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3 years ago

In ΔMNO, the measure of ∠O=90°, the measure of ∠N=70°, and OM = 3.3 feet. Find the length of MN to the nearest tenth of a foot.

Mathematics

1 answer:

Aleks04 [339]3 years ago

4 0

Answer:

Side MN = 3.5

Step-by-step explanation:

Side NO = 1.2011

Side OM = 3.3

Side MN = 3.51179

Angle ∠M = 20° = 0.34907 rad = π/9

Angle ∠N = 70° = 1.22173 rad = 7/18π

Angle ∠O = 90° = 1.5708 rad = π/2

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If r and s are positive integers, is \small \frac{r}{s} an integer? (1) Every factor of s is also a factor of r. (2) Every prime

Yuri [45]

Answer:

If statement(1) holds true, it is correct that $\small \frac{r}{s}$ is an integer.

If statement(2) holds true, it is not necessarily correct that $\small \frac{r}{s}$ is an integer.

Step-by-step explanation:

Given two positive integers $r$ and $s$ .

To check whether $\small \frac{r}{s}$ is an integer:

Condition (1):

Every factor of $s$ is also a factor of $r$ .

$r \geq s$

Let us consider an example:

$s = 5^2 \cdot 2\\r = 5^3 \cdot 2^2$

$\dfrac{r}{s} = \dfrac{5^3\cdot2^2}{5^2\cdot2} = 10$

which is an integer.

Actually, in this situation $s$ is a factor of $r$ .

Condition 2:

Every prime factor of s is also a prime factor of r.

(But the powers of prime factors need not be equal as we are not given the conditions related to powers of prime factors.)

Let

$r = 2^2\cdot 5\\s =2^4\cdot 5$

$\dfrac{r}{s} = \dfrac{2^3\cdot5}{2^4\cdot5} = \dfrac{1}{2}$

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So, the answer is:

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3 years ago

Find each measure m<1, m<2,m<3

Leno4ka [110]

Answer:

option 2.

m1 = 75 , m2 = 129 , m3 = 100

Step-by-step explanation:

with the rule that the internal angles of a triangle add up to 180 ° we can calculate the missing angles

x + 46 + 29 = 180

x = 180 - 46 -29

x = 105

a flat angle has 180 °

m1 + 105 = 180

m1 = 180 - 105

m1 = 75

46 + 54 + y = 180

y = 180 - 46 -54

y = 80

80 = z + 29

z = 80 - 29

z = 51

as they are two crossed lines the angle is reflected from the opposite side

with that principle and knowing that the angle of a turn is 360 °, if we subtract the 2 known angles and divide it by 2 we will obtain the missing angle (m2)

m2 * 2 = 360 - 51 * 2

m2 = 258/2

m2 = 129

m2 = 29 + m3

129 = 29 + m3

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3 years ago

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