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3 years ago

The store allowed 85 people in 5 hours .. how many people were allowed to enter per hour?

Mathematics

1 answer:

ale4655 [162]3 years ago

3 0

Answer:

17 people per hour

Step-by-step explanation:

85/5

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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:

$-6 < k < 2$

3 0

3 years ago

The difference of Donnie's height and 10 is 43

Tanzania [10]

Answer:

this question is missing something

6 0

3 years ago

Is the inequality true or false?<br><br> 8 + 5(2 x 4) ≥ 9 x 5

-BARSIC- [3]

9514 1404 393

Answer:

true

Step-by-step explanation:

Using the order of operations to evaluate the expressions, we have ...

8 + 5(8) ≥ 9(5)

8 +40 ≥ 45

48 ≥ 45 . . . . . true

5 0

3 years ago

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Find the distance between the points. (5,10) (5,4)

german

Answer:

Step-by-step explanation:

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3 years ago

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A ratio of dogs to cats a pet store is 1:3. There are 15 cats. how many dogs are at the pet store

DIA [1.3K]

From the ratio given we know that there is 3 times more cats than dogs.

If there are 15 cats, then there are 15/3 dogs or 5 dogs.

answer: 5 dogs

8 0

3 years ago