Express 4x^2 − 12x in the form (2x + a)^2 + b.

Which function has a range of y < 3?

Setler79 [48]

Using a graphing tool

Let's graph each of the cases to determine the solution of the problem

case A) $y=3(2^{x})$

see the attached figure N $1$

The range is the interval--------> (0,∞)

$y> 0$

therefore

the function $y=3(2^{x})$ is not the solution

case B) $y=2(3^{x})$

see the attached figure N $2$

The range is the interval--------> (0,∞)

$y> 0$

therefore

the function $y=2(3^{x})$ is not the solution

case C) $y=-2^{x}+3$

see the attached figure N $3$

The range is the interval--------> (-∞,3)

$y< 3$

therefore

the function $y=-2^{x}+3$ is the solution

case D) $y=2^{x}-3$

see the attached figure N $4$

The range is the interval--------> (-3,∞)

$y>-3$

therefore

the function $y=2^{x}-3$ is not the solution

the answer is

$y=-2^{x}+3$

5 0

2 years ago

Read 2 more answers

Two hockey teams, the Winnipeg Jets (yay!) and the Toronto Maple Leafs (boo!), miraculously make it to

monitta

Answer:

There is a 54% chance that the Jets will win the Stanley Cup.

Step-by-step explanation:

Since two hockey teams, the Winnipeg Jets and the Toronto Maple Leafs, miraculously make it to the Stanley Cup finals, where as soon as a team wins 3 games, the championship is over, and the schedule for the playoffs for home games is: Jets - Leafs - Jets - Leafs - Jets; since if the Jets are playing at home, there is a 60% chance they'll win, while if they are playing on the road, there is a 45% chance they'll win, to find the probability that the Jets win the Stanley Cup the following calculation must be performed:

(0.60 + 0.45 + 0.60 + 0.45 + 0.60) / 5 = X

2.70 / 5 = X

0.54 = X

Thus, there is a 54% chance that the Jets will win the Stanley Cup.

7 0

2 years ago

Given: AD = BC and AD || BC Prove: ABCD is a parallelogram.

maksim [4K]

Answer:

ABCD is a parallelogram

Step-by-step explanation:

Given: AD ≅ BC and AD ∥ BC Prove: ABCD is a

parallelogram. Statements Reasons 1. AD ≅ BC; AD ∥ BC

1. given 2. ∠CAD and ∠ACB are alternate interior ∠s 2.

definition of alternate interior angles 3. ∠CAD ≅ ∠ACB 3.

alternate interior angles are congruent 4. AC ≅ AC 4.

reflexive property 5. △CAD ≅ △ACB 5. SAS congruency

theorem 6. AB ≅ CD 6. ? 7. ABCD is a parallelogram 7.

5 0

2 years ago

Read 2 more answers

A random sample of 250 students at a university finds that these students take a mean of 15.2 credit hours per quarter with a st

Orlov [11]

Answer:

95% confidence interval for the mean credit hours taken by a student each quarter is [14.915 hours , 15.485 hours].

Step-by-step explanation:

We are given that a random sample of 250 students at a university finds that these students take a mean of 15.2 credit hours per quarter with a standard deviation of 2.3 credit hours.

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

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample credit hours per quarter = 15.2 credit hours

s = sample standard deviation = 2.3 credit hours

n = sample of students = 250

$\mu$ = population mean credit hours per quarter

Here for constructing 95% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.

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

P(-1.96 < $t_2_4_9$ < 1.96) = 0.95 {As the critical value of t at 249 degree of

freedom are -1.96 & 1.96 with P = 2.5%}

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

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

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

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

= [ $15.2-1.96 \times {\frac{2.3}{\sqrt{250} } }$ , $15.2+1.96 \times {\frac{2.3}{\sqrt{250} } }$ ]

= [14.915 hours , 15.485 hours]

Therefore, 95% confidence interval for the mean credit hours taken by a student each quarter is [14.915 hours , 15.485 hours].

The interpretation of the above confidence interval is that we are 95% confident that the true mean credit hours taken by a student each quarter will be between 14.915 credit hours and 15.485 credit hours.

8 0

2 years ago

Line jk passes through points j(-4,-5) and k(-6,3 if the equation of the lines is written in slope-intercept form,y=my+b what is

lidiya [134]

Written in 2-point form, the equation of the line is
y = (y2-y1)/(x2-x1)·(x-x1) +y1
y = (3-(-5))/(-6-(-4))·(x-(-4)) + (-5)
y = 8/-2·(x +4) - 5
y = -4x -21

The value of b is -21.

6 0

2 years ago