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VikaD [51]
3 years ago
5

(Geometry) The answers are x = 15 and y = 9 but I don't know how. Help me understand this

Mathematics
1 answer:
Kryger [21]3 years ago
4 0

Check the picture below.

\bf \stackrel{\measuredangle DAC}{4y+2x}~~=~~\stackrel{\measuredangle BCA}{9y-x}\implies 2x=5y-x\implies 3x=5y\implies \boxed{x=\cfrac{5y}{3}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle DAB}{[(4y+2x)+35]}~~+~~\stackrel{\measuredangle ADC}{5x+4}~~=~~180\implies 4y+2x+5x+39 = 180 \\\\\\ 4y+7x+39=180\implies 4y+7x=141\implies \stackrel{\textit{substituting "x"}}{4y+7\left( \boxed{\cfrac{5y}{3}} \right)} = 141

\bf 4y+\cfrac{35y}{3}=141\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( 4y+\cfrac{35y}{3} \right)=3(141)}\implies 12y+35y=423 \\\\\\ 47y=423\implies y=\cfrac{423}{47}\implies \blacktriangleright y = 9 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{x=\cfrac{5y}{3}}\implies x = \cfrac{5(9)}{3}\implies \blacktriangleright x = 15 \blacktriangleleft

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2 years ago
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3 years ago
Write an expression that means "eight less than the product of seven and m"
daser333 [38]

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8 0
2 years ago
Tom and Jimmy plan to leave at the same time from home and
raketka [301]

To find the distance between the homes of Tom and Jimmy, it is assumed

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Reasons:

The direction in which Tom and Jimmy walks = Towards each other

The speed at which Tom walks = 52 meters per minute

The speed with which Jimmy walks = 70 meters per minute

The time at which Tom leaves = 4 minutes earlier than Jimmy

The point at which they meet = The café

The rate of their speed = Constant

Required:

The distance between Tom and Jimmy home.

Solution:

Tom and Jimmy had a plan to walk at the same speed and meet up at the café.

We have;

The café is equal distance from Tom and Jimmy's houses.

Which gives the following simultaneous equation.

52 × (4 + t) = The distance of Tom's house from the café

70 × t = The distance of Jimmy's  house from the café

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52 × 4 = 70 × t - 52 × t = 18 × t

\displaystyle t = \frac{52 \times 4}{18}  = \frac{104}{9} = 11.\overline{6}

The time it take Jimmy to reach the café, <em>t</em> = \mathbf{11.\overline6} minutes

The distance between their homes, d = 52 × (4 + t) + 70 × t

∴ d = 52 × (4 + 11.\overline6) + 70 × 11.\overline6 = 1,617.\mathbf{\overline 7}

  • The distance between Tom and Jimmy's home = 1,617.\overline 7 meters

Learn more about simultaneous equations here:

brainly.com/question/12413726

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2 years ago
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Kobotan [32]

Answer:

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hope this helps

4 0
2 years ago
Read 2 more answers
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