Find the area of the figure. Round to the nearest hundredth where necessary.
24 m
28 m

The equations which can be used to find the measurement of each angle will be 6x-30=180.

The supplementary angles are defined as the angles whose sum is equal to 180°.

It is given that:-

One angle in a pair of supplementary angles has a value of 2x

The other angle is 30 degrees less than two times the first angle.

Now from the first condition, One angle in a pair of supplementary angles has a value of 2x we can write that:-

2x   +    A   =     180 .........................1

Now from the second condition,The other angle is 30 degrees less than two times the first angle

A     =    4x  -   30 ..............................2

Hence from the above two equations put the value of A in equation 1

the equation will be:-

2x    +   4x    -   30    =    180

6x      -      30        =   180

Hence the equations which can be used to find the measurement of each angle will be 6x-30=180.

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Answer:

<A = 60°

Step-by-step explanation:

The triangle is 180° Angle A and B add up to 118°

4y° + (3y + 13)° = 118°

7y + 13 = 118°

7y = 105

y = 15

Since you solve for y, plug your y into the angles to solve.

<A = 4y

<A = 4 * 15

<A = 60°

The answers for the questions are:

1) The dimensions of poster are 44cm by 56cm

2) The smallest poster area needed is 5328 square centimeter

3) The orientation that uses the lesser poster area is portrait.

4) He needs to trim 4.4cm of the height of poster

A rectangle is a quadrilateral with opposite sides equal and all angles 90°

Analysis:

1) since there are 3 photos per row, the spacing for the three photos are 4. Also since there are 3 photos on the column, the spacing would be 4

 width of poster = 2x4 + 3x12 = 8 + 36 = 44cm

  Height of poster = 4x2 + 3x16 = 56cm

2) possible combinations, are 8 picture on a row and 3 picture on a column

     width = 9spacing x 2cm + 8 pictures x 12 = 114cm

   length = 4 spacing x 2 + 3pictures x 16 = 56cm

   12 pictures on a row and 2 pictures on a column

     width = 13 spacing x 2cm + 12 pictures x 12 = 170cm

      length = 3 spacing x 2cm + 2 pictures x 16 = 38cm

    6 pictures on a row and 4 pictures on a column

      width = 7 spacing x 2cm + 6 pictures x 12 = 72cm

       length = 5 spacing x 2cm + 4 pictures x 16 = 74cm

    The smallest area is 74 x 72 = 5328 square centimeter

3.  For portrait,

     width = 6 photos x 12cm + 7 spacing x 2cm = 86cm

      length = 3 pictures x 16cm + 4 spacing x 2cm = 56cm

     For landscape,

     width = 6 photos x 16cm + 7spacing x 2cm = 110cm

      length = 3 pictures x 12cm + 4 spacing x 2 = 44cm

     The lesser poster area is portrait orientation with 86 x 56 = 4816 square centimeter.

4. Let the equal spacing be P

   for full width = 62cm

    4pictures x 12cm + 5 spacing x P = 62

   48 + 5p = 62

   5P = 62-48

   5P = 14

   P = 14/5 = 2.8cm

   length of poster using equal spacing of 2.8cm

   length would take 6 photos

   6 photos x 16 + 7 spacing x 2.8 = 115.6cm

   original length of poster is 120cm

  so he would need to trim  (120-115.6) = 4.4cm

In conclusion, The answers to the questions are:

1) dimensions of poster are 44cm by 56cm

2) The smallest poster area needed is 5328 square centimeter

3) The orientation that uses the lesser poster area is portrait

4) He needs to trim 4.4cm of the height of poster

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Answer:

  C = 25°, b = 62.3, c = 32.1

Step-by-step explanation:

The Law of Sines can be used to solve a triangle when two angles and a side opposite one of them is given.

__

The angle sum theorem can be used to find the third angle.

  C = 180° -A -B = 180° -30° -125° = 25°

__

The Law of Sines tells you ...

  a/sin(A) = b/sin(B) = c/sin(C)

  b = a(sin(B)/sin(A)) = 38·sin(125°)/sin(30°) ≈ 62.3

  c = a(sin(C)/sin(A)) = 38·sin(25°)/sin(30°) ≈ 32.1

The solution is ...

  C = 25°, b = 62.3, c = 32.1

The equivalent expression is -1

Answer:

the surface area is 648

Solution:

A=2(wl+hl+hw)=2·(9·9+13.5·9+13.5·9)=648

Answer:

[tex]P(\text{Science}|\text{Math})\approx64\%[/tex]

Step-by-step explanation:

[tex]\displaystyle P(\text{Science}|\text{Math})=\frac{P(\text{Science and Math})}{P(\text{Math})}\\\\P(\text{Science}|\text{Math})=\frac{0.45}{0.70}\\ \\P(\text{Science}|\text{Math})\approx0.643\approx64\%[/tex]

None of the answer choices have this solution apparently, so either you left out some option, mistyped them, or it wasn't there to begin with

Answer:

Step-by-step explanation:

Comment

(Fans who received a baseball) = 2500

Total number of seats in Yankee Stadium = 50086

P(those who got a baseball) = 2500 / 50086

Answer P(Those who got a baseball) = 0.04991 rounded.

Answer:

3.

m + 7 ≥ 20

Subtract 7 on both sides,

m ≥ 20 - 7

m ≥ 13

The answer is m ≥ 13.

( you need to include both > and =, that is ≥ )

4.

2.1x = 23.1

Divide 2.1 on both sides,

x = 23.1 / 2.1

x = 11

Answer:

For problem #3, we are given [tex]m+7\geq 20[/tex] so we would just subtract 7 from both sides to get rid of the 7 on the left and that would end up subtracting 7 from 20 also leaving us with [tex]m\geq 13[/tex].

For problem #4, we are given [tex]2.1x=23.1[/tex] so we would just divide both sides by 2.1 which would get rid of the 2.1 on the left and that would also make us divide 23.1 by 2.1 leaving us with [tex]x=11[/tex].

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

6 dollars for 12

Step-by-step explanation:

if she paid 5 dollars for 10, you would do 10/ 5 which would get you 2 dollars per apple so she would pay 6dollars for 12 apples

Answer:

Step-by-step explanation:

Formula:

In a square with sides each of length ‘a’ :

The diagonal D of the square = a√2

…………………………………………………………

The square ,in our example has 4 sides all of Length 4 ,then

D = 4√2

Step-by-step explanation:

A={1,2,3}

B={5,6}

n(a)=3

n(b)=2

Answer:

2: area is ≈153.93804 and circumfrence is ≈43.9823

3: area is ≈706.85835 and circumfrene is ≈94.24778

Step-by-step explanation:

The formula for area is A = pi r^2

for 2 you would plug 7 in for r, then square it, then multiply it by pi.

for 3 you would divide the diameter, 30, by 2 to get r (15), then square it then multiply by pi.

The formula for cirumfrence is C = 2 pi r

for 2 you would multiply 7 by 2, then multiply that by pi

for 3 you dont need to do much since the diameter (30) is already 2r. Basically all you need to do for that one is multiply 30 by pi

Will ran down the street to catch the bus.

Hope this helps, thanks,

CoDBiarex

Answer:

After basketball practice Julie hit the books.

Step-by-step explanation:

Informal English often uses slang words that not everyone understands.

Answer:

I would edit this answer and tell you what I hope would be the correct answer if you give me the problem you are confused with

Step-by-step explanation:

I can't help you otherwise

Sorry

Answer:

50,000   fifty-thousand

Step-by-step explanation:

Just use a calculator

Answer:

Step-by-step explanation:

Answer

When you put this into your calculator, you get - 7.2111. The closest point to that is L.

Answer: -7.2111 is closest to L

Using translation concepts, it is found that there was a horizontal compression of the function.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, there was a multiplication in the domain of the function, by a factor greater than 1, hence there was a horizontal compression of the function.

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Answer:

the second i think i dont know for sure

Answer:

∠CED = 70°

∠BCE = 134°

Step-by-step explanation:

Finding z :

Finding ∠CED :

Finding y :

Finding ∠BCE :

Answer:

∠CED = 70°

∠BCE = 134°

Step-by-step explanation:

We don't know if AB and DE are parallel (since there are no arrows on these line segments), therefore we cannot use the Alternate Interior Angles Theorem at this point to definitively say that ∠CDE = ∠ABC.

Angles around a point sum to 360°

Angles on a straight line sum to 180°

⇒ ∠ACB + ∠BCE = 180

⇒ ∠ACB + (7y - 6) = 180

⇒ ∠ACB = 180 - (7y - 6)

⇒ ∠ACB = 180 - 7y + 6

⇒ ∠ACB = 180 - 7y + 6

⇒ ∠ACB = 186 - 7y

The interior angles of a triangle sum to 180°

⇒ ∠ACB + ∠CBA + ∠BAC= 180

⇒ 186 - 7y + 64 + 3y + 10 = 180

⇒ 260 - 4y = 180

⇒ 4y = 80

⇒ y = 20

Using the found value of y to find ∠BCE:

⇒ ∠BCE = 7(20) - 6

⇒ ∠BCE = 134°

Angles on a straight line sum to 180°

⇒ ∠DCE + ∠BCE = 180

⇒ ∠DCE + 134 = 180

⇒ ∠DCE = 46°

The interior angles of a triangle sum to 180°

⇒ ∠DCE + ∠CED+ ∠EDC = 180

⇒ 46 + (9z - 2) + 8z = 180

⇒ 17z + 44 = 180

⇒ 17z = 136

⇒ z = 8

Using the found value of z to find ∠CED:

⇒ ∠CED = 9(8) - 2

⇒ ∠CED = 70°

To solve this problem, we have to figure out the time spent travelling and then use the speed-distance-time equation to find the distance between the two places. The distance between Seattle and St. Louis is 2295 miles.

To calculate the miles or distance between Seattle and St. Louis, we have to take into consideration that out of the 42 hours she spent in her journey, she stayed 15 hours over at St. Louis.

[tex]42 - 15 = 27[/tex]

She spent 27 hours travelling.

Her speed in the first journey was 50mi/h and her speed in the second journey was 35mi/h.

This implies she was faster in her first journey compared to her second journey.

Data;

[tex]speed = \frac{distance}{time} \\distance = speed * time[/tex]

Let's substitute the values

[tex]distance = (50 + 35) * 27 = 2295mi[/tex]

The distance between Seattle and St. Louis is 2295 miles

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Answer:

This is false

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find each term

The series is

The sum of series can be shown as

Find the sum

Answer:

180

Step-by-step explanation:

The given series means to sum the first 10 terms of the sequence [tex]a_t=2t+7[/tex]

[tex]\begin{aligned}\displaystyle \sum^{10}_{t=1}2t+7 & = (2 \cdot 1+7)+(2 \cdot 2+7)+...+(2 \cdot 9+7)+(2 \cdot 10+7)\\ & =2(1+2+...+9+10)+10(7)\\\\& = 2(1+2+...+9+10)+70\\\\ & = 2(55)+70\\\\& = 110+70\\\\ & = 180 \end{aligned}[/tex]

Answer:

[tex]y = 17[/tex]

Step-by-step explanation:

We were given the equation

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

and we were told that x = 3, therefore y would be

[tex]y = 3x + 8 \\ y = 3(3) + 8 \\ y = 9 + 8 \\ y = 17[/tex]

[tex]\cfrac{40.5}{8.1} ~~ \begin{cases} 40.5\implies \frac{405}{10}\\\\ 8.1\implies \frac{81}{10} \end{cases}\implies \cfrac{ ~~ \frac{405}{10} ~~ }{\frac{81}{10}}\implies \cfrac{405}{10}\cdot \cfrac{10}{81}\implies \cfrac{405}{81}\cdot \cfrac{10}{10} \\\\\\ \cfrac{5\cdot 81}{81}\cdot \cfrac{10}{10}\implies \cfrac{5}{1}\cdot \cfrac{81}{81}\cdot \cfrac{10}{10}\implies \cfrac{5}{1}\cdot 1\cdot 1\implies \cfrac{5}{1}[/tex]