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3 years ago

Jessica's bikes rents bikes for $10 plus $2 per hour. Arjun paid $18 to rent a bike. For how many hours did he rent the bike ?

Mathematics

1 answer:

irakobra [83]3 years ago

3 0

Arjun rented his bike for 4 hours

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Question 13

PtichkaEL [24]

Answer:

B. 30x

D. x(45-15)

Step-by-step explanation:

The distributive property lets you factor out the common factor of x. The sum of coefficients can be simplified to a single coefficient.

45x -15x = x(45 -15) = 30x

5 0

2 years ago

What would y=x^2 +x+ 2 be in vertex form

balu736 [363]

Answer:

$y = (x + \frac{1}{2} )^{2} + \frac{7}{4}$

Step-by-step explanation:

$y = {x}^{2} + x + 2$

We can covert the standard form into the vertex form by either using the formula, completing the square or with calculus.

$y = a(x - h)^{2} + k$

The following equation above is the vertex form of Quadratic Function.

Vertex — Formula

$h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a}$

We substitute the value of these terms from the standard form.

$y = a {x}^{2} + bx + c$

$h = - \frac{1}{2(1)} \\ h = - \frac{ 1}{2}$

Our h is - 1/2

$k = \frac{4(1)(2) - ( {1})^{2} }{4(1)} \\ k = \frac{8 - 1}{4} \\ k = \frac{7}{4}$

Our k is 7/4.

Vertex — Calculus

We can use differential or derivative to find the vertex as well.

$f(x) = a {x}^{n}$

Therefore our derivative of f(x) —

$f'(x) = n \times a {x}^{n - 1}$

From the standard form of the given equation.

$y = {x}^{2} + x + 2$

Differentiate the following equation. We can use the dy/dx symbol instead of f'(x) or y'

$f'(x) = (2 \times 1 {x}^{2 - 1} ) + (1 \times {x}^{1 - 1} ) + 0$

Any constants that are differentiated will automatically become 0.

$f'(x) = 2 {x}+ 1$

Then we substitute f'(x) = 0

$0 =2x + 1 \\ 2x + 1 = 0 \\ 2x = - 1 \\x = - \frac{1}{2}$

Because x = h. Therefore, h = - 1/2

Then substitute x = -1/2 in the function (not differentiated function)

$y = {x}^{2} + x + 2$

$y = ( - \frac{1}{2} )^{2} + ( - \frac{1}{2} ) + 2 \\ y = \frac{1}{4} - \frac{1}{2} + 2 \\ y = \frac{1}{4} - \frac{2}{4} + \frac{8}{4} \\ y = \frac{7}{4}$

Because y = k. Our k is 7/4.

From the vertex form, our vertex is at (h,k)

Therefore, substitute h = -1/2 and k = 7/4 in the equation.

$y = a {(x - h)}^{2} + k \\ y = (x - ( - \frac{1}{2} ))^{2} + \frac{7}{4} \\ y = (x + \frac{1}{2} )^{2} + \frac{7}{4}$

7 0

3 years ago

Find the number that makes the ratio equivalent to 3:4

boyakko [2]

One answer could be 6:8

6 0

2 years ago

A new novel is selling for $21.95. If it is on sale at 20% off, find the amount of the discount and the sale price.

Finger [1]

21.95×.2=4.39
21.95-4.39=17.56

the discount is $4.39
and the total sale price is $17.56

7 0

3 years ago

The graph for the equation y = x minus 4 is shown below.

Anon25 [30]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers