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2 years ago

How many solutions does the system of equations below have? y= 3x + 4 2y -8 = 6x

Mathematics

1 answer:

Cerrena [4.2K]2 years ago

3 0

Answer:

infinitely many solutions (infinite solutions)

Step-by-step explanation:

2y - 8 = 6x

+8 +8

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

2y = 6x + 8

$\frac{2y}{2}$ = $\frac{6x}{2}$ + $\frac{8}{2}$

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

y = 3x + 4

Because 3x + 4 = 3x + 4, there are infinitely many solutions to this system of equations. This is because they're the exact same equations. Any substitution for x will give you a true statement to y when compared to the other equation.

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A math book weighs 250 grams, a chemistry book weighs 200 grams, and a physics book weighs 250 grams. what is the total weight o

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The answer is 24.69 ounces

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3 years ago

Se golpea (chuta) un balón sobre el piso y sale dando botes parabólicos cada vez menores. Si se lanzo inicialmente con una veloc

Ipatiy [6.2K]

Answer:

a)d = 180,91 m

b)t = 11,76 seg

Step-by-step explanation:

Para el lanzamiento de proyectil, la ecuación que nos da la velocidad en V(y) es:

V(y) = Voy - g*t

en donde Voy = Vo * senα ( donde Vo es la velocidad inicial, α el angulo del disparo.

Si en esta ecuación hacemos V(y) = 0 estamos en el punto donde el componente en el eje y de la velocidad del proyectil es cero, ese punto es el punto medio del recorrido.

0 = Vo*sen 60⁰ - g*t

g*t = Vo* √3/2

t = { 32 [m/s] * √3 }2*9,8 [m/s²]

t = 16*√3 / 9,8

t = 2,8278 seg

El tiempo total del primer recorrido es entonces por simetría

t₁ = 2 * 2,8278 t₁ = 5,6556 seg

La distancia del primer impacto al suelo es:

x = Vox * t₁ ( Vox es constante Vx = Vo*cos 60⁰ )

x = 32 * (1/2) * 5,6556

x₁ = 90,49 m

Aplicando los mismos criterios ahora para el segundo bote

Ahora Vo = 32 - 32*(1/4)

V = 24 m/s

g*t = 24 * sen 50⁰

t = 24* 0,7660/ 9,8

t = 1,8759

2*t = 2*1,8759

t₂ = 3,7518 seg

x₂ = Vox * t₂

x₂ = 24* 0,6428*3,7518

x₂ = 57,88 m

Y para el tercer bote Vo = 24 - 24(1/4) Vo = 18 m/s α = 40⁰

t = 18 *0,6428/9,8

t = 1,18

2t = t₃ = 2*1,18

t₃ = 2,36 seg

x₃ = Vox * 2,36 Vox = Vo*cos 40 Vox = 18*0,7660

Vox = 13,79

x₃ = 13,79*2,36

x₃ = 32,54 m

La distancia total será

d = x₁ + x₂ + x₃

d = 90,49 + 57,88 + 32,54

d = 180,91 m

y el tiempo total será la suma de los tiempos

t = t₁ + t₂ + t₃

t = 5,65 + 3,75 + 2,36

t = 11,76 seg

8 0

3 years ago

Draw the image of the rectangle ABCD under dilation using Center p and scale factor 1/2

WINSTONCH [101]

Answer:

we can not draw on here

Step-by-step explanation:

7 0

3 years ago

Consider a prism with a height of 8 inches and a 14-inch by 14-inch square base, and a cylinder with a height of 10 inches and a

vekshin1

Answer:

782.5inch³

Step-by-step explanation:

The question is on volume of a prism and that of a cylinder

Finding the volume of the prism

V=Bh where B is the base area and h is the height

Base area=14"×14"=196 inch²

height =8"

v=196×8= 1568 in³

Finding volume of the cylinder

v= $\pi$ r²h where r is the radius of cylinder and h is the height of cylinder

r=10/2=5 inches and h=10 inches

v=3.142×5×5×10=785.5inch³

The difference in volume

Difference in volume=1568-785.5=782.5inch³

5 0

3 years ago

A spinner with 8 equal parts, labeled 1 to 8, is used in a board game. you spin the spinner one time. what is the theoretical pr

stiks02 [169]

Answer:

1 in 8; or 12.5% of the time

Step-by-step explanation:

There are eight outcomes. One of eight of those outcomes is a 2.

1/8 = 0.125

5 0

3 years ago