Find the following.
f(x) = x2, g(x) = 3x − 5
(a) (f + g)(x) =
(b) (f − g)(x) =
(c) (fg)(x) =
(d) (f/g)(x) =
What is the domain of
f/g?

Protractor postulate: given any angle, we can express its measure as a unique real number from 0 to 180 degrees.

The protractor postulate is a fundamental concept in geometry that establishes a way to measure angles using a protractor. According to this postulate, every angle can be uniquely represented by a real number between 0 and 180 degrees.

A protractor is a geometric tool with a semicircular shape and marked degrees along its edge. To measure an angle using a protractor, we align the center of the protractor with the vertex of the angle and the baseline of the protractor with one side of the angle. We then read the degree measure where the other side of the angle intersects the protractor.

The protractor is divided into 180 degrees, with 0 degrees being the starting point at the baseline of the protractor, and 180 degrees being at the opposite end of the baseline. By aligning the protractor with an angle, we can determine its measure as a real number within this range.

For example, if we measure an angle using a protractor and find that the other side intersects the protractor at 45 degrees, we can express the measure of the angle as 45 degrees. Similarly, if the intersection point is at 90 degrees, the angle measure would be 90 degrees. The protractor postulate guarantees that these angle measures are unique within the range of 0 to 180 degrees.

It is important to note that the protractor postulate assumes that angles can be measured using a protractor and that the measurement is accurate and reliable. The postulate provides a consistent and standardized way to assign a numerical value to an angle, allowing for precise communication and comparison of angles in geometric contexts.

In summary, the protractor postulate establishes that the measure of any angle can be expressed as a unique real number between 0 and 180 degrees. This concept is fundamental in geometry and allows for the measurement, comparison, and communication of angles using a protractor.

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Answer:

-45, -2.5, -1.1, 0.8, 95

Answer:

your answer would be -45, -2.5, -1.1, 0.8, 95

Step-by-step explanation:

if you put the listed numbers out on a number line you would start with the negative numbers on the left side going up to the positive numbers on the right side. -45 is the smallest number in this sequence so it will be the first number. then if you go further right on the number line you'll hit -2.5, then -1.1, then 0.8, then 95. these numbers are large so a number line wouldn't be logical but it always helps to visualize it. hope this helps!

The system of equations can be written as:-

10x + 4y = 42

6x + 8y = 14

A system of equations, also known as a set of simultaneous equations or an equation system, is a finite set of equations for which we sought common solutions in mathematics. A system of equations can be classified in the same way that a single equation can.

Given that in an online quiz, positive points are awarded for a correct answer, and negative points are awarded for an incorrect answer. Elena answers 10 questions correctly and 4 incorrectly and scores 42 points. Kiran answers 6 questions correctly and 8 incorrectly and scores 14 points.

The system of equations can be written as:-

10x + 4y = 42

6x + 8y = 14

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The total amount of blood drawn is 3.025 mL.

The given condition is that;

The amount of red blood cells in a blood sample is equal to the total amount of in the sample minus the amount of plasma.

From above condition we can assume following factors as;

Total amount of blood plasma in the sample = 5.5 mL

Amount of red blood cells = 45% = 45/100 = 0.45 mL

To find the total amount of blood drawn ( x );

From the above condition, the amount of red blood cells in a blood sample is equal to the total amount of in the sample minus the amount of plasma.

x = 5.5 - [5.5 * 0.45]

x = 5.5 - 2.475

x = 3.025

Hence, the total amount of blood drawn is 3.025 mL.

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Answer:

The formula for the area of a trapezoid is:

Area = (b1 + b2) / 2 x h

where b1 and b2 are the lengths of the two parallel bases, and h is the height.

We are given that the area of the trapezoid is 96 ft, the height is 8 ft, and one of the bases (b1) is 11 ft. We can use this information to find the length of the other base (b2).

Substituting the given values into the formula for the area of a trapezoid, we get:

96 = (11 + b2) / 2 x 8

Multiplying both sides by 2 and dividing by 8, we get:

24 = 11 + b2

Subtracting 11 from both sides, we get:

b2 = 13

Therefore, the length of the other base is 13 ft.

Answer:

  2/15

Step-by-step explanation:

You want to know the fraction that is 2/3 of 1/5.

In this context, "of" means "times."

  2/3 of 1/5 = (2/3)×(1/5) = (2·1)/(3·5) = 2/15

2/15 of the pets are alley cats.

In this scenario, the number of winning tickets follows a binomial distribution, since each ticket has a fixed probability of winning (1/4) and the trials (purchasing a ticket) are independent.

The probability that k out of n trials will be successful is given by the binomial probability mass function:

P(k) = (n choose k) * p^k * (1-p)^(n-k)

Where n is the number of trials (100 tickets), k is the number of successful trials (winning tickets), p is the probability of success (1/4), and (n choose k) is the binomial coefficient.

To find the probability that fewer than 20 tickets are winners we have to calculate the probability of getting 0 to 19 winning tickets.

P(x<20) = P(0) + P(1) + P(2) +...+ P(19)

using the above formula we can find the probability of getting k winning tickets

P(x<20) = P(0) + P(1) + P(2) +...+ P(19)

= (100 choose 0) * (1/4)^0 * (3/4)^100 + (100 choose 1) * (1/4)^1 * (3/4)^99 +.... + (100 choose 19) * (1/4)^19 * (3/4)^81

This can be calculated using a calculator or spreadsheet software, however, it's not possible for me to provide you with the exact answer as it involves multiple complex calculations.

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Answer:

Step-by-step explanation:

Main Answer:

To rationalize the given denominators, we will multiply both the numerator and denominator by a suitable expression that eliminates any radical or irrational terms.

Supporting Explanation:

(a) For the denominator √√x, we can multiply both the numerator and denominator by √x to rationalize it. This gives us 1/√x.

(b) For the denominator Va, we can multiply both the numerator and denominator by a to rationalize it. This gives us 1/a.

(c) For the denominator X^(2/5), we can multiply both the numerator and denominator by X^(3/5) to rationalize it. This gives us (X^(3/5))/(X^(2/5)) = X.

Overall, the rationalized denominators are: 1/√x, 1/a, and X.

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Answer:

a = 0, b = -15

Step-by-step explanation:

Given the following complex number;

x1 = 3(cosπ+isinπ)

x2 = 5(cosπ/2 - isinπ/2)

x1x2 = 15(cosπcosπ/2 - icosπsinπ/2+isinπcosπ/2 -i²sinπsinπ/2)

x1x2 = 15(0 - i(-1)+0 -0)

x1x2 = 15(-i)

x1x2 = -15i

x1x2 = 0-15i

Since

0 - 15i = a+ bi

Compare

a = 0

-15-  = bi

b = -15

Hence a = 0, b = -15

Answer:

-3

Step-by-step explanation:

You might find it easier to write -(11 - 8), which is -(3), or -3.

Answer:

8-11

Infront of 8 there will be+

so +8-11

- + = - so 8-11=-3

-3 is the answer of 8-11

Answer:

Concordat of 1801, agreement reached on July 15, 1801, between Napoleon Bonaparte and papal and clerical representatives in both Rome and Paris, defining the status of the Roman Catholic Church in France and ending the breach caused by the church reforms and confiscations enacted during the French Revolution .Step-by-step explanation:

Answer:

........

Step-by-step explanation:

(A) Given the points (5, -2) and (5, 6);

The slope m, of a line passing through two points is given as;

The slope of the line passing through the points (5, -2) and (5, 6) is undefined

(B) Given the points (-7, 3) and (-7, -3)

Similarly, the slope is given as;

The slope of the line passing through the points (-7, 3) and (-7, -3) is undefined.

The force required to keep a hockey puck sliding at a constant velocity, neglecting ice friction and air resistance, is equal to its weight. The correct option is "equal to its weight."

When a hockey puck is set in motion across a frozen pond and there is no ice friction or air resistance, the only force acting on the puck is its weight, which is the force due to gravity pulling it downward. According to Newton's first law of motion (the law of inertia), an object at a constant velocity will continue to move at that velocity unless acted upon by an external force.

Since the puck is already in motion and we want to maintain its constant velocity, the force required to counteract its weight and keep it sliding is equal to its weight. This is because the weight of an object is the force exerted on it by gravity, and in the absence of other forces, an equal and opposite force is needed to maintain the object's motion without acceleration.

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Answer:

Can I get image of it?

Step-by-step explanation:

Answer:

Image?

Step-by-step explanation:

Answer:

x = 1.5

Step-by-step explanation:

5x - 5 - 3x + 2 = 0

Combine like terms

2x - 3 = 0

Isolate variable x

Add 3 to both sides

2x = 3

Divide both sides by 2

x = 3 ÷ 2

x = 1.5

a) a square has 4 right angles and all 4 sides are the same lengths

b) not sure, I'll edit later when and if I know

c) isosceles triangle

Answer:

16 + x > 31, so x > 15

16 + 31 > x, so x < 47

Combining these inequalities, we have

15 < x < 47.

Since x is the shortest side of this triangle, and since the triangle is not isosceles,

15 < x < 16. So one possible value of x is 15.1.

Answer:

3S+2L=24

S+L=10

Step-by-step explanation:

I took the test

Answer:

2S + 3L = 24

S+L=10

Step-by-step explanation:

We will be using the Elimination Method for this question.

S = small || L = large

1. Multiply 2nd equation by -2 then bring down 1st equation:

(-2) (S + L= 10)

= -2S - 2L = -20

   2S + 3L =24

= 0S + L = 4

y = 4

2. Substitute L in either equation:

S + L = 10

S + (4) = 10

S = 6

3. Plug both S and L values into other equation:

2(6) + 3(4) = 24

12 + 12 = 24

Solution: (6, 4)

They will need to make 6 small and 4 large to get the most amount of money.

Answer:

I think that it will be (6)

Answer:

$2 for each candy bar

Step-by-step explanation:

16 - 2 = 14

14 / 7 = 2

Answer:

$2

Step-by-step explanation:

16-2=14

14/7=2

he spent $14 total on candy bars, divide that by 7, and each candy bar costs $2

Renting a car because your roommate moved out is the expense that would not be fit to file a Form 1040 Schedule A (Itemized Deduction Form).

Schedule A is used to report itemized deductions, which include specific categories of expenses that taxpayers can use to reduce their taxable income. These categories are: Uninsured medical and dental expenses that exceed a certain percentage of your adjusted gross income (AGI). State and local taxes, which may include income, sales, and property taxes. Charitable donations made to qualified organizations. Mortgage interest and points paid on a primary or secondary residence.

Paying a significant amount of uninsured medical expenses, donating a significant amount of money to the March of Dimes, and buying a house and claiming the home mortgage interest and points are all eligible expenses for Schedule A. However, renting a car because your roommate moved out is not an eligible expense for itemized deductions on Schedule A, as it does not fit into any of the allowable categories.

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The expense that would not be fit to file a Form 1040 Schedule A (itemized deduction form) is renting a car because your roommate moved out.

The other three options mentioned in the question are all eligible to be itemized deductions on Schedule A. Paying a significant amount of uninsured medical expenses and donating a significant amount of money to a charitable organization like March of Dimes are both eligible deductions. Buying a house and claiming the home mortgage interest and points is also a common deduction for homeowners.

However, renting a car due to a roommate moving out is not considered a deductible expense. It is important to keep track of all deductible expenses and consult with a tax professional to ensure accurate filing of tax returns.

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Answer:

r = 7

Step-by-step explanation:

Step 1: Write out equation

4r + 7 = 35

Step 2: Subtract 7 on both sides

4r + 7 - 7 = 35 - 7

4r = 28

Step 3: Divide both sides by 4

4r/4 = 28/4

r = 7

Solve 4r+7=35

4r=35-7

4r=28

r=7

:)

The matrix that shows the prices in U.S. dollars is:

[1.81  6.32  0.56 0.36]

Here we have a simple row matrix which can be written as:

[80  280  25  16]

You can see this as a row vector or something like that, notice that if we multiply this by an scalar, we just need to multiply each element by an scalar.

Now, we know that:

1 dollar = 44.32 Nu

then:

1 Nu = (1/44.32) dollars.

So to get the matrix in dollars, just multiply each number by (1/44.32), then we will get:

(1/44.32)*[80  280  25  16] = [80/44.32  280/44.32  25/44.32  16/44.32]

= [1.81  6.32  0.56 0.36]

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Answer:

Step-by-step explanation:

3/5

4/6

5/7

51/150

2/3

The laser starts at vertex $a$ and fires a laser beam towards point $x$ on side $\overline{bc}$ of the square $abcd$.

Let's consider the path of the laser beam. It will bounce off the sides of the square at a $45^\circ$ angle since the square has equal sides. Each time the laser beam hits a side, it reflects and changes direction by $90^\circ$.

We are given that the laser beam bounces off the sides $1998$ times before hitting point $x$. This means that it will hit each side $1999$ times (the initial hit plus $1998$ reflections). Since there are four sides to the square, the laser beam will make a total of $4 \times 1999 = 7996$ hits on the sides of the square.

Now, let's find the distance between vertex $a$ and point $x$.

Since the laser beam hits each side $1999$ times, the total distance it travels along the sides of the square is $1999$ times the perimeter of the square. The perimeter of the square is $4$ units, so the total distance is $1999 \times 4 = 7996$ units.

Since the side length of the square is $1$, the distance between vertex $a$ and point $x$ is $7996$ times the length of one side, which is $7996 \times 1 = 7996$ units.

Therefore, the distance between vertex $a$ and point $x$ is $7996$ units.

The distance between vertex $a$ and point $x$ is $7996$ units.

This means that the laser beam will hit point $x$ after traveling a distance of $7996$ units along the sides of the square.

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Time taken by Miguel car to drive is, 1.6 hour.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Miguel went for a drive in his new car. He drove at a speed of 53 miles per hour for 84.8 miles.

We know that;

⇒ Speed = Distance / Time

⇒ Time = Distance / Speed

Here, Speed = 53 miles per hour

Distance = 84.8 miles

Hence, We get;

⇒ Time = 84.8 / 53

⇒ Time = 1.6 hour

Thus, Time taken by Miguel car to drive is, 1.6 hour.

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Answer:This is what i could solve hope it helps :)

Number17

\(H = \frac{m(v^2-u^2}{2gx} \\Cross - multiply\\2Hgx = m (v^2-u^2)\\2Hgx = mv^2-mu^2\\\frac{2Hgx+mu^2}{m} = \frac{mv^2}{m} \\Divide -both -sides-of-the-equation-by-m\\v^2 = \frac{2Hgx+mu^2}{m}\\Square - root-both -sides -to -eliminate the square\\v =\sqrt{\frac{2Hgx+mu^2}{m}}\)

Step-by-step explanation:

Number 19

\(T =2\pi \sqrt{\frac{1}{MH}}\\Divide - both - sides-of-the-equation-by 2\pi\\\frac{2\pi \sqrt{\frac{1}{MH}}}{2\pi }=\frac{T}{2\pi }\\\sqrt{\frac{1}{MH}}=\frac{T}{2\pi }\\SQUARE-BOTH -SIDES\\\left(\sqrt{\frac{1}{MH}}\right)^2=\left(\frac{T}{2\pi }\right)^2\\\frac{1}{MH}=\frac{T^2}{4\pi ^2}\\CROSS-MULTIPLY\\MHT^2={4\pi ^2\\\\DIVIDE BOTH SIDES OF THE EQUATION BY HT^2\\M=\frac{4\pi ^2}{HT^2}\)

Number 20 &21

\(A =\frac{1}{2} m(v^2-u^2)\\Divide both sides by \frac{1}{2} m\\\frac{\frac{1}{2}m\left(v^2-u^2\right)}{\frac{1}{2}m}=\frac{A}{\frac{1}{2}m}\\2Am = v^2-u^2\\Move- v^2- to- the -other -side- to- isolate- u\\\\u^2 = 2Am-v^2\\Square-root-both-sides-to -eliminate-the-square-on-u.\\u = \sqrt{2Am-v^2}\)