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UkoKoshka [18]
3 years ago
11

(Before you answer I am looking for how I do it. I have the answers but I need to know an equation to do this instead of using l

ogic)
The sum of two consecutive even numbers is 30. How can you solve for the 2 numbers?
Mathematics
1 answer:
Tema [17]3 years ago
7 0

Answer:

14 and 16.

Step-by-step explanation:

We know that two consecutive even numbers is 30.

Let's let n be <em>any number</em>.

Then the first <em>even</em> number must be 2n.

This is because n can be any number, either even or odd. However, if we multiply it by 2, this <em>ensures</em> that 2n is even. Remember that any number multiplied by 2 yields an even number.

Therefore, the consecutive even number will be (2n+2). Not (2n+1), because that gives an odd number.

We know that they sum to 30. So, we can write the following equation.

(2n)+(2n+2)=30

And we solve from there:

4n+2=30\\\Rightarrow4n=28\\\Rightarrow n=7

So, the value of n is 7.

Therefore, the first even number is 7(2)=14.

And the consecutive even number is 16.

Edit: Typo

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Which inequality is represented by the graph? y≥35x−1.5 y≤35x−1.5 y&lt;35x−1.5 y&gt;35x−1.5
Setler79 [48]

Answer:

y > 0.6x - 1.5

Step-by-step Explanation:

We need two points, to get to the equation of the graph.

Since we've got the following equation for two points (x1, y1), (x2, y2):-

\boxed{ \mathsf{ \red{y - y_{1} =  \frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{1})  }}}

okay soo

I found two points that lie on this graph, not on the shaded region but yeah the dotted line which defines the graph.

one point is <u>(0, -1.5)</u> which lies on the y axis(the point where the dotted line touches the y axis)

other point is <u>(2.5, 0)</u> and this lies on the x axis

placing these points in the place of (x1, y1) and (x2, y2) in the above mentioned equation

\mathsf{\implies y - ( - 1.5) =  \frac{0 -( - 1.5)}{2.5 -0 } (x -0 )}

you can take any one as (x1, y1) or (x2, y2).

so upon solving the above equation we get

\mathsf{\implies (y  +  1.5) =  \frac{0  +  1.5}{2.5  } (x  )}

\mathsf{\implies y  +  1.5 =  \frac{ 1.5}{2.5  } x  }

\mathsf{\implies y  +  1.5 =  \frac{ \cancel{1.5}\:\:{}^3}{\cancel{2.5}\:\:{}^5 } x  }

\mathsf{\implies y  +  1.5 =  \frac{ 3}{5 } x  }

multiplying both sides by 5

\mathsf{5y + 7.5 = 3x}

okay so this is the required equation of the dotted line

now we'll find the inequality

for this check whether the origin (0,0) lies under the shaded region or not

in this case it does

so

replacing x and y with 0

\mathsf{\implies5(0) + 7.5 = 3(0)}

\mathsf{\implies0 + 7.5 = 0}

this is absurd, 7.5 is not equal to 0 so we're gonna replace that equals sign with that of inequality

7.5 is greater than 0! so,

\mathsf{\implies7.5 > 0}

this goes for the whole equation, since we didnt swap any thing from left to right side of the equation or vice versa we can use this sign, to obtain the required inequality

\mathsf{5y + 7.5 > 3x}

dividing this inequality by 5, since there's no co-efficient in front of y in the given answers

we get

y + 1.5 > 0.6x

taking 1.5 to the RHS

<h3>y > 0.6x - 1.5 </h3>

that is the last option

5 0
3 years ago
5x+7y=31 2x+4y=16 Which of the following systems could be used to solve the given system of equations by the addition method? 10
Pani-rosa [81]
Equation 1: 5x+7y=31
Equation 2: 2x+4y=16

We can either use the 'elimination' method or the 'substitution' method to solve this simultaneous equation.

In some cases one method is easier to use than the other. For this one, it would be easier to use the elimination method

We need to eliminate either the 'x' or the 'y' to begin with. Say we want to eliminate the 'x' terms, then the next step is to make the constant the same

Equation 1: the constant of 'x' is 5
Equation 2: the constant of 'x' is 2

To make the two constants the same, think of common multiple. The lowest common multiple for 5 and 2 is 10

Equation 1:  Multiply all terms by 2 to achieve 10x
Equation 2: Multiply all terms by 5 to achieve 10x

Equation 1: 10x+14y=62
Equation 2: 10x+20y=80

Once the constant of 'x' is the same, then we can start the elimination process. Since our aim is to eliminate, one of the 'x' need to be in negative form. We can either multiply Equation 1 or Equation 2 by (-1)

Equation 1: -10x - 14y = -62
Equation 2: 10x + 20y = 80

Hence the correct answer is: Third option




3 0
3 years ago
the equation a=1/2(b1+b2)h can be used to determine the area, a, of a trapezoid with height, h, and base lengths, b1 and b2. whi
galina1969 [7]

Answer:

b₁ = (2a – b₂h)/h; b₁ = (2a)/h – b₂; h = (2a)/(b₁ + b₂)

Step-by-step explanation:

A. <em>Solve for b₁ </em>

          a = ½(b₁ + b₂)h        Multiply each side by 2

        2a = (b₁ + b₂)h           Remove parentheses

        2a = b₁h + b₂h           Subtract b₂h from each side

2a - b₂h = b₁h                    Divide each side by h

         b₁ = (2a – b₂h)/h     Remove parentheses

         b₁ = (2a)/h – b₂

B. <em>Solve for h </em>

2a = (b₁ + b₂)h     Divide each side by (b₁ + b₂)

 h = (2a)/(b₁ + b₂)

5 0
3 years ago
Read 2 more answers
Pleases help quick please
Solnce55 [7]

Answer:

1 and 2

Step-by-step explanation:

\sqrt{2} = 1.41421356237

3 0
3 years ago
Read 2 more answers
When x=2 and y=4, by how much does the value of 4x^2 - y exceed the value of 3x^2 - 3y​
kakasveta [241]

Step-by-step explanation:

4(2)² - 4 =

4(4) - 4 = 12

3(2)² - 3(4)

3(4) - 12

12 - 12 = 0.

It exceeds the value by 12 :)

6 0
2 years ago
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