A regular polygon has exterior angles of 60°
What is the sum of the polygon’s interior angles?

Step-by-step explanation:

5.

[tex](5 + 4 \sqrt{7} ){x}^{2} + (4 - 2 \sqrt{7} ) x- 1 = 0[/tex]

Simplify both radicals.

[tex](5 + \sqrt{112) {x}^{2} } + (4 - \sqrt{28} )x - 1 = 0[/tex]

Apply Quadratic Formula

First. find the discramnint.

[tex](4 - \sqrt{28} ) {}^{2} - 4(5 + \sqrt{112} )( - 1) = 64[/tex]

Now find the divisor 2a.

[tex]2(5 + \sqrt{112} ) = 10 + 8 \sqrt{7} [/tex]

Then,take the square root of the discrimant.

[tex] \sqrt{64} = 8[/tex]

Finally, add -b.

[tex] - (4 + 2 \sqrt{7} )[/tex]

So our possible root is

[tex] - (4 + 2 \sqrt{7} ) + \frac{8}{10 + 8 \sqrt{7} } [/tex]

Which simplified gives us

[tex] \frac{ 4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } [/tex]

Rationalize the denominator.

[tex] \frac{4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } \times \frac{10 - 8 \sqrt{7} }{10 - 8 \sqrt{7} } = \frac{ - 72 - 12 \sqrt{7} }{ - 348} [/tex]

Which simplified gives us

[tex] \frac{6 + \sqrt{7} }{29} [/tex].

6. The answer is 2.

9514 1404 393

Answer:

  5. x = (6 +√7)/29; a=6, b=1, c=29

  6. x = 2

Step-by-step explanation:

The quadratic formula can be used, where a=(5+4√7), b=(4-2√7), c=-1.

  [tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-(4-2\sqrt{7})+\sqrt{(4-2\sqrt{7})^2-4(5+4\sqrt{7}})(-1)}{2(5+4\sqrt{7})}\\\\=\dfrac{-4+2\sqrt{7}+\sqrt{16-16\sqrt{7}+28+20+16\sqrt{7}}}{10+8\sqrt{7}}=\dfrac{4+2\sqrt{7}}{2(5+4\sqrt{7})}\\\\=\dfrac{(2+\sqrt{7})(5-4\sqrt{7})}{(5+4\sqrt{7})(5-4\sqrt{7})}=\dfrac{10-3\sqrt{7}-28}{25-112}=\boxed{\dfrac{6+\sqrt{7}}{29}}[/tex]

__

Use the substitution z=3^x to put the equation in the form ...

  z² -3z -54 = 0

  (z -9)(z +6) = 0 . . . . . factor

  z = 9 or -6 . . . . . . . . value of z that make the factors zero

Only the positive solution is useful, since 3^x cannot be negative.

  z = 9 = 3^2 = 3^x . . . . use the value of z to find x

  x = 2

Answer:

18.8

Step-by-step explanation:

Surface area=2*pi*r*(r+h)=2*pi*1*(3)=18.8

9514 1404 393

Answer:

  c = 14

  no extraneous solutions

Step-by-step explanation:

You can subtract the right-side expression, combine fractions, and set the numerator to zero.

  [tex]\dfrac{c-4}{c-2}-\left(\dfrac{c-2}{c+2}-\dfrac{1}{2-c}\right)=0\\\\\dfrac{c-4}{c-2}-\dfrac{1}{c-2}-\dfrac{c-2}{c+2}=0\\\\\dfrac{(c-5)(c+2)-(c-2)^2}{(c-2)(c+2)}=0\\\\\dfrac{(c^2-3c-10)-(c^2-4c +4)}{(c-2)(c+2)}=0\\\\\dfrac{c-14}{(c-2)(c+2)}=0\\\\\boxed{c=14}[/tex]

__

Check

  (14 -4)/(14 -2) = (14 -2)/(14 +2) -1/(2 -14) . . . . substitute for c

  10/12 = 12/16 -1/-12

  5/6 = 3/4 +1/12 . . . . true

There is one solution (c=14) and it is a solution to the original equation. There are no extraneous solutions.

Answer:

8r+8pg-pq

Step-by-step explanation:

The subtractable pg cancels out one of the 9 pg's. So 9 pg-1 pg= 8 pg

Hope this helps!

The coldest time of day in Mumbai is 5 hours after midnight.

Since the average temperature t hours after midnight in Mumbai, India, is given by:

T(t)=24.5-5.5sin((2pi(t+1))/24)

We have that

T(t) = 24.5 - 5.5sin((2π(t+1))/24)

The coldest time of day is when T(t) is minimum.

T(t)  is minimum when 5.5sin((2π(t+1))/24) is minimum where t is the coldest time of day at minimum temperature, T(t).

Since for a sine function, -1 ≤ sinФ ≤ 1, the minimum value of sinФ = -1.

So, T(t) = 24.5 - 5.5sin((2π(t+1))/24) is minimum when

5.5sin((2π(t+1))/24) is minimum.

Also, -5.5sin((2π(t+1))/24) = 5.5 × -1 at minimum temperature T(t)

So, 5.5 × -1 = 5.5 × -sin((2π(t+1))/24)

So, -sin((2π(t+1))/24) = -1

sin((2π(t+1))/24) = 1

Taking inverse sine of both sides, we have

sin⁻¹sin((2π(t+1))/24) = sin⁻¹(1)

((2π(t+1))/24) = π/2

Multiplying both sides by 24, we have

(2π(t+1))/24 × 24 = π/2 × 24

(2π(t+1)) = 12π

Dividing both sides by 2π, we have

2π(t+1)/2π = 12π/2π

t + 1 = 6

t = 6 - 1

t = 5 hours

So, the coldest time of day in Mumbai is 5 hours after midnight.

Learn more about average temperature here:

https://brainly.com/question/19388300

Answer:

AED 972

Step-by-step explanation:

Area of the wall = 9² = 81 m²

each m² costs AED 12

so 81 m² will cost 12×81 = AED 972

Answer:

-10

Step-by-step explanation:

Answer:

Step 1: 12-2a=3a-18

Step 2: 12-5a=-18

Step 3: -5a=-30

Step 4: a=6

I hope this helps!

pls ❤ and give brainliest pls

Answer:

x=4sqrt3 a=4 b=3  ,y=8sqrt3 c=8 d=3

Step-by-step explanation:

because this is a 30-60-90 triangle, it is easy to find the side lengths. the longer leg is sqrt(3) times the shorter leg so x= 12/sqrt(3) or 4sqrt(3). the hypotenuse is 2 times the shorter leg so y= 8sqrt(3)

Answer:

This type of study is called a simulation

Step-by-step explanation:

Answer:

I am not sure on the answer but i think its $9,000

Step-by-step explanation:

11,000x0.20=2,200

2,200+11,000=13,200

22,200-13,200=9,000

which would mean she got $9,000 from commissions.

if you did 100,000x0.03=3,000

9,000/3,000= 3

so she would have had 3 commissions worth over 100,000

Answer:

[tex]n=35[/tex]

Step-by-step explanation:

From the question we are told that:

Standard Deviation [tex]\sigma=4min[/tex]

Let

[tex]CI=95\%[/tex]

Since

Significance level [tex]\alpha[/tex]

[tex]\alpha =1-CI[/tex]

[tex]\alpha =1-0.95[/tex]

Therefore

[tex]Z_{\alpha/2}=Z_{0.025[/tex]

[tex]Z_{\alpha/2}}=1.96[/tex]

Generally the equation for Sample size is mathematically given by

[tex]n = (Z_{\alpha/2}* \frac{\sigma}{E})^2[/tex]

[tex]n= \frac{1.96 * 3}{1}^2[/tex]

[tex]n=35[/tex]

There are 30 possible combinations of teachers.

Given that at Tubman Middle School, there are 6 English teachers and 5 science teachers, to determine, if each student takes one English class and one science class, how many possible combinations of teachers are there, the following calculation must be performed:

To calculate possible combinations, the number of options A must be multiplied by the number of options B. Thus, the calculation would be as follows.

Therefore, there are 30 possible combinations of teachers.

Learn more about combinations in https://brainly.com/question/24180105.

Step-by-step explanation:

<TOS=122° [being vertically opposite angle]

Answer:

angleTOS =122°

EXPLANATION:

[ If two straight lines intersect at point O, vertically opposite angles are equal]As vertically opposite angles are equal; Hence AngleTOS=QOR=122°

Answer: x>12

so i think x is 16.

Answer:

(x-3)(5x+4)

x=3 x=-4/5

Answer:

(5x + 4)(x - 3)

Step-by-step explanation:

Hello!

Factor:

Think: What two numbers add up to -11 but multiply to (5)(-12)?

Answer: -15 and 4

Continue:

The factored expression is (5x + 4)(x - 3)

Answer:

147.3

Step-by-step explanation:

this is an hendecagon there is 11 sides the total interior measure is 1,620 if you divide that by each side which would be 11 you get 147.272727 which would ultimately round up to be 147.3

Answer:

not enough info

Step-by-step explanation:

Answer:

535 students passed and 107 students failed

Step-by-step explanation:

Create a system of equations where p is the number of students who passed and f is the number of students who failed:

p + f = 642

p = 5f

Solve by substitution by plugging in 5f as p into the first equation, then solving for f:

p + f = 642

5f + f = 642

6f = 642

f = 107

So, 107 students failed.

Find how many students passed by multiplying this by 5:

107(5)

= 535

535 students passed and 107 students failed.

Step-by-step explanation:

Disclaimer: When writing this on the paper use the theta symbol, I'm using x since I'm on mobile.

2.

i).

[tex] \sin(x) \tan(x) \sec(x) = \tan {}^{2} (x) [/tex]

[tex] \sin(x) \sec(x) \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \sin(x) \frac{1}{ \cos(x) } \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \frac{ \sin(x) }{ \cos(x) } \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \tan( x) ) \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \tan {}^{2} (x) = \tan {}^{2} (x) [/tex]

iii).

[tex] \sec {}^{2} (x) (1 - \sin {}^{2} ( x ) ) = 1[/tex]

[tex] \sec {}^{2} (x) ( \cos {}^{2} (x) ) = 1[/tex]

[tex] \frac{1}{ \cos {}^{2} (x) } \cos {}^{2} (x) = 1[/tex]

[tex]1 = 1[/tex]

v).

[tex] \cot {}^{2} (a) - \cos {}^{2} (a) = \cot {}^{2} (a) \cos {}^{2} (a) [/tex]

[tex] \frac{ \cos{}^{2} (x) }{ \sin {}^{2} (x) ) } - \cos {}^{2} (x) [/tex]

Factor out cosine

[tex] \cos {}^{2} (x) ( \frac{1}{ \sin {}^{2} (x) } - 1) [/tex]

Simplify

[tex] \cos {}^{2} (x) ( \frac{1 - \sin {}^{2} (x) }{ \sin(x) } [/tex]

[tex] \cos {}^{2} (x( \frac{ \cos {}^{2} (x) }{ \sin {}^{2} (x) } ) = [/tex]

[tex]( \cos {}^{2} ( x ) ( \cot {}^{2} (x) )[/tex]

Answer:

Area of parallelogram = 21

Step-by-step explanation:

A = BH

Plug in

A = 7×3

Solve

A = 21

The answer will be 21.

Step-by-step explanation:

second: (2.2,-1.4)

third: (2.2,-1.35)

Step-by-step explanation:

hope it helps✨

Answer:

you need to be more specific.

Step-by-step explanation:

Answer:

A)60°

Step-by-step explanation:

a straight line is 180° then

if a line bisect it in to a half it become 90°

then

the exterior angle of a triangle is equal to the sum of two interior angles

this means 150°-90°=60°

Answer: A) 60

Step-by-step explanation:

The line at the top signifies 180 degrees, as does any straight line. The 150° that intersects with P tells you that P must be 30 degrees, as 180 - 150 = 30.

The three angles of a triangle must always equal 180°. Angle R tells you that it’s 90°, shown by the square instead of a curve. If you subtract the value of P we found before, and the value of R we just found, you get your answer.

180 - 30 - 90 = 60.

Answer:

y + 4 = (x - 2)^2

Step-by-step explanation:

The vertex form of the equation of a vertical parabola is

y - k = a(x - h)^2, where (h, k) represents the vertex and a is a scaling factor which stretches or compresses the parabola vertically.  If all we know is the vertex (2, -4), then the desired equation is:

y + 4 = a(x - 2)^2

If there is no vertical stretching or compression, then the equation becomes:

y + 4 = (x - 2)^2

Answer:

y = x² - 4x

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (2, - 4) , with a = 1 , the equation is

y = (x - 2)² - 4 ← expand using FOIL

 = x² - 4x + 4 - 4

y = x² - 4x ← equation of parabola

Answer:

SOH-CAH-TOA

[tex]\sin \left(x\right)=\frac{6}{\sqrt{49+36}}[/tex] = 40.60°

SOH = SIN = OPP/HYP

SIN(Θ) = 6/[tex]\sqrt{49+36 }[/tex]

Step-by-step explanation:

Answer:

[tex]\Large \boxed{x_1=\frac{9+\sqrt{51} }{3} \ \ ; \ \ x_2=\frac{9-\sqrt{51} }{3} }[/tex]

Step-by-step explanation:

[tex]\displaystyle \Large \boldsymbol{} 3x(x+6)=-10 \\\\3x^2+18x=-10 \\\\3x^2+18x+10=0 \\\\D=324-120=204 \\\\ x_{1;2}=\frac{18\pm2\sqrt{51} }{6} =\frac{9\pm\sqrt{51} }{3}[/tex]

Answer:

Step-by-step explanation:

Volume of a cone formula is

[tex]V=\frac{1}{3}\pi r^2h[/tex] where r is radius and h is height. Filling in:

[tex]V=\frac{1}{3}(3.14)(10)^2(7)[/tex] and doing all the math on that and rounding gives us

V = 733 units cubed

Answer:

            Boys          Girls               Total

Walk      19              22                   41

Bus        23              10                   33

Cycle     40             56                   96

Total      82              88                  170