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elena-s [515]
3 years ago
8

A triangle has a perimeter of 18 inches. If one side has length 8 inches, find the length of the shortest side if the other leng

ths are in the ratio of 2 units : 3 units.
Mathematics
1 answer:
aalyn [17]3 years ago
8 0
a,b,c-\ sides\ of\ triangle\\\\a+b+c=18\ inches\\\\a=8inch\\\\\frac{b}{c}=\frac{2}{3}\\\\3b=2c\ \ --->b=\frac{2c}{3}\\\\8+\frac{2c}{3}+c=18\ |*3\\\\24+2c+3c=54\\\\5c=54-24\\\\5c=30\\\\c=\frac{30}{5}=6\\\\Length\ of\ shorter\ side\ is\ equal\ to\ 6\ inches.
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Write the equation in standard form. Identity the center and radius.<br> x² + y2 + 8x-4y-7=0
lorasvet [3.4K]

Answer:

equation;

(x + 4) {}^{2}  + (y - 2) {}^{2}  = 27

Center (-4,2)

Radius is

3 \sqrt{3}

Step-by-step explanation:

Since the x^2 and y^2 have the same coeffiecent this will be a circle in a form of

(x - h) {}^{2}  + (y - k)  {}^{2}  =  {r}^{2}

Where (h,k) is center

r is the radius

So first we group like Terms together

{x}^{2}  + 8x  +  {y}^{2}  - 4y - 7 = 0

Add 7 to both sides

{x}^{2}  + 8x +  {y}^{2}  - 4y = 7

( {x}^{2}  + 8x) +(  {y}^{2}  - 4y) = 7

Since the orginal form of the equation of the circle has a perfect square we need to complete the square for each problem

(\frac{8}{2} ) {}^{2}  = 16

and

( - \frac{4}{2} ) {}^{2}  = 4

so we have

{x}^{2}  + 8x + 16 +  {y}^{2}  - 4y + 4y = 7 + 16 + 4

{x}^{2}  + 8x + 16  +  {y}^{2}  - 4y + 4y = 27

(x + 4) {}^{2}  +  (y  - 2) {}^{2}  = 27

To find our center, h is -4 and k is 2

so the center is (-4,2)

The radius is

\sqrt{27}  = 3 \sqrt{3}

So the radius is 3 times sqr root of 3.

8 0
2 years ago
Which expression gives the measure of XYZ?
olasank [31]
The correct answer is B
4 0
3 years ago
Read 2 more answers
A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a ne
Leto [7]

Answer:

The 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative is (0.6247, 0.6923).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

Of the 533 randomly selected Americans surveyed, 351 were in favor of the initiative.

This means that n = 533, \pi = \frac{351}{533} = 0.6585

90% confidence level

So \alpha = 0.1, z is the value of Z that has a p-value of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6585 - 1.645\sqrt{\frac{0.6585*0.3415}{533}} = 0.6247

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6585 + 1.645\sqrt{\frac{0.6585*0.3415}{533}} = 0.6923

The 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative is (0.6247, 0.6923).

6 0
3 years ago
Solve the equation 2x-11=k for x
Lilit [14]

x = k/2 + 11/2

Step-by-step explanation:

\frac{k}{2} + \frac{11}{2} = \frac{k+11}{2}

hope this helped :)

4 0
2 years ago
Please help me with this questions
viktelen [127]

Answer:

See attached

Step-by-step explanation:

The answers added on the picture

8 0
3 years ago
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