Each exterior angle in a regular polygon has a measure of 18. How many sides does the polygon have? What is the sum of the measures of the interior angles?

Answer:

[tex]{ \tt{ \tan {}^{4} \theta + { \sec }^{2} \theta }} \\ { \tt{ = ({ \tan }^{2} \theta ){}^{2} + { \sec }^{2} \theta }} \\ = { \tt{ {-(1 - { \sec }^{2} \theta) }^{2} + { \sec }^{2} \theta }} \\ { \tt{ = -(1 - 2 { \sec }^{2} \theta + { \sec }^{4} \theta) + { \sec}^{2} \theta}} \\ { \tt{ = -(1 - { \sec }^{2} \theta) + { \sec }^{4} \theta}} \\ { \tt{ = -{ \tan}^{2} \theta + { \sec }^{4} \theta }} \\ = { \tt{ { \sec}^{4} \theta - { \tan }^{2} \theta}} \\ { \bf{hence \: proved}}[/tex]

Answer:

a. 5 hours

b. 40 kph

Step-by-step explanation:

300 km ÷ 60 km = 5 hours

200 km ÷ 5 hours = 40 kilometers per hour

Answer:

y = 3x-10

Step-by-step explanation:

When lines are parallel, they have the same slope

y = 3x+2 is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is 3

y = 3x+b

We have a point on the line

-1 = 3(3)+b

-1 = 9+b

-10 = b

y = 3x-10

Answer:

(a): x is 3 and ky is -1

(b): k is -2

Step-by-step explanation:

Let: 3x + ky = 8 be equation (a)

x - 2 ky = 5 be equation (b)

Then multiply equation (a) by 2:

→ 6x + 2ky = 16, let it be equation (c)

Then equation (c) + equation (b):

[tex] { \sf{(6 + 1)x + (2 - 2)ky = (16 + 5)}} \\ { \sf{7x = 21}} \\ { \sf{x = 3}}[/tex]

Then ky :

[tex]{ \sf{2ky = 3 - 5}} \\ { \sf{ky = - 1}}[/tex]

[tex]{ \bf{y = \frac{1}{2} }} \\ { \sf{ky = - 1}} \\ { \sf{k = - 2}}[/tex]

Simultaneous equations are used to represent a system of related equations.

The value of k when [tex]y = \frac 12[/tex] is -2

Given that:

[tex]3x + ky = 8[/tex]

[tex]x - 2ky = 5[/tex]

[tex]y = \frac 12[/tex]

Substitute [tex]y = \frac 12[/tex] in both equations

[tex]3x + ky = 8[/tex]

[tex]3x + k \times \frac 12 = 8[/tex]

[tex]3x + \frac k2 = 8[/tex]

[tex]x - 2ky = 5[/tex]

[tex]x - 2k \times \frac 12 = 5[/tex]

[tex]x - k = 5[/tex]

Make x the subject in [tex]x - k = 5[/tex]

[tex]x = 5 + k[/tex]

Substitute [tex]x = 5 + k[/tex] in [tex]3x + \frac k2 = 8[/tex]

[tex]3(5 + k) + \frac k2 = 8[/tex]

Open bracket

[tex]15 + 3k + \frac k2 = 8[/tex]

Multiply through by 2

[tex]30 + 6k + k = 16[/tex]

[tex]30 + 7k = 16[/tex]

Collect like terms

[tex]7k = 16 - 30[/tex]

[tex]7k = - 14[/tex]

Divide both sides by 7

[tex]k = -2[/tex]

Hence, the value of constant k is -2.

Read more about simultaneous equations at:

https://brainly.com/question/16763389

Answer:

634806 km travelled by the Moon as it orbits 2.62 radians about the Earth.

Step-by-step explanation:

convert to pi.

Answer:

-5/13

Step-by-step explanation:

sin theta = opp / hyp

sin theta = -12 /13

we can find the adj side by using the pythagorean theorem

adj^2 + opp ^2 = hyp^2

adj^2 +(-12)^2 = 13^2

adj^2 +144 =169

adj^2 = 169-144

adj^2 = 25

Taking the square root of each side

adj = ±5

We know that it has to be negative since it is in the third quad

adj = -5

cos theta = adj / hyp

cos theta = -5/13

Answer:

B) -5/13

Step-by-step explanation:

i hope it will help

plzz mark as brainliest if you want

Answer:

Mode

Step-by-step explanation:

If I'm not mistaken the mode is the value that appears most which in this case would mean the size that is bout the most.So he should use the mode which basically shows what size is bought the most and buy that size

The statistical measurements they would use to determine what sizes they should order the most is mode option (D) is correct.

It is defined as the highest frequency of data and how many times the element is repeated in the data set, known as the mode value.

We have:

A department store is ordering the fall line of shoes.

As we know, Statistics is a mathematical tool defined as the study of collecting data, analysis, understanding, representation, and organization. Statistics is described as the procedure of collecting data, classifying it, displaying that in a way that makes it easy to understand, and analyzing it even further.

The mean value for the given set of data or the closed value for each entry given in the set of data.

Thus, the statistical measurements they would use to determine what sizes they should order the most is mode option (D) is correct.

Learn more about the mode here:

brainly.com/question/300591

#SPJ5

Answer:

R = 35l-215

Step-by-step explanation:

total amount they earn = 35l

however, to account for the money used to rent the machines, we have to deduct 215 from the total cost.

hence,

R= 35l-215

total amount they raised = 35(26)-215 = $695

they would lose $215 if they were unable to aerate due to weather conditions

they could avoid this potential loss by checking the weather report before renting the machines

Answer:

21

Step-by-step explanation:

area of triangle = 1/2 * base * height

assuming the triangle is made by cutting the rectangle into half,

1/2 * 7 * 6 = 21

Answer:

the answer is 21

Step-by-step explanation:

Step-by-step explanation:

we solve for x

15x-(2/x)>1. /*x

15x^2 -2 > x. /-x

15x^2 -x -2 > 0

Solve the quadratic at zero

15x^2 -x -2=0

using the quadratic formula

x1,2 = [1+-sprt((-1)^2-4(15)(-2))]/2(15)

= [1+- sqrt (121)]/30

= [1+-11]/30

x1= 12/30= 2/5

x2= -10/30= -1/3

therefore this positive parabola is greater than zero or positive when

x< -1/3 and x> 2/5

Answer:

H0 : μ = 99

H1 : μ > 99

Z statistic = 0.5

Result is not significant at 5% level ;

Step-by-step explanation:

Given that :

σ = 10

μ = 99

Sample size, n = 25

H0 : μ = 99

H1 : μ > 99

The test statistic :

(xbar - μ) ÷ (σ/√(n))

Since the population standard deviation is known, we use the Z statistics.

Z = (100 - 99) ÷ (10/√(25))

Z = 1 / 2

Z = 0.5

The Z critical value at α = 0.05

Zcritical = 1.645

Zstatistic < Zcritical ; Hence, we fail to reject the H0.

Answer:

A and c

Step-by-step explanation:

1) Length arc = r*theta

5.11=1*theta. Theta is 5.11 rads

2) Law of cosines is the correct answer

Given:

The expression is:

[tex](m-3+4n)\cdot (-8)[/tex]

To find:

The equivalent expression by using the distributive property.

Solution:

Distributive property:

[tex]a(b+c)=ab+ac[/tex]

We have,

[tex](m-3+4n)\cdot (-8)[/tex]

Using the distributive property, we get

[tex](m-3+4n)\cdot (-8)=(m)\cdot (-8)+(-3)\cdot (-8)+(4n)\cdot (-8)[/tex]

[tex](m-3+4n)\cdot (-8)=-8m+24-32n[/tex]

Therefore, the equivalent expression is [tex]-8m+24-32n[/tex].

Answer:

24

Step-by-step explanation:

2*1+1+2*2+1+2*3+1+2*4+1=24

Answer:

Perimeter, P = 112 meters

Step-by-step explanation:

Translating the word problem into an algebraic expression, we have;

L = 6W  ...... equation 1

Given the following data;

To find the perimeter of the rectangle;

First of all, we would determine the dimensions of the rectangle using its area.

Mathematically, the area of a rectangle is given by the formula;

Area of rectangle = LW  ..... equation 2

Substituting eqn 1 into eqn 2, we have;

384 = 6W(W)

384 = 6W²

Dividing both sides by 6, we have;

W² = 384/6

W² = 64

Taking the square root of both sides, we have;

W = √64

Width, W = 8 meters

Next, we would find the length;

L = 6W

L = 6 * 8

Length, L = 48 meters

Lastly, we would determine the perimeter of the rectangle using the above dimensions;

Mathematically, the perimeter of a rectangle is given by the formula;

Perimeter = 2(L + W)

Substituting the values into the formula, we have;

Perimeter, P = 2(48 + 8)

Perimeter, P = 2(56)

Perimeter, P = 112 meters

Answer:

x=15.75 y=59

Step-by-step explanation:

In total there is 360 degrees. We know y is 59 so we will replace it with that.

59+59=118. 360-118=242. 242/2=121. 29+29=58. So we can subtract that to equal 63. Now 63=4x. We can divide so 2x=31.5. x=15.75.

Therefore, 15.75=x and 59=y

I hope this helped ^^.

Answer:

A

Step-by-step explanation:

Given

- 2x² + 5x - 3 ← factor out - 1 from each term

= - 1(2x² - 5x + 3) ← factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × 3 = 6 and sum = - 5

The factors are - 2 and - 3

Use these factors to split the x- term

2x² - 2x - 3x + 3 ( factor the first/second and third/fourth terms )

2x(x - 1) - 3(x - 1) ← factor out (x - 1) from each term

(2x - 3)(x - 1)

Then

- 2x² + 5x - 3 = - 1(2x - 3)(x - 1) → A

Answer:

= -8x^5 y^4

Step-by-step explanation:

Multiply the numbers: -2 . 4 = -8

-2x^3 yx^2 y^3

Simplify x^3 x^2 : x^5

= -8x^5yy^3

Simplify yy^3 : y^4

= -8x^5 y^4

Answer:

V=L x W x H

(4.7)(5.2)(4.7)(5)

=574.34 inch

Answer:

the answer is 140.6

Step-by-step explanation:

got it right on quiz

4x4=16 16x3=48 so I think the answer is 48

Answer:

IN MY OPINION D NO IS THE CORRECT ANSWER OF YOUR QUESTION.

Answer:

in my opinion d is the correct answer of your questions.

Step-by-step explanation:

Because subtract subtract sign is always add.

hope this will help you

thanks

Answer:

a is 1.58 and b is 0.42

Step-by-step explanation:

[tex]{ \sf{3 {x}^{2} - 6x + 2 = 0 }} \\ { \sf{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} }} \\ \\ { \sf{x = \frac{ - ( - 6)± \sqrt{ {( - 6)}^{2} - (4 \times 3 \times 2) } }{(2 \times 3)} }} \\ \\ { \sf{x = \frac{6± \sqrt{12} }{6} }} \\ \\ { \sf{x = 1.58 \: and \: 0.42}}[/tex]

Answer:

10

Step-by-step explanation:

i looked it up to be sure but if wrong very sorry.

Answer:

20=24

8. =? Cross multply

Answer:

The answer is "Option b".

Step-by-step explanation:

The significant variance shows that the numbers in the set are far from the mean and far from each other as well. Alternatively, a little variation implies the reverse. The variance value of 0, on either hand, shows that all values inside a set of numbers are the same. If you need yet another test, use a greater sample variance as the numerator of the test statistic to avoid having to reference tables of the F distribution that primary device from of the lower tail.

Answer:

Following are the calculated points to the given question:

Step-by-step explanation:

[tex]When\ x=-8\\\\y=\frac{1}{2}(-8)+1=-3\\\\[/tex]

so,  

[tex]Point \ A(-8,-3)[/tex]

[tex]When\ x=-4\\\\y=\frac{1}{2}(-4)+1=-1\\\\[/tex]

so,  

[tex]Point \ B(-4,-1)[/tex]

[tex]When\ x=0\\\\y=\frac{1}{2}(0)+1=1\\\\[/tex]

so,  

[tex]Point \ C(0,1)[/tex]

[tex]When\ x=2\\\\y=\frac{1}{2}(2)+1=2\\\\[/tex]

so,  

[tex]Point \ D(2,2)[/tex]

[tex]When\ x=6\\\\y=\frac{1}{2}(6)+1=4\\\\[/tex]

so,

[tex]Point \ E(6,4)[/tex]

Answer:

Base of the ladder is 3 meters away from the building.

Step-by-step explanation:

Let's use Pythagoras theorem to solve.

Pythagoras theorem says,

[tex]a^{2} +b^{2} =c^{2}[/tex]

Here let horizontal distance is "a''

Vertical distance of window is 4 m

So, b=4

The Rafi leans 5 m ladder against the wall. So, c=5.

[tex]a^{2} +4^{2} =5^{2}[/tex]

Simplify it

[tex]a^{2} +16=25[/tex]

Subtract both sides 16

[tex]a^{2} =9[/tex]

Take square root on both sides

a=±3

So, base of the ladder is 3 meters away from the building.

Answer:

perimeter is 36 cm

Step-by-step explanation:

Answer:

x = 26

Step-by-step explanation:

sin x =4/9

Take the inverse sin of each side

sin ^-1 (sin x) = sin^-1(4/9)

x=26.38779

To the nearest degree

x = 26