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3 years ago

The sum of two numbers, x and y, is 12. The difference of x and two times y is 6. What are the values of x and y?

2 answers:

5 0

We write to expressions since there are two unknown here which is x and y. The first expression is the sum of two numbers, x and y, is 12.

x + y = 12

The second expression is that the difference of x and two times y is 6.

x -2y = 6

Therefore, the values of x and y are 10 and 2.

netineya [11]3 years ago

5 0

Answer:

The values of x= 10 and y = 2

Step-by-step explanation:

Assume $x>y$

The first statement states that sum of two numbers, x and y, is 12

then, we can write this statement in algebraic expression:

$x+y =12$ ...[1]

The second statement states that the difference of x and two times y is 6.

we can write it as :

$x -2y =6$ ....[2]

Now, subtracting equations, we will eliminate x leaving an equation in y that we can solve:

⇒ [1]-[2] gives

$(x+y)-(x-2y) = 12-6$

$x+y-x+2y = 6$

On simplify we get;

3y=6 or

y=2

Now, substitute the value of y=2 in equation [1] we get;

$x+2=12$

On simplify, we get;

x =10

therefore, the values of x and y are, 10 and 2.

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6 plates and 5 cups cost 32.10 dollars. 7 plates and 6 cups cost 37.70 dollars. Each plate costs the same amount as the other pl

slavikrds [6]

Answer:

Plates are 2.80 Dollars and cups are 1.40 dollars

Step-by-step explanation:

Cups = c

Plates = p

6p + 5c = 23.80 ==> multiply by 6 ==> 36p + 30c = 142.80

7p + 6c = 28.00 ==> multiply by 5 ==> 35p + 30c = 140.00

Now use algebra to have the 30c be on one side and the rest on the other:

36p + 30c = 142.80 | -36p

30c = 142.80 - 36p

35p + 30c = 140.00 | -35p

30c = 140.00 - 35p

Now set them equal to each other about the 30c:

142.80 - 36p = 140.00 - 35p

Use algebra to solve for p:

142.80 - 36p = 140.00 - 35p | +36p

142.80 = 140.00 + p | - 140

2.80 = p

Go back to one of the "30c" equations and plug in the value for p:

30c = 140 - 35p

30c = 140 - 35(2.80)

30c = 140 - 98

30c = 42 | /30

c = 42/30

c = 1.4

8 0

3 years ago

Read 2 more answers

A hoop, a uniform solid cylinder, a spherical shell, and a uniform solid sphere are released from rest at the top of an incline.

Serjik [45]

Answer:

Step-by-step explanation:

Given

Hoop, Uniform Solid Cylinder, Spherical shell and a uniform Solid sphere released from Rest from same height

Suppose they have same mass and radius

time Period is given by

$t=\sqrt{\frac{2h}{a}}$ ,where h=height of release

a=acceleration

$a=\frac{g\sin \theta }{1+\frac{I}{mr^2}}$

Where I=moment of inertia

a for hoop

$a=\frac{g\sin \theta }{1+\frac{mr^2}{mr^2}}$

$a=\frac{g\sin \theta }{2}$

a for Uniform solid cylinder

$a=\frac{g\sin \theta }{1+\frac{mr^2}{2mr^2}}$

$a=\frac{2g\sin \theta }{3}$

a for spherical shell

$a=\frac{g\sin \theta }{1+\frac{2mr^2}{3mr^2}}$

$a=\frac{3g\sin \theta }{5}$

a for Uniform Solid

$a=\frac{g\sin \theta }{1+\frac{2mr^2}{5mr^2}}$

$a=\frac{5g\sin \theta }{7}$

time taken will be inversely proportional to the square root of acceleration

$t_1=k\sqrt{2}=1.414k$

$t_2=k\sqrt{\frac{3}{2}}=1.224k$

$t_3=k\sqrt{\frac{5}{3}}=1.2909k$

$t_4=k\sqrt{\frac{7}{5}}=1.183k$

thus first one to reach is Solid Sphere

second is Uniform solid cylinder

third is Spherical Shell

Fourth is hoop

3 0

3 years ago

Find the nth term of the following sequence: 7, 13, 19, 25,

Natalija [7]

The answer of the next term is 31

8 0

2 years ago

Read 2 more answers

3x + 40 = 11x -24 What does x equal?

pogonyaev

First, you would have to do 11x + 3x Since you're combining like terms.

Now your problem is 14x + 40 = -24

Now you would do 40 - -24 which is now 40+24 and equal to 64.

Now you divide 14 by 64 and you get 4.5

4 0

3 years ago

Read 2 more answers

Mia is tracking her savings account balance . She knows the equation to find her balance y in any year t, but she can't remember

motikmotik

Complete question is;

Mia is tracking her savings account balance. She knows the equation y = 8000p^(t) can be used to find her balance y in any year t, but she can't remember what p represents. Her balance 3⅔ years after opening her account, is $9,905.54. What is the value of p?

Answer:

p = 1.06

Step-by-step explanation:

We are told that the equation y = 8000p^(t) can be used to find her balance y in any year t.

Now, we are given t = 3⅔ = 11/3 years

Also, we are given balance after 11/3 years as;

y = $9,905.54

Thus;

Plugging the relevant values into y = 8000p^(t), we have;

9,905.54 = 8000p^(11/3)

p^(11/3) = 9905.54/8000

p = (9905.54/8000)^(3/11)

p = 1.06

4 0

3 years ago