aiculate the value of the expression $$ 3 x^{2}+4 x-5 $$ when $$ \begin{array}{lll}x=-1 & ext { b) } x=-2 & ext { c) } x=0\end{array} $$ he temperature in Moscow was $$ 2^{\circ} \mathrm{C} $$. Then it dropped to $$ 8^{\circ} \mathrm{C} $$ below zero. By om thany degrees did the temperature drop?

Question

aiculate the value of the expression $$ 3 x^{2}+4 x-5 $$ when $$ \begin{array}{lll}x=-1 & 	ext { b) } x=-2 & 	ext { c) } x=0\end{array} $$ he temperature in Moscow was $$ 2^{\circ} \mathrm{C} $$. Then it dropped to $$ 8^{\circ} \mathrm{C} $$ below zero. By om thany degrees did the temperature drop?

UpStudy AI · Accepted Answer

Sure, let's tackle both parts of your question step by step.

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## Part 1: Evaluating the Expression $$ 3x^{2} + 4x - 5 $$ for Different Values of $$ x $$

### a) When $$ x = -1 $$

$$
\begin{align*}
3x^{2} + 4x - 5 &= 3(-1)^{2} + 4(-1) - 5 \
&= 3(1) - 4 - 5 \
&= 3 - 4 - 5 \
&= -6
\end{align*}
$$

**Result:** $$ -6 $$

---

### b) When $$ x = -2 $$

$$
\begin{align*}
3x^{2} + 4x - 5 &= 3(-2)^{2} + 4(-2) - 5 \
&= 3(4) - 8 - 5 \
&= 12 - 8 - 5 \
&= -1
\end{align*}
$$

**Result:** $$ -1 $$

---

### c) When $$ x = 0 $$

$$
\begin{align*}
3x^{2} + 4x - 5 &= 3(0)^{2} + 4(0) - 5 \
&= 0 + 0 - 5 \
&= -5
\end{align*}
$$

**Result:** $$ -5 $$

---

## Part 2: Temperature Drop Calculation

### Problem Statement

- **Initial Temperature in Moscow:** $$ 2^{\circ}\mathrm{C} $$
- **Final Temperature:** $$ 8^{\circ}\mathrm{C} $$ below zero, which is $$ -8^{\circ}\mathrm{C} $$

### Calculation

To find out **by how many degrees the temperature dropped**, subtract the final temperature from the initial temperature:

$$
\text{Temperature Drop} = \text{Initial Temperature} - \text{Final Temperature}
$$

$$
\begin{align*}
\text{Temperature Drop} &= 2^{\circ}\mathrm{C} - (-8^{\circ}\mathrm{C}) \
&= 2^{\circ}\mathrm{C} + 8^{\circ}\mathrm{C} \
&= 10^{\circ}\mathrm{C}
\end{align*}
$$

**Result:** The temperature dropped by **10 degrees Celsius**.

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When $$ x = -1 $$, the expression $$ 3x^{2} + 4x - 5 $$ equals $$ -6 $$. When $$ x = -2 $$, it equals $$ -1 $$. When $$ x = 0 $$, it equals $$ -5 $$. The temperature in Moscow dropped by 10 degrees Celsius.

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