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Answer:

Question 9: False

Question 10: False

Step-by-step explanation:

The third side is always greater than the other two sides.

Question 9

a = 6, b = 6, c = 5

Since the third side is the smallest, it would not create a triangle.

Question 10

a = 7, b = 2, c = 5

Since the third side is the smallest, it would not create a triangle.

Answer:

Question 9: True

Question 10: False

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the last side.

To test if the three lengths create a triangle you would have to test the three combinations if the two numbers are greater than the last number.

The three lengths 6, 6, 5 create a triangle.

First check the first two numbers.

Next check the first and last number.

Last check the second and last number.

The answer for question 9 is TRUE.

The three lengths 7, 2, 5 create a triangle.

Check the first two numbers.

Check the first and last number.

Finally, check the second and last number.

The answer for question 10 is FALSE.

Answer:

(3,4,5)

(6,8,10)

(5,12,13)

(8,15,17)

(12,16,20)

(7,24,25)

(10,24,26)

(20,21,29)

(16,30,34)

(9,40,41)

Just choose 2 numbers from {1,2,3,4,5,6,7,8,...} and make sure the one you input for x is larger.

Post the three in the comments and I will check them for you.

Step-by-step explanation:

We need to choose 2 positive integers for x and y where x>y.

Positive integers are {1,2,3,4,5,6,7,.....}.

I'm going to start with (x,y)=(2,1).

x=2 and y=1.

[tex](2^2+1^2)^2=(2^2-1^2)^2+(2\cdot2\cdot1)^2[/tex]

[tex](4+1)^2=(4-1)^2+(4)^2[/tex]

[tex](5)^2=(3)^2+(4)^2[/tex]

So one Pythagorean Triple is (3,4,5).

I'm going to choose (x,y)=(3,1).

x=3 and y=1.

[tex](3^2+1^2)^2=(3^2-1^2)^2+(2\cdot3\cdot1)^2[/tex]

[tex](9+1)^2=(9-1)^2+(6)^2[/tex]

[tex](10)^2=(8)^2+(6)^2[/tex]

So another Pythagorean Triple is (6,8,10).

I'm going to choose (x,y)=(3,2).

x=3 and y=2.

[tex](3^2+2^2)^2=(3^2-2^2)^2+(2\cdot3\cdot2)^2[/tex]

[tex](9+4)^2=(9-4)^2+(12)^2[/tex]

[tex](13)^2=(5)^2+(12)^2[/tex]

So another is (5,12,13).

I'm going to choose (x,y)=(4,1).

[tex](4^2+1^2)^2=(4^2-1^2)^2+(2\cdot4\cdot1)^2[/tex]

[tex](16+1)^2=(16-1)^2+(8)^2[/tex]

[tex](17)^2=(15)^2+(8)^2[/tex]

Another is (8,15,17).

I'm going to choose (x,y)=(4,2).

[tex](4^2+2^2)^2=(4^2-2^2)^2+(2\cdot4\cdot2)^2[/tex]

[tex](16+4)^2=(16-4)^2+(16)^2[/tex]

[tex](20)^2=(12)^2+(16)^2[/tex]

We have another which is (12,16,20).

I'm going to choose (x,y)=(4,3).

[tex](4^2+3^2)^2=(4^2-3^2)^2+(2\cdot4\cdot3)^2[/tex]

[tex](16+9)^2=(16-9)^2+(24)^2[/tex]

[tex](25)^2=(7)^2+(24)^2[/tex]

We have another is (7,24,25).

You are just choosing numbers from the positive integer set {1,2,3,4,... } and making sure the number you plug in for x is higher than the number for y.

I will do one more.

Let's choose (x,y)=(5,1).

[tex](5^2+1^2)^2=(5^2-1^2)^2+(2\cdot5\cdot1)^2[/tex]

[tex](25+1)^2=(25-1)^2+(10)^2[/tex]

[tex](26)^2=(24)^2+(10)^2[/tex]

So (10,24,26) is another.

Let (x,y)=(5,2).

[tex](5^2+2^2)^2=(5^2-2^2)^2+(2\cdot5\cdot2)^2[/tex]

[tex](25+4)^2=(25-4)^2+(20)^2[/tex]

[tex](29)^2=(21)^2+(20)^2[/tex]

So another Pythagorean Triple is (20,21,29).

Choose (x,y)=(5,3).

[tex](5^2+3^2)^2=(5^2-3^2)^2+(2\cdot5\cdot3)^2[/tex]

[tex](25+9)^2=(25-9)^2+(30)^2[/tex]

[tex](34)^2=(16)^2+(30)^2[/tex]

Another Pythagorean Triple is (16,30,34).

Let (x,y)=(5,4)

[tex](5^2+4^2)^2=(5^2-4^2)^2+(2\cdot5\cdot4)^2[/tex]

[tex](25+16)^2=(25-16)^2+(40)^2[/tex]

[tex](41)^2=(9)^2+(40)^2[/tex]

Another is (9,40,41).

Answer:

  D.  (x, y) → (-x, -y)

Step-by-step explanation:

A. (x,y) → (y,x) . . . . reflects across the line y=x

B. (x,y) → (y,-x) . . . . rotates 90° CCW

C. (x,y) → (-y,-x) . . . . reflects across the line y=-x

D. (x,y) → (-x,-y) . . . . rotates 180° about the origin

Answer:

The correct option is D.

Step-by-step explanation:

If a point rotating 180° counterclockwise about the origin, then the sign of each coordinate is changed.

Consider the coordinates of a point are (x,y).

If a (x,y) rotating 180° counterclockwise about the origin, then the rule of rotation is defined as

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

In which (x,y) is the coordinate pair of preimage and (-x,-y) is the coordinate pair of image.

Therefore the correct option is D.

If a point reflects across the line y=x , then

[tex](x,y)\rightarrow (y,x)[/tex]

If a point rotated 90° clockwise, then

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

If a point reflects across the line y=-x, then

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

Answer:

-14/9

Step-by-step explanation:

Combine -2, -3, x, 2x, 4, 8.  We get -5 + 3x + 12.  This sum is -7.

Solve this equation for x:  3x + 7 = -7, so 3x = -14/3.

Then x is -14/9.

Answer:

-4.7

Step-by-step explanation:

-2 + (-3) + x + 2x + 4 + 8 =  -7

                    -5 + 3x +12 =  -7

                            3x + 7 =  -7

                                  3x = -14

                                    x = -14/3 = -4.7 °F

The value of x is -4.7.

Check:

-2 + (-3) + (-4.7) + 2(-4.7) + 4 + 8 = -7

                      -5 - 4.7 - 9.3 + 12 = -7

                                               -7 = -7

OK

Answer:

[tex]y=5e^{2x}[/tex]

Step-by-step explanation:

Let (x,y) represents a point P on the curve,

So, the slope of the curve at point P = [tex]\frac{dy}{dx}[/tex]

According to the question,

[tex]\frac{dy}{dx}=2y[/tex]

[tex]\frac{1}{y}dy=2dx[/tex]

Integrating both sides,

[tex]\int \frac{dy}{y}=2dx[/tex]

[tex]ln y=2x+ln C[/tex]

[tex]ln y-ln C = 2x[/tex]

[tex]ln(\frac{y}{C})=2x[/tex]

[tex]\frac{y}{C}=e^{2x}[/tex]

[tex]\implies y=Ce^{2x}[/tex]

Since, the curve is passing through the point (0, 5),

[tex]5=Ce^{0}\implies C=5[/tex]

Hence, the required equation of the curve is,

[tex]y=5e^{2x}[/tex]

Answer: 19.2 inches would be the most reasonable answer, since the first two is too small, and the last answer would be too tall.

if there was 2 feet of water, it would be 24 inches full. taking 1 gallon out, wouldn't make the difference to make it go up or down much.

Answer:

c) 19.2 inches

Step-by-step explanation:

Height of water when full = 2 feet = 24 inches

Radius of cylinder = 4 inches

Volume of tank = 5 gallon

Gallon per inch height of tank = [tex]\frac{5}{24}[/tex]

Inch per gallon of height = [tex]\frac{24}{5}[/tex]

So, when 1 gallon is removed

[tex]24-1\times \frac{24}{5}=\frac{96}{5}=19.2\ inches[/tex]

∴ Height of the water in the tank after Alex filled the 1 gallon jug is 19.2 inches.

Volume of cylinder after 1 gallon was removed

[tex]\pi r^2h=4\times 231\\\Rightarrow h=\frac{4\times 231}{\pi 4^2}\\\Rightarrow h=18.38\ inches[/tex]

∴Height of the water in the tank after Alex filled the 1 gallon jug is 18.38 inches

The different height arises due to the thickness of the rank which is not given.

The first method is more accurate

Answer:

20,845 square meters

Step-by-step explanation:

We can use the formula for area of a triangle to figure this out easily.

Area = [tex]\frac{1}{2}abSinC[/tex]

Where

a and b are the two side lengths of the triangle given, and

C is the ANGLE BETWEEN the two sides

Clearly, we see that one side is 218.5 and other is 224.5 and the angle between them is given by 58.2 degrees. Now we simply substitute these values into the formula and get the area:

[tex]A=\frac{1}{2}abSinC\\A=\frac{1}{2}(218.5)(224.5)Sin(58.2)\\A=20,844.99[/tex]

Rounding, we get the area to be 20,845 square meters

Answer:

20,845 m2

Step-by-step explanation:

I got it correct on founders edtell

Answer:

A regional soccer tournament has 64 participating teams.

In the first round of the tournament, 32 games are played.

In each successive round, the number of games played decreases by 1/2.

Part A:

We know;

[tex]a_n=a_1\times r^{n-1}[/tex]

[tex]a_1=32[/tex]

[tex]r=\frac{-1}{2}[/tex]

So, we get;

The rule for the number of games played in the nth round is given by:

[tex]a_n=32(\frac{1}{2})^{n-1}[/tex]

where [tex]1\leq n\leq 6[/tex]

Part B:

As in each successive round the rounds are decreasing by 1/2 we have.

round 1 = 32

round 2 = 16

round 3 = 8

round 4 = 4

round 5 = 2

round 6 = 1

So, the total number of games played in the regional soccer tournament are: [tex]32+16+8+4+2+1=63[/tex]

Answer:

63 games total

Step-by-step explanation:

edge 2021

Answer:

69.7 ft

Step-by-step explanation:

we know that

The function sine of angle of 35 degrees is equal to divide the opposite side to the angle of 35 degrees (the height of the vulture in a tree) by the hypotenuse ( the distance from the vulture to the roadkill)

Let

z -----> the distance from the vulture to the roadkill

sin(35°)=40/z

z=40/sin(35°)=69.7 ft

Answer:

69.7 feet.

Step-by-step explanation:

Let x represent the distance between vulture and roadkill.

We have been given that a vulture is perched 40 ft up in a tree and looks down at an angle of depression of a 35 and spots roadkill.

We can see from the attachment that vulture, roadkill and angle of depression  forms a right triangle with respect to ground, where, x is hypotenuse and 40 ft is opposite side.

[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

[tex]\text{sin}(35^{\circ})=\frac{40}{x}[/tex]

[tex]x=\frac{40}{\text{sin}(35^{\circ})}[/tex]

[tex]x=\frac{40}{0.573576436351}[/tex]

[tex]x=69.7378718[/tex]  

[tex]x\approx 69.7[/tex]  

Therefore, the roadkill is 69.7 feet away from the vulture.

Answer:

[tex]4032x^4[/tex]

Step-by-step explanation:

Use the 10th row of Pascal's Triangle to get you where you need to be.  You need 10 rows because any polynomial raised to the 9th power has 10 terms.  Those 10 terms are, in order:

1, 9, 36, 84, 126, 126, 84, 36, 9, 1

Setting up for the first 6 terms:

[tex]1(x^9)(2^0)+9(x^8)(2^1)+36(x^7)(2^2)+84(x^6)(2^3)+126(x^5)(2^4)+126(x^4)(2^5)+...[/tex]

The 6th term is the last one.  It goes on from there, but I stopped at the 6th term, since that is what you need.

Simplifying gives us:

[tex]126(x^4)(32)[/tex]

and multiplying gives us:

[tex]4032x^4[/tex]

The 6th term in the expansion of (x + 2)^9 is calculated using the binomial theorem, with the result being 4032x^4.

The 6th term in the expansion of the binomial expression (x + 2)9 is found using Binomial Theorem. The general formula for any term in the expansion of (a + b)^n, where n is a positive integer, is C(n, k) * (a^(n-k)) * (b^k), where C(n, k) is the combination of n items taken k at a time, and k is the term number minus 1.

For the 6th term, k equals 5 (since k = term number -1). By substituting these values into formula, you get: C(9, 5) * (x^(9-5)) * (2^5), which equals 126 * x^4 * 32, or 4032x^4.

So, the 6th term in the expansion of (x + 2)9 is 4032x^4.

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Answer:

[tex]\text{C.}\quad\left[\begin{array}{cc}22&-8\\7.8&-3\end{array}\right][/tex]

Step-by-step explanation:

It is convenient to let a spreadsheet or calculator do the tedious sum of products. Term C22 will be B21·A12 +B22·A22 = 0.6·0 +3·(-1) = -3, for example. Other terms are similarly computed. In general Crc will be the sum of Brx·Axc, where x = 1 or 2.

[tex]BA=\begin{bmatrix}2 & 8 \\0.6 & 3\end{bmatrix}\cdot \begin{bmatrix}3 & 0 \\2 & -1\end{bmatrix}\\BA=\begin{bmatrix}2\cdot3+8\cdot2 & 2\cdot0+8\cdot(-1) \\0.6\cdot3+3\cdot2 & 0.6\cdot 0+3\cdot(-1)\end{bmatrix}\\BA=\begin{bmatrix}22 & -8 \\7.8 & -3\end{bmatrix}[/tex]

Answer:

x = 3 or x = 2 or x = 0 thus: 5

Step-by-step explanation:

Solve for x over the real numbers:

x^2 = (6 x)/(5 - x)

Cross multiply:

x^2 (5 - x) = 6 x

Expand out terms of the left hand side:

5 x^2 - x^3 = 6 x

Subtract 6 x from both sides:

-x^3 + 5 x^2 - 6 x = 0

The left hand side factors into a product with four terms:

-x (x - 3) (x - 2) = 0

Multiply both sides by -1:

x (x - 3) (x - 2) = 0

Split into three equations:

x - 3 = 0 or x - 2 = 0 or x = 0

Add 3 to both sides:

x = 3 or x - 2 = 0 or x = 0

Add 2 to both sides:

Answer:  x = 3 or x = 2 or x = 0

Answer:

[tex]\frac{8}{17}[/tex] of fish in this aquarium are guppies.

Step-by-step explanation:

Let x be the number of guppies and y be the number of swordtails in the aquarium,

According to the question,

[tex]\frac{3}{4}\text{ of } x=\frac{2}{3}\text{ of }y[/tex]

[tex]\frac{3x}{4}=\frac{2y}{3}[/tex]

By cross multiplication,

[tex]9x=8y[/tex]

[tex]\implies \frac{x}{y}=\frac{8}{9}[/tex]

Thus, the ratio of guppies and swordtail fishes is 8 : 9

Let guppies = 8x, swordtail = 9x

Where, x is any number,

Since, the aquarium contains only two kinds of fish, guppies and swordtails,

So, the total fishes = 8x + 9x = 17x

Hence, the fraction of fish in the aquarium are guppies = [tex]\frac{\text{Guppies}}{\text{Total fishes}}[/tex]

[tex]=\frac{8x}{17x}[/tex]

[tex]=\frac{8}{17}[/tex]

To find what fraction of fish in the aquarium are guppies, you express the given relationship between the number of guppies and swordtails algebraically and solve for the number of guppies relative to the total number of fish, concluding that 8/17 of the fish in the aquarium are guppies.

If 3/4 of the number of guppies is equal to 2/3 of the number of swordtails, we can express this relationship using variables. Let G represent the number of guppies and S represent the number of swordtails in the aquarium. The given relationship can be written as (3/4)G = (2/3)S.

To find the fraction of fish that are guppies, we need to express G in terms of S first. By manipulating the equation, we multiply both sides by (4/3) to get G = (4/3)*(2/3)S = (8/9)S. This equation shows that the number of guppies is (8/9) times the number of swordtails.

Now, to find the total number of fish (T), we add the number of guppies and swordtails: T = G + S. Substituting the value of G from the equation above, we get T = (8/9)S + S = (17/9)S. The fraction of the total that are guppies is then G/T = [(8/9)S]/[(17/9)S] which simplifies to 8/17. Therefore, 8/17 of the fish in the aquarium are guppies.

Answer:

15

Step-by-step explanation:

So angle 2 and angle 4 have a relationship that is called same-side interior or consecutive interior angles.  The name there depends what class you are in but they mean the same thing.

If you have the transversal goes through parallel lines, then same-side interior angles will add up to 180 degrees.

So you are trying to solve the following equation for x:

angle2+angle4=180

2x+10+4x+80=180

Combine like terms:

6x+90=180

Subtract 90 on both sides:

6x     =90

Divide both sides by 6:

 x      =90/6

Simplify:

 x      =15

15 is x so that the lines are parallel

Answer:

x = 15°

Step-by-step explanation:

Notice that if A is // to B, then ∠2 and ∠4 are supplementary angles, i.e they add up to 180°. We can write this as:

∠2 + ∠4 = 180

(2x + 10) + (4x + 80) = 180

2x + 10 + 4x + 80 = 180

6x  + 90 = 180

6x  = 180 - 90

6x  = 90

x = 15°

bearing in mind that, we can always get the common ratio by simply dividing any term by the one before it, and if it's a geometric sequence, all divisions will yield the same "r" value.

Check the picture below.

Answer:

24 kilometers.

Step-by-step explanation:

The shortest path between two points is a straight segment that connects the two points.

Refer to the diagram attached. The 6-km segment and the 8-km segment are normal to each other. Together with the segment that joins the library and the house, the three segments now form a right triangle.

The length of the hypotenuse can be found with the Pythagorean Theorem.

[tex]\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{Leg 1})^{2} + (\text{Leg 2})^{2}}\\&= \sqrt{6^{2} + 8^{2}}\\&= \sqrt{36 + 64} \\&= \sqrt{100}\\&= \rm 10\;km\end{aligned}[/tex].

The length of the round-trip will equal to the sum of the length of the three segments: [tex]\rm 6\;km + 8\;km + 10\;km = 24\;km[/tex].

Answer:

Option D (12).

Step-by-step explanation:

The law of outcomes states that if there are m ways to do Event 1 and n ways to do Event 2, then if both Event 1 and Event 2 are combined, then the possible outcomes will be m*n. Similarly, in this case, there are 2 types of products, 2 types of materials, and 3 types of colours. So according to the law of outcomes, simply multiply the numbers to gain the total possible outcomes:

Possible outcomes = 2 * 2 * 3 = 4 * 3 = 12.

So Option D is the correct answer!!!

Answer:

12 is correct.

Step-by-step explanation:

The first step is to add 7 to both sides, applying the addition property of equality:

[tex]-2(4x-1)-7+7=5+7 \iff -2(4x-1)=12[/tex]

Answer:

The equation can become −2(4x − 1) = 12 by applying the commutative property of addition

Step-by-step explanation:

Answer:

C. t – 3.8 = 45.1

Step-by-step explanation:

Steve's time = 45.1 seconds

Tom finished 3.8 seconds later

So add 3.8 to steve's time to find tom's time (t)

t =s+3.8

t = 45.1 + 3.8

Subtract 3.8 from each side

t -3.8 =45.1 +3.8-3.8

t -3.8 = 45.1

Answer:

Its C.

Step-by-step explanation:

You better give the guy above me brainliest. I got the answer from the king above me

Answer:

Step-by-step explanation:

The length AC is 3, but the corresponding length FD is 1, so the dilation factor is FD/AC = 1/3.

The reflection is a left/right reflection, so it is across a vertical line. We suspect the only vertical line you are interested in is the y-axis. (It could be reflected across x=1/2, and then the only translation would be downward.)

The above transformations will put C' at (1, 0). Since the corresponding point D is at (2, -2), we know it is C' is translated by (1, -2) to get to D.

  C' + translation = D

  (1, 0) +(1, -2) = (2, -2)

Answer:

[tex]9x^2y-5xy[/tex]

Step-by-step explanation:

Split it up like this to make it easier to work with:

[tex]\frac{27x^2y}{3}-\frac{15xy}{3}[/tex]

Since the only thing in the denominator of those fractions is a 3, we can only divide the 27 by 3, not the x or y terms.  Same thing with the second fraction.  27 divided by 3 is 9 and 15 divided by 3 is 5, so

[tex]9x^2y-5xy[/tex]

is the solution.  It is not completely simplified, but that isn't what you asked for, so this should suffice as the answer.

Answer:

The probability that Andrew will be among the 4 volunteers selected and Karen will not is 2/7.

Step-by-step explanation:

From the given information it is clear that

The total number of volunteers, including Andrew and Karen = 8

The total number of volunteers, excluding Andrew and Karen = 8-2 = 6

We need to find the probability that Andrew will be among the 4 volunteers selected and Karen will not.

Total number of ways of selecting r volunteers from n volunteers is

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Total number of ways of selecting 4 volunteers from 8 volunteers is

[tex]\text{Total outcomes}=^8C_4=70[/tex]

Total number of ways of selecting 4 volunteers from 8 volunteers, so that Andrew will be among the 4 volunteers selected and Karen will not is

[tex]\text{Favorable outcomes}=^1C_1\times ^6C_3=1\times 20=20[/tex]

The probability that Andrew will be among the 4 volunteers selected and Karen will not is

[tex]P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]P=\frac{20}{70}[/tex]

[tex]P=\frac{2}{7}[/tex]

Therefore the probability that Andrew will be among the 4 volunteers selected and Karen will not is 2/7.

The probability that Andrew is selected and Karen is not from a group of 8 volunteers for a 4-person task is 2/7.

The question is asking about the probability of a specific event happening when a group of volunteers is randomly selected. The key to solving this problem is knowing how to calculate combinations.

There are 8 volunteers in total and we know that 4 people are to be selected. The total number of ways 4 people can be selected from 8 is given by the combination formula C(n, r) = n! / (r!(n-r)!), where n is the total number of elements, r is the number of elements to choose, and ! represents the factorial operator.

So, total combinations = C(8, 4) = 8! / (4!(8-4)!) = 70.

Now, we need to find the combinations in which Andrew is chosen and Karen is not. This situation is equivalent to selecting 3 people from the remaining 6 people (excluding Andrew and Karen). Therefore, these combinations = C(6, 3) = 6! / (3!(6-3)!) = 20.

The probability that Andrew will be among the 4 volunteers selected and Karen will not is therefore 20/70 = 2/7.

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Answer:

 55

Step-by-step explanation:

Let x represent the middle integer. Then the smallest is x-2 and the largest is x+2. Your requirement is that ...

  (x-2)/(x+2) > 2/3

  3x -6 > 2x +4 . . . . cross multiply

  x > 10 . . . . . . . . . . .add 6-2x

The smallest integer satisfying this requirement is x=11. The sum of the 5 integers is 5x = 55.

The smallest sum is 55.

Answer:

55

Step-by-step explanation:

Answer:

  No, the triangles are not similar

Step-by-step explanation:

The (reduced) side length ratios, shortest to longest, are ...

  12 : 18 : 20 = 6 : 9 : 10

and

  5 : 12 : 13

These are not the same, so the triangles are not similar.

Answer:

The last answer is correct.

Also known as E

Step-by-step explanation:

Answer:

⇒ Add 8x to both sides of the inequality

⇒ x>1/5

Step-by-step explanation:

First, you subtract by 5 from both sides of equation.

5-8x-5<2x+3-5

Solve.

-8x<2x-2

Then subtract by 2x from both sides of equation.

-8x-2x<2x-2-2x

Solve.

-10x<-2

Multiply by -1 from both sides of equation.

(-10x)(-1)>(-2)(-1)

Solve.

10x>2

Divide by 10 from both sides of equation.

10x/10>2/10

Solve to find the answer.

2/10=10/2=5 2/2=1=1/5

x>1/5 is final answer.

Hope this helps!

Answer: Add 8x to both sides of the inequality

D) on    e d g e n u i t y

Answer:

Step-by-step explanation:

Let f and p represent the costs of a file and a pen, respectively. The two purchases are ...

  f +3p = 32.85

  2f +8p = 83.50

Subtracting twice the first equation from the second gives an equation for the cost of pens:

  (2f +8p) -2(f +3p) = (83.50) -2(32.85)

  2p = 17.80 . . . . simplify

  p = 8.90 . . . . . . divide by 2

The cost of one pen is $8.90.

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Comment on "how do you do it?"

You are given two purchases related to the costs of two items. Write equations that describe the purchases. (The total cost is sum of the costs of each of the items, which will be the product of the number of items and the cost of each. You have been shopping, so you know this.)

Once you have a "system of equations", there are many ways they can be solved. You are usually instructed on "elimination" and "substitution" as methods of solution. Above, we used "elimination" to eliminate the "f" variable and give an equation only in "p".

Answer:

2x^3+8x^2-54x-84

Step-by-step explanation:

Answer:

2(x + 7)(x² - 3x - 6) = 2x³ + 8x² - 54x - 84

Step-by-step explanation:

Simplification is a method used to reduce the complexity or the component parts of an algebraic equation which makes it simpler and easier to understand.

The given equation is: 2(x + 7)(x² - 3x - 6).

Simplifying the given algebraic equation:

⇒ 2 (x + 7) (x² - 3x - 6)

⇒ (2x + 14) (x² - 3x - 6)

⇒ 2x³ + 14x² - 6x² - 42x - 12x - 84

⇒ 2x³ + 8x² - 54x - 84

Answer:

0

Step-by-step explanation:

100 - 10 = 90

90 - 30 = 60

60 - 10 = 40

40 - 10 = 30