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1 year ago

49x^2=-21x-2 quadratic functions

Mathematics

1 answer:

lara [203]1 year ago

3 0

Answer: 49x^2=-21x-2 quadratic functions -1/7and -2/7

Step-by-step explanation:

Quadratic function:

In elementary algebra, the quadratic formula is a formula that provides the solution to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring, completing the square, graphing and others.

Move terms to the left side

49 $x^{2}$ =-21x-2

49 $x^{2}$ -(-21x-2) =0

Distribute

49 $x^{2}$ -(-21x-2) =0

49 $x^{2}$ +21x+2=0

Use the quadratic formula

x=(-b±√ $b^{2}$ -4ac ) / 2a

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

49 $x^{2}$ +21x+2=0

let, a=49

b=21

c=2

Replace with values in this equation

X=(-b±√ $b^{2}$ -4ac ) / 2a

Simplify

Evaluate the exponent

Multiply the numbers

Subtract the numbers

Evaluate the square root

Multiply the numbers

x=(-21±7) /98

Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.Separate

x=(-21+7) /98

x=(-21-7) /98

Solve

Rearrange and isolate the variable to find each solution

x=-1/7

x=-2/7

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2. The National Safety Council routinely analyzes the benefit of seat belt use on driver safety. Their data showed that among 28

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Answer:

We conclude that there is difference in the proportion of deaths between the 2 groups.

Step-by-step explanation:

We are given that among 2823 drivers not wearing seat belts, 31 died as a result of injuries, and among 7765 drivers wearing seat belts 16 were killed.

Let $p_1$ = proportion of deaths when drivers were not wearing seat belts.

$p_2$ = proportion of deaths when drivers were wearing seat belts.

So, Null Hypothesis, $H_0$ : $p_1=p_2$ {means that there is no difference in the proportion of deaths between the 2 groups}

Alternate Hypothesis, $H_A$ : $p_1\neq p_2$ {means that there is difference in the proportion of deaths between the 2 groups}

The test statistics that would be used here Two-sample z test for proportions;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of deaths when drivers were not wearing seat belts = $\frac{31}{2823}$ = 0.011

$\hat p_2$ = sample proportion of deaths when drivers were wearing seat belts = $\frac{16}{7765}$ = 0.002

$n_1$ = sample of drivers not wearing seat belts = 2823

$n_2$ = sample of drivers wearing seat belts = 7765

So, the test statistics = $\frac{(0.011-0.002)-(0)}{\sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} } }$

= 4.438

The value of z test statistics is 4.438.

Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic doesn't lie 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 there is difference in the proportion of deaths between the 2 groups.

Also, Margin of error (E) = $1.96 \times \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} }$