An algebraic expression in mathematics is an expression that's made from variables and constants, together with algebraic operations (addition, subtraction, etc.). Expressions are made of terms.

Firstly, apply the distributive property as a(b+c)=ab+ac and get

$\begin{aligned}\frac{3}{4}\times \frac{1}{4}x+\frac{3}{4}\times 8-\frac{1}{2}x-2&=\frac{3}{8}\times 4-\frac{3}{8}\times x-\frac{1}{4}\\ \frac{3x}{16}+6-\frac{x}{2}-2&=\frac{3}{2}-\frac{3x}{8}-\frac{1}{4} \end$

Now, rearrange the terms by taking variable terms on the left-hand side and constant terms on the right-hand side as

$\frac{3x}{16}-\frac{x}{2}+\frac{3x}{8}=\frac{3}{2}-\frac{1}{4}-6+2$

Further, simplify the above expression by taking L.C.M as

$\begin{aligned}\frac{3x-8x+6x}{16}&=\frac{6-1}{4}-4\\ \frac{x}{16}&=\frac{5-16}{4}\\ \frac{x}{16}&=\frac{-11}{4}\end$

Then, multiply both sides with 4 and get

$\begin{aligned}4\times \frac{x}{16}&=4\times \frac{-11}{4}\\ \frac{x}{4}&=\frac{-11}{1}\end$

Furthermore, cross multiply both sides and get

$x=-44$

Hence, the value of x in the equation which is given $\frac{3}{4}\left(\frac{1}{4}x+8\right)-\left(\frac{1}{2}x+2\right)=\frac{3}{8}(4-x)-\frac{1}{4}$ is x=-44.

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8 0

2 years ago

Can someone help me with this question

horsena [70]

Step-by-step explanation:

Given: diameter = 16 in

hence radius, r is 16 ÷ 2 = 8 in

a) notice that the fan blades divide the circle into 3 equal sectors.

Each sector is hence 1/3 of the entire circumference of the circle

Arc Length of each sector (between blades),

= (1/3) x circumference

= (1/3) x 2πr

= (1/3) x 2 x 3.142 x 8

= 16.76 in (Answer)

b) similarly, the area between the blades

= (1/3) x πr²

= (1/3) x 3.142 x 8²

= 67.03 in² (answer)

c) The angular velocity is the radians per second that the tip moves

It is given that it moves 8π radians in 2 seconds

hence in 1 second, we expect the tip to move,

8π ÷ 2 = 4π rad/s (Answer)

6 0

4 years ago

: diameter of Circle P.<br><br><br><br> 1 = m 3 = 20°, then m =

posledela

The required value of Arc BC m = 140° Option B is correct.

Given that,
AD is the diameter of the circle,
∠1 = ∠3 = 20°
Arc BC is to be determined.

Arc is the measure of angle on the circumference of circle.

Here,
∠1 = arc AB
∠3 = arc CD
Now, for circle p
Since angle 1 and angle 2 are equal to the composition of the arc,
Arc AD = Arc AB + Arc BC + Arc CD = 180
20 + Arc BC + 20 = 180
Arc BC = 180 - 40

Arc BC = 140°

Thus, the required value of Arc BC m = 140° Option B is correct.

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3 0

1 year ago