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2 years ago

Find the value of X and give a reason for the relation ship between the angles.

Mathematics

1 answer:

Ostrovityanka [42]2 years ago

8 0

Answer:

x = 55

Step-by-step explanation:

(x - 14) + 99 + 220 = 360

x - 14 + 99 + 220 = 360

x - 14 + 319 = 360

x + 305 = 360

x = 360 - 305

x = 55

-TheUnknownScientist

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Given <img src="https://tex.z-dn.net/?f=%20log_%7B2%7D%28x%29%20%20%3D%20%20%5Cfrac%7B3%7D%7B%20log_%7Bxy%7D%282%29%20%7D%20

Naily [24]

Answer:

$\displaystyle y = x^{-\frac{2}{3}}$

Step-by-step explanation:

Logarithms

Some properties of logarithms will be useful to solve this problem:

1. $\log(pq)=\log p+\log q$

2. $\displaystyle \log_pq=\frac{1}{\log_qp}$

3. $\displaystyle \log p^q=q\log p$

We are given the equation:

$\displaystyle \log_{2}(x) = \frac{3}{ \log_{xy}(2) }$

Applying the second property:

$\displaystyle \log_{xy}(2)=\frac{1}{ \log_{2}(xy)}$

Substituting:

$\displaystyle \log_{2}(x) = 3\log_{2}(xy)$

Applying the first property:

$\displaystyle \log_{2}(x) = 3(\log_{2}(x)+\log_{2}(y))$

Operating:

$\displaystyle \log_{2}(x) = 3\log_{2}(x)+3\log_{2}(y)$

Rearranging:

$\displaystyle \log_{2}(x) - 3\log_{2}(x)=3\log_{2}(y)$

Simplifying:

$\displaystyle -2\log_{2}(x) =3\log_{2}(y)$

Dividing by 3:

$\displaystyle \log_{2}(y)=\frac{-2\log_{2}(x)}{3}$

Applying the third property:

$\displaystyle \log_{2}(y)=\log_{2}\left(x^{-\frac{2}{3}}\right)$

Applying inverse logs:

$\boxed{y = x^{-\frac{2}{3}}}$

7 0

2 years ago

Z varies directly as x2. If z = 16 when x = 2, find z when x = 5. ... Z=

PtichkaEL [24]

Answer:

100

Step-by-step explanation:

it is a bit unclear to me, what that problem description means.

if I understand it correctly, than z is directly depending on x².

so, z = 16 for x = 2. x² = 4

I pondered a little bit, as there are several possibilities to connect 16 with 4 as a driving factor (e.g. 2⁴ = 16, 4×4 = 16, 12 + 4 = 16).

I decided to go with the simplest interpretation with the usual meaning of "varies" (multiplication) : 4×x²

that would mean

z = 4×x² = 4×5² = 4×25 = 100

3 0

2 years ago

Help Me Find The X Please

Papessa [141]

Answer:

x = 16

y = 16 sqrt(3)

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/hyp

sin 60 = y/ 32

Multiply each side by 32

32 sin 60 = y

32 ( sqrt(3) /2) = y

16 sqrt(2)

cos theta = adj/ hyp

cos 60 = x /32

32 cos 60 = x

32 (1/2) =x

16 =x

4 0

2 years ago

Read 2 more answers

If the translation of (x,y)->(x-5, y+2) was applied to the triangle ABC below, what would be the coordinates for A' after the

Rainbow [258]

Answer: (-3,0)

To get this answer, we subtract 5 from the x coordinate and add 2 to the y coordinate. Point A is located at (x,y) = (2,-2) so we see that x = 2 and y = -2

Subtract 5 from the x coordinate: x-5 = 2-5 = -3. The new x coordinate is -3

Add 2 to the y coordinate: y+2 = -2+2 = 0. The new y coordinate is 0.

Therefore, using the rule (x,y) --> (x-5,y+2) has the mapping (2,-2) ---> (-3,0)

Check out the attached image.

4 0

3 years ago

the lightest zoo resident is a leaf cutter ant at 5 micrograms. the heaviest is a giraffe weighing 1,000 kilograms. about how ma

Kay [80]

200 times. Because 1000 divided of 5 is 200. You could divide it using the algorithm.

8 0

3 years ago

Read 2 more answers