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3 years ago

1. 112 2. 136 3. 68 4. 158 5. 129

Mathematics

1 answer:

RideAnS [48]3 years ago

3 0

Answer:

4. 158

Step-by-step explanation:

First let's make things a little simpler and put these arcs in terms of x. We know that the degree measure around the outside of a circle, regardless of its size, is 360. So let's say that arc BC is x. That means that arc BDC is 360 - x. This is because arc BC + arc BDC = 360. Substituting in our x's we have:

x + 360 - x = 360 and

360 = 360. (That's just the proof that putting in our x's as we did does in fact work!)

Following the formula then, we have

$22=\frac{1}{2}(360-x-x)$ and

$22=\frac{1}{2}(360-2x)$

Multiply both sides by 2 to get rid of the fraction and get

44 = 360 - 2x

Subtract 360 rom both sides to get

-316 = -2x

Divide both sides by -2 to get that x = 158

Since we are looking for arc BC and we designated arc BC as our x, that means that arc BC = 158.

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3 years ago

There are four cups of milk how many ounces of milk are in 4 cups (8 oz in a cup)

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Step-by-step explanation:

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2 years ago

Read 2 more answers

Nolan has some nickels and some dimes. He has no more than 19 coins worth no less than $1.30 combined. If Nolan has 5 nickels, d

Allushta [10]

Answer:

number of dimes 11 to 14

Step-by-step explanation:

given data

coin = 19

worth no less = $1.30

Nolan nickles = 5

solution

we convert 5 cent to dollars, it will be

5÷100 = $0.05

and

dime is worth 10 cents

so it will be 10 ÷ 100 = $0.1

so we consider here x as the number when nickels.

and we consider y as the number of dimes.

so here we can say

x + y ≤ 19 ..........................1

as here no less than $1.30 combined.

0.05 x + 0.1 y ≥ 1.3 ......................2

and

when Nolan has 5 nickels

put x = 5 in eq 1

5 + y ≤ 19

y ≤ 19 - 5

y ≤ 14

and

now we put x = 5 in eq 2

0.05 × 5 + 0.1y ≥ 1.3

0.25 + 0.1y ≥ 1.3

0.1y ≥ 1.3 - 0.25

0.1y ≥ 1.05

y ≥ 10.5

so all possible values for the number of dimes 11 to 14

7 0

3 years ago

Given that x and y are positive integers, solve the equation x² - 4y² = 13

zvonat [6]

<h3>Answer: x = 7 and y = 3</h3>

=====================================================

Explanation:

Apply the difference of squares rule

x² - 4y² = 13

x² - (2y)² = 13

(x - 2y)(x + 2y) = 13

Since x and y are positive integers, this means x-2y and x+2y are both integers as well.

The value 13 is prime. Its only factors are 1 and 13

Since the above equation shows 13 factoring into x-2y and x+2y, then we have two cases:

A) x-2y = 1 and x+2y = 13
B) x-2y = 13 and x+2y = 1

----------------

Let's consider case A

We have this system of equations

$\begin{cases}x-2y = 1\\x+2y = 13\end{cases}$

Add the equations straight down

x+x becomes 2x
-2y+2y becomes 0y = 0 which goes away
1+13 becomes 14

Therefore we have 2x = 14 solve to x = 7

From here, plug this into either equation to solve for y

x-2y = 1

7 - 2y = 1

-2y = 1-7

-2y = -6

y = -6/(-2)

y = 3

You should get the same result if you used x+2y = 13

----------------

Since we've found that x = 7 and y = 3, notice how case B is not possible

Example: x-2y = 13 becomes 7-2(3) = 13 which is false.

Also, x+2y = 1 would turn into 7+2(3) = 1 which is also false.

-----------------

Let's check those x and y values in the original equation

x² - 4y² = 13

7² - 4*(3)² = 13

49 - 4(9) = 13

49 - 36 = 13

13 = 13

The answer is confirmed.

4 0

2 years ago