Two vertices of a right triangle are (0,1) and (0,6). The area of the triangle is 10 square units. Which point could be the third vertex of the triangle?

Answers

Answer 1

Answer: The correct answer for the question that is being presented above is this one: "(4,1)."

The distance from (0,1) to (0,6) is 5 units.
The area of a triangle is
Area = bh/2
10 = 5b/2
20 = 5b
b = 4

The distance of the base is 4 units. So, from (0,1) count 4 units to the right but on the same y coordinate.

So the point is in (4, 1).

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Mrs. aviles is planning a fruit-cup party for a class of 18 students and two teachers. She spends $10 for a package of snacks and also takes orders in advance for fruit cups that cost $3 each. 1. describe the domain of the function both in words and numbers?
2. what is the range?

Answers

Answer:

domain is x = 3

Thus domain means that for every fruit cup costs $3

Range is f(20) = 60

Step-by-step explanation:

We are given;

Total students for the fruit cup party = 18

Total teachers for the fruit cup party = 2

Cost of each fruit cup =$ 3

Delivery charge = $ 10

Now, the total number of people attending the party = Total number of students + Total number of teachers

Thus;

Total number of people attending party = 18 + 2 = 20

Since cost of each fruit cup is $3.

Thus, for 20 fruit cups, the function is;

f(x) = 20x where x is cost of each fruit cup.

It means the cost of 20 fruit cups = $3 × 20 = $60

Thus, domain is x = 3

Thus domain means that for every fruit cup costs $3

Range is f(20) = 60

An object moves at a constant rate. The graph shows the object's height at different times.Which equation represents the situation?

A.
y = −15x + 900

B.
y = −15x − 900

C.
y = 15x − 900

D.
y = 15x + 900

Answers

With linear graphs, there's two things you need to find, the y intercept and the slope. The y intercept is literally where the line touches the y axis. Looking at the graph you can see that it's at 900, so your number by itself has to be +900. The slope then is found by seeing how much y changes for every change in x. So you have two points, (20,600) and (40,300) which tell you that the line moves down 300 when it moves across 20. Your slope is then -300/20 which is -15. This goes in front of your x and you get your equation. SO your answer would be

A. y = −15x + 900

Hope I helped:P

How many ninths to make 1/3

Answers

Answer:
3

Explanation:
Assume that the number of $(1)/(9)$ needed to make $(1)/(3)$ is x

Now, we would need to translate the givens into an equation and then solve for x.
The number of $(1)/(9)$ multiplied by x would give us $(1)/(3)$

This means that:
$(1)/(9)$ * x = $(1)/(3)$

$(x)/(9)$ = $(1)/(3)$

3x = 9

x = $(9)/(3)$

x = 3

Hope this helps :)

Answer: The correct answer is 3.

Step-by-step explanation:

Let the number of ninths needed be taken as 'x'

We need to find the number of ninths needed to make;

$(1)/(3)$ ,

The equation for this becomes:

$(1)/(9)* x=(1)/(3)\n\nx=(9)/(3)\n\nx=3$

Hence, we need 3 times ninths to get us the fraction of $(1)/(3)$ .

A square has an area of 144 in2 is reduced by a factor of 1/6

Answers

Answer:

If a square has an area of 144 square inches and is reduced by a factor of 1/6, it means that both the length and width of the square are multiplied by the square root of 1/6.

To find the new side length, we can take the square root of 1/6 and multiply it by the original side length.

Original side length = sqrt(144) = 12 inches

New side length = (1/6)^(1/2) * 12 inches

Simplifying the calculation:

New side length = (1/√6) * 12 inches

Now we can calculate the new side length:

New side length ≈ 3.27 inches (rounded to two decimal places)

To find the new area, we square the new side length:

New area = (3.27 inches)^2 ≈ 10.68 square inches (rounded to two decimal places)

Therefore, after reducing the square by a factor of 1/6, the new side length is approximately 3.27 inches, and the new area is approximately 10.68 square inches.

What are the period and amplitude of the function?A) period 3, amplitude 1.5
B) period 3, amplitude 3
C) period 4, amplitude 1.5
D) period 4, amplitude 3

Answers

Answer:

Option: A is the correct answer.

A) Period: 3 , amplitude : 1.5

Step-by-step explanation:

We know that Period of a function is the smallest value such that the function repeats after a fixed time.

and also the amplitude of the function is the height above or below the mid-line.

After looking at the graph we see that the period of the function is: 3

Since the function is repeating itself after every x=3.

Also, the mid-line of the function is: y= -0.5.

Hence, the height above the mid-line is: 1+0.5 = 1.5

Hence, amplitude= 1.5

period 3, amplitude 1.5

Find the fraction equivalent to 8/16 using division. a) 2/4 b) 4/8 c) 1/2 d) 3/6