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Vesnalui [34]
3 years ago
9

The sum of the square of two consecutive whole number is 25. Find the numbers

Mathematics
1 answer:
Gnom [1K]3 years ago
3 0
Don't you mean "the sum of the squares ..."?
The sum of the squares of two consecutive whole numbers is 25.  Find the numbers.  Let the first be represented by x and the second by x+1.
Then x^2+(x+1)^2=25.  Expanding, x^2+x^2+2x+1=25.
Rewriting this as a quadratic equation in standard form,

2x^2+2x+1=25, or 2x^2+2x-24=0.  Simplifying, x^2+x-12=0.
Factoring, (x-3)(x+4)=0.  Solving for x:  x-3=0, so x=3; x+4=0, so x=-4.
Choose the positive x value:  x=3.  Then the next consecutive number is 2+1=3+1=4.

Check:  Does 3^2 + 4^2 = 5^2 = 25?  Yes.
The numbers are 3 and 4.
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What is the primary difference between exponential and linear functions?
Yanka [14]

Answer:

A

Step-by-step explanation:

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An exponential function wouldn't be x^2, it would be 2^x! Or 3^x, or (1.738283)^x, etc. Therefore, D is eliminated.

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2 years ago
What are the remaining angle measures if the figure is to be a parallelogram?
goldfiish [28.3K]

The correct answer is  

m∠B ==101°,

m∠C =79°,

m∠D=101°

Step-by-step explanation:

  • As we know that, it is a parallelogram opposite angels are congruent
  • Therefore,  m∠A = m∠C and m∠B =m∠B
  • As we know that, If side a=79 then side c must also be equal to 79
  • When we consider all the angles and add them it must be equal to 360°
  • When we add 79+79 = 158°, which mean a=c= 158°
  • By subtracting all the sides of parallelogram which is 360- 158= 202°
  • If we divide it by 2 then we will get the value of the other side of the angle which is  b and d.
  • Dividing 202 by 2
  • \frac{202}{2} = 101°
  • Therefore, the value of b=d=101°
  • A Parallelogram is a flat shape with an opposite sides parallel and they are equal in length.
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3 0
3 years ago
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Solve |p + 2| = 10Solve |p + 2| = 10<br><br> {-12}<br> {-8, 8}<br> {-12, 8}
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By definition, we have

|p+2| = \begin{cases} p+2 &\text{ if } p+2 \geq 0 \\-p-2 &\text{ if } p+2 < 0 \end{cases}

So, we have to solve two different equations, depending of the possible range for the variable. We have to remember about these ranges when we decide to accept or discard the solutions:

Suppose that p+2\geq 0 \iff p \geq -2

In this case, the absolute value doesn't do anything: the equation is

p+2 = 10 \iff p = 10-2 = 8

We are supposing p \geq -2, so we can accept this solution.

Now, suppose that p+2 < 0 \iff p < -2. Now the sign of the expression is flipped by the absolute value, and the equation becomes

-p-2 = 10 \iff -p = 12 \iff p = -12

Again, the solution is coherent with the assumption, so we can accept this value as well.

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