Find value of P and Q

Find Value Of P And Q

Answers

Answer 1

Answer:

[tex] P= 6 \frac{1}{7}\\\\

Q = 4 \frac{2}{7}[/tex]

Step-by-step Explanation

[tex] \frac{5 + 3 \sqrt{2} }{5 - 3 \sqrt{2} } = P+Q\sqrt 2 \\ \\ \frac{(5 + 3 \sqrt{2}) }{(5 - 3 \sqrt{2}) } \times \frac{(5 + 3 \sqrt{2}) }{(5 + 3 \sqrt{2} )} = P+Q\sqrt 2 \\ \\ \frac{ {(5 + 3 \sqrt{2} )}^{2} }{ {(5)}^{2} - (3 \sqrt{2})^{2} } = P+Q\sqrt 2 \\ \\ \frac{ {5}^{2} + {(3 \sqrt{2} )^{2} + 2.5.3 \sqrt{2} } }{25 - 9 \times 2} = P+Q\sqrt 2 \\ \\\frac{ 25 + 18 + 30 \sqrt{2} }{25 - 18} = P+Q\sqrt 2 \\ \\\frac{ 43 + 30 \sqrt{2} }{7} = P+Q\sqrt 2 \\ \\ \frac{43}{7} + \frac{30 }{7} \sqrt{2} = P+Q\sqrt 2 \\ \\ equating \: like \: terms \: on \: both \: sides \\ \\ P = \frac{43}{7} \\ \\ \huge \red { \boxed{ P= 6 \frac{1}{7}}} \\ \\ Q = \frac{30}{7} \\ \\ \huge \orange { \boxed{ Q = 4 \frac{2}{7} }}[/tex]


Related Questions

33-(2c + 4) = 2(c + 7) +C​

Answers

Answer:

c=3

Step-by-step explanation:

C=3 ///////////// (ignore these bars pls XD)

Tell whether the relation is a function. {(-5, -3), (-1, 3), (4, 3), (8, 8)}

Answers

Given:

The relation is {(-5, -3), (-1, 3), (4,3), (8, 8)}.

To find:

Whether the given relation is a function or not.

Solution:

A relation is called a function, if there exist a unique output for each input.

We have, a relation given as

{(-5, -3), (-1, 3), (4,3), (8, 8)}

Here, all x-values are different. So, each x-value has a unique y-value.

Thus, there exist a unique output for each input.

Therefore, the given relation is a function.

Justin is considering two websites for downloading music. The costs are detailed here.

Website 1: a yearly fee of $30 and $1.50 for each download

Website 2: $2 for each download

What is a system of equations to represent the costs for one year?

Express your equations in the form of y=mx+b where x is the number of downloads for the year and y is the total cost for the year.

Enter your equations in the boxes.

Website 1:

Website 2:

Answers

Answer:

website 2 hope this helps

Aisha is a cyclist. She rode 3 ¾ miles in ⅓ hours. A. How fast was she going in miles per hour?

Answers

Answer:

11 1/4 miles per hour

Step-by-step explanation:

Put the mixed number in improper form to make it easier. You get 15/4 miles in 1/3 hours. You want the miles for 1 hour. So you multiply 15/4 miles by 3 to get 45/4 miles, or 11 1/4 miles per hour

PLS HELP MEEE ILLL GIVE BRAINLEST

Answers

Answer:40

Step-by-step explanation:

Smaller than 60 and 80.

Answer:

B

Step-by-step explanation:

Because I did this test before and I got this right :)

find The equation pleaseeeeee

Answers

Answer:

y=2x+4

Step-by-step explanation:

the slop is 2 hense 2x, and the y intercept is 4

y=2x+4 the first and the third straight year yoy of winning

Which ordered pair is a solution of the equation y+1=3(x-4)

Answers

Step-by-step explanation:

When x = 4 and y = -1,

(-1) + 1 = 3(4 - 4) = 0.

Hence (4, -1) is an ordered pair.

When x = 5 and y = 2,

(2) + 1 = 3(5 - 4) = 3.

Hence (5, 2) is an ordered pair.

Therefore the answer is C.

Solve for r. This is for combinations and permutations.

Answers

Answer:

○ D) A and C

Step-by-step explanation:

[tex]\displaystyle \frac{n!}{r![-r + n]!} = {}_nC_r[/tex]

All you need to do is plug each choice into the formula:

[tex]\displaystyle \frac{10!}{2![-2 + 10]!} \Longrightarrow \frac{[2][3][4][5][6][7][8][9][10]}{2[-2 + 10]!} \longrightarrow \frac{[2][3][4][5][6][7][8][9][10]}{2[(2)(3)(4)(5)(6)(7)(8)]} \\ \\ \boxed{45} = \frac{90}{2}[/tex]

OR

[tex]\displaystyle \frac{10!}{8![-8 + 10]!} \Longrightarrow \frac{[2][3][4][5][6][7][8][9][10]}{[(2)(3)(4)(5)(6)(7)(8)][-8 + 10]!} \\ \\ \boxed{45} = \frac{90}{2}[/tex]

So, from what you see, both values of [tex]\displaystyle r[/tex] work. In fact, when using the formula pertaining to combinations, you will see that each result has a “repetitive pattern”. This is something you must look out for when using this formula.

I am joyous to assist you at any time.

Question 8 (4 points) Find the values of x and y if NO = x + 2y, MO = 3x, PQ = 6x + 4, and OQ = 2y + 4.

Answers

Answer:

x = 12 and y = 16

Step-by-step explanation:

Given the following lengths;

NO = x + 2y,

MO = 3x,

PQ = 6x + 4, and

OQ = 2y + 4.

The following postulates are true;

MN = PQ

Since MO + ON = MN

MN = 3x + x+2y

MN = 4x + 2y

Recall that PQ = 6x+4

Equating both expressions;

4x + 2y=  6x+4

Collect like terms;

4x-6x + 2y = 4

-2x + 2y = 4

x - y = -4 ...... 1

Also MO = OQ

3x =  2y + 4

3x-2y= 4 ....2

from 1; x = -4 + y

Substitute into 2:

3x-2y= 4

3(-4+y)-2y = 4

-12+3y-2y = 4

-12+y = 4

y = 4 + 12

y = 16

Since x = -4+y

x = -4 + 16

x = 12

Hence x = 12 and y = 16

Create a sample division problem with a 2-digit divisor and give an incorrect answer, showing the steps taken to get the incorrect answer.

Answers

Answer:

Incorrect Answer Below

Step-by-step explanation:

Problem: We have a total of 28 candies that need to be divided evenly between 4 students.

(Incorrect) Solution: In order to solve this problem we can seperate the total number of candies into single digits and then divide each digit by 4 like so...

2 / 4 = 0.5

8 / 4 = 2

Now that we have the answer of both of these divisions we can simply add these values together to get the number of candies each student will get

0.5 + 2 = 2.5 candies

NEED ANSWERS ASAP!!( no need for explanation just final answers)

Answers

Answer

x, y

0, -4

1, -1

2, 2

3, 5

please click heart to give thanks :)

Answer:

Answer

x, y

0, -4

1, -1

2, 2

3, 5

Step-by-step explanation:

there's the math

Josie took a long multiple-choice, end-of-year vocabulary test. The ratio of the number of problems Josie got incorrect to the number of problems she got correct is : . If Josie missed questions, how many did she get correct? *---------- If josie missed 20 questions how many did she get correct--- PLEASE HELP ME

Answers

Answer:

36 correct answers

Step-by-step explanation:

Given that,

The ratio of the number of problems Josie got incorrect to the number of problems she got correct is 2:9.

Josie missed 8 questions

Let incorrect answers be 2x and that of correct answers be 9x.

ATQ,

2x = 8

x = 4

Correct answers = 9x

= 9(4)

= 36

Hence, she will get 36 correct answers.

Which quadrilaterals always have congruent diagonals? Select all that apply.

Answers

[tex]\huge {\colorbox {black}{\color{magenta}{✿Aиѕωє༉}}} [/tex]

RectanglesSquares

[tex]\huge\sf\underline{\underline{\red{❥︎ Thanks}}}[/tex]

Which quadrilaterals always have congruent diagonals?

[tex]\hookrightarrow[/tex] [tex]\bold{rectangle }[/tex]

[tex]\rightsquigarrow[/tex] [tex]\bold{ square }[/tex]

Colton is about to ride a straight water slide. The launching platform is at the top of a tower that is 8 meters tall. The splash pool at the end of the slide is 15 meters from the base of the tower. How long is the water slide itself? Show your work.

Answers

Answer:

The length of the water slide itself is 17 meters

Step-by-step explanation:

Here, we want to calculate the length of the water slide

from the description given in the question;

we have a right angled triangle where the height of the tower, the distance from the base of the tower and the length of the slide itself represents the sides of the triangle

From the description given in the question, the water slide length represents the slope of the right triangle formed

thus, mathematically by using Pythagoras’ theorem;

The square of the hypotenuse equals the sum of the squares of the two other sides

Let us call the length of the water slide y

y^2 = 8^2 + 15^2

y^2 = 64 + 225

y^2 = 289

y = √289

y = 17 meters

A paper cup is tossed 50 times. It lands right side up 11 times, upside down 14 times, and on its side 25 times. What percent of time did it land upside down?​

Answers

Answer

28 percent

Step-by-step explanation:

divide 14/50

Find the slope between:
(-1,-5)
(0, -1)

Answers

Answer: sry dunno

Step-by-step explanation:

Which number is divisible by both 5 and 6?
A. 132,359
B. 142,645
C. 164,780
D. 193,560

Answers

Answer:

D

Step-by-step explanation:

PLz help I need help

Answers

Answer:

Missing statements:

R2. Definition of corresponding anglesR3.  Corresponding angles postulateR5.  Supplement PostulateS7.  m∠2 + m∠3 = m∠1 + m∠3S8.  m∠1 + m∠3 = 180°

Jiangsu divided 751.6 by 10 to the second power and obtained a quotient of 0.7516. Yessenia thinks the quotient. Who has the reason? Explain your answer.

Answers

Answer:

Yessenia is correct.

Step-by-step explanation:

Supose Yessenia thinks the quotient is 7.516, then Yessenia is correct.

The reason why Yessenia is correct is that, if we interpret the question mathematically, we have:

[tex]= \dfrac{751.6}{10^2}[/tex]

[tex]= \dfrac{751.6}{100}[/tex]

From above the decimal point will shift to the left twice since we are dividing 751.6 by 100, which is:

= 7.516 and not 0.7516

Is a function or not a function?

Answers

Answer:

yes this is

Step-by-step explanation:

On a coordinate plane, 2 lines with negative slopes are shown. Line M N goes through points (negative 2, 0) and (negative 6, 8). Line M prime N prime goes through (6, negative 4) and (2, 4). Use the graph of the lines to determine if the two lines are parallel. Line MN was translated down units and right
units to create line M'N'.
The slope of Line M N .
The slope of Line M prime N prime .

Answers

Answer:

Line MN was translated down  

✔ 4

units and right  

✔ 8

units to create line M'N'.

 The slope of Line M N  

✔ −2

. The slope of Line M prime N prime  

✔ −2

.

Step-by-step explanation:

On edge 2021 Hope this helps :)

Answer: is in picture

Step-by-step explanation:

35 = 2b + 5b pls help

Answers

Step-by-step explanation:

2b+5b=7b

35=7b

35/7=5

b=5

Answer:

b=5

Step-by-step explanation:

2b+5b=35

7b=35

b=35/7

b=5

Work out the equation of the line which has a gradient of 3 and
passes through the point (-2, 4).​

Answers

Answer:

y=3x+10

Step-by-step explanation:

We can use standard form to write the equation of this line.

y=mx+b

where m=the slope (or gradient) of the line

and where b= the y-intercept

now to solve...

we know the slope (gradient) or m=3

so we can put this in the equation.

y=3x+b

now we must solve for b.

in order to this we can subsitute the coordinate (-2,4) into x and y since

a coordinates values/variable representation is (x,y) -> (-2,4)

So subsituting the coordinate in...

y=3x+b

4=3(-2)+b

simplify.

4=-6+b

b=10

This means the y-intercept=10

so...

y=3x+10

is the equation of the line.


Can someone please help? I need by 2:45 PM

Answers

Answer:

dilated coordinates are A(-18,-3) and B(-6,-12)

Step-by-step explanation:

distance of new segment is 15 units

distance formula = [tex]\sqrt){y-y_{1})^{2} +( x - x_{1})^{2} }[/tex]

HELP ASAPP PLEASE OR ELSE I WILL FAIL CLASS

Answers

7 +5x= -18
5x= -25
X= -5
B) one solution
C) i think it is : ( 14 + 10(-5))/ 12 = -36/ 12= -3

find the slope PLEASE HELP

Answers

Answer:

-1/4

1

-1/4

1

Step-by-step explanation:

Slope is obtained thus :

(y2 - y1) / (x2 - x1)

Slope ST :

S(1, 4) ; T(5, 3) ;

x1 = 1, y1 = 4 ; x2 = 5 ; y2 = 3

Slope ST = (3 - 4) / (5 - 1) = - 1 / 4

Slope TU :

T(5, 3) ; U(3, 1)

x1 = 5, y1 = 3 ; x2 = 3 ; y2 = 1

Slope TU = (1 - 3) / (3 - 5) = - 2/ - 2 = 1

Slope UV :

U(3, 1) ; V(-1, 2)

x1 = 3, y1 = 1 ; x2 = - 1 ; y2 = 2

Slope UV = (2 - 1) / (-1 - 3) = 1 /-4 = - 1/4

Slope SV:

S(1, 4) ; V(-1, 2)

x1 = 1, y1 = 4 ; x2 = - 1, y2 = 2

Slope SV = (2 - 4) / (-1 - 1) = - 2 / - 2 = 1

mark got 14 problems wrong on the test. his score was 72% correct.how many problems were on the test

Answers

9514 1404 393

Answer:

   50 problems

Step-by-step explanation:

The percentage wrong was  100% -72% = 28%. Then the number n of problems on the test was ...

  14 = 0.28·n

  n = 14/0.28 = 50

There were 50 problems on the test.

Roger spent 22 minutes on his math homework and 25.08 minutes on his spelling
homework. He spent percent more time on his spelling homework.

Answers

Answer:

114%

Step-by-step explanation:

okay, so we know he spent 22 minutes on math and 25.08 on spelling.

m=22

s=25.08

so to find a percent, you have to divide s/m

s/m= 25.08/22

s/m= 1.14

because this is a decimal, we have to convert it to a percent

114%

to check the answer, multiply 22 times 114%

the answer is 25.08, so we know we got the right answer.

Solve the following systems of equations for x:
2x + 3y = 5
4x – 3y = 1

Answers

Answer:

b

Step-by-step explanation:

2x+3y=5        rearrange   2x=5-3y  times all by 2    4x=10-6y

4x-3y=1                              4x=1+3y

1+3y=10-6y           6y+3y=10-1        9y=9     y=1

4x-3(1)=1      4x=1+3   4x=4          x=1

Answer:

B

Step-by-step explanation:

2x+3y=5

(2×1)+(3×1)==5

2+3=5

(4×1)-(3×1)=1

4-3=1

The relationship between the number of
$4 lunches you buy with a $100 school
lunch card and the money remaining on
the card

Answers

4x = 100

Here, the ‘x’ refers to how many lunches you buy, the 4 is the cost of each lunch, and 100 is the amount of money you have and can subtract from.
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