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3 years ago

What is the solution to 8x - 3(2x - 4) = 3(x - 6)?

Mathematics

1 answer:

barxatty [35]3 years ago

5 0

Answer:

X=+30 that's all I know, Sorry I couldn't help much :(

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An artist is using tiles and boards for a project. A tile has length 1/3 ft and width 1/3 ft. A board has length 1/4yd and width

Nezavi [6.7K]

We have been given that

The length of the tile is given by 1/3 feet.

The width of the tile is given by 1/3 feet.

The length of the board is given by 1/4 yd.

The width of the board is given by 1/4 yd.

We know that 1 feet = 0.33 yard

Hence, we have

The length of the tile = $\frac{1}{3} \cdot 0.33= 0.11$ yd

The width of the tile = $\frac{1}{3} \cdot 0.33= 0.11$ yd

Hence, the ratio of length of the tile to the length of the board is given by

$\frac{0.11}{1/4} \\
\\
\frac{44}{100} \\
\\
\frac{11}{25} \\$

Area of tile = $0.11 \times 0.11 = 0.0121$ square yd.

Area of board is $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$

Therefore, the ratio of the area of the tile to the area of the board is given by

$\frac{0.0121}{1/16} \\
\\
\frac{121}{625}$

6 0

3 years ago

Pluto's distance P(t)P(t)P, left parenthesis, t, right parenthesis (in billions of kilometers) from the sun as a function of tim

Xelga [282]

Answer: P(t) = 1.25.sin( $\frac{\pi}{3}$ .t) + 5.65

Step-by-step explanation: A motion repeating itself in a fixed time period is a periodic motion and can be modeled by the functions:

y = A.sin(B.t - C) + D or y = Acos(B.t - C) + D

where:

A is amplitude A=|A|

B is related to the period by: T = $\frac{2.\pi}{B}$

C is the phase shift or horizontal shift: $\frac{C}{B}$

D is the vertical shift

In this question, the motion of Pluto is modeled by a sine function and doesn't have phase shift, C = 0.

Amplitude:

a = $\frac{largest - smallest}{2}$

At t=0, Pluto is the farthest from the sun, a distance 6.9 billions km away. At t=66, it is closest to the star, P(66) = 4.4 billions km. Then:

a = $\frac{6.9-4.4}{2}$

a = 1.25

b

A time period for Pluto is T=66 years:

66 = $\frac{2.\pi}{b}$

b = $\frac{\pi}{33}$

Vertical Shift

It can be calculated as:

d = $\frac{largest+smallest}{2}$

d = $\frac{6.9+4.4}{2}$

d = 5.65

Knowing a, b and d, substitute in the equivalent positions and find P(t).

P(t) = a.sin(b.t) + d

P(t) = 1.25.sin( $\frac{\pi}{3}$ .t) + 5.65

The Pluto's distance from the sun as a function of time is

P(t) = 1.25.sin( $\frac{\pi}{3}$ .t) + 5.65

8 0

3 years ago

Consider the function y = acos(bx), where a > 0 and b > 0. Which change affects the locations of the x-intercepts of the g

Morgarella [4.7K]

Answer:

The correct option is;

Decrease b.

Step-by-step explanation:

The given information are;

The function in the question is given by the equation, y = a·cos(b·x)

Where;

a > 0 and b > 0

The location of the x-intercept is given by the values of x when y = 0 which are obtained as follows;

When y = 0, y = a·cos(b·x) = 0

Therefore;

cos(b·x) = 0/a = 0

∴ b·x = cos⁻¹(0) = π/2, 3·π/2, (4·n×π + π)/2

Therefore, as b decreases, x increases.

8 0

3 years ago

Read 2 more answers

Find the slope of the line that passes through (8, 6) and (2, 7).

Amiraneli [1.4K]

Vas happenin!!

Slope form - y2-y1/x2-x1

7-6/ 2-8

1/-6

Your slope is -6x

Hope this helps

-Zayn Malik

6 0

3 years ago

What is 0.57 x 1000 How do I solve this

Temka [501]

570 is the answer. since 1000 has 3 zeroes on the end of it, you take the decimal point and move it 3 spots to the right.

5 0

3 years ago