Question

1. Знайди х, якщо –х = 99. А 0 Б –99 В 99 Г –99 або 99 2. Яка з рівностей хибна? А 7 + (–15) = –8 Б 9 – (–16) = 25 В –27 – (–13) = –40 Г –16 + (–10) = –26 3. Які числа задовольняють нерівність |х| < 9? ( А –10 і 3 Б –7 і 7 В –3 і 10 Г –9 і 9 4. Установи відповідність між рівняннями (1-3) та їх коренями (А-Д). 1 17 – х = 23 А 5 2 х + 16 = –8 Б 6 3 –28 + х = –23 В –5 Г –6 Д –24 Запиши повне розв’язання завдань 5 – 7 5. Порівняй числа: а) –1 і 0; б) –17 і –27; в) –20 і 20; г) –23 і –24. 6. Порівняй значення виразів А і В, якщо: А = –43 + 25 – (–34) + (–19) – 17; В = –38 + 72 – 54 – (–38) + (–46). 7. На координатній площині побудуй прямокутник ABCD, якщо A (– 2; – 2), В (6; –2), С (6; 4). Запиши координати точки D. Знайди периметр і площу побудованого прямокутника (в одиничних відрізках).

Answer 1

1. Знайди х, якщо –х = 99.

To find the value of x, we need to solve the equation -x = 99. We can do this by multiplying both sides of the equation by -1, which will reverse the signs:

-x = 99

Multiplying both sides by -1:

x = -99

Therefore, the value of x is -99.

2. Яка з рівностей хибна? А 7 + (–15) = –8 Б 9 – (–16) = 25 В –27 – (–13) = –40 Г –16 + (–10) = –26

To determine which equation is incorrect, we can evaluate each equation and see if it holds true.

A) 7 + (-15) = -8 7 - 15 = -8 -8 = -8 (correct)

B) 9 - (-16) = 25 9 + 16 = 25 25 = 25 (correct)

C) -27 - (-13) = -40 -27 + 13 = -40 -14 = -40 (incorrect)

D) -16 + (-10) = -26 -16 - 10 = -26 -26 = -26 (correct)

Therefore, the equation that is incorrect is C) -27 - (-13) = -40.

3. Які числа задовольняють нерівність |х| < 9? ( А –10 і 3 Б –7 і 7 В –3 і 10 Г –9 і 9)

To find the numbers that satisfy the inequality |x| < 9, we need to consider the absolute value of x.

The absolute value of a number is the distance of that number from zero on the number line. It is always positive or zero.

For the given inequality, |x| < 9, it means that the distance of x from zero should be less than 9.

Therefore, the numbers that satisfy the inequality are:

A) -10 and 3 B) -7 and 7 C) -3 and 10 D) -9 and 9

4. Установи відповідність між рівняннями (1-3) та їх коренями (А-Д). 1 17 – х = 23 А 5 2 х + 16 = –8 Б 6 3 – 28 + х = –23 В –5 Г –6 Д –24

To find the roots of the equations, we need to solve each equation separately.

1) 17 - x = 23 Subtract 17 from both sides: - x = 6 Multiply both sides by -1: x = -6 Therefore, the root for equation 1 is -6 (corresponding to А).

2) 5 2 x + 16 = -8 Subtract 16 from both sides: 5 2 x = -24 Divide both sides by 5 2: x = -24 / 5 2 Therefore, the root for equation 2 is -24 / 5 2 (corresponding to Б).

3) 6 3 - 28 + x = -23 Combine like terms: -22 + x = -23 Add 22 to both sides: x = -1 Therefore, the root for equation 3 is -1 (corresponding to В).

4) -5 Therefore, the root for equation 4 is -5 (corresponding to Г).

Therefore, the correspondence between the equations and their roots is: А) 1 17 - х = 23 -> x = -6 Б) 5 2 х + 16 = -8 -> x = -24 / 5 2 В) 6 3 - 28 + х = -23 -> x = -1 Г) -5 Д) -24

5. Порівняй числа: а) –1 і 0; б) –17 і –27; в) –20 і 20; г) –23 і –24.

a) -1 and 0: -1 is less than 0.

b) -17 and -27: -17 is greater than -27.

c) -20 and 20: -20 is less than 20.

d) -23 and -24: -23 is greater than -24.

Therefore, the comparisons are: а) –1 < 0 б) –17 > –27 в) –20 < 20 г) –23 > –24

6. Порівняй значення виразів А і В, якщо: А = –43 + 25 – (–34) + (–19) – 17; В = –38 + 72 – 54 – (–38) – (–46).

To compare the values of A and B, we need to evaluate each expression separately.

A = -43 + 25 - (-34) + (-19) - 17 Simplifying the double negatives: A = -43 + 25 + 34 - 19 - 17 Combining like terms: A = -43 + 34 - 19 - 17 + 25 A = -43 + 34 - 36 + 25 A = -43 - 36 + 34 + 25 A = -79 + 59 A = -20

B = -38 + 72 - 54 - (-38) - (-46) Simplifying the double negatives: B = -38 + 72 - 54 + 38 + 46 Combining like terms: B = -38 + 38 + 72 + 46 - 54 B = 0 + 72 + 46 - 54 B = 72 + 46 - 54 B = 118 - 54 B = 64

Therefore, the comparison between A and B is: A < B (-20 < 64)

7. На координатній площині побудуй прямокутник ABCD, якщо A (– 2; – 2), B (6; – 2), C (6; 4). Запиши координати точки D. Знайди периметр і площу побудованого прямокутника (в одиничних відрізках).

To construct the rectangle ABCD, we need to plot the given points on a coordinate plane.

A (-2, -2), B (6, -2), C (6, 4).

The rectangle ABCD will have sides AB, BC, CD, and AD.

Since AB and CD are horizontal, their lengths are equal to the difference in x-coordinates: AB = CD = 6 - (-2) = 8.

Since BC and AD are vertical, their lengths are equal to the difference in y-coordinates: BC = AD = 4 - (-2) = 6.

To find the coordinates of point D, we can add the length of AB to the x-coordinate of C and the length of BC to the y-coordinate of A: D (6 + 8, -2 + 6) = D (14, 4).

The perimeter of the rectangle is the sum of the lengths of all four sides: Perimeter = AB + BC + CD + AD = 8 + 6 + 8 + 6 = 28.

The area of the rectangle is the product of the lengths of its adjacent sides: Area = AB * BC = 8 * 6 = 48 square units.

Therefore, the coordinates of point D are (14, 4), and the perimeter and area of the rectangle are 28 units and 48 square units, respectively.