(2x-y< -7
x-y≥-6 determine if (-10,5) is a solution to system

By algebra properties, the quadratic function x² - x - 20 = 0 is equivalent to the quadratic function (x + 1 / 2)² - 81 / 4 = 0.

In this problem we have a quadratic function whose form does not correspond with a perfect square trinomial, that is, a polynomial of the form (x + a)² = x² + 2 · a · x + a². Herein we can modify part of the function by means of completing the square, an application of algebra properties.

First, write the quadratic function described in the statement:

x² - x - 20 = 0

Second, use algebra properties until the square is complete:

x² - x - 20 = 0

x² - x = 20

x² - x + 1 / 4 = 20 + 1 / 4

(x + 1 / 2)² = 81 / 4

(x + 1 / 2)² - 81 / 4 = 0

To learn more on quadratic functions: https://brainly.com/question/1863222

#SPJ1

Answer:

Step-by-step explanation:

It's asking you to find the measures for all the angles.

For example, angle 1 would be 59° because it is equal to the angle across from it.

Angle 2 would equal 31° because it's a supplement angle to 59° and so on

option 3

The mean is the same as the average.

Answer:9 : 20

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

35 choices for first number

34 choices for second number (because it cannot be same as first)

34 choices for third number  ( because it cannot be same a second)

35 x 34 x 34 = 40 460 combos

Answer: 12.5 meters!

Step-by-step explanation:

1km = 1000 meters

So 5km = 5000 meters

So take 5000 divided by 400 = 12.5 meters

Answer:

12.5 is the answer for this question

The radius of the circle having the equation x² + y² - 10x + 6y + 18 = 0 is 4  units , the correct option is (b) .

In the question ,

it is given that ,

the circle is having equation ⇒ x² + y² - 10x + 6y + 18 = 0 ,

we know that ,

general equation of circle is ⇒ x² + y² + 2fx + 2gy + c = 0 ;

So , radius of circle is calculated using the below formula ,

radius [tex]=[/tex] √(f² + g² - c)

On comparing,  given equation of circle with general equation of circle ,

we get , the values of f = -5 and g = 3 .

So after substituting values of f , g and c in radius formula ,

we get ,

radius = √(25 + 9 - 18)

= √(34 - 18)

= √16 = 4 .

Therefore , the given circle has radius = 4 units .

The given question is incomplete , the complete question is

What is the radius of a circle whose equation is x² + y² - 10x + 6y + 18 = 0 ?

(a) 2 units

(b) 4 units

(c) 8 units

(d) 16 units

Learn more about Circle here

https://brainly.com/question/5720980

#SPJ4

Answer:

16

Step-by-step explanation:

The area of the surface is  5/3 [tex]\sqrt{14}[/tex][tex]\pi[/tex]

Consider that the part of the plane x+2y +3z=1 that lies inside the cylinder [tex]x^{2}[/tex] + [tex]y^{2}[/tex] =5

The surface area of an equation z= g(x,y) is given by the following formula:

[tex]\int\limits^d_d \sqrt {\alpha z/\alpha x]^{2} . [\alpha z/\alpha y]^{2} +1da[/tex]

where the D is the domain of integration.

Since the plane lies inside the cylinder[tex]x^{2}[/tex] + [tex]y^{2}[/tex] = 5, we have the domain of

D= ( (r,0) |0 [tex]\leq[/tex]r [tex]\leq[/tex][tex]\sqrt{5}[/tex],0[tex]\leq[/tex]θ[tex]\leq[/tex]2[tex]\pi[/tex])

The partial derivatives of z = 1/3 ( 1 - x - 2y) are

[tex]\alpha z/ \alpha x[/tex] = 1/3, [tex]\alpha z / \alpha y[/tex] = - 2/3

[tex]\int\limits^d_d \sqrt {[-1/3]^{2} . [-2/3]^{2} +1da[/tex]

= [tex]\int\limits^d_d \sqrt{14} / 9 da[/tex]

= [tex]\sqrt{14}/3 \int\limits^0_ {2^{\pi }[/tex] [tex]\int\limits^\sqrt{5[/tex]r dr dθ

Evaluating the integral we have

[tex]\sqrt{14}/3 \int\limits^0_ {2^{\pi }[/tex][tex]\int\limits^\sqrt{5[/tex]rdrdθ = [tex]\sqrt{14} /3[/tex] 2 [tex]\pi[/tex] [ 5/2]

                           = 5/3 [tex]\sqrt{14}[/tex][tex]\pi[/tex]

To learn more about the area of surface

https://brainly.com/question/2835293

#SPJ4

Carolyn made an error in her work because she did not correctly distribute the negative in Step 3.

A system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

The question gives:3x-2y=7 (1)y=x+2The question shows that Carolyn applies the substitution method because she replaces the variable y (equation 2) in equation 1. See the given step 2.

3x – 2y = 7

3x – 2(x + 2) = 7

3x – 2x - 4 = 7 - here it is the mistake. (Carolyn did not correctly distribute the negative).

Read more about solving systems equations here:

brainly.com/question/12691830

#SPJ1

888030 ways are there for teachers to select the students.

What is the combination?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Here, we have

A teacher selects 7 students from her class of 27 students.

We have to find how many ways are there for her to select the students of the chosen students.

The order of selecting the students does not matter here so the number of ways to select 7 students from the class of 27 to work together on a project is:

C(27,7) = 27!/(7!*(27-2)! = 888030

Hence, 888030 ways are there for teachers to select the students.

To learn more about the combinations from the given link

https://brainly.com/question/11732255

#SPJ4

The length L of an edge of each small cube if adjacent cubes touch but don't overlap is 3.45 nm.

The formula to be used for calculation is -

PV = Nkt, where P is pressure, V is volume, N is number of molecules, k is Boltzmann constant and T is temperature in Kelvin.

T = 273 + 27

Performing addition on Right Hand Side of the equation

T = 300 K

P = 101325 Pa

k = 1.38 × [tex] {10}^{-23} [/tex] J/K

Now finding the volume

V = (1 × 1.38 × [tex] {10}^{-23} [/tex] × 300)/101325

Performing multiplication and division on Right Hand Side of the equation

V = 4.09 × [tex] {10}^{-3} [/tex] m³

As we know, V = L³

So, L = [tex] {V}^{1/3} [/tex]

Keep the value of volume

L = [tex] { (4.09/1000) }^{1/3} [/tex]

Performing calculations

L = 3.45 × [tex] {10}^{-9} [/tex] m

Hence, length is 3.45 nm.

Learn more about volume -

https://brainly.com/question/29697963

#SPJ4

Answer:

Step-by-step explanation:

I will try to get the answer for you just give me a minute.!

Answer: the area of a rectangle is l x w length x width

Step-by-step explanation:

Answer: Formula of an area of a rectangle: Length x Width

Step-by-step explanation:

The statements that are true concerning the study that was carried out by the pharmaceutical company include the following: This study uses random sampling, This study uses blinding and This study uses a control group. That is option A, B and E.

A pharmaceutical company is defined as the company that has been certified to manufacture and distribute drugs such as the children's vitamin.

While selecting sample for the study, it was stated that 500 children grouped by age was randomly selected.

Out of the total samples, 250 was given the vitamin while the remaining half was given a placebo ( a blind) which would serve as concealment of the group allocation from them as they are serving as the control.

Learn more about drugs here:

https://brainly.com/question/26254731

#SPJ1

Answer:

A,B,C,

Step-by-step explanation:

PLATO

The probability that both children are boys is 1/2.

What is probability?

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. In everyday speech, the term "probability" refers to the likelihood that a specific event (or group of events) will take place, represented as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty).

Given in the question,

Mr. Smith has two children, one of them is boy.

So, the possible combinations are,

(Boy, Boy) and (Boy, Girl)

It means number of total outcomes is 2,

we have to find probability of (Boy, Boy)

It means number of favorable outcomes is 1,

The formula for the calculation of probability is:

Probability = number of favorable outcomes/ number of total outcomes,

So,

Probability = 1/2

Therefore, The probability that both children are boys is 1/2.

To know more about probability, go to link

https://brainly.com/question/13604758

#SPJ4

There is enough evidence to conclude that the new components have reduced the rate of defective chips produced.

At the null hypothesis, it is tested if there is not enough evidence that the amount has decreased, that it still is of 12, hence:

[tex]H_0: \mu = 12[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the amount has decreased, that is, it is less than 12, hence:

[tex]H_1: \mu < 12[/tex]

We have a left-tailed test, with a significance level of 0.05, hence the test statistic needed for there to be enough evidence is less than -1.645, which is the critical value.

The equation that determines the test statistic is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters in this problem are of:

[tex]\overline{x} = 8, \mu = 12, \sigma = 3.3586, n = 12[/tex]

Hence the test statistic is of:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{8 - 12}{\frac{3.3586}{\sqrt{12}}}[/tex]

z = -4.13.

Less than the critical value, hence there is enough evidence that the amount has decreased.

More can be learned about the test of an hypothesis at https://brainly.com/question/13873630

#SPJ1

The perimeter of the triangle is 50.96 inches.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

An isosceles triangle.

This means,
Two sides are equal.

Now,

The length of the altitude = 15 inches.

The length of the base = 11 inches.

Now,

The right triangle:

Base = 11/2 = 5.5 inches.

Height = 15 inches.

The other side = x

Applying the Pythagorean theorem.

x² = 5.5² + 15²

x² = 30.25 + 225

x² = 255.25

x = √255.25

x = 19.98 inches.

Now,

The perimeter of the triangle.

= 2x + 11

= 2 x 19.98 + 11

= 50.96 inches.

Thus,

The triangle's perimeter is 50.96 inches.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ1

The coefficient of determination resulting from a particular regression analysis was 0.85. Then, the correlation coefficient, assuming a positive linear relationship is 0.922.

The coefficient of determination, denoted R2 or r2 and pronounced "R-squared," is the proportion of predictable variation in the dependent variable from the independent variables.

R2 has several definitions, sometimes the same. One class of such cases involves simple linear regression where r2 is used instead of R2. If only one bin is included, r2 is simply the square of the sample correlation coefficient (that is, r) between the observed outcome and the observed prediction. If additional regressors are included, R2 is the square of the multiple correlation coefficient. In both cases, the coefficient of determination is usually between 0 and 1.

Regression analysis consists of a dependent variable (often called the "outcome" or "response" variable, or "label" in machine learning parlance) and one or more independent variables (often called "predictors"). ). ', 'covariate', 'explanatory variable' or 'feature'). The most common form of regression analysis is linear regression, which finds the best fit line (or more complex linear combination) to the data according to mathematical criteria. For example, the ordinary least-squares method computes a unique line (or hyperplane) that minimizes the sum of squared differences between the true data and that line (or hyperplane). For certain mathematical reasons (see linear regression), researchers can estimate the conditional expected value (or population mean) of the dependent variable given that the independent variable takes on a particular set of values . Less common forms of regression use slightly different techniques to estimate alternative site parameters (such as quantile regression and requirement analysis, or conditional expectations on a broader collection of nonlinear models. estimating values ​​(such as nonparametric regression). Regression analysis is primarily used for two conceptually distinct purposes.

Learn more about Regression Analysis:

https://brainly.com/question/28178214

#SPJ4

( x - 1 ) is the factor of f(x) as remainder is 0

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

According to the given information

The given polynomial is

f(x) = [tex]x^{3} + 4x^{2} +x -6[/tex]

According to the remainder theorem

( x - 1 ) will be the factor of f(x) , if f(1) is zero

So

= [tex]1^{3} + 4(1)^{2} + 1 -6[/tex]

= 1+4+1-6

= 6-6

= 0

So

( x - 1 ) is the factor of f(x) as remainder is 0

To know more about Polynomial

https://brainly.com/question/11536910

#SPJ1

The shorted distance from Asheboro to Fort Jennings is, 20.4 miles.

What is Pythagorean theorem?

The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.

In this problem we have to find the shortest  route from Asheboro to Fort Jennings using the roads shown.

From the given route the shorted distance from Asheboro to Fort Jennings is,

= 3 mi + 8 mi + (distance from North lean to Fort Jennings)

Let distance from North lean to Fort Jennings is x.

To find the value of x using Pythagorean theorem.

x^2 = 8^2 + 5^2

x^2 = 64 + 25

x^2 = 89

x = 9.433

x = 9.4

So, the total distance is, 3 mi + 8 mi + 9.4 mi =20.4 miles.

Hence, the shorted distance from Asheboro to Fort Jennings is, 20.4 miles.

To know more about Pythagorean theorem, click on the link

https://brainly.com/question/343682

#SPJ1

Complete question:

Complete question is attached below.

solve for y

y = 1.5x + 2

notice this is in form y = mx + b

m is slope, b is y intercept

m = 1.5

slope is 1.5

hope this helps :)

jeron

The correct statement regarding whether the graph represents a function is given as follows:

B. No, because it fails the vertical line test.

A graph is a relation, and it represents a function if each value of the input is mapped to only one output, that is, if the graph does not contain vertically aligned points.

From the graph given by the image at the end of the answer, the inputs for x > 2 are mapped to multiple outputs, meaning that a vertical line at any of these points would cross the function twice, meaning that the graph has vertically aligned points.

Since the graph has vertically aligned points, it fails the vertical line test, and hence the graph does not represent a function, and option B is correct.

The problem is given by the image shown at the end of the answer.

More can be learned about graphs and functions at https://brainly.com/question/12221040

#SPJ1

The mode in this situation is not defined because there is only one value for each of the mean and median.

Mean (15) and median (10) are two different measures of central tendency. The mean is the average of all values, while the median is the middle value when all the values are arranged in order. The mode is the most frequent value in a set of data, and there can be more than one mode. Since there is only one value for both the mean and median, there is no mode in this situation.

Learn more about mean here

https://brainly.com/question/15323584

#SPJ4

The required demand function for the marginal revenue function is P = 0.02x² - 0.025x.

Marginal Revenue is the revenue that is gained from the sale of an additional unit. It is the revenue that a company can generate for each additional unit sold; there is a marginal cost attached to it, which must be accounted for.

The marginal revenue function, find the demand capability is P = 0.02x² - 0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .

Considering that,

We need to find for the peripheral income capability, find the interest capability.

Recollect that the pay is zero assuming no things are sold:

R'(x) = 0.06x² - 0.05x + 138

p(x) is what.

That's what we know,

MR = dTR/dx = 0.06x² - 0.05x + 138

Incorporating the marginal revenue function , we get complete income capability,

MR = TR

= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 138x

= (0.06x³)/3 - (0.05x²)/2 + 138 x

TR = 0.02 x³ - 0.025 x² + 138 x

TR = (P)(Q) = (P)(x) = 0.02 x³ - 0.025 x² + 138 x

P = ( 0.02 x³ - 0.025 x² + 138 x)/x

P = 0.02x² - 0.025x + 138

In this manner, The marginal revenue function, find the interest capability is P = 0.02x² - 0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .

To know more about Marginal Revenue visit:

brainly.com/question/25404320

#SPJ4

The slope is the measure of the steepness and direction of a line. You can predict whether lines in a coordinate plane are parallel, perpendicular, or none by finding the slope of the lines.

There are two distinct points on any line that can be used to calculate its slope. Between two distinct points on a line, the slope formula calculates the ratio of vertical and horizontal changes. In mathematics, the slope is calculated as the ratio of the rise to the run, or as the rise divided by the run. The slope is a measure of how steep a line is in a coordinate plane.

Read more about How to calculate the Slope:

brainly.com/question/3493733

#SPJ4

Answer:

The slope is -2 and the y-intercept is (0,1)

the equation of the line that passes through the points − 1/3 and 1 11 is

y = 3x + 8 with slope 12 1/3.

1. Find the slope of the line.

m = (11 - -1/3) / (1 - -1/3)

m = 12 1/3

2. Using the point-slope equation, substitute the slope and one point from the line

y - y1 = m(x - x1)

y - -1/3 = 12 1/3 (x - (-1/3))

3. Solve for y

y = 12 1/3x + 8

Learn more about slope here

https://brainly.com/question/3605446

#SPJ4