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Elina [12.6K]
3 years ago
15

5

Mathematics
1 answer:
PolarNik [594]3 years ago
4 0

Answer:

A. y = -x -2

Step-by-step explanation:

thanks for the questions.

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$43 dinner; 18% gratuity whats the answer
Anika [276]

Answer:

Gratuity means (18/100)·43 = (18·43)/100 = 774/100 = $7.74;

Step-by-step explanation:


4 0
3 years ago
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test.
weqwewe [10]

9514 1404 393

Answer:

  (c)  Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100

Step-by-step explanation:

Try the numbers in the constraints to see if they work.

<u>Build hours</u>:

  (4 h/child bike)(10 child bikes) = 40 hours

  (6 h/adult bike)(12 adult bikes) = 72 hours

  total build hours: 40 +72 = 112, less than 120; constraint is met

<u>Test hours</u>:

  (4 h/child bike)(10 child bikes) = 40 hours

  (4 h/adult bike)(12 adult bikes) = 48 hours

  total test hours: 40 +48 = 88, less than 100; constraint is met

__

Both constraints are met, so the order can be filled.

6 0
2 years ago
HELPP I NEED TO TURN THIS IN 5 Mins!!!!!
zaharov [31]

Answer:

3. The vertex form of the function, f(x) = x² - 4·x - 17 is f(x) = (x - 2)² - 21

4. The solutions are, x = -2 + √10 and x = -2 - √10

5. The quadratic equation with vertex (3, 1) and a = 1 in standard form is given as follows;

f(x) = x² - 6·x + 10

Step-by-step explanation:

3. The function given in standard form is f(x) = x² - 4·x - 17, which is the form, f(x) = a·x² + b·x + c

The vertex form of the of a quadratic function can be presented based on the above standard form as follows;

f(x) = a(x - h)² + k

Where;

(h, k) = The coordinate of the vertex

h = -b/2a

k = f(h)

Comparing with the given equation, we have;

f(x) = a·x² + b·x + c = x² - 4·x - 17

a = 1

b = -4

c = -17

∴ h = -(-4)/(2 × 1) = 2

h = 2

k = f(h) = f(2) = 2² - 4 × 2 - 17 = -21

k = -21

The vertex form of the function, f(x) = x² - 4·x - 17 is therefore, given as follows;

f(x) = (x - 2)² - 21

4. The given equation for which we need to solve by completing the square is 2·x² + 8·x = 12

Dividing the given equation by 2 gives;

x² + 4·x = 6

Which is of the form, x² + b·x = c

Where;

a = 1

b = 4

c = 6

From which we add (b/2)² to both sides to get x² + b·x + (b/2)² = c + (b/2)²

Adding (b/2)² = (4/2)² to both sides of x² + 4·x = 6 gives;

x² + 4·x + 4 = 6 + 4

(x + 2)² = 10

x + 2 = ±√10

x = -2 ± √10

The solution are, x = -2 + √10 and x = -2 - √10

5. Given that the value of the vertex = (3, 1), and a = 1, we have;

The vertex, (h, k) = (3, 1)

h = 3, k = 1

Therefore, h = 3 = -b/(2 × a) = -b/(2 × 1)

∴ -b = 2 × 3 = 6

b = -6

k = f(h) = a·h² + b·h + c, by substitution, we have;

k = f(3) = 1 × 3² + (-6) × 3 + c = 1

∴ c = 1 - (1 × 3² + (-6) × 3) = 10

c = 10

The quadratic equation with vertex (3, 1) and a = 1 in standard form, f(x) a·x² + b·x + c is therefor;

f(x) = x² - 6·x + 10

4 0
3 years ago
The empire state building in New York City is 12,50 feet tall . It has 103 floors .Rounded the the nearest whole , what is the h
krok68 [10]
\frac{1250}{103} \approx 12.1359223

Each floor is about 12 feet tall.
8 0
3 years ago
All isosceles triangles are equilateral. <br> A.True <br> B.False
Flura [38]
False !! but opposite can be true !!
7 0
3 years ago
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