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3 years ago

Rewrite the following quadratic functions in intercept or factored form. Show your work.

Mathematics

2 answers:

puteri [66]3 years ago

4 0

Answer:

$(2x+3)^2$

Step-by-step explanation:

We are given the following the quadratic function and we are to rewrite it in intercept or factored form:

$y = 9 + 12x + 4x^2$

Rearranging the given function to get:

$y = 4x^2+12x+9$

Rewriting $4$ and $4$ in $y = 4x^2+12x+9$ as perfect squares:

$2^2x^2+12+3^2$

Now applying the exponent rule: $a^mb^m=(ab)^m$

$(2x)^2+12x+3^2$

Rewriting it in the form $(a+b)^2=a^2+2ab+b^2$ :

$(2x)^2+2(2x)(3)+3^2$

Here $a=2x$ and $b=3$ . So the factored form is $(2x+3)^2$

Vlad [161]3 years ago

3 0

Answer:

y = (2x + 3)(2x + 3) = (2x + 3)²

Step-by-step explanation:

We are given a quadratic function and we have to write it in factored form.

y = 9 + 12x + 4x²

y = 4x² + 12x + 9

We can break the mid-term in such a way that when they are multiplied, the factors give a product of 36x² and when added, they give a result of 12x, as show below:

y = 4x² + 6x + 6x + 9

Taking 2x common from the first two variables and 3 from the second two

y = 2x(2x + 3) + 3(2x + 3)

Taking 2x+3 common

y = (2x + 3)(2x + 3) = (2x + 3)²

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Which statements are true for the following expression? (9 + 1) · 5

kvasek [131]

Answer:

Step-by-step explanation:

add

9 + 1 = 10

multiply

10 * 5 = 50

Answer: 50

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2 years ago

Some scientists believe alcoholism is linked to social isolation. One measure of social isolation is marital status. A study of

frez [133]

Answer:

1) H0: There is independence between the marital status and the diagnostic of alcoholic

H1: There is association between the marital status and the diagnostic of alcoholic

2) The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

3) $\chi^2 = \frac{(21-33.143)^2}{33.143}+\frac{(37-41.429)^2}{41.429}+\frac{(58-41.429)^2}{41.429}+\frac{(59-46.857)^2}{46.857}+\frac{(63-58.571)^2}{58.571}+\frac{(42-58.571)^2}{58.571} =19.72$

4) $df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.72)=5.22x10^{-5}$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.72,2,TRUE)"

Since the p value is lower than the significance level so then we can reject the null hypothesis at 5% of significance, and we can conclude that we have association between the two variables analyzed.

Step-by-step explanation:

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Assume the following dataset:

Diag. Alcoholic Undiagnosed Alcoholic Not alcoholic Total

Married 21 37 58 116

Not Married 59 63 42 164

Total 80 100 100 280

Part 1

We need to conduct a chi square test in order to check the following hypothesis:

H0: There is independence between the marital status and the diagnostic of alcoholic

H1: There is association between the marital status and the diagnostic of alcoholic

The level os significance assumed for this case is $\alpha=0.05$

Part 2

The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

Part 3

The table given represent the observed values, we just need to calculate the expected values with the following formula $E_i = \frac{total col * total row}{grand total}$

And the calculations are given by:

$E_{1} =\frac{80*116}{280}=33.143$

$E_{2} =\frac{100*116}{280}=41.429$

$E_{3} =\frac{100*116}{280}=41.429$

$E_{4} =\frac{80*164}{280}=46.857$

$E_{5} =\frac{100*164}{280}=58.571$

$E_{6} =\frac{100*164}{280}=58.571$

And the expected values are given by:

Diag. Alcoholic Undiagnosed Alcoholic Not alcoholic Total

Married 33.143 41.429 41.429 116

Not Married 46.857 58.571 58.571 164

Total 80 100 100 280

And now we can calculate the statistic:

$\chi^2 = \frac{(21-33.143)^2}{33.143}+\frac{(37-41.429)^2}{41.429}+\frac{(58-41.429)^2}{41.429}+\frac{(59-46.857)^2}{46.857}+\frac{(63-58.571)^2}{58.571}+\frac{(42-58.571)^2}{58.571} =19.72$

Part 4

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.72)=5.22x10^{-5}$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.72,2,TRUE)"

7 0

3 years ago

Which property is shown below?

Tpy6a [65]

Answer:

Step-by-step explanation:

The identity property for addition tells us that zero added to any number is the number itself.

5 0

2 years ago

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A store buys frozen burritos from a supplier for $1.40 each. The store adds a markup of 80% to determine the retail price. This

boyakko [2]

$1.40 - price from a supplier = 100%
100% + 80% = 180% = 1,8 - the retail price

1,40 * 1,8 = $2,52 - the retail price

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2,52 * 0,75 = $1,89 - the sale price.

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3 years ago

The ratio of the side lengths of a quadrilateral is 3:3:5:8, and the perimeter is 380cm. What is the measure of the longest side

MariettaO [177]

Answer: The second option (160 cm)

Step-by-step explanation:

1. You can obtain the perimeter of a quadrilateral by adding the lenghts of the sides.

2. You know that the ratio of the side lengths is 3:3:5:8 and the perimeter is 380 centimeters.

3. Therefore, you can write the following expression, where x is an integer:

$3x+3x+5x+8x=380$