21. Q16
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Similar Question 1
<p>Solve each equation for <code class='latex inline'>x</code>.</p><p><code class='latex inline'>\dfrac{rx+sx}{t} = 1</code></p>
Similar Question 2
<p>Solve each equation for <code class='latex inline'>x</code>.</p><p><code class='latex inline'>mx + nx = p</code></p>
Similar Question 3
<p>Rearrange each formula to isolate the variable indicated using pencil and paper.</p><p><code class='latex inline'>A=P+I</code> for <code class='latex inline'>I</code> (investments)</p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>C = \pi d</code> for <code class='latex inline'>d</code></p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>A=\dfrac{1}{2}bh</code> for <code class='latex inline'>h</code> (area of a triangle)</p>
<img src="/qimages/157074" /><p>The speed-distance-time relationship for an object moving at a constant speed is described by the formula <code class='latex inline'>\displaystyle s=\frac{d}{t} </code>. Which of the following correctly describes <code class='latex inline'>\displaystyle d </code> in terms of <code class='latex inline'>\displaystyle s </code> and <code class='latex inline'>\displaystyle t ? </code></p><p><code class='latex inline'>\displaystyle \mathbf{A} \quad d=\frac{t}{s} </code></p><p><code class='latex inline'>\displaystyle \mathbf{B} \quad d=\frac{s}{t} </code></p><p> <code class='latex inline'>\mathbf{C } \quad \displaystyle d=s t </code></p><p><code class='latex inline'>\displaystyle \mathbf{D} \quad d=s-t </code></p>
<p>You may use Heron&#39;s formula:</p><p><code class='latex inline'> \displaystyle A = \sqrt{s(s -a )(s -b)(s- c)} </code> where a, b, and ac are the side lengths, and </p><p><code class='latex inline'> \displaystyle s = \frac{1}{2}(a + b+ c) </code></p><p>Show that Heron’s formula can also be written as follows:</p><p><code class='latex inline'>\displaystyle{A=\frac{1}{4}\sqrt{(a+b+c)(a+b-c)(b+c-a)(c+a-b)}}</code></p>
<p>Solve each equation for <code class='latex inline'>\displaystyle y . </code></p><p><code class='latex inline'>\displaystyle \frac{3}{4} y=15 x </code></p>
<p>If <code class='latex inline'>a-b=x</code>, what values of <code class='latex inline'>a,b,</code> and <code class='latex inline'>x</code> would make the equation <code class='latex inline'>a+x=b+x</code> true?</p>
<p>Solve the formula for the indicated variable.</p><img src="/qimages/44205" />
<p>Solve each equation or formula for the variable specified.</p><p><code class='latex inline'>\frac{6c-t}{7}=b</code>, for <code class='latex inline'>c</code></p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>v=\displaystyle{\frac{d}{t}}</code> for <code class='latex inline'>t</code> (speed)</p>
<p>Use opposite operations to rearrange, or &quot;solve,&quot; each formula to isolate the indicated variable.</p><p><code class='latex inline'>\displaystyle V=\pi r^{2} h </code>, for <code class='latex inline'>\displaystyle h </code></p>
<p>Solve each equation for <code class='latex inline'>x</code>.</p><p><code class='latex inline'>\dfrac{rx+sx}{t} = 1</code></p>
<p>Solve each equation for the given variable.</p><p><code class='latex inline'>2m - nx = x + 4</code> for <code class='latex inline'>x</code></p>
<p>Solve each equation for <code class='latex inline'>x</code>.</p><p><code class='latex inline'>\dfrac{x+2}{y-1} = 2</code></p>
<p>Solve each equation for <code class='latex inline'>\displaystyle y . </code></p><p><code class='latex inline'>\displaystyle -10 y=5 x </code></p>
<p>Rearrange each formula to isolate the variable indicated using pencil and paper.</p><p><code class='latex inline'>y=mx+b</code> for <code class='latex inline'>m</code> (linear relations)</p>
<p>Rearrange each formula to isolate the variable indicated using pencil and paper</p><p><code class='latex inline'>C=2\pi r</code> for <code class='latex inline'>r</code> (circumference of a circle)</p>
<p>Solve each formula for the indicated variable.</p><p><code class='latex inline'>\displaystyle S=2 \pi r^{2}+2 \pi r h </code>, for <code class='latex inline'>\displaystyle h </code></p>
<p>Solve the equation for <code class='latex inline'>k</code>.</p><p><code class='latex inline'>\displaystyle r-2 k=15 </code></p>
<p>Rearrange each formula to isolate the variable indicated using pencil and paper.</p><p><code class='latex inline'>C=\pi</code><code class='latex inline'>d</code> for <code class='latex inline'>d</code> (circumference of a circle)</p>
<p>A rectangular prism with height <code class='latex inline'>h</code> and with square bases with side length <code class='latex inline'>s</code> is shown.</p><p>a. Write a formula for the surface area <code class='latex inline'>A</code> of the prism.</p><p>b. Rewrite the formula to find <code class='latex inline'>h</code> in terms of <code class='latex inline'>A</code> and <code class='latex inline'>s</code>. If <code class='latex inline'>s</code> is 10 cm and <code class='latex inline'>A</code> is <code class='latex inline'>760 cm^2</code>, what is the height of the prism?</p><p>c. Suppose <code class='latex inline'>h</code> is equal to <code class='latex inline'>s</code>. Write a formula for <code class='latex inline'>A</code> in terms of <code class='latex inline'>s</code> only.</p>
<p>Rearrange each formula to isolate the variable indicated using pencil and paper</p><p><code class='latex inline'>A=P+I</code> for <code class='latex inline'>P</code> (investments)</p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>d = mt + b</code> for <code class='latex inline'>t</code></p>
<p>Rearrange each formula to solve for the indicated variable.</p><p><code class='latex inline'>\displaystyle y=m x+b </code>, solve for <code class='latex inline'>\displaystyle b </code></p>
<p>Rearrange each formula to isolate the variable indicated using pencil and paper</p><p><code class='latex inline'>y=mx+b</code> for <code class='latex inline'>b</code> (linear relations)</p>
<p>Solve each formula for the indicated variable.</p><p><code class='latex inline'>\displaystyle I=p r t </code>, for <code class='latex inline'>\displaystyle r </code></p>
<p>Solve each problem. Round to the nearest tenth, if necessary.</p><p>You can use the formula <code class='latex inline'>a = \dfrac{h}{n}</code> to find the batting average <code class='latex inline'>a</code> of a batter who has <code class='latex inline'>h</code> hits in <code class='latex inline'>n</code> times at bat. Solve the formula for <code class='latex inline'>h</code>. If a batter has a batting average of .290 and has been at bat 300 times, how many hits does the batter have?</p>
<p>Use opposite operations to rearrange, or &quot;solve,&quot; each formula to isolate the indicated variable.</p><p><code class='latex inline'>\displaystyle P=2(l+w) </code>, for <code class='latex inline'>\displaystyle l </code></p>
<p>Rearrange each formula to solve for the indicated variable.</p><p><code class='latex inline'>\displaystyle C=2 \pi r </code>, solve for <code class='latex inline'>\displaystyle r </code></p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>P=2l+2w</code> for <code class='latex inline'>w</code> (perimeter of a rectangle)</p>
<p>Solve each formula for the indicated variable.</p><p><code class='latex inline'>\displaystyle \frac{2}{5}(x+1)=g </code></p>
<p>Solve each formula for the indicated variable.</p><p><code class='latex inline'>\displaystyle R\left(r_{1}+r_{2}\right)=r_{1} r_{2} </code>, for <code class='latex inline'>\displaystyle R </code></p>
<p>Which expression best represents the value of <code class='latex inline'>\displaystyle x </code> in <code class='latex inline'>\displaystyle y=m x+b ? </code> <code class='latex inline'>\displaystyle \begin{array}{llll}\text { () } \frac{b-y}{m} & \text { (G) } \frac{y+b}{m} & \text { (H) } m(y-b) & \text { (1) } \frac{y-b}{m}\end{array} </code></p>
<p>Use opposite operations to rearrange, or &quot;solve,&quot; each formula to isolate the indicated variable.</p><p><code class='latex inline'>\displaystyle A=\frac{1}{2}(b \times h) </code>, for <code class='latex inline'>\displaystyle b </code></p>
<p>The distance an accelerating object travels is related to its initial speed, <code class='latex inline'>v</code>, its rate of acceleration, <code class='latex inline'>a</code>, and time, <code class='latex inline'>t</code>: <code class='latex inline'>d=vt+\displaystyle{\frac{1}{2}}at^2</code></p><p>An object travels 30 m while accelerating at a rate of 6 <code class='latex inline'>m/s^2</code> for 3 s. What was its initial speed?</p>
<p>The perimeter of an isosceles triangle is given by the formula <code class='latex inline'>\displaystyle P=2 a+b </code>, where <code class='latex inline'>\displaystyle a </code> is the length of each of the equal sides and <code class='latex inline'>\displaystyle b </code> is the length of the third side.</p><img src="/qimages/157083" /><p>a) Rearrange the formula to isolate <code class='latex inline'>\displaystyle b </code>.</p><p>b) Rearrange the formula to isolate <code class='latex inline'>\displaystyle a </code>.</p><p>c) An isosceles triangle has a perimeter of <code class='latex inline'>\displaystyle 43 \mathrm{~cm} </code>. The length of the two equal sides is unknown, but the third side length is <code class='latex inline'>\displaystyle 18 \mathrm{~cm} </code>. What is the length of each of the equal sides?</p>
<p>Describe and correct the error made in solving the literal equation at the right for <code class='latex inline'>n</code>.</p><img src="/qimages/22999" />
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>d=mt+b</code> for <code class='latex inline'>m</code> (distance-time relationships)</p>
<p>Solve each equation for the given variable.</p><p><code class='latex inline'>\dfrac{x}{a} - 1 = \dfrac{y}{b}</code> for <code class='latex inline'>x</code></p>
<p>Solve each equation for <code class='latex inline'>x</code>.</p><p><code class='latex inline'>A = Bxt + C</code></p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>P=I^2R</code> for <code class='latex inline'>R</code> (electrical power)</p>
<p>To isolate <code class='latex inline'>\displaystyle x </code> in <code class='latex inline'>\displaystyle a x=b </code>, what should you divide both sides by?</p><p>Find each indicated value.</p>
<p>Solve each equation or formula for the variable specified.</p><p><code class='latex inline'>4b-5=-t</code>, for <code class='latex inline'>b</code></p>
<p>Rearrange each formula to isolate the variable indicated using pencil and paper.</p><p><code class='latex inline'>Ax+By+C=0</code> for <code class='latex inline'>y</code> (linear relations) </p>
<p>The radius of Earth&#39;s orbit is <code class='latex inline'>\displaystyle 93,000,000 </code> miles.</p><p>a. Find the circumference of Earth&#39;s orbit assuming that the orbit is a circle. The formula for the circumference of a circle is <code class='latex inline'>\displaystyle 2 \pi r </code>.</p><p>b. Earth travels at a speed of 66,698 miles per hour around the Sun. Use the formula <code class='latex inline'>\displaystyle T=\frac{C}{V} </code>, where <code class='latex inline'>\displaystyle T </code> is time in hours, <code class='latex inline'>\displaystyle C </code> is circumference, and <code class='latex inline'>\displaystyle V </code> is velocity to find the number of hours it takes Earth to revolve around the Sun.</p><p>c. Did you prove that it takes 1 year for Earth to go around the Sun? Explain.</p>
<p>Solve each equation for <code class='latex inline'>x</code>.</p><p><code class='latex inline'>\dfrac{x}{a} = \dfrac{y}{b}</code></p>
<p>Solve each equation for <code class='latex inline'>x</code>.</p><p><code class='latex inline'>y = \dfrac{x - v}{b}</code></p>
<p>For </p><p><code class='latex inline'>\displaystyle d=vt+\displaystyle{\frac{1}{2}}at^2 </code></p><p>a) Rearrange the formula to isolate <code class='latex inline'>a</code>.</p><p>b) What acceleration would be required for the object in question 15 part b) to have travelled twice the distance in the same time interval?</p>
<p>Rearrange each formula to isolate the variable indicated using pencil and paper.</p><p><code class='latex inline'>V=IR</code> for <code class='latex inline'>R</code> (voltage)</p>
<p>Rearrange each formula to isolate the variable indicated using pencil and paper.</p><p><code class='latex inline'>F=ma</code> for <code class='latex inline'>a</code> (motion)</p>
<p>Solve each formula for the indicated variable.</p><p><code class='latex inline'>\displaystyle \frac{x}{a}-5=b </code></p>
<p>The power, <code class='latex inline'>P</code>, in an electric circuit is related to the voltage, <code class='latex inline'>V</code>, and resistance, <code class='latex inline'>R</code>, by the formula <code class='latex inline'>P=\dfrac{V^2}{R}</code>.</p><p>a) Find the power, in watts (W), when the voltage is 100 V (volts) and the resistance is 50 <code class='latex inline'>\Omega</code> (ohms).</p><p>b) What is the resistance of a circuit that uses 100 W of power with a voltage of 20 V?</p><p>c) The resistance of a circuit is 15 <code class='latex inline'>\Omega</code>. The same circuit uses 60 W of power. Find the voltage in the circuit.</p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>P=2l+2w</code> for <code class='latex inline'>l</code> (perimeter of a rectangle)</p>
<p>Solve each equation if the domain is {􏰸-3, -􏰸1, 2, 5, 8}.</p><p><code class='latex inline'>y=x-5</code></p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>P = a + b + c</code> for <code class='latex inline'>a</code></p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>F=ma</code> for <code class='latex inline'>m</code> (motion)</p>
<p>Rearrange each formula to solve for the indicated variable.</p><p><code class='latex inline'>\displaystyle P=2 l+2 w </code>, solve for <code class='latex inline'>\displaystyle l </code></p>
<p>Solve each equation or formula for the variable specified.</p><p><code class='latex inline'>a(y+1)=b</code>, for <code class='latex inline'>y</code></p>
<p>Solve each equation for <code class='latex inline'>x</code>.</p><p><code class='latex inline'>ax - x = c</code></p>
<p>Solve each formula for the indicated variable.</p><p><code class='latex inline'>\displaystyle s=\frac{1}{2} g t^{2} </code>, for <code class='latex inline'>\displaystyle g </code></p>
<p>NFL quarterbacks are rated for their passing performance by a type of weighted average as described in the formula below.</p><p><code class='latex inline'>R=[50+2000(C\div A)+8000(T\div A)-10,000(I\div A) +100(Y\div A)]\div24</code></p><p>In this formula,</p><p>• R represents the rating,</p><p>• C represents number of completions,</p><p>• A represents the number of passing attempts,</p><p>• T represents the number to touchdown passes,</p><p>• I represents the number of interceptions, and</p><p>• Y represents the number of yards gained by passing.</p><p>In the 2000 season, Daunte Culpepper had 297 completions, 474 passing attempts, 33 touchdown passes, 16 interceptions, and 3937 passing yards. What was his rating for that year?</p>
<p>Solve each equation or formula for the variable specified.</p><p><code class='latex inline'>h=at-0.25vt^2</code>, for <code class='latex inline'>a</code></p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>A=\pi r^2</code> for <code class='latex inline'>r</code> (area of a circle)</p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>y=mx+b</code> for <code class='latex inline'>x</code> (linear relations)</p>
<p>Solve each equation for the given variable.</p><p><code class='latex inline'>C = \dfrac{5}{9}(F - 32)</code> for <code class='latex inline'>F</code></p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>V=IR</code> for <code class='latex inline'>I</code> (voltage)</p>
<p>Suppose a segment on a number line has endpoints with coordinates <code class='latex inline'>a</code> and <code class='latex inline'>b</code>. The coordinate of the segment&#39;s midpoint <code class='latex inline'>m</code> is given by the formula <code class='latex inline'>m = \dfrac{a + b}{2}</code>.</p><p>a. Find the midpoint of a segment with endpoints at 9.3 and 2.1.</p><p>b. Rewrite the given formula to find <code class='latex inline'>b</code> in terms of <code class='latex inline'>a</code> and <code class='latex inline'>m</code>.</p><p>c. The midpoint of a segment is 3.5. One endpoint is at 8.9. Find the other endpoint.</p>
<p>Solve each equation for <code class='latex inline'>x</code>.</p><p><code class='latex inline'>4(x - b) = x</code></p>
<p>Solve the equation for <code class='latex inline'>k</code>.</p><p><code class='latex inline'>\displaystyle 4 k+h=-2 k-14 </code></p>
<p>Rearrange each formula to solve for the indicated variable.</p><p><code class='latex inline'>\displaystyle A=\frac{b h}{2} </code>, solve for <code class='latex inline'>\displaystyle h </code></p>
<p>Solve for x.</p><p><code class='latex inline'>\displaystyle \frac{a}{b}(2 x-12)=\frac{c}{d} </code></p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>P = 2(l + w)</code>, for <code class='latex inline'>l</code></p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>A=s^2</code> for <code class='latex inline'>s</code> (area of a square)</p>
<p>The period (time for one complete swing back and forth) <code class='latex inline'>p</code>, in seconds, of a pendulum is related to its length, <code class='latex inline'>L</code>, in metres, by the formula <code class='latex inline'>p=2\pi \sqrt{\displaystyle{\frac{L}{g}}}</code>, where <code class='latex inline'>g=9.8m/s^2</code> is a constant. Solve this formula for <code class='latex inline'>L</code>, and find the length needed for the pendulum to have a period of 1 s.</p>
<p>Write an equation and solve for the variable specified.</p><p>Five minus twice a number <code class='latex inline'>p</code> equals six times another number <code class='latex inline'>q</code> plus one. Solve for <code class='latex inline'>p</code>.</p>
<p>The distance an accelerating object travels is related to its initial speed, <code class='latex inline'>v</code>, its rate of acceleration, <code class='latex inline'>a</code>, and time, <code class='latex inline'>t</code>: <code class='latex inline'>d=vt+\displaystyle{\frac{1}{2}}at^2</code></p><p>Rearrange this formula to isolate <code class='latex inline'>v</code>.</p>
<p>The formula for keyboarding speed <code class='latex inline'>(s)</code> is <code class='latex inline'>s=\displaystyle{\frac{w-10e}{t}}</code>, where <code class='latex inline'>e</code> is the number of errors, <code class='latex inline'>w</code> is the number of words typed, and <code class='latex inline'>t</code> is the time, in minutes. Solve the formula for <code class='latex inline'>e</code> and find the number of errors made by Sara, who typed 400 words in 5 min, and had a keyboarding speed of 70 words per minute.</p>
<p>Solve for x.</p><p><code class='latex inline'>\displaystyle \frac{a-c}{x-a}=m </code></p>
<p>Rearrange each formula to isolate the variable indicated using pencil and paper</p><p><code class='latex inline'>P=4s</code> for <code class='latex inline'>s</code> (perimeter of a square)</p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>V=\pi r^2h</code> for <code class='latex inline'>h</code> (volume of a cylinder)</p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>A=\pi r^2</code> for <code class='latex inline'>r</code> (area of a circle)</p>
<p>Solve each equation for <code class='latex inline'>x</code>.</p><p><code class='latex inline'>mx + nx = p</code></p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>d =2r</code>, for <code class='latex inline'>r</code></p>
<p>Solve each equation or formula for the variable specified.</p><p><code class='latex inline'>\frac{5x+y}{a}=2</code>, for <code class='latex inline'>a</code></p>
<p>The equation for the perimeter of a rectangle is <code class='latex inline'>P=2l+2w</code>. Suppose the perimeter of rectangle <code class='latex inline'>ABCD</code> is 24 centimeters.</p><p>Choose five values for <code class='latex inline'>w</code> and find the corresponding values of <code class='latex inline'>l</code> 􏶏.</p>
<p>Rearrange each formula to isolate the variable indicated using pencil and paper.</p><p><code class='latex inline'>d=vt</code> for <code class='latex inline'>t</code> (distance)</p>
<p>Rearrange each formula to solve for the indicated variable.</p><p><code class='latex inline'>\displaystyle V=l w h </code>, solve for <code class='latex inline'>\displaystyle h </code></p>
<p>Solve <code class='latex inline'>\triangle ABC</code>, if <code class='latex inline'>\angle A =</code> 58°, <code class='latex inline'>b= 10.0</code>cm,and <code class='latex inline'>c = 14.0</code> cm.</p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>V=s^3</code> for <code class='latex inline'>s</code> (volume of a cube)</p>
<p>Solve each equation for the given variable.</p><p><code class='latex inline'>ax + 2xy = 14</code> for <code class='latex inline'>y</code></p>
<p>Solve each formula for the indicated variable.</p><p><code class='latex inline'>\displaystyle v=s^{2}+\frac{1}{2} s h </code>, for <code class='latex inline'>\displaystyle h </code></p>
<p>The equation <code class='latex inline'>\displaystyle s=\frac{w-10 e}{t} </code> models the speed in words per minute, <code class='latex inline'>\displaystyle s </code>, at which someone types. The speed, <code class='latex inline'>\displaystyle s </code>, is related to the number of words typed, <code class='latex inline'>\displaystyle w </code>, the number of errors, <code class='latex inline'>\displaystyle e </code>, and the time spent typing in minutes, <code class='latex inline'>\displaystyle t </code>.</p><p>Alex types 525 words in <code class='latex inline'>\displaystyle 5 \mathrm{~min} </code>, with 10 errors. What is Alex&#39;s typing speed?</p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>c^2=a^2+b^2</code> for <code class='latex inline'>a</code> (Pythagorean theorem)</p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>P=2l+2w</code> for <code class='latex inline'>w</code> (perimeter of a rectangle)</p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>A = P + I</code>, for <code class='latex inline'>P</code></p>
<p>Solve each equation or formula for the variable specified.</p><p><code class='latex inline'>\frac{3ax-n}{5}=-4</code>, for <code class='latex inline'>x</code></p>
<p>The equation for the perimeter of a rectangle is <code class='latex inline'>P=2l+2w</code>. Suppose the perimeter of rectangle <code class='latex inline'>ABCD</code> is 24 centimeters.</p><p>Solve the equation for 􏶏<code class='latex inline'>l</code>.</p>
<p>The relationship between Celsius and Fahrenheit is represented by <code class='latex inline'>C = \dfrac{5}{9}(F - 32)</code></p> <ul> <li>Determine the Celsius temperature that is equivalent to <code class='latex inline'>58 ^oF</code>.</li> </ul>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>v =u + at</code>, for <code class='latex inline'>a</code></p>
<img src="/qimages/42509" /><p>USING STRUCTURE Use the values <code class='latex inline'>\displaystyle -2,5,9 </code>, and 10 to complete each statement about the equation <code class='latex inline'>\displaystyle a x=b-5 </code>.</p><p>a. When <code class='latex inline'>\displaystyle a=\underline{\text { and } b=}, x </code> is a positive integer.</p><p>b. When <code class='latex inline'>\displaystyle a=\underline{\text { and } b=}, x </code> is a negative integer.</p>
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>a=\displaystyle{\frac{v}{t}}</code> for <code class='latex inline'>v</code> (acceleration)</p>
<p>Solve each equation or formula for the variable specified.</p><p><code class='latex inline'>km+5x=6y</code>, for <code class='latex inline'>m</code></p>
<p>Solve each equation for <code class='latex inline'>x</code>.</p><p><code class='latex inline'>S = C +xC</code></p>
<p><code class='latex inline'>\displaystyle a=1,052+1.08 t </code></p><p>The speed of a sound wave in air depends on the air temperature. The formula above shows the relationship between <code class='latex inline'> a </code> , the speed of a sound wave, in feet per second, and <code class='latex inline'> t </code> , the air temperature, in degrees Fahrenheit <code class='latex inline'> \left({ }^{\circ} \mathrm{F}\right) </code> .</p><p>Which of the following expresses the air temperature in terms of the speed of a sound wave?</p><p>(A) <code class='latex inline'>\displaystyle t=\frac{a-1,052}{1.08} </code></p><p>(B) <code class='latex inline'>\displaystyle t=\frac{a+1,052}{1.08} </code></p><p>(C) <code class='latex inline'>\displaystyle t=\frac{1,052-a}{1.08} </code></p><p>(D) <code class='latex inline'>\displaystyle t=\frac{1.08}{a+1,052} </code></p>
<p>Use the formula for the area of a trapezoid.</p><img src="/qimages/24548" /><p>Solve the formula for <code class='latex inline'>h</code>.</p>
<p>Rearrange each formula to isolate the variable indicated using pencil and paper.</p><p><code class='latex inline'>A=P+I</code> for <code class='latex inline'>I</code> (investments)</p>
<p>Rearrange each formula to solve for the indicated variable.</p><p><code class='latex inline'>\displaystyle A=l w </code>, solve for <code class='latex inline'>\displaystyle w </code></p>
<p>Rearrange each formula to isolate the variable indicated.</p><p> <code class='latex inline'>P=I^2R</code> for <code class='latex inline'>I</code> (electrical)</p>
<p>Use opposite operations to rearrange, or &quot;solve,&quot; each formula to isolate the indicated variable.</p><p><code class='latex inline'>\displaystyle P=\frac{E}{t} </code>, for <code class='latex inline'>\displaystyle E </code></p>
<p>Solve the formula for the indicated variable.</p><img src="/qimages/44204" />
<p>Rearrange each formula to isolate the variable indicated.</p><p><code class='latex inline'>a = \frac{F }{m}</code> for <code class='latex inline'>F</code></p>
<p>Solve for x.</p><p><code class='latex inline'>\displaystyle a(3 t x-2 b)=c(d x-2) </code></p>
<p>Solve each equation for <code class='latex inline'>\displaystyle y . </code></p><p><code class='latex inline'>\displaystyle 12 y=3 x </code></p>
<p>The equation for the perimeter of a rectangle is <code class='latex inline'>P=2l+2w</code>. Suppose the perimeter of rectangle <code class='latex inline'>ABCD</code> is 24 centimeters.</p><p>State the independent and dependent variables.</p>
<p>A person&#39;s index of cardiorespiratory fitness can be found by taking three 30 -s pulse measurements over the course of one workout. The index is determined by the formula <code class='latex inline'>\displaystyle I=\frac{50 d}{a+b+c} </code></p><p>where <code class='latex inline'>\displaystyle I </code> represents the fitness index, <code class='latex inline'>\displaystyle d </code> represents the duration of the physical activity in seconds, and <code class='latex inline'>\displaystyle a, b </code>, and <code class='latex inline'>\displaystyle c </code> are the three 30 -s pulse measurements. If a fitness index of <code class='latex inline'>\displaystyle 73.5 </code> is found over a 5 -min high-impact physical activity with two pulse measurements of 70 and 60 being recorded, what is the third pulse measurement?</p>
<p>Solve each equation or formula for the variable specified.</p><p><code class='latex inline'>\frac{by+2}{3}=c</code>, for <code class='latex inline'>y</code></p>
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