write two different expressions that are equivalent to 12-15x use factoring to write one of the expressions

The x-coordinate of the vertex of the equation y = 2x2 − 4x + 12 The x-coordinate of the vertex of the equation y = 4x2 + 8x + 3

dolphi86 [110]

So since the vertex falls onto the axis of symmetry, we can just solve for that to get the x-coordinate of both equations. The equation for the axis of symmetry is $x=\frac{-b}{2a}$ , with b = x coefficient and a = x^2 coefficient. Our equations can be solved as such:

y = 2x^2 − 4x + 12: $x=\frac{4}{2*2}=\frac{4}{4}=1$

y = 4x^2 + 8x + 3: $x=\frac{-8}{2*4}=\frac{-8}{8}=-1$

In short, the vertex x-coordinate's of y = 2x^2 − 4x + 12 is 1 while the vertex's x-coordinate of y = 4x^2 + 8x + 3 is -1.

6 0

3 years ago

Help me at this thanks...please this is an urgency

Ira Lisetskai [31]

Answer:

if simplified is 30

Step-by-step explanation:

600 x 360/7,200

3 0

3 years ago

Read 2 more answers

HELP CONGRUENT ANGLES

Gemiola [76]

$\dfrac{RP}{RQ}=\dfrac{LJ}{LK}\\
\dfrac{RP}{1.6}=\dfrac{5.4}{3.2}\\
3.2RP=8.64\\
RP=2.7$

6 0

3 years ago

The tensile strength of stainless steel produced by a plant has been stable for a long time with a mean of 72 kg/mm2 and a stand

Elanso [62]

Answer:

95% confidence interval for the mean of tensile strength after the machine was adjusted is [73.68 kg/mm2 , 74.88 kg/mm2].

Yes, this data suggest that the tensile strength was changed after the adjustment.

Step-by-step explanation:

We are given that the tensile strength of stainless steel produced by a plant has been stable for a long time with a mean of 72 kg/mm 2 and a standard deviation of 2.15.

A machine was recently adjusted and a sample of 50 items were taken to determine if the mean tensile strength has changed. The mean of this sample is 74.28. Assume that the standard deviation did not change because of the adjustment to the machine.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean strength of 50 items = 74.28

$\sigma$ = population standard deviation = 2.15

n = sample of items = 50

$\mu$ = population mean tensile strength after machine was adjusted

Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level of

significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $74.28-1.96 \times {\frac{2.15}{\sqrt{50} } }$ , $74.28+1.96 \times {\frac{2.15}{\sqrt{50} } }$ ]

= [73.68 kg/mm2 , 74.88 kg/mm2]

Therefore, 95% confidence interval for the mean of tensile strength after the machine was adjusted is [73.68 kg/mm2 , 74.88 kg/mm2].

Yes, this data suggest that the tensile strength was changed after the adjustment as earlier the mean tensile strength was 72 kg/mm2 and now the mean strength lies between 73.68 kg/mm2 and 74.88 kg/mm2 after adjustment.

8 0

3 years ago

Select the relations that are functions.

liraira [26]

Answer:

option A, C and D

Step-by-step explanation:

Each relation is a function if each input has only one output

{a, 1), (6, 1), (C, 1)

This relation is a function because each input has only one output

{a, a),(a, b),(a, c)}

This relation is not a function because input 'a' has only three output

{(1, a), (2, a),(3, a)}

This relation is a function because each input has only one output

{a, a), (b, b), (C, c)}

This relation is a function because each input has only one output

7 0

2 years ago