Find the sum and product of the roots for each quadratic equation. x²-2 x+1=0 .

Answer:

The answer is below

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are  obtuse, scalene, equilateral, isosceles etc.

An isosceles triangle is a triangle with two equal sides, the base angles of an isosceles triangle is equal.

Since ΔMNP is an isosceles triangle with MN = PN, then:

∠QMN = ∠QPN (base angles of an isosceles triangle are equal)

∠MNQ = ∠PNQ (NQ bisects ∠MNP producing two equal angles)

∠MQN = ∠PQN (right angles)

The amount of snow that Gabriella would have on her lawn t hours of snow melting is; S(t) = 12.5 - 0.5t

The snow started melting at a rate of 0.5 inches per hour and it is known that 3 hours  after the storm ended, the depth of snow was down to 11 inches.

Snow melted in 3 hours = 0.5 * 3 = 1.5 inches

Thus;

The Initial depth of snow = 11 + 1.5 inches = 12.5 inches.

Now, depth of snow on Gabriella's lawn = Initial depth - 0.5(Number of hours)

Let S(t) be the depth of snow on  Gabriella's lawn, in inches, t hours after the snow stopped falling.

Thus; S(t) = 12.5 - 0.5t

Read more about Constant Rates at; https://brainly.com/question/16302622

#SPJ1

325

Step-by-step explanation:

The scale factor of the point will be ( 1 /  4).

The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

Given that under a dilation centered at the origin, the vertex, (2, 3), of a polygon is moved to the point (−8, −12).

The scale factor will be calculated as below:-

Scale factor = ( 2 / 8 ) = ( 1 / 4 )

Therefore, the scale factor of the point will be ( 1 /  4).

To know more about scale factors follow

https://brainly.com/question/25722260

#SPJ2

The cost of the popcorn is $8.

The equation that represents the total cost of your friend's purchase, including the cost of the popcorn, can be written as:

Total cost = Cost of the drink + Cost of the popcorn

To know more about how to calculate the total cost of your friend's purchase, refer here:

To calculate the total cost, we need to add the cost of the drink to the cost of the popcorn. Given that the drink cost $6, we can represent it as "Cost of the drink = $6." Let's denote the cost of the popcorn as "Cost of the popcorn = P." Since we want to find the total cost, we can substitute the given values into the equation:

Total cost = $6 + P

The total cost of your friend's purchase was given as $14. Substituting this value into the equation, we get:

$14 = $6 + P

To solve for the cost of the popcorn, we need to isolate the variable P on one side of the equation. We can do this by subtracting $6 from both sides:

$14 - $6 = $6 + P - $6

$8 = P

The answer is $8, the cost for popcorn is $8.

To know more about cost, refer here:

https://brainly.com/question/14566816#

#SPJ11

Answer:

100,000 + 30,000 + 900 + 80 + 7

(Brainliest please! :D)

Answer:

Your answer is option #1

100,000 + 30,000 + 900 + 80 + 7

The surface areas are 756.87 km², 2567.6 in², 853.91 yd², 749.72 cm² and the area to paint is 3268.60 in²

Figure 9

This is calculated as

Area = Base area + 1/2 * Perimeter * Slant height

So, we have

Surface area = (1/4 * 14² * √3) + 1/2 * (14 + 14 + 14) * 32

Surface area = 756.87 km²

Figure 10

This is calculated as

Area = Sum of side areas

So, we have

Surface area = 2 * 1/2 * (35 + 10) * 20.3 + 32 * 17 + 10 * 17 + 20.3 * 17 + 35 * 17

Surface area = 2567.6 in²

Figure 11

Start by calculating the radius using

(2r)² = 19.4² - 14.4²

2r = 13

So, we have

r = 6.5

This area is then calculated as

Area = 2πr(h + r)

So, we have

Area = 2 * 22/7 * 6.5(14.4 + 6.5)

Surface area = 853.91 yd²

Figure 12

This area is calculated as

Area = lw + l√[(w/2)² + h²] + w√[(l/2)² + h²]

So, we have

Area = 15 * 18 + 18√[(15/2)² + 12²] + 15√[(18/2)² + 12²]

Surface area = 749.72 cm²

Without painting the bottom, the area is

Area = 2 * 1/2 * 34 + 42.8 + 36 * √(34² + 42.8²) + 34 * 36

Evaluate

Area = 3268.60 in²

Unclear dimensions

Read more about surface areas at

https://brainly.com/question/26403859

#SPJ1

Answer:

piip;[-p-o-ul0i

Step-by-step explanation:

The equality of the respective angles and the proportionality of the corresponding sides determine if two triangles are comparable.

Triangle A: 53, 71, Triangle B: 53, 71; Similar

Triangle C: 90, 37, Triangle D: 90, 53; Similar

Triangle E: 63, 45 Triangle F:14, 71; Not similar

Triangle G, 121, Triangles H: 70, Not similar

If two of one triangle's angles are congruent with two of the

angles of a different triangle, then the two triangles are comparable.

Similarity hypothesis, angle, and AA

Given that: The interior product of the AA similarity hypothesis

The angle sum property of a triangle states that the angles of a triangle are 180°,

Consequently, the third angle is also congruent when two angles are

congruent

53, 71 in Triangle A and 53, 71 in Triangle B; similar

Based on the AA similarity postulate, the triangles are similar.

Triangles C (90, 37) and D (90, 53) have similar angles.

Supplied that the given angles are identical to each of their complimentary angles, the triangle is similar.

Triangle F: 14, 71 Triangle E: 63, 45; not comparable

There are no parallel triangles.

Triangles H: 70, not identical to Triangle G's 121,

The details are insufficient.

To Learn more about AA similarity postulate visit :

brainly.com/question/11289488

#SPJ13

Answer:

Step-by-step explanation:

22.50

The equation of curve of best fit is y = -30.17x + 14.49. To find the curve of best fit, we would require two equations which are explained in details below.

Data;

The equation of straight line is y = ax + b

If we modify it to fit into this problem,

\(\sum y = na + b \sum X ... equ(i)\\\sum xy = a \sum x + b \sum x^2 ...equ(ii)\)

Let's substitute the values into the equations and solve

\(\sum y = na + b \sum X ... equ(i)\\\sum xy = a \sum x + b \sum x^2 ...equ(ii)\\50.9 = 6*a + b*16 ...equ(i)\\24.6 = a*16 + b*35 ...equ(ii)\\50.9 = 6a + 16b ...equ(i)\\24.6 = 16a + 35b ...equ(ii)\)

Let's solve both equation (i) and equation (ii)

\(50.9 = 6a + 16b...equ(i)\\24.6 = 16a + 35b ...equ(ii)\\a = -30.17, b = 14.49\)

We can substitute the values of a and b into the equation

\(y = ax + b\\y = -30.17x + 14.49\)

The equation of curve of best fit is y = -30.17x + 14.49

Learn more on equation of best fit on linear regression here;

https://brainly.com/question/9366563

Answer:

for seven cabins it should be 14.7 trees, im not sure about 3 cabins, sorry :(

Answer:

3) 6.3

7) 14.7

Step-by-step explanation:

Use ratios to solve the table

10.5/5 = x/3

cross multiply

31.5 = 5x

x = 6.3

10.5/5 = x/7

73.5 = 5x

x = 14.7

To determine how long it will take to fill the tank when both taps are turned on simultaneously.

The first tap fills the tank in 6 hours, so its rate is 1/6 of the tank per hour.

The second tap fills the tank in 12 hours, so its rate is 1/12 of the tank per hour.

When both taps are turned on simultaneously, their rates are additive. So the combined rate is (1/6 + 1/12) = 3/12 = 1/4 of the tank per hour.

Therefore, it will take 4 hours to fill the vacant tank when both taps are turned on simultaneously.

Learn more about determine here;

https://brainly.com/question/29898039

#SPJ11

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

Know more about matrix here:

brainly.com/question/24079385

#SPJ4

Answer:

15. $232.50

16. $325.50

Step-by-step explanation:

15)108.50-46.50=62

7-3=4

62/4=15.5

15.5*15=232.5

16) 15.5*21=325.5

Answer:

4 miles: 3 hours has a unit rate of 4/3 = 1.33 miles/hour which is greater than 17

7 miles: 1 hour has a unit rate of 7 miles/hour which is greater than 17.

Answer:

2/7

Step-by-step explanation:

\(slope = \frac{1 - 3}{2 - 9} \\ = \frac{ - 2}{ - 7} \\ = \frac{2}{7} \)

The frequency of A allele after a single generation of mutation can be found as follows: Frequency of A allele after a single generationp(A) = p(A) x (1 - m) + q(a) x m

where,
m = mutation rate = 10^-6p(A) = frequency of A allele in initial generation = 0.75q(a) = frequency of a allele in initial generation = 0.25Thus,p(A) = 0.75 x (1 - 10^-6) + 0.25 x 10^-6 = 0.74999925

And the frequency of a allele will beq(a) = 1 - p(A) = 1 - 0.74999925 = 0.25000075

Therefore, the frequency of the A and a alleles in the next generation will beA: 0.74999925 and a: 0.25000075.

This is option D.

To know more about generation Visit:

https://brainly.com/question/12841996

#SPJ11

what do you need help on ?????......???????..............

By answering the presented question, we may conclude that I used the following procedures to produce this graph.

Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph contains vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle.

I used the following procedures to produce this graph:

I classified the personnel as full-time, part-time, and temporary.

I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."

I used the following procedures to produce this graph:

I classified the personnel as full-time, part-time, and temporary.

I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."

I made the segmented bar graph using these percentages.

The graph was made using Excel technology. You may make a similar graph with Excel or any other software that supports segmented bar graphs.

To know more about graphs visit:

https://brainly.com/question/11950136

#SPJ1

The  pounds of chocolate-covered almonds needed is 9 pounds while the pounds of chocolate-covered peanuts is 36 pounds.

The first step is to set up linear equations that represent the information in the question

7.5a + 5b  = (7 x 45)

7.5a + 5b = 315 equation 1

a + b = 45 equation 2

Where:

The elimination method would be used to solve the questions

Multiply equation 2 by 5

5a + 5b = 225 equation 3

Subtract equation 3 from equation 2:

2.5a = 90

Divide both sides of the equation by 2.5

a = 90 / 2.5

a = 36

Substitute for a in equation 2:

36 + b = 45

b = 45 - 36

b = 9.

To learn more about system of equations, please check: https://brainly.com/question/25875552

#SPJ4

Answer:

Step-by-step explanation:

Here,

These two angles when added forms a 180° that straight line .

Hence,

These are supplementary angles.

Answer:

3/4

Step-by-step explanation:

In total there are 8 cobblers and 6 out of those 8 are apple cobblers so the fraction would be 6/8 but in simplest form its 3/4.

Answer:

-1/4(3)

Step-by-step explanation:

Answer: It's 50

Step-by-step explanation:

3.4 divided by 6.8 is 0.5 and 18-16 (the exponents) is 2. since ur dividing your subtracting the exponents. so then u get 0.5*10^2 but it cant be lower than 1 so u move the decimal in 0.5 one space to the right which then leads you to get 5*10^1 or 5*10 which is 50.

The finite difference approximation for a Neumann boundary condition, \(\left(\frac{df}{dx}\right)\), at node \(n\) (right boundary) to \(O(h^2)\) is given by

\(\left(\frac{df}{dx}\right)_n \approx \frac{f_{n-2} - 4f_{n-1} + 3f_n}{2h}\),

where \(f_{n-2}\), \(f_{n-1}\), and \(f_n\) represent the function values at nodes \(n-2\), \(n-1\), and \(n\) respectively, and \(h\) represents the spacing between the nodes.

To derive this approximation, we start with the Taylor series expansion of \(f_{n-1}\) and \(f_n\) around \(x_n\):

\(f_{n-1} = f_n - hf'_n + \frac{h^2}{2}f''_n - \frac{h^3}{6}f'''_n + \mathcal{O}(h^4)\),

\(f_{n-2} = f_n - 2hf'_n + 2h^2f''_n - \frac{4h^3}{3}f'''_n + \mathcal{O}(h^4)\).

By subtracting \(4f_{n-1}\) and adding \(3f_n\) from the second equation, we eliminate the first-order derivative term and retain the second-order derivative term. Dividing the result by \(2h\) gives us the desired finite difference approximation to \(O(h^2)\).

In conclusion, the finite difference approximation for a Neumann boundary condition, \(\left(\frac{df}{dx}\right)\), at node \(n\) (right boundary) to \(O(h^2)\) is \(\left(\frac{df}{dx}\right)_n \approx \frac{f_{n-2} - 4f_{n-1} + 3f_n}{2h}\). This approximation is obtained by manipulating the Taylor series expansion of \(f_{n-1}\) and \(f_n\) to eliminate the first-order derivative term and retain the second-order derivative term, resulting in a second-order accurate approximation.

Learn more about function here:

https://brainly.com/question/31062578

#SPJ11

Answer: its C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

The answer is actually B.

Step-by-step explanation:

3(1+4x)=12x

(3)(1)+(3)(4x)=12x(Distribute)

3+12x=12x

12x+3=12x

Step 2: Subtract 12x from both sides.

12x+3−12x=12x−12x

3=0

Step 3: Subtract 3 from both sides.

3−3=0−3

0=−3

(Can't be negative)

Answer:

6 sides

360/60=6

pls mark brainliest

The number of sides in the building is 6

6 sides

Given :

Melissa is walking around the outside of a building that is in the shape of a regular polygon.

She determines that the measure of one exterior angle is 60 degree

We know that the measure of exterior angle of any regular polygon is 360 degrees.

one exterior angle is 60°

The number of sides of regular polygon is total exterior angle / one exterior angle

Number of sides of regular polygon =\(\frac{360}{60}=6\)

So, the building have 6 sides .

Learn more :  brainly.com/question/8083053

The answer to the question "(1) 42mod11" is 9.

The answer to the question "Modular Arithmetic: Please solve the following questions. (1) 42mod11" is:

The concept of "Modular Arithmetic" is a system of arithmetic that involves only integers. In modular arithmetic, numbers "wrap around" after they reach a certain value called the modulus.

To solve the given question, we can use the following steps:

Step 1: Find the modulus of the given number. In this case, the modulus is 11.

Step 2: Divide the given number by the modulus. In this case, 42/11 = 3 with a remainder of 9.

Step 3: The remainder is the answer to the question. So, 42mod11 = 9.

Therefore, the answer to the question "(1) 42mod11" is 9.

I hope this answer helps you! If you have any further questions, feel free to ask.

Learn more about Modular Arithmetic

brainly.com/question/29022762

#SPJ11