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3 years ago

Which expression represents the product of 25 and 9 divided by 5?

Mathematics

2 answers:

Mademuasel [1]3 years ago

5 0

Answer:

25+9÷5

Step-by-step explanation:

Nat2105 [25]3 years ago

3 0

"The product of" means multiplication, so the equation will be:

(25 × 9) ÷ 5

(25 × 9)/5

Also, not sure if you need it, but to find the answer solve the equation in the parenthesis first.

25 × 9 = 225

Now we have 225 ÷ 5. Divide to solve.

225 ÷ 5 = 45

I hope this helps :)

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Mary puts 200 fish into a pond. If the fish are guaranteed to increase at an annual rate of 14%, how many fish will be in the po

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Answer:

340

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2 years ago

Find the set of values of k for which the line y=kx-4 intersects the curve y=x²-2x at 2 distinct points?

Sonbull [250]

Answer:

$-6 < k < 2$

Step-by-step explanation:

Given

$y = x^2 - 2x$

$y =kx -4$

Required

Possible values of k

The general quadratic equation is:

$ax^2 + bx + c = 0$

Subtract $y = x^2 - 2x$ and $y =kx -4$

$y - y = x^2 - 2x - kx +4$

$0 = x^2 - 2x - kx +4$

Factorize:

$0 = x^2 +x(-2 - k) +4$

Rewrite as:

$x^2 +x(-2 - k) +4=0$

Compare the above equation to: $ax^2 + bx + c = 0$

$a = 1$

$b= -2-k$

$c =4$

For the equation to have two distinct solution, the following must be true:

$b^2 - 4ac > 0$

So, we have:

$(-2-k)^2 -4*1*4>0$

$(-2-k)^2 -16>0$

Expand

$4 +4k+k^2-16>0$

Rewrite as:

$k^2 + 4k - 16 + 4 >0$

$k^2 + 4k - 12 >0$

Expand

$k^2 + 6k-2k - 12 >0$

Factorize

$k(k + 6)-2(k + 6) >0$

Factor out k + 6

$(k -2)(k + 6) >0$

Split:

$k -2 > 0$ or $k + 6> 0$

So:

$k > 2$ or k $> -6$

To make the above inequality true, we set:

$k < 2$ or $k >-6$

So, the set of values of k is:

$-6 < k < 2$

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2 years ago

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IrinaVladis [17]

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