7 Substitute the given values and then solve for the unknown in each of the following common formulas a $$ x=a+a t $$ b $$ s=a t+\frac{1}{2} a t^{2} $$. Solve for a given $$ \mathrm{r}=6 \mathrm{a}=2 $$ and $$ t=4 $$. c $$ A=A\left(\frac{a+b}{2} ight) $$ Solve for $$ = $$ given $$ s=20, t=2 $$ and $$ a=4 $$. d $$ A=r\left(1+\frac{r}{100} ight) $$ Solve for $$ b $$ given $$ A=10 h=4 $$ and $$ a=3 $$ Solve for $$ r $$ given $$ A=1000 $$ and $$ P=8 imes 0 $$ 8 The perimeter of a square is $$ 9 f \mathrm{~cm} $$. Determinc its side iength. 9. The sum of two consccutive $$ \mathrm{S}^{\mathrm{m}} $$ Joen is 35 . What are the numbers 10) I ride four times fiver than 1 jog. If a trip took me 45 minuter and 1 spent 15 of thece mimute jogering 3 km . how far did 1 ride?

Question

7 Substitute the given values and then solve for the unknown in each of the following common formulas a $$ x=a+a t $$ b $$ s=a t+\frac{1}{2} a t^{2} $$. Solve for a given $$ \mathrm{r}=6 \mathrm{a}=2 $$ and $$ t=4 $$. c $$ A=A\left(\frac{a+b}{2}ight) $$ Solve for $$ = $$ given $$ s=20, t=2 $$ and $$ a=4 $$. d $$ A=r\left(1+\frac{r}{100}ight) $$ Solve for $$ b $$ given $$ A=10 h=4 $$ and $$ a=3 $$ Solve for $$ r $$ given $$ A=1000 $$ and $$ P=8 	imes 0 $$ 8 The perimeter of a square is $$ 9 f \mathrm{~cm} $$. Determinc its side iength. 9. The sum of two consccutive $$ \mathrm{S}^{\mathrm{m}} $$ Joen is 35 . What are the numbers 10) I ride four times fiver than 1 jog. If a trip took me 45 minuter and 1 spent 15 of thece mimute jogering 3 km . how far did 1 ride?

UpStudy AI · Accepted Answer

Certainly! Let's tackle each of the problems step by step.

---

## **Problem 7**

**Substitute the given values and solve for the unknown in each of the following formulas.**

### **a. $$ x = a + a t $$**

**Given:**
- $$ a = 2 $$
- $$ t = 4 $$

**Solution:**
$$
x = a + a t = 2 + 2 \times 4 = 2 + 8 = 10
$$

**Answer:** $$ x = 10 $$

---

### **b. $$ s = a t + \frac{1}{2} a t^2 $$**

**Given:**
- $$ a = 2 $$
- $$ t = 4 $$

**Solution:**
$$
s = a t + \frac{1}{2} a t^2 = 2 \times 4 + \frac{1}{2} \times 2 \times 4^2 = 8 + \frac{1}{2} \times 2 \times 16 = 8 + 16 = 24
$$

**Answer:** $$ s = 24 $$

---

### **c. $$ A = h \left( \frac{a + b}{2} \right) $$**

*Note: There seems to be a typographical error in the original formula. It appears to be the area formula for a trapezoid:*

$$
A = h \left( \frac{a + b}{2} \right)
$$

**Given:**
- $$ A = 20 $$
- $$ h = 2 $$
- $$ a = 4 $$

**Find:** $$ b $$

**Solution:**
$$
20 = 2 \left( \frac{4 + b}{2} \right)
$$
$$
20 = 2 \times \frac{4 + b}{2} \quad \Rightarrow \quad 20 = 4 + b
$$
$$
b = 20 - 4 = 16
$$

**Answer:** $$ b = 16 $$

---

### **d. $$ A = P \left(1 + \frac{r}{100}\right) $$**

*Note: Assuming the formula represents simple interest or a similar financial formula where $$ A $$ is the amount, $$ P $$ is the principal, and $$ r $$ is the rate.*

**Given (for solving $$ r $$):**
- $$ A = 1000 $$
- $$ P = 800 $$ *(Assuming "P = 8 × 100 = 800" based on context)*

**Find:** $$ r $$

**Solution:**
$$
1000 = 800 \left(1 + \frac{r}{100}\right)
$$
$$
\frac{1000}{800} = 1 + \frac{r}{100} \quad \Rightarrow \quad 1.25 = 1 + \frac{r}{100}
$$
$$
\frac{r}{100} = 1.25 - 1 = 0.25 \quad \Rightarrow \quad r = 0.25 \times 100 = 25\%
$$

**Answer:** $$ r = 25\% $$

---

## **Problem 8**

**The perimeter of a square is $$ 9 $$ cm. Determine its side length.**

**Given:**
- Perimeter ($$ P $$) = 9 cm

**Find:** Side length ($$ s $$)

**Solution:**
$$
P = 4s \quad \Rightarrow \quad s = \frac{P}{4} = \frac{9}{4} = 2.25 \text{ cm}
$$

**Answer:** Each side of the square is **2.25 cm** long.

---

## **Problem 9**

**The sum of two consecutive numbers is 35. What are the numbers?**

**Let:**
- First number = $$ n $$
- Second number = $$ n + 1 $$

**Given:**
$$
n + (n + 1) = 35
$$
$$
2n + 1 = 35
$$
$$
2n = 35 - 1 = 34 \quad \Rightarrow \quad n = 17
$$

**Numbers:**
- First number = 17
- Second number = 17 + 1 = 18

**Answer:** The two consecutive numbers are **17** and **18**.

---

## **Problem 10**

**I ride four times faster than I jog. If a trip took me 45 minutes and I spent 15 of those minutes jogging 3 km. How far did I ride?**

**Given:**
- Total trip time = 45 minutes
- Jogging time = 15 minutes
- Jogging distance = 3 km
- Riding speed = 4 × jogging speed

**Find:** Riding distance

**Solution:**

1. **Calculate Jogging Speed:**
$$
\text{Jogging Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{3 \text{ km}}{15 \text{ minutes}} = \frac{3 \text{ km}}{0.25 \text{ hours}} = 12 \text{ km/h}
$$

2. **Calculate Riding Speed:**
$$
\text{Riding Speed} = 4 \times 12 \text{ km/h} = 48 \text{ km/h}
$$

3. **Calculate Riding Time:**
$$
\text{Riding Time} = \text{Total Time} - \text{Jogging Time} = 45 \text{ minutes} - 15 \text{ minutes} = 30 \text{ minutes} = 0.5 \text{ hours}
$$

4. **Calculate Riding Distance:**
$$
\text{Riding Distance} = \text{Speed} \times \text{Time} = 48 \text{ km/h} \times 0.5 \text{ hours} = 24 \text{ km}
$$

**Answer:** You rode **24 kilometers**.

---

If you have any further questions or need additional clarification, feel free to ask!
**Problem 7 Solutions:** a. $$ x = 10 $$ b. $$ s = 24 $$ c. $$ b = 16 $$ d. $$ r = 25\% $$ **Problem 8:** Each side of the square is **2.25 cm**. **Problem 9:** The numbers are **17** and **18**. **Problem 10:** You rode **24 kilometers**.

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