MATHEMATICS HIGH SCHOOL

Given the following exponential function, identify whether the change representsgrowth or decay, and determine the percentage rate of increase or decrease.
y = 2600(0.3)^x

Answers

Answer 1
Answer:

Answer:

The change represents decay.The percentage decrease is 97%

Step-by-step explanation:

The change represents decay because the exponential base is less than 1. In this problem, the base is 0.3, which is smaller than 1. To find the percentage decrease, you must subtract 100% from 3%. This gives us a decrease of 97%.

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Is the set of multiples of 4 closed under addition? Explain why or provide a counterexample if not.A. Yes, because the sum of any two multiples of 4 is also a multiple of 4.


B. Yes, because the sum of any two multiples of 4 is also a multiple of 8.


C. No, and a counterexample is –4 + (–8) = –12.


D. No, and a counterexample is 26 + 16 = 42.

Answers

The right answer for the question that is being asked and shown above is that: "B. Yes, because the sum of any two multiples of 4 is also a multiple of 8." the set of multiples of 4 closed under addition

the sum of two numbers is 44. the smaller number is 20 less than the larger number. what are the numbers?

Answers

sum means add
x and y are the numbers
sum i 44
x+y=44

smaller s 20 les than larger
x=20+y
or
y=20+x
doesn't matter, just pick one
x=20+y

substue 20+y for x since they are equal
x+y=44
(20+y)+y=44
20+y+y=44
20+2y=44
subtract 20 from both sides
2y=24
divide by 2
y=12
subsitue
x=20+y
x=20+12
x=32

the numbers are 12 and 32
x+(x-20)=44
2x= 64
x=32

Therefore the bigger number is 32 and the smaller number is 12
32+12=44

The function f(x) = −x2 − 9x + 10 shows the relationship between the vertical distance of a diver from a pool's surface f(x), in feet, and the horizontal distance x, in feet, of a diver from the diving board. What is a zero of f(x), and what does it represent?A: x = 1; the diver jumps in the pool at 1 foot per second
B: x = 10; the diver jumps in the pool at 10 feet per second
C: x = 1; the diver hits the water 1 foot away horizontally from the board
D: x = 10; the diver hits the water 10 feet away horizontally from the board

Answers

Answer
C: x = 1; the diver hits the water 1 foot away horizontally from the board

Explanation
The question requires you to solve for x.
 f(x) = −x² − 9x + 10 

When f(x)=0

−x² − 9x + 10 = 0
                      = x²+9x-10 = 0
The product in this expression is -10
The factors of this expression is 9
Factors are 10 and -1.

x²+9x-10 = x²-1x+10x-10 = 0
               =x(x-1)+10(x-1) = 0
               =(x+10)(x-1) = 0
This means that;
x+10=0      or  x-1=0
x = -10            x = 1.
Since distance can not be negative, x =1.


                        

Answer:

x = 1; the diver hits the water 1 foot away horizontally from the board

Step-by-step explanation:

took the test :)

A traffic helicopter pilot 60 meters above the road spotted two antique cars. The angles of depression are 10.2 and 8.7 degrees. How far apart are the cars? A. 58.6 B. 392.1 C. 333.5 D. 57.8

Answers

Answer:

A. 58.6 meters

Step-by-step explanation:

Angle of depression denotes the angle when looking down from a certain height.

tan10.2=(60)/(AD)\n\Rightarrow AD=(60)/(tan10.2)

tan 8.7=(60)/(AB)\n\Rightarrow AB=(60)/(tan8.7)

DB = AB-AD

\n\Rightarrow DB =(60)/(tan8.7)-(60)/(tan10.2)\n\Rightarrow DB = 392.1-333.47\n\Rightarrow DB = 58.63\ meters

The cars are 58.6 meters apart.
58.6 is the answer to your question

Perimeter of a triangle with the given sides 12in 9in 15in

Answers

36 in for the triangle the perimeter is the outside length so it...
to find a perimeter add all the sides of the shape.  so 12+9+15 is 36.  the perimeter of the triangle is 36

a spherical fountain il has a radius of 1.5 feet. find the volume of the fountain to the nearest tenth of a cubic foot

Answers

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.

Substituting the given value of r = 1.5 feet, we get:

V = (4/3)π(1.5)^3

V ≈ 14.1 cubic feet (rounded to the nearest tenth)

Therefore, the volume of the spherical fountain is approximately 14.1 cubic feet.
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