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3 years ago

How to write an inequality stating the restrictions of x

Mathematics

1 answer:

inessss [21]3 years ago

6 0

For example
1>x>3
says x is less than 1 and greater than 3

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Identify the vertex, axis of symmetry, minimum or maximum, domain, and range of the function f(

alekssr [168]

Identify the vertex, axis of symmetry, minimum or maximum, domain, and range of the function ()=−(+)^−

Answer:

vertex = (-4, -5)

Axis of symmetry = -4

use the (-4, -5) to find the minimum value

$Domain = ( - \infty, \infty ) , [ x | x\ is\ real ]\\\\Range = [ -5, \infty ), y\geq -5$

Solution:

Given function is:

$f(x) = (x+4)^2 - 5$

The equation in vertex form is given as:

$y = a(x-h)^2+k$

Where, (h, k) is constant

On comparing give function with vertex form,

h = -4

k = -5

Vertex is (-4 , -5)

Axis of symmetry : x co-ordinate of vertex

Thus, axis of symmetry = -4

The coefficient of x^2 is positive in given function.

Thus the vertex point will be a minimum

$Minimum\ value = f(\frac{-b}{a})$

$f(x) = x^2 + 8x + 16 - 5\\\\f(x) = x^2 + 8x + 11$

$f(x) = ax^2+bx+c$

On comparing,

a = 1

b = 8

$x = \frac{-b}{2a} = \frac{-8}{2 \times 1} = -4$

$f(-4) = (-4)^2 + 8(-4) + 11 = 16 - 32 + 11 = -5$

Thus, use the (-4, -5) to find the minimum value

Domain and range

$f(x) = (x+4)^2 - 5$

The domain is the input values shown on the x-axis

The range is the set of possible output values f(x)

Therefore,

$Domain = ( - \infty, \infty ) , [ x | x\ is\ real ]\\\\Range = [ -5, \infty ), y\geq -5$

4 0

2 years ago

Please help! thankjs

olga_2 [115]

Answer:

20th: 100 nth: 5

Step-by-step explanation:

the table is multiplying by 5

so 5 × 20 = 100

8 0

2 years ago

-3x2( 7x2 - x + 4) What is the answer

Lerok [7]

Answer:

6x-108

Step-by-step explanation:

-3 · 2(7 · 2 - x + 4)

= ((−3)(2))((7)(2) +− x + 4)

= −84 + 6x − 24

= 6x − 108

The answer is 6x - 108

6 0

2 years ago

If you place a 17-foot ladder against the top of a 8-foot building, how many feet will the bottom of the ladder be from the bott

Goshia [24]

Answer:

15 feet

Step-by-step explanation:

This problem involves using the Pythagorean theorem, since the figure made with the ladder, building, and ground would make a right triangle. You are given the values 17ft and 8ft, which is enough to plug into the Pythagorean theorem.

The ladder, 17ft, would be the longest side (hypotenuse). The 8ft building would be one of the legs of the right triangle.

1. Plug your given values correctly into the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

$8^{2} + b^{2} = 17^{2}$

2. Now solve for b, which is your unknown distance (the distance the bottom of the ladder is from the bottom of the building).

$8^{2} + b^{2} = 17^{2}$ --> Square 8 and 17

$64 + b^{2} = 289$ --> Subtract 64 from both sides

$b^{2} = 225$ --> Square root both sides to get b by itself

b = 15

3. The distance is 15 feet

*Note: to make solving this problem easier, try drawing out the given situation, namely the building and the ladder

7 0

2 years ago

Is 2 3/4 <, >, or = to 2.75%

lesya692 [45]

2 3/4 = 2.75

so

2 3/4 = 2.75%

6 0

3 years ago