б) $$ -15+(-28) ; $$ 2. Найдите расстояние между точками координатной прямой: а) $$ P(-6) $$ и $$ Q(-15) $$; б) $$ S(-5,7) $$ и $$ T(0,9) $$. 3. Ретите уравнение: а) $$ 4,6-x=-2,5 $$; б) $$ y+6 \frac{9}{16}=-3 \frac{7}{24} $$. 4. Цева товара повысилясь с 7800 до 9750 р. На сколько процент повысилась цена товара? 5*. Решите уравнение $$ |b+5|=11 $$.

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UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$\left|-5.7-0.9\right|$$
- step1: Subtract the numbers:
  $$\left|-6.6\right|$$
- step2: Calculate the absolute value:
  $$6.6$$
Calculate or simplify the expression $$ -15+(-28) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$-15+\left(-28\right)$$
- step1: Remove the parentheses:
  $$-15-28$$
- step2: Subtract the numbers:
  $$-43$$
Solve the equation $$ y+6 \frac{9}{16}=-3 \frac{7}{24} $$.
Solve the equation by following steps:
- step0: Solve for $$y$$:
  $$y+6\frac{9}{16}=-3\frac{7}{24}$$
- step1: Convert the expressions:
  $$y+\frac{105}{16}=-\frac{79}{24}$$
- step2: Move the constant to the right side:
  $$y=-\frac{79}{24}-\frac{105}{16}$$
- step3: Subtract the numbers:
  $$y=-\frac{473}{48}$$
Solve the equation $$ 4.6-x=-2.5 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$4.6-x=-2.5$$
- step1: Move the constant to the right side:
  $$-x=-2.5-4.6$$
- step2: Subtract the numbers:
  $$-x=-7.1$$
- step3: Change the signs:
  $$x=7.1$$
Solve the equation $$ |b+5|=11 $$.
Solve the equation by following steps:
- step0: Solve for $$b$$:
  $$\left|b+5\right|=11$$
- step1: Separate into possible cases:
  $$\begin{align}&b+5=11\&b+5=-11\end{align}$$
- step2: Solve the equation:
  $$\begin{align}&b=6\&b=-16\end{align}$$
- step3: Rewrite:
  $$b_{1}=-16,b_{2}=6$$
Calculate or simplify the expression $$ |-6 - (-15)| $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left|-6-\left(-15\right)\right|$$
- step1: Remove the parentheses:
  $$\left|-6+15\right|$$
- step2: Add the numbers:
  $$\left|9\right|$$
- step3: Calculate the absolute value:
  $$9$$
Calculate or simplify the expression $$ (9750-7800)/7800*100 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(9750-7800\right)}{7800}\times 100$$
- step1: Remove the parentheses:
  $$\frac{9750-7800}{7800}\times 100$$
- step2: Subtract the numbers:
  $$\frac{1950}{7800}\times 100$$
- step3: Reduce the fraction:
  $$\frac{1}{4}\times 100$$
- step4: Reduce the numbers:
  $$1\times 25$$
- step5: Simplify:
  $$25$$
Let's solve the problems step by step:

1. **Calculate $$ -15 + (-28) $$**:
   $$
   -15 + (-28) = -43
   $$

2. **Find the distance between points on the number line**:
   - a) For points $$ P(-6) $$ and $$ Q(-15) $$:
   $$
   | -6 - (-15) | = | -6 + 15 | = | 9 | = 9
   $$
   - b) For points $$ S(-5.7) $$ and $$ T(0.9) $$:
   $$
   | -5.7 - 0.9 | = | -6.6 | = 6.6
   $$

3. **Solve the equations**:
   - a) For the equation $$ 4.6 - x = -2.5 $$:
   $$
   x = 4.6 + 2.5 = 7.1
   $$
   - b) For the equation $$ y + 6 \frac{9}{16} = -3 \frac{7}{24} $$:
   $$
   y = -3 \frac{7}{24} - 6 \frac{9}{16} = -\frac{473}{48}
   $$

4. **Calculate the percentage increase in price**:
   The price increased from 7800 to 9750:
   $$
   \text{Percentage increase} = \frac{9750 - 7800}{7800} \times 100 = 25\%
   $$

5. **Solve the equation $$ |b + 5| = 11 $$**:
   This gives two cases:
   $$
   b + 5 = 11 \quad \Rightarrow \quad b = 6
   $$
   $$
   b + 5 = -11 \quad \Rightarrow \quad b = -16
   $$
   Thus, the solutions are $$ b_1 = -16 $$ and $$ b_2 = 6 $$.

### Summary of Results:
1. $$ -15 + (-28) = -43 $$
2. Distance $$ P $$ to $$ Q $$ = 9; Distance $$ S $$ to $$ T $$ = 6.6
3. $$ x = 7.1 $$; $$ y = -\frac{473}{48} $$
4. Percentage increase = 25%
5. Solutions for $$ |b + 5| = 11 $$ are $$ b_1 = -16 $$ and $$ b_2 = 6 $$
1. $$ -15 + (-28) = -43 $$ 2. Distance between $$ P(-6) $$ and $$ Q(-15) $$ is 9 units; distance between $$ S(-5.7) $$ and $$ T(0.9) $$ is 6.6 units. 3. $$ x = 7.1 $$; $$ y = -\frac{473}{48} $$ 4. The price increased by 25%. 5. The solutions for $$ |b + 5| = 11 $$ are $$ b = -16 $$ and $$ b = 6 $$.

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