Which ratio is equivalent to 4:32?
1:6
8:60
1:8
3:16

Final answer:

The bank has 15 quarters and 12 dimes.

Explanation:

This problem can be solved using systems of equations. Let's define the variables: let D represent the number of dimes and Q represent the number of quarters.

From the problem, we have two equations:

• D + Q = 27 (the total number of coins)
• 0.10D + 0.25Q = 4.95 (the total value of the coins)

Multiply the first equation by 0.10 to make the coefficients of D the same in both equations:

• 0.10D + 0.10Q = 2.70

Subtract this from the second equation to find Q:

• 0.15Q = 2.25. Consequently, Q = 15 quarters.

Substitute Q = 15 into the first equation to find D:

• D + 15 = 27, hence D = 12 dimes.

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Answer:3

Step-by-step explanation:So 1/4and 12 is translated to multiply so you multiply 1/4x12=12/4=3 so its 3

Step-by-step explanation:

as I can see this the answer is

x = 25/78

in decimal

x = 0.320

Final answer:

The problem involves joint variation with variables y, x, and z. After finding the constant of variation, we substitute the given values into the joint variation equation and determine that x = 16.67

Explanation:

First, we establish the equation of joint variation, which in this context is y = kxz, where 'k' is the constant of variation. When y=13, x=26, and z=6, we insert these values into the equation to solve for 'k'. This gives us k = y/(xz) = 13/(26*6) = 0.08333.

Now that we have the constant 'k', we can find the value of 'x' when y=25 and z=18. We rearrange our equation to solve for 'x', resulting in x = y/(kz). Substituting the known values, we get x = 25/(0.08333*18) = 25/1.5 = 16.67. Therefore, if y varies jointly with x and z, and y=25 when z=18, then x = 16.67.

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The value of x from the given equation is -8. Luca did mistake while multiplying 5 inside the terms of a bracket.

The given equation is 2-6x=5-5(x-1).

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation can be solved as follows:

Using distributive property multiply 5 to the terms in a bracket.

That is, 2-6x=5-5x+5

⇒ 2-6x=10-5x

Add 5x to both the sides of an equation

That is, 2-6x+5x=10-5x+5x

⇒ 2-x = 10

Subtract 2 to both the sides of an equation

That is, -x=8

Multiply -1 to to both the sides of an equation

So, x=-8

The value of x from the given equation is -8. Luca did mistake while multiplying 5 inside the terms of a bracket.

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Answer:

A sequence that has a contant addition/subtraction to get to the next term

for example:

-3, 0, 3, 6, ...

to get to the next term, we'll need to add 3 each time

Step-by-step explanation:

Answer:

The constant of variation is constant.  

Step-by-step explanation:

1, 3, 5, 7, 9, . . . is an arithmetic sequence because it is constant with a direct variation of 2. (1 + 2 = 3; 3 + 2 = 5; . . .)

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