Factor the following expression:

\[ y^2 - 16y + 64 = 128 \]

Find the common factor of $5x$ and $15y$.

If the cost of 1 kg of mango is ₹60, what would be the cost of 5 kg of mangoes?

Question

High School

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Answer :

LiamAlexanderSmith LiamAlexanderSmith · Answer 1 · 2025-02-11T12:41:58-05:00

Let's break down the given parts of the question one by one.

Factorise: [tex]y^2 - 16y + 64 = 128[/tex]
First, let's bring all terms to one side of the equation:
[

y^2 - 16y + 64 - 128 = 0
]

Simplifying inside the equation gives:

[tex]y^2 - 16y - 64 = 0[/tex]

Now, we need to factor the quadratic equation. Let's find two numbers that multiply to [tex]-64[/tex] and add up to [tex]-16[/tex].

Those numbers are [tex]-8[/tex] and [tex]-8[/tex]:

[tex](y - 8)(y - 8) = (y - 8)^2 = 0[/tex]

So, the factorised form of [tex]y^2 - 16y + 64 = 128[/tex] is [tex](y - 8)^2 = 0[/tex].

Find the common factor of [tex]5x[/tex] and [tex]15y[/tex]
To find the common factor, we first look at the coefficients of the terms:
- The coefficient of [tex]5x[/tex] is 5.
- The coefficient of [tex]15y[/tex] is 15.
The greatest common factor (GCF) of 5 and 15 is 5.
Therefore, the common factor of [tex]5x[/tex] and [tex]15y[/tex] is 5.

If the cost of 1 kg of mango is [tex]\text{₹}60[/tex], then what would be the cost of 5 kg mango?
To find the cost of 5 kg, we multiply the cost of 1 kg by 5:
[

\text{Cost of 5 kg} = 60 \times 5 = 300
]

Hence, the cost of 5 kg of mango is [tex]\text{₹}300[/tex].