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3 years ago

Let f(x)=x2+6x−16 . Enter the x-intercepts of the quadratic function in the boxes. and

Mathematics

1 answer:

gizmo_the_mogwai [7]3 years ago

8 0

Answer:

x = - 8, x = 2

Step-by-step explanation:

Given

f(x) = x² + 6x - 16

To find the x- intercepts equate f(x) to zero, that is

x² + 6x - 16 = 0 ← in standard form

(x + 8)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 2 = 0 ⇒ x = 2

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Consider the system of inequalities.

Ugo [173]

Answer:

The point is (-1,5) and (0,0) also satisfies the given inequalities

The solution of the given inequalities

(x, y) = (4 , -2 )

Step-by-step explanation:

Step(i):-

Given system of equations are

3x + 2y < 8

-5x - 9y > -2

The solution of the given equations are

3x + 2y = 8 multiply '5'

-5x - 9y = -2 multiply '3'

15 x + 10 y = 40 ...(i)

-15x - 27 y = -6.....(ii)

Adding (i) and (ii) , we get

- 17 y = 34

y = -2

Substitute y = -2 in equation 3x + 2y =8

3x - 4 =8

3x = 12

x =4

The solution of the given system of inequalities

(x, y) = (4 , -2 )

Step(ii):-

3x + 2y < 8

-5x - 9y > -2

The point is (-1,5)

-3 + 10 < 8

7 < 8

5 - 45 > -2

-40 > -2

The point (0,0) also satisfies the given inequalities

Final answer :-

The point is (-1,5) and (0,0) also satisfies the given inequalities

7 0

3 years ago

A state license plate consists of three letters followed by three digits. If repetition is allowed, how many different license p

Nuetrik [128]

A state license plate consists of three letters followed by three digits. If repetition is allowed, the number of different ways in which license plates are possible is 17,576,000.

<h3>What is a permutation?</h3>

An arrangement of items in a specific order is referred to as a permutation. When the order of the arrangements counts, it is a mathematical technique that establishes the total number of alternative arrangements in a collection.

Calculation for the permutation -

Three letters are followed by three digits on a state license plate.

26 letters from a to z and 10 numbers from 0 to 9 make up the alphabet.

The potential of arrangements is due to the license plate's composition of three letters and three numerals.

Total ways = 26×26×26×10×10×10

= 17,576,000

Therefore, the number of different ways in which license plates are possible is 17,576,000.

To know more about the permutation, here

brainly.com/question/1216161

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7 0

2 years ago