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3 years ago

Two functions are graphed on the coordinate plane.

Mathematics

1 answer:

rosijanka [135]3 years ago

7 0

Answer:

Option B

Step-by-step explanation:

We can see that, from the picture provided, the graphs intersect at points( 0, 4 ) and ( - 4, 4 ), respective to functions f( x ) and g( x ). These intersection points makes each function equivalent to one another, and hence -

Function f( x ) where x = - 4 / Function g( x ) where x = - 4,

$f( - 4 ) = 4,\\g( - 4 ) = 4\\----------\\f ( - 4 ) = g ( - 4 )$

Respectively function f( x ) where x = 0 / Function g( x ) where x = 0,

$f( 0 ) = 4,\\g( 0 ) = 4\\----------\\f ( 0 ) = g ( 0 )$

Your solution should be option b, " f(-4) = g(-4) and f(0) = g(0) "

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Noah wants to buy a 5 year annuity that pays $1000 at the end of each year, starting one year from now. It earns interest at 6.2

pav-90 [236]

Answer:

cost is $4183.87

Step-by-step explanation:

given data

time t = 5 year

amount A = $1000

rate r = 6.25 % = 0.0625

to find out

how much it will cost

solution

we will apply here formula for present value of annuity that is express as

present value = amount × $\frac{1-(1+r)^{-t}}{r}$ ....................1

put here all these value we get cost we will pay

present value = amount × $\frac{1-(1+r)^{-t}}{r}$

present value = 1000 × $\frac{1-(1+0.0625)^{-5}}{0.0625}$

present value = 4183.869221

so cost is $4183.87

5 0

3 years ago

Karen is 6 yrs older than her sister Michelle and Michelle is two years younger than their brother David If the sum of their age

frosja888 [35]

You are told the ages of Karen and David in terms of Michelle's age.
Let m = Michelle's age.

Michelle's age = m
Karen's age = m + 6

Michelle is two years younger than David, so David is two years older than Michelle.

David's age = m + 2

Add the ages and get 62.

m + m + 6 + m + 2 = 62

3m + 8 = 62

3m = 54

m = 18

Michelle is 18 years old

Karen is 6 years older, so she is 24 years old.

David is 2 years older than Michelle, so he is 20 years old.

4 0

3 years ago

a toy manufacturer has designed a new piece for use in building models. It is a cube with side lengths 7 mm and has a 3 mm in di

Ray Of Light [21]

Given that the cubical piece has side (s) 7 mm, and a cylindrical hole of diameter (d) as 3 mm.

The volume of the piece can be calculated as,

$\begin{gathered} \text{Volume of piece}=\text{ Volume of cube}-\text{ Volume of cylinder} \\ V=s^3-\frac{\pi}{4}d^2s \\ V=7^3-\frac{\pi}{4}(3)^2(7) \\ V=343-\frac{63\pi}{4} \\ V\approx293.52mm^3 \\ V\approx293.52\times10^{-9}\text{ }m^3 \end{gathered}$

It is mentioned that the material costs $207 per cubic meter, so the cost (c) of 1 piece is calculated as,

$\begin{gathered} \text{Cost of 1 piece}=\text{ Cost per unit volume}\times\text{ Volume of 1 piece} \\ c=207\times293.52\times10^{-9} \\ c\approx60758.64\times10^{-9} \end{gathered}$

This is the cost (in dollars) for 1 piece.

Given that the manufacturer wants to produce 1,000,000 such pieces, so the total cost (TC) is calculated as,

$\begin{gathered} \text{Total Cost}=\text{ Cost per piece}\times\text{ No. of pieces} \\ TC=60758.64\times10^{-9}\times1,000,000 \\ TC=60758.64\times10^{-9}\times10^6 \\ TC=60758.64\times10^{-3} \\ TC=60.75864 \\ TC\approx60.75 \end{gathered}$

Thus, the total prototypes will cost around $60.75

7 0

1 year ago

−2(x+1/4)+1=5 whats the value of x

harkovskaia [24]

The value of x is: Solve for x by simplifying both sides of the equation, then isolating the variable.

x=−9/4

4 0

3 years ago

300 ml over 15 min is what rate of ml per hour

Mama L [17]

Answer:

1200 ml per hour

Step-by-step explanation:

To compute what rate is 300 ml over 15 mins as a rate of ml per hour, we do a rule of 3, using a variable x as that amount of ml we don't know yet. We should have everything in the same units, so instead of writing 1 hour we write 60 minutes:

$\frac{300~ml}{15~min}=\frac{x~ml}{60~mins}$