Find the value of the given trigonometric function.
cos 420°

Step-by-step explanation:

the sum of interior angles in a triangle is 180°.

the sum of interior angles of a polygon, is the product of the number of triangles in the polygon (that can be created from a single vertex or corner via lines to all other corners) and 180°.

so, in reality, the number of triangles in each polygon is two less than the number of sides (because the lines to the 2 neighboring corners are sides and do not create triangles).

so the formula for the sum of all interior angles is

(n - 2) × 180

with n being the number of sides of the polygon.

in our case

(14 - 2) × 180 = 12×180 = 2160°

Answer:

0.1317

Step-by-step explanation:

Answer:

20x + 2

Step-by-step explanation:

Answer:

5 would be the midian

Step-by-step explanation:

You would need to add 0+2+4+6+8+10

Then count how many numbers there are (6)

Then put it in a fraction

30/6

Then divide and then you get 5

Answer:

21,67

Step-by-step explanation:

0+2+4+6+8+10 all divided by numbers in the set data[6]=21,67

Answer:

[tex]\text{k = 4, 5, 6, 7, 8... and onwards}[/tex]

Step-by-step explanation:

The product of k/3 and 12 be greater than 12.

⇒ k/3 × 12 > 12

The first step in determining the possible values of "k" is to simplify the left-hand-side (L.H.S) of the inequality.

⇒ (12 × k)/3 > 12

⇒ (12 ÷ 3) × k > 12

⇒ (4) × k > 12

The next step in determining the possible values of "k" is to isolate the variable. To do this, we can divide 4 both sides.

⇒ [4 × k]/4 > 12/4

⇒ k > 12/4

⇒ k > 3

To satisfy the inequality, the value of k must be greater than 3. Thus, the values of k could be [tex]\text{4, 5, 6... }[/tex] and so on.

Step-by-step explanation:

sum of angles in ∆ = 180

48+6x-28+2x = 180

20+4x = 180

4x = 160

x = 40

b = 212

c = 80

Answer:

[tex]\\\text{Width} = \dfrac 92 ~ \text{ft}\\\\\text{Length} = 10~ \text{ft}[/tex]

Step by step explanation:

[tex]\text{Width} =x\\\\\text{Length}=2x+1\\\\~~~~~~~\text{Area} = 45~\text{ft}^2\\\\\implies x(2x+1) =45\\ \\\implies 2x^2+x = 45\\\\\implies 2x^2 +x-45=0\\\\\implies 2x^2+10x -9x -45 =0\\\\\implies 2x(x+5) -9(x+5)=0\\\\\implies (2x-9)(x+5) =0\\\\\implies x=\dfrac 92, ~~ x\neq -5\\\\\text{Hence,}\\\\\text{Width} = \dfrac 92 ~ \text{ft}\\\\\text{Length} = 2\cdot \dfrac 92 +1 = 10~ \text{ft}[/tex]

Answer:

Length 10 ft.

Width 4.5 ft.

Step-by-step explanation:

If the width is x ft then the length is 2x + 1 ft.

Area = width * length, so:

45 = x(2x + 1)

45 = 2x^2 + x

2x^2 + x - 45 = 0

2x^2 + 10x - 9x - 45 = 0

2x(x + 5) - 9(x + 5) = 0

(2x - 9)(x + 5) = 0

x = 4.5, -5.

So x = 4.5   ( as the width cannot be negative).

Therefore the dimenions of the rectangle are

width = 4.5 ft, length = 2(4.5) + 1 = 10 ft.

Answer:

y = 29

Step-by-step explanation:

Since it is a vertical angle, both angles represented by the equations are equal. Meaning we can set them equal to each other and find y by simplifying.

4y-8 = 79+y

-79     -79

4y-87 = y

-4y       -4y

-87 = -3y

Divided by -3

29 = y

Answer:

1/2

Step-by-step explanation:

The slope is the rise over the run, also known as the change in y value over the change in x value

m = 2/4  =1/2

We know it is positive since it goes up from the left to the right

Answer:

g(x) = 5x² + 3

Step-by-step explanation:

8 units are added directly to each input so just subtract 5 from that to get + 3.

Answer:

160

Step-by-step explanation:

FEJ angle is the large angle and the number in red shows how big it is. Remember the whole thing is 180 degrees.

Answer:

y = - ½(x - 2)² + 3

Step-by-step explanation:

Answer:

Angle AFE = 102(degree symbol)

Step-by-step explanation:

supplementary means two angles that add up to 180

hope this helps! :)

Answer:

The angle supplementary to ∠AFB is ∠EFA.

The reason why this is, is because a supplementary angle consists of two angles that have a sum of 180°.

Supplementary angles combine to form a straight line.

In this case, ∠EFA is the supplement of ∠AFB because, ∠EFA is the other part of the angle, AFB, that creates a full straight line(180°).

And to find the value of m∠EFA you would need to arrange an equation.

Since we know that the given angle measure of AFB is 78°, ∠EFA would have to equal a different measure so that both measures will have a sum of 180°.

We will consider the value of m∠EFA to be 'x' in our equation, so;

x + 78 = 180°

Solve for x:-

-78        -78

x = 102°, therefore m∠EFA = 102°.

Answer:

[tex]\frac{7}{3}[/tex]

Step-by-step explanation:

Substitute -1 in place of y in the equation:

[tex]3x -4(-1)=11\\3x=7\\x=\frac{7}{3}[/tex]

Answer:

(7/3, -1)

Step-by-step explanation:

3x -4y=11

Let y = -1

3x -4(-1) = 11

3x +4 =11

Subtract 4 from each side

3x+4-4 = 11-4

3x = 7

Divide each side by 3

3x/3 = 7/3

x = 7/3

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5.7\\ h=10 \end{cases}\implies \begin{array}{llll} V=\pi (5.7)^2(10)\implies V=324.9\pi \\\\\\ V\approx 1020.7 \end{array}[/tex]

Explanation:

The volume formula ...

  V = BH

is a formula for the volume of a general prism whose cross sections parallel to the base all have area B. The distance between the parallel bases is represented by H.

__

To use this formula to find the volume of a tent, the area of the end of the tent would be substituted for B, and the length of the tent (distance between the ends) would be substituted for H.

An appropriate formula would need to be used for the end area.

The distance between you and your friend rounded  to the nearest tenth is 10.7 feet.

The distance between you and your friend can be found using cosine rule.

Therefore,

c²  =a² + b² - 2ab cos C

Therefore,

let

x = distance between him and his friend

x² = 7² + 6² - 2 × 7 × 6 cos 110°

x² = 49 + 36 - 84 × -0.34202014332

x² = 49 + 36 + 28.7296920394

x² = 113.729692039

x = √113.729692039

x = 10.6644124076

x = 10.7 ft

learn more on triangle here: https://brainly.com/question/2838446

Answer:

8 3/4

Step-by-step explanation:

because each serving is 04 cups all you need to do is divide 3 1/2 by 0.4.

first convert 3 1/2 into decimal which would be 3.5. then divide 3.5 by 0.4

3.5/0.4

=3.5x10/0.4x10

=35/4

=8 3/4

Answer:

[D] 1/14

Step-by-step explanation:

Question to answer:

What is the probability of picking an orange marble and flipping tails?

Solve:

let see how many orange marbles are there:

As we can see there is 1 orange marble out of 7 total. The probability of picking an orange marble is 1/7.

Now let see how many side a coin have:

As we can see the probability of flipping tails is 1/2 because 1 side is tails out of 2 sides total.Now multiply straight across:

1/2 × 1/7

→ 1 × 1 = 1

→ 2 × 7 = 14

Thus, the result is 1/14

Hence, the answer is [D] 1/14

~lenvy~

Answer:

[tex]\sf D)\quad\dfrac{1}{14}[/tex]

Step-by-step explanation:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

[tex]\implies \sf P(\textsf{orange marble})=\dfrac{1}{7}[/tex]

[tex]\implies \sf P(\textsf{tails})=\dfrac{1}{2}[/tex]

[tex]\implies \sf P(\textsf{orange marble})\:AND\:P(\textsf{tails})=\dfrac{1}{7} \times \dfrac{1}{2}=\dfrac{1}{14}[/tex]

[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}} \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount}\\ pymnt=\textit{periodic payments}\dotfill &279\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &22 \end{cases}[/tex]

[tex]A=279 \left[ \cfrac{\left( 1+\frac{0.06}{4} \right)^{4 \cdot 22}-1}{\frac{0.06}{4}} \right]\implies A=279\left[\cfrac{1.015^{88}~~ - ~~1}{0.015} \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 50348.47~\hfill[/tex]

no se cómo se hace está operación de verdad lo siento

Step-by-step explanation:

I hope this helps, you can ask any question for clarification

Answer:

They both have a y intercept of 0

Step-by-step explanation:

Linear equations are written in the form y = mx + b. m is the slope and b is the y-intercept. It also states that they intersect at the origin, so they must have a y-intercept of 0.

38.1 units^2

Step-by-step explanation:

you can use the formula: 1/2(ab)(sin c)

plug it in: 1/2(16*7)(sin 138)

simplify: 57sin138

plug it into your calculator: 38.1 (rounded)

If you found this answer helpful, I would appreciate if you gave me the brainliest award :D.

Answer:

37.5

Step-by-step explanation:

For acellus

Answer:

Step-by-step explanation:

a.16×25×10×4

= 100 * 160

= 16,000

b,49×99​

= 49 * 100 - 49

= 4900 - 49

= 4,851.

Answer:

12.2

Step-by-step explanation:

use the Pythagorean theorem to determine the diagonal

9.9^2 + 7.2^2 = d^2

d = 12.2