The x component of vector is 5.3 units, and its y component is -2.3 units. The angle that vector makes with the x-axis is closest to?

The restricted values in (x^2 - 3x - 2)/-4y * (2x - 2)/(-xy^2 + 2y^2) are x ≠2 and y ≠ 0

The complete question is added as an attachment

The equation is given as:

(x^2 - 3x - 2)/-4y * (2x - 2)/(-xy^2 + 2y^2)

Set the products of the denominators to 0

-4y * (-xy^2 + 2y^2) = 0

Split the equation

-4y = 0 or (-xy^2 + 2y^2) = 0

Remove the bracket

-4y = 0 or -xy^2 + 2y^2 = 0

Divide both sides by -4 in -4y = 0

y = 0

Factor out y^2 in -xy^2 + 2y^2 = 0

y^2(-x + 2) = 0

This means that y^2 = 0 or -x + 2= 0

This gives y = 0 or -x + 2 = 0

Solve for x in -x + 2 = 0

x = 2

Hence, the restricted values in (x^2 - 3x - 2)/-4y * (2x - 2)/(-xy^2 + 2y^2) are x ≠2 and y ≠ 0

Read more about restricted values at

https://brainly.com/question/11308359

#SPJ1

The above pattern follows an arithmetic sequence with a common difference of 14 and first term of 13

The pattern can be represented as follows:

13, 27, 41, 55

The first term of the sequence is 13 and the common difference is 14.

The above pattern is an arithmetic sequence.

Therefore, the following can be used to find the nth term.

nth term = a + (n - 1)d

where

Therefore,

a = 13

d = 27 - 13 = 14

Let's find the next term

5th term = 13 + (5 - 1)14

5th term = 13 +(4)14

5th term = 13 + 56

5th term = 69

learn more on patterns here: https://brainly.com/question/21961097

#SPJ1

The rate of interest applied on the amount is 15%.

According to the statement

we have given that the sum of money amounts to Rs. 2175 in 3 years and to Rs. 2625 in 5 years.

And we have to find the rate of interest on this money.

So, For this purpose,

The given equation is:

Money in 3 years = 2175

Money in 5 years = 2625

Amount increased in 2 years = 2625-2175

Amount increased in 2 years = 450

And amount increased per year = 450/2

Amount increased per year = 225.

SI in 3 years=450/2 *3=Rs. 675

Principal amount= 2175-675=1500

so again,

R=(I*100)/(P*T)

R=15%

So, The rate of interest applied on the amount is 15%.

Learn more about rate of interest here

https://brainly.com/question/14714045

#SPJ1

Answer:

29, 21, 84

Step-by-step explanation:

Let the first number be x.

The second number is x - 8.

The third number is 4(x - 8).

Their sum is 134.

x + (x - 8) + 4(x - 8) = 134

x + 5(x - 8) = 134

x + 5x - 40 = 134

6x = 174

x = 29

x - 8 = 29 - 8 = 21

4(x - 8) = 4(29 - 8) = 4(21) = 84

Answer:

Read Explanation

Step-by-step explanation:

The domain is a list of all possible x-values, this graph starts at 0 and proceeds to positive infinity, making the domain:

[0,∞)

The range is a list of all possible y-values, this graph starts at -1 and proceeds to positive infinity, making the range:

[-1,∞)

x-intercepts Are where the line crosses the x-axis, in this graph the line only crosses the x-axis at x of 2. Making its only x-intercept 2.

y-intercepts Are where the line crosses the y-axis, in this graph the line only crosses the y-axis at y of -1. Therefore its y-intercept is -1.

In function notation when a question asks for f(x) its asking for the y values at the given x-values. At x of 3 the y value equals 1.

Answer:

The actual prime factors of 60 are 2, 3, and 5.

Step-by-step explanation:

Greetings !

Use a factor tree to express 60 as a product of prime factors. So the prime factorization of 60 is 2 × 2 × 3 × 5, which can be written as 2² × 3 × 5.

The system of equations is -x + y = 4 and -2x + y = 0

To do this, we make use of the following ordered pairs

(4, 8)

The above point represents April 2008.

Let the system of equations be

mx + ny = 4

2mx + ny = 0

Substitute (4, 8) for x and y in the above equations.

4m + 8n = 4

8m + 8n = 0

Subtract both equations

4m - 8m = 4

This gives

-4m = 4

Divide by 4

m = -1

Substitute m = -1 in 8m + 8n = 0

-8 + 8n = 0

This gives

8n = 8

Divide by 8

n = 1

So, the system of equations is -x + y = 4 and -2x + y = 0

The system of equations is -x + y = 4 and -2x + y = 0

See attachment for the graph of the system of equation

The above is represented in the (a) part of this solution

Verify that the solution is (4, 8)

We have:

-x + y = 4 and -2x + y = 0

Substitute (4, 8) for x and y in the above equations.

-4 + 8 = 4 --- true

-2*4 + 8 = 0 --- true

Both equations are true

Hence, the system of equations have been verified

Read more about system of equations at:

brainly.com/question/14323743

#SPJ1

Answer:

X = -10

Step-by-step explanation:

2 = -8 -X

2+X = -8

X = -10

Answer:

x = - 10

Step-by-step explanation:

Comment

The trick to any equation like this one is to get the numbers on one side and the term with an unknown on the other side. That way, your last step is to divide by the number in front of the letter into a number on the other side.

Solution

2 = - 8 - x                                 Add 8 to both sides

2 + 8 = -8 + 8 - x                      Combine

10 = - x                                     The number in front of x is - 1. Divide.

10/-1 = -x/-1                        

-10 =x

The letter usually has to be expressed as a number greater than 0. In other words x is positive for this question

Answer:

x = 0, x = 5

Step-by-step explanation:

x² - 5x = 0 ← factor out x from each term

x(x - 5) = 0

equate each factor to zero and solve for x

x = 0

x - 5 = 0 ⇒ x = 5

The solution of the questions is given as

a)

The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)

b)

This is a case with two separate arguments. (This is a two-tailed case)

c)

Test Statistic is given by:

z= 2.00

d)

Critical values of Z come from the table and equal [tex]\pm[/tex]1.96.

e)

, p-value = 0.0455

f)

CI= (3.006, 3.594)

g)

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

h)

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

i) Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.

j)

The choices you choose in Questions 7, 8, and 9 are identical.

a)

The null hypothesis states that mu equals 3.0. ( the average GPA at KSU is equal to 3.0) (Claim)

The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)

b)

This is a case with two separate arguments.

c)

Test Statistic is given by:

[tex]z=\frac{\barx-u^0}{σ/Vn}\\\\z=33 - 3.0/1.5/V100[/tex]

z= 2.00

d)

[tex]\alpha = 0.05[/tex]

Critical values of Z come from the table and equal [tex]\pm[/tex]1.96.

e)

Z Score = 2.00

reading from table, p-value = 0.0455

f)

Confidence Interval:

[tex]CI= \barx \pm \frac{ZX\sigma }{\sqrt((n)}[/tex]

[tex]CI =3.3 \pm 1.96 x 1.5 / \sqrt{100}[/tex]

CI= (3.006, 3.594)

g)

The disparity is noteworthy given that the computed value of Z = 2.00 is higher than the crucial value of z = 1.96. Cast doubt on the null hypothesis.

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

h)

The difference may be considered statistically significant since the p-value of 0.0455 is lower than the alpha threshold of 0.05. Cast doubt on the null hypothesis.

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

i)

The difference is statistically significant since the value of 3.0 is not included in the confidence range (3.006 - 3.594). Cast doubt on the null hypothesis.

Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.

j)

The choices you choose in Questions 7, 8, and 9 are identical.

Read more about  probability

https://brainly.com/question/795909

#SPJ1

The area of quadrilateral ABCD exists equivalent to the area of triangle ABD plus the area of triangle ADC

Heron's Formula exists a technique for estimating the area of a triangle when you know the lengths of all three sides.

Therefore, the total area of  quadrilateral abcd exists 28.53 [tex]$$units^2[/tex].

Let a, b, and c be the lengths of the sides of a triangle.

The area is given by:

[tex]$$A = \sqrt{p(p-a)(p-b)(p-c)}[/tex]

where p exists half the perimeter

[tex]$p = \frac{a+b+c}{2}[/tex]

To estimate the area of triangle ABD

we have

a = AB = 2.89 units

b = BD = 8.59 units

c = DA = 8.6 units

To estimate the perimeter

[tex]$p = \frac{2.89+8.59+8.6}{2}[/tex]

= 10.4 units

To estimate the area

[tex]$A = \sqrt{10.04(10.04-2.89)(10.04-8.59)(10.04-8.6)}[/tex]

[tex]$A = \sqrt{10.04(7.15)(1.45)(1.44)}[/tex]

[tex]$A = \sqrt{149.89}[/tex]

A = 12.24 [tex]$$units^2[/tex]

To estimate the area of the triangle ADC

we have

a = AC = 4.3 units

b = AD = 8.6 units

c = DC = 7.58 units

To estimate the half perimeter p

[tex]$p = \frac{4.3+8.6+7.58}{2}[/tex]

= 10.24 units

To estimate the area

[tex]$A = \sqrt{10.24(10.24-4.3)(10.24-8.6)(10.24-7.58)}[/tex]

[tex]$A = \sqrt{10.24(5.94)(1.64)(2.66)}[/tex]

[tex]$A = \sqrt{265.35}[/tex]

A = 16.29 [tex]$$units^2[/tex]

To estimate the total area

A = 12.24+16.29 = 28.53 [tex]$$units^2[/tex].

Therefore, the total area of  quadrilateral abcd exists 28.53 [tex]$$units^2[/tex].

To learn more about total area of  quadrilateral refer to:

https://brainly.com/question/27991573

#SPJ4

If a quadrilateral exists as a parallelogram, then opposite sides exist congruent and parallel.

If a quadrilateral exists as a parallelogram, then opposite sides exist congruent and parallel.

Given: AB = 6cm , BC = 5cm, AD = 4cm, CD = 7cm and BD = 6cm​

Draw a line AB with 6cm with A as the center draw an arc of radius 4 cm. And draw another arc of 6cm to cut the previous arc at D with B as the center draw an arc of radius 5cm. And with D draw another arc of 7cm to cut the previous arc at C. Join the lines of the quadrilateral.

Now ABCD exists as a required quadrilateral.

To learn more about quadrilateral refer to:

https://brainly.com/question/23935806

#SPJ9

The resultant of subtractions of u = <-8, 4> and v = <2, 7> are

-u-v = <6, -11>,

u-v = <-10, -3>,

and v-u= <10,3>.

What is a vector in simple definition?

The resultant of subtractions of u = <-8, 4> and v = <2, 7> are

-u-v = <6, -11>,

u-v = <-10, -3>,

and v-u= <10,3>.

Given that,

The results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.

We have to determine,

The value of -u-v, u-v, and v-u.

According to the question,

The results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.

The value of -u-v is,

-u -v = - < -8 ,4 > - <2,7>

-u -v = <8, -4> - < 2, 7 >

-u - v = < 8 - 2 , -4 - 7 >

-u -v =  < 6 , - 11 >

The value of u-v is,

u -v = < -8 ,4 > - < 2,7 >

u - v = < - 8  - 2, 4 - 7 >

u - v = < 10 ,3>

The value of v - u is,

v - u = < 2 , 7>  - < - 8,4 >

v - u = <  2 + 8 ,  7 - 4 >

v - 4 = <  10 , 3 >

Hence, The resultant of subtractions of u = <-8, 4> and v = <2, 7> are

-u-v = <6, -11>,

u-v = <-10, -3>,

and v-u= <10,3>.

Learn more about vector

brainly.com/question/14480157

#SPJ4

Haler ran farther than Tyler in 10 minutes. She covered an extra 0.05 miles compared to Tyler.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Tyler can run 1 mile in 8 minutes and 20 seconds.

Time taken = 8 mins + 20 sec (0.33 min) = 8.33 minutes

Speed = distance / time = 1 mile / 8.33 = 0.12 mile per min

In 10 minutes, distance = 0.12 mile per min * 10 min = 1.2 mile

Haler is given by:

y = 8x; where y is time and x is distance.

In 10 minutes, distance = y/8 = 10/8 = 1.25 miles

Haler ran farther than Tyler in 10 minutes. She covered an extra 0.05 miles compared to Tyler.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The function [tex]H(t) = -16t^2 + 64t[/tex] exists in a parabola.

The axis of symmetry of a parabola exists at the midpoint between the two real roots.

The roots exist the solutions of H(t) = 0

To estimate the roots equation exists [tex]-16t^2 + 64t = 0[/tex]

Factor t(-16t + 64) = 0

t = 0 and -16t + 64 =0

-16t + 64 = 0

t = 64 / 16 = 4

t = 4

Then the two roots are t = 0 and t = 4, and the axis of symmetry exists

t = (0+4)/2 = 4/2 = 2

The axis of symmetry exists at t = 2.

It represents the time at which the ball is at the higher point, the maximum height.

You can find the maximum height replacing t = 2 in the function H(t)

[tex]H(t) = -16(2^2) + 64(2)[/tex]

= 64 feet.

And you can also deduce that the second part of the flight will take 2 seconds, for a total flight time of 4 seconds.

To learn more axis of symmetry refers to:

https://brainly.com/question/21191648

#SPJ4

Answer:

answer is a

Step-by-step explanation:

it takes 2 seconds for the ball to reach maximum height and 2 seconds to fall on the ground.

t = 2; it takes the ball 2 seconds to reach the maximum height and 2 more seconds to fall back to the ground

Took the FLVS test!

Answer:

B 1233 ft^2

Step-by-step explanation:

I hope this is right

The value of each variable in the two-way table is:

a = 7

b = 31

c = 28

d = 13

e = 65

A Venn diagram uses circles that overlap each other to show the relationship between two or more sets of items. A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns.

a = females that favor the left. Looking at the Venn diagram, this number is 7.

b = total number of females : 24 + 7 = 31

c = males that favor the right = total number of males - males that favor the left34 - 6 = 28

d = Total number of people who favor the left = 7 + 6 = 13

Total number of baseball players = 65

To learn more about two way frequency tables, please check: brainly.com/question/27344444

#SPJ1

Answer:

C. 35.1

Step-by-step explanation:

First get the length of AC by using the Pythagorean Theorem, that ends up being about 11.18. Then you need to get the radius of the circle so you divide 11.18 by 2 and get 5.59. Then plug 5.59 for r into 2(pi)(r). 2(pi)(5.59) = 5.123

Answer:

Answer B is correct

Step-by-step explanation:

First, let us find the diameter (AC) of the circle using the Phythogerem theorem.

AC² = AB² + BC²

AC² = 2² + 11²

AC² = 4 + 121

AC² = 125

AC = √ 125

AC = 5√5

And now let us find the circumference of the circle.

C = π × d

C = π × 5√5

C = 5√5π in

The Jacobian for this transformation is

[tex]J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}[/tex]

with determinant [tex]|J| = 12[/tex], hence the area element becomes

[tex]dA = dx\,dy = 12 \, du\,dv[/tex]

Then the integral becomes

[tex]\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv[/tex]

where [tex]R'[/tex] is the unit circle,

[tex]\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1[/tex]

so that

[tex]\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv[/tex]

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

[tex]\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}[/tex]

Then

[tex]\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}[/tex]

The option c is correct. The linear representation model is best for this situation out of the exponential, quadratic model.

According to the statement

we have given that:

Monthly Rate = $20, Number of customers = 5000

If there is a decrease of $1 in the monthly rate, the number of customers increase by 500.

And we have to find that The type of model that best fits the given situation.

So, according to the linear representation model

Monthly Rate = $20, Number of customers = 5000

Let us decrease the monthly rate by $1.

Monthly Rate = $20 - $1  = $19, Number of customers = 5000 + 500 = 5500

Let us decrease the monthly rate by $1 more.

Monthly Rate = $19 - $1  = $18, Number of customers = 5500 + 500 = 6000

Here, we can see that there is a linear change in the number of customers whenever there is decrease in the monthly rate.

We have 2 pair of values here,

x = 20, y = 5000

x = 19, y = 5500

Let us write the equation in slope intercept form:

y = mx + c

And Slope of a function is

m = y₂ - y₁ / x₂ - x₁

Then

m = 5500 - 5000 / 19 - 20

m = -500

So, the equation become

y = -500x +c

And find the value of by putting the values.

So, c = 15000

And the equation become

y = -500x + 15000.

According to this linear model is perfect for this situation.

So, The linear representation model is best for this situation.

Learn more about linear representation here

https://brainly.com/question/15602982

#SPJ1

The output, y, when the input, x, is -5 is -2

The input is given as:

-5

This means that

x = -5

This is so because x represents the input

From the graph, we have the following highlight

The line of the graph passes through the point x = -5

On the graph;

When x = -5, the value of y is -2

This means that the output, y, when the input, x, is -5 is -2

Read more about functions at:

https://brainly.com/question/2328150

#SPJ1

Answer:

Step-by-step explanation:

Quick Answer 1

Solution

x = 0.747 / 0.0747

When you do the division, you get 10. That means that you need to divide 0.747 by just 1 ten to get 0.0747

Answer:

Once

Step-by-step explanation:

You have to divide once because if you divide a decimal by 10, you add a zero before the decimal point

Answer:

a) 18

b) 48

c) 192

a) 30

b) 150

Step-by-step explanation:

Answer:

1

a ) 18

b ) 48

c ) 144

2

a ) 30

b ) 150..

[tex]...[/tex]

In regression, the difference between the confidence interval and the prediction interval formula is "The addition of 1 to the quantity under the radical sign i.e., standard error".

The formula for the confidence interval is

[tex]y_h[/tex] ± [tex]t_{(1-\alpha /2,n-2)[/tex] × √(MSE([tex]\frac{1}{n}[/tex] + ([tex]x_h[/tex] - μ)²/∑([tex]x_i[/tex] - μ)²))

The formula for prediction interval is

Prediction interval = Sample estimate ± (t multiplier × standard error)

[tex]y_{new}[/tex] = [tex]y_h[/tex] ± [tex]t_{(1-\alpha /2,n-2)[/tex] × √(MSE(1 + [tex]\frac{1}{n}[/tex] + ([tex]x_h[/tex] - μ)²/∑([tex]x_i[/tex] - μ)²))

Where μ = x bar.

From the above, the prediction interval has one additional MSE term in the standard error calculation. But in the confidence interval, only one term is used.

So, the difference between them occurs in the standard error value.

The formula shows it by adding 1 to the quantity under the radical sign.

Thus, the difference is in the standard error.

Learn more about the confidence and prediction intervals here:

https://brainly.com/question/24245026

#SPJ1

The figure in the question is a box with dimensions of 6 in. by 2 in. by 9 in., which gives;

The dimensions of the box in the given figure are;

Length, L = 9 in.

Width, W = 2 in.

Height, H = 6 in.

The surface area, A, of a box is found using the following formula;

A = 2•L•W + 2•L•H + 2•H•W

Therefore;

A = 2×9×2 + 2×9×6 + 2×2×6 = 168

The volume of a box, V, is calculated as follows;

For the given figure, therefore;

V = 9 × 2 × 6 = 108

Cost of packaging per square inch, c = $0.004

Cost to package the figure, C, is therefore;

Which gives;

C = $0.004/in.² × 168 in.² = $0.672

Learn more about working with formulas in mathematics here:

https://brainly.com/question/16735912

#SPJ1

With the help of the area formulae of rectangles and triangles and the concept of surface area, the surface area of the composite figure is equal to 276 square centimeters.

The surface area of the truncated prism is the sum of the areas of its six faces, which are combinations of the areas of rectangles and right triangles. Then, we proceed to determine the surface area:

A = (12 cm) · (4 cm) + 2 · (3 cm) · (4 cm) + 2 · (12 cm) · (3 cm) + 2 · 0.5 · (12 cm) · (5 cm) + (5 cm) · (4 cm) + (13 cm) · (4 cm)

A = 48 cm² + 24 cm² + 72 cm² + 60 cm² + 20 cm² + 52 cm²

A = 276 cm²

With the help of the area formulae of rectangles and triangles and the concept of surface area, the surface area of the composite figure is equal to 276 square centimeters.

To learn more on surface areas: https://brainly.com/question/2835293

#SPJ1

percentage of students say they have witnessed hazing and did not report it are  = 95%

No matter how voluntarily a person is to take part, hazing, initiation or deposition are all actions that are demanded of someone when they join or participate in a group and which humiliate, degrade, abuse, or imperil them.

involves humiliating a person or group. involves making fun of someone or something. involves or includes the deliberate destruction of or removal of private or public property for the purpose of affiliation with, initiation into, or as a requirement for continuing membership in an organization.

Paddling, beating, or other types of attack. Branding. consumption of disgusting substances or mixtures under duress or force.

To know more about initiation visit:

https://brainly.com/question/28177523

#SPJ4

Into how many equal parts can the same cake be cut if the cuts can only be made along the gridlines, cake can be cut into 20 equal parts.

This is further explained below.

Generally, In spreadsheet software, gridlines are the light gray lines that divide the cells, rows, and columns. Gridlines are often used to maintain track of data. Gridlines are widely used in popular spreadsheet programs like Spreadsheet.

In conclusion, If the cuts can only be done along the gridlines, the cake may be divided into 20 equal pieces when cutting along the lines.

Read more about gridlines

https://brainly.com/question/2773987

#SPJ1

The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and

r(1, 1, 0) is x + y + z = 2  .

According to the question

Let the points

p(0, 1, 1) = (x1,y1,z1)

q(1, 0, 1)= (x2,y2,z2)

r(1, 1, 0)= (x3,y3,z3)

now,

The equation of the plane through the points

i.e

The formula of equation of a plane passing through three non collinear points

[tex]\left[\begin{array}{ccc}x-x1&y-y1&z-z1\\x2-x1&y2-y1&z2-z1\\x3-x1&y3-y1&z3-z1\end{array}\right] = 0[/tex]

by substituting the values in the formula of equation of a plane

[tex]\left[\begin{array}{ccc}x-0&y-1&z-1\\1-0&0-1&1-1\\1-0&1-1&0-1\end{array}\right] = 0[/tex]

[tex]\left[\begin{array}{ccc}x&y-1&z-1\\1&-1&0\\1&0&-1\end{array}\right] = 0[/tex]  

x(1) - (y-1)(-1) + (z-1)(1) = 0

x + y - 1 + z - 1 = 0

x + y + z = 2

Hence, the equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2  .

To know more about equation of the plane here:

https://brainly.com/question/17013160

#SPJ4

Considering the equation of the parabola, the coefficients are given as follows: p = 5, q = -20, r = 19.

The graph is the one given at the side of the question.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the turning point is (2,-1), hence h = 2, k = -1, and the equation has the following format:

y = a(x - 2)² - 1

The curve passes through (3,4), that is, when x = 3, y = 4, and we use it to find a.

y = a(x - 2)² - 1

4 = a(3 - 2)² - 1

a = 5.

Hence the equation is:

y = 5(x - 2)² - 1

Placing it into standard form, we have that:

y = 5(x² - 4x + 4) - 1

y = 5x² - 20x + 19

Hence the coefficients are:

p = 5, q = -20, r = 19.

More can be learned about the equation of a parabola at https://brainly.com/question/17987697

#SPJ1