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jeyben [28]
3 years ago
14

There are 3 consecutive even integers.if twice the first integer added to the third is 268,216,find all three integers

Mathematics
1 answer:
nalin [4]3 years ago
8 0
We can use a system of equations to solve this.

Notice that we are required to find 3 consecutive even integers.

This can be represented as x, y, and z, where x is the smallest integer, y is the next largest, and z is the largest of the three.
x = x
y = x + 2
z = y + 2

Take a moment to make sense of the above system of equations.
I can simplify the system a bit more by plugging in the second equation into the third one.

z = (x + 2) + 2
z = x + 4

Now the new system of equations is 
x = x
y = x + 2
z = x + 2

Now for the second part of this problem. We are given this equation
2x + z = 268216

You may notice that we no longer need the second equation, y = x + 2. Also, the first equation is redundant, so we can ignore it.

That leaves us with this system:
z = x + 4
2x + z = 268216

What do you think we should do? We can plug in z to solve for x.

2x + (x + 4) = 268216
3x + 4 = 268216
3x = 268212
x = 89404

Now we know the first number in the sequence! Then we can find the other two numbers, because we know that the next numbers must be the next largest even numbers in sequence!
89404, 89406, and 89408 are your answers.
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viktelen [127]

Answer:

B.6

Step-by-step explanation:

f(2)=(2+1)2

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4 0
3 years ago
the area of a rectangle is 90 in2^. the ratio of the length to the width is 5:2. find the length and the width
-BARSIC- [3]

Length and width of rectangle is 15 inches and 6 inches respectively

<h3><u>Solution:</u></h3>

Given that area of a rectangle is 90 square inch

Ratio of length to the width = 5: 2.

Need to determine length and width of rectangle.  

As ratio of length to the width is 5 : 2

Lets assume length of rectangle = 5x inches and width of rectangle = 2x inches.

<em><u>The formula for area of rectangle is given as:</u></em>

\text { Area of rectangle }=\text { length of rectangle } \times \text { width of rectangle}

Substituting the given value of area of rectangle and assumed value of length and width of rectangle we get:

\begin{array}{l}{90=5 x \times 2 x} \\\\ {=>90=10 x^{2}}\end{array}

On solving the above expression for x we get

\begin{array}{l}{=>\frac{90}{10}=x^{2}} \\\\ {=>x^{2}=9} \\\\ {=>x=\sqrt{9}=3}\end{array}

\begin{array}{l}{\text { Length of rectangle }=5 \times x=5 \times 3=15 \text { inches }} \\\\ {\text { Width of rectangle }=2 \times} x=2 \times} 3=6 \text { inches }}\end{array}

Hence length and width of rectangle is 15 inches and 6 inches.

4 0
4 years ago
The cities Cleveland, Ohio; Erie, Pennsylvania; and Rochester, New York, in respective order, lie approximately in a straight li
Ann [662]

Answer:

  Erie to Rochester is 145 miles

Step-by-step explanation:

If we designate the points of interest as C, E, and R, we are told that ...

  CE + ER = CR . . . . . the various distances are segments of a straight line

For CE = 94 and CR = 239, we can fill in the given information and solve for ER.

  94 + ER = 239

  ER = 239 -94 . . . . . . subtract 94 from both sides of the equation

  ER = 145

The distance from Erie to Rochester is 145 miles.

7 0
4 years ago
Find the area. <br><br> A. 188 in.2<br> B. 278 in.2<br> C. 322 in.2<br> D. 250.5 in.2
agasfer [191]
A 188 inches .2 Because you have to run them all to the nearest five
8 0
3 years ago
Patterns find next 2 numbers 1.) 7,4,1,-2,__,__ <br> 2.) 1,4,9,16,__,__ <br> 3.) 0,1,8,27,__,__
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Answer:

1. 7, 4, 1, -2, -5, -8

2. 1, 4, 9, 16, 25, 36

3. i'm not sure about this one.


3 0
3 years ago
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