Which expressions are equivalent to x+2y+x+2?

Bela started studying how the number of branches on her tree grows over time. Every 2.9 years, the number of

kati45 [8]

Answer:

The required function that models the number of branches t years since Bela began studying her tree is

number of branches = $60(1.83)^{\frac{t}{2.9} }$

Step-by-step explanation:

Let t be the time in years

Initially Bela's tree had 60 branches.

therefore the function that can be used to model the number of branches after t years will be given by

number of branches( after t years) $= 60\times(1 + \frac{83}{100})^{\frac{t}{2.9} } = 60(1.83)^{\frac{t}{2.9} }$

7 0

3 years ago

You are making a picture frame of uniform width for a picture that is to be displayed at the local museum. The picture is 3.25 f

SCORPION-xisa [38]

$x-\ width\ preferred\\\\
Area=width*length\\\\
length=3,25feet\\
Area=15feet^2\\\\
15=3,25*x\ \ \ \ | divide\ by\ 3,25\\\\x=4,61feet\\\\It\ should\ be\ 4,61\ feet \ long.
$

8 0

3 years ago

List the independent and dependent variables for each situation:

natulia [17]

Part (a)

Independent variable = age
Dependent variable = height

"depends on age" indicates that age is independent.

-----------------------------------
Part (b)

Independent variable = amount of sleep
Dependent variable = mood

The key word is "determines". The stuff before this word is the independent variable which affects the dependent variable.
-----------------------------------
Part (c)

Independent variable = time water has been running
dependent variable = amount of water in the tub

Time is usually the independent variable
-----------------------------------
Part (d)

Independent variable = speed
dependent variable = distance from home

-----------------------------------
Part (e)

Independent variable = amount of homework done
dependent variable = speed

This seems like an odd pairing of homework and speed. Could there be a typo? I noticed that part (f) is very similar

-----------------------------------
Part (f)

Independent variable = amount of hw that is assigned
dependent variable = amount of homework done

Like with part (a), the stuff before "depends" is the dependent variable

4 0

4 years ago

Given that <img src="https://tex.z-dn.net/?f=2%20%7B%7D%5E%7Bx%7D%20%20%3D%200.125" id="TexFormula1" title="2 {}^{x} = 0.12

Luda [366]

Take the natural log of both sides

ln(2^x)=ln(.125)
Xln(2)=ln(.125)
X=ln(.125)/ln(2)
X=-3

ALTERNATIVE ROUTE:
You know that 0.125 is equal to 1/8
And 1/2^3 is also equal to 1/8
So since you need the reciprocal to match it the exponent is a negative

5 0

3 years ago

Read 2 more answers

When 238 is divided by the natural number n, the quotient is 3 more than n, and there is no remainder. What is n?

brilliants [131]

Answer:

n = 14

Step-by-step explanation:

Write the equation in algebraic (numbers and symbols) form

$\frac{238}{n}$ = n + 3 Rearrange the equation

$n\frac{238}{n}$ = n(n + 3) Multiply both sides by 'n'

238 = n(n + 3) On the left, multiplying and dividing by 'n' cancels out

238 = n² + 3n Distributed right side

0 = n² + 3n - 238 Rearranged to standard form for quadratic equations

Remember standard form for quadratic equations is: ax² + bx + c = 0

State the variables a, b and c:

a = 1; b = 3; c = -238

When a quadratic equation is in standard form, you can use the quadratic formula to solve for 'n'. (Usually, you see the variable 'x', but the quadratic formula can solve for 'n' as if it is 'x', as long as it's in standard form.)

$n = \frac{-b±\sqrt{b^{2}-4ac}}{2a}$ (ignore the Â, it's a formatting error)

$n = \frac{-(3)±\sqrt{(3)^{2}-4(1)(-238)}}{2(1)}$ Substitute the values for 'a', 'b' and 'c' from the equation

$n = \frac{-3±\sqrt{9-(-952)}}{2}$ In the root, two negatives make a positive

$n = \frac{-3±\sqrt{9+952}}{2}$ Add inside the root

$n = \frac{-3±\sqrt{961}}{2}$ Find the square root of 961

$n = \frac{-3±{31}{2}$ Split the equation at the ±

Split for adding:

$n = \frac{-3+31}{2}$ Simplify

n = 14

Split for subtracting:

$n = \frac{-3-31}{2}$ Simplify

n = -17

You get the answers 14 and -17 for 'n'. Decide which one is 'inadmissible', meaning it can't be right even if it solves the equation.

The problem says 'n' is a natural number. Natural numbers are all non-partial numbers count up from 1. (Non-partial means as a fraction, they are reduced to a number over 1). Since -17 is less than 1, it is inadmissible because it is not a natural number.

Therefore, 'n' is 14.

8 0

3 years ago