assume the substance has a half-life of 11 years and the initial amount is 126 grams.How long will it be until only 15 % remains?

Answers

Answer 1

Answer: (126) times (1/2 to the x/11 power) = 15% times 126

(1/2) to the x/11 power = 0.15

Take the log of both sides :

(x/11) times log(1/2) = log(0.15)

Multiply both sides by 11 :

'x' times log(1/2) = 11 x log(0.15)

Divide both sides by " log(1/2) " :

x = 11 x log(0.15)/log(1/2) = 30.107 years (rounded)

That's the time it takes for any-size sample of this substance
to decay to 15% of its original size.

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What is the standard equation of the circle in the graph?

Answers

Answer:

Standard Equation Of Circle is $(x-h)^2+(y-k)^2+r^2$

Step-by-step explanation:

Let we are given a circle in graph with center P whose coordinate are ( h , k ) and radius of the circle is r units.

Then the standard equation of circle is written as ,

$(x-h)^2+(y-k)^2=r^2$

If center becomes origin then, Equation become

$x^2+y^2=r^2$

x^2 + y^2 = radius^2
Is that what your adking for? This is for a circle around the origin.

Can someone show me how to do this? What volumes of 60% hydrochloric acid solution and 30% hydrochloric acid solution must be mixed to make 125mL of 36% hydrochloric acid solution?

Answers

u need two equations.x + y = 125
0.60x + 0.30y = (0.36)(125)

x + y = 125
0.60x + 0.30y = 45

solve for a variable in the first equation
y = 125 - x

plug into the second equation
0.60x + 0.30(125 - x) = 45
0.60x + 37.5 - 0.30x= 45
0.30x + 37.5 = 45
0.30x = 7.5
x = 25

plug the answer for x into the first equation
25 + y = 125
y = 100

What is the value of x in the equation 3x – 4y = 65, when y = 4?

Answers

27 because 4*4=16. 65+16=81 and 81 divided by 3=27

The upper-left coordinates on the a rectangle are (-4,4), and the upper-right coordinates are (4,4). The rectangle has a perimeter of 20 units

Answers

Step-by-step explanation:

im pretty sure this is it.

you would have to count the units between the two pints given and count it twice (since a rectangles opposite side are equal)

To solve this problem, firstly, let's find the width of the rectangle. The width of the rectangle is the horizontal distance between the upper-left and upper-right points. In the Cartesian coordinate system, this simply means taking the difference between the x-coordinates of these points. We find the difference between 4 (x-coordinate of upper-right point) and -4 (x-coordinate of upper-left point). This gives us 8 units, which is the width of our rectangle.

Now that we know the width, we can proceed to find the length. We know that the perimeter (total distance around the rectangle) is given by the formula 2L + 2W, where L is the length and W is the width of the rectangle.

We know that the perimeter is 20 units and the width is 8 units.

We can substitute these values into the formula and solve for L (the length):

20 = 2L + 2*8

Simplifying the right side gives us:

20 = 2L + 16,

Subtracting 16 from both sides gives us:

4 = 2L

Finally, divide both sides by 2 to solve for L:

L = 2 units.

So, the

Answer: width of the rectangle is 8 units and the length is 2 units.

Write y= -3/4 x-6 in standard form using integers.

Answers

Answer:

3x + 4y = -24.

Step-by-step explanation:

y= -3/4 x-6

Multiply through by 4:

4y = -3x - 24

3x + 4y = -24.

what are the solutions to the quadratic equation (5y 6)2 = 24? y = and y = y = and y = y = and y = y = and y =

Answers

If you would like to find the solutions to the quadratic equation (5y + 6)^2 = 24, you can do this using the following steps:

(5y + 6)^2 = 24
25y^2 + 2 * 6 * 5y + 36 = 24
25y^2 + 60y + 36 - 24 = 0
25y^2 + 60y + 12 = 0
25 * (y + 6/5)^2 - 24 = 0
1. y = -6/5 - (2 * sqrt(6))/5
2. y = (2 * sqrt(6))/5 - 6/5

The correct result would be y = -6/5 - (2 * sqrt(6))/5 and y = (2 * sqrt(6))/5 - 6/5.

The solution to the quadratic equation is y = -2.18 and y = -0.22