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2 years ago

7

Half of Ethan's string is equal to 2/3 of Kayla's string. The total length of their strings is 10 feet. How much longer is Ethan

's string than Kayla's? Drawing

2 answers:

IgorC [24]2 years ago

5 0

Answer:

Ethan's string is $=\frac{10}{7}$ feet longer than Kayla's string.

Step-by-step explanation:

Let Ethan's string = x feet

and Kayla's string = y feet

According to question,

Half of Ethan's string is equal to 2/3 of Kayla's string that is,

$\frac{1}{2}x=\frac{2}{3}y$

$\Rightarrow x=\frac{4}{3}y$ ..............(1)

Also,The total length of their strings is 10 feet that is,

$x+y=10$

Put value of x from (1),

$\frac{4}{3}y+y=10$

Solving for y, we get,

$\Rightarrow y(\frac{4}{3}+1)=10$

$\Rightarrow y(\frac{4+3}{3})=10$

$\Rightarrow y(\frac{7}{3})=10$

$\Rightarrow y=\frac{10 \times 3}{7}$

$\Rightarrow y=\frac{30}{7}$

Thus, Length of Kayla's string is $\frac{30}{7}$ feet.

and Put value of y in (1) to get value of x,

$\Rightarrow x=\frac{4}{3} \times \frac{30}{7}$

$\Rightarrow x=\frac{40}{7}$

Thus, Length of Ethan's string is $\frac{40}{7}$ feet.

Length of Ethan's string is longer than Kayla's string = Length of Ethan's string-Length of Kayla's string.

$=\frac{40}{7}-\frac{30}{7}$

$=\frac{10}{7}$

Thus, Ethan's string is $=\frac{10}{7}$ feet longer than Kayla's string.

german2 years ago

3 0

Answer: $\frac{10}{7}$ meters

Step-by-step explanation:

Let x be the length of Kaya's string and y be the length of Ethan's string

Then According to the question, we have the following equations

$\frac{1}{2}y=\frac{2}{3}x\\\Rightarrow\ y=\frac{4}{3}x......(1)\\x+y=10....(2)$

Substitute the value of y from (1) in (2), we get

$\frac{4}{3}x+x=10\\\Rightarrow\frac{4x+3x}{3}=10\\\Rightarrow\ \frac{7x}{3}=10\\\Rightarrow\ x=\frac{30}{7}$

The length of Kaya's string = $\frac{30}{7}$ feet

The length of Ethan's string = $\frac{4}{3}\times\frac{30}{7}=\frac{40}{7}$ meters

The difference in their lengths= $\frac{40}{7}-\frac{30}{7}=\frac{10}{7}$

Hence, Ethan's string is $\frac{10}{7}$ meters longer than the Kaya's string.

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Answer:

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Step-by-step explanation:

We have that:

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<em>The translation that maps the vertex of the graph of the function f(x) = x² onto the vertex of the function g(x) = x² - 10x + 2 is </em><u>5 units to the right and 23 units down.</u>

Explanation:

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The general form of a quadratic equation is Ax² + Bx + C = 0, where A ≠ 0, and B and C may be any real number. And the graph of such equation is a parabola with a minimum or maximum value at its vertex.

The vertex form of the graph of such function is: A(x - h)² + k

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The method is transforming the form of the function by completing squares:

Subtract 2 from both sides: g(x) - 2 = x² - 10x

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Subtract 23 from both sides: g(x) = (x - 5)² - 23

That is the searched vertex form: g(x) = (x - 5)² - 23.

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