Question

7 the perimeter of the rectangle is 58 units. solve for the value of x. a. x = 27.5 b. x = 7 c. x = 25.5 d. x = 6 8 there are 10 cups of oatmeal in the box of quaker oatmeal. if each serving is \\( \frac { 1 } { 3 } \\) of a cup, how many servings are in the box? a. 3 b. 30 c 300 d. 10 9 an inequality in one variable is shown. \\( - \frac { 2 } { 3 } x + \frac { 1 } { 4 } x \geq 6.5 \\) what values of x make the inequality true? a. \\( x \geq 15.6 \\) b. \\( x \leq 15.6 \\) c. \\( x \geq - 15.6 \\) d. \\( x \leq - 15.6 \\) 10 curtis wants to build a model of a 180 - meter tall building. he will be using a scale of 1.5 centimeters = 3.5 meters. how tall will the model be? round your answer to the nearest tenth. 11 within a trail mix recipe, \\( \frac { 2 } { 5 } \\) of the recipe was dried fruit. three - fourths of the dried fruit was raisins. what fraction of the trail mix recipe was raisins? 12 alyssa read 25 pages of a new book the first day she bought it. after the first day, she read 5 pages a day. the book was 350 pages. which equation can be used to determine how many days it will take alyssa to finish her book? a. \\( 5 x = 350 \\) b. \\( 5 x - 25 = 350 \\) c. \\( 25 x + 5 = 350 \\) d. \\( 5 x + 25 = 350 \\)

Explanation:

Question 7

Step1: Use the perimeter formula for a rectangle

The perimeter formula for a rectangle is \(P = 2(l + w)\), where \(l=(3x + 4)\) and \(w = 4\), and \(P=58\). So, \(58=2((3x + 4)+4)\).

Step2: Simplify the equation

First, divide both sides by 2: \(\frac{58}{2}=(3x + 4)+4\), which gives \(29=3x+8\).

Step3: Solve for \(x\)

Subtract 8 from both sides: \(29 - 8=3x\), so \(21 = 3x\). Then divide by 3: \(x=\frac{21}{3}=7\).

Step1: Use the division formula for finding the number of servings

The number of servings \(n=\frac{\text{Total amount of oatmeal}}{\text{Amount per serving}}\). Here, the total amount is 10 cups and the amount per serving is \(\frac{1}{3}\) cup. So \(n = 10\div\frac{1}{3}\).

Step2: Calculate the division

When dividing by a fraction, we multiply by its reciprocal. So \(n=10\times3 = 30\).

Step1: Combine like - terms

First, find a common denominator for \(-\frac{2}{3}x+\frac{1}{4}x\). The common denominator of 3 and 4 is 12. So \(-\frac{2}{3}x+\frac{1}{4}x=-\frac{8}{12}x+\frac{3}{12}x=-\frac{5}{12}x\). The inequality becomes \(-\frac{5}{12}x\geq6.5\).

Step2: Solve for \(x\)

Multiply both sides by \(-\frac{12}{5}\). Remember that when multiplying or dividing an inequality by a negative number, the inequality sign flips. So \(x\leq6.5\times(-\frac{12}{5})\). \(6.5\times(-\frac{12}{5})=\frac{13}{2}\times(-\frac{12}{5})=-\frac{156}{10}=-15.6\).

Answer:

B. \(x = 7\)

Question 8