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3 years ago

True or false, there is no solution to the systems of inequalities shown below

Mathematics

2 answers:

miss Akunina [59]3 years ago

8 0

False
Because if you plot a graph to both the equation as i have attached the image.. you can see there can be multiple solution to the above system of inequalities.

WARRIOR [948]3 years ago

4 0

False.
there are solutions to this system of inequalities.
-> For a quick check you can take random x, e.g. consider x=0, and substitute it   in the inequality, which gives
  y<5 and y>4 .
  there are infinite number of y satisfying these conditions.
-> You can solve it graphically to get exact solution. draw the line y=3x+5 and y = -x+4. The common region, below y=3x+5 and above y=-x+4 , is the solution for the system of inequalities.

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An equiangular triangle has one side of length six inches. What is the height of the triangle, drawn from that side, to the near

tino4ka555 [31]

Answer:

The height of the triangle is 5.2 inches

Step-by-step explanation:

we know that

An <u>equiangular triangle</u> is a triangle where all three interior angles are equal in measure

Remember that an equilateral triangle has three equal sides and three equal interior angles

An equiangular triangle Is the same that an equilateral triangle. The measure of its interior angles is equal to 60 degrees

Let

h ----> the height of triangle

b ---> the length side of the triangle

Applying Pythagoras Theorem

$h^2=b^2-(b/2)^2$

we have

$b=6\ in$

substitute

$h^2=6^2-(6/2)^2$

$h^2=36-9$

$h^2=27$

$h=\sqrt{27}\ in$

$h=5.2\ in$

see the attached figure to better understand the problem

5 0

3 years ago

Thirty percent (30%) of the bulbs in a large box are defective. If 12 bulbs are selected randomly from the box, calculate the pr

AleksandrR [38]

The probability that exactly 6 are defective is 0.0792.

Given:

30% of the bulbs in a large box are defective.

If 12 bulbs are selected randomly from the box.

To find:

The probability that exactly 6 are defective.

Solution:

Probability of defective bulbs is:

$p=30\%$

$p=\dfrac{30}{100}$

$p=0.3$

Probability of non-defective bulbs is:

$q=1-p$

$q=1-0.3$

$q=0.7$

The probability that exactly 6 are defective is:

$P(x=r)=^nC_rp^rq^{n-r}$

$P(x=6)=^{12}C_6(0.3)^6(0.7)^{12-6}$

$P(x=6)=924(0.3)^6(0.7)^{6}$

$P(x=6)=0.0792478958$

$P(x=6)\approx 0.0792$

Therefore, the probability that exactly 6 are defective is 0.0792.

Learn more:

brainly.com/question/12917164

8 0

3 years ago

How you do multiply complex numbers ? Example : (9 - 4i) (8 + 6i)

Andrew [12]

You multiply them just as you would multiply any normal polynomials, except there is a special rule. Since we know that i = √-1, the rule is that i² = -1. So, let's multiply:

$(9-4i)(8+6i) = 72+54i-32i-24i^2$