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3 years ago

Urgent help ! similar figures use the similarity relationship to find the indicated value

Mathematics

1 answer:

masya89 [10]3 years ago

5 0

Answer:

FE = 28 and YZ = 28

Step-by-step explanation:

In similar triangles the ratios of corresponding sides are equal.

(4)

$\frac{BC}{FG}$ = $\frac{BD}{FE}$ , substitute values

$\frac{39}{4x+2}$ = $\frac{42}{5x-2}$ ( cross- multiply )

39(5x - 2) = 42(4x + 2) ← distribute parenthesis on both sides

195x - 78 = 168x + 84 ( subtract 168x from both sides )

27x - 78 = 84 ( add 78 to both sides )

27x = 162 ( divide both sides by 27 )

x = 6

Thus

FE = 5x - 2 = 5(6) - 2 = 30 - 2 = 28

(5)

$\frac{ST}{SZ}$ = $\frac{RT}{YZ}$ , substitute values

$\frac{40}{35}$ = $\frac{3x-7}{2x+2}$ ( cross- multiply )

35(3x - 7) = 40(2x + 2) ← distribute parenthesis on both sides

105x - 245 = 80x + 80 ( subtract 80x from both sides )

25x - 245 = 80 ( add 245 to both sides )

25x = 325 ( divide both sides by 25 )

x = 13

Thus

YZ = 2x + 2 = 2(13) + 2 = 26 + 2 = 28

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Julia is going to the store to buy candies. Small candies cost $4 and extra-large candies cost $12.She needs to purchase at leas

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Small candies $=9$

Extra large candies $=12$

Step-by-step explanation:

Let small candies $=x$

Extra large candies $=y$

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$x+y\geq20$

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Solve for

$x+y=20.......(1)\\4x+12y=180.....(2)\\eqn(2)-eqn(1)\times4\\8y=100\\y=\frac{100}{8} \\y=\frac{25}{8} \\from\ eqn(1)\\x+\frac{25}{2}=20\\ x=20-\frac{25}{2} \\x=\frac{15}{2}$