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Len [333]
3 years ago
8

Find two consecutive integers whose sum is 67. Which of the following equations could be used to solve the problem?

Mathematics
1 answer:
Hunter-Best [27]3 years ago
3 0
The desired answer is probably that
  2x + 1 = 67
is the equation that can be used to solve the problem. In this case, x represents the smallest integer.

_____
I like to work problems in consecutive integers by considering their average. Here, it is 67/2 = 33.5. The two consecutive integers whose average is 33.5 are 33 and 34, the solution to the problem. For this, the first equation applies, where x is the value halfway between the two integers. (This answer (2x=67) would likely get marked wrong by your computer grading system.)
You might be interested in
Let x^2+15x=49
Slav-nsk [51]
<span>x^2 + 15x + 56.25 = 105.25

    "Completing the square" is one of many different techniques for solving a quadratic equation. What you do is add a constant to both sides of the equation such that the lefthand side can be factored into the form a(x+d)^2. For instance, squaring (X+D) = X^2 + 2DX + D^2. Notice the 2DX term. That is the same term as the 15x term in the problem. So 2D = 15, D = 7.5. And D^2 = 7.5^2 = 56.25.
So we have
 x^2 + 15x + 56.25 = 49 + 56.25
 Which is
 x^2 + 15x + 56.25 = 105.25
  Which is the answer desired.

   Now the rest of this is going beyond the answer. Namely, it's answering the question "Why does complementing the square help?" Well, we know that the left hand side of the equation can now be written as
 (x+7.5)^2 = 105.25

   Now take the square root of each side
 (x+7.5) = sqrt(105.25)

   And let's use both the positive and negative square roots.
So x+7.5 = 10.25914226
 and
 x+7.5 = -10.25914226

   And let's find X.
 x+7.5 = 10.25914226
 x = 2.759142264

   x+7.5 = -10.25914226
 x = -17.75914226

   So the roots for x^2 + 15x - 49 is 2.759142264, and -17.75914226</span>
3 0
3 years ago
Read 2 more answers
11. Find the H.C.F of 96 and 120.<br>​
Veronika [31]

Answer:

24.

Step-by-step explanation:

The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

The factors of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Then the greatest common factor is 24.

3 0
3 years ago
total amount = P (1 + i)t What is the total amount that First Consumer Bank will receive after lending Jane $7,000 for three yea
ICE Princess25 [194]
P= principal (initial deposit) ($7000)
i= interest (5%)
t= # of years (3)

Total amount = P (1 + i)^t
T= $7000(1 + 5%)^3
T= 7000(1.05)^3
multiply exponents before regular multiplication
T= 7000(1.157625)
Total= $8,103.38 after 3 years

Hope this helps! :)
6 0
3 years ago
Resolve into factors. p4+7p2q2+16q4​
uranmaximum [27]

Step-by-step explanation:

p⁴+8p²q²+16q⁴

(p²)²+2×p²×4q²+(4q²)²

We know that,

  • (a+b)²=a²+2ab+b²

Therefore,

  • (p²)²+2×p²×4q²+(4q²)²
  • (p²+4q²)²
  • (p²+4q²)(p²+4q²)
7 0
2 years ago
Solve for x. Explain the steps taken to find the solution.<br><br> 3/2 + 3x/5 = 9/2 4x/5
Sladkaya [172]

Answer:

iymb usy,jikdokjjjzkkjzjkjhhg6993

6 0
3 years ago
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