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1 year ago

Please help!!! find y and x

Mathematics

1 answer:

andrew11 [14]1 year ago

5 0

Answer:

a) y = 16/x²

b) x = 4/5

Step-by-step explanation:

You want the equation for y in terms of x when y is inversely proportional to the square of x, and y is 16 when x is 1. Further, you want the value of x when y is 25.

<h3>(a) Relation</h3>

The wording "inversely proportional to the square" means the form of the equation is ...

y = k/x² . . . . . . where k is the constant of proportionality

The value of k can be found from the given (x, y) pair.

k = x²y = (1)²(16) = 16

The equation is ...

y = 16/x²

<h3>(b) Value of x</h3>

Solving for x gives ...

x = √(16/y)

Then the value of x for y = 25 is ...

x = √(16/25)

x = 4/5

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Step-by-step explanation:

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3 years ago

7. Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

morpeh [17]

Hey there!

Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

Answer :

x = -4 or x = 2 ✅

Explanation :

Quadratic formula : ax² + bx + c = 0 where a ≠ 0

The number of real-number solutions (roots) is determined by the discriminant (b² - 4ac) :

If b² - 4ac > 0 , There are 2 real-number solutions

If b² - 4ac = 0 , There is 1 real-number solution.

If b² - 4ac < 0 , There is no real-number solution.

The roots of the equation are determined by the following calculation:

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

Here, we have :

a = 1
b = 2
c = -8

1) Calculate the discriminant :

b² - 4ac ⇔ 2² - 4(1)(-8) ⇔ 4 - (-32) ⇔ 36

b² - 4ac = 36 > 0 ; The equation admits two real-number solutions

2) Calculate the roots of the equation:

▪️ (1)

$x_1 = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x_1 = \frac{ - 2 - \sqrt{36} }{2(1) } \\ \\ x_1 = \frac{ - 2 - 6}{2} \\ \\ x_1 = \frac{ - 8}{2} \\ \\ \blue{\boxed{\red{x_1 = -4}}}$

▪️ (2)

$x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 2 + \sqrt{36} }{2(1)} \\ \\ x_2 = \frac{ - 2 + 6}{2} \\ \\ x_2 = \frac{4}{2} \\ \\ \red{\boxed{\blue{x_2 = 2}}}$

>> Therefore, your answers are x = -4 or x = 2.

Learn more about quadratic equations:

brainly.com/question/27638369

6 0

2 years ago

Read 2 more answers

Please include step by step

mote1985 [20]

Answer:

x=2 AB=hypotenus(h) angle ACB is 90

BC=p angle CAB is 30 also angle of refrence

Step-by-step explanation:

sin[30]=p/h

(1/2)=x/4

2x=4

x=2

5 0

4 years ago

Help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Airida [17]

Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

$x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6$

4 0

1 year ago

Solve 2X-3(x+4)=3x-4

Phoenix [80]

Answer: x=4

Step-by-step explanation:

2x-3(x+4)=3x-4

distribute 2x-3x-12=3x-4

combine like terms 5x-12=3x-4

Move everything to one side 2x-8=0

Get x by itself 2x=8

Divide by 2 x=4

6 0

3 years ago