What value of k make the equation 7(14k + 15) -7 = 19k + 6 (-13 + 15k) true?

The sign on a clearance rack tells customers the price is 1/2 the lowest marked price. If an item is marked $9.98, how much will

Artyom0805 [142]

Answer:

4.99

Step-by-step explanation:

9.98 divide by 2

3 0

3 years ago

PLEASE HELP ME WITH GEO TEST!

pantera1 [17]

Answer:

The first one is ur answer

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

A sample of a radioactive substance decayed to 97% of its original amount after a year. (Round your answers to two decimal place

Andrej [43]

Answer:

a) The half life of the substance is 22.76 years.

b) 5.34 years for the sample to decay to 85% of its original amount

Step-by-step explanation:

The amount of the radioactive substance after t years is modeled by the following equation:

$P(t) = P(0)(1-r)^{t}$

In which P(0) is the initial amount and r is the decay rate.

A sample of a radioactive substance decayed to 97% of its original amount after a year.

This means that:

$P(1) = 0.97P(0)$

Then

$P(t) = P(0)(1-r)^{t}$

$0.97P(0) = P(0)(1-r)^{0}$

$1 - r = 0.97$

So

$P(t) = P(0)(0.97t)^{t}$

(a) What is the half-life of the substance?

This is t for which P(t) = 0.5P(0). So

$P(t) = P(0)(0.97t)^{t}$

$0.5P(0) = P(0)(0.97t)^{t}$

$(0.97)^{t} = 0.5$

$\log{(0.97)^{t}} = \log{0.5}$

$t\log{0.97} = \log{0.5}$

$t = \frac{\log{0.5}}{\log{0.97}}$

$t = 22.76$

The half life of the substance is 22.76 years.

(b) How long would it take the sample to decay to 85% of its original amount?

This is t for which P(t) = 0.85P(0). So

$P(t) = P(0)(0.97t)^{t}$

$0.85P(0) = P(0)(0.97t)^{t}$

$(0.97)^{t} = 0.85$

$\log{(0.97)^{t}} = \log{0.85}$

$t\log{0.97} = \log{0.85}$

$t = \frac{\log{0.85}}{\log{0.97}}$

$t = 5.34$

5.34 years for the sample to decay to 85% of its original amount

8 0

4 years ago

a taxi driver fills the gas tank and. calculates that the car traveled 356.25 miles using 9.5 gallons of gas how many miles per

earnstyle [38]

Answer:

37.5 Miles Per Gallon

Step-by-step explanation:

You find the unit rate of miles per gallon by dividing the miles by the gallons

356.25/9.5

= 37.5

7 0

3 years ago

Solve the following system of equations. 2x+y=3 I= 2y - 1 x= y=

marin [14]

Note: I am assuming your second equation is:

x = 2y - 1

Answer:

The solution to the system of equations is:

x = 1

y = 1

Step-by-step explanation:

Given the system of equations

2x+y=3

x = 2y - 1

solving the system of equations using the elimination method

$\begin{bmatrix}2x+y=3\\ x=2y-1\end{bmatrix}$

Arrange equation variables for elimination

$\begin{bmatrix}2x+y=3\\ x-2y=-1\end{bmatrix}$

Multiply x-2y=-1 by2: 2x-4y=-2

$\begin{bmatrix}2x+y=3\\ 2x-4y=-2\end{bmatrix}$

subtracting the equations

$2x-4y=-2$

$-$

$\underline{2x+y=3}$

$-5y=-5$

now solve -5y = -5 for y

$-5y=-5$

Divide both sides by -5

$\frac{-5y}{-5}=\frac{-5}{-5}$

Simplify

$y=1$

For 2x+y=3 plug in y=1

$2x+1=3$

subtract 1 from both sides

$2x+1-1=3-1$

Simplify

$2x=2$

Divide both sides by 2

$\frac{2x}{2}=\frac{2}{2}$

Simplify

$x=1$

Therefore, the solution to the system of equations is:

x = 1

y = 1

8 0

3 years ago