MATHEMATICS HIGH SCHOOL

Yis directly proportional to the square of xy=96 when x = 4

Find a formula for y in terms of x

Answers

Answer 1
Answer:

Answer:

y=6x^2

Step-by-step explanation:

y being directly proportional to the square of x means that the ratio between the two will always be equal to some constant (let's call it k). In equation form, we'd say:

(y)/(x^2)=k

We're told that y = 96 when x = 4, so we can plug those values in to find k:

(96)/(4^2)=(96)/(16)=6=k

Our more general equation is now

(y)/(x^2)=6

If we want to put y in terms of x, we need to get the y by itself on one side of the equation, which we can do here by multiplying both sides by x², giving us

y=6x^2
Answer 2
Answer:

Final answer:

The question is about finding the equation given that y is directly proportional to the square of x. Based on the values in the question, the constant of proportionality 'k' is calculated as 6. Hence, the formula for y in terms of x is y = 6 * x^2.

Explanation:

When we say, y is directly proportional to the square of x, it simply means there is a constant constant of proportionality 'k', such that y = k * x2. Given in the problem, when x = 4, y = 96, we can substitute these values into the equation to solve for 'k'. This results in 96 = k * (42) which simplifies to 96 = 16k, and solving this gives us k = 6. Therefore, the formula for y in terms of x is y = 6 * x2.

Learn more about Proportional relationships here:

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Hilbert's axioms changed Euclid's geometry.
True
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The answer to you're question is true

Which ordered pair is a solution of the equation y = 5x? (–2, 10) (–5, 25) (–3, 15) (–2, –10)

Answers

the answer is (-2,-10) you just need to plug them in.

Which expression is equivalent to n2 + 26n + 88 for all values of n?(n + 8)(n + 11)

(n + 4)(n + 22)

(n + 4)(n + 24)

(n + 8)(n + 18)

Answers

Answer:

Option B is correct.

The expression which is equivalent to  n^2+26n+88  is; (n+22)(n+4)

Explanation:

Given the equation: n^2+26n+88 for all values of n.

The quadratic equation in this form; ax^2+bx+c =0

First find two numbers that multiply to give ac and add to give b.

From the given equation;

a =1 , b = 26 and c =88

then,

the two number that multiply to give ac =88 is, 22 or 4

and they add up to give b=26 (i.e 22+4)

Now, rewrite the middle term i.e 26n with 22n and 4n , we have

n^2+22n+4n+88=0

Now, factor the first two terms and last two terms,

n(n+22)+4(n+22)

we see that (n+22) is common to both terms so, we have;

(n+22)(n+4)

Therefore, the expression (n+22)(n+4) is equivalent to  n^2+26n+88

Check:

(n+4)(n+22) = n\cdot n+ 22n+4n+88=n^2+26n+88   [ True]
Solutions 

The expression equivalent to n^2 + 26n + 88  is 

n^2 + 26n + 88
(n + 4)(n + 22)

Which properties should you use to solve the equation4x+2= 18 ?

Answers

x=4

4x+2=18

x has to be alone, so you dived both sides by 2

4x=18-2

4x=16

divide both sides by 4

x=4

Answer:

Addition property of equality and multiplication property of equality

Step-by-step explanation:

Addition Property of Equality: This property states that you can add or subtract the same value to both sides of an equation without changing its solution.

Here's the step-by-step solution, emphasizing the properties used:

Start with the equation:

4x + 2 = 18

Use the Addition Property of Equality to isolate the variable "x." Subtract 2 from both sides to move the constant term to the other side of the equation:

4x + 2 - 2 = 18 - 2

Simplify both sides by applying the Addition Property of Equality:

4x = 16

To further isolate "x," use the Multiplication Property of Equality, which states that you can multiply or divide both sides of an equation by the same nonzero value. Divide both sides by 4 to solve for "x":

(4x) / 4 = 16 / 4

Simplify both sides using the Multiplication Property of Equality:

x = 4

So, in solving the equation 4x + 2 = 18, you primarily used the Addition Property of Equality and the Multiplication Property of Equality to isolate and solve for "x."

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Answers

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7x = 168 + 7
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FJG = 6x - 15
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Answers

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cosβ=√33/√49=√33/7
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