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4 years ago

The large rectangle was reduced to create the small rectangle.

Mathematics

1 answer:

Nastasia [14]4 years ago

7 0

Answer:

The ratio must be guaranteed.

Therefore,

18/6 =12/x

=> x= 6*12/18 = 4

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The curve y= (k+2)x^2 meets the line y=(k+3)x +3. Find the range of possible values of k.

Greeley [361]

$(k+2)x^2=(k+3)x+3\\
(k+2)x^2-(k+3)x-3=0\\
\Delta\geq0 \wedge k\not=-2\\
\Delta=(-(k-3))^2-4\cdot(k+2)\cdot(-3)\\
\Delta=(-k+3)^2+12k+24\\
\Delta=k^2-6k+9+12k+24\\
\Delta=k^2+6k+33\\
k^2+6k+33\geq0\\
\Delta=6^2-4\cdot1\cdot33=36-132=-9$

3 0

3 years ago

The height of a trapezoid is 8 in. And its area is 96 in2. One base of the trapezoid is 6 inches longer than the other base. Wha

Vsevolod [243]

Answer:

The lengths of the bases are 9 inches and 15 inches.

Step-by-step explanation:

The area of trapezoid is

$=\frac12(\textrm{ sum of parallel sides})\times height$

Given that the height of a trapezoid is 8 in. and its area is 96 in².

Assume the bases of the trapezoid be b₁ and b₂.

Since one base of the trapezoid 6 in. longer than the other.

Let, b₁=b₂+6

The area of the trapezoid is

$=\frac 12 (b_1+b_2)\times8$ in²

$=\frac12 (b_2+6+b_2)\times 8$ in²

$=\frac12(2b_2+6)\times8$ in²

According to the problem,

$\frac12(2b_2+6)\times8 =96$

$\Rightarrow 2b_2+6=\frac{96\times 2}{8}$ [ Multiplying $\frac28$ ]

$\Rightarrow 2b_2+6=24$

$\Rightarrow 2b_2=24-6$

$\Rightarrow 2b_2=18$

$\Rightarrow b_2=\frac{18}{2}$

$\Rightarrow b_2=9$

Then, $b_1=b_2+6$

=9+6

=15 in

The lengths of the bases are 9 inches and 15 inches.

5 0

4 years ago

Which table of values represent a linear relationship?

Alekssandra [29.7K]

The answer is table 3 because it is consistent and the pattern is add 2

5 0

3 years ago

30 PTS <br> Please make sure everything is easy to understand

Semenov [28]

So for number one you would start with parentheses (-2 x 4) and that would get you -8 and then you would forget about the parentheses and drop everything else down and now the problem would be -8 x 3 and remember anytime you have a number by parentheses it’s multiplication and that dot by the parentheses also stands for multiplication so -8 x 3 would get you -24. You could also look at it as positive 8 x 3 and that would get you 24 and then you could just add that negative sign to the 24

8 0

3 years ago

At the scene of a crime, the police have found a blood stain, a footprint, and some threads from a fabric. All are presumed to h

zubka84 [21]

Answer:

There is a 0.175% chance of finding such a person who has all three characteristics.

Out of 4,000 people, 7 people would likely to match all three characteristics.

Step-by-step explanation:

A crime has been committed and after analyzing the evidence, police has found out that:

The criminal's blood type is a type found in only 10% of the population.
The criminal's footprint is a size 13 men's shoe and only 7% of the population wears such shoe size.
Only 25% of the population owns clothing made from a fabric that matches the thread samples found at the scene.

We required to find out the probability of selecting a random person who would match all of these characteristics.

Since it is given that the three characteristics are independent of each other then the required probability is

P(all 3 characteristics) = P(1st characteristic)*P(2nd characteristic)*P(3rd characteristic)

P(all 3 characteristics) = (10/100)*(7/100)*(25/100)

P(all 3 characteristics) = 1750/1,000,000

P(all 3 characteristics) = 7/4000

P(all 3 characteristics) = 0.00175

P(all 3 characteristics) = 0.175%

So out of 4,000 people, 7 people would likely to match all three characteristics.

There is a 0.175% chance of finding such a person who has all three characteristics

3 0

3 years ago