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2 years ago

1-2

Mathematics

1 answer:

EleoNora [17]2 years ago

3 0

Answer:

f(-3) = g(-3)

Step-by-step explanation:

Let's look at each option to which one is true with regard to the given functions on the graph.

The option that is correct is the option that shows where the graph of f(x) and g(x) intercepts or cut across each other.

Now, take a look at the graph, the line of both functions intercepts at x = -3. At this point, the value of f(-3) and g(-3) is equal to -4.

Therefore: f(-3) = g(-3)

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2.The number of grams A of a certain radioactive substance present at time, in yearsfrom the present, t is given by the formulaA

professor190 [17]

Answer:

Given that,

The number of grams A of a certain radioactive substance present at time, in years

from the present, t is given by the formula

$A=45e^{-0.0045(t)}$

a) To find the initial amount of this substance

At t=0, we get

$A=45e^{-0.0045(0)}$ $A=45e^0$

We know that e^0=1 ( anything to the power zero is 1)

we get,

$A=45$

The initial amount of the substance is 45 grams

b)To find thehalf-life of this substance

To find t when the substance becames half the amount.

A=45/2

Substitute this we get,

$\frac{45}{2}=45e^{-0.0045(t)}$

$\frac{1}{2}=e^{-0.0045(t)}$

Taking natural logarithm on both sides we get,

$\ln (\frac{1}{2})=-0.0045(t)^{}$ $(-1)\ln (\frac{1}{2})=0.0045(t)$ $\ln (\frac{1}{2})^{-1}=0.0045(t)$ $\ln (2)=0.0045(t)$ $0.6931=0.0045(t)$ $t=\frac{0.6931}{0.0045}$ $t=154.02$

Half-life of this substance is 154.02

c) To find the amount of substance will be present around in 2500 years

Put t=2500

we get,

$A=45e^{-0.0045(2500)}$ $A=45e^{-11.25}$ $A=45\times0.000013=0.000585$ $A=0.000585$

The amount of substance will be present around in 2500 years is 0.000585 grams

4 0

2 months ago

Given: MNFD is a trapezoid.

Rama09 [41]

A trapezoid with legs MN = FD is an isosceles trapezoid.
An isosceles trapezoid has diagonals that are congruent, therefore: MF = ND.
A quadrilateral with diagonals congruent and perpendicular is a square.
In a square, the height coincides with the side.
The area of a square is given by A = s²
Therefore, the area of MNFD is h²

6 0

2 years ago

A hot air balloon descends to the ground. The function h(t) = 210 – 15t can be used to describe the altitude of the balloon as i

Olin [163]

It is D if its correct i will explain why

4 0

2 years ago

Read 2 more answers

Pleas help me I have so much more left to do

Serjik [45]

Answer:

2 11/14 squared feet

Step-by-step explanation:

Area of a rectangle = length x width

Give length = 3 1/4 and

Width = 3/4

Therefore,

Area = 3 1/4 x 3/4

Change the mixed size fraction to an improperly fraction

We have A = 13/4 x 3/4

39/14

2 11/14 squared feet

6 0

2 years ago

Homework: 7.1 hw

Scrat [10]

Answer:

a. $ 2,431.01 = 4 years

b. $ 4,584.04 = 17 years

c. 4.57 years = $ 2,499.57

d. 8.3 year = $ 2,998.48

e. $ 2,431.01 = 4 years

Step-by-step explanation:

Compound Interest Equation

A = P(1 + r/n)nt

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

5 0

2 years ago