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3 years ago

Which of the following has a finite solution for a three-variable system of equations?

Mathematics

1 answer:

nydimaria [60]3 years ago

6 0

Answer:

A. three planes intersecting at a point

Step-by-step explanation:

Whenever three planes intersect at a point, then we have an ordered triplet (x,y,z) that is a solution to the associated system of equation.

This is a unique solution and it is finite.

However three planes intersecting at a line gives infinitely many solutions.

Three or two parallel planes may have no solution or or infinitely many solutions when they coincide.

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Suppose you had d dollars in your bank account. You spent $22 but have at least $42 left. How much money did you have initially?

german

1) What left

$\boxed {d-22 \geq 42}$

*Obs: remember that left at least 42 dollars. In other words, the left over is equal or more than 42 dollars.

2) At the beginning

$d-22 \geq 42 \\ \\ \boxed {d \geq 64}$

Letter C

4 0

2 years ago

13. En un pueblo, 5 personas escucharon una noticia. En una hora, cada una de ellas

Vera_Pavlovna [14]

Answer:

En 5 horas se habrá enterado todo el pueblo.

Step-by-step explanation:

Sabemos que en un pueblo 5 personas escucharon una noticia.

Una hora más tarde, cada una de ellas le contó la noticia a otras 5.

Luego, éstas contaron la noticia a otras 5 y así sucesivamente.

Nadie cuenta ni escucha la noticia más de una vez y en ese pueblo hay un poco más de 19000 habitantes.

La ecuación a desarrollar para resolver el problema es la siguiente :

Comenzamos con 5 personas que escucharon la noticia a la ''hora 0''.

Una hora más tarde, cada una de ellas le contó a 5 personas, es decir , pasada la primera hora tendremos :

$5+5^{2}=30$ (I)

Las 5 personas originales de la ''hora 0'' más 25 personas que se enteraron pasada la primera hora. La ecuación que planteamos es la siguiente :

$5^{1}+5^{2}+5^{3}+...+5^{x}>19000$ (II)

Buscamos el valor de $x$ que satisface la ecuación (II).

Probando y realizando las sumas encontramos que :

$5^{1}+5^{2}+5^{3}+5^{4}+5^{5}+5^{6}>19000$

$19530>19000$

El valor de $x$ que satisface (II) es $x=6$ .

Para hallar el número de horas nos fijamos que en (I) el valor del mayor exponente del 5 es el número 2. Para ese valor 2, el tiempo que pasó es una hora.

Entonces para nuestro $x=6$ , el número de horas que pasaron son 5 horas (1 menos que el valor de $x$ )

Todo el pueblo se habrá enterado en 5 horas de la noticia.

7 0

3 years ago

A 34-foot pole casts a 30-foot shadow. At the same time, a nearby tree casts a 24-foot shadow. How tall is the tree?

artcher [175]

Answer:

27.2 ft

Step-by-step explanation:

Let's set up a ratio that represents the problem:

Object's Height (ft) : Shadow (ft)

Substitute with the dimensions of the 34 foot pole and its 30 foot shadow.

34 : 30

Find the unit rate:

The unit rate is when one number in a ratio is 1.

Let's make the Shadow equal to one by dividing by 30 on both sides.

Object's Height (ft) : Shadow (ft)

34 : 30

/30 /30

1.13 : 1

Now, let's multiply by 24 on both sides to find the height of the tree.

Multiply:

Object's Height (ft) : Shadow (ft)

1.13 : 1

x24 x24

27.2 : 24

Therefore, the tree is 27.2 feet tall.

7 0

2 years ago

Sally gets paid $15.00 dollars per hour for a 40-hour work week and y dollars for each hour she works over 40 hours. What is the

Anna35 [415]

The equation x = 600 + 8y represents the earnings of Sally if she works 48 hours.

<u>Step-by-step explanation:</u>

Sally gets paid $15.00 dollars per hour for a 40-hour weekly work.
She gets y dollars for each extra hour she works over 40 hours.

<u>The equation can be framed as :</u>

Let,

x be the total pay she could get for 48 hours.
The amount she earned for 40 hours = 40 × $15 ⇒ $600
The amount she earned for extra hours = 8 × y ⇒ 8y

The equation is given as,

Total earnings = amount earned for 40 hours + amount for extra 8 hours.

⇒ x = 600 + 8y

Therefore, the equation x = 600 + 8y represents the earnings of Sally if she works 48 hours.

4 0

2 years ago

Part III: Bailey works part-time at a movie theater. The theater pays employees an hourly wage based on their length of employme

aleksklad [387]

From the given table, the points can be written as : (6,7.55) , (12,7.85), (18, 8.15) and (24, 8.45)

Slope $m=\frac{_{y2}-_{y1}}{_{x2}-_{x1}}$

m = $\frac{7.85-7.55}{12-6}$

m = 0.05

slope intercept form of line = $y=mx+c$

We plug m = 0.05, x = 6 and y = 7.55 and find c.

$7.55=0.05(6)+c$

c= 7.25

Required equation: $y=0.05x+7.25$ ... Answer

5 0

3 years ago