8(3x – 2) ≤ 2(7x + 12)?

Answers

Answer 1
Answer:

Answer:

The answer is x ≤ 4                        


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The area of the base of a square notepad is 2.25 square inches. What is the length of one side of the base of the notepad?

Answers

Area= (1 side)^2
⇒ 2.25 in^2= (1 side)^2
⇒ 1 side= √(2.25) in
⇒ 1 side= 1.5 in

The length of 1 side of the base of the notepad is 1.5 inch~

Plumber gets 75 cents per km travelled what would he get if he travelled 120 kms for the day

Answers

You would just multiple 75 cents by 120 km.  That'd give you the amount. 120 x 0.75= 90.  That is $90. 

Evaluate [(30 + 6) − 32] ÷ 9 ⋅ 2.

Answers

Use PEMDAS:

[(30+6) -3^2] / 9* 2
= (36 -9)/ 9* 2
= 27/9* 2
= 3*2
= 6

The final answer is 6~

Answer: just use PEMDAS

[(30+6) -3'2] / 9'2

= (36 -9)/ 9'2

= 27/9'2

= 3'2

= 6

Step-by-step explanation:

what is the solution to the system of equations? y =1/3 x – 10 2x y = 4 (–8, 6) (–6, 16) (6, –8) (16, –6)

Answers

Answer:

Option C is correct.

Solution to the given system of equation is (6 , -8)

Step-by-step explanation:

Given the system of equation:

y= (1)/(3) x-10             ......[1]

2x+y =4                           .....[2]

Substitute the equation [1] in [2] we get;

2x +(1)/(3)x -10 =4

Combine like terms;

(7)/(3)x -10 =4

Add 10 to both side of an equation:

(7)/(3)x -10 +10=4+10

Simplify:

(7)/(3)x =14

Divide both sides by  (3)/(7) we get;

(3)/(7) * (7)/(3)x = 14 * (3)/(7)

Simplify:

x = 6

Substitute the value of x =6 in equation [1] we get;

y= (1)/(3)(6)-10

or

y= 2-10  

Simplify:

y = - 8

therefore, the solution to the given system of equation is; (6 , -8)

You can also see in the graph as shown below:

y = 1/3 x - 10
2x + y = 4
2x + 1/3 x - 10 = 4
7/3 x = 14
x = 6
y = 1/3(6) - 10 = 2 - 10 = -8
Therefore solution is (6, -8)

Z=1+4iFind the angle 0(theta) in degrees that z makes in the complex plane.
Round your answer, if necessary, to the nearest tenth. Express 0(theta) between -180 and 180 degrees.

Answers

Answer:

76.0 degrees

Step-by-step explanation:

Just got it right on the Khan Academy quiz.

Final answer:

The angle θ that z makes in the complex plane is approximately 75.96°.

Explanation:

The complex plane is a mathematical concept used in complex numbers. It's a two-dimensional Cartesian coordinate system where the horizontal axis represents the real part of a complex number, and the vertical axis represents the imaginary part. Complex numbers are plotted as points in this plane, facilitating operations like addition, subtraction, multiplication, and division of complex numbers.

To find the angle θ that z makes in the complex plane, we can use the formula: θ = arctan(y/x), where x and y are the real and imaginary parts of z respectively. In this case, x = 1 and y = 4 as given. Plugging these values into the formula, we get: θ = arctan(4/1). Using a calculator, we find that θ ≈ 75.96°.

Learn more about Complex Plane here:

brainly.com/question/33093682

#SPJ2

Divide 7/24 by 35/48 and reduce the quotient to the lowest fraction

Answers

Given:
1st fraction - 7/24
2nd fraction - 34/48

Rules in dividing fractions:

1) Get the reciprocal of the 2nd fraction.
34/48 becomes 48/34

2) Multiply the 1st fraction to the reciprocal of the 2nd fraction
7/24 * 48/34 = 7*48 / 24*34 = 336/816

3) Simplify the fraction
336/816 ⇒ 112/272 ⇒ 56/136 ⇒ 14/34 ⇒ 7/17

336 ÷ 3 = 112
816 ÷ 3 = 272

112 ÷ 2 =   56
272 ÷ 2 = 136

  56 ÷ 4 =   14
136 ÷ 4 =   34

  14 ÷ 2  =     7
  34 ÷ 2 =   17

7/24 ÷ 35/48 = 7/17
7/24 ÷ 35/48

= 7/24 × 48/35.    7 into 35 is 5. 24 into 48 is 2.

= 2/5