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BlackZzzverrR [31]
3 years ago
9

Explain how you can determine the number of real number solutions of a system of equations in which one equation is linear and t

he other is quadratic–without graphing the system of equations.
Mathematics
2 answers:
DerKrebs [107]3 years ago
4 0

Isolate one variable in the system of equations. Use substitution to create a one-variable equation. Then, set the quadratic equation equal to zero and find the discriminant. If the discriminant is negative, then there are no real number solutions. If the discriminant is zero, then there is one real number solution. If the discriminant is positive, then there are two real number solutions.

fenix001 [56]3 years ago
4 0

Answer:

e2020

Step-by-step explanation:

Use substitution to create a one-variable equation.

Set the quadratic equation equal to zero and find the discriminant.

The value of the discriminant will tell you how many real number solutions the system of equations has

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What is the volume of a right circular cylinder with a diameter of 46. 25 cm and a height of 18. 5 cm? Enter your answer in the
Sedbober [7]

The volume of the right circular cylinder is 31064.54 cm³.

What is the formula for the volume of cylinder?

Formula:

V = πr²h.............. Equation 1

Since,

V = Volume of the right circular cylinder

r = radius of the base of the cylinder

h = height of the cylinder.

We have given that,

r = 46.25/2 = 23.125 cm

h = 18.5 cm

π = 3.14

We have to calculate volume of right circular cylinder.

Therefore,

Substitute these values into equation 1

V = 3.14(23.125²)(18.5)

V = 31064.54 cm³

Therefore

The volume of the right circular cylinder is 31064.54 cm³.

Learn more about the volume of a cylinder here:

brainly.com/question/1082469

3 0
3 years ago
Trevor spent $27 and now has no money left. What did he have before his purchase
Sav [38]

Answer:$27

Step-by-step explanation:

x-27=0

0+27=27

27-27=0

8 0
3 years ago
Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.â  Suppose a small group of 11 Allen's humming
alexira [117]

Answer:

3.15-1.28\frac{0.38}{\sqrt{11}}=3.003    

3.15+ 1.28\frac{0.38}{\sqrt{11}}=3.297    

So on this case the 80% confidence interval would be given by (3.003;3.297)

And the margin of error is given by:

ME = 1.28\frac{0.38}{\sqrt{11}}= 0.147    

Step-by-step explanation:

Previous concepts

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".

\bar X=3.15 represent the sample mean

\mu population mean (variable of interest)

\sigma=0.38 represent the population standard deviation

n=11 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.80 or 80%, the value of \alpha=0.2 and \alpha/2 =0.1, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NOR.INV(0.1,0,1)".And we see that z_{\alpha/2}=1.28

Now we have everything in order to replace into formula (1):

3.15-1.28\frac{0.38}{\sqrt{11}}=3.003    

3.15+ 1.28\frac{0.38}{\sqrt{11}}=3.297    

So on this case the 80% confidence interval would be given by (3.003;3.297)

And the margin of error is given by:

ME = 1.28\frac{0.38}{\sqrt{11}}= 0.147    

8 0
3 years ago
Find the equation of the line containing the points (20,-7) and (10,-2). Type your answer in this order and don't use spaces or
aliina [53]

(\stackrel{x_1}{20}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{20}}}\implies \cfrac{-2+7}{-10}\implies -\cfrac{1}{2}

\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{-\cfrac{1}{2}}(x-\stackrel{x_1}{20}) \\\\\\ y+7=-\cfrac{1}{2}x+10\implies y=-\cfrac{1}{2}x+3

4 0
2 years ago
Given M is the midpoint ABA. The coordinate of A are (-4,2) and the cordinates of M are (1,1). Find the coordinate of B. Choose
4vir4ik [10]

Answer:

The coordinate of B is (6,0)

Step-by-step explanation:

Given;

coordinate of A = (-4,2) = (x₁, y₁)

coordinate of M = (1,1)

let coordinate of B = (x₂, y₂)

Mid-point is given by;

M = \frac{X_1 + X_2}{2} , \frac{Y_1 + Y_2}{2}\\\\M= (1,1)\\\\1,1 =\frac{X_1 + X_2}{2} , \frac{Y_1 + Y_2}{2}\\\\ \frac{X_1 + X_2}{2}  = 1 ----equation (1)\\\\\frac{Y_1 + Y_2}{2} = 1 -----equation(2)\\\\Solving \ equation(1)\\\\\frac{-4+ X_2}{2}  = 1\\\\-4+ X_2 = 2\\\\X_2 = 2+4\\\\X_2 = 6\\\\Solving \ equation(2)\\\\\frac{Y_1 + Y_2}{2} = 1\\\\\frac{2+ Y_2}{2} = 1\\\\2+Y_2 = 2\\\\Y_2 = 2-2\\\\Y_2 = 0\\\\B = (X_2, \ Y_2)\\\\B = (6, \ 0)

Therefore, the coordinate of B is (6,0)

5 0
3 years ago
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