Satoko has 30 tokens to spend at an arcade. The three lines represent the cost of playing Satoko's three favorite

Please help! acellus

ch4aika [34]

Answer:

The number that belongs in the green box is equal to 909.

General Formulas and Concepts:
Algebra I

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Trigonometry

[Right Triangles Only] Pythagorean Theorem:
$\displaystyle a^2 + b^2 = c^2$

a is a leg
b is another leg
c is the hypotenuse

Step-by-step explanation:

Step 1: Define

Identify given variables.

a = 30

b = 3

c = x

Step 2: Find x

Let's solve for the general equation that allows us to find the hypotenuse:

[Pythagorean Theorem] Square root both sides [Equality Property]:
$\displaystyle \begin{aligned}a^2 + b^2 = c^2 \rightarrow c = \sqrt{a^2 + b^2}\end{aligned}$

Now that we have the formula to solve for the hypotenuse, let's figure out what x is equal to:

[Equation] Substitute in variables:
$\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2}\end{aligned}$
Evaluate:
$\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2} \\& = \boxed{ \sqrt{909} } \\\end{aligned}$

∴ the hypotenuse length x is equal to √909 and the number under the square root, our answer, is equal to 909.

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Learn more about Trigonometry: brainly.com/question/27707750

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Topic: Trigonometry

3 0

2 years ago

Keiko, Chang, and Abdul sent a total of 109 text messages over their cell phones during the weekend. Keiko sent 7 fewer messages

lbvjy [14]

9514 1404 393

Answer:

Keiko: 17
Chang: 24
Abdul: 68

Step-by-step explanation:

Let c represent the number of messages sent by Chang. Then Keiko sent (c-7) messages, and Abdul sent 4(c-7) messages. The total number sent was ...

c + (c -7) +4(c -7) = 109

6c -35 = 109 . . . . . . . . . . simplify

6c = 144 . . . . . . . . . . . add 35

c = 24 . . . . . . . . . . . divide by 6

c-7 = 17

4(c-7) = 68

Keiko sent 17, Chang sent 24, and Abdul sent 68 text messages.

5 0

3 years ago

Lif a/b =⅔ find the value of 2a²+3b²/a²+b²

Contact [7]

Answer:

95/4

Step-by-step explanation:

Given,

a/b =2/3

Therefore, 2a²+3b²/a²+b² = ?

We get,

a/b = 2/3

So, we can write

a = 2 and b = 3

Now,

2×(2)² + 3×(3)²/(2)² + (3)² [Putting the values of a and b]

= 2×4 + 3×9/4 + 9

= 8 +27/4 + 9

= (32+27+36)/4 [ Taking L.C.M, we get 4]

= 95/4

4 0

3 years ago

A shopkeeper purchased hammocks for $800 and sold them at a discount of 25%. What was the selling price? Choose the correct opti

myrzilka [38]

Answer:

B

Step-by-step explanation:

25% of 800 is 200, so 800-200 is 600

6 0

2 years ago

A local nursery sells a large number of ornamental trees every year. The owners have determined the cost per tree C for buying a

Karo-lina-s [1.5K]

The minimum cost is achieved when 150 trees are produced giving a minimum cost of $27.5

Polynomial is an expression that involves the operations of addition, subtraction, multiplication of variables.

Let C represent the cost for buying and caring for n trees. Given that:

C = 0.001n² - 0.3n + 50.

The minimum cost is at dC/dn = 0, hence:

dC/dn = 0.002n - 0.3

0.002n - 0.3 = 0

0.002n = 0.3

n = 150

C(150) = 0.001(150)² - 0.3(150) + 50 = 27.5

The minimum cost is achieved when 150 trees are produced giving a minimum cost of $27.5

Find out more at: brainly.com/question/25836610

8 0

3 years ago