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fiasKO [112]
2 years ago
8

The Grand Old Duke of York had 10 000 men. He lost 10% of them on way to the top of

Mathematics
1 answer:
harkovskaia [24]2 years ago
3 0

Answer:

76.5%

Step-by-step explanation:

He lost 10% of them on way to the top of the hill

10% of 10,000 men

= 0.1 * 10,000

= 1,000 men

Remaining men = 10,000 - 1,000

= 9,000 men

15% of the rest as he marched them back down the hill.

15% of 9,000 men

= 0.15 × 9000

= 1,350 men

Total men remaining = 9000 - 1,350

= 7,650 men

% remaining =

x% of 10000 men = 7,650

x/100 * 10,000 = 7,650

Cross product

10,000x =7,650 * 100

10,000x = 765,000

x = 765,000/10,000

= 76.5%

x = 76.5%

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3 years ago
Read 2 more answers
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
I need help with this problem:(​
steposvetlana [31]

Answer:

8

Step-by-step explanation:

According to Euclidean theorem

m^2 = 4×16

m^2 = 64

m = 8

3 0
3 years ago
The graph of a rational function has local maximum at (-1,0) and (8,0). The complex number 2+3i is a zero of the function. What
Natali5045456 [20]

Answer:

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2 years ago
How do i find x?
lina2011 [118]

Answer:

<h3>   To find x you need to divide polygon into triangles</h3><h3>The formula : "the sum of exterior angles=360°" is false for concaved polygons</h3>

Step-by-step explanation:

α = 180° - 135° = 45°

β = 180° - 120° = 60°

γ = 180° - 60° = 120°

δ = 180° - x

ε = 180° - 80° = 100°

If we divide the pentagon into five triangles then:

5•180° = α + β + γ + δ + ε + 4x

900° = 45° + 60° + 120° + x + 100° + 4x

900° = 325° + 5x

5x = 575°

x = 115°

60° + 120° + 135° + 80° + 115° = 510° ≠ 360°

8 0
3 years ago
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