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Andru [333]
3 years ago
7

Half of Robert's piece of wire is equal to ⅔ of Maria's wire. The total length of their wires is 12 feet. How much longer is Rob

ert's wire than Maria's?
Mathematics
1 answer:
____ [38]3 years ago
8 0

Answer:

Robert's piece of wire is 5 feet long

and Maria's piece of wires is 7 feet long

Step-by-step explanation:

Suppose x and y are Robert's and Maria's piece of wires respectively.

We can write following equation using this statement "Half of Robert's piece of wire is equal to ⅔ of Maria's wire".

\frac{1}{2} x = \frac{2}{3} y  --------------(1)

The total length of their wires is 12 feet.

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

=> x=12-y

Substitute x=12-y in equation (1)

\frac {1}{2} (12-y) = \frac{2}{3} y

6-\frac{1}{2} y = \frac {2}{3} y

6 = \frac {2} {3} y + \frac {1} {2} y

y=7

Put y=7 in equation (2)

x+7 = 12 \\x  =5

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Please answer will mark as brainist!
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Step-by-step explanation:

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Pls help :) determine which function has a greater rate and explain how you know.
Nesterboy [21]

Using exponential function concepts, it is found that the second function has a greater rate, as 0.8 > 0.2.

<h3>What is an exponential function?</h3>

It is modeled by:

y = ab^x

In which:

  • a is the initial value, that is, y when x = 0.
  • b is the rate of change, as a decimal.

Function 1 is given by:

y = 2(0.2)^x

Hence the rate is b = 0.2.

Considering the values on the table, function 2 is given by:

y = (0.8)^x

Hence the rate is b = 0.8.

Hence, the second function has a greater rate, as 0.8 > 0.2.

More can be learned about exponential function concepts at brainly.com/question/14398287

4 0
2 years ago
I NEED HELP QUICKLY!!! What is the sum of the first 140 positive multiples of 3?
garri49 [273]

Answer:

C

Step-by-step explanation:

The multiples of 3 are

3, 6, 9, 12, 15, ...........

The terms form an arithmetic sequence with common difference of 3.

The sum to n terms is

S_{n} = \frac{n}{2} [2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 3 and d = 3, thus

S_{140} = \frac{140}{2} [ (2 × 3) + (139 × 3) ]

                            = 70(6 + 417) ] = 70 × 423 = 29610 → C

5 0
3 years ago
Need help finding the x, y, and z. please and thank you
Reptile [31]

The first step in any problem is to look at what you are given. When solving systems of linear equations, it is often helpful to eliminate one or more of the variables by adding or subtracting a multiple of one equation with a multiple of another. It is convenient when at least one of the multipliers is 1.

Here, we can cancel the y-terms in the 2nd and 3rd equations simply by adding them together. This gives

... (5x +y -4z) +(-3x -y +5z) = (41) +(-45)

... 2x +z = -4 . . . . simplified

Likewise, we can add 3 times the second equation to the first to cancel y in that sum.

... 3(5x +y -4z) +(2x -3y +z) = 3(41) + (-1)

...15x +3y -12z +2x -3y +z = 123 -1

...17x -11z = 122 . . . . simplified

Now that we have 2 equations in x and z, we can go through the same process. We observe that the coefficient of z is +1 in the first equation and -11 in the second. The means we can cancel the z terms by adding 11 times the first equation to the second:

... 11(2x +z) +(17x -11z) = 11(-4) +122

...22x +17x = 78 . . . . . . simplify a little bit

... x = 78/39 = 2 . . . . . . divide by 39

From above, we find

... z = -4 -2x = -4 -2·2 = -8

... y = 41 -5x +4z = 41-5(2) +4(-8) = 41 -42 = -1

The solution is (x, y, z) = (2, -1, -8).

_____

The method of elimination used here will vary with the system of equations. If you want to employ a consistent method, you can use Cramer's Rule, Gaussian elimination, or matrix methods. Since you apparently don't mind help from technology, learning to do this on your graphing calculator can also be a good idea.

4 0
3 years ago
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