Find the domain of the function. (Enter your answer using interval notation.)

Answer:

64 cups of lemon juice

Explanation:

First, you can determine with the information provided the amount of cups of lemon needed to prepare sixteen cups of lemonade:

5 cups of lemonade→2 cups of lemon juice

16 cups of lemonade→x

x=(16*2)/5=6.4 cups of lemon juice

Now, you now that for sixteen cups that is the amount in a gallon you need 6.4 cups of lemon juice and you can use a rule of three to determine the amount needed for ten gallons of lemonade:

1 gallon of lemonade→6.4 cups of lemon juice

10 galons of lemonade→x

x=(10*6.4)/1=64 cups of lemon juice

According to this, the answer is that 64 cups of lemon juice are needed to make ten gallons of lemonade.

Answer:

see explanation

Step-by-step explanation:

Using sum to product identities

cos x - cos y = - 2sin([tex]\frac{x+y}{2}[/tex] )sin([tex]\frac{x-y}{2}[/tex] ) = 2sin([tex]\frac{x+y}{2}[/tex] )sin([tex]\frac{y-x}{2}[/tex] )

cos x + cos y = 2cos([tex]\frac{x+y}{2}[/tex] )cos([tex]\frac{x-y}{2}[/tex] )

Note that

sin10° = sin(90 - 10)° = cos80°

Thus

[tex]\frac{2sin(\frac{10+80}{2})sin(\frac{80-10}{2}) }{2cos(\frac{10+80}{2})cos(\frac{80-10}{2}) }[/tex] ← cancel 2 from numerator/ denominator

= [tex]\frac{sin45}{cos45}[/tex] × [tex]\frac{sin35}{cos35}[/tex]

= tan45° × tan35° { tan45° = 1 ]

= 1 × tan35°

= tan35° ← as required

Answer:    see proof below

Step-by-step explanation:

* Use the following Co-function Identity: sin A = cos(90 - A)

* Use the following Sum to Product Identities:

 cos x - cos y = 2 sin [(x + y)/2] · sin [(x - y)/2]

 cos x + cos y = 2 cos [(x + y)/2] · cos [(x - y)/2]

* Use the Unit Circle to evaluate cos 45 = sin 45 = √2/2

Proof LHS → RHS

[tex]\text{LHS:}\qquad \qquad \qquad \qquad \quad \dfrac{\cos 10-\sin 10}{\cos 10+\sin 10}\\\\\\\text{Co-function Identity:}\qquad \dfrac{\cos 10 -\cos (90-10)}{\cos 10+\cos (90-10)}\\\\\\\text{Product to Sum Identity:}\quad \dfrac{2\sin (\frac{10+80}{2})\sin (\frac{80-10}{2})}{2\cos (\frac{10+80}{2})\cos (\frac{80-10}{2})}\\\\\\\text{Simplify:}\qquad \qquad \qquad \qquad \dfrac{2\sin (45)\sin (35)}{2 \cos (45)\cos (35)}[/tex]

[tex].\qquad \qquad \qquad \qquad \qquad = \dfrac{2(\frac{\sqrt2}{2}) \sin (35)}{2(\frac{\sqrt2}{2}) \cos(35)}\\\\\\.\qquad \qquad \qquad \qquad \qquad = \tan (35)[/tex]

LHS = RHS:   tan 35 = tan 35   [tex]\checkmark[/tex]

Ans option 3? it can be converted to a fraction!

Answer:

it depends on the number of decimals

Step-by-step explanation:

Answer:

f(x) = (1/2)(x-2)^2(x+1)(x+2)

Step-by-step explanation:

You can determine this by looking at the zeroes of the graph. For any zero that goes through the x-axis, the power of that zero is odd. For any zero that that "bounces" from the x-axis, the power of that zero is even.

Starting from left to right, we can see that the first zero, -2, goes through the x-axis. That means (x+2) is raised to an odd power. The second zero, -1, also goes through, so (x+1) is raised to an odd power. The last zero, 2, bounces off the x-axis, so (x-2) is raised to an even power. The only functions that satisfy this criteria are function 1 and 2.

However, we are not done yet. We need to figure out which multiplier value (1/2, 1/4) is correct. To do this, we plug in 0 for x, since we know that the y-intercept is 4. When we plug in 0, we see that f(0) = 4 for the first function. Therefore, the first function is the answer.

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Answer:

90 inches³

Step-by-step explanation:

Given that:

A small rectangular prism sitting on top of a larger rectangular prism. The top prism measures 5 inches by 1 inch by 2 inches.

The bottom prism measures 5 inches by 4 inches by 1 plus 3 inches

Volume of rectangular prism = (width * length * height)

Volume of smaller prism: ( 5 * 1 * 2) inches = 10inch³

Volume of larger prism : (5 * 4 * (1 +3)) inches

(5 * 4 * (1 +3)) inches = (5 * 4 * 4) inches = 80 inches³

Total volume of the new packaging:

Volume of smaller + volume of larger prism

10 inches³ + 80 inches³ = 90 inches³

Answer:

The expression of density of the material with a density of 6 pound per pint in grams per liter (g/L) is 5756.75 g/L

Step-by-step explanation:

The density of the material is 6 pounds per pint of volume

The given conversion factors are;

1 pint (pt) = 2 cups (cups)

1 cup (cup) = 8 fluid ounces (fl oz)

Therefore;

2 cups (cups) = 2 × 8 fluid ounces = 16 fl oz

Also given;

1 fluid ounce = 29.574 mililiters (mL)

16 fl oz = 16 × 29.574 mL = 473.184 mL

1 liter (L) = 1000 mililiters (mL)

∴ 1 mL = 1/1000 L = 0.001 L

473.184 mL = 473.184 ×  0.001 L = 0.473184 L

1 pound (lb) = 0.454 kilograms (kg)

6 lb = 6 × 0.454 kg = 2.724 kg

1 kg = 1000 grams (g)

2.724 kg = 2.724 ×  1000 grams (g) = 2724 g

Therefore, with 6 lb = 2724 g and 1 pt = 0.473184 L, the density, d, of the material in grams per liter that has a density of 6 pounds per pint is given as follows;  

d = 2724 g/(0.473184 L)= 5756.75 g/L

The expression of density of the material with a density of 6 pound per pint in grams per liter (g/L) = 5756.75 g/L = 5756.75 g/L.

21 is composite because its factors are 1, 3, 7 and 21. If a number has 3 or more factors, then it's composite.

46: 1, 23, 46.

57: 1, 3, 19, 57.

Hope this helps!

#HaveAnAmazingDay

[tex]GraceRosalia[/tex]

The numbers 21, 46, and 57 are composite numbers.

Given,

21, 46 and 57

We need to identify which are prime or composite numbers.

Prime number - The numbers whose factor is only 1 and itself.

Example: 2, 5, 7

2 x 1 = 2

5 x 1 = 5

7 x 1 = 7

Composite number - The numbers which have factors other than itself and 1.

Example: 4, 6, 8

4 = 2 x 2

6 = 2 x 3

8 = 2 x 4

Find the factors

21 - 7 x 3

46 - 2 x 23

57 - 3 x 19

We see that each number has factors other than 1 and itself.

So,

21, 46, and 57 are composite numbers.

Thus 21, 46, and 57 are composite numbers.

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Answer:

Step-by-step explanation:

25

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

Work Shown:

1 pint = 2 cups

8 pints = 16 cups (multiply both sides by 8)

We have an 8 pint bottle costing $16.80, so we can say

8 pints = 16.80 dollars

1 pint = 2.10 dollars (divide both sides by 8)

Answer:

$2.10

Step-by-step explanation:

2 cups in 1 pint

16 cups= 8 pints

16 cups = 16.80

16.80 divided by 8 = 2.1

Answer:

infinite solutions

y = x - 1/4

Step-by-step explanation:

4x - 4y = 1

4y = 4x - 1

y = x - 1/4

substitute

4x - 4(x - 1/4) = 1

4x - 4x + 1 = 1

0 = 0

infinite solutions

Answer:

18 yards i think

Step-by-step explanation:

Answer:

65000(1.02)^n.

Step-by-step explanation:

Salary = 65000(1.02)^n   where n is the number of years he has worked for the company.

So after one year he earns $6500* 1.02 and after 2 years $65000 * 1.02^2.

The exponential function represents Mark's salary is [tex]65000(1.02)^n.[/tex]

The mathematical expression f(x)=exp or e^x denotes the exponential function.

The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

Given that Mark just landed a great job as an engineer where he will make $65,000 a year. The company he will work for guarantees a 2% pay increase each year so its employees' salaries keep up with inflation. At the end of the first year, Mark will have made $65,000.

The exponential function for the salary will be written as:-

[tex]Salary = 65000(1.02)^n[/tex]  

where n is the number of years he has worked for the company.

So after one year, he earns $6500 x 1.02, and after 2 years $65000 x 1.02².

Therefore, the exponential function represents Mark's salary is [tex]65000(1.02)^n.[/tex]

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Answer:

£0.83

Step-by-step explanation:

This is a simple subtraction problem.

You have 10 pence. You buy something with 9.17 pence.

10 - 9.17

0.83

Label your answer in pence.

£0.83

Good luck mate :)

Answer:

20

Step-by-step explanation:

(2√5)²=

4*5=20

Answer: 16 is the correct answer.

Step-by-step explanation: -n if n=-16 --16 two negatives equal positive and makes it +16.

Answer:

Step-by-step explanation:

let us total the amount in her portfolio

Company A was worth $2690

Company B was worth $2980.

Total = $5670

when The stock in Company A decreases by 20%  she will have

$2690 *0.8=  $2152

Company A will worth $2152

when The stock in Company B decreases by 10%  she will have

$2980 *0.9=  $2682

Company A will worth  $2682

In all after the decline in are portfolio is $2152+$2682= $4834

the difference for the original amount in her investment is = $5670-$4834

= $836

The total percentage decrease in the investor's stock account

= (836/5670)*100= 0.147*100= 14.7 %

Answer:

14.7%

Step-by-step explanation:

It’s 14.7%

Pls make me brainliest

Answer:

Option (3)

Step-by-step explanation:

To construct a line parallel to the line through point Q we will follow the following steps,

1). We join two points P (on the line) and point Q above the line PT with the help of a straightedge.

2). Now we will copy the angle QPT at point P with the help of a compass (Arcs as shown in the figure)

3). Finally we will join points Q and S to construct a line QS parallel to the line PT.

Therefore, Option (3) will be the answer.

Answer:

$151.20

Step-by-step explanation:

(22.40x0.75)+(22.40x5)+22.40=151.20

Answer:

Gaming Functions

Step-by-step explanation:

I think your teacher is implying for you to explain the function and the "works" behind the game. Maybe talk about the game's programming or the way it's overall structured?

0t

Step-by-step explanation:

4t-3-(3t+1)=5t-4

4t-3-3t-1=5t-4

t-3-1=5t-4

t-4=5t-4

t=5t

0=6t

0=t

(Im not 100% sure about this but i think this is the answer)

answer is 15

[tex]f(x)=5x+40\\f(-5)=5(-5)+40\\f(-5)=-25+40\\f(-5)=15[/tex]

If f(x) = 5x + 40, then the value of f(x) when x = -5 is: 15.

option D is correct.

Here, we have,

given that,

f(x) = 5x + 40

now, we have to find the value of f(x) when x = -5.

To find the value of f(x) when x = -5,

we substitute -5 into the function f(x) = 5x + 40:

we get,

f(-5) = 5(-5) + 40

= -25 + 40

= 15

Therefore, f(x) when x = -5 is 15.

Hence, If f(x) = 5x + 40, then the value of f(x) when x = -5 is: 15.

option D is correct.

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Step-by-step explanation:

If we are solving for t, we have to remember that we have to isolate the variable (get its on its own). Since -1 is with t on the same side of the equation right now, we have to move the -1 to the other side of the equation. To do so, we add it's opposite to the right side (+1). Then, the -1 cancels out so we are left with an isolated t.

-6 = t - 1 (+1)

-6 = t

But we are not done yet! Whatever we do on one side, we have to do on the other side. Since we added 1 to the right, we have to add 1 on the left, too. So we add 1 to -6.

(+1) -6 = t

-6 + 1 = -5

-5 = t

Our final answer: t = - 5 (it can also be written as - 5 = t, but most people prefer the variable going first)

Step-by-step explanation:

Remember: the formula for solving for volumes:

l • w • h

An easy way to do this is to convert all the numbers to decimals.

3 1/2 = 3.5

5 1/4 = 5.25

4 = 4

Now, we can multiply.

3.5 • 5.25 • 4 = 73.5

Convert 0.5 to a fraction: 1/2

Our final answer: D: [tex]73 \frac{1}{2}[/tex]

Answer:

t = 10.

Step-by-step explanation:

We can combine like terms, getting 11t - 5 = 105.

Add both sides by 5, getting 11t = 105 + 5 = 110.

We can then divide both sides by 11, getting t = 10.

Answer:

About 11.62 by 11.62

A square had equal sides so you find the square root of 135 and that is rounded to 11.62.

So the perimeter would be about 46. But 46.48 exactly.

Answer:

P≈46.48

A= Area

135

Step-by-step explanation:

It is true as A consist {7,8,9,10,11,12} and B consists of{9,11,13} and C consist of {7,8,10,12} and D has{7,12} there are the set of numbers from 7 to 13 only so the answer is true that U={7,8,9,10,11,12,13}.

Answer:

1. 24 different 4-digit numbers can be formed.

Step-by-step explanation:

2. The probability that the number 3 will be the first or third digit is 1:1, which is equal to 1/2 and 50%

3. The probability is 3:1, 3/4, or 75%

4.  What is the probability that the first digit will be the number 3 and the second digit will be the number 7? Answer: 1/12