulo vale 130°.  

2.- ¿Cuántos lados tiene, en cada caso, el polígono cuyos ángulos  

interiores suman respectivamente 1080°, 900°, 1260°?  

Solución:  

Despejando de la fórmula el valor de n, tenemos que:  

. 2

180

suma angulos n = ° + , y esto aplicado a cada valor de la suma de los  

ángulos internos, obtenemos que los valores de n son 8, 7 y 9  

respectivamente.  

3.- ¿Cuánto vale cada ángulo exterior de un octágono regular?  

Solución:  

Aplicando el teorema de que la suma de los ángulos exteriores  

de un polígono es 360°, entonces cada ángulo exterior vale  

360°/8 = 45°  

4.- Calcular los ángulos exteriores de un triángulo rectángulo que tiene  

un ángulo agudo doble del otro.  

Solución:  

Se tiene que la suma de los ángulos interiores es  

180°*(n-2)= 180° y éste a su vez es igual a 90° + x + 2x,  

despejando x de 3x = 90°, x= 30°, entonces los ángulos  

interiores son 30°, 60° y 90°, teniendo como ángulos exteriores  

150°, 120° y 90°.

Step-by-step explanation:

Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.

To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:

A = \(Pe^(^r^t^)\)

where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:

640 = \(Pe^(^0^.^0^3^5^*^9^)\)

640 = Pe^0.315

P =\(640/e^0^.^3^1^5\)

P = 432.43

Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.

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To calculate the average speed of the lap record, we need to know the distance covered and the time taken.

Distance = 5.303 km

Time = 1 minute and 24 seconds = 84 seconds

To convert seconds to hours, we divide by 3600 (the number of seconds in an hour):

\( \frac{84 \: seconds \:}{3600} = 0.02333 \: hours\)

Now we can calculate the average speed:

\(Average \: speed = \frac{d}{t} = \frac{5.303km}{0.02333} \)

Average speed = 227.59 km/h

Answer:

you got this Playa I believe in you

Answer:   the first one 8.2   the second one  49.2

Step-by-step explanation:

The area of the rectangle will be 16 square cm.

The area is the space occu[ied by any shape in a two-dimensional space. The area of the rectangle is defined as, the product of the length and the width of the rectangle and is measured in square units.

Given that, the rectangle is having a width of 2 cm and a length of 8 cm. The area of the rectangle will be calculated as,

Area of rectangle = Length x Width

Area of rectangle = 8 x 2

Area of rectangle = 16 square units

Therefore, the area of the rectangle is 16 square cm.

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The complete question is given below.

What is the area of the rectangle with a length of 8 cm and a width of 2 cm?

Answer:

D. 211

Step-by-step explanation:

180-19=161

161+50=211

19+(211(x)-50)=180

211° is the value of x since if u substitute it u will get your answer note that angle on a straight line is 180°

The (g.f)(x)  of the two functions is:

(g.f) (x) = 6x + 37

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

To find (g.f) (x), follow the steps below:

1. Substitute the value of f(x) into the function g(x).

2. Then simplify the expression.

That is:

f(x) = 3x+18

g(x) = 2x+1

Thus, we have:

(g.f) (x) = g(f(x))

(g.f) (x) = g(3x+18)

(g.f) (x) = 2(3x+18) + 1

(g.f) (x) = 6x+36 + 1

(g.f) (x) = 6x + 37

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The steps to sketch the graph of a rational function in the appropriate order is in the order: 1,4,2,3

The steps to sketch the graph of a rational function will be first to find the function's zeros and vertical asymptotes, and plot them on a number line, the second step is to choose test numbers to t the left and right of each of these places, and find the value of the function at each test number., the third step is to use test numbers to find where the function is a positive and where it is negative and the last step is to sketch the function's graph, plotting additional points as guides as negative.

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Place the steps to sketch the graph of a rational function in the appropriate order.

1)find the function's zeros and vertical asymptotes, and plot them on a number line.

2) use test numbers to find where the function is positive and where it is negative.

3) sketch the function's graph, plotting additional points as guides as negative.

4)choose test numbers to t the left and right of each of these places, and find the value of the function at each test number.​

Answer:

parallel

Step-by-step explanation:

Answer:

See below:

Step-by-step explanation:

To find the slope, we use the following formula:

\(\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

For this case, we can use (6,60) as the first set of points.

We can use (4,70) as the second set of points.

Now, we can use the formula, 70-60 is for the top of the fraction (10)

We can do 4-6 to find the bottom, which is (-2)

Now, if we add the fraction back we get -> 10/-2 which is -5 for slope!

To find out the y intercept, it in simple words is "What is y when x is 0?".

We can do that by using the slope intercept formula: \(y=mx+b\).

Once we insert our slope which is -2 we get: \(y=-2x+b\)

We can now substitute a point, lets use (6,60) so we can find out b.

We now get the equation: \(60=-5(6)+b\).

If we solve for that we get 90!

Once we input that, we get, \(y=-5x+90\)

Now we put in x as 0 and we get our y intercept as 90!

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Step-by-step explanation:

Multiply -7/-6 x 7 x 1/3 write in simplest form

274.32 is the answer. Tell me if I need to be more precise.

Answer:

45

Step-by-step explanation:

I really don't but it seems right

Answer:

b

Step-by-step explanation:

just did it on edge

Yes,  This is established by the Rank-Nullity Theorem, A counter-example would be a transformation that is not linear.

Yes, all linear transformations have a matrix representation. The theorem that establishes this is the Matrix Representation Theorem. This theorem states that given a linear transformation T : V → W where V and W are vector spaces over a field F, then there is a unique matrix A such that T(v) = Av for any v in V. This theorem proves that any linear transformation can be represented by a matrix.

A counter-example of a linear transformation that does not have a matrix representation is a transformation that maps a vector in one vector space to a vector in a different vector space. For example, if V is a vector space over the field F, and W is a vector space over another field K, then the linear transformation T : V → W does not have a matrix representation since the size of the matrix would need to be different for each vector in the different vector spaces.

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a rectangle is bounded by the x-axis and the semicircle

y = 36 − x 2

Answer:

y= -3/5 x

Step-by-step explanation:

I hope this helps!!!

Answer:

https://brainly.com/question/16425127

Step-by-step explanation:

Answer:

ummm... There is no table

Step-by-step explanation:

Answer:

Do you have a picture

Step-by-step explanation:

Answer:

x = 6.24

Step-by-step explanation:

x =

Tan32° = OPP/ADJ

Tan32° = x/10

0.624 = x/10

cross-multiply

x = 6.24

Answer:

RP 10.000

Step-by-step explanation:

What it true?

supone que este número es sustituido por la letra m

(3xm) -28 = 89

tenemos que sumar 28 en los dos lados

3xm = 117

para saber que numero es m tenemos que dividir por 3 los dos lados

m = 117/3

m = 39

The seven ordered pairs that fit on the axes of the graph include the following:

In order to use the given polynomial function to complete the table, we would have to substitute each of the values of x (x-values) into the polynomial function and then evaluate as follows;

When the value of x = -3, the output value of this polynomial function is given by;

y = x³ + 6

y = (-3)³ + 6

y = -27 + 6

y = -21

By observing critically the graph (see attachment), we can logically deduce that it represents a polynomial function.

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Answer:

3

Step-by-step explanation:

\(1 + 2 = 3\)

answer= 3

The Income Statements under Absorption Costing and Variable Costing are as follows:

                                                       Absorption Costing     Variable Costing

Sales (19,500 units)                              $2,145,000               $2,145,000

Cost of goods sold                                $1,491,750               $1,365,000

Gross profit                                            $653,250                 $780,000

Selling and administrative expenses:

Fixed factory overhead                                          $162,500

Variable selling and

 administrative expenses    $296,400                  296,400

Fixed selling and

 administrative expenses       114,800    411,200    114,800   573,700

Net Income                                          $242,050                $206,300

The difference between Absorption Costing and Variable Costing is that the Ending Inventory costs under Variable Costing include only direct materials, direct labor, and variable factory overhead.  Absorption Costing includes all the variable factory costs plus fixed factory overhead (a period cost) in the Ending Inventory costs.

Sales (19,500 units)                              $2,145,000

Production costs (25,000 units):

Direct materials                $1,017,500

Direct labor                          487,500

Variable factory overhead 245,000

Fixed factory overhead       162,500

Total production costs      1,912,500

Cost per unit = $76.50 ($1,912,500/25,000)

Less Ending inventory        420,750               (5,500 x $76.50)

Cost of goods sold                              $1,491,750

Gross profit

Selling and administrative expenses:

Variable selling and administrative expenses $296,400

Fixed selling and administrative expenses 114,800 411,200

Sales (19,500 units)                              $2,145,000

Production costs (25,000 units):

Direct materials                $1,017,500

Direct labor                          487,500

Variable factory overhead 245,000

Total variable production costs  1,750,000

Cost per unit = $70 ($1,750,000/25,000)

Less Ending inventory       385,000               (5,500 x $70)

Cost of goods sold                              $1,365,000

Gross profit

Selling and administrative expenses:

Variable selling and

administrative expenses $296,400

Fixed factory overhead       162,500

Fixed selling and administrative expenses 114,800 411,200

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Answer:

10%

Step-by-step explanation:

Original medication = 40 my

It was increased to 45mg

The increase can be calculated as follows

45-40

= 5

Percent Increase can be calculated as follows

= 4/40 ×100

= 0.1×100

= 10%

Hence the increase is 10%

The way the flashback in these paragraphs advance the plot is C. It introduces Evan's motivation for working in the garden with Grandfather.

The technique of flashback in storytelling involves interrupting the chronological order of events to depict an earlier event or scene. It uses time travel to furnish the audience with necessary backstory, context, or a deeper understanding of the characters.

The technique of flashbacks is frequently employed as a means of divulging previous occurrences, recollections, or incidents that hold significance to the present narrative being conveyed.

Hence, it can be seen from the given text that the use of flashback helps show the motivation which Evans had for working in the garden with Grandfather

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Answer: The equation used to find the value of x is 5x - 4 = 3x + 10. The value of x is determined to be 7.

Step-by-step explanation:

Four less than the product of a number (x) and 5 = 5x - 4

8 more than 2 added to 3 times the number = 3x + 2 + 8 = 3x + 10

Four less than the product of a number (x) and 5 is equal to 8 more than 2 added to 3 times the number => 5x - 4 = 3x + 10

                                                         5x - 3x = 10 + 4

                                                         2x = 14

                                                         x = 14/2

                 therefore,                      x = 7

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