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3 years ago

I need help on this problem

Mathematics

1 answer:

AlladinOne [14]3 years ago

4 0

Answer:

y² - 2y - 4x + 9 = 0 (*)

a = 1 b = -2 c = -4x + 9

Δ = b² - 4ac = 4 - 4(9 - 4x) = 4 - 36 + 16x = 16x - 32

if (*) have the solutions => Δ ≥ 0

⇔ 16x - 32 ≥ 0 ⇔ x ≥ 2

with x ≥ 2 => y = $\frac{2+\sqrt{16x-32} }{2}=\frac{2+4\sqrt{x-2} }{2}=1+2\sqrt{x-2}$

or y = $1-2\sqrt{x-2}$

Step-by-step explanation:

You might be interested in

Nineteen less than 6 times a number is the same as 16 more than the number. The equation is The solution is x -7 7.

Crank

Answer:

The number is 7

Step-by-step explanation:

let the said number be x

Nineteeen less than 6 times a number;

6x - 19

equals; 16 more than the number; this is 16 + x

Thus;

6x - 19 = 16 + x

6x-x = 16 + 19

5x = 35

x = 35/5

x = 7

3 0

3 years ago

(1 point) How many ways can you give 9 (identical) apples to your 5 favourite Mathematics lecturers (without any restrictions)?

cricket20 [7]

Answer:

126

Step-by-step explanation:

Total number of apples = 9

Number of favourite Mathematics lecturers = 5

To find number of ways in which 9 (identical) apples can be given to your 5 favourite Mathematics lecturers, find $C(9,5)$

Combination refer to selection of items such that order does not matter.

Use $C(n,p)=\frac{n!}{p!(n-p)!}$

Put $n=9,p=5$

$C(9,5)=\frac{9!}{5!(9-5)!}\\=\frac{9!}{5!4!}\\=\frac{9(8)(7)(6)5!}{5!4!} \\=\frac{9(8)(7)(6)}{4(3)(2)(1)}\\=126$

7 0

3 years ago

I need help on the question and I need to do it because I’m on a time schedule

VladimirAG [237]

Answer:

126∏

Step-by-step explanation:

area = 2 * area of the circle + area of the rectangular surface

area = 2 * r² * ∏ + 2 * r * ∏ * h

area = (2 * r² + 2 * r * h) * ∏

area = (2 * 7² + 2 * 7 * 2) * ∏

3 0

4 years ago

Factor completly . x^5 -x^4 - x^3

diamong [38]

Answer

Step-by-step explanation:

7 0

3 years ago

In triangle △ABC, ∠ABC=90°, BH = altitude

Ainat [17]

Answer: The exact length of segment HC is sqrt(3) units

The approximate length is roughly 1.73205080756888 (round that however you need to)

==============================================

Work Shown:

Let x = length of HC

Since AH = 3*HC, this means AH = 3*x

Draw out the picture. This step is optional but helpful in my opinion. The drawing is attached below.

After adding in the altitude BH, we have three similar triangles. So we can form the proportion shown below to solve for x

HC/BH = BH/AH

HC/3 = 3/AH ... replace BH with 3

x/3 = 3/AH ... replace HC with x

x/3 = 3/(3x) ... replace AH with 3x

x/3 = 1/x ... reduce

x*x = 3*1 ... cross multiply

x^2 = 3

x = sqrt(3) ... which is shorthand for "square root"

HC = sqrt(3)

HC = 1.73205080756888 which is approximate

3 0

3 years ago

I need help on this problem ​

I need help on this problem