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
zysi [14]
3 years ago
6

Write down the quadratic equation whose roots are $x = -7$ and $x = 1,$ and the coefficient of $x^2$ is 1. Enter your answer in

the form "$x^2 + bx + c = 0$".
Mathematics
1 answer:
pav-90 [236]3 years ago
4 0
<h2>Steps:</h2>

So firstly, since we know that the coefficient of x² is 1, this means that this is our base equation:

y = x² + bx + c

Now, since we know that the roots are -7 and 1, set y = 0 and set x = -7 and 1 and simplify:

0=(-7)^2+b(-7)+c\\0=49-7b+c\\-49=-7b+c\\\\0=1^2+b(1)+c\\0=1+b+c\\-1=b+c\\\\-49=-7b+c\\-1=b+c

Now with this, we can set up a system of equations to solve for b and c. For this, I will be using the elimination method. For this, subtract the 2 equations:

\begin{alignedat}{2}-49&=-7b+c\\-(-1&=b+c)\\-48&=-8b\end{alignedat}

Now that the c variable has been eliminated we can solve for b. For this, divide both sides by -8 and your first part of your answer is b = 6.

Now that we know the value of b, plug it into either equation to solve for c:

-49=-7(6)+c\\-49=-42+c\\-7=c\\\\-1=6+c\\-7=c

<h2>Answer:</h2>

<u>Putting it together, your final answer is x² + 6x - 7 = 0.</u>

You might be interested in
If y varies inversely as the square of x, and y = 1/8 when x = 1, find y when x = 5.
Kisachek [45]
Y = k / x² ( y varies inversely as the square of x ) 
y = 1/8 when x = 1:
1/8 = k / 1²
8 k = 1
k = 1/8
For x = 5:
y = 1/8  / 5² = 1/8 : 25 = 1/8 · 1/25 = 1/200
Answer: A ) 1/200


6 0
3 years ago
Which of the following appear in the diagram below
Nataly_w [17]
Uh... What diagram? I cant understand what you are tryimng to ask if i dont even know where the diagram is. Just saying.

8 0
3 years ago
Cable Strength: A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the ca
KatRina [158]

Answer:

95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

Step-by-step explanation:

We are given that the engineers take a random sample of 45 cables and apply weights to each of them until they break. The mean breaking weight for the 45 cables is 768.2 lb. The standard deviation of the breaking weight for the sample is 15.1 lb.

Since, in the question it is not specified that how much confidence interval has be constructed; so we assume to be constructing of 95% confidence interval.

Firstly, the Pivotal quantity for 95% confidence interval for the population mean is given by;

                            P.Q. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean breaking weight = 768.2 lb

            s = sample standard deviation = 15.1 lb

            n = sample of cables = 45

            \mu = population mean breaking strength

Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

<u>So, 95% confidence interval for the population mean, </u>\mu<u> is ;</u>

P(-2.02 < t_4_4 < 2.02) = 0.95  {As the critical value of t at 44 degree

                                           of freedom are -2.02 & 2.02 with P = 2.5%}  

P(-2.02 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 2.02) = 0.95

P( -2.02 \times {\frac{s}{\sqrt{n} } } < {\bar X-\mu} < 2.02 \times {\frac{s}{\sqrt{n} } } ) = 0.95

P( \bar X-2.02 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X+2.02 \times {\frac{s}{\sqrt{n} } } ) = 0.95

<u>95% confidence interval for</u> \mu = [ \bar X-2.02 \times {\frac{s}{\sqrt{n} } } , \bar X+2.02 \times {\frac{s}{\sqrt{n} } } ]

                                     = [ 768.2-2.02 \times {\frac{15.1}{\sqrt{45} } } , 768.2+2.02 \times {\frac{15.1}{\sqrt{45} } } ]

                                     = [763.65 lb , 772.75 lb]

Therefore, 95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

3 0
3 years ago
Is negative 5 a rational number
In-s [12.5K]
Its a rational number but also a integer and could never be a whole number because its a negative and whole numbers are always positive
 
7 0
3 years ago
What is the following quotient? Square root 120/ square root 30<br> 2<br> 4<br> 210<br> 3/10
svlad2 [7]

Answer:

2

Step-by-step explanation:

sqrt(120)/ sqrt(30)

We know that sqrt(a)/ sqrt(b) = sqrt(a/b)

sqrt(120/30)

sqrt(4)

2

5 0
3 years ago
Other questions:
  • Calculate the area of the surface S. S is the portion of the cone (x^2/4)+(y^2/4)=(z^2/9) that lies between z=4 and z=5
    11·1 answer
  • Can somebody help me with this problem
    7·1 answer
  • Find an angle between 0° and 360° that is coterminal with –150°.​
    8·1 answer
  • A jar has marbles in it. Three tenths of the marbles are red. Five tenths of the marbles are blue. Two tenths of the marbles are
    10·2 answers
  • What is the value of cos (tan^-1 1)
    13·2 answers
  • PLEASEEE HELP QUICK!!!! find the midpoint of (5,11) and (4,-2)​
    7·2 answers
  • PLEASE ANSWER I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS GOOD PLEASE
    6·2 answers
  • What is the difference 1 1/2 - 3/4 ?
    11·1 answer
  • PLEASE HELP ME GUYS ×0×<br><br>Find the RATIO and the EXACT VALUE of the given Tan A.​
    14·1 answer
  • I'm abt to burn my house down follow my insta, rsokolskiy9, for the full video
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!