Question

1. without solving, determine whether the solution of \\(\frac{1}{3}x = 21\\) is greater than or less than 21. explain.

1. the volume \\( v \\) of a cylinder is \\( 65\pi \\) cubic centimeters. the height \\( h \\) of the cylinder is 5 centimeters. use the formula \\( v = bh \\) to find the area \\( b \\) of the base of the cylinder.

1. the total area of this shape is 44 square inches. the area of the triangle is 20 square inches. write and solve an equation to find the area of the rectangle. (image of a triangle on top of a rectangle)

1. the temperature in a crater on the moon is \\( 0^\circ \text{c} \\) at 9:00 a.m. the temperature decreases \\( 16^\circ \text{c} \\) every hour. when will the temperature be \\( -76^\circ \text{c} \\)?

1. one-sixth of the daisies and one-third of the roses in a garden are blooming. there are 12 blooming daisies and 20 blooming roses. how many daisies and roses are in the garden?

1. you and two friends owe $64 for a meal. you divide the bill in the ratio \\( 3:5:8 \\). how much did each person pay for the meal?

Explanation:

Question 17

Step1: Analyze the coefficient

The equation is $\frac{1}{3}x = 21$. The coefficient of $x$ is $\frac{1}{3}$, which is a positive fraction less than 1.

Step2: Relate to multiplication/division

When you solve for $x$, you would multiply both sides by 3 (the reciprocal of $\frac{1}{3}$). Since multiplying a number by a number greater than 1 (3 > 1) will increase the value, the solution for $x$ (which is $21\times3$) will be greater than 21.

Step1: Recall the formula

We are given the formula for the volume of a cylinder $V = Bh$, where $V$ is volume, $B$ is the area of the base, and $h$ is the height.

Step2: Substitute known values

We know $V = 65\pi$ and $h = 5$. Substitute these into the formula: $65\pi=B\times5$.

Step3: Solve for B

To find $B$, divide both sides of the equation by 5: $B=\frac{65\pi}{5}=13\pi$.

Step1: Define variables and equation

Let $A_{triangle}$ be the area of the triangle, $A_{rectangle}$ be the area of the rectangle, and $A_{total}$ be the total area. The equation is $A_{triangle}+A_{rectangle}=A_{total}$.

Step2: Substitute known values

We know $A_{triangle} = 20$, $A_{total}=44$. So the equation becomes $20 + A_{rectangle}=44$.

Step3: Solve for $A_{rectangle}$

Subtract 20 from both sides: $A_{rectangle}=44 - 20 = 24$.

Answer:

The solution of $\frac{1}{3}x = 21$ is greater than 21 because to solve for $x$, we multiply 21 by 3 (the reciprocal of $\frac{1}{3}$), and multiplying by a number greater than 1 increases the value.

Question 18