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Alex787 [66]
3 years ago
14

Y is directly proportional to x when y=30, x=6

Mathematics
1 answer:
rosijanka [135]3 years ago
4 0

Answer:

a) y = 5x

b) y = 60

Step-by-step explanation:

Since, y is directly proportional to x when y=30, x=6

\therefore \:  y \:  \alpha \:  \: x \\ \therefore \:  y =  kx ...(1) \\ plug \: y = 30 \: and \: x = 6  \: in \: eq \: (1)\\ 30 = k \times 6 \\ k =  \frac{30}{6}  \\ k = 5 \\ plug \: k = 5 \: in \: (1) \\ y = 5x....(2) \: (required \: equation) \\ plug \: x = 12 \: in \: eq \: (2) \\ y = 5 \times 12 \\  \huge \red{ \boxed{y = 60}}

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Solve the quadratic equation by completing the square. <br> x^2 - 10x + 18 = 0
serious [3.7K]
Okay so basically, you subtract 18 on both sides since the 18 doesn't work, making the equation 
<span>x</span>²<span> - 10x = -18
So then you add (b/2)</span>²<span>, which is 25, to both sides, to get 
</span><span>x</span>²<span> - 10x + 25 = 7
</span><span>After this, you factor.
</span><span>(x-5)(x-5) = 7
</span><span>Then you simplify.
(x-5)</span>²<span> = 7
Then you solve for x.
</span>√(<span>x-5)</span>²<span> = </span>√7
x-5 = (+ or -)√7

~ x= 5 (+ or -)√7 ~

Hope this helps!

3 0
3 years ago
What is the unit form of 7÷4
Natasha2012 [34]

Answer:

1.75

Step-by-step explanation:

7 ÷ 4 = 1.75

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6 0
3 years ago
Work out the nth of this sequence:
Gekata [30.6K]

Answer:

a_n = -11 +3(n -1)

Explanation:

The nth term of an arithmetic sequence is explicitly defined as a_n = a_1 +d(n -1) where a_1 is the first term of the sequence and d is the the common difference.

From the given first five terms of the sequence we can see that the first term is 11 so a_1 = 11.

The common difference, d, can be calculated by a_n - a_{n -1} so we'll find the common difference of the given sequence by letting n = 2

d = a_2 - a_{2 -1} \\d = a_2 -a_{1} \\d = -8 -(-11) \\ d = -8 +11 \\ d = 3.

Now let's plug everything we know.

a_1 = -11

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6 0
2 years ago
What is the slope of (2,-1) and (8,4)
qaws [65]

Answer:

5/6

Step-by-step explanation:

slope = 4-(-1)/8-2 = 5/6

5 0
1 year ago
67000 dollars is placed in an account with an annual interest rate of 8.25%. how much will be in the account after 28 years, to
anastassius [24]

Answer:

The Amount of money in the account after 28 years is $616,674.5

Step-by-step explanation:

Given as :

The principal amount placed in the account = p = $67,000

The rate of interest = r = 8.25%

The time period of amount in the account = t = 28

Let the Amount of money in the account = $A

Now<u>, From Compound Interest method</u>

Amount = Principal × (1+\dfrac{\textrm rate}{100})^{\textrm time}

A = p × (1+\dfrac{\textrm r}{100})^{\textrm t}

Or, A = $67,000 × (1+\dfrac{\textrm 8.25}{100})^{\textrm 28}

Or, A = $67,000 × (1.0825)^{28}

Or, A = $67,000 × 9.2041

∴ A = $616,674.7

So, The Amount of money in the account = A = $616,674.5

Hence, The Amount of money in the account after 28 years is $616,674.5  Answer

5 0
2 years ago
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