2x = 4y + 8, x - 2y = 4
System of Equations

Answers

Answer 1

Answer:

[tex]y = 2 \\ {0 \: and \:2}[/tex]

Step-by-step explanation:

-2 + 2(3) =-2 +6 = 4 for the 2nd equation

2(-2) + 4(3) = -4 +12 = 8 for the 2nd equation

(-2,3) satisfies both equations

let x = 0, then y= 2 (0,2) is another solution

there's multiple solutions, including (-2,3) and (0,2). That eliminates all answers except the first

Try graphing the two equations. They're the same line, with an infinite number of points on the line, which means an infinite number of solutions.

Answer 2

Answer:

infinite number of solutions

Step-by-step explanation:

Given the 2 equations

2x = 4y + 8 → (1)

x - 2y = 4 → (2)

Rearrange (2) making x the subject by adding 2y to both sides

x = 4 + 2y → (3)

Substitute x = 4 + 2y into (1)

2(4 + 2y) = 4y + 8 ← distribute and simplify left side

8 + 4y = 4y + 8

Since both sides are the same this indicates the system has an infinite number of solutions.

one possible solution is, found by choosing a value for y and substituting into (3)

y = 1 : x = 4 + 2(1) = 4 + 2 = 6 , that is

(6, 1 )

Other possible solutions may be generated in the same way.


Related Questions

If 9 exercise books cost
$540.00. how much will
14 of such cost?​

Answers

Answer:

$840 dollars

Step-by-step explanation:

Divide 540 by 9 to get the cost of 1 book then multiply it by 14

Answer:

$840

Step-by-step explanation:

[tex]\frac{14}{9}: \frac{y}{540}[/tex]

y × 9 = 540 × 14

9y = 7560

9y ÷ 9 = 7560 ÷ 9

y = 840

If you apply the changes below to the absolute value parent function, fx) = |xl, what is the equation of the new function?

• Shift 2 units to the right.
• Shift 3 units down.

A. g(x) = lx- 2l - 3

B. g(x) = lx+ 2l - 3

C. g(x) = lx+3l -2

D. g(x) = lx - 3l- 2​

Answers

Answer:

it's A

Step-by-step explanation:

just took the test

g(x) = lx- 2l - 3 is the equation of the new function when the  parent function f(x) = |xl shift 2 units to the right and Shift 3 units down.

The given parent function is  fx) = |xl.

We need to shift the parent function  2 units to the right and 3 units down.

To shift the absolute value function 2 units to the right.

We need to replace x with x - 2 inside the absolute value, as follows:

g(x) = |x - 2|

To shift the function 3 units down

We need to subtract 3 from the entire function, as follows:

g(x) = |x - 2| - 3

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can someone pls pls help me?

Answers

Answer:

5

Step-by-step explanation:

25=5x5

Answer:

z = 5 meters

Step-by-step explanation:

since the area = 25 [tex]m^2[/tex] and the only value is z, we have to multiply a number by itself that will equal  25 [tex]m^{2}[/tex].

z × z = 25 [tex]m^{2}[/tex]

5 × 5 = 25 [tex]m^{2}[/tex]

Out of 50 people surveyed, 42 respond ‘yes’ to the survey question. What is the probability of a ‘yes’ response? Write your answer as a decimal.

Answers

Answer:

0.84

Step-by-step explanation:

Given

Total no. of observation = 50

Given, No. of observations that told yes = 42

Therefore,

Probability of getting response as yes

[tex] = \frac{42}{50} [/tex]

[tex] = \frac{21}{25} [/tex]

In decimal form ,

= 0.84 (Ans)

a. List all the factors of 42.
b. What is the greatest common factor of 42 and 15?
C. What is the greatest common factor of 42 and 50?

Ahhhh please help!!!

Answers

Greatest common factor (GCF) of 42 and 50 is 2.

HELP PLEASE I WILL MARK BRAINLIEST

Answers

Answer:

A

Step-by-step explanation:

I just took This test

Line m is parallel to line n.If the slope of line m is -2,what is the slope of line n?

Answers

Answer:

-2

Step-by-step explanation:

they are parallel so same slope but different y intercepts

Math geometry help please show work thanks

Answers

Part (a)

Refer to the diagram below to see the two triangles separated.

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

Part (b)

If the 3 meter portion is perpendicular to the horizontal portion, then the triangles are similar. We can prove this using the AA similarity theorem. One pair of angles would be the shared overlapping 25 degree angles. The other pair of congruent angles would be the two 90 degree angles. We only need two pairs of congruent angles to use AA. You could use three pairs (and the aptly named AAA theorem) but that's overkill in my book.

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

Part (c)

There are a few ways to approach this, but one way is shown below

y/3 = (8.4+6.6)/(6.6)

y/3 = 15/(6.6)

6.6y = 3*15 .......... cross multiply

6.6y = 45

y = 45/(6.6)

y = 6.81818 approximately

When rounding to one decimal place, we get y = 6.8

Si alicia se gasta 2 pesos, le quedaría el doble de dinero que si se gastara 4 pesos ¿cuantos tiene alicia?

Answers

Answer:

La cantidad de dinero que tiene Alicia es 6 pesos.

Step-by-step explanation:

Un sistema de ecuaciones lineales es un conjunto de dos o más ecuaciones lineales, en el cual se relacionan dos o más incógnitas.

Resolver un sistema de ecuaciones consiste en encontrar el valor de cada incógnita para que se cumplan todas las ecuaciones del sistema. Es decir, se debe buscar los valores de las incógnitas, con los cuales al reemplazar, deben dar la solución planteada en las ecuaciones.

Siendo:

x= cantidad de dinero que tiene Alicia.y= dinero que le quedaría a Alicia si gasta 4 pesos.

Entonces el sistema de ecuaciones a resolver es:

[tex]\left \{ {{x-2=2*y} \atop {x-4=y}} \right.[/tex]

Sustituyendo la ecuación 2 en la primer ecuación:

x-2= 2*(x -4)

Resolviendo:

x -2= 2*x -2*4

x -2= 2*x -8

-2 + 8= 2*x -x

6= x

Entonces, la cantidad de dinero que tiene Alicia es 6 pesos.

What is the length of side s of the square shown below?

Answers

Answer:

A.[tex]\sqrt{2}[/tex]

Step-by-step explanation:

s = cos45° x 2

=> s = [tex]\frac{\sqrt{2} }{2}[/tex] x 2

=> s = [tex]\sqrt{2}[/tex]

Answer:

lookin cute in the reflection my man ;)

Step-by-step explanation:

Find the values of x and y. Write your
answer in simplest form

Answers

Answer:

ok so the angles are

60

90

30

so we can just use the formulas

y=15

x=25.981 or 26

Hope This Helps!!!

The cost of 4 mangoes and 5 pears is Rs 260. If the cost of 1 mango is Rs 40, find the cost of 1 pear.

Answers

Answer:

Step-by-step explanation:

cost of 5 pears=260-40*4

=260-160

= Rs 100

cost of 5 pears=Rs 100

cost of 1 pear=Rs 100/5

=Rs 20

Answer:

1 pear = Rs. 20

Step-by-step explanation:

Multiply 4 by 40

4 x 40 = 160

Subtract 160 with 260

260 - 160 = 100

Divide 100 by 5

100 / 5 = 20

One pear = Rs. 20

what's the answer
show full explanation
wrong ones are gonna get reported ​

Answers

Answer:

Step-by-step explanation:

Hope this helps u!!

Answer:

Hope u got it :)

Step-by-step explanation:

[tex]9x^2 - 30xy + 25y^2 = (3x)^2 - 2 (15xy) + (5y)^2[/tex]

                           [tex]= (3x)^2 - 2(3x \times 5y) + (5y)^2\\\\[/tex]

[tex]This \ is \ of \ the \ form \ a^2 - 2ab + b^2 , \ that \ is \ (a-b)^2\\\\a = 3x, \ b = 5y[/tex]

[tex]9x^2 - 30xy + 25y^2 = (3x - 5y)^2[/tex]

oh and alsoo can someone plzzzzz add an explanation

Answers

Answer:

Brian sold 35 tickets

Step-by-step explanation:

42/6 = 7

7 x 5 = 35

35/42 = 5/6

Brian sold 35 tickets

(I know this isn't part of the question, but Brain didn't sell 7 tickets)

Need help on this one! 10 points

Answers

A is the correct form
Option 4: 84/2 over 121

sin^2x + cos^2x = 1
sin^2x + (7/11)^2 = 1
sin^2x + 49/121 = 1
sin^2x = 72/121
sinx = square root of 72/121
sinx = (6 root 2) / 11

sin2x = 2sinxcosx
sin2x = 2[(6 root 2)/11] (7/11)
sin2x = (2*6*7*root 2) / (11*11)
sin2x = 84 root 2 / 121 :)

The instructions on the bag on concrete mix say to add 2 gallons of water to each 8 pounds bag of conceit mix

Answers

Answer:

4 pound

Step-by-step explanation:

From the question :

2 gallons of water = 8 pound bag

Number of pound bag per gallon of water ;

Let the number of pound = x

Using cross multiplication, we'll have :

2 gallons = 8 pounds

1 gallon = x pounds

Cross multiply

2x = 8

x = 8 /2

x = 4

Hence, 1 gallon of water mixes 4 pound bag of concrete.

Ashley deposits $200 into an account that pays simple interest at a rate of 3% per year. how much money will she make in 3 years.​

Answers

I think The answer is $18

Which numbers have 23 as their absolute value?
I need help like fast- pls

Answers

Answer:

- 23 and 23

Step-by-step explanation:

Absolute value is the distance from a number to zero on a number line. Absolute value is always positive.

- 23 is 23 space away from 0, and so is 23.

Give FIVE (5) real life examples of functions

Answers

Answer:

Physics - The position of a particle experimenting an uniform accelerated motion. (Quadratic function)

Chemistry - The velocity of the chemical reaction as a function of temperature. (Exponential function)

Physics - Convective heat transfer of an element with its surroundings. (Linear function)

Physics - Time conversion from seconds to minutes. (Linear function)

Physics - Radiative heat transfer from an element. (Quartic function)

Step-by-step explanation:

There are many examples of applications of function in real life:

Physics - The position of a particle experimenting an uniform accelerated motion. (Quadratic function)

[tex]y = y_{o} + v_{o}\cdot t + \frac{1}{2}\cdot a \cdot t^{2}[/tex] (1)

Where:

[tex]y[/tex] - Current position.

[tex]y_{o}[/tex] - Initial position.

[tex]v_{o}[/tex] - Initial velocity.

[tex]a[/tex] - Acceleration.

[tex]t[/tex] - Time.

Chemistry - The velocity of the chemical reaction as a function of temperature. (Exponential function)

[tex]k = A\cdot e^{-\frac{E_{o}}{R\cdot T} }[/tex] (2)

Where:

[tex]A[/tex] - Frequency factor.

[tex]E_{o}[/tex] - Activation energy.

[tex]R[/tex] - Ideal gas constant.

[tex]T[/tex] - Temperature.

[tex]k[/tex] - Kinetic constant.

Physics - Convective heat transfer of an element with its surroundings. (Linear function)

[tex]\dot Q = h\cdot A_{s} \cdot (T-T_{\infty})[/tex] (3)

Where:

[tex]h[/tex] - Convective constant.

[tex]A_{s}[/tex] - Surface area.

[tex]\dot Q[/tex] - Heat transfer rate.

[tex]T_{\infty}[/tex] - Temperature of the surroundings.

[tex]T[/tex] - Surface temperature of the element.

Physics - Time conversion from seconds to minutes. (Linear function)

[tex]t' = \frac{1}{60}\cdot t[/tex] (4)

Where:

[tex]t[/tex] - Time, in seconds.

[tex]t'[/tex] - Time, in minutes.

Physics - Radiative heat transfer from an element. (Quartic function)

[tex]\dot Q = \epsilon \cdot \sigma \cdot A_{s}\cdot T^{4}[/tex] (5)

Where:

[tex]\dot Q[/tex] - Heat transfer rate.

[tex]T[/tex] - Surface temperature of the element.

[tex]A_{s}[/tex] - Surface area.

[tex]\epsilon[/tex] - Emissivity.

[tex]\sigma[/tex] - Stefan-Boltzmann constant.

The sum of two numbers is 8. Their difference is 24. What are the two numbers ? Write a system of linear equations and solve using the elimination method.

Answers

Answer:

x=16

Step-by-step explanation:

let:

> x be one number

> y be the other number

system of Equations:

> x+y=8

> x-y=24

Using elimination method the y's cancel each other out, and we are left with

2x = 32

divide by 2 on both sides to get x by itself

AND

x=16

Find the area of the sector. Use 3.14 for it.
PLEASE HURRY

Answers

Answer:

the answer is a

Step-by-step explanation:

formula= (angle / 360) x π x (diameter / 2)^2

i this case we have the radius already so

= (240/360)*(pi)*(11)^2

=2/3(3.14)*(121)

= around 253.29

= which leads me to believe a is correct

Answer:

Solution given;

angle =240°

radius [r]=11cm

we have

length of arc =240°/360°×π*r²

=240°/360°×2×3.14*11²=253.29cm²

length of the arc is 253.29cm².

does else anybody worry about the future?.
like i still dont know what i wanna do after highschool and i haven't cared where i end up but somehow i just get anxious thinking about it

Answers

Answer:

i worry ab mine all the time bc like im the type of person thats called an over thinker i over think alot and it just gives me alot of anxidy so ur not the only one lol

Step-by-step explanation:

Which function has the same domain as y=2square root x? O y=square root of 2x O y=2 cube root of x O y square root of x-2 O y=cube root of x-2

Answers

Answer:

A

Step-by-step explanation:

Domaine of y=2 square root x is x>=0 same for y=square root 2x

Answer: First option or A on your test

Step-by-step explanation: y= root of 2x

On a school trip to a theme park, 4 busses each carry 70 students.
35% of the students are bringing their own lunch.
1
7
of the students are buying lunch when they get to the theme park.
The teachers are worried that some students have not made plans for lunch.
Find how many students have not made plans for lunch.

Answers

Answer:

165 Students Have No Made Plans For Lunch.

Step-by-step explanation:

According To the Question,

Given,On a school trip to a theme park, 4 busses each carry 70 students Then Total Number Of Students on a trip is 70×4=280 Students.And,35% of the students are bringing their own lunch. Thus,35% Of 280 Students is 98 Students. Then Remaining 182 Students not bring their own lunch.

Now, 17 of the students are buying lunch when they get to the theme park. Thus students Who have not made plans for lunch is 182-17⇒165Students

A florist sold 16 flower bouquets yesterday, including 8 lily bouquets. Based on past data, how many of the next 10 bouquets sold should you expect to be lily bouquets?

Answers

Answer:

The answer is 5

Step-by-step explanation:

Hope this answer helps you :)

Have a great day

Mark brainliest

The number of 10 bouquets sold should you expect to be lily bouquets will be 5.

What are ratios and proportions?

A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other.

Given that a florist sold 16 flower bouquets yesterday, including 8 lily bouquets. Based on past data. The number of bouquets sold is 10.

The number of the Lily bouquets will be calculated as:-

Number = ( 8 / 16 ) x 10

Number = ( 1 / 2)  x 10

Number = 5

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-\frac{1}{10}-x^3+x^4+3x

10
1

−x
3
+x
4
+3x

Answers

Answer:

Its really simple

Step-by-step explanation:

first you take the 10 then turn it into joe then mama

Answer:

-1/10 - 1x^3 + x^4 + 3x

Step-by-step explanation:

negative one tenth minus 1x exponet 3 plus x exponent 4 plus 3x

A rectangle has sides measuring (2x + 7) units and (5x + 9) units.

Part A: What is the expression that represents the area of the rectangle? Show your work.
Part B: What are the degree and classification of the expression obtained in Part A?
Part C: How does Part A demonstrate the closure property for polynomials?

Answers

Part A

Use the FOIL rule to expand out the expression below

(2x+7)(5x+9)

2x*5x + 2x*9 + 7*5x + 7*9

10x^2 + 18x + 35x + 63

10x^2 + 53x + 63  is the final answer for part A

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

Part B

The degree is 2. This is a quadratic trinomial.

The degree is simply the largest exponent after expanding everything out. The degree directly determines the type of polynomial. Since the degree is 2, we have a quadratic. The polynomial is a trinomial because it has 3 terms.

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

Part C

Imagine we had a machine in which we deposit 2 coins into it. One would happen on either side. After the coins are deposited, a third coin pops out. The 2 coins going in and the third coin coming out are the same currency. This represents an example of closure.

In mathematics, the idea of closure is taking any two objects of the same type, applying an operation on them, and getting the same type of object as the input.

For example, we could take two whole numbers and multiply them together. The result is always a whole number. The set of whole numbers is closed under multiplication because you can't leave the set (hence the gate is closed not letting anything out).

Similarly, taking any two polynomials and multiplying them together will always lead to some other polynomial. Part A shows this in action because (2x+7), (5x+9) and 10x^2 + 53x + 63 are all polynomials.

[tex]\rm 10x^{2} + 53x + 63[/tex] is the expression that represents the area of the rectangle. This is a trinomial expression.

What is a quadratic equation?

A quadratic equation is the polynomial of second degree in one variable only. The standard form of a quadratic equation is [tex]\rm ax^{2} +bx+c=0[/tex]

Where, x is the variable and a,b, and c are real numbers.

Part A

Let length of a rectangle = (2x+7)

Let width of a rectangle = (5x+9)

The area of the rectangle = length × width

=   (2x+7)(5x+9)

= 2x × 5x + 2x × 9 + 7 × 5x + 7 × 9

= [tex]\rm 10x^{2} + 18x + 35x + 63[/tex]

Therefore, [tex]\rm 10x^{2} + 53x + 63[/tex] is the expression that represents the area of the rectangle.

Part B

The degree is 2 in the expression. This is a trinomial expression.

The degree is simply the largest exponent. The degree directly represents the type of polynomial. Since the degree is 2. The polynomial is a trinomial because it has 3 terms.

Part C

Applying multiplication operations such that taking any two polynomials and multiplying them together will always lead to some other polynomial. Part A shows this multiplication because (2x+7), (5x+9) and [tex]\rm 10x^{2} + 53x + 63[/tex] are all polynomials.

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A rectangle has an area of 48 square feet and a perimeter of 32 feet. Which of the following could be its dimensions?

12 ft and 4 ft
6 ft and 8 ft
2 ft and 24 ft
3 ft and 16 ft

Answers

Answer:

12 feet and 4 feet

Step-by-step explanation:

12 times 4 is 48

and the perimeter is 12 times 2 and 4 times 2 which is 32

hope this helped :D

A. 12ft and 4ft. Pretty sure I’m right

please can someone help asap ? thank you ! :)

Answers

Answer:

[tex] \frac{x + 2}{3x - 1} [/tex]

Step-by-step explanation:

Things you should before solving this question :-

a²- b² = (a + b)(a - b)

where a and b are any two variables.

SIMPLIFYING THE EXPRESSION

[tex] \frac{ {x}^{2} - 9 }{3 {x}^{2} + 8x - 3} \div \frac{x - 3}{x + 2} \\ [/tex]

using the identity discussed above

[tex] \frac{ (x + 3)(x - 3) }{3 {x}^{2} + 8x - 3} \div \frac{x - 3}{x + 2} [/tex]

simplifying 3x² + 8x - 3

[tex] \frac{ {x}^{2} - 9 }{3 {x}^{2} + 9x -x - 3} \div \frac{x - 3}{x + 2} [/tex]

as 8x can be written as 9x - x

[tex] \frac{ (x - 3)(x + 3) }{3 {x}(x + 3) - 1(x + 3)} \div \frac{x - 3}{x + 2} \\ \frac{ (x - 3)(x + 3) }{(3 {x} - 1)(x + 3) } \div \frac{x - 3}{x + 2} [/tex]

flipping the fraction that follows division sign and inserting multiply in place of divide

[tex] \frac{ (x - 3)(x + 3) }{(3 {x} - 1)(x + 3) } \times \frac{x + 2}{x - 3} [/tex]

canceling (x - 3) and (x + 3) as they're common in both denominator and numerator

[tex] \frac{x + 2}{3x - 1} [/tex]

The Bawden family is shopping for a new television. They are making their decision based on brand and size. The family has 20 possible outcomes for choosing a television. Which is a possible number of brands and sizes that the family has to choose from? 10 brands and 10 sizes O 5 brands and 4 sizes 4 brands and 16 sizes 2 brands and 20 sizes Save and Exit Mark this and return.

Answers

Answer:

the naswer is 5

Step-by-step explanation:

Answer:

The Answer is B.

Step-by-step explanation:

B:  5 Brands and 4 Sizes

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