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Lapatulllka [165]

3 years ago

15

This rectangle has 9 straight Lines and 14 squares. Can you find them?

1 answer:

juin [17]3 years ago

7 0

Answer:two dimensional shapes

Step-by-step explanation:

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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

Help with the geometry pls and thx

astraxan [27]

Answer:

1. p->q

2. p<->q

3. :.p^q

Step-by-step explanation:

I hope this will help you

3 0

3 years ago

The temperature was -13°F and then rose 9°F.

faust18 [17]

Answer:

it would be -4 degrees F

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

How many different simple random sampmes of size 5 can be obtained from a pppulation whose size is 43?

Nesterboy [21]

Answer:

Number of random samples = 962598

Step-by-step explanation:

A random sample represents the responses for a certain survey of a part of the population.

A sample size is the part of the population being surveyed.

For a population $N$ the number of different random samples that can be chosen for a sample size $x$ can be calculated as = $NCx$

This can be calculated as :

$NCx=\frac{N!}{x!(N-x)!}$

Given:

Population size = 43

Sample size = 5

Number of random samples = $43C5$

⇒ $\frac{43!}{5!(43-5)!}$

⇒ $\frac{43!}{5!(38)!}$

⇒ $\frac{43\times42\times41\times40\times39}{5\times4\times3\times2\times1}$ [Canceling out the common terms]

⇒ $962598$ (Answer)

4 0

3 years ago

Dawn Lingua bought three yards of cloth to make some curtains. The cloth was on sale for $2.25 per yard. How much did Dawn pay f

AURORKA [14]

$2.25 <span>$7.0875</span>
$2.25
$2.25
---------
$6.75
x Tax 5%
$7.0875

7 0

3 years ago