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2 years ago

PLEASE HELP find the vertex of f(x)=x^2+2x+3 (make sure you show your work)

Mathematics

1 answer:

kotegsom [21]2 years ago

4 0

Answer:

(- 1, 2)

Step-by-step explanation:

Given a quadratic in standard form y = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

$x_{vertex}$ = - $\frac{b}{2a}$

f(x) = x² + 2x + 3 ← is in standard form

with a = 1 and b = 2, hence

$x_{vertex}$ = - $\frac{2}{2}$ = - 1

Substitute x = - 1 into f(x) for corresponding value of y

f(- 1) = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2

vertex = (- 1, 2 )

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a pentagon is a regular pentagon that has 5 sides, so each side has the same length that is (x - 1.5)cm. The perimeter is 22.5 c

Ivanshal [37]

Answer:

Step-by-step explanation:

5(x - 1.5) = 22.5

5x - 7.5 = 22.5

5x = 15

x = 3

8 0

2 years ago

A car starts with a dull tank of gas. After driving around 5he city, 1/7 of the gas has been used. With the rest of the gas in t

Sati [7]

Answer:

$\frac{2}{7}$

Step-by-step explanation:

Given:

A car starts with a dull tank of gas

1/7 of the gas has been used around the city.

With the rest of the gas in the car, the car can travel to and from Ottawa three times.

Question asked:

What fractions of a tank of gas does each complete trip to Ottawa use?

Solution:

Fuel used around the city = $\frac{1}{7}$

Remaining fuel after driving around the city = 1 - $\frac{1}{7}$

= $\frac{7 - 1}{7} = \frac{6}{7}$

According to question:

As from the rest of the gas in the car that is $\frac{6}{7}$ , the car can complete 3 trip to Ottawa which means,

By unitary method:

The car can complete 3 trip by using = $\frac{6}{7}$ tank of gas.

The car can complete 1 trip by using = $\frac{6}{7} \div 3$

= $\frac{6}{7} \times\frac{1}{3}$

= $\frac{6}{21}$

= $\frac{2}{7}$ tank of gas

Thus, $\frac{2}{7}$ tank of gas used for each complete trip to Ottawa.

5 0

3 years ago

Please help!!<br> (This is Algebra 1!)

yKpoI14uk [10]

Answer:

$242.78

Step-by-step explanation:

Given :

Room cost for 1 night = $199

Tax rate = 22% or 0.22

Tax for room for 1 night = 0.22 x $199 = $43.78

Total cost for one night,

= room cost + tax

= $199 + $43.97

= $242.78

5 0

2 years ago

Plz help with any of them it’s a emergency

devlian [24]

To find a perimeter, add all sides together:

9) 12 + 12 + 8 + 8 = 20 + 20 = 40 in
10) 3 + 3 + 3 + 3 = 6 + 6 = 12 cm

To find area, multiply length and width, or base and height:

11) 3 x 6 = 18
12) 10 x 30 = 300 ft
13) 12 x 12 = 144 cm
14) 7 x 4 = 28 m

15)
Perimeter: 2(2) + 2(16) = 4 + 32 = 36
Area: 1 x 16 = 16

hope this helps

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3 years ago

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Lana71 [14]

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3 years ago

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