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Solve linear equations with variables on both sides: word problems

ixl.com/math/grade−7-7/percent-of-change\newlineRelaunch to update\newlineApps\newlineGC G C \newlineSlsd\newlineBathroom\newlineYouTube\newlineAmazon.com Shop...\newlineSouthern Lehigh S... Γ \quad \mathbf{\Gamma} Chat Now! - Powe...\newlineDiscorery Atlas: ln⁡… \ln \ldots \newlinePlay Blooket\newlineAmazon.com Shop...\newlineAll Bookm\newline□1 \square \sqrt{1} \newlineMy IXL\newlineLearning\newlineAssessment\newlineAnalytics\newlineCaleah\newlineSeventh grade\newline00.1010 Percent of change\newlineBL77\newlineYou have prizes to reveal! Go to your game board.\newlineVideo\newlineQuestions\newlineWhat is the percent of change from 7575 to 3636 ?\newline52% 52 \% increase\newline64% 64 \% increase\newline52% 52 \% decrease\newline64% 64 \% decrease\newline22\newlineSmartScore\newlineout of 100100\newlineSubmit\newline1010\newlineWork it out\newlineNot feeling ready yet? These can help:\newlineAdd, subtract, multiply, or divide two decimals\newlineConvert between percents, fractions, and decimals\newlineSolve percent problems using strip models\newlineLesson: Percent change\newlineCompany | Blog | Help center | User guides | Tell us what you think | Testimonials | Contact us | Terms of service | Privacy policy\newline(22)LEEARNING (c) 20242024 IXL. Learning. All rights reserved.
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11. Diketahui matriks B berordo 2×2 2 \times 2 , yaitu:\newlineB=[2413] B=\left[\begin{array}{ll} 2 & 4 \\ 1 & 3 \end{array}\right] \newline⇒ \Rightarrow Menentukan determinan dengan operasi baris elementer, yaitu:\newlineB=[2413]⟶B1↔B2B=[1324]B=[2524]b \begin{array}{l} B=\left[\begin{array}{ll} 2 & 4 \\ 1 & 3 \end{array}\right] \underset{B 1 \leftrightarrow B 2}{\longrightarrow} B=\left[\begin{array}{ll} 1 & 3 \\ 2 & 4 \end{array}\right] \\ B=\left[\begin{array}{lll} 2 & 5 \\ 2 & 4 \end{array}\right] b \\ \end{array} \newline⇒ \Rightarrow Maka determinan dari matriks B B adalah :\newline∼det⁡(B)=(a×d)−(b×c)=(2×4)−(5×2)=8−10=−2 \begin{aligned} \sim \operatorname{det}(B) & =(a \times d)-(b \times c) \\ & =(2 \times 4)-(5 \times 2) \\ & =8-10 \\ & =-2 \end{aligned}
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Twin Rivers has a population of 90,80090,800, and its population has been increasing by 800800 people each year. White Stone has a population of 87,20087,200, and its population has been increasing by 1,2001,200 people each year. These trends in population change are expected to continue.\newlineWhich equation can you use to find tt, the number of years it will take for the two cities to have the same population?\newlineChoices:\newline(A) 90,800+800t=87,200+1,200t90,800 + 800t = 87,200 + 1,200t\newline(B) 90,800−800t=87,200+1,200t90,800 - 800t = 87,200 + 1,200t\newlineHow long will it take for the two cities to have the same population?\newlineSimplify any fractions.\newline____ years\newline
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Jeanette and Carlos are participating in a novel-writing challenge. Jeanette has already started her novel and has written 4848 pages so far. She will write an additional 44 pages each week. Carlos is just getting started, and he will write 1010 pages each week.\newlineWhich equation can you use to find ww, the number of weeks it will take for Carlos to write as many pages as Jeanette?\newlineChoices:\newline(A) 48+4w=10w48 + 4w = 10w\newline(B) 48+10w=4w48 + 10w = 4w\newlineHow long will it take for Carlos to have written as many pages as Jeanette?\newline____\_\_\_\_ weeks\newline
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Rashida was asked to determine whether f(x)=x2−∣x∣ f(x)=x^{2}-|x| is even, odd, or neither. Here is her work:\newlineStep 11: Find expression for f(−x) f(-x) \newlinef(−x)=(−x)2−∣(−x)∣=x2+∣x∣ \begin{aligned} f(-x) & =(-x)^{2}-|(-x)| \\ & =x^{2}+|x| \end{aligned} \newlineStep 22: Check if f(−x) f(-x) is equal to f(x) f(x) or −f(x) -f(x) \newlinex2+∣x∣ x^{2}+|x| isn't the same as f(x)=x2−∣x∣ f(x)=x^{2}-|x| or −f(x)=−x2+∣x∣ -f(x)=-x^{2}+|x| .\newlineStep 33: Conclusion\newlinef(−x) f(-x) isn't equivalent to either f(x) f(x) or −f(x) -f(x) , so f f is neither even nor odd.\newlineIs Rashida's work correct? If not, what is the first step where Rashida made a mistake?\newlineChoose 11 answer:\newline(A) Rashida's work is correct.\newline(B) Rashida's work is incorrect. She first made a mistake in Step 11.\newline(C) Rashida's work is incorrect. She first made a mistake in Step 22.\newline(D) Rashida's work is incorrect. She first made a mistake in Step 33.
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Felix was asked whether the following equation is an identity:\newline(x2+1)2=(x2−1)2+(2x)2 \left(x^{2}+1\right)^{2}=\left(x^{2}-1\right)^{2}+(2 x)^{2} \newlineHe performed the following steps:\newline(x2+1)2 \left(x^{2}+1\right)^{2} \newline↪ Step 1=x4+x2+x2+1 \stackrel{\text { Step } 1}{\hookrightarrow}=x^{4}+x^{2}+x^{2}+1 \newline↪ Step 2=x4+2x2+1 \stackrel{\text { Step } 2}{\hookrightarrow}=x^{4}+2 x^{2}+1 \newline↪ Step 3=x4+2x2+1−2x2+2x2 \stackrel{\text { Step } 3}{\hookrightarrow}=x^{4}+2 x^{2}+1-2 x^{2}+2 x^{2} \newline↪ Step 4=(x4−2x2+1)+4x2 \stackrel{\text { Step } 4}{\hookrightarrow}=\left(x^{4}-2 x^{2}+1\right)+4 x^{2} \newline↪ Step 5=(x2−1)2+(2x)2 \stackrel{\text { Step } 5}{\hookrightarrow}=\left(x^{2}-1\right)^{2}+(2 x)^{2} \newlineFor this reason, Felix stated that the equation is a true identity.\newlineIs Felix correct? If not, in which step did he make a mistake?\newlineChoose 11 answer:\newline(A) Felix is correct.\newline(B) Felix is incorrect. He made a mistake in step 11.\newline(C) Felix is incorrect. He made a mistake in step 33.\newline(D) Felix is incorrect. He made a mistake in step 55.
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Philip is downloading applications (apps) and songs to his tablet. He downloads 77 apps and 66 songs. Each song takes an average of 00.88 minutes longer to download than each app. If it takes 2121.77 minutes for his downloads to finish, which of the following systems could be used to approximate a a , the average number of minutes it takes to download one app, and s s , the average number of minutes it takes to download one song?\newlineChoose 11 answer:\newline(A) a+s=21.7 a+s=21.7 \newline6s=7a−0.8 6 s=7 a-0.8 \newline(B) a+s=21.7 a+s=21.7 \newline7a=6s−0.8 7 a=6 s-0.8 \newline(C) 7a+6s=21.7 7 a+6 s=21.7 \newlines=a−0.8 s=a-0.8 \newline(D) 7a+6s=21.7 7 a+6 s=21.7 \newlinea=s−0.8 a=s-0.8
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