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Anna [14]
2 years ago
8

Series of math questions

Mathematics
1 answer:
nordsb [41]2 years ago
8 0

\huge\fbox{Answer ☘}

<h2>1 ) </h2>

when x = 3 ; y = 2

\bold\blue{✯\:\:\:2x + y}

substitue x = 3 and y = 2 in the given equation !

\bold{2(3) + 2 = 6 + 2 } \\  \bold{ =  > 8}

<h2>—————————————</h2>

<h2>2 ) </h2>

We've to divide 328 in the ratio of 1 : 3

let the respective distribution be x and 3x.

Then ,

\bold{x + 3x = 328} \\\bold{ 4x = 328 }\\ \bold{x =  \cancel\frac{328}{4} } \\  \\ \bold{x = 82}

the respective shares are :

x = $82

3x = $246

<h2>—————————————</h2>

<h2>3 ) </h2>

6 pens cost $90

therefore ,

cost of 1 pen =

\cancel \frac{90}{6}  = 15 \\

further ,

cost of 9 such pens = $15 × 9 = $135

<h2>—————————————</h2>

<h2>4 )</h2>

0.5 of a pound = 113.398 grams

<h2>—————————————</h2>

hope helpful~

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Find the center, vertices, and foci for the ellipse 25x^2 + 64y^2 = 1600
Alisiya [41]

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Equation               25x² + 64y² = 1600

Process

1.- Divide all the equation by 1600

                             25x²/1600 + 64y²/ 1600 = 1600/1600

-Simplify

                              x²/64 + y²/ 25 = 1

2.- Equation of a horizontal ellipse

                             \frac{x^{2} }{a^{2}} + \frac{y^{2}}{b^{2}} = 1

3.- Find a, b and c

    a² = 64             a = 8

    b² = 25             b = 5

-Calculate c with the Pythagorean theorem

                   a² = b² + c²

-Solve for c

                   c² = a² - b²

-Substitution

                   c² = 8² - 5²

-Simplification

                  c² = 64 - 25

                  c² = 39

-Result

                  c = √13

4.- Find the center

          C = (0, 0)

5.- Find the vertices

          V1 = (-8, 0)     V2 = (8, 0)

6.- Find the foci

          F1 = (-√13, 0)   F2 = (√13, 0)

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