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2 years ago

Please help me with this.

Mathematics

1 answer:

Rama09 [41]2 years ago

4 0

The image of the point (1, 2, 3) is (3, 7)

<h3>How to determine the image?</h3>

The given parameters are:

Point = (1, 2, 3)
Transformation rule = (3x, 2y + z)

In (1, 2, 3), we have:

x = 1; y = 2 and z = 3

When the rule is applied, we have:

Image = (3x, 2y + z)

Image = (3 * 1, 2 *2 + 3)

Evaluate

Image = (3, 7)

Hence, the image of the point (1, 2, 3) is (3, 7)

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What is the probability that a randomly chosen four-digit integer (no leading zeros) has distinct digits and ends with the digit

S_A_V [24]

Answer:

c. 0.0498

Step-by-step explanation:

First of all, let us find the number of four digit numbers possible.

There are 4 digits and let us have a look at the possibility of each digit.

Number of possible options for Unit's digit = 10

Number of possible options for ten's digit = 10

Number of possible options for hundred's digit = 10

Number of possible options for thousand's digit = 9 (because 0 can not be there to make it a 4 digit number)

Total number of possible outcomes = $10\times 10\times 10\times 9 = \bold{9000}$

As per the given condition, unit's digit is 7.

So, number of possible options for unit's digit = 1

Number of possible options for thousand's digit = 8 (7 and 0 can not be there to make it a 4 digit number)

Number of possible options for hundred's digit = 8 (7 and one digit used in thousand's place can not be there)

Number of possible options for ten's digit = 7 (7, two digits used at thousand's and hundred's places)

Number of possible outcomes as per given conditions = $1\times 8\times 8\times 7 = \bold{448}$

Formula for probability of an event E can be observed as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

$P(E) = \dfrac{448}{9000} =\bold{0.0498}$

6 0

3 years ago

What are the vertex and x-intercepts of the graph of the function given below?

madreJ [45]

VERTEX
To determine the vertex (coordinate x) of parabola y = ax² + bx + c, use this following formula
x vertex = $-\dfrac{b}{2a}$

y = x² - 2x - 48
a = 1, b = -2, c = -48
plug in the numbers
x vertex = $-\dfrac{b}{2a}$
x vertex = $-\dfrac{(-2)}{2(1)}$
x vertex = $\dfrac{2}{2}$
x vertex = 1

To find y vertex, substitute the value of x vertex to the parabola equation
y = x² - 2x - 48
y = 1² - 2(1) - 48
y = 1 - 2 - 48
y = -49

The vertex is (1, -49)

X-INTERCEPT
x-intercept located in x axis, that means y = 0. Substitute y = 0 to the parabola equation
x² - 2x - 48 = y
x² - 2x - 48 = 0
(x - 8)(x + 6) = 0
x = 8 or x = -6
The x-intercepts are (8,0) and (-6,0)

The answer is first option

5 0

4 years ago

Read 2 more answers

A plant grows 3/8 inch every month. How many inches

hram777 [196]

Answer:

B. 3 3/4

Step-by-step explanation:

3/8 * 10 = 30/8

30/8 = 3 3/4

8 0

3 years ago