The athlete drink 16 ounces of water every two hours starting at 7:30 AM and continuing for the next 14 hours. A) how many quarts did the athlete consume? B) how many pints of water did the athlete consume? ​

Using it's concept, it is found that the domain of the function is [tex]0 \leq x \leq 182[/tex], that is, the constraints are:

The domain of a function is the set that contains all possible values for the functions.

In this problem, the input of the function is how much he spends on food.

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The domain of a function is the set of input values the function can have.

The constraints on the domain are: the amount (x) is at least $0, and it is at most $182

From the question, Dev's budget on food is given as:

[tex]Budget = \$182[/tex]

This means that, he cannot spend more than $182.

Represent the amount with x.

So, we have:

[tex]x \le 182[/tex]

Also, he cannot spend a negative amount.

So, we have:

[tex]x \ge 0[/tex]

So, the domain is:

[tex]x \ge 0[/tex] and [tex]x \le 182[/tex]

Rewrite as:

[tex]0 \le x[/tex] and [tex]x \le 182[/tex]

Combine both inequalities

[tex]0 \le x \le 182[/tex]

Hence, the constraints on the domain are: the amount (x) is at least $0, and it is at most $182

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Answer:

wat?

Step-by-step explanation:

merry christmas....yey!!

Step-by-step explanation:

.....................

Answer:

-5

Step-by-step explanation:

I hope this helps!

Answer:

-5

Step-by-step explanation:

The slope of the line in this format is the coefficient of x, or the number in front of x.

[tex]\text{Given that,}\\\\(x_1,y_1) = (-1,-2)~~ \text{and}~~ (x_2,y_2) = (-2,2)\\\\\text{Slope, m =} \dfrac{y_2-y_1}{x_2 -x_1} = \dfrac{2 -(-2)}{-2-(-1)} = \dfrac{2+2}{-2+1} = \dfrac{4}{-1} = -4[/tex]

Answer:

three hours every 1 book

Step-by-step explanation:

36-12

6-2

3-1

Answer:

y is 1

Step-by-step explanation:

6+1=7, so 7 is = to 6+1

Answer: $45.50

Step-by-step explanation:

30% discount means 30% off the original price

1. find 30% of 65$

=.3*65

=19.5

2. subtract that from 65$

=65-19.5

=45.5

the discount price was $45.50

Answer:

3

Step-by-step explanation:

235 + 23

She uses 235, so 23 is left

235 + something + something = 235 + 23

235 + 20 + something = 235 + 23

subtract 235 from both sides

20 + something = 23

20 + something = 20 + 3

the missing number is 3

The missing number is 3.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

Kenya uses mental math to find the sum of 235 and 23.

She uses mental math.

That means,

she breaks the term in simple manner.

And she uses 235, 20, and one other number.

And the other number is 23 - 20 = 3

So, addition,

235 + 23

= 235 + 20 + 3

= 258

Therefore, the required number is 3.

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Answer:

1

Step-by-step explanation:

We can use the slope formula to find the slope

m = ( y2-y1)/(x2-x1)

    = ( -15 - -14) / ( -11 - (-10))

    = (-15+14) /(-11 + 10)

   = -1 / -1

   = 1

Answer:

The answer is 1

Step-by-step explanation:

Answer:

a. A(x) = 3x² - 8x + 5

b. x = ⁸/₃

Step-by-step explanation:

a.

A(x) = shaded area

A(x) = (2x - 3)² - (x - 2)²

= 4x² - 12x + 9 - (x² - 4x + 4)

= 4x² - x² - 12x + 4x + 9 - 4

= 3x² - 8x + 5

b.

ΔABF area = ⁵/₄ cm²

A(x) = 4(⁵/₄)

= 5

Substitution:

3x² - 8x + 5 = A(x) = 5

3x² - 8x + 5 = 5

3x² - 8x = 0

x(3x - 8) = 0

3x - 8 = 0

x = ⁸/₃

x = 0

Since x > 2, x = 0 is not valid;

So, x = ⁸/₃

Answer:

2/7 or -30/7

Step-by-step explanation:

Use the quadratic formula

a = 7, b = 2, c = -1

-2 + or - (sqrt (2^2 - 4 * 7 * -1) / 2 * 7

-2 + or - 32/14

-2 + or -  16/7

2/7, or -30/7

Answer:

Step-by-step explanation:

7x² + 2x - 1 = 0

x = (-2 ±[tex]\sqrt{2^2 - 4(7)(-1)}[/tex] )/ (2(7))

x = (-2 ± [tex]\sqrt{32}[/tex] ) /14

x = (-2 ± 4[tex]\sqrt{2}[/tex] ) /14

x = [tex]\frac{-1}{7}[/tex] ± [tex]\frac{2}{7}[/tex][tex]\sqrt{2}[/tex]

B = 180-31

B = 149

Answer: 149

Answer:

$151.2

Step-by-step explanation:

To find the price after the tax is implemented,

set a relationship x/140=8/100 (8/100) basically means 8%.

cross multiply (140)(8)=1120. Then divide it by 100x, you get $11.2.

But that's just 8 percent of the total amount. So you need to add onto the original price, 140+11.2=$151.2.

Here is the set up:

Let h = balloon's vertical distance.

sin(40°) = h/1165

sin(40°)(1165) = h

748.847565

748.85 feet = h

Done.

The balloon's vertical distance above the ground is 1388.40 feet to the nearest hundredth.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

From a hot-air balloon,

Mariana measures a 40° angle of depression to a landmark that's 1165 feet away, measuring horizontally.

Let h be the vertical distance.

Use tanθ = perpendicular / base

Here, perpendicular = 1165 feet and base = h and θ = 40°

Substituting the values,

tanθ = perpendicular / base

tan40° = 1165 / h

h = 1165 / tan40

h = 1165 /  0.839095

h = 1388.40059 feet.

h ≈ 1388.40 feet to the nearest hundredth.

Therefore, vertical distance is 1388.40 feet

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Answer:

Total profit=$35x+$18(130-x)

Total profit=$35x+$2340-$18x

Total profit=$17x+$2340

Step-by-step explanation:

Answer:

:)))))

Step-by-step explanation:

<3

Answer:

the answer is -21

Step-by-step explanation:

(4²-42)+(3²-4)

=16-42+(9-4)

=-26+5

=-21

Answer:

-13°F is the change in temperature.

Step-by-step explanation:

The change in temperature is,

→ -1 + x = -14

→ x = -14 + 1

→ [ x = -13 ]

Hence, -13°F is the change.

Step-by-step explanation:

3x-3 = x+5 add 3 on both sides

3x = x+8 subtract x in both sides

2x = 8 divide both sides by 2

x = 4

Answer:

the answer is 196515

Step-by-step explanation:

If u already knew the why u put upped the question?

Answer:

720 mi²

Step-by-step explanation:

The map has a scale of 1 in: 30 mi, meaning that for every inch you see on the map, in the real-life location, it will measure 30 miles. So we can find the area of the park on the map and then turn it into miles using the scale:

Area of a rectangle:

[tex]A=bh[/tex]

Replace the known values:

[tex]A=(4)(6)\\ A=24[/tex]

The area on the map is 24 mi², we can turn it to miles using the scale by multiplying our result with 30:

[tex]A=(24)(30)\\ A=720[/tex]

And last but not least, don't forget to put the unit!

Recall the half-angle identity for sine,

sin²(x/2) = (1 - cos(x))/2

Then the given equation is identical to

sin²(θ) = 1 - cos(θ)

Also recall the Pythagorean identity,

sin²(θ) + cos²(θ) = 1

Then we rewrite the equation as

1 - cos²(θ) = 1 - cos(θ)

Factoring the left side, we have

(1 - cos(θ)) (1 + cos(θ)) = 1 - cos(θ)

and so

(1 - cos(θ)) (1 + cos(θ)) - (1 - cos(θ)) = 0

and we factor this further as

(1 - cos(θ)) (1 + cos(θ) - 1) = 0

which gives

cos(θ) (1 - cos(θ)) = 0

Then either

cos(θ) = 0   or   1 - cos(θ) = 0

cos(θ) = 0   or   cos(θ) = 1

[θ = arccos(0) + 2nπ   or   θ = -arccos(0) + 2nπ]

…   or   [θ = arccos(1) + 2nπ   or   θ = -arccos(1) + 2nπ]

(where n is any integer)

[θ = π/2 + 2nπ   or   θ = -π/2 + 2nπ]   or   [θ = 0 + 2nπ]

In the interval 0 ≤ θ < 2π, we get three solutions:

• first solution set with n = 0   ⇒   θ = π/2

• second solution set with n = 1   ⇒   θ = 3π/2

• third solution set with n = 0   ⇒   θ = 0

So, the first choice is correct.

Answer:

-7/2

Step-by-step explanation:

-4(-2u+3)-u=3(u-7)-5

8u-12-u=3u-21-5

8u-u-12=3u-26

7u-12=3u-26

7u-3u-12=-26

4u-12=-26

4u=-26+12

4u=-14

u=-14/4

simplify

u=-7/2

Answer:

u = - 3.5

Step-by-step explanation:

Before solving this you have to know that,

(-) × (-) = (+)

(-) × (+) = (-)

(+) × (+) = (+)

Let us solve now.

[tex]-4(-2u+3)-u=3(u-7)-5[/tex]

[tex]8u-12-u=3u-21-5[/tex]

[tex]7u-12=3u-26[/tex]

[tex]7u-3u=12-26[/tex]

[tex]4u=-14[/tex]

[tex]\frac{4u}{4} = \frac{-14}{4}[/tex]

[tex]u=-3.5[/tex]

Hope this helps you.

Let me know if you have any other questions :-)

Answer:

É 5x3=15

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

I got it right bro man my guy I got you