find the area of a pentagon with an apothem of 7 centimeters

Answer:

AB = 75

BC = 60

AC = 45

m∠A = 53°

m∠B = 37°

m∠C = 90°

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

[tex]\sf \tan(A)=\dfrac{60}{45}[/tex]

Therefore:

To find the length of AB (the hypotenuse), use Pythagoras’ Theorem:

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

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

⇒ AC² + BC² = AB²

⇒ 45² + 60² = AB²

⇒ AB² = 5625

⇒ AB = √5625

⇒ AB = 75

To find m∠A:

[tex]\implies\sf \tan(A)=\dfrac{60}{45}[/tex]

[tex]\implies\sf A=\tan^{-1}\left(\dfrac{60}{45}\right)[/tex]

[tex]\implies\sf A=53^{\circ}\:(nearest\:degree)[/tex]

m∠C = 90° (as it is a right angle)

The interior angles of a triangle sum to 180°

⇒ m∠A + m∠B + m∠C = 180°

⇒ 53° + m∠B + 90° = 180°

⇒ m∠B = 180° - 53° - 90°

⇒ m∠B = 37°

Answer:

Step-by-step explanation:

B is the image of D

6 left

2 down

Answer: C (in choices)

B is the image E

6 down

5 left

Answer: D  (in choices)

C is the image of D

1 left

2 down

Answer: F (in choices)

Step-by-step explanation:

n + 34 = 34 + n

commutative means you can change the sequence of the parts without changing the overall result.

g × h = h × g

s + 0 = s

b × 1 = b

the identity property points are to show that adding 0 or multiplying by 1 does not change anything.

Answer:

14 packages

Step-by-step explanation:

profit = revenue - expenses

we want profit to be 0

0 = revenue - expenses

revenue = 5.60 per package = 5.60 * number of packages

expenses = 56 + 1.60 per package = 56 + 1.6 * number of packages

0 = revenue - expenses

let's say the number of packages = n

0 = 5.6 * n - (56 + 1.6 * n)

= 5.6n - 56 - 1.6n

= -56 + 4n

add 56 to both sides to isolate the variable and its coefficient

56 = 4n

divide both sides by 4 to isolate the variable

n = 14

Answer:

Part 1

Set B

Part 2

We can use the FOIL method to multiply these expressions:

[tex]\textsf{FOIL}: \quad(a+b)(c+d)=ac+ad+bc+bd[/tex]

However, as all the expression are in the format [tex](a+b)^2[/tex], we can use the shortcut:  [tex](a+b)^2=a^2+2ab+b^2[/tex]

Part 3

Using the shortcut to find the products:

[tex]\begin{aligned}\implies (x+5)(x+5)& =(x+5)^2\\ & =x^2+2(x)(5)+5^2\\ & =x^2+10x+25\end{aligned}[/tex]

[tex]\begin{aligned}\implies (2x+9)(2x+9) & = (2x+9)^2\\ & = (2x)^2+2(2x)(9)+9^2\\ & = 4x^2+36x+81\end{aligned}[/tex]

[tex]\begin{aligned}\implies (x+1)^2 & = x^2+2(x)(1)+1^2\\ & = x^2+2x+1\end{aligned}[/tex]

Part 4

A new example of a multiplication problem based on the structure of Set B is:  [tex](3x+2)(3x+2)[/tex]

[tex]\begin{aligned}\implies (3x+2)(3x+2) & = (3x+2)^2\\ & = (3x)^2+2(3x)(2)+2^2\\ & = 9x^2+12x+4\end{aligned}[/tex]

Part 5

An example of a multiplication problem that would NOT be included in Set B based on its structure is: [tex](x+2)(x-2)[/tex]

We cannot use the derived Set B shortcut (from part 2) to multiply this expression.  Instead, we would have to use a different shortcut of "The Difference of Two Squares" to find the product of this example expression.

Answer:

Step-by-step

the total number of balls in the in the bag is 10

Then

the probability of drawing a red ball on the first draw is 4/10.

…………………………………………………………

Now , if the first ball drawn is not replaced.

Then

the probability of drawing a red ball on the Second draw is 3/9.

……………………………………………

Conclusion:

the probability that two balls drawn at random from the bag will be red if the first ball drawn is not replaced is :

(4÷10)×(3÷9)

= (2÷5)×(1÷3)

= 2÷15

= 0.133333333333

Answer:

Kia makes 19.25 dollars an hour.

Step-by-step explanation:

6x4+8=32 (hours: 6 hours for 4 days, and 8 hours for 1 day)

616 divided by 32 = 19.25

Answer: √7 / 2 - 3/2

Step-by-step explanation:

√7-2x+5=8
=>  -2x + √7 = 3
=> x =  √7 / 2 - 3/2

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{-8}-\underset{x_1}{1}}}\implies \cfrac{-7+1}{-9}\implies \cfrac{-6}{-9}\implies \cfrac{-2}{-3}\implies \cfrac{2}{3}[/tex]

The slope of the line that passes through the points (1,−1) and (−8,−7) is m = 2/3.

Slope tells how vertical a line is. The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.

Its slope would be: [tex]m = \dfrac{y-q}{x-p}[/tex]

Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

If a line passes through two points, then its slope can be calculated with the following :

 [tex]m = \dfrac{y-q}{x-p}[/tex]

Plugging in our values, we get:

[tex]m = \dfrac{-7 + 1}{-8 - 1}[/tex]

Now, let's simplify our result:

[tex]m = \dfrac{-7 + 1}{-8 - 1}\\\\m = \dfrac{-6}{-9}[/tex]

m = 2/3

Therefore, the slope of the line that passes through the points (1,−1) and (−8,−7) is m = 2/3.

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Answer:

put a point on the 9 (the line on the left of 10) and on the -6 (the line to the left of -5).

a. 9 is located to the right of -6

b. use the symbol >

Step-by-step explanation:

Answer:

1.6.36 cm

2

Step-by-step explanation:

Using sine rule to find the length of the BC.

Answer:

E = 90

Step-by-step explanation:

E represents the maximum value in the data set , that is

E represents the value 90

Answer:

E is 90

Step-by-step explanation:

the end of the box and whisker plot is the last number in chronoligical order. So the one all the way on the right, e is 90

Answer:

Around 77%

Step-by-step explanation:

10/13 = 0.769

Answer:

1) 38.9%

Step-by-step explanation:

There are 18 total pieces of candy, 4 of which are blue, and 3 of which are yellow. So the probability of randomly selecting one blue or one yellow piece of candy is

[tex] \frac{3}{18} + \frac{4}{18} = \frac{7}{18} = 38.9\%[/tex]

Step-by-step explanation:

−5x2−5x+30

=5(−x+2)(x+3)

Answer:

5(−x+2)(x+3)

Answer:

I used Desmos to graph your requirements, and i took a screenshot of the graph. Credit to Desmos for the great graphing system.

Step-by-step explanation:

Answer:

see image

Step-by-step explanation:

Anytime you see f(x) that just means y.

So f(x)=5 just means

y = 5

Anytime you have an equation to graph that is in the format

"y= anumber", that is a Horizontal line. So the first piece of your graph is the horizontal line thru 5. But also that's only for x>=3. It includes the 3 with the "or=to" underline. So the point must be a solid filled-in point. (Some weird books or teachers use a [ square bracket.) Same logic works for the second piece of the function. f(x) = -6 is the same as y= -6 and is a horizontal line thru -6. But the point at (3, -6) is an Open dot! See image.

Answer:

i believe its 5/10 or 1/2

Step-by-step explanation:

|-7| + 3|4|

7 + 12

19

hope it helps...!!!

Answer: Heyaa! ~

Your Answer Is 19, Which is C.

Step-by-step explanation:

Order of operations:

  PEMDAS

Hopefully this helps you! ^

Answer: If this is a 2D box, the length would be 2

Step-by-step explanation:

Answer:

11x⁴+12x³-9x²-8x

Step-by-step explanation:

M.a.t.h.w.a.y

Answer:

We can see that our y-value of our coordinates do not change so we can just subtract the first x-value from the second x-value.

[tex]x_2 - x_1[/tex]

[tex]4 - (-4)[/tex]

[tex]8[/tex]

The option that best matches our answer is Option B, [tex]8[/tex]

Hope this helps!  Let me know if you have any questions

Answer:

7.8

Step-by-step explanation:

since the shape is a right angled triangle,

we use Pythagoras theorem to find

X= ✓6^2+5^2 = √36+25=. √61 =7.8

Answer:

x = 6

Step-by-step explanation:

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

(-1 - 1) / (-1 - x)

If the slope is 2/7, it would be (-2/-1-x, where x would have to be 6)

(-2)/(-7) = 2/7, so x = 6

Check:

(-1 - 1) / (-1 - 6)

(-2)/(-7)

2/7 (Correct :))

Hope it helps :D

Answer:

Answer:

A=61, B=74

Step-by-step explanation:

Because all the angles in a triangle add up to 180:

(2x+4) + (2x-9) + x = 180

If you solve that for x, you will get that x=35. Now you just plug in x to the angles A and B.

Answer:

x=66

Step-by-step explanation:

35-13=22

22*3=66

x=66

Answer:

X=66

Step-by-step explanation:

66 divided by 3 =22

13+22=35

Answer:

Step-by-step explanation:

13). ( x - 2 )( x + 6 ) = 9 × 20

x² + 4x - 12 = 180

x² + 4x - 192 = 0

( x - 12 )( x + 16 ) = 0

[tex]x_{1}[/tex] = - 16

[tex]x_{2}[/tex] = 12

14). ( x + 4 )[( x + 4 ) + 3x ] = 8 × ( 8 + 19 )

( x + 4 )( 4x + 4 ) = 216

4( x + 4 )( x + 1 ) = 216

( x + 4 )( x + 1 ) = 54

x² + 5x + 4 - 54 = 0

x² + 5x - 50 = 0

( x - 5 )( x + 10 ) = 0

[tex]x_{1}[/tex] = - 10

[tex]x_{2}[/tex] = 5

15). x( x + 16 ) = 15²

x² + 16x - 225 = 0

( x - 9 )( x + 25 ) = 0

[tex]x_{1}[/tex] = - 25

[tex]x_{2}[/tex] = 9

16). Now is your turn. You can do it!

The measurements are given in the solution below.

Circle definition states a shape that consists of points, in a two-dimensional plane, equidistant from a given point.

Given that the circles we need to find the given missing values,

Using the properties of the circles,

1) (x-2) (x+6) = 20 × 9

x² + 6x - 2x - 12 = 180

x² + 4x - 192 = 0

x = 12 or x = -16.

2) 8 × (8+19) = x+4 (x+4 + 3x)

216 = x + 4 × (4x + 4)

216 = 4x² + 4x + 16x + 16

4x² + 20x - 200 = 0

x² + 5x - 50 = 0

x = 5 or x = -10

3) 15² = 16x

x = 225/16

x = 14.06
4) (x+7)² = 18 × 14

x² + 49 + 14x = 252

x² + 14x - 203 = 0

x = 8.87

x = -22.87

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Answer:

5.4 meters per square second

Step-by-step explanation:

If that rover was on the Earth the weight of it would be 620 N (62*10)

In the new planet the gravitational acceleration is not same as the earth it's definitely less than that of the earth

Let's take the gravity constant of the plant as x.

so, 62*x= 334.8 N

x= 334.8/62

x= 5.4