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3 years ago

Identifiy the initial amount a and the decay factor b in the exponential function y=5×0.5^×

Mathematics

1 answer:

xenn [34]3 years ago

6 0

Answer:

$a=5\\ \\b=0.5$

Step-by-step explanation:

Given the exponential decay function $y=5\cdot (0.5)^x$

When $x=0,$ then

$y=5\cdot (0.5)^0=5\cdot 1=5,$

so the initial amount is $a=5$

The exponential decay function $y=a\cdot b^x$ has the decay factor $b.$

In your case, the eexponential decay factor is $b=0.5$

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If line GH is perpendicular to line HJ, then GJ is ____ HJ.

valentinak56 [21]

Option A: >

Solution:

Given a triangle GHJ.

The line GH is perpendicular to line HJ.

This means the triangle is a right angled triangle.

In ΔGHJ, GH is the base of the triangle and

HJ is a height of the triangle.

Then the third side must be the hypotenuse of the right triangle.

We know that by the Pythagoras theorem,

$(\text {Hypotenuse})^2=(\text{Base})^2+(\text{Height})^2$

$(\text {GJ})^2=(\text {GH})^2+(\text {HJ})^2$

This clearly shows that the hypotenuse is greater than the height.

⇒ GJ > HJ

Option A: > is the correct answer.

If line GH is perpendicular to line HJ, then GJ is > HJ.

3 0

3 years ago

sales taxes in the town where Amanda lives at 7% Amanda paid $35 in sales taxes on a new stereo what was the price of the stereo

Tema [17]

$37.45 hbf bgdfgfdbgfnhmjndbfvbdtjmuknhydbgfvck,iytnhjbgfvds

8 0

2 years ago

1/2+1/4=____ and 1/12 + 1/6=___ and 1/4+1/6+1/12=_____ . explain

BlackZzzverrR [31]

1/2+ 1/4
= 2/4+ 1/4
= 3/4

1/12+ 1/6
= 1/12+ 2/12
= 3/12
= 1/4

Therefore, 1/4+ 1/6+ 1/12
= (1/12+ 1/6)+ (1/12+ 1/6)
= 2*(1/12+ 1/6)
= 2* (1/4)
= 2/4
= 1/2

Hope this helps~

8 0

3 years ago

Read 2 more answers

Pleaseeeeeeeee answer if you do your the best at life!!!!!

jenyasd209 [6]

x+(-8)= -12

x-8= -12

x= -12+8

x=-4

-3 + x = 10

x=10+3

x=13

-2+x= -5

x=-5+2

x=-3

4 0

2 years ago

Read 2 more answers

How would you solve these 2 maths problems?

sweet-ann [11.9K]

Answer:

see explanation

Step-by-step explanation:

(9)

Expand and simplify right side and compare coefficients of like terms on left side.

(x - 2)(x² + ax + b) + c

= x³ + ax² + bx - 2x² - 2ax - 2b + c

= x³ + x²(a - 2) + x(b - 2a) - 2b + c

compare with

x³ + 2x² - 3x + 4

x² terms

a - 2 = 2 ( add 2 to both sides )

a = 4

x terms

b - 2a = - 3 ← substitute a = 4

b - 8 = - 3 ( add 8 to both sides )

b = 5

constant terms

- 2b + c = 4 ← substitute b = 5

- 10 + c = 4 ( add 10 to both sides )

c = 14

Thus a = 4, b = 5 and c = 14

-------------------------------------------------

(10)

Since both functions cross the x- axis at - 2 then (- 2, 0) satisfies both, that is

f(- 2) = $(-2)^{4}$ + a(- 2)³ + b(- 2)² + 36(- 2) + 144 = 0, that is

- 16 - 8a + 4b - 72 + 144 = 0

- 8a + 4b + 56 = 0

- 8a + 4b = - 56 → (1)

and

g(- 2) = $(-2)^{4}$ + (a + 3)(- 2)³ - 23(- 2)² + (b + 10)(- 2) + 40 = 0, that is

- 16 - 8(a + 3) - 92 - 2(b + 10) + 40 = 0

- 16 - 8a - 24 - 92 - 2b - 20 + 40 = 0

- 8a - 2b - 112 = 0

- 8a - 2b = 112 → (2)

Subtract (1) from (2) term by term

- 6b = 168 ( divide both sides by - 6 )

b = - 28

Substitute b = - 28 into (2)

- 8a + 56 = 112 ( subtract 56 from both sides )

- 8a = 56 ( divide both sides by - 8 )

a = - 7

Thus a = - 7 and b = - 28

5 0

3 years ago