List all the factors of 40

Jackson went into a movie theater and bought 8 bags of popcorn (x) and 2 candies (y), costing a total of $58. Cooper went into t

Sophie [7]

Answer:

(a)

$8x + 2y = 58$

$4x + 5y = 49$

(b)

Bag of popcorn = $6

Candy = $5

Step-by-step explanation:

Given

$candy = y$

$popcorn = x$

Jackson: x = 8; y= 2; Total = 58

Cooper: x = 4; y= 5; Total = 49

Solving (a): System of equation

For Jackson:

$8x + 2y = 58$

This is done by multiplying each variable by the quantity.

Same will be applied to Cooper's purchase:

Cooper:

$4x + 5y = 49$

Solving (b): Price of 1 bag of popcorn and 1 candy

This implies that we solve for x and y

$8x + 2y = 58$ ----- (1)

$4x + 5y = 49$ -------- (2)

Multiply the second equation by 2

$2(4x + 5y = 49)$

$8x + 10y = 98$ -------- (3)

Subtract the (1) from (3)

$8x - 8x + 10y - 2y = 98 - 58$

$10y - 2y = 98 - 58$

$8y = 40$

Solve for y

$y = 40/8$

$y = 5$

Substitute 5 for y in (1)

$8x + 2y = 58$

$8x + 2 * 5 = 58$

$8x + 10 = 58$

$8x = 58 - 10$

$8x = 48$

Solve for x

$x = 48/8$

$x = 6$

This implies:

Bag of popcorn = $6

Candy = $5

4 0

3 years ago

If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is n

natali 33 [55]

Answer:

$f^{-1}=3ln_2(\frac{t}{100})$

f^-1 represents the number of hours the bacteria developed

Step-by-step explanation:

$f(t) = 100 \cdot 2^\frac{t}{3}$

To find inverse of a function , replace f(t) with y

$y= 100 \cdot 2^\frac{t}{3}$

replace t with y and y with x

$x= 100 \cdot 2^\frac{y}{3}$

solve for y

divide both sides by 100

$\frac{x}{100} =2^\frac{y}{3}$

take ln on both sides

$ln \frac{x}{100} =\frac{y}{3}ln 2$

divide both sides by ln

$ln_2(\frac{x}{100}) =\frac{y}{3}$

multiply by 3 on both sides

$y=3ln_2(\frac{x}{100})$

Replace x with t and y with f^-1

$f^{-1}=3ln_2(\frac{t}{100})$

f^-1 represents the number of hours the bacteria developed

7 0

3 years ago

How do i write an equation in vertex form?

Arte-miy333 [17]

Answer:

Step-by-step explanation:

1) Vertex form of a quadratic equation is y=a(x-h)2+k, where (h,k) is the vertex of the parabola.

2) The vertex of a parabola is the point at the top or bottom of the parabola.

3) 'h' is -6, the first coordinate in the vertex.

4) 'k' is -4, the second coordinate in the vertex.

5) 'x' is -2, the first coordinate in the other point.

8 0

3 years ago

Olive oil has a density of 0.9 g/mL. What is the mass of 200 mL of olive oil?

lesantik [10]

Known, density= mass/ volume
The volume is given as 200ml
Set up an equation and cross-multiply
You get mass = 180g, answer is B

3 0

3 years ago

A deli is offering two specials. The roast beef special gives a profit of $2.30 per sandwich, whereas the turkey special gives a

Sedaia [141]

We put the information above in a table as shown below
The number of bread available is 120, so the first constraint is
The number of cheese available is 160 slices, so the second constraint is
The next constraint is the profit

7 0

3 years ago