Algebra 2 please help!!

Answer:

constant of proportionality = 10

Step-by-step explanation:

Direct proportion equation :

y = kx, where k is the constant of proportionality

Answer:

y=2.50x+4

Step-by-step explanation:

Answer:

The answer would be 11 3/8 pounds for cat food

Step-by-step explanation:

A ∩ B is the intersection of sets A and B, which is the set of elements that are in both A and B.

A = {2, 3, 5, 7} and B = {1, 2, 5, 10}, so A ∩ B = {2, 5}.

B ∩ D^c is the intersection of set B and the complement of set D, which is the set of elements in B that are not in D.

B = {1, 2, 5, 10} and D^c = {1, 4, 6, 8, 9, 10}, so B ∩ D^c = {1, 10}.

A^c is the complement of set A, which is the set of elements in U that are not in A.

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {2, 3, 5, 7}, so A^c = {1, 4, 6, 8, 9, 10}.

C ∩ D is the intersection of sets C and D, which is the set of elements that are in both C and D.

C = {1, 2, 3, 6} and D = {3, 5, 7}, so C ∩ D = {3}.

B u D^c is the union of set B and the complement of set D, which is the set of elements that are in B or in the complement of D, or both.

B = {1, 2, 5, 10} and D^c = {1, 4, 6, 8, 9, 10}, so B u D^c = {1, 2, 4, 5, 6, 8, 9, 10}.

Thus, this can be the universal set.

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Step-by-step explanation:

do

y2-y1

x2-x1

(-1+1)/(4-8)

IN THEVPLACE OF x in the EQUATION OF f(x) we find that x-4 is plugged in..

THIS brings us to a result that g(x) is accompanied by x-4

\(g(x) = x - 4\)

and For f(x) it shows

\(f(x) = {x}^{3} + {x}^{ \frac{3}{2} } - 1\)

SINCE THE POSITION OF THE X VALUES OF WHICH x-4 was plugged in has to be reserved.

PLEASE IF YOU DON'T UNDERSTAND MESSAGE ME QUICKLY.

Answer:

y = 2x + 3

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

In a deck of cards, there are 13 hearts and 13 diamonds

13+13 = 26 hearts or diamonds

P( hearts or diamonds) = numbers of hearts or diamonds / total

                                       =26/52

                                       = 1/2

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Answer:

2 1/6 ft

Step-by-step explanation:

This problem bothers on subtraction of fraction

Given data

Total length of rope 3 1/2 feet

Let's convert mixed fraction to proper fraction = 7/2ft

First piece of rope = 1 1/3ft

= 4/3ft

Hence the second piece of the rope is = 7/2-4/3= 21-8/6= 13/6

Second piece = 2 1/6 ft

Answer:

Using the Pythagorean Theorem, we know x^2 + 46^2 is equal to 65^2. With that in mind, it is important to note:

65^2 = 4,225

46^2 = 2,116

To find the missing angle, we must subtract 2,116 from 4,225 and then identify the difference’s square root.

4,225 - 2,116 = 2,109

√2,109 ≈ 45

Hence, x ≈ 45.

Step-by-step explanation:

25% of the students in the seminar are shorter than 65 inches.

To find the percentage of students who are shorter than 65 inches, we first need to find the number of students whose height is less than 65 inches:

There are three students who are shorter than 65 inches: 62, 60, and 58.

Therefore, the percentage of students who are shorter than 65 inches is:

(3 students / 12 students) × 100% = 25%

Note that the value given for 1% × 5 does not appear to be relevant to this question, and is not necessary for the calculation of the percentage of students who are shorter than 65 inches.

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Answer: F

Step-by-step explanation:

Answer: correct answer is A

Step-by-step explanation:

Remember that the coordinates (−2,−5π3) tell us the radius r=−2 and the angle θ=−5π3. So the point should be on the circle labeled 2 and form an angle of −5π3 with the negative x-axis. Point A is the correct point.

The true statement is (c) No; the slopes of segment EF and segment DF are not opposite reciprocals.

Right triangles have a pair of perpendicular lines

Coordinates

The coordinates are given as:

Start by calculating the slopes of lines DF and EF using:

\(m = \frac{y_2 -y_1}{x_2 -x_1}\)

So, we have:

\(m_{DF} = \frac{0 + 1}{0 +2}\)

\(m_{DF} = \frac{1}{2}\)

Also, we have:

\(m_{EF} = \frac{0 -2 }{0+2}\)

\(m_{EF} = \frac{-2 }{2}\)

\(m_{EF} = -1\)

For the triangle to be a right triangle, then the calculated slopes must be opposite reciprocals.

i.e.

\(m_1 = -\frac{1}{m_2}\)

By comparison, the slopes of both lines are not opposite reciprocals.

Hence, the true statement is (c)

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Answer:

c

Step-by-step explanation:

The land area of North America is 9,455,941.77 square miles.

Percentage can be described as the fraction of an amount expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to represent percentages is %.

In order to determine the land area of North America, multiply the total land area of the Earth by the percentage of the land area of North America.

Land area of North America = percentage of the land area of North America x total land area

16.5% x  57,308,738

0.165 x 57,308,738 = 9,455,941.77 square miles

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Answer:

21 children

Step-by-step explanation: 6.50x+8.75y=259

This equation came from the cost of the tickets for the children and adults.

x+y=35

This comes from the group of 35 people that consists of children and adults.

We can use substitution to solve for x and y.

x=35-y

6.50(35-y)+8.75y=259

227.5-6.50y+8.75y=259

227.5+2.25y=259

2.25y=31.5

y=14

Now that we have found y, we can plug it into any of the equations to find x.

x+14=35

x=21

Therefore, there are 21 children and 14 adults in the group.

Answer:A

Step-by-step explanation:

yes

Answer:

y= 11x

Step-by-step explanation:

find the slope: 22-11/2-1= 11/1 or 11

To find the y-intercept you can use the slope by subtracting 11 (inverse operation) from the y value of (1,11). So the y- intercept is (0,0). To write the equation plug in 11 for m and 0 for b. Since 0 has no value the equation would be y= 11x

The mass of the CO2 produced IS 630 Kg

Gasoline is a kind of fuel that is composed mostly of isooctane. In most engines, gasoline is widely used hence the demand for the product is high. We know that the combustion of an alkane (of which gasoline is one) would produce carbon dioxide and water according to a balanced reaction equation.

The balanced reaction equation for the combustion of gasoline is shown in the image attached to this answer.

Since  a Puerto Rico hospital uses 3 gallons of gasoline per hour, and there are 24 hours in a day, it the follows that 72 gallons of gasoline are used per day. This 72 gallons is the equivalent of 272.88 L

Now;

Given that the density of gasoline = 748.9 g/L

Mass of gasoline = 748.9 g/L * 272.88 L = 204 Kg

Number of moles of gasoline =  204 * 10^3/114 g/mol = 1789.5 moles

If 2 moles of gasoline produces 16 moles of CO2

1789.5 moles produces  1789.5 moles * 16 moles/2 moles = 14316 moles

Mass of CO2 =  14316 moles * 44 g/mol = 630 Kg

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Answer:

Step-by-step explanation:

Answer:

34.836

Step-by-step explanation:

sin(C)=opp/hyp=16/28=4/7

C= inverse sin = 34.836 deg

The angle of the right-angled triangle using trigonometric ratio is 34.84°.

Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.

For the given situation,

The diagram shows the right-angled triangle.

The hypotenuse side, h = 28

The perpendicular side, p =16

The trigonometric ratio that relates hypotenuse side and the  perpendicular side is sine θ.

\(Sine \theta=\frac{perpendicular}{hypotenuse}\)

⇒ \(Sine\theta = \frac{16}{28}\)

⇒ \(Sine \theta=0.5714\)

⇒ \(\theta = Sine^{-1} (0.5714)\)

⇒ \(\theta = 34.84\)

Hence we can conclude that the angle of the right-angled triangle using trigonometric ratio is 34.84°.

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The sum of  3x2 + 9 + 5x3 is 30

We need to find the  sum of 3x2 + 9 + 5x3

First we have to multiply which is then followed by addition.

Addition is the process of adding two or more numbers together to get their sum. Addition in math is a primary arithmetic operation, used to calculate the total of two or more numbers

3x2 + 9 + 5x3

= 6 + 9 + 15

= 30

Therefore, the sum of  3x2 + 9 + 5x3 is calculated by adding the terms, and it is 30

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Answer: (−∞,8)∪(8,∞),{y|y≠8}

Step-by-step explanation:

Answer: The range of a function is the set of all possible output values (y-values) for a given function.

For the function y = 3/x+8, we can find the range by analyzing the domain of the function. The domain of a function is the set of all input values (x-values) for which the function produces a valid output value.

The range of this function is all real numbers, since the denominator x+8 can't be equal to zero.

However, we can't express the range of the function as a specific set of numbers because the range is defined as all real numbers. The answer would be R

It's worth noting that if we change the function for example to y = 3/x-8, the domain would be x≠8 and the range would be y<-8/3

Step-by-step explanation:

Trapezium T is reflected across line x = 3 to form trapezium U and reflected across line x = 7 to form tralpelzium V

The figure is attached

Reflection across a line is a geometric transformation which mirrors a point, shape or figure exactly across a pre-defined plane known as the Line of Reflection.

In other words, the size and general outline are kept in tact while orientations are adjusted. Furthermore, each corresponding point on either side of the Line of Reflection is found to be equidistant from the said axis and lies along a perpendicular line.

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Answer:

The answer would be 5 and -12

Answer

θ is undefined for the condition given.

Explanation

θ = Cos⁻¹ (-8)

Cos θ ranges from -1 to 1, that is, -1 ≤ Cos θ ≤ 1

So, Cos θ = -8 that led to θ = Cos⁻¹ (-8) isn't pssible for Cosine.

Hope this Helps!!!

The prove of the given trigonometric function is given below.

The given trigonometric function is,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x))

Now proceed left hand side of the given expression:

We can write the expression  as,

⇒[(sin²(x))² - (cos²(x))²]/(sin²(x) - cos²(x))

Since we know that ,

Algebraic identity:

a² - b²  = (a-b)(a+b)

Therefore the above expression be

⇒(sin²(x) - cos²(x))(sin²(x) + cos²(x))/(sin²(x) - cos²(x))

⇒(sin²(x) + cos²(x))

Since we know that,

Trigonometric Identities come in handy when trigonometric functions are used in an expression or equation. Trigonometric identities hold for all values of variables on both sides of an equation. Geometrically, these identities include one or more trigonometric functions (such as sine, cosine, and tangent).

Then,

sin²(x) + cos²(x)² = 1 is an trigonometric identity

Hence,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x)) = 1

Hence proved.

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