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Nat2105 [25]
3 years ago
11

Find three consecutive even integers whose sum is -300

Mathematics
1 answer:
Andreas93 [3]3 years ago
7 0
Let n represent the unknown numbers. 

*we add 2 and 4 to the numbers so that we are sure that they will be even*


n + (n+2) + (n+4) = - 300    *simplify*

n + n + 2 + n + 4 = - 300   

3n+6=-300
     -6  -6
---------------         *Get constants and variables to either side*
3n = - 306
---     ------            *Isolate the variables*
3         3
 
n= - 102

Then plug this in for the above values


n+2= - 102+2= -100
n+4= - 102+4 = -98


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One number exceeds another by 2 the sum of the number is 48 what are the numbers
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x-\ first\ number\\y-\ second\ number\\\\
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4 years ago
Peter is at a lumber yard. He gets 2 free boxes of nails for every 10 boards he buys. Write an expression for the number of boxe
Natali5045456 [20]
The algebraic expression n<span>/10, where </span>n<span> is the number of boards, represents the number of times he gets 2 free boxes of nails. So 2(</span>n<span>/10), or </span>n/5, is the number of boxes, and 100(n/5), or 20n<span>, is the number of nails. Substituting 90 in for </span>n<span>, Peter will get 1,800 nails.</span>
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3 years ago
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Graph the image of the figure after a dilation with a scale factor of 2 centered at (-7, - 2).
tigry1 [53]

Answer:

Sorry this is late!

Step-by-step explanation:

8 0
3 years ago
A circle has a radius of 3 in, what is the length of the arc created by an angle measure 1 radian?
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Step-by-step explanation:

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Find the equations of the following lines
White raven [17]

You need these two basic solutions and facts to find the equation of a line:

  • If you know the gradient m and one point (x_0,y_0):

y-y_0=m(x-x_0)

  • If you know the gradient two points (x_1,y_1),\ (x_2,y_2):

\dfrac{x-x_2}{x_1-x_2}=\dfrac{y-y_2}{y_1-y_2}

  • The slope of a line is the coefficient m when you write it in the y=mx+q form
  • Parallel lines have the same slope
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We can use this list to solve all the exercises:

b)

Use the first equation to get

y-1=-4(x-2) \iff y=-4x+9

c)

Use the second equation to get

\dfrac{x-4}{2-4}=\dfrac{y-2}{-1-2} \iff \dfrac{x-4}{-2}=\dfrac{y-2}{-3}\iff 3(x-4)=2(y-2) \iff 3x-12=2y-4 \iff 2y = 3x-8 \iff y = \frac{3}{2}x-4

d) same as c)

e) We derive the slope of the line by writing it as

5y = -x-15 \iff y = -\dfrac{1}{5}x-3

So, the slope is -1/5. From here, it's the same as b)

f) same as e)

g) Again we find the slope as

3x+y+2=0\iff y=-3x-2

so the slope is -3, and a perpendicular line has slope 1/3. From there, it's the same as b).

6 0
4 years ago
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