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Greeley [361]
3 years ago
5

4y - 7 = 5x2 - x + 2 + 3y

Mathematics
1 answer:
zalisa [80]3 years ago
6 0

Answer:

y = 9 + -1x + 5x2

Step-by-step explanation:

Simplifying

4y + -7 = 5x2 + -1x + 2 + 3y

Reorder the terms:

-7 + 4y = 5x2 + -1x + 2 + 3y

Reorder the terms:

-7 + 4y = 2 + -1x + 5x2 + 3y

Solving

-7 + 4y = 2 + -1x + 5x2 + 3y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-3y' to each side of the equation.

-7 + 4y + -3y = 2 + -1x + 5x2 + 3y + -3y

Combine like terms: 4y + -3y = 1y

-7 + 1y = 2 + -1x + 5x2 + 3y + -3y

Combine like terms: 3y + -3y = 0

-7 + 1y = 2 + -1x + 5x2 + 0

-7 + 1y = 2 + -1x + 5x2

Add '7' to each side of the equation.

-7 + 7 + 1y = 2 + -1x + 7 + 5x2

Combine like terms: -7 + 7 = 0

0 + 1y = 2 + -1x + 7 + 5x2

1y = 2 + -1x + 7 + 5x2

Reorder the terms:

1y = 2 + 7 + -1x + 5x2

Combine like terms: 2 + 7 = 9

1y = 9 + -1x + 5x2

Divide each side by '1'.

y = 9 + -1x + 5x2

Simplifying

y = 9 + -1x + 5x2

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3 years ago
Two corresponding sides of similar triangles are 2 cm and 5 cm. What is the area of the second triangle if the area of the first
Stella [2.4K]

Answer:

(1) Area of second triangle= 50 cm^2.

(2) Area of ΔABC=98 cm^2.

   and Area of ΔDFG=175 cm^2.

Step-by-step explanation:

<em>" For two similar triangles the ratio of sides is equal to the ratio of square of their areas".</em>

i.e. if a,b are the corresponding sides of two similar triangles and let A and B denote the area of two triangles then we have the relation as:

\dfrac{a^2}{b^2}=\dfrac{A}{B}

(1)

for the first question:

we have a=2, b=5.

A=8 cm^2.

Hence,

\dfrac{2^2}{5^2}=\dfrac{8}{B}\\\\\dfrac{4}{25}=\dfrac{8}{B}

B=50 cm^2.

Hence, the area of second triangle is 50 cm^2.

(2)

In second option we have:

a=6 and b=5.

A-B=77 cm^2.

A=77+B

\dfrac{6^2}{5^2}=\dfrac{A}{B}\\  \\\dfrac{36}{25}=\dfrac{77+B}{B}\\  \\36B=25\times77+25B\\\\36B-25B=25\times77\\\\11B=25\times77\\\\B=25\times7\\\\B=175

Hence area of second triangle i.e. ΔDFG is 175 cm^2.

and area of first triangle i.e. ΔABC=175-77=98 cm^2.




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2 years ago
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VikaD [51]

Answer:

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Step-by-step explanation:


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Using graphing technology, (see the graph)  they intersect at x≈-1 and x≈8.1

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