1. Which among the verbal phrases does not diminished be operation subtraction (-)?
2. Multiplication indicates a multiplying action. Which of the following pair of expressions
A. less than
D. decreased by
expresses multiplication?
1. multiplied by, of
2. times, the ratio of
3. the product of, thrice a number
4. the difference of, the product of
C.
B. 1 and 3
1 and 4
A 1 and 2
D. 1, 2, 3, 4
3. What is the correct relation symbol of "is greater than or equal to"?
B. <
A >
C. 2
D. s
4. Twelve times a number x is equal to thrice the same number increased by three is the
same as which mathematical sentence?
A. 12x = 3y + 3
B.12x = 3x + 3C. 12x = y + 3
D. 12x = x + 3
5. Which of the following verbal phrases correspond to 4x + 3?
A. Four increased by three
C. The product of a number x added to three
B. Four times a number x increased by three D. The prcduct of 4x and three
6. Which of the following is the mathematical translation of "The product of three and a
number a is greater than or equal to 6."?
A. 3a < 7
B. 3a > 7
C. 3a s 6
D. 3a 2 6​

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step-by-step explanation:

$54.99 includes 500 min. if she does not exceed 500 min then her bill is $54.99

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9

1) the property is   ixi = a ⇔x = a   o x = -a

4(x-5)+3= 15⇒4x-20+3 = 15⇒4x-17= 15⇒4x = 15+17⇒4x = 32⇒x =32/4= 8

4(x-5) +3= -15⇒4x-20 +3 = -15⇒4x-17= -15⇒4x =-15+17⇒4x = 2⇒x =2/4= 1/2

the values are x =8 and x = 0,5

i'm pretty sure the answer is a. decreases with increase in