Element X is a radioactive isotope such that every 13 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 90 grams, how long would it be until the mass of the sample reached 62 grams, to the nearest tenth of a year?

Hi there!

[tex]\large\boxed{-n^2 + 4n}[/tex]

Begin by evaluating f - g:

4n - 5 - (n² - 5)

Simplify:

4n - 5 - n² + 5  = 4n - n²

Or it can be written as -n² + 4n to match the first answer choice.

Answer:

y = 2x + 3

Step-by-step explanation:

The slope can be found by taking two points, for instance: (0,3) and (3,9) which lie on the graph.  Find the slope between the two, remember rise over run:

(9-3)/(3-0) = 6/3 = 2

The y-intercept is (0,3)

So b in the y= mx + b equation is 3.

m is the slope, so it is 2.

y = 2x + 3

Answer:

For the triangle, its area is 32.1 inches.

For the trapezoid, its area is 170 feet.

Step-by-step explanation:

The formula for finding the area of a triangle is A = h * b/2, where h is for height and b is for base. There seems to be two measurements at the base of the triangle so what I did is I added together 3.5 and 7.2 and got 10.7. The slant measurement of the triangle isn't important in this formula so just pretend 5.5 in isn't there. Multiply 10.7 (base) to 6 (height) and you'll get 64.2. Now divide the product by 2 and you'll get 32.1 inches as the area of the triangle.

The formula for finding the area of a trapezoid is A = ((a + b)/2)h, where a is base A, b is base B, and h is the height. This formula looks a bit complicated but if you know a bit of PEMDAS, then you'll understand the formula. Again, there are two measurements at the base of the trapezoid but simply, I added them to get 24 and the slants don't make any use for this formula either. Add 10 (base A) and 24 (base B) to get 34. Now divide 34 by 2 and you'll get 17. Finally, multiply the product to 10 (height) and you'll get 170 feet as the area of the trapezoid.

If you don't know PEMDAS, just comment something related to "Can you explain what PEMDAS is?" or "What is PEMDAS?" and I will answer your question as quick as I possibly can. I hope this helps!

Given:

The graph of a function.

To find:

The average rate of change of h over the interval [tex]5\leq t\leq 9[/tex].

Solution:

The average rate of change of a function f(x) over the interval [a,b] is:

[tex]m=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

So, the average rate of change of h over the interval [tex]5\leq t\leq 9[/tex] is:

[tex]m=\dfrac{h(9)-h(5)}{9-5}[/tex]

From the given graph it is clear that [tex]h(9)=7,h(5)=3[/tex]. Substituting these values, we get

[tex]m=\dfrac{7-3}{9-5}[/tex]

[tex]m=\dfrac{4}{4}[/tex]

[tex]m=1[/tex]

Therefore, the average rate of change of h over the interval [tex]5\leq t\leq 9[/tex] is 1.

Answer:

sksjdkddudjdjn sjjdkdls

Answer:

Therefore, we have to round down: the whole number ones place value of 15.403, 15, remains 15, and the decimal point and all digits (.403) are removed.

Answer:

∠ A = 70°

Step-by-step explanation:

The opposite angles in a cyclic quadrilateral are supplementary, then

∠ A + ∠ Q = 180°

∠ A + 110° = 180° ( subtract 110° from both sides )

∠ A = 70°

Answer:

Evelyn's dance class on Saturday starts at 11:05 A.M.

Step-by-step explanation:

I know this because if her class takes an hour and 40 minutes you would subtract the hour and 40 minutes from 12:45 so you could do 12 - 1 which equals 11. Then you would do 45 - 40 which equals 5. And last you would put the new times together so it would be, 11:05. Her dance class starts at 11:05 A.M.

Answer: 120 cubed inches

Step-by-step explanation:

First, multiply them all together. 6x10x2 = 120 cubed inches

Answer:

56.549 cm   (choice 1)

Step-by-step explanation:

If the area of the square if 36 cm, then each side is 6 cm.

That means the diameter for each semi circle is also 6 cm.

Formula for a semi circle is 1/2(πr²)

We need the radius, which is half the diameter. So the radius is 6÷2= 3

Now plug in to the formula.

A= 1/2(π3²)

A= 14.137 (nearest hundredths)

Now multiply that by 4, because there are 4 semi circles

4(14.137)= 56.549 cm (nearest hundredths)

Answer:

its 6 square units

Step-by-step explanation:

count how many boxes the that contain blue and devide by 2

Answer:

6

Step-by-step explanation:

There are 3 parts to each side. All three of them are the same so we only have to find the area of one different parts

Area of One Side

Triangle

The side of a square is 1 square unit.

each leg of the triangle is 1 unit

The area of 1 triangle = 1/2 * 1 * 1 = 1/2

Area of 1 side

There are 3 equal parts (3 triangles) that make up a side.

Area of the three triangles = 3 * 1/2 = 3/2 = 1.5

Area of all 4 sides

4 * 1.5 = 6

The area of the blue colored figure is 6 units.

Answer:

w^2 -18w + 81

Step-by-step explanation:

Simply, what we have to do here is to divide the coefficient of w by 2, then square it

we have this as -18/2 = -9

Squaring is -9^2 = 81

Answer:

76

Step-by-step explanation:

so the sequence(pattern) is it increases by 5

there are 2 ways to solve this promblem

one count on your toes and hands by 5 starting at one until u get to 10 fingers and 5 toes. soon the promblems will get harder and you cant do that

other way multiply 5 by 15 and add it to 1

t( 15 ) = t( 1 ) + [ 14 × ( Constant value ) ]

________________________________

t( 1 ) = 1

&

Constant value = t( 2 ) - t( 1 ) = t( 3 ) - t( 2 )

Constant value = 6 - 1

Constant value = 5

________________________________

Thus :

t ( 15 ) = 1 + [ 14 × 5 ]

t( 15 ) = 1 + 70

t( 15 ) = 71

Answer:

Flexibility: Stretching

Endurance: Being able to dance for periods of time

Answer:

The mode is the number that appears the most in a data set, therefore the mode is $4 since it is the only number appearing twice

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

rotten oranges=10/100*20

200/100

2 dozen

good oranges=total dozen-rotten oranges

20-2

18 d0zen were good oranges.

Given:

Consider the given expression is:

[tex]\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}[/tex]

To find:

The simplified form of the given expression.

Solution:

We have,

[tex]\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}[/tex]

By using the quotient property of exponents, we get

[tex]=x^{4-2}y^{-4-(-2)}z^{-2-4}[/tex]              [tex]\left[\because \dfrac{a^m}{a^n}=a^{m-n}\right][/tex]

[tex]=x^{2}y^{-4+2}z^{-6}[/tex]

[tex]=x^{2}y^{-2}z^{-6}[/tex]

By using negative exponent property, we get

[tex]=\dfrac{x^{2}}{y^{2}z^{6}}[/tex]           [tex]\left[\because a^{-n}=\dfrac{1}{a^n}\right][/tex]

The simplified form of the given expression is [tex]\dfrac{x^{2}}{y^{2}z^{6}}[/tex].

Therefore, the correct option is B.

Answer:

Hello! answer:

rectangle a: 8

rectangle b: 24

figure: 32

Step-by-step explanation:

Hello I'll show a demonstration, with a picture and explanation. Ok so as shown in the picture i circled the base and height those are basically what you have to multiply to find the area.

we are given the height for rectangle a but not the base so we have to find it we know the base at the bottom for the whole thing is 5 and the base for B is. 3 so we can just subtract 3 from 5 to find A's base so... 5 - 3 = 2

now we have everything we need to find the area so....

4 × 2 = 8 so rectangle a is 8

3 × 8 = 24 so rectangle b is 24

then for the whole figure we can just add those two up for the entire area so...

24 + 8 = 32 therefore the figures area is 32 Hope that helps!

Answer:

[tex](a)\ y = 2x +8[/tex]

[tex](b)\ y = 0[/tex]

[tex](c)\ y = -5[/tex]

Step-by-step explanation:

Given

[tex]y = x^2[/tex]

First, graph [tex]y = x^2[/tex] (See attachment)

We are not limited to any particular linear equation; as long as we meet the required condition

Solving (a): Equation of a line that intersects [tex]y = x^2[/tex] at two points

Select any two points on opposite sides of the curve

The selected points are:

[tex](x_1,y_1) = (-2,4)[/tex]

[tex](x_2,y_2) = (4,16)[/tex]

Calculate slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{16 - 4}{4 - -2}[/tex]

[tex]m = \frac{12}{6}[/tex]

[tex]m = 2[/tex]

The equation is then calculated using:

[tex]y = m(x - x_1) + y_1[/tex]

This gives:

[tex]y = 2(x - -2) + 4[/tex]

[tex]y = 2(x +2) + 4[/tex]

Open bracket

[tex]y = 2x +4 + 4[/tex]

[tex]y = 2x +8[/tex]

Solving (b): Equation of a line that intersects [tex]y = x^2[/tex] at one point

A good illustration of this is x-axis

Because it intersects with the line at just one point, which is origin (0,0).

The equation of line at this point is:

[tex]y = 0[/tex]

Solving (c): Equation of a line that does not intersect [tex]y = x^2[/tex]

Here, we make use of any horizontal line below the x-axis

Select any two horizontal points below the x-axis

[tex](x_1,y_1) = (-5,-5)[/tex]

[tex](x_2,y_2) = (5,-5)[/tex]

Calculate slope

[tex]m = \frac{-5--5}{5--5}[/tex]

[tex]m = \frac{0}{10}[/tex]

[tex]m = 0[/tex]

The equation is then calculated using:

[tex]y = m(x - x_1) + y_1[/tex]

[tex]y = 0(x - -5) + (-5)[/tex]

[tex]y = 0-5[/tex]

[tex]y = -5[/tex]

Answer:

43

Step-by-step explanation:

we have two rectangles so we will divide them into 2.

first rectangles is 7m and 4m. 7 x 4 = 28

2nd rectangles is 3m and 5m 3 x 5 = 15

15 + 28 = 43.

Answer:  Refer to the screenshot below

I've filled in the boxes with the proper answers

====================================================

Explanation for problem 1

In line 1, I used the distributive rule a*(b+c) = a*b+a*c. On the left side the 3(n+2) becomes 3n+6. On the right side, the 9(6-n) becomes 54-9n

On the next line, I added 9n to both sides. The 3n on the left side updates to 3n+9n = 12n.

For the third line, I subtracted 6 from both sides. Then the last line involves dividing both sides by 12 to fully isolate n. To confirm the solution n = 4, plug it back into the original equation. You should get the same thing on both sides after simplifying.

------------------------------------

Explanation for problem 2

The steps here are similar as problem 1, but this time we're involving fractions. Unfortunately, these steps don't involve clearing out the fractions which is often a handy trick to use.

We use the distributive rule on line 1

For line 2, we subtract 2m/9 from both sides. Think of 2m/3 as 6m/9 to help combine the fractions. The denominators must be the same for you to be able to add or subtract fractions.

For line 3, we subtract 4/3 from both sides. Think of 4/3 as 12/9.

The last step is to multiply both sides by 9/4, which is the reciprocal of 4/9. Your teacher made a typo on the right hand side of the last line. It should read [tex]\frac{4}{9}m[/tex] and not [tex]\frac{2}{9}m[/tex]. Refer to the previous line.

Answer:

b=27,-13

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Steps:

|b-7|=20

Activate the law of absolute values

b - 7 = -20 or b-7=20

b = 27 or b = -13

Answer:

[tex]b = 27[/tex]

Step-by-step explanation:

[tex]20 = |b - 7| [/tex]

[tex]b - 7 = 20[/tex]

[tex]b = 20 + 7[/tex]

[tex]b = 27[/tex]

Answer:

[tex]x = 1\frac{4}{5}[/tex]

Step-by-step explanation:

Factor and set each factor equal to zero.

Answer:

Step-by-step explanation:

30x-45=5x

30x-5x=45

25x=45

x=45/25

x=9/5

Answer:

3 terms

Step-by-step explanation:

There are three terms in the expression "4xy + 3xy + 2".

The terms are: 4xy, 3xy, and 2.

4xy and 3xy are variables while the 2 is a constant.

Answer:

3 terms!

Step-by-step explanation:

the numbers are called terms just remeber that and it will be easy.

Answer: d.

2x + x = 180: 60°and 120°

Step-by-step explanation:

Let x= one of the supplements.  (smaller)

As per given , measure of second angle = 2x

We know that,

The sum of two supplements = 180 degrees

Then,

smaller angle + larger angle =180°

i.e. x+2x = 180°

3x= 180°

x=60°

then, 2x = 2 (60°) = 120°

hence, the correct option is d.

2x + x = 180: 60°and 120°

Answer:

2/3

Step-by-step explanation: