Write an equation and solve. Round to the nearest hundredth where necessary.
ssential
44 is 11% of what number?

Answer:

rectangle, square

Step-by-step explanation:

A rectangle always has 4 congruent angles. A square is a rectangle, so a square always has 4 congruent angles.

A parallelogram and a rhombus may or may not have 4 congruent angles.

Answer: rectangle, square

Answer:

Only a square and rectangle

Step-by-step explanation:

Both have angles of only 90 deg.

Answer:

Jay needs a 94 on his next test to get an average of 93 on all of his exams.

Step-by-step explanation:

The way test averages work is you take the sum of all of your tests and divide it by the number of tests. So he got an 87 on test 1, a 98 on test 2, and an unknown score on test 3 because he hasn't taken it yet.

Let x = that unknown score. The number of tests is 3. So we set up our equation as:

(87 + 98 + x) / 3

He wants an average of 93 so we set the equation equal to just that.

(87 + 98 + x) / 3 = 93

In order to isolate the numerator equation by itself, we multiply both side by 3. That way the 3 in the denominator on the left side cancels out. You now have:

87 + 98 + x = 93(3)

Simplify:

185 + x = 279

Now to get x by itself, we subtract 185 from both sides:

x = 279 - 185

x = 94

He needs a score of 94 on the next test for the test average that he wants.

Answer:

x=-7, y=2

Step-by-step explanation:

You are given the matrix equation

[tex]\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right] \cdot \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}-18\\13\end{array}\right][/tex]

Find the inverse matrix for the matrix

[tex]\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right][/tex]

1. The determinant is

[tex]\left|\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right]\right|=2\cdot 3-(-1)\cdot (-2)=6-2=4[/tex]

2.

[tex]a_{11}=2 \Rightarrow A_{11}=3\\ \\a_{12}=-2 \Rightarrow A_{12}=-(-1)=1\\ \\a_{21}=-1 \Rightarrow A_{21}=-(-2)=2\\ \\a_{22}=3 \Rightarrow A_{22}=2[/tex]

3. Inverse matrix is

[tex]\dfrac{1}{4}\left[\begin{array}{cc}3&1\\2&2\end{array}\right]^T=\dfrac{1}{4}\left[\begin{array}{cc}3&2\\1&2\end{array}\right][/tex]

So, the solution of the equation is

[tex]\left[\begin{array}{c}x\\y\end{array}\right]=\dfrac{1}{4}\left[\begin{array}{cc}3&2\\1&2\end{array}\right]\cdot \left[\begin{array}{c}-18\\13\end{array}\right]=\\ \\=\dfrac{1}{4}\left[\begin{array}{cc}3\cdot(-18)+2\cdot 13\\1\cdot (-18)+2\cdot 13\end{array}\right]=\dfrac{1}{4}\left[\begin{array}{c}-28\\8\end{array}\right]=\left[\begin{array}{c}-7\\2\end{array}\right][/tex]

Answer:

p - q

Step-by-step explanation:

Given the factors

(x + p)(x - q) ← expanding the factors

= x² - qx + px - pq ← collect like terms

= x² + px - qx - pq ← factor out x in each of the x- terms

= x² + (p - q)x - pq

The coefficient of the x- term is p - q

In a scale model, Figure A has one side measuring 45 units and another side measuring x, while Figure B has corresponding sides of 27 and 18 units. By setting up a proportion, x is determined to be 30 units.

To find the value of x, we can set up a proportion based on the given information:

In Figure A, one side is 45, and in Figure B, it corresponds to a side of 27.

In Figure A, the other side is x, and in Figure B, it corresponds to a side of 18.

So, we can set up the following proportion:

(45 / 27) = (x / 18)

Now, cross-multiply and solve for x:

45 * 18 = 27x

810 = 27x

Now, divide by 27 to find the value of x:

x = 810 / 27

x = 30

So, the value of x is 30.

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Answer:

The difference of five times a number and nine

Step-by-step explanation:

The correct option is the difference of five times a number and nine.

Let the number be = x

Five times a number = 5x

Here difference means subtraction:

The difference of five times a number and nine would be 5x-9....

Answer:

D

Step-by-step explanation:

2022 Russian Invasion of Ukr- I mean got it right on Edge 2022

Answer:

The correct option is A

Step-by-step explanation:

Lets suppose that the third side is hypotenuse.

We will apply Pythagorean theorem:

c²= a²+b²

where,

a=12 inches

b=15 inches

Now substitute the values in the theorem:

c²=(12)²+(15)²

c²=144+225

c²=369

Take square root on both sides:

√c²=√369

c= 19.2 inches.

Now assume that the third side is a leg:

Here we will find the value of b.

a=12 inches

c= 15 inches.

b= ?

Now substitute the values in the theorem:

c²=a²+b²

(15)²=(12)²+b²

225=144+b²

Move the constant to the L.H.S

225-144=b²

81=b²

Take square root on both sides:

√81=√b²

9=b

Now we will find the difference of the third sides:

19.2-9 = 10.2

Thus the length of the third side is 10.2 inches

The correct option is A....

Answer:

A.

Step-by-step explanation:

Answer:

[tex]\large\boxed{(b)\ \dfrac{x+2}{x-3}}[/tex]

Step-by-step explanation:

[tex]\dfrac{1}{x+1}+\dfrac{x}{x-3}-\dfrac{-x-5}{x^2-2x-3}=(*)\\\\x^2-2x-3=x^2-3x+x-3=x(x-3)+1(x-3)=(x-3)(x+1)\\\\(*)=\dfrac{1(x-3)}{(x+1)(x-3)}+\dfrac{x(x+1)}{(x+1)(x-3)}+\dfrac{-(-x-5)}{(x+1)(x-3)}\\\\=\dfrac{x-3+x^2+x+x+5}{(x+1)(x-3)}=\dfrac{x^2+(x+x+x)+(-3+5)}{(x+1)(x-3)}\\\\=\dfrac{x^2+3x+2}{(x+1)(x-3)}=\dfrac{x^2+2x+x+2}{(x+1)(x-3)}=\dfrac{x(x+2)+1(x+2)}{(x+1)(x-3)}\\\\=\dfrac{(x+2)(x+1)}{(x+1)(x-3)}\qquad\text{cancel (x + 1)}\\\\=\dfrac{x+2}{x-3}[/tex]

Answer:

x> 5

Step-by-step explanation:

x - 8 > -3

Add 8 to each side

x - 8+8 > -3+8

x> 5

Answer:

[tex]\huge \boxed{x>5}[/tex]

Step-by-step explanation:

First, add by 8 from both sides of equation.

[tex]\displaystyle x-8+8>-3+8[/tex]

Simplify, to find the answer.

[tex]-3+8=5[/tex]

[tex]\huge \boxed{x>5}[/tex], which is our answer.

Answer:

a = -4.

Step-by-step explanation:

If the are perpendicular then the slope of one graph will be - 1 / slope of the other.

Convert each equation to slope-intercept form:

x + 2y + 3 = 0

2y = = -x - 3

y = (-1/2)x - 3/2 (Slope/intercept form)

So the slope of the line perpendicular to this  will be - 1 / (-1/2) = 2.

Consider the other line:

ax + 2y + 3 = 0

2y = -ax - 3

y = (-a/2) x - 3/2 (Slope/intercept form)

So the slope for this line    - a/2 and it equals 2.

-a/2 = 2

-a = 2*2 = 4

a = -4 (answer).

To determine the value of $a$ such that the graph of the equation $ax + 2y + 3 = 0$ is perpendicular to the graph of the equation $x + 2y + 3 = 0$, we'll need to find the slopes of the two lines represented by these equations since two lines are perpendicular if and only if the product of their slopes is $-1$ (the slopes are negative reciprocals of each other).
Let's find the slope of the first line.
The equation of the first line is $x + 2y + 3 = 0$. We can rearrange this to find $y$ in terms of $x$:
\[2y = -x - 3\]
\[y = \frac{-x}{2} - \frac{3}{2}\]
The slope of this line, denoted by $m_1$, is the coefficient of $x$:
\[m_1 = -\frac{1}{2}\]
Now, let's find the slope of the second line.
The equation of the second line is $ax + 2y + 3 = 0$. Rearranging this to solve for $y$ in terms of $x$, we get:
\[2y = -ax - 3\]
\[y = -\frac{a}{2}x - \frac{3}{2}\]
The slope of this line, denoted by $m_2$, is the coefficient of $x$:
\[m_2 = -\frac{a}{2}\]
Now, for the lines to be perpendicular, their slopes must satisfy the following condition:
\[m_1 \cdot m_2 = -1\]
Substituting the known slopes into the equation, we get:
\[-\frac{1}{2} \cdot \left(-\frac{a}{2}\right) = -1\]
\[\frac{a}{4} = -1\]
\[a = -4\]
Therefore, the value of $a$ that ensures the graph of the equation $ax + 2y + 3 = 0$ is perpendicular to the graph of the equation $x + 2y + 3 = 0$ is $a = -4$.

Answer:

C

Step-by-step explanation:

(-3,0)

I did it in the quiz and the test.

Got it correct.

Answer:

30√3 - 21 √6

Step-by-step explanation:

The given expression is:

3√2 (5√6 -7√3)

We cannot subtract the values inside the bracket because the values inside the radicals are not same.

So multiply 3√2 with the bracket.

=3*5√2*6 -  3*7√2*3

=15√12 - 21√6

Now break √12

=15√4*3 - 21√6

write √4*3 separately:

=15√4 *√3 - 21√6

We know that √4 = 2

=15*2*√3 - 21√6

=30√3 - 21 √6

Therefore the answer is 30√3 - 21 √6 ....

Answer: [tex]AC=10.5[/tex]

Step-by-step explanation:

Assuming that [tex]b=AC[/tex] and given the following equation:

 [tex]tan(55\°)=\frac{15}{b}[/tex]

You need to solve for "b" in order to find the lenght of AC asked in the exercise.

 Therefore, with this procedure you get that the lenght of AC is the following:

[tex]\frac{15}{tan(55\°)}=b[/tex]

[tex]b=AC=10.5[/tex]

Step-by-step explanation:

84 ounces / 27 turtles = 3.111 ounces per turtle

Or in fractional form, 3 ¹/₉ ounces per turtle.

Each turtle gets 3.11 ounces if Each of the 27 turtles in the pet store needs to be fed

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

Each of the 27 turtles in the pet store needs to be fed.

There is one bag of turtle food that weighs 84 ounces.

Each turtle gets the food = 84/27

= 3.11 ounces

Thus, each turtle gets 3.11 ounces if Each of the 27 turtles in the pet store needs to be fed

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Answer:

49

Step-by-step explanation:

We are going to use PEMDAS to simplify

[tex]3^3-10+(2 \cdot 4^2)[/tex]

First step is P.

P refers to the parenthesis or anything acting as a grouping symbol.

We notice the following operations there are multiplication and exponents.

According to PEMDAS, after parenthesis we do the exponents so let's do the exponent in the ( ).

[tex]3^3-10+(2 \cdot 16)[/tex]

Now we still have to finish P up. That is we need to do the one last operation in the ( ).

[tex]3^3-10+(32)[/tex]

Nothing left to perform in the () so we can just write:

[tex]3^3-10+32[/tex]

Now there are no more grouping symbols left.

The next letter is E and it stands for exponents so we must evaluate anything we can that has an exponent.

[tex]27-10+32[/tex]

Now after E we have M and D which means to multiply and divide as you the expression from left to right.

There is no multiplication and division so moving on.

A and S means to do the addition and subtraction as it occurs left to right:

[tex]17+32[/tex]

[tex]49[/tex]

Answer:

(x, y ) → (x + 4, y - 3 )

Step-by-step explanation:

A translation of 4 units to the right is a positive shift in the x- direction, that is,

The x- coordinate of the image is the original + 4

A translation of 3 units down is a negative shift in the y- direction, that is

The y- coordinate of the image is the original - 4

Putting the 2 together

(x, y ) → (x + 4, y - 3 )

[tex]\dfrac{B_x \sqrt{74_x}}{1D_x}+J_x51_x=4G3_x[/tex]

A=10, B=11, C=12, etc.

[tex]\dfrac{11\cdot x^0\cdot \sqrt{7\cdot x^1+4\cdot x^0}}{1\cdot x^1+13\cdot x^0}+19\cdot x^0\cdot (5\cdot x^1+1\cdot x^0)=4\cdot x^2+16\cdot x^1+3\cdot x^0\\\\\dfrac{11\sqrt{7x+4}}{x+13}+19(5x+1)=4x^2+16x+3\\\\\dfrac{11\sqrt{7x+4}}{x+13}+95x+19=4x^2+16x+3\\\\11\sqrt{7x+4}+95x(x+13)+19(x+13)=(4x^2+16x+3)(x+13)\\\\11\sqrt{7x+4}+95x^2+1235x+19x+247=4x^3+52x^2+16x^2+208x+3x+39\\\\11\sqrt{7x+4}=4x^3-27x^2-1043x-208\\\\121(7x+4)=(4x^3-27x^2-1043x-208)^2[/tex]

[tex]121(7x+4)=(4x^3-27x^2-1043x-208)^2\\\\847x+484=16 x^6 - 216 x^5 - 7615 x^4 + 54658 x^3 + 1099081 x^2 + 433888 x + 43264\\\\16 x^6 - 216 x^5 - 7615 x^4 + 54658 x^3 + 1099081 x^2 + 433041 x +42780=0[/tex]

Now, the "only" thing that remains to do is solving the above equation.

While making this problem I only made sure it has a solution. I didn't try to solve it myself and I didn't know it will end up with such "convoluted" polynomial. Sorry to everyone who tried to solve it... m(_ _)m

I think the best way to approach it is using the rational root theorem since we know that [tex]x\in\mathbb{N}[/tex]. Moreover we can deduce that [tex]x\geq19[/tex] since there is [tex]J[/tex] and [tex]J=19[/tex].

After you succesfully solve it, you should get the answer [tex]x=20[/tex].

To find the exact value of cos(127.5), we can use the half angle identity for cosine. By substituting the angle into the half angle identity and simplifying, we find that cos(127.5) is approximately ±0.99992.

The cosine function is a trigonometric function that relates the angle of a right triangle to the ratio of the adjacent side to the hypotenuse. To find the exact value of cos(127.5), we can use the half angle identity for cosine. This identity states that cos(θ/2) = ±√((1 + cos(θ))/2), where θ is the original angle.

In this case, we have θ = 255 degrees (since 127.5 is half of 255). Using the half angle identity, we can calculate cos(127.5) as follows:

Therefore, the exact value of cos(127.5) is approximately ±0.99992.

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The slope is [tex]-10[/tex] and the y-intercept is [tex]1[/tex].

This function is written in slope-intercept form, which is [tex]y=mx+b[/tex].  In this form, [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

In this case, [tex]m=-10[/tex] and [tex]b=1[/tex], so those are the answers to this problem.

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have the following equation:

[tex]y = -10x + 1[/tex]

So we have to:

[tex]m = -10\\b = 1[/tex]

Answer:

[tex]m = -10\\b = 1[/tex]

Answer:

A

Step-by-step explanation:

3y (-5)(y+2)

3y(-5y-10)

3y-5y-10

-2y-10

-2y-10

3y - 5(y +2)

Use the distributive property:

3y - 5y +10

Combine like terms:

-2y+10

The answer is B.

Answer:

TRUE:

When x≈2.7, the graphs of f(x) and g(x) intersect

f(x)=g(x) when x=0

Step-by-step explanation:

The graphs of two function y=f(x) and y=g(x) are shown in attached diagram.

These two graphs intersect at two points (0,-3) and about (2.7,2.3). This means that

f(0)=g(0)=-3

and

f(2.7)=g(2.7)=2.3

So, x=0, y=-3 is the solution to the system (the solution to the system is ordered pair (x,y), not only x)

Points (1.5,0) and (2,0) are not solutions, because they are not points of graphs intersection.

When x≈2.7, the graphs of f(x) and g(x) intersect (TRUE)

f(x)=g(x) when x=0 (TRUE)

Answer:

f(x)=g(x) when x=0.

x=0 is a solution to the system.

When x≈2.7, the graphs of f(x) and g(x)intersect because they are equal to each other at that value.

Answer:62

Step-by-step explanation:

F=c+32

C=30

F=30+32

F=62

The Fahrenheit temperature equivalent to 30°C (using the formula  F = C + 32) is  62°F.

The Fahrenheit temperature equivalent to 30°C can be found using the temperature conversion formula F = C + 32, where F is the temperature in Fahrenheit and C is the temperature in Celsius.

To find the temperature in Fahrenheit, substitute 30 for C:

F = 30°C + 32 = 62°F

ANSWER

(0, 1), (1,3), (2, 9), (3, 27)

EXPLANATION

For an exponential function, there is a common ratio among the terms.

Therefore we need to examine the y-values of the ordered pairs to see which one has a common ratio.

For the first option, the y-values are:

0,1,8,27

[tex] \frac{27}{8} \ne \frac{8}{1} [/tex]

For the second option, the y-values are:

1,2,5,10

[tex] \frac{10}{5} \ne \frac{5}{2} [/tex]

For the third option, the y-values are:

0,3,6,9

[tex] \frac{9}{6} \ne \frac{6}{3} [/tex]

For the last option, the y-values are:

1,3,9,27

[tex] \frac{27}{9} = \frac{9}{3} = \frac{3}{1} = 3[/tex]

Since there is a common ratio of 3, the set of ordered pairs (0, 1), (1,3), (2, 9), (3, 27) could generate an exponential sequence.

Answer:

The sum is [tex]9,331[/tex]

Step-by-step explanation:

we have

[tex]1,6,36,...[/tex]

we have

[tex]a1=1[/tex]

[tex]a2=6[/tex]

[tex]a3=36[/tex]

Find the common ratio r

[tex]a2/a1=6/1=6[/tex]

[tex]a3/a2=36/6=6[/tex]

The common ratio is r=6

The formula to calculate the sum in a geometric sequence is equal to

[tex]S=a1\frac{(1-r^{n})}{(1-r)}[/tex]

where

n is the number of terms

r is the common ratio

a1 is the first term

we have

[tex]n=6[/tex]

[tex]a1=1[/tex]

[tex]r=6[/tex]

substitute

[tex]S=(1)\frac{(1-(6)^{6})}{(1-6)}[/tex]

[tex]S=\frac{(1-(6)^{6})}{(-5)}[/tex]

[tex]S=9,331[/tex]

Final answer:

To simplify (f+g)(2) with given functions f(x)=x+1 and g(x)=x^2-x, calculate the functions' values at x=2 and sum them, resulting in (f+g)(2) = 5.

Explanation:

To find and simplify the expression (f+g)(2), you first need to determine the individual functions f(x) and g(x) at the value x = 2, and then sum them.

The function f(x) is given by f(x) = x + 1. At x = 2, f(2) = 2 + 1 = 3.

The function g(x) is given by g(x) = x2 - x. At x = 2, g(2) = 22 - 2 = 4 - 2 = 2.

Adding these two results together, we get (f+g)(2) = f(2) + g(2) = 3 + 2 = 5.

Answer:

(-2,12)

Step-by-step explanation:

it is the closest because it is only 2 units away

The coordinates of points on the Cartesian plane, are given by a pair of values

Reason:

The given coordinates are; (-6, 0), (-2, -12), (4, 2), (5, 1)

Method:

A point is close to the y-axis where the magnitude x-coordinate value is low

By observation, the coordinates of the point having the lowest magnitude of the x-value, is the point (-2, -12)

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Answer:

See explanation

Step-by-step explanation:

Triangle ABC ha vertices at: A(-3,6), B(0,-4) and (2,6).

Let us apply 90 degrees clockwise about the origin twice to obtain 180 degrees clockwise rotation.

We apply the 90 degrees clockwise rotation rule.

[tex](x,y)\to (y,-x)[/tex]

[tex]\implies A(-3,6)\to (6,3)[/tex]

[tex]\implies B(0,4)\to (4,0)[/tex]

[tex]\implies C(2,6)\to (6,-2)[/tex]

We apply the 90 degrees clockwise rotation rule again on the resulting points:

[tex]\implies (6,3)\to A''(3,-6)[/tex]

[tex]\implies (4,0)\to B''(0,-4)[/tex]

[tex]\implies (6,-2)\to C''(-2,-6)[/tex]

Let us now apply 90 degrees counterclockwise  rotation about the origin twice to obtain 180 degrees counterclockwise rotation.

We apply the 90 degrees counterclockwise rotation rule.

[tex](x,y)\to (-y,x)[/tex]

[tex]\implies A(-3,6)\to (-6,-3)[/tex]

[tex]\implies B(0,4)\to (-4,0)[/tex]

[tex]\implies C(2,6)\to (-6,2)[/tex]

We apply the 90 degrees counterclockwise rotation rule again on the resulting points:

[tex]\implies (-6,-3)\to A''(3,-6)[/tex]

[tex]\implies (-4,0)\to B''(0,-4)[/tex]

[tex]\implies (-6,2)\to C''(-2,-6)[/tex]

We can see that A''(3,-6), B''(0,-4) and C''(-2,-6) is the same for both the 180 degrees clockwise and counterclockwise rotations.

Triangle ABC ha vertices at: A(-3,6), B(0,-4) and (2,6).

Let us apply 90 degrees clockwise about the origin twice to obtain 180 degrees clockwise rotation.

We apply the 90 degrees clockwise rotation rule.

(x,y) --- (y, -x)

A(-3, 6) > (6, 3)

B(0, 4) > (4, 0)

C(2, 6) > (6, -2)

We apply the 90 degrees clockwise rotation rule again on the resulting points:

(6, 3) > A'(-3, 6)

(4, 0) > B'(0, -4)

(6, -2)> C'(-2, -6)

Let us now apply 90 degrees counterclockwise  rotation about the origin twice to obtain 180 degrees counterclockwise rotation.

We apply the 90 degrees counterclockwise rotation rule.

(x,y) --- (-y, x)

A(-3, 6) > (-6, -3)

B(0, 4) > (-4, 0)

C(2, 6) > (-6, 2)

We apply the 90 degrees counterclockwise rotation rule again on the resulting points:

(-6, -3) > A'(3, -6)

(-4, 0) > B'(0, -4)

(-6, 2) > C'(-2, -6)

We can see that A'(3,-6), B'(0,-4) and C'(-2,-6) is the same for both the 180 degrees clockwise and counterclockwise rotations.

Ez why to copy

Answer:

A) 12,14,16

B) 3x+1=16

Step-by-step explanation:

A)

They already gave you the equation to solve:

n+(n+2)+(n+4)=42

n+n+2+n+4=42

Put like terms together:

n+n+n+2+4=42

Combine the like terms:

3n+6=42

Subtract 6 on both sides:

3n=42-6

Simplify:

3n=36

Divide both sides by 3:

n=36/3

Simplify:

n=12

If n=12,

then

n+2=14 and

n+4=16.

Check the addition of those numbers: 12+14+16=26+16=42.

B)

There is a lot of equations that have a solution of 5.

It might be good start with x=5.

Then just remember whatever you do to one side, you must do to the other.

x=5

Multiply both sides by 3:

3x=15

Add 1 on both sides:

3x+1=16

An example of equation that solution 5 is 3x+1=16.

Answer:

7776π  or

24,429.02 unit^3 to the nearest  hundredth.

Step-by-step explanation:

The formula for the volume of a sphere is V = 4/3 π r^3   where r is the radius.

Here V = 4/3 * π * 18^3

= 7776π unit^3.

Answer:

7776 pi

Step-by-step explanation:

Answer:

See attachment

Step-by-step explanation:

The given function is:

[tex]f(x)=3^{x-1}+2[/tex]

This is an exponential function with a horizontal asymptote at  [tex]y=2[/tex]

There is a translation of the form [tex]f(x)=g(x-1)+2[/tex]

The graph of the parent function [tex]g(x)=3^{x}[/tex] is shifted to the right 1 unit and shifted up by 2 units.

See attachment for graph.