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3 years ago

Find x . Please and thank you

Mathematics

1 answer:

Mila [183]3 years ago

8 0

Answer:

x = 6

Step-by-step explanation:

In similar triangles, corresponding sides are in same ratio

$\frac{x+3}{3}= \frac{6}{2}\\\\ \frac{x+3}{3}=3\\\\x+3 = 3*3\\\\x+3 = 9\\\\x = 9-3\\\\x = 6$

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Select the procedure that can be used to show the converse of the

Vera_Pavlovna [14]

Answer:

The correct option is C

Step-by-step explanation:

I attached an image that forms the complete question.

The converse Pythagorean theorem states that, "If the square of the longest side of a triangle is equal to the square of the other two sides, then the triangle is a right triangle."

That is if c is the longest side of a triangle and then a and b are the other sides, then if,

c² = a² + b², the triangle is a right triangle.

Looking at all the options, option C fits the theorem well. Because

3² + 4² = 5² implies the triangle is a right triangle and the converse theorem is established.

The option D also looks close, but it's not correct because you can just draw any two sides and put the right angle in between them. The longest is always the part of the triangle that is opposite to the right angle, 90°. If for instance, you draw 3 and 5 then put the right angle in between them, 4 will take the position of the longest side which is wrong.

Therefore, the correct option is c.

7 0

3 years ago

7.4 Centimeters to kilometers

Ket [755]

Answer:

.00074 km

Step-by-step explanation:

7.4 cm * 1 m * 1km =7.4/100/100=.00074

100 cm 100m

7 0

3 years ago

What is the slope of the line? y = -2/7x A. -2 B. -2/7 C. 0 D. 2/7

denis-greek [22]

The slope of the line is -2/7

3 0

3 years ago

Read 2 more answers

Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation:

Vikentia [17]

Answer:

$\= x = 18.5$ , $\sigma = 5.15$

$15.505 < \mu < 21.495$

$14.93 < \mu < 22.069$

Step-by-step explanation:

From the question we are are told that

The sample data is 21, 14, 13, 24, 17, 22, 25, 12

The sample size is n = 8

Generally the ample mean is evaluated as

$\= x = \frac{\sum x }{n}$

$\= x = \frac{ 21 + 14 + 13 + 24 + 17 + 22+ 25 + 12 }{8}$

$\= x = 18.5$

Generally the standard deviation is mathematically evaluated as

$\sigma = \sqrt{\frac{\sum (x- \=x )^2}{n}}$

$\sigma = \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}$

$\sigma = 5.15$

considering part b

Given that the confidence level is 90% then the significance level is evaluated as

$\alpha = 100-90$

$\alpha = 10\%$

$\alpha = 0.10$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{ \alpha }{2} } = 1.645$

The margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E =1.645 * \frac{5.15 }{\sqrt{8} }$

=> $E = 2.995$

The 90% confidence interval is evaluated as

$\= x - E < \mu < \= x + E$

substituting values

$18.5 - 2.995 < \mu < 18.5 + 2.995$

$15.505 < \mu < 21.495$

considering part c

Given that the confidence level is 95% then the significance level is evaluated as

$\alpha = 100-95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{ \alpha }{2} } = 1.96$

The margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E =1.96 * \frac{5.15 }{\sqrt{8} }$

=> $E = 3.569$

The 95% confidence interval is evaluated as

$\= x - E < \mu < \= x + E$

substituting values

$18.5 - 3.569 < \mu < 18.5 + 3.569$

$14.93 < \mu < 22.069$

8 0

3 years ago

Write the equation of the circle with the given center and radius.

34kurt

Step-by-step explanation:

The standard equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$

Center = (h, k)

Center = (0,2)

h = 0

k = 2

r = 5

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

$(x - 0)^2 + (y - 2)^2 = 5^2$

Center = (-4,-5)

h = -4

k = -5

r = $\sqrt{2}$

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

$(x - (-4))^2 + (y - (-5))^2 = \sqrt{2}^2$

$(x + 4))^2 + (y + 5))^2 = \sqrt{2}^2$

Center =(-1,3)

h = -1

k = 3

r = 8

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

$(x - (-1))^2 + (y - 3)^2 = 8^2$

$(x + 1)^2 + (y - 3)^2 = 8^2$

Center: (9,0)

h = 9

k = 0

r = $\sqrt{3}$

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

$(x - 9)^2 + (y - 0)^2 = \sqrt{3}^2$

4 0

4 years ago