Consider the following equations:


−x − y = 1

y = x + 3


If the two equations are graphed, at what point do the lines representing the two equations intersect?



a

(−1, 2)


b

(−2, 1)


c

(1, −2)


d

(2, −1)

Answer:

length times width so.... 24

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:

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:

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:

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:

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:

work is shown and pictured

Answer:

11x

Step-by-step explanation:

(x + 2)(x + 9)

x2 + 9x + 2x + 18

x2 + 11x + 18

This is one possibility :)

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!!!

Answer:

-3=x^2/-27

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

x=9 or x=-9

Step-by-step explanation:

Answer:

Federal tax amount = $18,425

Step-by-step explanation:

Given:

Total sales amount = $335,000

Federal tax rate = 5.5%

Find:

Federal tax amount = ?

Computation:

⇒ Federal tax amount = Total sales amount × Federal tax rate

⇒ Federal tax amount = $335,000 × 5.5%

⇒ Federal tax amount = $335,000 × 0.055

⇒ Federal tax amount = $18,425

Therefore, total amount of federal tax owed is $18,425

________________________________

Hey!!

Solution,

(x-2)(X+5)=0

Either,

x-2=0

X=0+2

X=2

or,

X+5=0

X=0-5

X=-5

Hope it helps

Good luck on your assignment

____________________________

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:

scale factor = 3

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, larger to smaller.

scale factor = [tex]\frac{BC}{TB}[/tex] = [tex]\frac{12}{4}[/tex] = 3

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:

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:

6x - 10

Step-by-step explanation:

2x + 4x = 6x

6 + 4 = 10

6x - 10

Answer:

69.08

Step-by-step explanation:

Area equals pi r times 2

A equals 3.14 times 11 times 2

Step-by-step explanation:

area of circle = pi r^2

area = 22/7 × 11yd× 11yd

area = (2662yd^2)/7

area = 380.3 yd^2

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:

" Expected Payoff " ⇒ $ 1.80 ; Type in 1.80

Step-by-step explanation:

Take the probability of winning into consideration;

[tex]Total Number of Tickets - 500,\\Tickets 1 Person Can Enter - 1 Ticket,\\\\Probability of Winning - 1 / 500,\\Money Won - 900 Dollars,\\\\Proportionality - 1 / 500 = x / 900 - where, x = " Expected Payoff "\\1 / 500 = x / 900 - CrossMultiplication,\\\\500 * x = 900,\\x = 900 / 500,\\x = 1.80 Dollars Won!\\\\Conclusion ; x = 1.80 Dollars[/tex]

Solution ; " Expected Payoff " ⇒ $ 1.80

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

Step-by-step explanation:

The mean is the average summing all values together and dividing by the number of values been investigated.

Hence since no values exist between 201-350 that means the mean can not be there.

Answer:

The relative frequency of the class 201 - 350 is 0.

Step-by-step explanation:

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:

[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:

165

Step-by-step explanation:

First, m<UTS=m<UTV+m<VTS by Angle Addition Postulate.  Then, you substitute all the values that you provided for the angles.  15x+15=x+15+140.  You then solve for x.

15x+15=x+155

14x=140

x=10

You then plug back in 10 for X in the value of m<UTS.  15(10)+15=165

Answer:

I think the commission amount is $210

Answer:

C

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

the number of occurs over 0

Answer:

Using triangular inequality:

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

Answer: B) -8/9

Step-by-step explanation:

I would start by looking inside the parenthesis to see if anything could be simplified. We see the terms -5 and -3x, and upon realizing that there is no way to simplify, we can go ahead and just simplify the left side of the equation as much as we can before worrying about breaking the equation down. Distribute the -9 to the -5 and the -3x (multiply -9 by -5 and -9 by -3x). Multiplying two negative numbers will result in a positive value, so the left side of your equation should end up looking like this: 45+27x=21. Now, we can start working to get the variable on its own. Subtract 45 from both sides of the equation. On the left side this cancels out and leaves you with 27x. On the right side you have more of the negative value than positive value, so you end up with -24. The equation now looks like this: 27x=24. The only thing left to do is divide the equation by 27. On the left side of the equation, this leaves you with just x. On the right side, you get -24/27. Normally at this point I would divide out to get the decimal form (I prefer working with decimals) but bc the answer choices are all fractions there's not really a good use to, so instead let's just find the greatest common denominator (GCD) which would be 8. (Just as a clarification the GCD is the largest number you can divide both numbers by evenly.) Divide both the numerator and denominator by eight leaves you with -8/9. Therefore, x= -8/9.