What is the measure of the central angle.

15 is the same as the product of 3 and a number. Which equation models this sentence?

adelina 88 [10]

Question

15 is the same as the product of 3 and a number. Which equation models this sentence?

15=3x

15=x-3

15=3+x

15=x divided by 3

Answer:

Step-by-step explanation:

15 = 3x

x = 15 : 3

x = 5

.........................

check

15 = 3 * 5

15 = 15

the answer is good

3 0

3 years ago

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Julian wrote this number pattern on the board:

geniusboy [140]

Answer:

Step-by-step explanation:

10, 24 and 38 are composite numbers.

(10 can be divided by 5 and 2; 24 can be divided by 8, 3, 12 and 2; 38 can be divided by 19 and 2).

The others are prime numbers.

3 0

3 years ago

How do you do this. Please give a full answer and explain why.

OverLord2011 [107]

Law of Exponent

$\displaystyle \large{ {a}^{ - n} = \frac{1}{ {a}^{n} } }$

Compare the terms.

$\displaystyle \large{ {a}^{ - n} = {( - 2)}^{ - 3} }$

Therefore, a = -2 and n = 3. From the law of exponent above, we receive:

$\displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{ {( - 2)}^{ 3} } }$

Exponent Def. (For cubic)

$\displaystyle \large{ {a}^{3} = a \times a \times a }$

Factor (-2)^3 out.

$\displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{( - 2) \times ( - 2) \times ( - 2)}}$

(-2) • (-2) = 4 | Negative × Negative = Positive.

$\displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{4 \times ( - 2)}}$

4 • (-2) = -8 | Negative Multiply Positive = Negative.

$\displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{ - 8}}$

If either denominator or numerator is in negative, it is the best to write in the middle or between numerator and denominators.

Hence,

$\displaystyle \large \boxed{ {( - 2)}^{ - 3} = - \frac{1}{ 8}}$

The answer is - 1 / 8

3 0

2 years ago

Assume that military aircraft use ejection seats designed for men weighing between 141.8 lb and 218 lb. If women's weights are

Mariulka [41]

Answer:

$P(141.8$

And we can find this probability with this difference and using the normal standard table:

$P(-0.639$

Then the answer would be approximately 55.3% of women between the specifications. And that represent more than the half of women

Step-by-step explanation:

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(173.6,49.8)$

Where $\mu=173.6$ and $\sigma=49.8$

We are interested on this probability

$P(141.8$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(141.8$

And we can find this probability with this difference and using the normal standard table:

$P(-0.639$

Then the answer would be approximately 55.3% of women between the specifications. And that represent more than the half of women

8 0

3 years ago

A triangle is dilated by a scale factor of 1/5 and then rotated 90 degree clockwise about the origin. Why is the image similar t

yan [13]

Answers:
The corresponding angles of the triangles are congruent
The image is a reduction of the pre-image
Neither the dilation nor the rotation change the shape of the triangle

Explanation:
For shapes to be similar:
1- there should be a ratio between the sides
2- angles in first shape should be congruent to angles in second shape

Now, a scale factor of 0.2 means that the sides of the image are 0.2 of the length of the original shape. However, angles are not changes

Let's check the choices:
1- The corresponding sides of the triangles are congruent:
This option is incorrect as dilation changes the lengths of the sides

2- The corresponding angles of the triangles are congruent:
This option is correct as neither dilation nor rotation alters the measures of the angles

3- The corresponding sides of the image are 5 times as long as those of the pre-image:
This option is incorrect as the sides of the image are only 0.2 times as long as those of the pre-image

4- The image is a reduction of the pre-image:
This option is correct as the sides of the image are 0.2 times those of the pre-image which means that the shape is reduced

5- Neither the dilation nor the rotation change the shape of the triangle:
This option is correct as both dilation and rotation are rigid transformations that do not alter the shape of the triangle (a triangle remains a triangle only with different side lengths)

6- The rotation reduces the size of the triangle:
This option is incorrect as rotation does not alter the size of the shape. It only changes its position

Hope this helps :)

3 0

3 years ago

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