Could someone please help me with this math problem? NO LINKS!! I will give brainliest!!

Mathematics

1 answer:

Marat540 [252]2 years ago

7 0

Answer:

y = (x + 1)²

Step-by-step explanation:

y = 1 + x² + 2x

⇒ x² + 2x + 1 = y

⇒ (x + 1)(x + 1) = y

⇒ (x + 1)² = y

y-intercept when x = 0:

(0 + 1)² = 1² = 1

Therefore, intercepts the y-axis at (0, 1)

x-intercept when y = 0

(x + 1)² = 0

x + 1 = 0

x = -1

Therefore, intercepts (touches) x-axis at (-1, 0)

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Three friends met for a book club at a coffee shop, each friend ordered a cup of coffee and two donuts. the total of the order w

4vir4ik [10]

Answer:

$Cost\ of\ donut=\frac{49}{24}\approx \$2.042\\\\cost\ of\ donuts=\frac{49}{4}\approx \$12.25$

Step-by-step explanation:

$Let\ cost\ of\ coffee=y\\\\cost\ of\ one\ donut=x\\\\Each\ friend\ buy\ one\ coffee\ and\ two\ donuts\\\\Amount\ for\ 1\ friend=Cost\ of\ coffee+2\times cost\ of\ donut\\\\Amount\ for\ 1\ friend=y+2x\\\\Amount\ required\ for\ 3\ friend=3\times Amount\ for\ 1\ friend\\\\Amount\ required\ for\ 3\ friend=3\times (y+2x)\\\\Amount\ required\ for\ 3\ friend=3y+6x\\\\Total\ bill=\$ 22\\\\3y+2x=22\\\\Given\ cost\ of\ coffee=\$3.25\\\\y=\$3.25$

$Hence\ solution\ of\ following\ system\ of\ equation\ will\ give\ cost\ of\ donut:\\\\3y+6x=22\\\\y=3.25\\\\\\Substitute\ y=3.25\ in\ first\ equation\\\\3\times 3.25+6x=22\\\\9.75+6x=22\\\\6x=22-9.75\\\\6x=12.25\\\\x=\frac{12.25}{6}\\\\x=\frac{49}{24}\approx \$2.042\\\\Cost\ of\ donut=\frac{49}{24}\approx \$2.042$

See attached diagram.

$Each\ friend\ takes\ 2\ donuts\\\\Total\ donuts=Number\ of\ friends\times 2\\\\Total\ donuts=3\times 2=6\\\\cost\ of\ donuts=number\ of\ donuts\times cost\ of\ 1\ donut\\\\cost\ of\ donuts=6\times \frac{49}{24}\\\\cost\ of\ donuts=\frac{49}{4}\approx \$12.25$