All categories

3 years ago

What are the zeros of the function? f(x) = 8x2 + 2x – 21

Mathematics

2 answers:

Naddika [18.5K]3 years ago

4 0

X= 3/2 and -7/4
Factored is: (2x-3)(4x+7) you can find zeros by setting each of them to zero

amid [387]3 years ago

3 0

Answer:

$x=\frac{3}{2}$ and $x=-\frac{7}{4}$

Step-by-step explanation:

Since, the zeroes are the input values in which the value of a function is zero,

Here, the given function,

$f(x)=8x^2+2x-21$

For zeroes,

f(x) = 0

$\implies 8x^2 + 2x - 21 =0$

By middle term splitting,

$8x^2 + 14x - 12x - 21=0$

$2x(4x+7) - 3(4x+7)=0$

$(2x-3)(4x+7)=0$

By zero product property,

2x - 3 = 0 or 4x + 7 = 0

⇒ x = 3/2 or x = -7/4

Hence, the zeroes of the given equation are $x=\frac{3}{2}$ and $x=-\frac{7}{4}$

You might be interested in

In San Jose a sample of 73 mail carriers showed that 30 had been bitten by an animal during one week. In San Francisco in a samp

dsp73

Answer:

$(0.411-0.7) - 1.96 \sqrt{\frac{0.411(1-0.411)}{73} +\frac{0.7(1-0.7)}{80}}=-0.4401$

$(0.411-0.7) + 1.96 \sqrt{\frac{0.411(1-0.411)}{73} +\frac{0.7(1-0.7)}{80}}=-0.1380$

We are confident at 95% that the difference between the two proportions is between $-0.4401 \leq p_B -p_A \leq -0.1380$

1. -.4401 ≤ p1 - p2 ≤ -.1380

4. The rate of mail carriers being bitten in San Jose is statistically less than the rate San Francisco at α = 5%

Step-by-step explanation:

In San Jose a sample of 73 mail carriers showed that 30 had been bitten by an animal during one week. In San Francisco in a sample of 80 mail carriers, 56 had received animal bites. Is there a significant difference in the proportions? Use a 0.05. Find the 95% confidence interval for the difference of the two proportions. Sellect all correct statements below based on the data given in this problem.

1. -.4401 ≤ p1 - p2 ≤ -.1380

2. -.4401 ≤ p1 - p2 ≤ .1380

3. The rate of mail carriers being bitten in San Jose is statistically greater than the rate San Francisco at α = 5%

4. The rate of mail carriers being bitten in San Jose is statistically less than the rate San Francisco at α = 5%

5. The rate of mail carriers being bitten in San Jose and San Francisco are statistically equal at α = 5%

Solution to the problem

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_1$ represent the real population proportion for San Jose

$\hat p_1 =\frac{30}{73}=0.411$ represent the estimated proportion for San Jos

$n_1=73$ is the sample size required for San Jose

$p_2$ represent the real population proportion for San Francisco

$\hat p_2 =\frac{56}{80}=0.7$ represent the estimated proportion for San Francisco

$n_2=80$ is the sample size required for San Francisco

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_1 -\hat p_1) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$(0.411-0.7) - 1.96 \sqrt{\frac{0.411(1-0.411)}{73} +\frac{0.7(1-0.7)}{80}}=-0.4401$

$(0.411-0.7) + 1.96 \sqrt{\frac{0.411(1-0.411)}{73} +\frac{0.7(1-0.7)}{80}}=-0.1380$

We are confident at 95% that the difference between the two proportions is between $-0.4401 \leq p_B -p_A \leq -0.1380$

Since the confidence interval contains all negative values we can conclude that the proportion for San Jose is significantly lower than the proportion for San Francisco at 5% level.

Based on this the correct options are:

1. -.4401 ≤ p1 - p2 ≤ -.1380

4. The rate of mail carriers being bitten in San Jose is statistically less than the rate San Francisco at α = 5%

8 0

3 years ago

Over the last three evenings, Rita received a total of 91 phone calls at the call center. The third evening, she received 2 time

tatyana61 [14]

Rita received 24 phone calls on the first evening, and 19 phone calls on the second evening and 48 phone calls on the third evening at the call center.

Step-by-step explanation:

As per given details,

Rita received a total of 91 phone calls at the call center over the last three evenings.

Let us assume the number of phone calls Rita received in the first evening is X.

The second evening Rita received 5 fewer calls than the first evening

=>X-5

The third evening Rita received 2 times as any calls as the first evening

=>2X

Now as given sum of total number of calls received in the three evenings is

X + X-5 + 2X = 91

4X - 5 = 91

4X = 96

X =24.

Therefore total calls received on first evening is X = 24

On the second evening X-5 = 24-5 = 19

On the third evening 2X = 48.

4 0

3 years ago

7x = -84<br> Solve the equation

4vir4ik [10]

Answer:x = -12

Step-by-step explanation:<!>BRAINLIEST APPERICATED<!>

5 0

3 years ago

Read 2 more answers

Team A is located on the south bank of a river. Teams B and C are located on the north bank. The angle formed from Team C to Tea

creativ13 [48]

The correct answer is 58.5

6 0

3 years ago

10) The second angle in a triangle is 3° less than twice the first angle. The third angle measure 8° more than

andre [41]

Answer:

35, 67 and 78

Step-by-step explanation:

the angles are:

n, 2n-3 and 2n+8

there are 180 degrees in a triangle, so adding those terms together will give us 180

5n + 5 = 180

180 - 5 = 175

5n = 175

175 / 5 = 35

n = 35

now we have n we can put it in to the formula we have for the angles at the start:

n = 35

2n - 3 = 67

2n + 8 = 78

so the angles are

35, 67 and 78

8 0

3 years ago