1. draw a right triangle that is also isosceles. 2. determine the length of the radius. 3. label the coordinates of the two points on the graph below. identify a 3rd point that is on the graph. 4. solve the equation: $\frac{x}{2}-8 = 19$. 5. write an expression to represent the perimeter of a triangle with sides 2a - 3, 2a, and 3a + 1. 6. to join a local dancing group, jan has to pay a $100 sign - up fee plus $25 per month. write an equation for the cost (y) based on the number of months (x). 7. what does it mean to bisect a segment or an angle? 8. what number goes on top?

Question

Accepted Answer

1. **Draw a right - isosceles triangle**:
   - A right - isosceles triangle has one right angle ($90^{\circ}$) and two equal sides. You can draw a triangle with two legs of equal length, for example, 3 units each, and the right angle between them.
2. **Determine the length of the radius**:
# Explanation:
## Step1: Recall the radius - diameter relationship
The diameter $d$ of a circle is related to the radius $r$ by the formula $d = 2r$.
Given $d=27$ meters.
## Step2: Solve for the radius
We can rewrite the formula as $r=\frac{d}{2}$. Substituting $d = 27$ meters, we get $r=\frac{27}{2}=13.5$ meters.
# Answer:
13.5 meters
3. **Label the coordinates of the two points on the graph and identify a third point**:
   - Without seeing the actual graph, assume the two points have coordinates $(x_1,y_1)$ and $(x_2,y_2)$. If the graph represents a linear function $y=mx + b$, to find a third point, we can use the slope - intercept form. First, find the slope $m=\frac{y_2 - y_1}{x_2 - x_1}$, then choose an $x$ value (say $x_3$) and calculate $y_3=mx_3 + b$.
4. **Solve the equation $\frac{x}{2}-8 = 19$**:
# Explanation:
## Step1: Isolate the term with $x$
Add 8 to both sides of the equation. $\frac{x}{2}-8 + 8=19 + 8$, which simplifies to $\frac{x}{2}=27$.
## Step2: Solve for $x$
Multiply both sides of the equation by 2. $x=27\times2 = 54$.
# Answer:
54
5. **Write an expression for the perimeter of the triangle**:
# Explanation:
## Step1: Recall the perimeter formula
The perimeter $P$ of a triangle is the sum of the lengths of its sides. The side lengths of the triangle are $2a-3$, $2a$, and $3a + 1$.
## Step2: Calculate the perimeter
$P=(2a-3)+2a+(3a + 1)$. Combine like terms: $P=(2a+2a + 3a)+(-3 + 1)=7a-2$.
# Answer:
$7a - 2$
6. **Write an equation for the cost ($y$) based on the number of months ($x$)**:
# Explanation:
## Step1: Identify the fixed and variable costs
The sign - up fee of $100$ is a fixed cost, and the cost per month of $25$ is a variable cost.
## Step2: Write the equation
The cost $y$ is the sum of the fixed cost and the variable cost. So, $y = 25x+100$.
# Answer:
$y = 25x + 100$
7. **What does it mean to bisect a segment or an angle?**
# Brief Explanations:
To bisect a segment means to divide it into two equal - length parts. To bisect an angle means to divide it into two equal - measure angles.
# Answer:
To bisect a segment is to divide it into two equal - length parts; to bisect an angle is to divide it into two equal - measure angles.
8. **What number goes on top?**
   - In a pyramid - like number structure where each number is the sum of the two numbers below it, the number on top is the sum of the two 8s below it. So the number on top is $8 + 8=16$.
# Answer:
16

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the radius - diameter relationship

Step2: Solve for the radius

Step1: Isolate the term with \(x\)

Step2: Solve for \(x\)

Step1: Recall the perimeter formula

Step2: Calculate the perimeter

Answer: