three points of -x + 2y = 2

Answer:

First rationalize the surd

(√3 +√2)(√3 - √2)/(√3 - √2)(√3 -√2)

The final answer will be 5 + 2√6

So x = 5 + 2√6

I) x + 1/x

5 + 2√6 + 1/5 + 2√6

Find the LCM

The final answer will be 10

ii) x² +1/x²

(5 + 2√6)² + 1/(5 +2√6)²

= 49 + 20√6 + 1/49 + 20√6

Find the LCM

The final answer will be 98

For i) x = 10

ii) x = 98

Hope this helps.

Answer:

i) 10

ii) 98

Step-by-step explanation:

x= (√3+√2)/(√3-√2)

i)

ii)

Answer:

x = -6

Step-by-step explanation:

-4x - 3(2x + 8) = 36

-4x - 6x - 24 = 36

-10x = 60

-x = 6

x = -6

Answer:

[tex]x = - 6[/tex]

Step-by-step explanation:

[tex] - 4x - 3(2x + 8) = 36 \\ - 4x - 6x - 24 = 36 \\ - 10x = 36 + 24 \\ - 10x = 60 \\ \frac{ - 10x}{ - 1 0} = \frac{60}{ - 10} \\ x = - 6[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

x= 5t - a

Step-by-step explanation:

6x + a = 5(x+t)

If you expand 5(x+t), you will get 5x + 5t

i.e. 6x + a = 5x + 5t

Add the additive inverse of 5x to both sides (The additive inverse of 5x is -5x)

i.e. 6x + a - 5x = 5x + 5t - 5x

     x + a = 5t

Then, add the additive inverse of "a" to both sides (The additive inverse of a is -a)

i.e. x + a - a = 5t - a

x = 5t - a

Hope this helps!!!

Just subtract 100 - 50 and you get x = 50

Answer:

x = 50

Step-by-step explanation:

100 -50 = 50

50+50=100

Have a wonderful day and stay safe!

Answer:

6x - 10

Step-by-step explanation:

2x + 4x = 6x

6 + 4 = 10

6x - 10

Answer:

1i) nth term = 12(-b/4)^(n-1)

ii) nth term = 3(-1/9)^(n-1)

2i) Sixth term= (-3b^5)/256

ii) Eight term = -1/1594323

Question:

The complete question as found on brainly (question-10746111):

Write down the nth term of each of the following G.Ps whose first two terms are given as follows. Also find the term stated besides each G.P.

i) 12,-3b,......sixth term

ii) 3,-1/3,..........;8th term?

Step-by-step explanation:

1) To solve terms involving Geometric progressions (GPs), we would first state the variables that are to be incorporated in the formula.

i) 12,-3b,......;sixth term

1st term = a= 12

r = common ratio = 2nd term /1st term

r = -3b/12 = -b/4

Then we would find the nth term

See attachment for details

ii) 3,-1/3,..........;8th term

1st term = a= 3

r = common ratio = 2nd term /1st term

r = (-⅓)/3 = (-⅓)(⅓) = -1/9

Then we would find the nth term

See attachment for details

2) we are to determine the sixth term in (i) and eight term in (ii)

See attachment for details

Sixth term= (-3b^5)/256

Eight term = -1/1594323

Answer:

6

Step-by-step explanation:

the number of occurs over 0

Answer:

Average speed of boat = 3.67 km/h

Average speed of stream = 0.63 km/h

Step-by-step explanation:

30 km upstream in 10 hours gives a speed of 30/10 = 3 km/h relative speed of boat and stream

Same way, 44 km in 10 hrs = 4.4 km/h relative speed of boat and stream.

Let the speed of the stream be y

Let the speed of both be x, then

x - y = 3.... (1)

x + y = 4.4.... (2)

Subtract 1 from 2

2y = 1.4

y = 1.4/2 = 0.7 km/h

substitute value of y in 1

x - 0.7 = 3

x = 3.7 km/h

Also, 40 km upstream in 13 hrs gives speed of 3.08 km/h

55 km in 13 hrs gives 4.2 km/h

Let speed of boat be x and that of stream be y

x - y = 3.08.... (1)

x + y = 4.2..... (2)

Subtract 1 from 2

2y = 1. 12

y = 0.56 km/h

Substitute value of y in 1

x - 0.56 = 3.08

x = 3.64 km/h

Average speed of boat = (3.7 + 3.64)/2

= 3.67 km/h.

Average speed of stream = (0.7 + 0.56)/2 = 0.63 km/h

Answer:

As we know that,

[tex]\bigstar \: \: \sf Time = \dfrac{Distance}{Speed} \\ \\ [/tex]

[tex]\bigstar\:\underline{\boldsymbol{According\: to \:the\: Question\:now :}} \\[tex]

[tex]:\implies \sf \dfrac{30}{x - y} + \dfrac{44}{x + y} = 10 \\ \\ \\ [/tex]

[tex]:\implies \sf \dfrac{40}{x - y} + \dfrac{55}{x + y} = 13 \\ \\ \\[/tex]

[tex]\sf Let \: \dfrac{1}{x - y} = \textsf{\textbf{m}} \sf \: \: and \: \: \sf{\dfrac{1}{x + y} = \textsf{\textbf{n} }}\\ \\ \\[/tex]

[tex]:\implies \sf 30m + 44n = 10\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (i)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]:\implies \sf 40m + 55n = 13\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (ii)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]\qquad\tiny \underline{\frak{ Multiply \: equation \: (ii) \: by \: 3 \: and \: equation \: (i) \: by \: 4 :}} \\[/tex]

[tex]:\implies \sf 120m + 176n = 40\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (iii)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]:\implies \sf 120m + 165n = 39\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (iv)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]\qquad\tiny \underline{\frak{ Substracting \: equation \: (iii) \: from \: equation \: (iv) \: we \: get :}} \\[/tex]

[tex]\sf 120m + 176n = 40 \\ \\

\sf 120m + 165n = 39 \\ \\ [/tex]

[tex]\sf \: \: ( - ) \:\:\: \: \: ( - ) \: \: \: \: \: \: \: ( - ) [/tex]

_____________________

[tex]\: \: \: \: \qquad\sf 11n= 1 \\[/tex]

[tex]\: \: \: \: \: \qquad\sf n= \dfrac{1}{11} \\ \\ [/tex]

[tex]\qquad\tiny {\frak{ Put\: n = \dfrac{1}{11}\:in\:equation \: (i) \: we \: get :}} \\[/tex]

[tex]\dashrightarrow\:\:\sf 30m + 44 \times \dfrac{1}{11} = 10 \\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf 30m= 10 - 4 \\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf 30m= 6 \\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf m= \dfrac{6}{30} \\ \\ \\ [/tex]

[tex]\dashrightarrow\:\:\sf m= \dfrac{1}{5} \\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf \dfrac{1}{x - y} = m\\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf x - y= 5\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (v)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf \dfrac{1}{x + y} = n\\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf x + y= 11\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (vi)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]\qquad\tiny {\frak{Adding\:equation \: (v) \: and \: equation \: (vi) \: we \: get :}} \\[/tex]

[tex]:\implies \sf 2x = 16 \\ \\ \\[/tex]

[tex]:\implies \underline{ \boxed{ \textsf {\textbf{x = 8 km/hr}}}} \\ \\[/tex]

[tex]\qquad\tiny {\frak{Putting\:x = 8\: in \: equation \: (v) \: we \: get :}} \\[/tex]

[tex]:\implies \sf 8 - y = 5 \\ \\ \\ [/tex]

[tex]:\implies \sf y = 8 - 5 \\ \\ \\[/tex]

[tex]:\implies \underline{ \boxed{ \textsf {\textbf{y = 3 km/hr}}}} \\ \\[/tex]

[tex]\bigstar\:\underline{\sf{Therefore\: speed\: of \:boat\: in\: still \:water\: and\: speed\: of\: stream:}} \\[/tex]

[tex]\bullet\:\:\textsf{Speed of boat in stream = \textbf{8 km/hr}}\\[/tex]

[tex]\bullet\:\:\textsf{Speed of boat in still water = \textbf{3 km/hr}}\\[/tex]

Answer:

q=10

Step-by-step explanation:

-10+10q=9q

-10=-q

q=10

Answer:

'''A ray has one endpoint and extends indefinitely in one direction. A pair of opposite rays are two rays that have the same endpoint and extend in opposite directions. Rays are always named with two points and the first point in the name must be the endpoint.'''

Answer:

d=-2 c=-3

Step-by-step explanation:

3c-8d=7

4(c+2d=-7)

3c-8d=7

4c+8d=-28

4c+3c-8d+8d=7-28

7c=-21

c=-3

c+2d=-7

-3+2d=-7

2d=-4

d=-2

Given.

[tex](3c-8d=7)=(c+2d=-7)[/tex]

Multiply 4 to the second equation.

[tex]4(c+2d=-7)[/tex]

[tex]3c+8d=-28[/tex]

Compare the like terms.

[tex]4c+3c-8d+8d=7-28[/tex]

Solve.

[tex]7c=-21[/tex]

Divide 7 to both sides

[tex]\frac{7c}{7}=\frac{-21}{7}[/tex]

[tex]c=-3[/tex]

Substitute (-3) for c into the original second equation.

[tex]c+2d=-7[/tex]

[tex]-3+2d=-7[/tex]

Add (3) to both sides.

[tex](-3+2d=-7)+3[/tex]

[tex]2d=-4[/tex]

Divide (2) to both sides.

[tex]\frac{2d}{2}=\frac{-4}{2}[/tex]

[tex]d=-2[/tex]

Check your work.

[tex]3(-3)-8(-2)=7[/tex]

[tex]-9+16=7[/tex]

[tex]7=7[/tex]

[tex]c+2d=-7[/tex]

[tex]-3+2(-2)=-7[/tex]

[tex]-3-4=-7[/tex]

[tex]-7=-7[/tex]

Therefore your answer is.

[tex]c=-3\\d=-2[/tex]

Answer:

x=3               x = -8           x = 11

Step-by-step explanation:

f(x) = (x − 3)(x + 8)(x − 11)

Using the zero product property

0 = (x − 3)(x + 8)(x − 11)

0 = x-3      0 = x+8     0 = x-11

x=3               x = -8           x = 11

Answer:

x=3               x = -8           x = 11

Hope this helps!

Answer: 20

Step-by-step explanation:

(i) Sona got 10 answers correct.

1 correct answer = 3 marks

10 correct answers = 10×3 = 30 marks but she got only 20

1 wrong answer = -1 mark

that means she attempted 10 incorrect answers.

No.of questions in the test= no.of incorrect + no.of correct answers

10+10= 20

Answer:

14.

Step-by-step explanation:

Simplify:

f(x)-g(x)

3x^2+1 - (1-x)

3x^2+ x

Solve:

(f-g)(2)

3(2)^2 + 2= 3*4+2

= 14

Answer:

-3=x^2/-27

x^2=(-3)(-27)

x=9 or x=-9

Step-by-step explanation:

================================================

Explanation:

We have

f(-5) = 0 and f(2) = 4

This means the two points (-5,0) and (2,4) are on this line

----------

Find the slope of the line through (x1,y1) = (-5,0) and (x2,y2) = (2,4)

m = (y2 - y1)/(x2 - x1)

m = (4 - 0)/(2 - (-5))

m = (4 - 0)/(2 + 5)

m = 4/7 is the slope

----------

Plug m = 4/7 and (x1,y1) = (-5,0) into the point-slope formula. Solve for y.

y - y1 = m(x - x1)

y - 0 = (4/7)(x - (-5))

y = (4/7)(x + 5)

y = (4/7)x + (4/7)*5

y = (4/7)x + 20/7

f(x) = (4/7)x + 20/7

This linear equation has a slope of 4/7 and a y intercept of 20/7.

The equation for f ( x ) would be; f(x) = (4/7)x + 20/7

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

We are given f(-5) = 0 and f(2) = 4

This means the two points (-5,0) and (2,4) are on this line

To Find the slope of the line through (x1,y1) = (-5,0) and (x2,y2) = (2,4)

m = (y2 - y1)/(x2 - x1)

m = (4 - 0)/(2 - (-5))

m = (4 - 0)/(2 + 5)

m = 4/7 is the slope

Then substitute m = 4/7 and (x1,y1) = (-5,0) into the point-slope formula. Solve for y;

y - y1 = m(x - x1)

y - 0 = (4/7)(x - (-5))

y = (4/7)(x + 5)

y = (4/7)x + (4/7)*5

y = (4/7)x + 20/7

f(x) = (4/7)x + 20/7

The linear equation has a slope of 4/7 and a y intercept of 20/7.

Learn more about slope here:

https://brainly.com/question/2503591

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Answer:

Final potential energy = 24 Joule

The velocity with which object must be thrown = [tex]4 \sqrt{10}[/tex] m/s

Step-by-step explanation:

Given:

Mass of object, m = 0.30 Kg

Height of object, h = 8 m

Acceleration due to gravity, g = 10 [tex]ms^{-2}[/tex]

a) Formula for Potential Energy:

[tex]E_p =mgh[/tex]

Where m is the mass of object

g is acceleration due to gravity and

h is the height of object

Putting the values of m, g and h

[tex]E_p = 0.3 \times 10 \times 8\\\Rightarrow E_p =24 J[/tex]

b) Formula for initial and final velocity:

[tex]v^{2} =u^{2} +2gh[/tex]

where v is the final velocity

u is the initial velocity with which the object is thrown

g is acceleration due to gravity and

h is the height obtained by object

here v = 0 at the height 8 m because it will come to rest at the point it attains the maximum height.

h = 8m

g = -10 [tex]ms^{-2}[/tex] (negative because the object's velocity is decreasing)

Putting the values to find 'u':

[tex]0^{2} =u^{2} +2 \times -10 \times 8\\\Rightarrow u^{2} = 160\\\Rightarrow u = 4 \sqrt{10}\ m/s[/tex]

Answer

Step-by-step explanation:

Law of sines: SinB/15 = SinA/BC

B = 90

A = 180-90-21=69°

BC= (15*SinA)/SinB = (15*sin69)/1 ≈ 14m

Answer:

f(2) = 11

hope this helps

Step-by-step explanation:

3(2)+5

6+5

11

Answer:

11

Step-by-step explanation:

3(2)+5=11

Substitution -- :D

Answer:

A. 5/72

Step-by-step explanation:

5 + 4 + 3 = 12 marbles

5/12  - the probability that the student picks a blue marble.

1/6 - the probability that 4 is on the cube

The probability that the student picks a blue marble from the bag, and then rolls a 4

5/12 * 1/6 = 5/72

Answer:

0.25

Step-by-step explanation:

As a decimal, 0.25

As a fraction, 1/4

As a percentage, 25%

Answer:

0.25

Step-by-step explanation:

1/4

= 1*25/4*25

= 25/100

(Multiplying to both numerator and denominator doesn't change the value)

Now to write 25/100 as a decimal

The decimal point goes two places to the left in 25

(Since 100 has 2 zeroes so two values back)

25/100 = .25

= 0.25

Answer:

[tex]25:35[/tex]

Step-by-step explanation:

[tex]\frac{60}{5+7}[/tex]

[tex]\frac{60}{12}[/tex]

[tex]=5[/tex]

[tex]5:7[/tex]

[tex]5 \times 5 :7 \times 5[/tex]

[tex]25:35[/tex]

Answer:

x=S/4

Or

x=S(1/4)

Step-by-step explanation:

Surface Area(S)=4x

Where

x=length

Inverse by solving for x without switching the variables

S=4x

Divide both sides by 4

S/4=4x/4

S/4=x

x=S/4

Or can also be written as

x=S(1/4)

Answer:

work is shown and pictured

Answer:

The correct option is;

The expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 - 6) = negative 18 and Negative 12 (1) minus 6 = negative 18

Step-by-step explanation:

The parameters given are;

First expression 3 × X × (5 - 4) + 3 ×(X - 6)

Second expression -12 × X - 6

Therefore;

For the first expression, for all X, e have;

3 × X × 1 + 3 ×(X - 6) = -3·X  + 3·X -18 = -18

The second expression gives -12·X - 6

When both expressions are equal, we have;

-12·X - 6 = -18

∴ X = (-18 + 6)/(-12) = 1

Hence the correct option is that the expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 - 6) = negative 18 and Negative 12 (1) minus 6 = negative 18.

Answer:

The expressions are not equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (2) minus 6 = negative 30

Or

Answer A

Step-by-step explanation:

Apparently, we're trying to see if ...

 -3(x)(5 -4) + 3(x -6) = -12(x) -6

by evaluating the expressions for x=2:

 -3(2)(5-4) +3(2 -6) ?= -12(2) -6

 -6 -12 ?= -24 -6

 -18 ≠ -30 . . . . . . . . . shows expressions are not equivalent

Answer:

3 2/3

Step-by-step explanation:

Divide 11 by 3 using long division method. then place the quotient as whole number and reminder as numerator and dividend as denominator

The fraction 1 1/3 as an improper fraction is 4/3

From the question, we have the following parameters that can be used in our computation:

Fraction =  1 1/3

When converted to an improper fraction, we have

Numerator = 3 * 1 + 1

Evaluate

Numerator = 4

The denominator remains the same

So, we have

Fraction =  4/3

Hence, the fraction is 4/3

Read more about fraction at

brainly.com/question/31896427

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Answer:

Using triangular inequality:

[tex]0< s\leq 3+8\\\ 0<s\leq 11\\[/tex]

Answer:

80 feet

Step-by-step explanation:

Given that x is the horizontal distance in feet and  f(x) is the vertical distance in feet. The minimum point of a function is its lowest point. For a quadratic equation, at its minimum or  maximum point, the slope of the graph is equal to zero.

For the table of the function given below, it can be seen that the lowest point occurs when x = 80 feet, at this point, the value of f(x) is at its lowest which is 0.

Therefore at the minimum point, it is 80 feet far from the wall .

Answer:

The answer is C!

Step-by-step explanation:

Your welcome

Answer:

11x

Step-by-step explanation:

(x + 2)(x + 9)

x2 + 9x + 2x + 18

x2 + 11x + 18

This is one possibility :)