1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nesterboy [21]
3 years ago
12

Use the quadratic formula to solve for the roots of the following equation. x 2 – 4x + 13 = 0

Mathematics
2 answers:
diamong [38]3 years ago
8 0

x = [ -(-4)  +/- sqrt ( (-4)^2 - 4*1*13) ] / 2

x =  (4 + sqrt -36) / 2 ,  (4 - sqrt -36) / 2

x = (4 +  6i) / 2 ,  (4 - 6i) 2

x  = 2 + 3i ,  2 - 3i   Answer

Artyom0805 [142]3 years ago
5 0
  • Quadratic Formula: x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} , with a = x^2 coefficient, b = x coefficient, and c = constant

With our equation, plug in the values:

x=\frac{4\pm \sqrt{(-4)^2-4*1*13}}{2*1}

Next, solve the exponent and multiplications:

x=\frac{4\pm \sqrt{16-52}}{2}

Next, solve the subtraction:

x=\frac{4\pm \sqrt{-36}}{2}

Next, factor out i (i = √-1):

x=\frac{4\pm \sqrt{36}i}{2}

Next, solve the square root:

x=\frac{4\pm 6i}{2}

Lastly, divide and <u>your answer is:</u>

x=2\pm 3i

You might be interested in
What is the range of the function y= 2sinx​
Nana76 [90]
<h2>Hello!</h2>

The answer is: [-2,2]

<h2>Why?</h2>

The range of a function shows where the function can exist in the y-axis.

To know the range of the function, we have to isolate x,

So

y=2sinx\\\frac{y}{2}=sinx\\ Sin^{-1}(\frac{y}{2}) = x

The only possible values that y can take go from -2 to 2. Taking values out of these values will give as result a non-real number.

Therefore,

The range of  the function is [-2,2]

Have a nice day!

4 0
3 years ago
Read 2 more answers
A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name br
natima [27]

Answer:

Step-by-step explanation:

Given that:

A study is conducted and the study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands.

a)

Thus; we formulate the null and the alternative hypotheses as follows:

The proportion is ; \frac{64}{100} = 0.64

Null hypothesis:    {H_0}:p = 0.64  

The Null hypothesis states that there is no evidence that “the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%”.

Alternative hypothesis: {H_a}:p \ne 0.64H

The Alternative hypothesis states that there is evidence that “the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%”.

b)

The proportion of the population = 0.64

The sample size n = 100

The number of shoppers = 52  stating that the supermarket brand was as good as the national brand

The sample proportion \hat  p = \frac{52}{100}

\hat  p = 0.52

The z - value is calculated by the formula:

z = \dfrac{\hat p-p}{\frac{\sqrt{ p(1-p)}}{100 }}

z = \dfrac{0.52-0.64}{\frac{\sqrt{ 0.64(1-0.64)}}{100 }}

z = \dfrac{-0.12}{0.048 }}

z = -2.50

Since z = -2.50

the p-value = 2P(Z ≤ -2.50)

p-value = 2 × 0.0062

The p-value = 0.0124

c)

At  significance level,  ∝ = 0.05 ; The p-value = 0.0124

According to  the rejection rule, if p-value is less than 0.05 then we will reject null hypothesis at ∝ = 0.05

Hence, the p-value =0.0124 < ∝ (=0.05)

According to the reject rule; reject null hypothesis.

Conclusion: There is no evidence at all that the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%.

d) we know that the significance level of ∝  = 0.05

The value{z__{0.05}}  is obtained as:

P\left( {\left| Z \right| \le z} \right) = 0.05

Now; to determine Z ; we locate the probability value of 0.05 form the table of standard normal distribution. Then we proceed to the left until the  first column is reached and  the value is 1.90. Also , we move upward until we reach the top and the value is 0.06. Now; the intersection of the row and column results the area  to the left of z

This implies that :P(Z \leq -1.96)=0.05

The critical value for left tail is -1.96 and the critical value for right tail is 1.96.

Conclusion:

The critical value is -1.96 and the value of test statistic is - 2.50.  Here, we can see that  the value of test statistic is lesser than the critical value. Hence, we can be concluded that there is evidence that reject the null hypothesis.

Therefore, Yes, the national brand ketchup manufacturer is pleased with the conclusion.

5 0
3 years ago
Which can be used to expand the expression below?
KiRa [710]

Answer:

Distributive Property

Step-by-step explanation:

We have

5(3x - 6/7)

Distributive Property would work because 5 has to be mutliplied by 3x and -6/7 to rid the parenthesis and also give a final answer for the equation. Any others will lead to a wrong answer.

7 0
3 years ago
Read 2 more answers
What is 2x+8y=12 in slope intercept form <br>as well as x-2y=0 in slope intercept form 
earnstyle [38]
the \ slope \ intercept \ form \ is : \\ \\ y= mx +b \\ \\ 2x+8y=12 \ \ |-2x \\ \\8y=-2x+12\ \ /:8\\ \\y=-\frac{2}{8}x+\frac{12}{8}

y=-\frac{1}{4}x+\frac{3}{4}\\ \\ m=-\frac{1}{4}



x-2y=0 \ \ | -x \\ \\-2y=-x \ \ /:(-2)\\ \\y=\frac{1}{2}x \\ \\ m= \frac{1}{2}






8 0
3 years ago
Read 2 more answers
X+3/2 - X-2/2 = 1 Hence find p, if 1/X + p = 1​
jek_recluse [69]

Answer:

pie =1 so hence find p x+3+2 -X-22+1 =1

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • Whats commutative property of multiplication.
    6·1 answer
  • IN NEED OF ANSWER :( A flower bed is in the shape of a triangle with one side twice the length of the shortest​ side, and the th
    9·1 answer
  • Question 14 of 20 :
    5·1 answer
  • What is 8-8 to the power of -1 ?
    14·1 answer
  • Jay had these daily balances on his credit card for his last billing period. He did not pay the card in full the previous month.
    5·1 answer
  • During gym class yesterday. Jason was able to throw a football about 66 feet down the field. Using the
    6·2 answers
  • K(x)= -3x - 3; find k(-2)
    12·1 answer
  • Hi I need help plssssssss
    12·1 answer
  • A recipe for a loaf of bread requires 2/3 cup of flour. How many cups of flour would it take to make 15 loaves of bread?
    7·1 answer
  • Find the value of x.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!