MATHEMATICS HIGH SCHOOL

Define a variable, write an inequality, and solve each problem. Check your solution.1. Half of a number is at least 14
2. The opposite of 1/3 a number is greater than 9
3. 1/5 of a number is at most 30

Answers

Answer 1
Answer: A variable= an unknown number

1. (1/2)x ≥ 14
x ≥ 28
Check:
1/2(28) ≥ 14
14 ≥ 14

2. -(1/3)x > 9
x < -27
Check:
-(1/3)(-30) > 9
10 > 9

3. (1/5)x ≤ 30
x ≤ 150
Check:
(1/5)(140) ≤ 30
28 ≤ 30

Related Questions

1. Which of the following is the factored form of the expression: 3x2 – 4x? A. x(3x - 4) B. x(3 – 4x) C. (3x -1) (x -1) D. (3x +1)(x -1) 2. Which is a completely factored form of the expression: x2 + 21x +20 ? A. (x + 5)(x + 4) B. (x + 10)(x + 2) C. (x + 20)(x + 1) D. (x + 21)(x - 1) 3. Which expression is factored form of 4x2 -9? A. 2(x - 3)2 B. (x - 3)2 C. 2(x + 3)(x - 3) D. (2x + 3)(2x - 3) 4. Below are factored forms of the expression: 12x3 – 36x2 . Which expression has the greatest common factor as the first term? A. 3x (4x2 – 12x) B. 4x2(3x -9 C. 12x2(x – 3) D. 12x(x2 - 3x) 5. Adele’s lawn has an area of (x2 -5x -6) square feet and a length of (x + 1) feet. What is the width of the lawn in feet? A. (x -6) B. (x +6) C. (x2 -4x -5) D. (x2 -6x -7) 6. The expression below represents the area, in square meters, of a rectangle: X2 + 5x -24 Which of the following pairs of expressions could represent the length and width, in meters, of the rectangle? A. (x – 3) and (x + 8) B. (x – 4) and (x + 6) C. (x – 6) and (x + 4) D. (x – 8) and (x + 3) 7. What is the complete factorization of 32 – 8z2? A. -8(2 + z)(2 –z) B. 8(2 + z)(2 – z) C. -8(2 + z)2 D. 8(2 – z)2 8. What is the greatest common factor of: 12x2 , 24x2y2 , and 46xy? A. 4x B. 3x C. 6x D. 2x 9. Which expression is equivalent to: 2x2 -3x -35? A. (2x + 7)(x - 5) B. (2x - 7) (x + 5) C. (2x - 5)(x + 7) D. (2x + 5)(x - 7) 10. What are the factors of 81x2 + 36x + 4? A. (9x + 2)(x +2) B. (9x +2)(9x +2) C. (9x -2)(9x -2) D. (9x +2)(9x -2) 11. The top of a rectangular table has an area of: 18x2+ 69x +60. The width of the table is 3x + 4. What is the length of the table? (Show proof by multiplying – show your work) 12. Simplify: (x2 +2x)(5x -3) A. 11x2 -3 B. 6x3 -6x C. 5x3 + 7x2 – 6x D. 5x3 – 13x2 -6x 13. Factor by grouping: 30g5 +24g3h – 35g2h2 - 28h3 Show your work! 14. Which is the correct way to factor the polynomial : x2 -16? A. (x -4)(x -4) B. (x -4)(x +4) C. (x +4)(x -2)(x +2) D. Not factorable 15. The area of a square painting is: 81p2 + 90p +25. What is the length of one side? Prove by multiplication – show your work.
4x5+6divided by 3 using bidmas
What is 25% of 860 i remember percentages just need touch up how to do them
A survey shows that the probability that an employee gets placed in a suitable job is 0.65. A psychometric test consultant claims that he could help place any employee in a suitable job based on the result of a psychometric test. The test has an accuracy rate of 70%. An employee working in a particular company takes the test. The probability that the employee is in the right job and the test predicts that he is in the wrong job is_______The probability that the employee is in the wrong job and the test predicts that he is in the right job is ________
Help, please answer this for me, I can't figure it out.

19x+(1/2)ax=x+9 solve for x

Answers

   19x + ¹/₂ax = x + 9
     - x             - x
    18x + ¹/₂ax = 9
x(18) + x(¹/₂a) = 9
    x(18 + ¹/₂a) = 9
     18 + ¹/₂a   18 + ¹/₂a
                  x = 9/(18 + ¹/₂a)

I need help with this question! ​

Answers

2. Jayden ran a whole mile in one hour

Answer:

1: 3 miles

2: 1 mile

Step-by-step explanation:

Estimate the sum of 1,537 times 242 then find out the sum

Answers

estimate- 4,520
if you multiply -371954
Adding- 1779

Find the equation of the tangent line to the curve y=2sinxy
2
sin
x
at the point (π/6,1)
π
6
1
.

The equation of this tangent line can be written in the form y=mx+b
y
m
x
b
where

Answers

Final answer:

To find the equation of the tangent line to the curve y=2sinx at the point (π/6,1), we take the derivative to find the slope and then use the point-slope form of the line equation. The result is y = √3x + 1 - √3π/6.

Explanation:

The subject of this question is calculus and focuses specifically on finding the equation of the tangent line to the curve y=2sinx at a given point. To do this, we use the formula y=mx+b.

Firstly, the slope of the tangent line is obtained by taking the derivative of the function at the point of tangency. The derivative of y=2sinx is y'=2cosx. For the given point (π/6,1), the slope (m) would be 2cos(π/6) = √3.

Secondly, we use the point-slope form of the line equation to find b. Inserting the values of the slope (m) and the given point into the equation, we get 1 = √3(π/6) + b. Solving for b gives b = 1 - √3π/6.

Finally, the equation of the tangent line is y = √3x + 1 - √3π/6.

Learn more about Tangent Line here:

brainly.com/question/34259771

#SPJ2
 Hello
f(x) = 2sin(x)
f(π/6) = 1 
f'(x) 2cos(x)
f'(π/6) = 2×co(π/6) = 2 × root(3)×0.5  =root(3)
The equation of this tangent line is : y= root(3)(x-π/6)+1
y = root(3)x+1 - π/6(root(x))  in the form y=mx+b
m = root(3)   and   b = 1 - π/6(root(x))

Evaluate.

[42 ÷ (2 + 3 • 2)] + [4 • (36 – 52)]

I really need help!!!

Answers

Ok so first we do 2 + 3 = 5 * 2 = 10 / by 42 = 4.2

other side 36 - 52 = 16 * 4 = 64 now add     4.2 + 64 = 68.2

Which one of the following is a true statement about a circle inscribed in a regular polygon? A. The area of the circle is equal to the area of the polygon.
B. The sides of the polygon are chords of the circle.
C. The vertices of the polygon are on the circumference of the circle.
D. The sides of the polygon are tangents of the circle.

Answers

Given that a circle is inscribed in a regular polygon, it is true that the sides of the polygons are tangents of the circle. The area of the circle is always less than the area of the polygon. When the polygon is inscribed in the circle, then the sides of the polygon are chords of the circle and the vertices of the polygon are on the circumference of the circle. Answer is D. 
Other Questions
The functions f(x) and g(x) are shown below:f(x) = 0.05x g(x) = (0.05)x Which statement best describes the graph of f(x) and g(x)?
!!!!!!!!!! help me Find the  Angle   !!!! Help me solve this question very confused ! !!thank you
Please help me with these five math questions1. z = 2/3 for z - 1/5 = 5/8True or False2. t = 9 for 10 ½ = t + 1 ½True or False3. k + 2 1/9 = 1 1/34. Jose ran 8 ¼ miles to practice for an upcoming marathon. His training goal is to be able to run 15 ¾ miles. Write an equation for the additional amount of miles, m, Jose needs to reach his goal.5. Solve the equation above for m.
After distributing the terms (2x + 3) (4x – 5), you get a new expression of the formax+ bx + cWhat is the value of a?What is the value of b?What is the value of c?