Write 8 statements and reasons for the proof

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1 (#3)

The formula for a regular octagon inscribed in a circle of radius [tex]r[/tex] is [tex]A=2\sqrt{2}r^2[/tex]. Hence, [tex]A=2\sqrt{2}(4)^2=16*2\sqrt{2}=32\sqrt{2}\approx45.255m^2[/tex].

Thus, C is the correct answer

Problem 2 (#4)

Using the co-function identity [tex]\displaystyle \sin\biggr(x+\frac{\pi}{2}\biggr)=\cos(x)[/tex], the equation can be rewritten as [tex]cos(x)=\frac{\sqrt{3}}{2}[/tex]. Using a unit circle, it's easy to see that the answer is [tex]\displaystyle\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}[/tex].

Thus, C is the correct answer

Problem 3

[tex]f(x)=g(x)\\\\2\sin^2 x-1=-\cos(x)\\\\2(1-\cos^2 x)-1=-\cos(x)\\\\2-2\cos^2 x-1=-\cos(x)\\\\1-2\cos^2 x=-\cos(x)\\\\2\cos^2x-\cos(x)-1=0[/tex]

Let [tex]u=\cos(x)[/tex], hence:

[tex]2u^2-u-1=0\\\\(2u+1)(u-1)=0[/tex]

[tex]\displaystyle2u+1=0\\\\2u=-1\\\\u=-\frac{1}{2}\\ \\\cos(x)=-\frac{1}{2}\\ \\x=\biggr\{\frac{2\pi}{3},\frac{4\pi}{3}\biggr\}[/tex]

[tex]u-1=0\\\\u=1\\\\\cos(x)=1\\\\x=\{0\}[/tex]

So, the solution set is [tex]\displaystyle\biggr\{0,\frac{2\pi}{3},\frac{4\pi}3}\biggr\}[/tex]

Thus, B is the correct answer

Problem 4 (#8)

If we construct a right triangle in Quadrant I with an opposite leg length of 1 unit and an adjacent leg length of 1 unit, this shows that [tex]\displaystyle\tan\theta=\frac{opposite}{adjacent}=\frac{1}{1}=1[/tex]. Since [tex]\displaystyle \csc\theta=\frac{1}{\sin\theta}[/tex] and [tex]\displaystyle\sin\theta=\frac{opposite}{hypotenuse}[/tex], we must solve for the hypotenuse with the Pythagorean Theorem:

[tex](opposite)^2+(adjacent)^2=(hypotenuse)^2\\1^2+1^2=(hypotenuse)^2\\1+1=(hypotenuse)^2\\2=(hypotenuse)^2\\\sqrt{2}=hypotenuse[/tex]

Therefore, since [tex]\displaystyle \sin\theta=\frac{opposite}{hypotenuse}=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}[/tex], then [tex]\displaystyle \csc\theta=\frac{1}{\sin\theta}=\frac{1}{\frac{\sqrt{2}}{2}}=\frac{2}{\sqrt{2}}=\frac{2\sqrt{2}}{2}=\sqrt{2}[/tex].

Thus, B is the correct answer

Problem 5 (#9)

As no angles are given and only side lengths, we are forced to use the Law of Cosines to solve for the angles:

Angle A:

[tex]a^2=b^2+c^2-2bc\cos(A)\\400^2=500^2+600^2-2(500)(600)\cos(A)\\160000=250000+360000-600000\cos(A)\\160000=610000-600000\cos(A)\\-450000=-600000\cos(A)\\\frac{3}{4}=\cos(A)\\ A\approx41.410^\circ[/tex]

Angle B:

[tex]b^2=a^2+c^2-2ac\cos(B)\\500^2=400^2+600^2-2(400)(600)\cos(B)\\250000=160000+360000-480000\cos(B)\\250000=520000-480000\cos(B)\\-270000=-480000\cos(B)\\\frac{9}{16}=\cos(B)\\B\approx55.771^\circ[/tex]

Angle C:

By the Triangle Angle-Sum Theorem, [tex]C\approx82.819^\circ[/tex]

Hence, we can conclude that angle A is the smallest angle the swimmers must turn between the buoys.

Thus, C) 41.410° is the correct answer

Problem 6 (#unknown)

As we are given two angles and a side length, we can use the Law of Sines to find side length "b". Firstly, we need angle C so we can set up the proportion to find "b". By the Triangle Angle-Sum Theorem, [tex]m\angle C=60^\circ[/tex].

[tex]\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\\\\\frac{\sin(64^\circ)}{b}=\frac{\sin(60^\circ)}{8}\\\\8\sin(64^\circ)=b\sin(60^\circ)\\\\b=\frac{8\sin(64^\circ)}{\sin(60^\circ)}\\ \\b\approx8.303[/tex]

Thus, B is the correct answer (how ironic lol)

Problem 7 (#13)

[tex]\displaystyle\sqrt{2}\cos2x=\sin^2x+\cos^2x\\\\\sqrt{2}\cos2x=1\\\\\cos2x=\frac{1}{\sqrt{2}}\\\\\cos2x=\frac{\sqrt{2}}{2}\\ \\2x=\frac{\pi}{4},\frac{7\pi}{4}\\ \\x=\frac{\pi}{8},\frac{7\pi}{8}[/tex]

Hence, B is the correct answer

Problem 8 (#14)

[tex]\displaystyle \sec\theta=2\\\\\frac{1}{\cos\theta}=2\\ \\\cos\theta=\frac{1}{2}\\ \\\theta=\frac{\pi}{3}+2\pi n,\frac{5\pi}{3}+2\pi n[/tex]

Thus, D is the correct answer

Problem 9 (#19)

The bottom graph looks correct as the period of the tangent function is [tex]\frac{\pi}{|b|}=\frac{\pi}{2}[/tex].

Yo your question is extremely un readable but im gonna assume you are asking what is more than a hundred inches

8 feet 6 inches = 104 inches

8 feet = 96 inches

3 yards = 108 inches

2 yards 19 inches =  91 inches

Answer:

Zimbabwe is a Bantu word for stone houses so the answer is C

Answer:

161.75

(You can use a calculator to calculate this)

Answer:

161.75

Step-by-step explanation:

Answer:

1974 mm^3

Step-by-step explanation:

The formula to find the volume of a rectangular prism/cuboid: l x w x h, where l is the length, w is the width and h is the height.

1) Input the values into the formula and solve it.

= 47 x 14 x 3

= 1974 mm^3

The curves of the labor market are illustrations of demand and supply, and the curves are all linear functions

The equations are given as:

D = 36 - 2W

S₁ = 9 + W ---- domestic (i.e. without immigrants)

S₂ = 10 + 2W ---- total (i.e. including immigrants)

See attachment for the graph

This is the point of intersection between the curves of S₁ and D.

From the graph, we have:

(W, D) = (9,18)

Hence, the equilibrium wage rate before immigration is $9, and the number of workers that would be hired is 18

This is the point of intersection between the curves of S₂ and D.

From the graph, we have:

(W, D) = (6.5,23)

Hence, the equilibrium wage rate after immigration is $6.5, and the number of workers that would be hired is 23

Substitute 6.5 for W in S₁ = 9 + W

S₁ = 9 + 6.5

S₁ = 15.5

Remove decimal

S₁ = 16

Hence, the number of domestic workers that would be hired is 16

Substitute 6.5 for W in S₂ = 10 + 2W

S₂ = 10 + 2 * 6.5

S₂ = 23

Subtract S₁ = 16 from S₂ = 23

Immigrants = 23 - 16

Immigrants = 7

Hence, the number of immigrants that would be hired is 7

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Answer:

$[tex]\frac{6000\cdot \:365^{1825}}{365.08^{1825}}[/tex]

Step-by-step explanation:

[tex]x(1+.\frac{.08}{365})^{5\cdot \:365} =6000[/tex]

[tex]x\frac{365.08^{1825}}{365^{1825}}=6000[/tex]

[tex]x\frac{365.08^{1825}}{365^{1825}}\cdot \:365^{1825}=6000\cdot \:365^{1825};\quad \ne \mathrm{True}[/tex]

[tex]365.08^{1825}x=6000\cdot \:365^{1825};\quad \ne \mathrm{True}[/tex]

[tex]\frac{365.08^{1825}x}{365.08^{1825}}=\frac{6000\cdot \:365^{1825}}{365.08^{1825}};\quad \ne \mathrm{True}[/tex]

[tex]x=\frac{6000\cdot \:365^{1825}}{365.08^{1825}};\quad \ne \mathrm{True}[/tex]

you cannot simplify further because of the high exponents

It is simply extremely hard to do compound interest problems backwards if it gets compounded daily

Mark brainliest please!

Answer:

6 gallons because 3/4 is the same as 6/8 so therefore 6 gallons would be 3/4 full

The amount of water in gallons in the fish tank is A = 6 gallons

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

If Levi wants to fill the fish tank so it is only 3/4 full, then he only needs to fill it with 3/4 of its total capacity.

A = (3/4) x 8

On simplifying the equation , we get

A = 6 gallons

Hence , Levi should put 6 gallons of water in the fish tank to fill it to 3/4 of its total capacity

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Answer:

-4

Step-by-step explanation:

Answer: If f(x) = -x2 - 3x + 5, then the value of f(-3) is -4.

Answer:

f(-3) = 14

Step-by-step explanation:

f(-3) just means to fill in -3 for x.

2x^2 + 3x + 5

becomes

2(-3)^2 + 3(-3) + 5

Exponent first.

2(9) + 3(-3) + 5

Multiplication

18 + -9 + 5

Add.

14

Answer:

A: (-3,4) (-3,6) (-5,6) (-7,4)

B: The transformation would be described as a reflection over the y axis

C:  The transformation does result in a congruent figure because the shape doesn't change in size or shape and in length or width

Step-by-step explanation:

So our plots from the figure are: (3,4)  (3,6)  (5,6)  (7,4)

So using the rule (x, y) → (-x, y) are new points would be:

(-3,4)

(-3,6)

(-5,6)

(-7,4)

This rule (x, y) → (-x, y) is used for the type of transformation that is a reflection but over the y axis.

Answer:

47 percent

Step-by-step explanation:

we need to see the shapes

Answer:

2,307.69 per biweekly paycheck and 2,500 per semi monthly paycheck

Step-by-step explanation:

If you didn't already know, monthly pay has 12 paychecks, semi-monthly pay has 24 paychecks, biweekly pay has 26 paychecks, and weekly pay has 52 paychecks. If you break down 60k into these paychecks, here are the results: $60,000/12 equals $5,000 (monthly pay) $60,000/24 equals $2,500 (semi-monthly pay)

hope this helps

Therefore, the production cost for a packet of Super tea is $923.91.

Since Brenya Estate produces a high quality tea branded Super by blending three types of tea coded A, B and C in the ration 1½ : 5 : 1, and originally Type A tea costs GHS 1,600 type B costs GHS 800 and type C costs GHS 1,700 per Kg to produce, and Brenya Tea Estate packs Super tea in packets of 825g each. Blending and packing costs are 40 per Kg, to determine the production cost for a packet of Super tea, the following calculation must be made:

Therefore, the production cost for a packet of Super tea is $923.91.

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Answer:

10

Step-by-step explanation:

AB²=8²+6²

=64+36

=100

AB=10

Answer:

10 units

Step-by-step explanation:

Pythagorean Theorem:

a² + b² = c²

6² + 8² = c²

c = √100

10 units

Applying the formula for the area of a sector and length of an arc, the value of k is calculated as: 27.

Area of a sector of a circle = ∅/360 × πr²

Length of arc = ∅/360 × 2πr

Given the following:

Find ∅ of the sector using the formula for length of acr:

∅/360 × 2πr = 6π

Plug in the value of r

∅/360 × 2π(9) = 6π

∅/360 × 18π = 6π

Divide both sides by 18π

∅/360 = 6π/18π

∅/360 = 1/3

Multiply both sides by 360

∅ = 1/3 × 360

∅ = 120°

Find the area of the sector:

Area = ∅/360 × πr² = 120/360 × π(9²)

Area = 1/3 × π81

Area = 27π

Therefore, the value of k is 27.

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Answer:

£11.04

Step-by-step explanation:

1.38 x 8 = 11.04

Answer:

B

Step-by-step explanation:

[tex][(8+15) \times 3] \div 3\\= \frac{(8+15) \times 3}{3}\\= \frac{8 + 15}{1}\\= 8 + 15 = 23[/tex]

Answer:

E={1,2,3}

Step-by-step explanation:

First one is the correct answer

Answer:

27°

Step-by-step explanation:

SOH CAH TOA

sinx = opposite/hypotenuse

sinx = 10/21  ≈ 0.47619047619 radians

0.47619047619 · (180/π)

≈ 85.71/π

≈ 27°

Answer:

Jackson can play for 21 more minutes.

Step-by-step explanation:

If 9 minutes = 30% or 0.3

then we can set up a ratio to cross multiply.

(9/30) = (x/100)

then croos multiply and divide to isolate and solve for x.

(9 * 100) / 30 = 30

That means 100% of Jackson's time is 30 minutes.

30 - 9 = 21. So jackson can play for 21 more minutes before he uses all of his time.

But by the time he figures all of this out he'll probably have to turn it off anyways :)

Answer:

1024

Step-by-step explanation:

n(10) =2^10

n(10) = 1024

Answer:

53.2 square feet

638.4 square inches

Step-by-step explanation:

The formula for area of parallogram is l x w.

91.2 inches to feet is 7.6 feet.

7.6 is the width and 7 is the length.

7.6 x 7 = 53.2

Answer: B. Your courses will not be as diverse.

Step-by-step explanation:

      A four-year college will have many different classes and courses you can take in different areas. Trade school courses focus on a specific skill, such as being a dentist or an electrician. This means the answer to your question is;

         B. Your courses will not be as diverse.

Answer: B: Your courses will not be as diverse

Step-by-step explanation: Trade schools focus on preparing you for a specific trade rather than general studies

Answer:

the discriminant of g positive

Step-by-step explanation:

the discriminant of g positive because the graph of g cross the x-axis in two points.

PART A

WT = 30

30 = 3HF + 2FA

30 = 3x + 2y

2y = 30 - 3x

y = 15 - 3/2x

0 = 15 - 3/2x

3/2x = 15

x or EH = 10

y = 15 - 3/2(10)

y = 15 - 15

y or FA = 0

Okay so this problem doesn't make sense because FA cannot = 0. I know I did the first part right - change of variables. I'm just not sure if we can use the information in part b to answer part a... Anyway, I hope this helps!

Answer:

Step-by-step explanation:

Find the horizontal asymptotes by comparing the degrees of the numerator and denominator.

Vertical Asymptotes:

x=1

Horizontal Asymptotes:

y=0

No Oblique Asymptotes

Answer: Abby would be able to make 12 hamburgers.

Step-by-step explanation:

You have to divide 2.28 and 0.19 and you would get 12 so the answer is 12.