What is (-4,9) as an inequality

What are the coordinates of the vertex of the function f(x)=x2+10x-3?

Vlad1618 [11]

Answer:

(- 5, - 28 )

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² + 10x

f(x) = x² + 2(5)x + 25 - 25 - 3

= (x + 5)² - 28 ← in vertex form

with (h, k) = (- 5, - 28)

Vertex = (- 5, - 28 )

5 0

3 years ago

Grades on a standardized test are known to have a mean of 1000 for students in the US. The test is administered to 453 randomly

Mademuasel [1]

Answer:

a: 1003 < µ < 1023

b: See attached photo for answers

c: see below

d and e: See second attached photo

f: See below

Step-by-step explanation:

a. to find a confidence interval, first find the error with the formula,

E = Z(σ/√n) where Z is the value of the z-score that relates to the confidence level, σ is the standard deviation of the population (or of the sample if the population standard deviation isn't given), and n is the sample size

For this problem, E = 1.96(108/√453) = 9.95 = 10

Now add and subtract that value form the sample average...

x - E < µ < x + E becomes 1013 - 10 < µ 1013 + 10

simplifies to 1003 < µ < 1023

b. See attached photo for hypothesis test results...

c. H0: µ = 1013

Ha: µ > 1013 (claim)

They want to test if it's greater than their first attempt, so this claim becomes the alternate hypothesis. We're testing against their first attempt, that's why µ = 1013, not 1000

d and e. See second attached photo for hypothesis test results...

f. There is enough evidence to support the claim that the students second attempt was an improvement from their first attempt. They happened to take a 2 hour tutoring course between tests. This doesn't prove that the tutoring was effective thought. It very well might have been effective, but also, the students taking the test again means they've already seen the test and know what to expect, which could have also boosted their scores.

8 0

4 years ago

A football team is on the 35-yard line. The quarterback is sacked at the line of scrimmage. The team gains 0 yards, so they are

Lelu [443]

This is called the "Additive Identity Property (of Addition)". Any number plus or minus 0 is still that number.

$x+0 = 0$

$x-0 = 0$

This is reflected in the second equation here.

3 0

4 years ago

Gompers is trying to cut a round pizza into the largest possible number of pieces with 3 straight cuts of the knife. He can't r

anzhelika [568]

<span>The first two cuts can intersect at only 1 pt regardless of where they are placed. So 4 pieces there. The last cut can only intersect each other cut a 1 pt, regardless of placement. As long as the intersection is different than the first intersection, then you will have 7 pieces.</span>

3 0

3 years ago

two sister decided to watch all the episodes of a popular tv show on DVD. Abby has already watched 9 episodes and will continue

adoni [48]

After 9 days, they will both have watched 18 episodes.

5 0

3 years ago