Given the following table with selected values of f (x) and g(x), evaluate f (g(2)).

x –5 –4 –1 2 4 7
f (x) 0 2 7 –1 –6 –4
g(x) –8 –1 2 4 7 1

–4
2
4
–6

The vertex of the parabola is ( 0, -4). The correct option is F.

A vertex of a parabola is the point at which the parabola changes direction. It is the point on the parabola where the curve reaches its minimum or maximum value, depending on whether the parabola opens upward or downward.

A parabola is a type of conic section, a geometric shape formed by the intersection of a plane and a cone. In particular, a parabola is formed when a plane intersects a right circular cone parallel to one of its generating lines.

From the given graph the vertex of the parabola is,

Vertex = ( 0, -4 )

Therefore, the vertex is (0,-4).

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Answer: Here you go.

Step-by-step explanation:

To calculate the volume of excavation needed for the water line, we first need to calculate the cross-sectional area of the trench.

The trench has a width of 18 inches and a depth of 3 feet, or 36 inches. So the cross-sectional area of the trench is:

18 inches x 36 inches = 648 square inches

Next, we need to subtract the cross-sectional area of the water line from the cross-sectional area of the trench to get the area of the excavation. The water line has a 3.5 inch outside diameter, so the radius is 1.75 inches. The cross-sectional area of the water line is:

π x (1.75 inches)^2 = 9.62 square inches

The area of the excavation is therefore:

648 square inches - 9.62 square inches = 638.38 square inches

To convert square inches to cubic feet, we need to multiply by the length of the trench in feet. The length of the trench is 500 feet. So the volume of excavation needed for the water line is:

638.38 square inches x 500 feet = 1,909,140 cubic inches

To convert cubic inches to cubic feet, we divide by 12^3 (12 inches per foot, cubed):

1,909,140 cubic inches ÷ (12 x 12 x 12) = 11.04 cubic feet

Therefore, the volume of excavation needed for the water line is approximately 11.04 cubic feet.

The solution to the system of equations is given below.

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

Given is the system of equations as shown in the image.

{ 1 } -

x - 2y = - 7

2x + 5y = 8

We can write -

x = 2y - 7

Now -

2(2y - 7) + 5y = 8

4y - 14 + 5y = 8

9y = 22

{y} = 22/9

x = 44/9 - 7

x = 44/9 - 63/9

{x} = - 19/9

{ 2 } -

5x - 3y = 16

3x + 6y = 18

We can write -

5x - 3y = 16

x + 2y = 9

So -

x = 9 - 2y

5(9 - 2y) - 3y = 16

45 - 10y - 3y = 16

45 - 13y = 16

45 - 16 = 13y

13y = 29

y = 29/13

x = 9 - 58/13

x = 117/13 - 58/13

x = 59/13

Similarly, we can solve the other two system of equations.

Therefore, the solution to the system of equations is given above.

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The equivalent number of inches is given as follows:

The equivalent number of inches is obtained applying the proportions in the context of the problem.

A proportion is applied as the unit conversion rate from feet to inches is given as follows:

1 feet = 12 inches.

Hence the measures are converted from feet to inches multiplying the amounts by 12, as follows:

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Answer:

0

Step-by-step explanation:

plug in 7 for "P"

so 10 - [7+3]

solve the inside first, which is 10, therefore 10-[10] leaving you with no solution or 0 as answer

Answer:

The slope of a line parallel to Y-axis is zero.

The journal entries for the aforementioned transactions in May are as follows:

1. a $48,000 profit from the selling of ordinary stock:

Cash 48,000

Stock 48,000

2. Paid $880 in rent for the office for the month:

Rent Expense 880

Cash 880

3. $1,750 worth of supplies were bought on credit:

Supplies 1,750

Accounts Payable 1,750

4. Paid fees, cash received, $12,600:

Cash 12,600

Fees Earned 12,600

5. $1,000 creditor account payment:

Accounts Payable 1,000

Cash 1,000

6. Spent $375 in transportation expenses for the month as well as $250 in other expenses:

Automobile Expense 375

Miscellaneous Expense 250

Cash 625

7. $3,900 in office salaries were paid for the month:

Salaries Expense 3,900

Cash 3,900

8. $2,400 in earned fees that the client will pay the next month:

Accounts Receivable 2,400

Fees Earned 2,400

9. determined that the $280 cost of the supplies used:

Supplies Expense 280

Supplies 280

10. Dividends paid, $2,400:

Retained Earnings 2,400

Cash 2,400

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Answer:

El valor obtenido para x es una solución a la ecuación y, por lo tanto, es un punto en la gráfica de la función. Esto significa que el punto (x,y) en la gráfica se encuentra en la recta que representa la ecuación

Step-by-step explanation:

The number of days that he was in Europe will be 42 days.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since Jordan went to Europe for vacation. He spent 1/3 of his time in Spain.

If he was in Spain for 14 days, the number of days that he was in Europe will be:

1/3 × x = 14

x = (14 × 3)

x = 42 days

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Jordan went to Europe for vacation. He spent 1/3 of his time in Spain. If he was in Spain for 14 days, how long was he in Europe?

Answer:

Step-by-step explanation:

Let's assume that the first car used x gallons of gas during the week, then the second car used (75 - x) gallons of gas because the total gas consumption by both cars is 75 gallons.

The first car's fuel efficiency is 30 miles per gallon, so it traveled (30x) miles during the week.

The second car's fuel efficiency is 35 miles per gallon, so it traveled (35(75 - x)) miles during the week.

The total distance traveled by both cars is given as 2425 miles, so we can set up the equation:

30x + 35(75 - x) = 2425

Expanding the equation:

30x + 2625 - 35x = 2425

Simplifying:

-5x = -200

x = 40

Therefore, the first car used 40 gallons of gas during the week, and the second car used (75 - 40) = 35 gallons of gas during the week.

Answer: Car 1 used 40 gallons and car 2 used 35 gallons.

Step-by-step explanation: In this problem, we will use a system of equations to reach our answer. We can let x be the gallons consumed by the first car, and y be the gallons consumed by the second car(these are both for one particular week only). We know the total consumption of gas is 75 gallons so the gallons consumed by car 1 and car 2 have to add up to 75. We can then create the equation x+y=75. We know that car 1 has an efficiency of 30 miles per gallon and 35 miles per gallon for car 2. The miles produced by x gallons in car 1 can be represented by 30x=# of miles. we can use 35y = # of miles for car 2. We know the combined total of miles from both cars is 2425 so we can make the equation 30x+35y=2425 miles. Now that we have our equations, we can simply solve them to find our answers.

x+y=75

x=75-y                   Isolating a variable

30x+35y=2425    

30(75-y)+35y=2425            Substituting the variable we isolated

2250-30y+35y=2425

2250+5y=2425

5y=175

y=35

x+(35)=75

x=40

y=35 and x=40

Car 1 used 40 gallons and car 2 used 35 gallons.

Hope this helps!

Answer:

First, if it's a simple interest problem, convert R percent to r a decimal, r = R/100 = 9%/100 = 0.09 per year, then, solving our equation

I = 4000 × 0.09 × 2

I = 4000 × 0.18

I = $720.00

The simple interest accumulated on a principle of $4,000.00 at a rate of 9% per year for 2 years is $720.00.

Hope this helps. (Compound interest will be added if the equation needs it)

The probability of getting a pair of 10s is 1/26.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Here,

Total number of outcomes = 52

Number of outcomes = 2

So, the probability is 2/52

= 1/26

Therefore, the probability of getting a pair of 10s is 1/26.

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Answer:

pemdas

Step-by-step explanation:

pemdas means Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction

you always want to go left to right

when using pemdas.

example 4^5 • (9-8)

you start from left to right

we would work in parentheses because that is what pemdas said to do.

Answer:45

Step-by-step explanation: see how if you cut off that spike and you plug it in the non-shaded part it fits. Now you’ve got yourself a rectangle so the area is 3+2= 5 x 9= 45

Let's use the given information to set up equations to solve for the ages of the family members.

We know that the mean age of the family is 23 years, so we can write:

(sum of ages) / 7 = 23

sum of ages = 161

We also know that the median age is 16 years, which means that the ages of the family members can be arranged in order from smallest to largest, and the middle age (or the average of the two middle ages, if there are an even number of ages) is 16. We can use this information to set up an equation:

(3rd smallest age + 4th smallest age) / 2 = 16

3rd smallest age + 4th smallest age = 32

Next, we know that the range of the ages is 35 years, which means that the difference between the largest age and the smallest age is 35. We can use this information to set up another equation:

largest age - smallest age = 35

Finally, we know that the modes (the most common ages) are 12 years and 45 years. This means that there are two family members whose ages are 12 years and two family members whose ages are 45 years. We can use this information to set up two more equations:

number of 12-year-olds + number of 45-year-olds = 4

12 x number of 12-year-olds + 45 x number of 45-year-olds = sum of ages

We now have five equations and five unknowns (the ages of the seven family members). We can solve for these unknowns using algebra. One possible set of ages that satisfies all of the equations is:

2, 2, 12, 16, 20, 45, 64

(Note that the ages do not have to be integers, but this particular set of ages happens to be integers and satisfies all of the given conditions.)

Answer:

x is greater than or equal to 3

Step-by-step explanation:

I'm gonna assume you meant 3x-8

Treat it as an equation

3x-8 =1, 3x=9, x=3

If its x^3 -8

x^3 -8 =1, x^3=9, x is greater than or equal to the cubed root of 9

the ticket price needs to be lowered by approximately $8.33 in order to fill all seats in the stadium.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, A baseball team plays in a stadium that holds 58,000 spectators. With the ticket price at $10, the average attendance at recent games has been 33,000.

Let's assume that if the ticket price is lowered by $x, the corresponding increase in attendance is 3000x.

Then, if the ticket price is lowered by $x, the new attendance will be:

33,000 + 3000x

We want to find the ticket price that will result in full capacity, which is 58,000 spectators.

So, we can set the new attendance equal to 58,000 and solve for x:

33,000 + 3000x = 58,000

3000x = 25,000

x = 25,000/3000

x ≈ 8.33

Therefore, the ticket price needs to be lowered by $8.33 to $1.67 in order to fill all seats in the stadium.

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Complete question:

A baseball team plays in a stadium that holds 58,000 spectators. With the ticket price at $10, the average attendance at recent games has been 33,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000. how much ticket price to be lowered so that all seats will be full?

Therefore, John is incorrect, as buying a 2-liter bottle of orange juice is actually slightly more expensive per liter than buying a 1.5-liter bottle of cola.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

2.1.1 To determine how many packets of patties Julia should buy, we need to know the total number of patties needed for the school function. Let's assume that each person will eat one patty.

If there are 300 people attending the function, then Julia needs to buy:

300 x 1 = 300 patties

Each packet of patties contains 12 patties, so the number of packets needed can be calculated as follows:

300 patties ÷ 12 patties/packet = 25 packets

Therefore, Julia should buy 25 packets of patties.

2.1.2 To justify Julia's calculation, we can use algebra. Let's assume that the number of packets of patties she buys is x. We know that there are 12 patties in each packet, so the total number of patties is 12x. We also know that if she buys 42 packets, there will be a leftover of 4 patties.

This can be represented as the following equation:

12x + 4 = 42 x 12

Simplifying this equation:

12x = 500 - 4 = 496

x = 496/12 = 41.33 (rounded to two decimal places)

Since we can't buy a fractional number of packets, Julia would need to buy 42 packets of patties. This would give her a total of:

12 x 42 = 504 patties

She would then have 4 leftover patties, as calculated earlier. Therefore, Julia's calculation is correct.

2.2.1 To determine whether buying a 2-liter bottle of orange juice is cheaper than buying a 1.5-liter bottle of cola, we need to compare the price per liter of each drink.

For orange juice, the price per liter is:

R18.95 ÷ 2 liters = R9.475/liter

For cola, the price per liter is:

R14.50 ÷ 1.5 liters = R9.67/liter

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The answer to this question is as follows It's vital to keep in mind that equation while this is the same phrase you used, the x only applies to the cost of the water and not the cost of the popcorn.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.  

The formula to calculate Theodore's overall spending is:

3x + 4.50

This is due to the fact that he purchased three waters at a cost of x each, for a total cost of x, and a bag of popcorn at a cost of $4.50. The entire amount of money he spent may be calculated by adding these two expenses.

By condensing the formula 3x + 4.50, we obtain:

7.50x

It's vital to keep in mind that while this is the same phrase you used, the x only applies to the cost of the water and not the cost of the popcorn.

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The value of the speed(v) is 5.14 km/hr

Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement. Put another way, speed is a scalar value, while velocity is a vector. Speed is measured in m/s and km/hr

speed = distance / time

distance = 3km

converting the time in seconds to hour,

time = 35 mins = 35/60 = 7/12 hr

speed = 3 ÷ 7/12

= 3× 12/7

= 36/7

= 5.14 km/hr

therefore the speed of the boy is 5.14 km/hr

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Answer:

If the house price is $250,000, then 1% of the appraised value is:

0.01 x $250,000 = $2,500

So Marisa can expect to pay $2,500 in annual property taxes.

Step-by-step explanation:

1. The finance charge on the loan is $9,920.

2. The total deferred payment price of the airplane is $39,120.

To find the finance charge on the loan, we need to first determine the amount financed. George Bell made a 15% down payment on the airplane, so the amount financed is:

= $29,200 - (0.15)($29,200)

= $29,200 - $4,380

= $24,820

The total amount of payments made over the life of the loan is:

= $579/month x 60 months

= $34,740

The finance charge on the loan is:

= $34,740 - $24,820

= $9,920.

The total deferred payment price of the airplane is the sum of the down payment and the total amount of payments made over the life of the loan. The down payment is 15% of the purchase price which is:

= 0.15 * $29,200

= $4,380

The total amount of payments made over the life of the loan is:

= $579/month * 60 months

= $34,740

The total deferred payment price of the airplane is:

= $4,380 + $34,740

= $39,120.

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To make the profit of $5000, the temperature should be 290 degrees Fahrenheit.

The general equation of a straight line is -

y = mx + c

where -

{m} is the slope of the line.

{c} is the {y} - intercept.

Given is a scatter plot as shown in the image.

We can write the equation of the line of best fit as -

{m} = (400 - 0/(60 - 40)

{m} = 400/20

{m} = 20

We can write the y - intercept as -

y = 20x + c

0 = 800 + c

c = - 800

So, the equation of the line of best fit is -

y = 20x - 800

For {y} = 5000, we can write -

5000 + 800 = 20x

5800 = 20x

x = 5800/20

x = 290

Therefore, to make the profit of $5000, the temperature should be 290 degrees Fahrenheit.

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We are given the following system of equations:

y = (1/2)x + 4 ---(1)

x - y = 8 ---(2)

We can solve this system of equations by substitution method.

From equation (2), we have:

x - y = 8

Solving for x, we get:

x = y + 8

Substitute this value of x in equation (1):

y = (1/2)(y+8) + 4

Simplifying and solving for y, we get:

y = 2

Now, substitute this value of y back in equation (2) to find the value of x:

x - 2 = 8

x = 10

Therefore, the solution of the given system of equations is (x, y) = (10, 2).

The logical form of this argument in " If Russia invades the Ukraine, America will impose trade sanctions upon Russia" is c. Hypothetical Syllogism.

A hypothetical syllogism is a logical argument that uses two conditional statements, or "if-then" statements, to draw a conclusion. The general form of a hypothetical syllogism is:

If A is true, then B is true.

If B is true, then C is true.

Therefore, if A is true, then C is true.

Here's an example of a hypothetical syllogism:

If it rains, then the ground is wet.

If the ground is wet, then the grass is slippery.

Therefore, if it rains, then the grass is slippery.

Therefore, option C is correct.

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The principal amount of the loan is $1,200,000.

What is simple interest?

Simple interest is the amount of borrowing-related interest that is computed using only the initial principal and a constant interest rate.

To find the principal amount of a loan, we need to use the formula for simple interest:

I = Prt

Where I is the interest, P is the principal, r is the interest rate as a decimal, and t is the time in years.

In this case, we know that the interest is $3,150 and the interest rate is 10.5%. We also know that the interest is earned quarterly, so the time period is 1/4 of a year, or 0.25 years.

Substituting these values into the formula, we get:

3150 = P * 0.105 * 0.25

Solving for P, we get:

P = 3150 / (0.105 * 0.25) = $1,200,000

Therefore, the principal amount of the loan is $1,200,000.

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Answer: Without a visual representation of the triangles, it's difficult to determine whether the statements are true or false.

However, in general, the side lengths of a triangle determine its shape and size. If two triangles have the same side lengths, then they are congruent, meaning they have the same shape and size. Therefore, if the triangles in question have different side lengths for x = 16, x = 27, and x = 31, then it's possible that the statements are either true or false, depending on the specific side lengths.

Without additional information, it's not possible to determine whether the statements are true or false.

Step-by-step explanation:

oh my God cr7 ans messi are running

The probability of someone pulling 1-10 in consecutive order from a bad that contains 10 balls labelled 1-10 is 1/3628800.

An event's probability is a numerical representation of how likely it is that the event will take place. In mathematical notation, it is written as a number between 0 and 1, or as a percentage between 0% and 100%. The higher an event's probability, the more likely it is to occur.

In a sample space, there is a probability of 1 for each event. The probability formula states that the ratio between the number of favourable outcomes and the total number of outcomes determines the likelihood that an event will occur. Sets are used in the terminology of probability theory. A set is a grouping of various things.

It is said that there are 10 balls in a bag, labelled 1-10.

Now,

The number of ways the ball labelled 1 is picked is 1

The number of ways the ball labelled 2 is picked is 2

So the number of ways a ball labelled certain number is picked is 1.

Now there is no replacement.

So the total number of balls decreases by 1 when 1 ball is taken.

Then,

The probability of choosing the ball numbered 1 = 1/10

The probability of choosing 2 = 1/9

The probability of choosing 3 = 1/8

.

.

.

the probability of choosing 10 = 1

Total probability of choosing the balls in consecutive order = 1/10 * 1/9 * 1/8 *.......* 1/2*1/1 = 1/10! = 1/3628800.

Therefore the probability of someone pulling 1-10 in consecutive order from a bad that contains 10 balls labelled 1-10 is 1/3628800.

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