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3 years ago

Triangle ABC is a scaled copy of triangle DEF. Side AB measures 12

Mathematics

1 answer:

Dima020 [189]3 years ago

4 0

Answer:

1. The scale factor here is 1.5

2. The scale factor here is 2/3

Step-by-step explanation:

Here, we shall be dealing with scales of triangles.

we have two triangles;

ABC and DEF

longest sides are in the ratio;

12 : 8

1. What scale factor translates DEF to ABC?

The ratio of the length can be beaten down to 3:2

So therefore, we can see that by multiplying the sides of of DEF by 1.5, we can arrive at the sides of ABC

So the scale factor here is 1.5

2. This is like the other way round of what we have above.

By multiplying the sides of ABC by 2/3, we shall have the sides of DEF

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Simplify (-5x^3)^-2 using only positive exponents

mihalych1998 [28]

Hope you know that x^(-1) = 1/x used this you get

(-5x^3)^-2 = 1/(-5x^3)^2 = 1/{(-5^2)(x^6)} = 1/(25x^6)

hope helped

5 0

3 years ago

Read 2 more answers

¿Cuáles son los procedimientos a ambos lados de la igualdad que se deben realizar para calcular el valor de la incógnita x en la

PilotLPTM [1.2K]

Answer:

Los procedimientos que se deben realizar para calcular la incógnita x en la ecuación 2x+5=7 son:

El 5 que está sumando a la izquierda del igual, se pasa a restar a la derecha del igual.
El 2 que multiplica a x a la izquierda del igual, se pasa a dividir a la derecha del igual.

Step-by-step explanation:

Siguiendo los procedimiento descritos en la respuesta, para calcular el valor de la incógnita:

2x + 5 = 7

Seguimos el primer paso: el 5 que está sumando a la izquierda del igual, se pasa a restar a la derecha del igual:

2x = 7 - 5

Seguimos el segundo paso: el 2 que multiplica a x a la izquierda del igual, se pasa a dividir a la derecha del igual:

$x=\frac{7-5}{2}$

Como puedes ver, así se despejaría la incógnita x y solo faltaría operar los datos en la ecuación para obtener la respuesta:

$x=\frac{2}{2}$
$x=1$

El resultado que nos daría la incógnita x sería 1. Podemos probar el resultado en la ecuación original para comprobar el resultado que obtuvimos:

2x + 5 = 7
2 *(1) + 5 = 7
2 + 5 = 7
7 = 7

Así, identificamos que los procesos realizados fueron correctos.

3 0

2 years ago

Irina-Kira [14]

Answer:

No.

Step-by-step explanation:

The central Limit Theorem states that the sample size must be greater than 30 for an approximate normal distribution.

6 0

2 years ago

A robotic machine fills containers with an acid solution at the rate of 50 + 5 t milliliters (mL) per second, where t is in seco

Alika [10]

Answer:

12,000

Step-by-step explanation:

The machine fills the containers at a rate of 50+5t milliliters (mL) per second.

Therefore, the rate of change of the number of containers, N is:

$\dfrac{dN}{dt}=50+5t, 0\leq t\leq 60$

$dN=(50+5t)dt\\$Taking integrals of both sides\\\int dN=\int (50+5t)dt\\N(t)=50t+\frac{5t^2}{2}+C $(C a constant of integration)\\\\When t=0, , No containers are filled, therefore:$ N(t)=0\\0=50(0)+\frac{5(0)^2}{2}+C\\C=0\\$Therefore, N(t)=50t+2.5t^2$

When t=60 seconds

$N(60)=50(60)+2.5(60)^2\\N(60)=12000$ mL$

Therefore, 12,000 milliliters of acid solution are put into a container in 60 seconds.

7 0

2 years ago

Six times a number, increased by 3 is is 27. find the number

Mekhanik [1.2K]

Answer : The number is 4.

Step-by-step explanation:

Given : 

six times a number, increased by 3 is is 27.

To Find: 

The number.

Solution : 

Let the number is x

six times a number is 6x

Increased by 3 = 6x+3

According to the given question :

Solving the value x : 

6x+3 =27

6x = 27-3

6x = 24

x = 24/6

x = 4

Hence, the number is 4.

6 0

3 years ago