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mariarad [96]
3 years ago
7

If a translation maps point (3, 2) to (4, 5); or T : (3, 2) (4, 5), indicate the image for (2, 4).

Mathematics
1 answer:
tiny-mole [99]3 years ago
7 0
A translation :
T : ( 3 , 2 ) → ( 4, 5 )
T : ( x, y ) → ( x + 1, y + 3 )
2 + 1 = 3
4 + 3 = 7
Answer:
The image for ( 2, 4 ) is ( 3, 7 ).
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Type the correct answer in each box. (____)
trapecia [35]

Answer:

1. -16; 2. +64; 3. 16

Step-by-step explanation:

The formula for the volume of a cylinder is

V = πr²x

Data:

r = (x - 8)   mm

V = 1024π mm³

Calculations:

1. Find the cubic equation  

V = πr²h

1024π = π(x - 8)² × x

Divide each side by π

1024 = x(x - 8)²  

1024 = x(x² - 16x  + 64)

1024 =    x³ - 16x² + 64x

x³ - 16x² + 64x - 1024 = 0

2. Solve the cubic equation

The general formula for a third-degree polynomial is

f(x) = ax³ + bx² + cx + d

Your polynomial is  

f(x) = x³ - 16x² + 64x - 1024

a = 1; d = -1024

According to the <em>rational roots theorem</em>, the possible roots are

factors of d/factors of a

Factors of d = ±1, ±2, ±4, ±8, ±16, ± 32, ± 64, ±128, ±256, ±512, ±1024

Factors of a = ±1

Potential roots are x = ±1, ±2, ±4, ±8, ±16, ± 32, ± 64, ±128, ±256, ±512, ±1024

That's a lot of possibilities to check by trial and error. I will just use the one that works.

Try x = 16 by synthetic division.

16|1  -16   64  -1024

  <u>|     16     0   1024 </u>

   1     0   64        0

So,

(x³ - 16x² + 64x - 1024)/(x – 16) = x² + 64

and

(x - 16)(x² + 64) = 0

x - 16 = 0        x² + 64 =    0

     x = 16       x²         = -64

                       x          =  ±8i

There is only one real root: x = 16 mm

6 0
3 years ago
359, 357, 348, 347, 337, 347, 340, 335, 338, 348, 339, 356, 336, 358 a. median: 359 mode: 358 c. median: 347 mode: 347 AND 348 b
Elodia [21]

Answer:

Option C (Median: 347 and Mode: 347 and 348)

Step-by-step explanation:

Median is the middle point of the data and mode is the most repeated observation is the data. The first step involved in calculating the median it to list the observations in the ascending order. This gives:

335, 336, 337, 338, 339, 340, 347, 347, 348, 348, 356, 357, 358, 359

The second step is to identify the middle number (in case the observations are in odd numbers) or numbers (in case the observations are in even numbers) after the ascending order step has been done. It can be observed that the middle numbers in this data set are 347 and 347. Since there are two numbers, so their average will be the median of this data set. Therefore, the median is 347. It can be seen that maximum repetitions are 2 times for 347 and 348. So the mode is 347 and 348.

Therefore, Option C is the correct answer!!!

5 0
3 years ago
solo el 20% de los empleados de la población civil que está en una base militar restringida porta su identificación personal. Si
prisoha [69]

Usando la distribución binomial, hay una probabilidad de 0.8926 = 89.26% de que el guardia de seguridad encuentre al menos uno en la base militar restringida.

<h3>¿Qué es la distribución binomial?</h3>

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

Los parámetros son:

  • n es el número de ensayos.
  • p es la probabilidad de éxito en un ensayo
  • x es el número de éxitos

En este problema, hay que:

  • 20% de los empleados de la población civil que está en una base militar restringida porta su identificación personal, o sea p = 0.2.
  • Llegan 10 empleados, o sea, n = 10.

La probabilidad de que el guardia de seguridad encuentre al menos uno en la base militar restringida es dada por:

P(X \geq 1) = 1 - P(X = 0)

En que:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074

Por eso:

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1074 = 0.8926

Hay una probabilidad de 0.8926 = 89.26% de que el guardia de seguridad encuentre al menos uno en la base militar restringida.

Puede-se aprender más a cerca de la distribución binomial en brainly.com/question/25132113

3 0
2 years ago
What is the 10th term in the pattern with the formula 5n + 100?
yanalaym [24]
Easy
first term is n=1
so 10th term is n=10

5(10)+100=50+100=150

150 is 10th term
5 0
3 years ago
M(-2,-6) Across the y-axis: Across the x-axis
Anon25 [30]

Answer:

I need points sorry

Step-by-step explanation:

7 0
3 years ago
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