Geometry help I don’t know any of this stuff!!

Geometry Help I Dont Know Any Of This Stuff!!

Answers

Answer 1

Answer:

radius chordsecant linecenterpoints of tangency circumference

Related Questions

Find the measure of the missing angles.

Answers

Answer:

Step-by-step explanation:

PLS HELP! VERY URGENT PICTURE INCLUDED!!

Answers

Answer:

y = 6x ^2 - 6x + 9

Step-by-step explanation:

hopefully it's visible

:)

find the solution of the general equation of the differential equation:
(1-cosx)y' - ysinx =0, x ≠ k2π

Answers

Notice that the condition x ≠ 2πk for (presumably) integer k means cos(x) ≠ ±1, and in particular cos(x) ≠ 1 so that we could divide both sides by (1 - cos(x)) safely. Doing so lets us separate the variables:

(1 - cos(x)) y' - y sin(x) = 0

==>   (1 - cos(x)) y' = y sin(x)

==>   y'/y = sin(x)/(1 - cos(x))

==>   dy/y = sin(x)/(1 - cos(x)) dx

Integrate both sides and solve for y. On the right, substitute u = 1 - cos(x) and du = sin(x) dx.

∫ dy/y = ∫ sin(x)/(1 - cos(x)) dx

∫ dy/y = ∫ du/u

ln|y| = ln|u| + C

exp(ln|y|) = exp(ln|u| + C )

exp(ln|y|) = exp(ln|u|) exp(C )

y = Cu

y = C (1 - cos(x))

What is the answer to 11.24 divided by 9

Answers

Answer:

1.24

Step-by-step explanation:

oahsofhasdf0as0dfadera

Choose Yes or No to tell if each statement is true.

3
.
072
>
3
.
2

Choose...

728
.
307
>
729
.
07

Choose...

12
.
040
=
12
.
04

Choose...

531
.
135
<
531
.
315

Choose...

Answers

Answer:

1. No 2. No 3. Yes 4. Yes

Step-by-step explanation:

Compare the value of each digit from the leftmost digit.

How do you Graph 3x+4y< -16 on the coordinate plane

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Take note of the inequality symbol. It is < (not ≤), so the "equal to" case is not included. That means the line 3x+4y=-16 is not part of the solution set. That boundary line is graphed as a dashed line.

Take note of where the variables are in relation to the inequality symbol. Both are on the "less than" side, so the shading of the graph will be where the values of x and y are less than those on the boundary line. The boundary line has a negative slope, so the values less than those on the boundary are to the left and below the line.

Plot the dashed boundary line 3x +4y = -16, or y = -3/4x -4, and shade the area below and to its left.

Teddy wants to taste all of the flavors of ice cream at the mall, one by one. Tasting any one flavor will change the way the next flavor taste after it. The flavors are chocolate, vanilla, strawberry, birthday cake, Rocky Road, and butter pecan. In how many ways can he taste the ice cream.
A. 30
B.120
C. 360
D.720

Answers

Answer: (d)

Step-by-step explanation:

Given

There are six flavors of ice-cream that is chocolate, vanilla, strawberry, birthday cake, rocky road, and butter pecan

First ice-cream can be tasted in 6 different ways

Second can be in 5 ways

similarly, remaining in 4, 3, 2 and 1 ways

Total no of ways are  [tex]6\times5\times 4\times 3\times 2\times 1=720\ \text{ways}[/tex]

Option (d) is correct.

Line JK passes through points J(–3, 11) and K(1, –3). What is the equation of line JK in standard form?

7x + 2y = –1
7x + 2y = 1
14x + 4y = –1
14x + 4y = 1

Answers

9514 1404 393

Answer:

  (b) 7x + 2y = 1

Step-by-step explanation:

You don't need to know how to find the equation. You just need to know how to determine if a point satisfies the equation. Try one of the points and see which equation fits. (The numbers are smaller for point K, so we prefer to use that one.)

  7(1) +2(-3) = 1 ≠ -1 . . . . . tells you choice A doesn't work, and choice B does

The equation is ...

  7x +2y = 1

__

Additional comment

The equations of choices C and D have coefficients with a common factor of 2. If the constant also had a factor of 2, we could say these equations are not in standard form, and we could reject them right away. Since the two points have integer values for x and y, we can reject these equations anyway: the sum of even numbers cannot be odd.

Answer:

b

Step-by-step explanation:

find the surface area of the triangular prism below.

Answers

Step-by-step explanation:

At first you need to take its lateral surface area by using the perimeter of base of the triangle and the height of prism.

Then after calculating it you need to find out its total surface area which is asked in the question and that is calculated by adding the area of both triangles of the prism in the lateral surface area.

Then that's your answer.

9514 1404 393

Answer:

  544 square units

Step-by-step explanation:

The surface area is the sum of the area of the two triangular bases and the three rectangular faces. The relevant area formulas are ...

  A = 1/2bh . . . . area of a triangle with base b and height h

  A = LW . . . . . are of a rectangle of length L and width W

__

  SA = 2(1/2)(12)(8) + (10 +10 +12)(14)

  SA = 96 +448 = 544 . . . square units

I really need help!!!​

Answers

Answer:

the third option (a=1, h=0, k=6)

Step-by-step explanation:

if I understand correctly what your teacher wants from you, then you need find a (the factor of x² in the equation) and the vertex (turnaround point) of the parabola represented by such a quadratic equation.

the vertex point coordinates are called (h, k).

the general form of such an equation equation is

y = ax² + bx + c

so, we have a right away : a=1

now we can make this quickly by using common sense, or a bit more complex by going through mathematical formulas.

the fast, practical way is to know that y=x² is the very basic parabola with its vertex at (0, 0).

y = x² + 6 is simply the same parabola just lifted up (y direction) by 6 units, that makes the vertex (0, 6).

in pure theory, though, we need to find the transformation from the general y = ax² + bx + c form to

y = a(x - h)² + k

we see right away that k = f(h) = h² + 6

y = a(x² - 2xh + h²) + k

a=1

y = x² - 2xh + h² + k = x² - 2xh + h² + h² + 6 =

= x² - 2xh + 2h² + 6

comparing with y = x² + 6

we know that

-2×h = 0

as we have no term with just x.

=> h = 0

2h² + 6 = k

2×0² + 6 = 6 = k

How many of each coin does he have?

_____nickels

_____quarters

Answers

[Redacted] - Wrong Answer

Which of the following equations is written in standard form?
A. 2+3x−6y=0
B. 4x−2y=0
C. −8x+4y=1
D. −3y+x−4=0

Answers

Answer:

Choice B.

[tex]4x - 2y = 0[/tex]

Step-by-step explanation:

Has integer coefficients and equal to 0.

how far from "0 is the green rectangle

Answers

Option 4

3-1/2"

Must click thanks and mark brainliest

Answer:

3 1/2

Step-by-step explanation:

That’s the distance from 0 to the green rectangle

1 simplify 6x64 ÷ 16 +7-21​

Answers

Answer:

10

Step-by-step explanation:


A rectangle with the dimensions of 2 feet
by 8 feet is similar to a rectangle with the
dimensions of
А 4 feet by 16 feet
B. 6 feet by 12 feet
C 12 feet by 32 feet
D 22 feet by 28 feet

Answers

Answer: A. 4ft by 16ft

Given rectangle: 2 feet by 8 feet. Similar rectangle: Option A (4 feet by 16 feet).

Use the concept of the rectangle defined as:

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

Given that,

Rectangle dimensions: 2 feet by 8 feet

And here are the options provided:

A) 4 feet by 16 feet

B) 6 feet by 12 feet

C) 12 feet by 32 feet

D) 22 feet by 28 feet

To determine if two rectangles are similar,

Compare their corresponding side lengths.

In this case,

A rectangle with dimensions 2 feet by 8 feet.

After simplifying it we can write 1:4

Let's check each option to see if it matches the similarity:

A) 4 feet by 16 feet:

The ratio of the corresponding side lengths is 2:8, which simplifies to 1:4. However, the given rectangle has side lengths of 4:16,

Which simplifies to 1:4 as well.

So, option A is similar to the given rectangle.

B) 6 feet by 12 feet:

The given rectangle has side lengths of 6:12,

Which simplifies to 1:2.

So, option B is not similar to the given rectangle.

C) 12 feet by 32 feet:

The given rectangle has side lengths of 12:32,

Which simplifies to 3:8.

So, option C is not similar to the given rectangle.

D) 22 feet by 28 feet:

The given rectangle has side lengths of 22:28,

Which simplifies to 11:14.

So, option D is not similar to the given rectangle.

To learn more about rectangle visit:

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Adam sleeps for nine hours each night, five nights a week, and 11 hours for two nights a week.
Which is closest to the percentage of the whole week that Adam spends sleeping?
A) 25%
B) 30%
C) 33%
D) 40%
E) 50%

Answers

Answer:

E

Step-by-step explanation:

The percentage of the whole week that Adam spends in sleeping is 33%.

What is percentage?

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

How to find percentage of a number?

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

According to the give question.

Adams sleeps for nine hours each night, five nights a week.

⇒ Number of hours he sleep for five nights = 5 × 9 = 45 hours

Also, 11 hours for two nights a week.

So, the total number of hours Adam sleeps in a week = 45 + 11 = 56 hours

And, total number of hours in a week = 24 × 7 = 168

Therefore,

The percentage of the whole week that Adam spends in sleeping

= (total number of hours Adam sleep in a week/Total numbers of hour in a week) × 100

[tex]=\frac{56}{168}[/tex] × 100

= 33.33%

= 33%

Hence, the percentage of the whole week that Adam spends in sleeping is 33%.

Find out more information about percentage here:

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∫[tex]\frac{x+2019}{x^{2}+9 }[/tex]

Answers

Split up the integral:

[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \int\frac{x}{x^2+9}\,\mathrm dx + \int\frac{2019}{x^2+9}\,\mathrm dx[/tex]

For the first integral, substitute y = x ² + 9 and dy = 2x dx. For the second integral, take x = 3 tan(z) and dx = 3 sec²(z) dz. Then you get

[tex]\displaystyle \int\frac x{x^2+9}\,\mathrm dx = \frac12\int{2x}{x^2+9}\,\mathrm dx \\\\ = \frac12\int\frac{\mathrm du}u \\\\ = \frac12\ln|u| + C \\\\ =\frac12\ln\left(x^2+9\right)[/tex]

and

[tex]\displaystyle \int\frac{2019}{x^2+9}\,\mathrm dx = 2019\int\frac{3\sec^2(z)}{(3\tan(z))^2+9}\,\mathrm dz \\\\ = 2019\int\frac{3\sec^2(z)}{9\tan^2(z)+9}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\tan^2(z)+1}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\sec^2(z)}\,\mathrm dz \\\\ = 673\int\mathrm dz \\\\ = 673z+C \\\\ = 673\arctan\left(\frac x3\right)+C[/tex]

Then

[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \boxed{\frac12\ln\left(x^2+9\right) + 673\arctan\left(\frac x3\right) + C}[/tex]

Explain how you would solve the following system of equations using substitution. math step in your explanation, too!! This is the system that you should use: y= 4x -5 y = 3x -3

Answers

Answer:

[tex]x=2\\y=3[/tex]

Step-by-step explanation:

Solve by substitution method

[tex]y=4x-5\\y=3x-3[/tex]

First, solve [tex]y=4x-5[/tex] for [tex]y[/tex]:

Substitute [tex]4x-5[/tex] for [tex]y[/tex] in [tex]y=3x-3[/tex]

[tex]y=3x-3[/tex]

[tex]4x-5=3x-3[/tex]

[tex]4x-3x=5-3[/tex]

[tex]x=2[/tex]

Now that we have the value of x

substitute [tex]2[/tex] for [tex]x[/tex] in [tex]y=4x-5[/tex]

[tex]y=4x-5[/tex]

[tex]y=4(2)-5[/tex]

[tex]y=8-5[/tex]

[tex]y=3[/tex]

∴ The value of [tex]x[/tex] is [tex]2[/tex] and the value of [tex]y[/tex] is [tex]3[/tex]

A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. In a random sample of 36 bins, the sample mean amount was 50.67 pounds and the sample standard deviation was 3.9 pounds.
a) Conduct the appropriate hypothesis test using a 0.1 level of significance.
b) What is the test statistic? Give your answer to four decimal places.
c) What is the P-value for the test? Give your answer to four decimal places.
d) What is the appropriate conclusion?
i. Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is larger than 0.1.
ii. Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is smaller than 0.1.
iii. Reject the claim that the mean amount per bin is 50 pounds because the P-value is larger than 0.1.
iv. Reject the claim that the mean amount per bin is 50 pounds because the P-value is smaller than 0.1.

Answers

Answer:

Step-by-step explanation:

99% =2.58

 xbar / Point Est. 50.67

 µ 50

σ 3.9

n 36

Confidence Interval  

50-> (48.9,52.44) -> Fail to Reject H0  

Test Statistic 1.0308

P-Value 0.1549

What is the equation of a line that passes through the point (1,8) and is perpendicular to the line whose equation is y=x/2+3?

Answers

Answer:

m=1/2

y-8=1/2(x-1)

y-8=1/2x-1/2

multiply through by 2

2y-16=x-1

2y-16+1-x=0

2y-15-x=0

2y-x-15=0

Three jackets cost as much as five shirts. Each jacket costs $16 more
than each shiri. What is the cost of one shirt?

Answers

Answer:

$3.20

Step-by-step explanation:

Divide the number 16 (as in the cost per Jacket) by 5. (The amount of shirts you could buy with $16)

Then once you have divided 16 by 5, your answer should be 3.2, so the cost of one shirt is $3.20

During a 1966 Tabiona High School track meet, Levere ran the 100 yard dash in
10.63 seconds. Ross took second with a time of 10.98 seconds.
a. Levere’s time was _______% shorter than Ross’.
b. Ross’ time was _______% longer than Levere’s.
c. Levere’s time was _______% of Ross’.

Answers

Answer:

a) 3.19

b) 3.29

c) 96.81

Step-by-step explanation:

Question a:

Levere's: 10.63s

Ross: 10.98s

10.98 - 10.63 = 0.35s shorter than 10.98s, so:

0.35*100%/10.98 = 3.19% shorter.

Question b:

35s longer than 10.63s, so:

0.35*100%/10.63 = 3.29% longer.

Question c:

3.19% shorter, so 100 - 3.19 = 96.81% of Ross.

Help with this Area question

Answers

Step 1: Find the area of the rectangle

A = base x height

A = 39 x 20

A = 780

Step 2: Find the area of the semi-circles

---Two semi-circles is the same as one whole circle, so I will be finding the area of one whole circle.

A = pi x r^2

A = pi x 10^2

A = 100pi = 314

Step 3: Find the area of the figure

Area = area of the rectangle - area of the semi-circles

A = 780 - 314

A = 466 cm^2

Hope this helps!

Answer:

466 cm^2

Step-by-step explanation:

This one is done basically the same as the other.

Rectangle = 20 x 39

Circle = (3.14) x 10^2

Rectangle = 780

Circle = 314

rectangle - circle

780 - 314 = 466

Determine if f(x, y) = 10 − x^2 − y^2
is increasing or decreasing at (7, −3) if we
take y to be constant and let x vary. Also determine if f(x, y) is increasing at
(7, −3) if we take x to be constant and let y vary.

Answers

Answer:

Step-by-step explanation:

f(x,y)=10-x^2-y^2

To find derivative of z w.r.t. x is treat any other variable as a constant.

dz/dx=0-2x-0

dz/dx=-2x

Evaluating this at (7,-3) gives us dz/dx=-2(7)=-14.

Since this result is negative, it mrans as x increases z decreases.

f(x,y)=10-x^2-y^2

To find derivative of z w.r.t. y is treat any other variable as a constant.

dz/dx=0-0-2y

dz/dx=-2y

Evaluating this at (7,-3) gives us dz/dy=-2(-3)=6.

Since this result is positive it mrans as y increases z decreases.

HELP ASAP!!!!
Lydia is creating floral centerpieces for a friend's wedding. She is trying to decide the amount of tulips and peonies she should include in the centerpieces. The table below shows the number of flowers she plans to use in each centerpiece. The total number of flowers used for each centerpiece should be no more than 21 flowers.


Flower Type Number

Sweet Pea 8

Hyacinth 2

Tulip t

Gardenia 3

Peony p


First, select the inequality that can be used to represent the number of peonies, p, and tulips, t, Lydia can use in each centerpiece. Then, select possible combinations of peonies and tulips that could be in a centerpiece to satisfy the inequality.

answers

13 - (t + p) ≤ 21

13 + p + t ≥ 21

3 tulips and 9 peonies

2 tulips and 3 peonies

13 + t + p ≤ 21

6 tulips and 4 peonies

5 tulips and 3 peonies

21 - p + t ≥ 13

Answers

9514 1404 393

Answer:

13 + t + p ≤ 215 tulips and 3 peonies2 tulips and 3 peonies

Step-by-step explanation:

"No more than 21" means "less than or equal to 21." The total of flowers Lydia has listed is ...

  8 + 2 + t + 3 + p = 13 +p +t

Lydia wants this less than or equal to 21, so the appropriate inequality is ...

  13 +p +t ≤ 21

__

Subtracting 13 from both sides gives us a relation that helps us better see the possible values of p and t.

  p +t ≤ 8

Then suitable numbers of peonies and tulips will numbers that total 8 or less. Of the choices listed, ones that match that requirement are ...

  2 tulips and 3 peonies

  5 tulips and 3 peonies

What's the dependent variable shown in the table?


A)

The amount of water given to the plant

B)

The color of the flowers

C)

The number of flowers on the plant

D)

The speed at which the plant grows

Answers

Answer:

The number of flowers on the plant

Step-by-step explanation:

Answer:

C: Number of flowers on the plant

Step-by-step explanation:

i got it right on my test

Please help! Question and answers are in the pic

Answers

So far she worked 4 days at 5 1/2 hours a day for a total of 22 hours.

22 hours x $8.50 = $187

Subtract that from the cost of the computer:

899-187 = $712

She needs $712 more.

Amount she makes per shift: $8.50 x 5 1/2 hours = $46.75

Divide what she needs by amount per shift:

712 / 46.75 = 15.22 shifts

She needs to work 16 more shifts.

We have that 2a+1=1 and b-a=1. What is the value of b?

Answers

Answer:

b=1

Step-by-step explanation:

2a+1 =1

Subtract 1 from each side

2a+1-1 = 1-1

2a=0

a=0

Now find b from the second equation

b-a =1

b-0=1

b=1

Answer:

Equation: 2a+1=1

Subtract 1 from both sides: 2a=0

Divide by 2: a=0

Equation: b-a=1

Substitute: b-0=1

Combine: b=1

So, b=1.

Let me know if this helps.

You need to build a box from an 8 inchby 10 inch piece of cardboard. To do this, you cut out squares of length x from the four corners of the box in order to fold the sides up. Verify that the volume of the box is given by the equation:

V= 4x^3â36x^2+ 80x

Answers

Answer:

Step-by-step explanation:

From the attached image below, let assume we have a square of diameter x by x which is to be cut from each corner of the cardboard sheet.

Thus, from the diagram

the length = 8 - 2x   the width = 10 - 2x  and the height = x

So, the volume V = L*w*h

Volume (V) = (8 - 2x) (10 - 2x) x

V = (80 - 16x - 20x +4x²)x

V = 80x -36x² + 4x³

By rearrangement:

V = 4x³ - 36x² + 80x

Write the following as an expression: How much water do I need to add to l liters of pure alcohol to obtain a solution of 45% alcohol? The answer is an EXPRESSION, not an actual answer!! WILL MARK BRAINLIST!!!

Answers

Answer: [tex]\dfrac{11}{9}I[/tex]

Step-by-step explanation:

Given

There is [tex]l[/tex] liter of pure alcohol

Suppose [tex]x[/tex] liters of water is added

After addition of water, alcohol becomes 45% in concentration

[tex]\Rightarrow \dfrac{l}{x+l}=45\%\\\\\Rightarrow \dfrac{I}{0.45}=x+I\\\\\Rightarrow \dfrac{20}{9}I-I=x\\\\\Rightarrow x=\dfrac{11}{9}I[/tex]

Thus,  [tex]\dfrac{11}{9}I[/tex] of water is added to the pure alcohol.

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Buff is considering a new packaging machine. The initial cost is $10,000 and we would save $4,000 per year in labor costs. If our MARR is 12% and our projects must have a 3-year discounted payback period, should we purchase this packaging machine? Yes NoNot enough nformation to answer. Help ! With step by step solution Been stuck on this since yesterday !!?!? Help!!! , is this all correct please help me 4571119?a. 41b. 35c. 23d. 29 "Find the area and the circumference of a circle with diameter of 8m" The company has net sales revenue of $3.6 million during 2018. The company's records also included the following information: Assets 12/31/17 12/31/18 Property, plant and equipment $ 2.3 million $ 2.5 million Licensing agreements $ 0.5 million $ 0.4 million Goodwill $ 0.3 million $ 0.3 million Investments $ 0.4 million $ 0.5 million What is the company's fixed asset turnover ratio for 2018 The input sin(20) is sampled at 20 ms intervals by using impulse train sampling: i. Construct the input and sampled signal spectra. The postwar policy of the United States known as Containment wasdesigned toO overthrow dictatorships.O reunify GermanyO prevent the spread of communism. The Berlin Conference dividedVAFRIQUEIndia AntarcticaArizonaAfrica A triangle has base of 7 1/8 feet and height 6 1/4 feet. Find the area of a triangle as a mixed number. brianna practices the panio 30 minutes each day write an expression for the number of hours she practises in d days Read the paragraph. Then answer the question that follows.Perhaps you wanted pizza for dinner, but were out voted by the rest of the family who wanted chili. This is similar to what happens in a community. One person has to give up a right for the good of the group. Sometimes citizens' duties and rights conflict with each other. A good example is a public protest. People have the right to meet in groups and share ideas. However, a protest can disrupt traffic or other normal activities. A city must provide extra police protection to keep people safe. Therefore, the city has the right to require permission in advance for a protest. Government must make laws to balance the rights of individuals and different groups of people.Which of the following statements best describes this paragraph? The paragraph contains categories of comparison. The paragraph contains a simile. The paragraph contains no text connections. The paragraph contains an analogy. Is u=12 a solution of 8u1=6u? ASAP!! Please help me out here WHAT IS ONE OF THE MOST IMPORTANT FUNCTIONS OF ANY LEGAL SYSTEM? Evaluate the expression (2x over xy ) for x = 4 and y == 2. 11. What is "the hook" in a Whats is the hook in a text?the final paragraphwhat gets the reader's attentionthe ways ideas developthe way the text is organized Antigone and Ismene heard with horror what Creon had decided. To Ismene, shocking as it was, overwhelming her with anguish for the pitiful dead body and the lonely, homeless soul, it seemed, nevertheless, that nothing could be done except to acquiesce [to accept without protest]. She and Antigone were utterly alone. All Thebes was exulting that the man who had brought war upon them should be thus terribly punished. "We are women," she told her sister. "We must obey. We have no strength to defy the State." "Choose your own part," Antigone said. "I go to bury the brother I love.""The Royal House of Thebes""Is it not better to be poor and free than to have great wealth and be slaves?" she [Boadicea] asked. "And the Romans take not only our freedom but our wealth. They want to make us both slaves and beggars. Let us rise. O brothers and sisters, let us rise, and drive these robbers out of our land! Let us kill them every one! Let us teach them that they are no better than hares and foxes, and no match for greyhounds! We will fight, and if we cannot conquer, then let us dieyes, every one of usdie rather than submit.""The Story of a Warrior Queen"How do the archetypes in these passages support the universal theme that one's values are worth risking one's life for?Both Antigone and Boadicea are warriors who decide to go to war for what they believe is right.Both Antigone and Boadicea are heroes who go to battle against their enemies.Both Antigone and Boadicea are heroines who choose their values over their lives, knowing they may die in the process.Both Antigone and Boadicea are villains who transgress the law in order to fight for their values. Solve the following formula for a.