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Law Incorporation [45]
3 years ago
15

What is the discriminant in the quadratic equation x2 + 11x + 121 = x + 96?      A. 0 B. 100 C. 20 D. 200

Mathematics
2 answers:
Marizza181 [45]3 years ago
8 0
X² + 11x + 121 = x + 96

x² + 11x - x + 121 - 96 = 0

x² + 10x + 25 = 0.  Compare to ax² + bx + c = 0.

a = 1, b = 10, c = 25.

Discriminant, Δ = (b² - 4ac)

=  (10² - 4*1*25)

= (100 - 100)

= 0.

Discriminant = 0

Option A.
Maurinko [17]3 years ago
7 0
Given:
x² + 11x + 121 = x + 96

First, we need to convert it into a quadratic equation.

x² + 11x - x + 121 - 96 = 0
x² + 10x + 25 = 0

a = 1 ; b = 10 ; c = 25

Quadratic formula:

x = (-b <u>+</u> (√b² - 4ac)) ÷ 2a

The discriminant is under the radical sign

discriminant ⇒ b² - 4ac ⇒ 10² - 4(1)(25) ⇒ 100 - 100 = 0

Correct answer is A. 0
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babymother [125]

Ansgilcx dhsvguydfsjhujvcouwaihgraeuvyjsghdnvufyiekghabsuivkjkesd

Step-by-step explanation:

3 0
2 years ago
A sample of 1200 computer chips revealed that 45% of the chips fail in the first 1000 hours of their use. The company's promotio
yaroslaw [1]

Answer:

z=\frac{0.45 -0.48}{\sqrt{\frac{0.48(1-0.48)}{1200}}}=-2.08

p_v = P(Z

So the p value obtained was a low value and using the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of chips that fail in the first 1000 hours of their use is not significantly less than 0.48.   

Step-by-step explanation:

Data given and notation

n=1200 represent the random sample taken

\hat p=0.45 estimated proportion of chips that fail in the first 1000 hours of their use

\mu_0 =0.48 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion si less then 0.48:  

Null hypothesis:p\geq 0.48  

Alternative hypothesis:p < 0.48  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion  is significantly different from a hypothesized value .

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.45 -0.48}{\sqrt{\frac{0.48(1-0.48)}{1200}}}=-2.08

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

p_v = P(Z

So the p value obtained was a low value and using the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of chips that fail in the first 1000 hours of their use is not significantly less than 0.48.  

6 0
3 years ago
Can you help me with my work
andrezito [222]

Answer:

1. x = ±9

2. x=\pm \sqrt{13}

3. 12 and -12.

4. Antoine is incorrect. There exists two solutions x=5 and x= -5.

Step-by-step explanation:

According to the questions,

Problem 1. x^{2}-81=0 i.e. x^{2}=81 i.e. x = ±9.

Problem 2. 2x^{2}-26=0 i.e. x^{2}-13=0 i.e. x^{2}=13 i.e. x=\pm \sqrt{13}

Problem 3. [tex]f(x)=x^{2}-144[tex]

To find the roots, we take, [tex]x^{2}-144=0[tex] i.e. [tex]x^{2}=144[tex] i.e. x = ±12.

Thus, the options are 12 and -12.

Problem 4. We have [tex]f(x)=x^{2}+25[tex]

For the roots, we take, [tex]x^{2}+25=0[tex] i.e. [tex]x^{2}=25[tex] i.e. x = ±5.

Thus, Antoine is not correct and two solutions namely x=5 and x= -5 exists.

8 0
2 years ago
5w²-5w=0 . -10n²+35n=0 . 2x²+15x=0 . 18c²+6c=0 . -32y²-24y=0
love history [14]

5 {w}^{2}  - 5w = 0\Leftrightarrow 5w(w - 1) = 0\Leftrightarrow w = 0 \: \vee \: w = 1 \\  - 10 {n}^{2}  + 35n = 0\Leftrightarrow  - 5n(2n - 7) = 0\Leftrightarrow n = 0 \: \vee \: n =  \frac{7}{2}  \\ 2 {x}^{2}  + 15x = 0\Leftrightarrow x(2x + 15) = 0\Leftrightarrow x = 0 \: \vee \: x =  \frac{15}{2}  \\ 18 {c}^{2}  + 6c = 6c(3c + 1) = 0\Leftrightarrow c = 0  \: \vee \: c =  -  \frac{1}{3}  \\  - 32 {y}^{2}  - 24y = 0\Leftrightarrow  - 8y(4y + 3) = 0\Leftrightarrow y = 0 \:\vee \: y =  -  \frac{3}{4}  \\ 3 {k}^{2}  = 6k\Leftrightarrow k = 0 \: \vee \: k = 2 \\ 6 {h}^{2}  = 3h\Leftrightarrow h = 0 \: \vee \: h =  \frac{1}{2}  \\ 4 {s}^{2}  = 10s\Leftrightarrow s = 0 \: \vee \: s =  \frac{5}{2}  \\  - 42 {z}^{2}  = 14z\Leftrightarrow z = 0 \:\vee \: z =  -  \frac{1}{3}

6 0
3 years ago
A right angle always has a measurement of less than 90 degrees. True or false?
Darya [45]
A right angle always has 90 degrees. So this is false.
4 0
2 years ago
Read 2 more answers
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