Math / Algebra

QuestionPoint $S$ is the midpoint of line RT. RS is $3 x+20$ and RT is $12 x-10$ . What is the length of RS? Round your answer to the nearest hundredth if necessary. Your Answer:
Answer
Question 3 (2 points)

Studdy Solution

STEP 1

1. Point $S$ is the midpoint of line $RT$ .
2. $RS = 3x + 20$ .
3. $RT = 12x - 10$ .
4. We need to find the length of $RS$ .

STEP 2

1. Understand the relationship between the segments.
2. Set up an equation using the midpoint property.
3. Solve the equation for $x$ .
4. Substitute $x$ back into the expression for $RS$ to find its length.

STEP 3

Understand the relationship between the segments. Since $S$ is the midpoint of $RT$ , we know that $RS = ST$ .

STEP 4

Set up an equation using the midpoint property. Since $S$ is the midpoint, $RS = ST$ and $RT = RS + ST = 2 \times RS$ .
Therefore, $RT = 2 \times (3x + 20)$ .

STEP 5

Solve the equation for $x$ .
Substitute the expression for $RT$ into the equation:
$12x - 10 = 2 \times (3x + 20)$
Simplify the right side:
$12x - 10 = 6x + 40$
Subtract $6x$ from both sides:
$6x - 10 = 40$
Add 10 to both sides:
$6x = 50$
Divide by 6:
$x = \frac{50}{6}$
$x \approx 8.33$

STEP 6

Substitute $x$ back into the expression for $RS$ to find its length.
$RS = 3x + 20$
$RS = 3(8.33) + 20$
$RS = 24.99 + 20$
$RS \approx 44.99$
The length of $RS$ is approximately $\boxed{44.99}$ .

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QuestionPoint $S$ is the midpoint of line RT. RS is $3 x+20$ and RT is $12 x-10$ . What is the length of RS? Round your answer to the nearest hundredth if necessary. Your Answer:
Answer
Question 3 (2 points)

Studdy Solution

STEP 1

1. Point $S$ is the midpoint of line $RT$ .
2. $RS = 3x + 20$ .
3. $RT = 12x - 10$ .
4. We need to find the length of $RS$ .

STEP 2

1. Understand the relationship between the segments.
2. Set up an equation using the midpoint property.
3. Solve the equation for $x$ .
4. Substitute $x$ back into the expression for $RS$ to find its length.

STEP 3

Understand the relationship between the segments. Since $S$ is the midpoint of $RT$ , we know that $RS = ST$ .

STEP 4

Set up an equation using the midpoint property. Since $S$ is the midpoint, $RS = ST$ and $RT = RS + ST = 2 \times RS$ .
Therefore, $RT = 2 \times (3x + 20)$ .

STEP 5

Solve the equation for $x$ .
Substitute the expression for $RT$ into the equation:
$12x - 10 = 2 \times (3x + 20)$
Simplify the right side:
$12x - 10 = 6x + 40$
Subtract $6x$ from both sides:
$6x - 10 = 40$
Add 10 to both sides:
$6x = 50$
Divide by 6:
$x = \frac{50}{6}$
$x \approx 8.33$

STEP 6

Substitute $x$ back into the expression for $RS$ to find its length.
$RS = 3x + 20$
$RS = 3(8.33) + 20$
$RS = 24.99 + 20$
$RS \approx 44.99$
The length of $RS$ is approximately $\boxed{44.99}$ .

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QuestionPoint SSS is the midpoint of line RT. RS is 3x+203 x+203x+20 and RT is 12x−1012 x-1012x−10. What is the length of RS? Round your answer to the nearest hundredth if necessary. Your Answer:AnswerQuestion 3 (2 points)

Studdy Solution

STEP 1

1. Point S S S is the midpoint of line RT RT RT.2. RS=3x+20 RS = 3x + 20 RS=3x+20.3. RT=12x−10 RT = 12x - 10 RT=12x−10.4. We need to find the length of RS RS RS.

STEP 2

1. Understand the relationship between the segments.2. Set up an equation using the midpoint property.3. Solve the equation for x x x.4. Substitute x x x back into the expression for RS RS RS to find its length.

STEP 3

Understand the relationship between the segments. Since S S S is the midpoint of RT RT RT, we know that RS=ST RS = ST RS=ST.

STEP 4

Set up an equation using the midpoint property. Since S S S is the midpoint, RS=ST RS = ST RS=ST and RT=RS+ST=2×RS RT = RS + ST = 2 \times RS RT=RS+ST=2×RS.Therefore, RT=2×(3x+20) RT = 2 \times (3x + 20) RT=2×(3x+20).

STEP 5

STEP 6

Substitute x x x back into the expression for RS RS RS to find its length.RS=3x+20 RS = 3x + 20 RS=3x+20RS=3(8.33)+20 RS = 3(8.33) + 20 RS=3(8.33)+20RS=24.99+20 RS = 24.99 + 20 RS=24.99+20RS≈44.99 RS \approx 44.99 RS≈44.99The length of RS RS RS is approximately 44.99 \boxed{44.99} 44.99​.

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QuestionPoint $S$ is the midpoint of line RT. RS is $3 x+20$ and RT is $12 x-10$ . What is the length of RS? Round your answer to the nearest hundredth if necessary. Your Answer:
Answer
Question 3 (2 points)

1. Point $S$ is the midpoint of line $RT$ .
2. $RS = 3x + 20$ .
3. $RT = 12x - 10$ .
4. We need to find the length of $RS$ .

1. Understand the relationship between the segments.
2. Set up an equation using the midpoint property.
3. Solve the equation for $x$ .
4. Substitute $x$ back into the expression for $RS$ to find its length.

Understand the relationship between the segments. Since $S$ is the midpoint of $RT$ , we know that $RS = ST$ .

Set up an equation using the midpoint property. Since $S$ is the midpoint, $RS = ST$ and $RT = RS + ST = 2 \times RS$ .
Therefore, $RT = 2 \times (3x + 20)$ .

Substitute $x$ back into the expression for $RS$ to find its length.
$RS = 3x + 20$
$RS = 3(8.33) + 20$
$RS = 24.99 + 20$
$RS \approx 44.99$
The length of $RS$ is approximately $\boxed{44.99}$ .