(sec 12A - 1)/(sec 6A -1) = tan 12A / tan 3A

A given line has the equation 10x+2y=-2.

Karolina [17]

Answer:

5x+y=12

Step-by-step explanation:

10x+2y=-2=5x+y=12

4 0

1 year ago

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Jenny studied the characteristics of two species of bacteria. The number of bacteria of species A, A(t), after t hours is repres

Marina CMI [18]

<h3><u>Answer:</u></h3>

The function N(t) is given as:

$N(t)=3+(0.25t)^3-8(1.06)^t$

<h3><u>Step-by-step explanation:</u></h3>

Jenny studied the characteristics of two species of bacteria.

The number of bacteria of species A, A(t), after t hours is represented by the function:

$A(t) = 5+(0.25t)^3$

The number of bacteria of species B, B(t), after t hours is represented by the function:

$B(t) = 2 + 8(1.06)^t$

N(t) denotes the difference in the number of bacteria; hence N(t) is given by after t hours as:

N(t)=A(t)-B(t)

$N(t)= 5+(0.25t)^3-(2 + 8(1.06)^t)$

which on simplifying gives:

$N(t)=5+(0.25t)^3-2-8(1.06)^t\\\\N(t)=5-2+(0.25t)^3-8(1.06)^t\\\\N(t)=3+(0.25t)^3-8(1.06)^t$

Hence,

5 0

1 year ago

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Which equation represents this number sentence? Two more than one-third of a number is 8

Natali [406]

Answer:

B. $2+\frac{1}{3}n=8$

Step-by-step explanation:

Let n be the number.

We are asked to write an mathematical expression for the given word phrase.

One third of a number, n, would be $\frac{1}{3}n$ .

Two more than one third of a number, n, would be $2+\frac{1}{3}n$ .

We are told that Two more than one-third of a number is 8. We can represent this information in an equation as:

$2+\frac{1}{3}n=8$

Therefore, option B is the correct choice.

8 0

1 year ago

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The admission fee at a movie theater is $5 for children and $9 for adults. If 3200 people go to the movies and $24000 is collect

Usimov [2.4K]

For this problem, let x be the number of children and y for adults. Formulate the equations: 1st equation, x + y = 3,200 and 2nd equation 5x + 9y = 24,000. Re-arrange 1st equation into x = 3200 - y. Then, substitute into 2nd equation, 5(3,200-y) + 9y = 24,000. Then, solve for y. The 16,000 - 5y + 9y = 24000. Final answer is, y = 2000 adults went to watch the movie.

6 0

2 years ago

Joe scored 10 points in the basketball game. This is 2 more than one-sixth of the points scored by the team. Which equation, whe

marissa [1.9K]

(1/6) x + 2 = 10

Step-by-step explanation:

Step 1 :

Let x be the number of points scored by the team.

Given Joe has scored 2 points more than one sixth of the point scored bynthe team

Step 2:

Based on the above given information the equation which gives the points scored by Joe is as follows:

(1/6) x + 2

Given that Joe has scored 10 points, we have

(1/6)x + 2 = 10

Step 3:

When we solve the above equation for x , we get the total number of points scored by the team

7 0

2 years ago

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