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Inga [223]
3 years ago
8

A triangle has two sides of length 9 and 6. What is the smallest possible whole-number length for the third side?

Mathematics
2 answers:
erica [24]3 years ago
8 0

Answer:

c=4

Step-by-step explanation:

a=9, b=6, c=?

|a-b|<c<|a+b| (Triangle inequality)

|9-6|<c<|9+6|

|3|<c<|15|

3<c<15

then c=4 (smallest possible)

natka813 [3]3 years ago
5 0

Answer:

4

Step-by-step explanation:

Let the third side = x.

The sum of any two sides must be greater than the third side

9+6 > x

15 > x

9 + x > 6

x > 6-9

x > -3

6+ x > 9

x > 9-6

x > 3

So 3 < x < 15

Therefore the smallest whole number length the third side could have is 4.

The largest whole number length the third side could  have is 14.

I hope this was helpful, please mark as brainliest

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Alina [70]

Answer:

⋆ Help please! ⋆ This is a test! ⋆ No links! ⋆

Step-by-step explanation:

5 0
2 years ago
Calculate the discriminant to determine the number solutions. y = x ^2 + 3x - 10
Nataly_w [17]

1. The first step is to find the discriminant itself. Now, the discriminant of a quadratic equation in the form y = ax^2 + bx + c is given by:

Δ = b^2 - 4ac

Our equation is y = x^2 + 3x - 10. Thus, if we compare this with the general quadratic equation I outlined in the first line, we would find that a = 1, b = 3 and c = -10. It is easy to see this if we put the two equations right on top of one another:

y = ax^2 + bx + c

y = (1)x^2 + 3x - 10

Now that we know that a = 1, b = 3 and c = -10, we can substitute this into the formula for the discriminant we defined before:

Δ = b^2 - 4ac

Δ = (3)^2 - 4(1)(-10) (Substitute a = 1, b = 3 and c = -10)

Δ = 9 + 40 (-4*(-10) = 40)

Δ = 49 (Evaluate 9 + 40 = 49)

Thus, the discriminant is 49.

2. The question itself asks for the number and nature of the solutions so I will break down each of these in relation to the discriminant below, starting with how to figure out the number of solutions:

• There are no solutions if the discriminant is less than 0 (ie. it is negative).

If you are aware of the quadratic formula (x = (-b ± √(b^2 - 4ac) ) / 2a), then this will make sense since we are unable to evaluate √(b^2 - 4ac) if the discriminant is negative (since we cannot take the square root of a negative number) - this would mean that the quadratic equation has no solutions.

• There is one solution if the discriminant equals 0.

If you are again aware of the quadratic formula then this also makes sense since if √(b^2 - 4ac) = 0, then x = -b ± 0 / 2a = -b / 2a, which would result in only one solution for x.

• There are two solutions if the discriminant is more than 0 (ie. it is positive).

Again, you may apply this to the quadratic formula where if b^2 - 4ac is positive, there will be two distinct solutions for x:

-b + √(b^2 - 4ac) / 2a

-b - √(b^2 - 4ac) / 2a

Our discriminant is equal to 49; since this is more than 0, we know that we will have two solutions.

Now, given that a, b and c in y = ax^2 + bx + c are rational numbers, let us look at how to figure out the number and nature of the solutions:

• There are two rational solutions if the discriminant is more than 0 and is a perfect square (a perfect square is given by an integer squared, eg. 4, 9, 16, 25 are perfect squares given by 2^2, 3^2, 4^2, 5^2).

• There are two irrational solutions if the discriminant is more than 0 but is not a perfect square.

49 = 7^2, and is therefor a perfect square. Thus, the quadratic equation has two rational solutions (third answer).

~ To recap:

1. Finding the number of solutions.

If:

• Δ < 0: no solutions

• Δ = 0: one solution

• Δ > 0 = two solutions

2. Finding the number and nature of solutions.

Given that a, b and c are rational numbers for y = ax^2 + bx + c, then if:

• Δ < 0: no solutions

• Δ = 0: one rational solution

• Δ > 0 and is a perfect square: two rational solutions

• Δ > 0 and is not a perfect square: two irrational solutions

6 0
3 years ago
Which recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n &gt; 1? 9.6, 4.8, 2.4, 1.2, 0.6, ..
White raven [17]
Hello,

The formula is f(n)= \dfrac{f(n-1)}{2}&#10;&#10;
4 0
3 years ago
Pls help me for brainliest answer
Ket [755]

Answer with Step-by-step explanation:

a)3n + 4 \\  \\n = 1 \\ 3 \times 1 + 4 \\ 3 + 4 \\  =7 \\  \\ n = 2 \\ 3 \times 2 + 4 \\ 6 + 4 \\  = 10 \\  \\ n = 3 \\ 3 \times 3 + 4 \\ 9 + 4 \\  = 13 \\  \\ n = 4 \\ 3 \times 4 + 4 \\ 12 + 4 \\  = 16 \\  \\ n = 10 \\ 3 \times 10 + 4 \\ 30 + 4 \\  = 34 \\

So in this sequence,

1st term = 7

2nd term = 10

3rd term = 13

4th term = 16

10th term = 34

b)4n - 5 \\  \\ n = 1 \\ 4 \times 1 - 5 \\ 4 - 5 \\  =  - 1 \\  \\ n = 2 \\ 4 \times 2 - 5 \\ 8 - 5 \\ =  3 \\  \\ n = 3 \\ 4 \times 3 - 5 \\ 12 - 5 \\  = 7 \\  \\ n = 4 \\ 4 \times 4 - 5 \\ 16- 5 \\  = 11 \\  \\ n = 10 \\ 4 \times 10 - 5 \\ 40 - 5 \\  = 35

In this sequence,

1st term = -1

2nd term = 3

3rd term = 7

4th term = 11

10th term =35

5 0
3 years ago
The ratio to baseball to football 2 baseballs 6 footballs
ahrayia [7]

It would be 2:6, or 2 to 6.

I hope this helps :)

4 0
3 years ago
Read 2 more answers
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