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3 years ago

Simplify (2x + 3)(x – 4) = ?

1 answer:

5 0

Use the FOIL method (first, outside, inside, last) to multiply:

2x^2-8x+3x-12

This can be simplified even more into:

2x^2-5x-12.

Hope this helped!

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You wish to find a 95% confidence interval for the mean number of times men change channels with a remote control during a comme

gogolik [260]

For margin of error to be a maximum of 3:
3 = z*(SD / sqrt(n)), where z is the z-score, SD is the standard deviation and n is the sample size.
z = 1.96 for a 95% confidence interval, and we are given SD = 15.
3 = 1.96*15/sqrt(n)
sqrt(n) = 9.8
n = 96.04 ~ 96 commercials.

4 0

3 years ago

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

3 years ago

I need help on this question can someone please help me?

Svetllana [295]

I really hate these algebra problems pretending to be geometry.

Anyway angles B and D are congruent in a parallelogram. Geometry part done.

4n - 2 = 2n + 32

2n = 34

n = 17

Answer: 17, which is the 3rd choice

3 0

3 years ago

Read 2 more answers

Which graph represents the solution set of the compound inequality -4≤3x-1 and 2x+4≤18?

Bond [772]

Answer:

can you put the pic of the graph plzz

Step-by-step explanation:

thx

4 0

3 years ago

Read 2 more answers

Point S is on line segment RT. Given RS = 4x – 10, ST = 2x – 10, and

borishaifa [10]

Answer:

The numerical length of RS is 22 units

Step-by-step explanation:

∵ Point S is on the line segment RT

→ That means S divide RT into two parts RS and ST

∴ RS + ST = RT

∵ RS = 4x - 10

∵ ST = 2x - 10

∵ RT = 4x - 4

→ Substitute them in the statement above

∴ 4x - 10 + 2x - 10 = 4x - 4

→ Add the like terms in the left side

∴ (4x + 2x) + (-10 + -10) = 4x - 4

∴ 6x + (-20) = 4x - 4

∴ 6x - 20 = 4x - 4

→ Add 20 to both sides

∴ 6x -20 + 20 = 4x - 4 + 20

∴ 6x = 4x + 16

→ Subtract 4x from both sides

∴ 6x - 4x = 4x - 4x + 16

∴ 2x = 16

→ Divide both sides by 2 to find x

∴ $\frac{2x}{2}=\frac{16}{2}$

∴ x = 8

→ Substitute the value of x in Rs to find its length

∵ RS = 4(8) - 10

∴ RS = 32 - 10

∴ RS = 22 units

The numerical length of RS is 22 units

3 0

3 years ago