Writing is not that easy...but grammarly can help! this sentence is grammatically correct, but it's wordy and hard to read :0

Tom [10]

Answer: the function g(x) has the smallest minimum y-value.

Explanation:

1) The function f(x) = 3x² + 12x + 16 is a parabola.

The vertex of the parabola is the minimum or maximum on the parabola.

If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.

The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.

When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).

Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.

Then, finding the minimum value of the function is done by finding the vertex.

I will change the form of the function to the vertex form by completing squares:

Given: 3x² + 12x + 16

Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4

That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).

Then the minimum value is 4 (when x = - 2).

2) The othe function is g(x)= 2 *sin(x-pi)


The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.

When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2

Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.

7 0

3 years ago

Solve the variable Show ALL steps. -25 + x = 37

vodomira [7]

Answer:

x=62

Step-by-step explanation:

1. add + 25 to both sides because when you have a negative you have to add.

2. When you add 25 to 37 you get 62.

therefore 62 is the answer

6 0

3 years ago

Read 2 more answers

I need help with range and domain

Katyanochek1 [597]

Answer:

69

Step-by-step explanation:

lol lol lol lol lol lol lol

4 0

3 years ago

National data indicates that 35% of households own a desktop computer. In a random sample of 570 households, 40% owned a deskt

Elan Coil [88]

Answer:

Yes, this provide enough evidence to show a difference in the proportion of households that own a desktop.

Step-by-step explanation:

We are given that National data indicates that 35% of households own a desktop computer.

In a random sample of 570 households, 40% owned a desktop computer.

Let p = population proportion of households who own a desktop computer

SO, Null Hypothesis, $H_0$ : p = 25% {means that 35% of households own a desktop computer}

Alternate Hypothesis, $H_A$ : p $\neq$ 25% {means that % of households who own a desktop computer is different from 35%}

The test statistics that will be used here is One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of 570 households who owned a desktop computer = 40%

n = sample of households = 570

So, test statistics = $\frac{0.40-0.35}{{\sqrt{\frac{0.40(1-0.40)}{570} } } } }$

= 2.437

Since, in the question we are not given with the level of significance at which to test out hypothesis so we assume it to be 5%. Now at 5% significance level, the z table gives critical values of -1.96 and 1.96 for two-tailed test. Since our test statistics doesn't lies within the range of critical values of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that % of households who own a desktop computer is different from 35%.

3 0

3 years ago

Latita had 12 marbles. she gave 2 marbles to her friend she has 10/12 of her marbles left write answer in simplest form

zloy xaker [14]

The answer would be 5/6.

3 0

3 years ago