Factor completely x2 - 8x + 16.
(x + 4)(x + 4)
(X - 4)(x - 4)
(x + 4)(x - 4)
(x-2)(x - 8)

We know that after a dreary day of rain, the sun peeks through the clouds and a rainbow forms. So you notice the rainbow is the shape of a parabola as shown in the first figure. This parabola has the following equation:

[tex]y=-x^2+36[/tex]

On the other hand, in the distance you notice that an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. So let's choose two points on the graph of the parabola to build up the equation of the line:

[tex]\bullet \ If \ x=-5, then: \\ \\ y=-(-5)^2+36=11 \\ \\ So: \\ \\ P_{1}(-5,11) \\ \\ \\ \bullet \ If \ x=4, then: \\ \\ y=-(4)^2+36=20 \\ \\ So: \\ \\ P_{2}(4,20)[/tex]

Therefore, the equation of the line using these two points is:

[tex]y-20=\frac{20-11}{4-(-5)}(x-4) \\ \\ y-20=\frac{9}{9}(x-4) \\ \\ y-20=x-4 \\ \\ y=x+20-4 \\ \\ y=x+16[/tex]

FOR THE PARABOLA, THE TABLE IS:

[tex]Other \ two \ points: \\ \\ \bullet \ If \ x=0, then: \\ \\ y=-(0)^2+36=36 \\ \\ So: \\ \\ P_{3}(0,36) \\ \\ \\ \bullet \ If \ x=1, then: \\ \\ y=-(1)^2+36=35 \\ \\ So: \\ \\ P_{4}(1,35)[/tex]

So the table is:

[tex]\left[\begin{array}{cc}x & y\\-5 & 11\\4 & 20\\0 & 36\\1 & 35\end{array}\right][/tex]

FOR THE LINE, THE TABLE IS:

[tex]Other \ two \ points: \\ \\ \bullet \ If \ x=0, then: \\ \\ y=x+16=0+16=16 \\ \\ So: \\ \\ P_{3}(0,16) \\ \\ \\ \bullet \ If \ x=1, then: \\ \\ y=x+16=1+17=17 \\ \\ So: \\ \\ P_{4}(1,17)[/tex]

So the table is:

[tex]\left[\begin{array}{cc}x & y\\-5 & 11\\4 & 20\\0 & 16\\1 & 17\end{array}\right][/tex]

The domain represents the horizontal distance while the range represents the height. In this situation, all values don't make sense. First, the rainbow starts in a point on the earth's crust. Also, the airplane starts at a point on the runway, so this doesn't include all the real numbers. A similar thing happens to the height since the airplane turns into an horizontal way at a moment of its trip and this doesn't include all the real numbers.

x-intercepts:

The x intercepts are the points at which the graph passes through the x-axis, that is, when [tex]y=0[/tex]. So:

[tex]-x^2 + 36=0 \\ \\ x^2=36 \\ \\ x=\pm\sqrt{36} \\ \\ x=\pm 6[/tex]

So the x intercepts are [tex]x_{1}=6 \ and \ x_{2}=-6[/tex]

y-intercepts:

The y-intercept is the point at which the graph passes through the y-axis, that is, when [tex]x=0[/tex]. So:

[tex]y=-x^2+36 \\ \\ y=-(0)^2+36 \\ \\ y=36[/tex]

So the y-intercept is [tex]b=36[/tex]

In conclusion, if we take the x-axis as the ground, the x-intercepts represent the beginning and the end of the rainbow while the y-intercept represent its maximum height.

The equation of this line is:

[tex]y=x+16[/tex]

As you can see, the slope [tex]m=1[/tex] is positive, therefore the line I've created is positive. This means as x increases y increases, but how do x and y increase? Well, they increase as the airplane is taking off, so this means the horizontal distance and the height increase.

The system of equations we created is:

[tex]\left\{ \begin{array}{c}y=x+16\\y=-x^{2}+36\end{array}\right.[/tex]

Remember that in Part 1, chose two points on the graph of the parabola to build up the equation of the line, so the solutions to this system is indeed those two points:

[tex]P_{1}(-5,11) \ and \ P_{2}(4,20)[/tex]

They represents that the airplane cuts through the rainbow at those two points.

A piecesewise function is a function defined by two or more equations over a domain. Our piecewise function is shown in the second figure below and is defined by:

[tex]f(x)=\left\{ \begin{array}{c}x+16\quad if\quad-16\le x\le-5\\-x^{2}+36\quad if\quad-5\le x\le4\\x+16\ \quad if\quad4\le x\le24\\40\quad if\quad x\ge24\end{array}\right.[/tex]

To graph this function, let's follows these steps:

STEP 1: Graph [tex]y=x+16[/tex] from -16 to -5. This represents the graph of the trajectory of the airplane before touching the rainbow.

STEP 2: Graph [tex]y=-x^2+36[/tex] from -5 to 4. This is represents the graph of the rainbow as the airplane passes under its path.

STEP 3: Graph [tex]y=x+16[/tex] from 4 to 24. This is represents the graph of the trajectory of the airplane after touching the second point of the rainbow.

STEP 4: Graph [tex]y=x+16[/tex] from 24 and forward. This is represents the graph of the trajectory of the airplane when turning into an horizontal way.

Answer:

[tex](g \circ f)(x)=10x^2-60[/tex]

Answer:[tex]10x^2-60[/tex]

Step-by-step explanation:

[tex](g \circ f)(x)=g(f(x))[/tex]

Replace [tex]f(x)[/tex] with [tex]x^2-6[/tex].

This gives us:

[tex](g \circ f)(x)=g(f(x))[/tex]

[tex](g \circ f)(x)=g(x^2-6)[/tex]

This means to replace the old input variable with new input, [tex](x^2-6)[/tex].

Let's do that:

[tex](g \circ f)(x)=10(x^2-6)[/tex]

They probably want you to distribute:

[tex](g \circ f)(x)=10x^2-60[/tex]

Answer:

10x^2-60

Step-by-step explanation:

(G o F)(x) is the same as g(f(x)). We know that f(x)=x^2-6. So now you have to find g(x^2-6). To solve for that plug in x^2-6 in for x in the original equation for g(x). You get 10(x^2-6) or 10x^2-60

Answer:

The pen costs $5.05, and the pencil costs $0.05

Step-by-step explanation:

First, we define 2 variables for the two prices.

Let x = price of the pen.

Let y = price of the pencil.

Now we use the given information to write two equations.

"A pen and a pencil together cost $5.10. "

x + y = 5.1

"The pen cost $5 more than the pencil. "

y = x + 5

The system of equations is:

x + y = 5.1

y = x + 5

Since the second equation is already solved for y, we will use the substitution method to solve the system of equations.

Substitute y of the first equation by x + 5.

x + x + 5 = 5.1

2x + 5 = 5.1

2x = 0.1

x = 0.05   (price of the pencil)

Now substitute 0.05 for x in the second equation.

y = 0.05 + 5

y = 5.05     (price of the pen)

The pen costs $5.05, and the pencil costs $0.05

Final answer:

The pencil costs $0.05 and the pen costs $5.05, with the pen being $5 more expensive than the pencil and the total cost for both being $5.10.

Explanation:

To solve this problem, we need to create equations based on the information given. Let's assign x as the cost of the pencil and x + $5.00 as the cost of the pen, since the pen costs $5 more than the pencil.

According to the problem, the total cost of both items is $5.10, so we can write the equation as follows:

Combining the like terms, we get:

Subtracting $5.00 from both sides, we find:

Dividing both sides by 2 to solve for x:

Thus, the pencil costs $0.05, and the pen, which costs $5 more, is $5.05.

Answer:

MPN

Step-by-step explanation:

Answer:

C.  m < A = 152.5 degrees.

Step-by-step explanation:

Use the Cosine Rule:

a^2 = b^2 + c^2 - 2.b.c.cos A

34^2 = 18^2 + 17^2 - 2.18.17 cos A

2.18.17 cos A = 18^2 + 17^2 - 34^2

cos A =  (18^2 + 17^2 - 34^2) / (2.18.17)

cos A = -0.88725

m < A = 152.5 degrees.

Answer:

C.) 152.5

Step-by-step explanation:

I got it correct on founders edtell

-2xy+3x-2xy+3x ( original equation)

-2xy-2xy+3x+3x ( just rearranging)

-4xy+6x

Answer :-4xy+6x- D.

Answer:

The correct answer is option D.  -4xy + 6x

Step-by-step explanation:

It is given an expression, −2xy + 3x − 2xy + 3x  

To simplify the given expression

Let the expression be −2xy + 3x − 2xy + 3x

−2xy + 3x − 2xy + 3x   = -2xy - 2xy + 3x + 3x     [write similar terms together]

 = -4xy + 6x

Therefore the correct answer is option D.

-4xy + 6x

Answer:

[tex]9 {x}^{2} + 2x - 5[/tex]

Step-by-step explanation:

I have answered ur question

Step-by-step explanation:

To find the equation of the line, start by finding the slope. You can do this by using the slope formula below.

m(slope) = (y2 - y1)/(x2 - x1)

m = (2 - -1)/(-5 - 10)

m = 3/-15

m = -1/5

Now that we have the slope, we can use it along with either point in point-slope form to get the equation.

y - y1 = m(x - x1)

y - 2 = -1/5(x + 5)

y - 2 = -1/5x - 1

y = -1/5x + 1

Answer: In slope intercept formula it is y=-1/5x+3

Step-by-step explanation:

Answer:

Shortest side=5, Largest side=13, Other side=12

Step-by-step explanation:

Let's define the shortest side of the triangle as x, since the other two sides are defined in terms of this one.

The longest side is 2 less than 3 times the shortest side, then it is 3 * x - 2.

The other side is 2 more than twice the shortest side, then it is 2 * x + 2.

By the problem directions, we know that the perimeter or sum of sides is 30.

x + 3x - 2 +  2*x + 2 = 30

Adding all the terms "with x" together and all terms "without x" together, we get...

6*x = 30

Solving for x (dividing both sides by 6), we get...

x = 30/6 = 5

Finally,

Shortest side: 5

Largest side: 3 * 5 - 2 = 13

Other side: 2 * 5 + 2 = 12

The length of each side of the triangle are 5 in, 12 in and 13 in respectively

Given:

Perimeter of the triangle = 30 in

let

shortest side = x

other side = 2x + 2

Longest side = 3x - 2

Perimeter of the triangle = shortest side + other side + Longest side

30 = x + (2x + 2) + (3x - 2)

30 = x + 2x + 2 + 3x - 2

30 = 6x

divide both sides by 6

x = 30 / 6

x = 5

Therefore,

shortest side = x

= 5 in

other side = 2x + 2

= 2(5) + 2

= 10 + 2

= 12 in

Longest side = 3x - 2

= 3(5) - 2

= 15 - 2

= 13 in

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Answer:

Step-by-step explanation:

This is a question that uses the Pythagorean Theorem.

a = 35 feet

b = x            which is the height of the tree.

c = 3*x + 1   so we are trying to find x.  Substitute into a b and c

a^2 + b^2 = c^2

35^2 + x^2 = (3x + 1)^2        

35^2 + x^2 = 9x^2 + 6x + 1     Subtract x^2 from both sides.

35^2 = 8x^2 + 6x + 1               Subtract 35^2 from both sides.

0 = 8x^2 + 6x + 1 - 35^2

0 = 8x^2 + 6x - 1224

Does this factor?

(x + 12.75)(x - 12)

x - 12 = 0 is the only value that works.

x = 12

The tree is 12 feet high.

Note: I used the quadratic formula to solve this.

Answer:

12 ft

Step-by-step explanation:

Let the height of the tree is h.

So the distance of top of the tree = 3 h + 1

Distance of base of tree = 35 ft

So, by use of Pythagoras theorem

[tex]\left ( 3h+1 \right )^{2}=h^{2}+35^{2}[/tex]

[tex]8h^{2}+6h-1224=0[/tex]

[tex]4h^{2}+3h-612=0[/tex]

[tex]h=\frac{-3\pm \sqrt{9+4\times 4\times 612}}{8}[/tex]

[tex]h=\frac{-3\pm 99}{8}[/tex]

Take positive sign

h = 12 ft

Thus, the height of tree is 12 ft.

Answer:

b = 101.52

Step-by-step explanation:

b^2 = a^2 + c^2 - 2ac CosB

b^2 = 105^2 + 9^2 - 2(105)(9) Cos 65°

b^2 = 11 106 - 798.75

b^2 = 10 307.25

b = 101.52

Answer:101.52

Step-by-step explanation:

Given

a=105

c=9

[tex]B=65^{\circ}[/tex]

using cosine rule

[tex]2acCosB=a^2+c^2-b^2 [/tex]

[tex]2(105)(9)Cos65=105^2+9^2-b^2[/tex]

[tex] b^2=11025+81-798.7485[/tex]

b=101.524

Answer:

54°

Step-by-step explanation:

Corn made up 15 % of the vegetables, so

Corn makes up 15 % of the degrees in the circle.

There are 360 degrees in a circle, so

15/100 × 360° = 54 °

The measure of the central angle for corn is 54°.

The solution of the inequation 18x + 6 [tex]>[/tex] 12x + 18 is x [tex]>[/tex] 2.

An inequation is a mathematical statement that represents an inequality relationship between two expressions. It compares the relative values of the two expressions, indicating whether one is greater than, less than, or not equal to the other.

Solving an inequation involves finding the values of the variables that satisfy the inequality. This can often be done by using algebraic techniques, such as simplifying and rearranging the expressions, isolating the variable, and applying appropriate rules and operations.

To solve the above inequation, let's assume that it is an equation.

Then,

18x + 6 = 12x + 18

18x - 12x = 18 - 6

6x = 12

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

x = 2.

Thus the inequation in simplifying is x [tex]>[/tex] 2.

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Final answer:

The result to the inequality 18x 6> 12x 18 is x> 2. This is set up by abating 12x from both sides, also abating 6, and also dividing by 6 to insulatex.

Explanation:

To break the inequality 18x 6> 12x 18, we need to insulate the variable x on one side.

Abate 12x from both sides 18x- 12x 6> 18.

Simplify the equation 6x 6> 18.

Abate 6 from both sides 6x> 12.

Divide both sides by 6 to break for x x> 2.

The result to the inequality is x lesser than 2. This gives a range of values for x that will satisfy the original inequality. thus, any number lesser than 2 for x makes the inequality true.

Answer:

Part 1) The measure of angle x is 24°

Part 2) The measure of angle y is 66°

Step-by-step explanation:

step 1

Find the measure of angle m∠IKL

we know that

m∠JKI+m∠IKL=180° ----> supplementary angles (form a linear pair)

we have

m∠JKI=48°

substitute

48°+m∠IKL=180°

m∠IKL=180°-48°=132°

step 2

Find the measure of angle x

we know that

The triangle IKL is an isosceles triangle

so

m∠KIL=m∠KLI=x

Remember that

The sum of the interior angles of a triangle must be equal to 180 degrees

m∠IKL+2x=180°

132°+2x=180°

2x=180°-132°

x=24°

step 3

In the right triangle JIL

Angles x and y are complementary

so

x+y=90°

24°+y=90°

y=90°-24°

y=66°

Answer:

B) Find the ratio of minutes to miles, 4:1. Multiply 7.5 by 4

Step-by-step explanation:

A bicyclist rides the same number of miles every minute. The ratio table below shows the number of miles she rides during certain amounts of time.

Biking Times and Distances        

Number of Minutes         Number of Miles

10                                             2.5

16                                              4

?                                              7.5

48                                              12

Which statement explains how to find the number of minutes it takes to bike 7.5 miles?

B) Find the ratio of minutes to miles, 4:1. Multiply 7.5 by 4....

Answer:

Option B.

Step-by-step explanation:

A bicyclist rides the same number of miles in one minute.

Ratio table is given as

Number of minutes    Distances (miles)

       10                                   2.5

        16                                   4

        x                                    7.5

       48                                  12

We have to find the number of minutes taken by a biker to bike 7.5 miles

So the ratio between minutes to the distance biked will be = [tex]\frac{10}{2.5}=4:1[/tex]

Now this ratio will be similar to the ratio = [tex]\frac{x}{7.5}=x:7.5[/tex]

Now [tex]\frac{4}{1}=\frac{x}{7.5}[/tex]

x = 7.5×4 = 30 minutes

Therefore, Option B will be the answer.

The type of tessellation used to cover a surface completely using one type of regular polygon is regular tessellation.

Tessellation is defined as the process of covering of a surface or a plane using the geometric shapes.

One geometric shape will not overlap with the other and there will not be any gaps in between.

Regular tessellation is the tiling which uses one type of regular polygon to form a pattern.

In semi-regular tessellation, two or more regular polygons are used such that each vertex is the same.

Here, it is only used one type of regular polygon. No other polygons are used.

So it can't be semi-regular tessellation.+

So it is regular tessellation.

Hence the tessellation is regular tessellation.

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Answer:

Step-by-step explanation:

3.

Final answer:

To find f(10) using a recursive formula, we can calculate intermediate values starting from f(1) and applying the given rule to find f(10) as 2.

Explanation:

The function is defined as follows:

f(1)=-1.5

f(n+1)=f(n)+0.5

To find f(10), we can use the given recursive formula to calculate subsequent values:

f(2) = f(1) + 0.5 = -1.5 + 0.5 = -1

f(3) = f(2) + 0.5 = -1 + 0.5 = -0.5

Continuing this pattern, we find f(10) = 2

Answer:

the radius of the circle= 4m

Step-by-step explanation:

Given:

Area of circle=16π m2

radius,r of circle=?

Formula of area of circle is given as

Area=πr^2

Putting values we get

16π=πr^2

r^2=16

r=4

the radius of the circle= 4m !

Given the area [tex]A=\pi r^2=16\pi[/tex] we can solve the formula for radius.

[tex]A=\pi r^2\Longrightarrow r=\sqrt{\dfrac{A}{\pi}}[/tex]

So,

[tex]r=\sqrt{\dfrac{16\cdot\not{\pi}}{\not{\pi}}}=\sqrt{16}=4[/tex]

The radius is 4m.

Hope this helps.

r3t40

Answer:-1

Step-by-step explanation:x>2x+1=x-2x>1

-x>1,x<- 1

Answer:

-1

Step-by-step explanation:

Answer:

C. (2, 1)

Step-by-step explanation:

-3y = x-5

x+ 5y = 7

Subtract x from both sides in the first equation. Write the second equation below it.

-x - 3y = -5

x + 5y = 7

Add the two equations above.

2y = 2

Divide both sides by 2.

y = 1

Substitute y with 1 in the second original equation and solve for x.

x + 5(1) = 7

x + 5 = 7

Subtract 5 from both sides.

x = 2

Answer: C. (2, 1)

Answer:

○ C. (2, 1)

Step-by-step explanation:

{-3y = x - 5 [Move -x to the left of the equivalence symbol]

{x + 5y = 7

{-x - 3y = -5

{x + 5y = 7

____________

2y = 2

__ _

2 2

y = 1 [Plug this back into both equations to get the x-coordinate of 2]; 2 = x

I am joyous to assist you anytime.

Answer:

d=1

Step-by-step explanation:

Let's start by combining like terms.

-3-d=-2-2d

+d. +d

-3= -2-d

+2 +2

-1= -d

/-1. /-1

d=1

Answer:

Percent form: 41.65%

Fraction form: [tex]\frac{833}{2000}[/tex]

Step-by-step explanation:

33% of men support John Smith.

67% of women support John Smith.

Lets say, for instance, that there are 20 polled individuals -- 10 women and 10 men.

However, since 1.5 times as many men voted as women, we have to apply our poll to 15 men and 5 women.

33% of the 15 men makes 5 men who voted for Smith and 10 who did not.

67% of the 5 women makes 3.33 women who voted for Smith and 1.67 who did not.

Add these numbers together.

8.33 total voters were cast for John Smith, while 11.67 were not.

Now, divide 8.33 by 20 and multiply by 100 to obtain a percentage.

[tex]\frac{8.33}{20} \\.4165\\41.65[/tex]

41.65% of voters voted for John Smith according to the results of the poll.

According to an informal poll, with 1/3 of men and 2/3 of women supporting John Smith, and 1.5 times more men than women voting, 2/3 of the total vote should be cast for John Smith.

We need to calculate the fraction of the total vote that would be cast for John Smith according to the informal poll. Let's denote the number of women voters as w and the number of men as m. According to the poll, 1/3 of men and 2/3 of women will vote for John Smith. On election day, 1.5 times as many men as women voted, which means m = 1.5w.

The total votes for John Smith would be (1/3)m + (2/3)w. Substituting m with 1.5w, we get:

Total votes for John Smith = (1/3)(1.5w) + (2/3)w

This simplifies to:

Total votes for John Smith = 0.5w + (2/3)w = (1.5/3)w + (2/3)w = (1.5/3 + 2/3)w = (3/3 + 2/3)w = (5/3)w

The total votes cast would be m + w, substituting again we get 1.5w + w = 2.5w.

To find the fraction of total votes that would be for John Smith, we divide the total votes for John Smith by the total votes cast:

Fraction for John Smith = (5/3)w / (2.5)w

Since w is in both the numerator and denominator, it cancels out, and we're left with:

Fraction for John Smith = (5/3) / (2.5)

Converting 2.5 to a fraction gives us 5/2, so:

Fraction for John Smith = (5/3) / (5/2)

By dividing fractions, we invert and multiply:

Fraction for John Smith = (5/3) * (2/5) = 2/3

Therefore, according to the poll, 2/3 of the total vote should be cast for John Smith.

Answer:

They can buy 160 commercial vans, 80 small trucks and 40 large trucks.

Step-by-step explanation:

The company plans to spend $8 million on 280 new vehicles.

Commercial van = $25,000

Small truck = $30,000

Large Truck = $40,000

Let 'x' be commercial van, 'y' small truck and 'z' large truck. Therefore:

x + y + z = 280

Also, we know that x = 2y

Therefore: 3y + z = 280

Also we know that:

25,000x + 30,000y + 40,000z = 8,000,000

50,000y + 30,000y + 40,000z = 8,000,000

80,000y + 40,000z = 8,000,000

Therefore, we need to solve the following system of equation:

3y + z = 280  [1]

80,000y + 40,000z = 8,000,000  [2]

We have that the results are: y=80, z=40 and x=160.

Therefore, they can buy 160 commercial vans, 80 small trucks and 40 large trucks.

[tex]d=11\text{ ft}\\V=\dfrac{4}{3}\pi r^3\\r=\dfrac{d}{2}=\dfrac{11}{2}=5.5\\\\V=\dfrac{4}{3}\pi \cdot (5.5)^3\approx697\text{ ft}^3[/tex]

Answer:

A. is less than the radius.

Step-by-step explanation:

If a point is inside a circle, the distance from the center of the circle to that point is option (A) is less than the radius is the correct answer.

A circle is a collection of all points in a plane which are at a constant distance from a fixed point. A circle is a round-shaped figure that has no corners or edges.

For the given situation,

The distance from the center of the circle to any point on it's circumference is called radius.

So, when we consider the distance from the center of the circle, then the term should be related to radius.

Hence we can conclude that if a point is inside a circle, the distance from the center of the circle to that point is option (A) is less than the radius is the correct answer.

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I believe the answer is B. I apologize if this is incorrect

Answer:

B) 168.8

Step-by-step explanation:

Amongst all the options given, B is the correct answer.

!!

Answer:

Step-by-step explanation:

According to the first expression:

2(10-k): where,

2:shows the double amount of money which ELI has

10:shows the amount of money which ELI had at the starting.

k:shows the amount of money which is lost.

10-k:shows the amount of money which ELI has after losing some amount.

According to the second expression:

20-2k where,

20:shows the twice of initial amount.

k: is the amount of money which is lost

2k:s hows the twice of amount which is lost

20-2k: shows the amount of money which is left with ELI after his mom gave him some money....

Answer:

24

Step-by-step explanation:

hbdhdjjdjchchcbndndnxnndjdjdjdjjsjdhjdjxjxjjdjcncnncnfjfjdjdnndndnd

Answer:

there are 3.3399 moles in 318 grams! ✔️

Step-by-step explanation:

So we know that 100 grams MgCl2 to mol = 1.0503 mol.

Therefore, to find the number of moles in 318g of the compound, we use the rule of three:

if 1.0503 mol -------------> 100 grams

       X            <------------- 318 grams

The solution is: X = (318*1.0503)/100 = 3.3399 mol.

Summarizing, there are 3.3399 moles in 318 grams! ✔️

Answer:

A.) Figure A

Step-by-step explanation:

because the first part "If..." always goes on the inside of the 2 circles