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Whitepunk [10]
1 year ago
14

SOLVE FOR X AND THEN SOLVE FOR A

Mathematics
2 answers:
Licemer1 [7]1 year ago
4 0

Answer:

Step-by-step explanation:

A + B= 180°

(5x+20)+(9x-92)=180°

14x-72=180°

14x=252

x=18

A=5(18)+20

A=110

Nadusha1986 [10]1 year ago
4 0

Answer:

x = 18 , ∠ A = 110°

Step-by-step explanation:

∠ A and ∠ B are same- side interior angles and sum to 180° , that is

5x + 20 + 9x - 92 = 180

14x - 72 = 180 ( add 72 to both sides )

14x = 252 ( divide both sides by 14 )

x = 18

Then

∠ A = 5x + 20 = 5(18) + 20 = 90 + 20 = 110°

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A movie theater has a seating capacity of 387. The theater charges $5.00 for children, $7.00 for students, and $12.00 of
Rainbow [258]

Answer:

The attendance was 198 children, 90 students and 99 adults.

Step-by-step explanation:

We define:

c: children attendance

s: students attendance

a: adult attendance

The equation that describes the total ticket sales is:

5c+7s+12a=2808

We also know that the children attendance doubles the adult attendance:

c=2a

The third equation is the seating capacity, which we assume is full:

c+s+a=387

We start by replacing variables in two of the equations:

c=2a\\\\s=387-c-a=387-2a-a=387-3a

Then, we solve the remaining equation for a:

5c+7s+12a=2808\\\\5(2a)+7(387-3a)+12a=2808\\\\10a+(2709-21a)+12a=2808\\\\10a+12a-21a=2808-2709\\\\a=99

Then, we solve for the other two equations:

c=2a=2*99=198\\\\s=387-3a=387-3*99=387-297=90

The attendance was 198 children, 90 students and 99 adults.

8 0
3 years ago
2 1/3 + 3/7 divided by 2 1/3 x 1 3/7​
oee [108]

Answer: \frac{29}{35}

Step-by-step explanation:

1. Make sure all your denominators are the same, you can do this by multiplying them all by 3 or 7, 2 and 1/3 would become 2 7/21, 3/7 would become 9/21, 2 and 1/3, would become 2 and 7/21, and so on and so forth, leaving us with

2\frac{7}{21}+\frac{9}{21} / 2\frac{7}{21} * 1\frac{9}{21}

2. Now, I would go and solve each side of the equation because we divide them, we can add 2\frac{7}{21} and \frac{9}{21}  together to get  2\frac{16}{21}, because 7 + 9 = 16

2\frac{16}{21} / 2\frac{7}{21} * 1\frac{9}{21}

3. We can do the same thing to the other side, by multiplying the two of them. I'm going to convert both of them to just fractions, 2\frac{7}{21} becomes \frac{49}{21} and 1\frac{9}{21} becomes \frac{30}{21}

\frac{49}{21} *  \frac{30}{21}

Now we can reduce them, and for our first fraction divide the top and bottom by 7, giving us  \frac{7}{3} and the second one by 3, which gives us  \frac{10}{7}

\frac{7}{3} * \frac{10}{7} now we cross divide, where we replace the 7's with ones because they're right across from each other to get  \frac{1}{3} and  \frac{10}{1}, or just 10.

\frac{1}{3} * 10 =  \frac{10}{3}

4. So now we can do a similar thing with the first half of our equation and convert it into a fraction and not a mixed number.

\frac{58}{21} / \frac{10}{3}

Now we multiply divide them, and the easiest way I learned how to do this was by keep the first fraction in its place, and flipping the denominator and numerator of the second, and multiplying them.

so   \frac{58}{21} * \frac{3}{10} which if we multiply both sides, you get \frac{174}{210}

I'll save you some times and simplify it for you, the greatest common factor is 6 so we divide the top and bottom by 6 to get

\frac{29}{35}

4 0
2 years ago
At Simba Travel Agency, the price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per meter.
Alexus [3.1K]

Answer: $110


Step-by-step explanation:

Given: At Simba Travel Agency, the price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per meter.

F(d)models the fee (in dollars) for climbing d meters.

F(d)=110+0.12d

To find the initial amount, substitute d=0 int the above function, we get

F(0)=110+0.12(0)=110


Hence, the initial fee= $110.

5 0
3 years ago
Read 2 more answers
In the triangle below, what is the cosine of 45?
Colt1911 [192]
Cosine = adjacent / hypotenuse
cosine = 1 / square root (2)

7 0
3 years ago
Read 2 more answers
A tourist in London looks up at the clock in Big Ben tower and finds that it is exactly 8:00. When she looks up at the clock lat
Andrew [12]

To answer that question we need to use THE RULE OF THREE, this rule will help us solving linear relation problems.

Solution is:

The hour hand will turn (1/36)×π

The Table

Step      minute hand                hour hand

0-5         (1/6)×π                            (1/72)×π

  10        (2/6)×π                           (1/36)×π

  15        (3/6)×π   = π/2                (1/24)×π

  20       (4/6)×π   = (2/3)×π          (1/18)×π

  25       (5/6)×π                           (5/72)×π

  30       (6/6)×π   = π                   (1/12)×π

  35        (7/6)×π                          (7/72)×π

  40        (8/6)×π                          (8/72)×π

  45        (9/6)×π  = (3/2)×π         (3/24)×π

  50        ( 10/6)×π                       ( 10/72)×π

  55        (11/6)×π                          (11/72)×π

  60         (12/6)×π  = 2×π            (12/72)×π    = π/6

  • We know that each complete minute hand turn, is a 2×π angle turn, then a 5 minutes turn is (1/12) × 2×π = (π/6)
  • We will use that relationship to build the table and answer the question

If   2×π  angle for a minute hand turn is equal to 1 hour, then

(2/6) angle for a minute hand turn is equal to  "x" turn in the hour hand

So by Rule of Three, we proceed

2×π         ( Of minute hand)   ⇒    (1/6)×π   (of hour hand)

(2/6)× π   ( Of minute hand)   ⇒        x

Solving for x

2×π × x   = (2/6)× π × (1/6)×π

2× x  =  (2/36)×π

x = (1/36)×π

Now to build the table in 5 minutes steps:

Related Link: brainly.com/question/19586594

7 0
2 years ago
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