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icang [17]
3 years ago
13

Find two consecutive positive integers such the sum of their squares is 145

Mathematics
1 answer:
White raven [17]3 years ago
8 0

Answer:

8 and 9

Step-by-step explanation:

Let these two consecutive positive numbers  be  x  and x + 1

so...   x^2 + (x + 1)^2 = 145

x^2 + x^2 + 2x + 1 = 145

2x^2 + 2x + 1 = 145

2x^2 + 2x  = 144

2*(x^2 + x) = 144

(x^2 + x) = 72

x^2 + x - 72 = 0

Use the Diamond method for factoring.

-72 = 9 * -8   and  9 + (-8) = 1

x^2  + x - 72  =  (x - 8)*(x + 9) = 0

so  x = 8  or x = -9,  but   x > 0  so only x = 8

 

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Trains Two trains, Train A and Train B. weigh a total of 196 tons. Train A is heavier than Train B. The
aleksklad [387]

Answer:

Train A = 128

Train B = 68

Step-by-step explanation:

We can set up a system of equations for this problem

Let A = # of tons of Train A

Let B = # of tons of Train B

A + B = 196

A = B + 60

Now, we plug in A for the first equation, using substitution

(B+60) + B = 196

2B + 60 = 196

Subtract 60 from both sides

2B = 136

Divide both sides by 2

B = 68

Plug in 68 for B in the 2nd equation

A = 68 + 60

A = 128

Checking work: 128 + 68 = 196 :D hope this helped

5 0
2 years ago
Is (-4,4) the solution of the system. 4x+5y>-6 and -2x+7y>20
nikklg [1K]

Answer:

  It is <em>a</em> solution, one of an infinite number of solutions.

Step-by-step explanation:

You can check to see if the given point is in the solution set:

  4(-4) +5(4) = -16 +20 = 4 > -6 . . . . yes

  -2(-4) +7(4) = 8 +28 = 36 > 20 . . . yes

The offered point satisfies both inequalities, so is in the solution set. It is not <em>the</em> solution, but is one of an infinite number of solutions.

7 0
3 years ago
Solve the equation. 11 6 = n + 7 9 6 11 ​ =n+ 9 7 ​ start fraction, 11, divided by, 6, end fraction, equals, n, plus, start frac
belka [17]

Answer:

n = 19/18

Step-by-step explanation:

Given:

11/6 = n + 7/9

Find n

11/6 = n + 7/9

Subtract 7/9 from both sides of the equation

11/6 - 7/9 = n + 7/9 - 7/9

11/6 - 7/9 = n

(99-42) / 54 = n

n = 57/54

n = 19/18

4 0
3 years ago
The sides of a rectangle are in the ratio of 4:5. If the width is 28 in., find the length, the perimeter, and the area of this r
nadezda [96]
If the width is 28 inches, then divide that by 4 and you get 7. You multiply that by 5 to get the length. That would be 35. Just to check, you know that the width 28 and length 35 are in ratio 4:5 if you divide by 7. The perimeter would be 2(35+28)=63*2=126. So the perimeter is 126. The area would be 35*28 which is 980. To sum up, the answers are as follows.

Length: 35 in
Perimeter: 126 in
Area: 980 inches squared.
5 0
3 years ago
What is the measure of angle I, m
strojnjashka [21]

Answer:

angle I =110

70 +I = 180 (opp side of parallelogram are equal)

I = 180 - 70

angle I =110

3 0
2 years ago
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