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Zolol [24]
3 years ago
10

Which set of sides will make a triangle? -Middle School math-

Mathematics
2 answers:
belka [17]3 years ago
5 0
Answer: 10 cm, 5 cm, 9 cm

In order to make a triangle, the sum of the two shorter side lengths must be greater than the length of the longest side.

5, 2, 3    ⇒    5 = 5    ⇒    not a triangle
1, 3, 1      ⇒    2 < 3    ⇒    not a triangle
10, 3, 4   ⇒    7 < 10   ⇒    not a triangle
trasher [3.6K]3 years ago
3 0
Hey there!

The biggest side in the set of 3 lengths needs to be lower than the sum of the two lower numbers. So 3 is not lower than 1+1. 10 is not less than 3+4. 5 is the same as 3+2. This is not possible because this makes a line. So the biggest side can’t equal the sum of the two lower sides. 10 is less than 5+9. So the answer would be the last one. 10 cm, 5 cm, 9 cm.

I hope this helps!
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Please show the steps​
notka56 [123]

Answer:

  x = -3, 0, or 7

Step-by-step explanation:

After removing common factors, the remaining quadratic can be factored by comparison to the factored form of a quadratic.

__

<h3>Step 1</h3>

Write the equation in standard form.

  4x³ -16x² -84x = 0

<h3>Step 2</h3>

Factor out the common factor from all terms.

  = 4x(x² -4x -21) = 0

<h3>Step 3</h3>

Compare to the factored form of a quadratic:

  (x +a)(x +b) = x² +(a+b)x +ab

This tells you the constants 'a' and 'b' in the factors can be found by considering ...

  (a+b) = -4 . . . . the coefficient of the x term of the quadratic

  ab = -21 . . . . . the constant term of the quadratic

It is often helpful to list factor pairs of the constant:

  -21 = (-21)(1) = (-7)(3) . . . . integer pairs that have a negative sum

The sums of these pairs are -20 and -4. We are interested in the latter. We can choose ...

  a = -7, b = 3

<h3>Step 4</h3>

Put it all together.

  4x³ -16x² -84 = (4x)(x -7)(x +3) = 0 . . . . . factored form of the equation

<h3>Step 5</h3>

Apply the zero product rule. This rule tells you the product of factors will be zero when one or more of the factors is zero:

  4x = 0   ⇒   x = 0

  x -7 = 0   ⇒   x = 7

  x +3 = 0   ⇒   x = -3

Solutions to the equation are x ∈ {-3, 0, 7}.

_____

<em>Additional comment</em>

What we did in Step 3 is sometimes referred to as the X-method of factoring a quadratic. The constant (ab product) is put at the top of the X, and the sum (a+b) is put at the bottom. The sides of the X are filled in with values that match the product and sum: -7 and 3. The method is modified slightly if the coefficient of x² is not 1.

A graphing calculator often provides a quick and easy method of finding the real zeros of a polynomial.

3 0
2 years ago
What is 7+3t over 4 = -t over 8
katrin [286]
7+3t       -t
------- = -----  is the relevant equation here.  We don't ask, "What is 7+3t over
   4          8    -t over 8," but rather "Solve the following equation for t."

Cross multiplying, 56 + 24t = -4t
 
                                       -56
Then:  28t = 56, and t = ------ = -2 (answer)
                                         28

The solution to "<span>What is 7+3t over 4 = -t over 8" is t = -2.</span>
5 0
3 years ago
Scientific notation<br> 9.78 × 10^5 - 732,000<br> It has to be either 2.46 × 10^5 or 2.46 × 10^3
Morgarella [4.7K]

Answer:

2.46\times 10^5

Step-by-step explanation:

9.78 \times 10^5 - 732,000\\= 9.78 \times 10^5 - 7.32 000\times 10^5\\= 9.78 \times 10^5 - 7.32\times 10^5\\= 2.46\times 10^5

3 0
3 years ago
What will be a unit measure for a canyon?
Margaret [11]
Probably miles, canyons are HUGE, it's only logical to use miles
6 0
3 years ago
On tuesday shanice bought five hats. on wednesday half of all the hats that she had were destroyed. equation for... on thursday
wlad13 [49]

If X is the number of hats . . . reading backwards . . .

Thursday = Wednesday + Tuesday

17 = 1/2 X + 5

Solving:

17 - 5 = 1/2 X

12 = 1/2 X

24 = X

So she had 24 on Monday.



8 0
3 years ago
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