y = 2x + 3
2y = 4x + 6

The system of equations has _____ solution(s).

A.no
B.one
C.infinite

Considering the expression of a line, the equation of the line that passes through the pair of points (-66) and (3,-2) is 8/9x +y= 2/3.

Linear equation

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression y = mx + b, the value of the ordinate to the origin b can be obtained.

The standard form of the line is Ax +By= C

Equation in this case

In this case, being (x₁, y₁)= (-6, 6) and (x₂, y₂)= (3, -2), the slope can be calculated as:

m= (-2 - 6)÷ (3 - (-6))

m= (-2 - 6)÷ (3 + 6)

m= (-8)÷ 9

m= -8/9

Considering point 2 and the slope, you obtain:

-2= (-8/9)×3 + b

-2= -8/3 + b

-2 +8/3= b

2/3= b

The equation of the line is y= -8/9x +2/3.

Finally, the standard form of the line is 8/9x +y= 2/3

Answer: 1) 9 days

2) a)37.5%

b)50%

c) 33.33%

Step-by-step explanation:

1) - Let's call:

x: number of days the company supposed to finish the order.

- You know that the company had to produce 40 items daily, but it produced 20 items more daily and finished the order 3 days ahead of time. Therefore, you can express this as following:

[tex]40x=(40+20)(x-3)\\40x=60(x-3)[/tex]

- Solve for [tex]x[/tex]:

[tex]40x=60x-180\\-20x=-180\\x=9[/tex]

(The answer is 9 days)

2) a) The percent that belongs to three people if eight eight people share equally in an inheritance, can be calculated as following:

[tex]\frac{3}{8}*100=37.5[/tex]%

b) The percent that belongs to three people if six people share equally in an inheritance (because two of the people are disinherited) can be calculated as following:

[tex]\frac{3}{6}*100=50[/tex]%

c) - The increase goes from 1/8 to 1/6, therefore, you must subtract them:

[tex]\frac{1}{6}-\frac{1}{8}=\frac{1}{24}=0.04167[/tex]

- Divide the result by 1/8 and multiply by 100 to obtain the percent:

[tex]\frac{0.04167}{\frac{1}{8}}*100=33.33[/tex]%

1. The graph of y=2/3x-2 is the top right corner, the -2 in the equation makes the line cross the y axis at -2

2. The slope is always with x and the y intercept is the second part of the equation.

The equation would be y = 5/6x -3

3.  The slope is the change in Y over the change in X

slope = 10-7 / 2 -  -1 = 3/3 = 1

Using the line formula y = mx+b, solve for b using the first point and the slope:

7 = 1 (-1)x +b

b = 7+1

b =8

The equation is -x +y =8

4. the jar starts with 6 , then they add 2 each day, multiply 2 by the number of days (x) and add it to 6:

The equation would be y = 2x + 6

5. point (5,9) slope = 2

Point-slope formula is written as y - y1 = m(x-x1)

y1 = 9, x1 = 5, m = 2

equation becomes y-9 =2(x-5)

Answer:

The answer is the first graph

The equation is y = 5/6x -3

The next equation is -x +y =8

The equation after would be y = 2x + 6

And, the final answer is y-9 =2(x-5)

Hope this helps!

Answer:

I'd say about 720 hotdogs.

Step-by-step explanation:

Answer:

y=8

Step-by-step explanation:

We need to find the equation for the line.

The first step is to find the slope

We need 2 points  (0,2) (2,3)

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

          = (3-2)/(2-0)

          = 1/2

We know the y intercept ( where it crosses the y axis)  at 2

Lets use the slope intercept form of the line

y= mx+b

y = 1/2 x+2

If we want to find the value of y when x =12 , substitute the value of x=12

y =1/2 * 12 +2

y = 6+2

y=8

18. Answer: D

Step-by-step explanation:

First, find the measure of the missing angle.

65° + 57° + x = 180°

      122° + x = 180°

                x = 58°

Next, match up the angles with the opposite sides:

65° ⇄ Swim

58° ⇄ Bike

57° ⇄ Run

Lastly, put them in order from least to greatest:

   57° < 58° < 65°

⇒ Run < Bike < Swim

The only multiple choice option that is correct is Bike > Run.

*****************************************************************************

19. Answer: 22.3°

Step-by-step explanation:

[tex]sin\theta = \dfrac{opposite}{hypotenuse}[/tex]

[tex]sinD= \dfrac{EF}{DE}[/tex]

[tex]sinD= \dfrac{19}{50}[/tex]

[tex]D= sin^{-1}\bigg(\dfrac{19}{50}\bigg)[/tex]

D = 22.3°

Answer:

option A  :  graph is a function

Step-by-step explanation:

(a) option is given is a graph

For graph , the function should pass vertical line test

Draw vertical line for every value of x

The vertical lines cross only one red point at a time

So the graph is a function

(b) When each input has only one output then it is a function

in option B , input 3 has two output -5  and 0

so it is not a function

(c) in option C , input 3 has two output 14  and 19

so it is not a function

(d) in option d , input -1 has two output -11  and 5

so it is not a function

Answer:

2.5 rad ( to the nearest tenth )

Step-by-step explanation:

the time difference between the given times is 24 minutes

In 1 hour the hand moves 2π radians, hence in 1 minute moves

[tex]\frac{2\pi }{60}[/tex], thus in 24 minutes moves

[tex]\frac{2\pi }{60}[/tex] × 24 ≈ 2.5 radians

Answer:

the answer is x=5 for a fact

Step-by-step explanation:

Answer:

the answer would be x=5

f(x) + n - translate the graph n units up

f(x) - n - translate the graph n units down

f(x + n) - translate the graph n units left

f(x - n) - translate the graph n units right

|f(x)| - reflect over x-axis for x < 0.

[tex]f(x)=|x+2|-5[/tex]

Graph g(x) = x

g(x + 2) = x + 2 → translate 2 units left

|g(x + 2)| = |x + 2| → reflect over x-axis for x  < 0

|g(x + 2)| - 5 = |x + 2| - 5 → translate 5 units down

Answer:

B

Step-by-step explanation:

The square root of 131 is 11.445 and so it lies between 11 and 12 on a number line.

See where it goes on a number line below:-

Answer:     73.55%

Step-by-step explanation:

p = (100-a) e^-b(0.07)

we have a = 20 and b =1.2

  = (100-20) e^-(1.2)(0.07)

=    80(e^-0.084)

= 80(0.919431)

= 73.55%

Answer:

The correct answer is 93.6%

Step-by-step explanation:

Got it right on Edge 2020

Answer:

Yes, the side lengths of ΔABC forms a Pythagorean triple

Step-by-step explanation:

Given : A right angled triangle ABC

           Side lengths - 3,4 and 5

To Find: . Do the side lengths form a Pythagorean triple?

Solution :

Hypotenuse (longest side) = 5

To check we need to use Pythagoras theorem :

[tex]Hypotenuse^{2} =Perpendicular^{2} +Base^{2}[/tex]

[tex]5^{2} =3^{2} +4^{2}[/tex]

[tex]25 =9 +16[/tex]

[tex]25 =25[/tex]

Since Pythagoras theorem is verified . So, the side lengths form the Pythagorean triplet.

Hence  the side lengths of ΔABC forms a Pythagorean triple

Answer:

No real solutions

129

Step-by-step explanation:

The quadratic formula is

-b ± sqrt(b^2 -4ac)

----------------------------

2a

3x^2 =2x-1

Lets get the equation in proper form

3x^2 -2x+1 = 2x-1-2x+1

3x^2 -2x+1 =0

a=3  b=-2 c=1

Lets substitute what we know

2 ± sqrt((-2)^2 -4(3)(1))

----------------------------

2(2)

-2 ± sqrt(4-12)

----------------------------

2(2)

-2 ± sqrt(-8)

----------------------------

4

No real solutions

The quadratic formula is

-b ± sqrt(b^2 -4ac)

----------------------------

2a

2x^2 -10= 7x

Lets get the equation in proper form

2x^2 -7x-10 = 7-7x

2x^2 -7x-10 =0

a=2  b=-7 c=-10

Lets substitute what we know, we are only looking for what is inside the radical

(b^2 -4ac)

((-7)^2 -4(2)(-10))

(49 +80)

129

Distribute

2x × 2x^4 + 2x × -6x^3 + 2x ×4x^2 + 2x × - 3x

Take out the constants

(2 × 2)xx^4 + 2x × -6x^3 + 2x × 4x^2 + 2x × -3x

Simplify 2 × 2 to 4

4xx^4 + 2x × -6x^3 + 2x × 4x^2 + 2x × -3x

Use Product Rule: x^a x^b = x^a + b

4x^1 + 4 + 2x × -6x^3 + 2x ×4x^2 + 2x × -3x

Simplify 1 + 4 to 5

4x^5 + 2x × -6x^3 + 2x × 4x^2 + 2x × -3x

Take out the constants

4x^5 + (2 × -6)xx^3 + 2x × 4x^2 + 2x × -3x

Simplify 2 × -6 to -12

4x^5 - 12xx^3 + 2x × 4x^2 + 2x × -3x

Use the Product Rule: x^a x^b = x^a + b

4x^5 - 12x^1 + 3 + 2x × 4x^2 + 2x -3x

Simplify 1 + 3 to 4

4x^4 - 12x^4 + 2x ×4x^2 + 2x × -3x

Take out the constants

4x^5 - 12x^4 + (2 × 4)xx^2 + 2x × -3x

Simplify 2 × 4 to 8

4x^5 - 12x^4 + 8xx^2 + 2x × -3x

Use the Product Rule: x^a x^b = x^a + b

4x^5 - 12x^4 + 8x^ 1 + 2 + 2x × -3x

Simplify 1 + 2 to 3

4x^5 - 12x^4 + 8x^3 + 2x × -3x

Take out the constants

4x^5 - 12x^4 + 8x^3 + (2 × -3)xx

Simplify 2 × -3 to -6

4x^5 - 12x^4 + 8x^3 - 6xx

Use the Product Rule: x^a x^b = x^a + b

4x^5 - 12x^4 + 8x^3 - 6x^2

Answer:

4x^5 - 12x^4 + 8x^3 - 6x^2

Step-by-step explanation:

Answer:

x is greater than or equal to 358

Step-by-step explanation:

1. Subtract 100 from 18,000

2. Divide by 50 to get your number of seven letter words

Answer:

55

Step-by-step explanation:

The equation of inverse variation is

y = k/x,

where k is a constant.

We can use the given x- and y-coordinates to find k.

y = k/x

15 = k/11

k = 165

The inverse variation equation for this problem is

y = 165/x

For y = 3,

3 = 165/x

3x = 165

x = 55

Answer:

C

Step-by-step explanation:

given x varies inversely as y then the equation relating them is

x = [tex]\frac{k}{y}[/tex] ← k is the constant of variation

To find k use the given condition x = 11 when y = 15

k = xy = 11 × 15 = 165 , hence

x = [tex]\frac{165}{y}[/tex] ← inverse variation equation

when y = 3, then

x = [tex]\frac{165}{3}[/tex] - 55 → C

Answer:

38 = FH

Step-by-step explanation:

Because this is a rectangle, IG = FH

We know that IE + EG = FH

We also know that IE = EG   (perpendicular bisectors)

IE = EG

3x+4 = 5x-6

Subtract 3x from each side

3x-3x+4 = 5x-3x-6

4 = 2x-6

Add 6 to each side

4+6 =2x

10 =2x

Divide by 2

10/2 =2x/2

5=x

Now lets find FH

IE + EG = FH

3x+4 + 5x-6  = FH

Combine like terms

8x-2 = FH

Substitute in x =5

8*5-2

40-2

38 = FH

Answer:

40-2

38 = FH

Step-by-step explanation:

Answer: x = 6

Step-by-step explanation:

[tex]\dfrac{3}{x}+\dfrac{1}{3}=\dfrac{5}{6}[/tex]

[tex](6x)\dfrac{3}{x}+(6x)\dfrac{1}{3}=(6x)\dfrac{5}{6}[/tex]  multiplied by common denominator

18 + 2x = 5x

      -2x   -2x

18         = 3x

÷3          ÷3

6          =  x

Since "x" is in the denominator, the restriction is that x ≠ 0.  If the solution was x = 0, then the solution would not be valid and would be eliminated as an answer.

Remember that "x" is just an unknown value.  It is possible to add two fractions together and have their sum be a fraction.

For example: [tex]\dfrac{1}{5} + \dfrac{2}{5} = \dfrac{3}{5}[/tex] could be written as [tex]\dfrac{1}{5} + \dfrac{2}{x} = \dfrac{3}{5}[/tex].  When we solve it, we will get x = 5.

******************************************************************************************

Answer: Edward

Step-by-step explanation:

[tex]f(x)=\dfrac{(x-1)(x+2)(x+4)}{(x+1)(x-2)(x-4)}[/tex]

The denominator cannot equal zero, so:

Those x-values are the asymptotes, which is where the function is undefined.

Answer:

the only point is (0,1) if u would look at the graph i post

Step-by-step explanation:

The point which lies on the graph of f(x) = (1/3)x will satisfy the function thus point (-1, -1/3) will lie on the graph thus option (D) is correct.

A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.

In order to plot the graph, we need to find out y's values corresponding to x's value

As per the given function,

f(x) = (1/3)x

Substitute, x = 0,

y = f(0) = (1/3)0 = 0

So,(0,1) will not lie on the graph.

Similarly, (3, 27) and (−2, 9) also do not lie on the graph.

Substitute (-1,-1/3)

-1/3 = (1/3)(-1) = -1/3

Thus, it will be the point of the function.

Hence "The point which lies on the graph of f(x) = (1/3)x will satisfy the function thus point (-1, -1/3) will lie on the graph".

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The solution is Option B.

The number of old houses in the city are 35 houses

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the value of A is

The number of new houses = 3

The number of old houses = 7

So , the ratio of old houses to new houses = number of old houses : number of new houses

Substituting the values in the equation , we get

Ratio of old houses to new houses = 7 : 3

Now , the number of new houses = 15

So , the number of old houses A is given by the proportion equation ,

7 : 3 : : A : 15

On simplifying the equation , we get

7/3 = A / 15

Multiply by 15 on both sides of the equation , we get

A = ( 7 x 15 ) / 3

A = 7 x 5

A = 35 houses

Therefore , the value of A is 35 houses

Hence , the number of old houses is 35

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Final answer:

The correct number of old houses is found by determining how many times the 3:7 ratio of new to old houses fits into the 15 new houses and then applying that to the 7 old houses in the ratio, which results in 35 old houses.

Explanation:

The question asks to find the number of old houses in a city given the ratio of new to old houses and the number of new houses. There is a ratio of 3 new houses for every 7 old houses. If there are 15 new houses, we need to find how many times the ratio fits into the number of new houses and then apply that same multiplier to the number of old houses.

To find this, we divide the number of new houses by the number of new houses in the ratio:

Number of times the ratio fits = 15 new houses ÷ 3 new houses per ratio = 5 times

Now, we multiply the number of old houses in the ratio by 5:

Number of old houses = 7 old houses per ratio × 5 times = 35 old houses

Therefore, the correct answer is B. 35.

The simplest form of  [tex]2\frac{5}{8}[/tex] ÷ [tex]2 \frac{1}{2}[/tex]  is  [tex]1\frac{1}{20}[/tex] .

               [tex]2\frac{5}{8}[/tex]  ÷ [tex]2\frac{1}{2}[/tex]

       write the mixed fraction to improper fraction

             = [tex]\frac{21}{8}[/tex] ÷ [tex]\frac{5}{2}[/tex]

  Now change the division sign to the multiplication sign by writing the second number as [tex]\frac{2}{5}[/tex] .

             = [tex]\frac{21}{8}[/tex] × [tex]\frac{2}{5}[/tex]

             = [tex]\frac{21}{20}[/tex]

  Write the above improper fraction into a mixed fraction.

            = [tex]1\frac{1}{20}[/tex]  

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Answer:

The correct answer has already been given (twice). I'd like to present two solutions that expand on (and explain more completely) the reasoning of the ones already given.

One is using the hypergeometric distribution, which is meant exactly for the type of problem you describe (sampling without replacement):

P(X=k)=(Kk)(N−Kn−k)(Nn)

where N is the total number of cards in the deck, K is the total number of ace cards in the deck, k is the number of ace cards you intend to select, and n is the number of cards overall that you intend to select.

P(X=2)=(42)(480)(522)

P(X=2)=61326=1221

In essence, this would give you the number of possible combinations of drawing two of the four ace cards in the deck (6, already enumerated by Ravish) over the number of possible combinations of drawing any two cards out of the 52 in the deck (1326). This is the way Ravish chose to solve the problem.

Another way is using simple probabilities and combinations:

P(X=2)=(4C1∗152)∗(3C1∗151)

P(X=2)=452∗351=1221

The chance of picking an ace for the first time (same as the chance of picking any card for the first time) is 1/52, multiplied by the number of ways you can pick one of the four aces in the deck, 4C1. This probability is multiplied by the probability of picking a card for the second time (1/51) times the number of ways to get one of the three remaining aces (3C1). This is the way Larry chose to solve the this.

Step-by-step explanation:

Hi There!

Answer:

4/52 (With cards picked before put back.)

3/48 (With cards picked before not put back.)

Step-by-step explanation:

A standard deck of cards is made up of 52 cards.

There are 4 kings in a deck.

4/52

Bob has a 4/52 chance of picking a king.

I don't know if the cards he picked prior to this he put back or not. If he didn't then it's 3/48.

Hope This Helps :)

Answer:

The midpoint of TS is (-1,-3)

The coordinates of M should be (8,18)

Step-by-step explanation:

Answer:

He now makes 16.50 per hour

Step-by-step explanation:

15.00 x .10 = 1.50

15.00 + 1.50 = 16.50

Answer:true

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

Answer: 23.13 lbs

Step-by-step explanation:

Weight in May + Weight gained = Weight in July

       4.5            +         18.63        =

                     23.13                      =

NOTE: Make sure to line up the decimal point when adding decimals:

    4.50

+  18.63

   23.13