For f(x) = 2x +1 and g(x) = x2-7, find (f/g)(x)

The function best models the data in the table is y=2.5x+5.

From the given table, the coordinate points are (-1, 2.5) and (0, 5).

Here, slope (m) = (5-2.5)/(0+1)

m = 2.5

Substitute m=2.5 and (x, y)=(0, 5) in y=mx+c, we get

5=2.5(0)+c

c=5

So, the equation is y=2.5x+5

Therefore, the function best models the data in the table is y=2.5x+5.

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Answer:

\(m=\frac{17}{37}\)

Step-by-step explanation:

When given two coordinates, you must use this formula to find the slope of a line:

\(m= \frac{y_{2} - y_{1}}{x_{2}-x{1}}\)

where m is your slope.

So, plug in your coordinates. Remember, a coordinate is denoted by (x,y). So, for example, your \(x_{1}\) would be -18 and your \(x_{2}\) would be 19.

\(m =\frac{4--13}{19--18}\)

\(m =\frac{17}{37}\)

And that would be your slope. (Answer choice D.)

There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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Answer:

$37.5

Step-by-step explanation:

30 = 0.8x

x = $37.5

Answer:

Brace girders

As a horizontal link between foundations or pile heads, the braces are dimensioned with the relationship between free span and the height of the beam, L / h <10, preferably 7, but the height should not be less than 40 cm.

Answer:

1/3 + n

Step-by-step explanation:

Let "n" be any number. Keep in mind that plus means addition.

1/3 + n

Best of Luck!

Answer:

n + 1/3n

Step-by-step explanation:

Andrea should plan to spend 4.2 hours walking back.

Let's start by finding the total distance Andrea runs. Since she runs the full distance of the race and then walks back the same distance, the total distance she covers is twice the race distance.

Let D be the race distance. Therefore, the total distance Andrea covers is 2D.

Next, we can use the formula:

time = distance / speed

The time it takes for Andrea to run the race distance at a speed of 7mph is:

time to run = D / 7

Similarly, the time it takes for Andrea to walk back the same distance at a speed of 3mph is:

time to walk = D\3

The total time Andrea spends training is 6 hours, so we can write:

time to run + time to walk = 6

Substituting the expressions for time to run and time to walk, we get:

D / 7 + D / 3 = 6

We can simplify this equation by finding a common denominator for the fractions:

(3D + 7D) / (3 × 7) = 6

10D / 21 = 6

Multiplying both sides by 21:

10D = 126

D = 12.6 miles

Now that we know the race distance, we can find the time it takes Andrea to walk back:

time to walk = D / 3 = 12.6 / 3 = 4.2 hours

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Probability that a coin pulled at random from the jar will not be a dime or penny is 20 or 13.

Given that,

6 quarters, 3 dimes, 4 nickels, and 10 pennies are included in the jar.

We have to find what is the probability that a coin pulled at random from the jar won't be a dime or a penny.

We know that,

6 quarters, 3 dimes, 4 nickels, and 10 pennies are included in the jar.

6+3+4+10 =23

Probability that a coin pulled at random from the jar will not be a dime is 23-3=20

Probability that a coin pulled at random from the jar will not be a penny is 23-10=13

Therefore, Probability that a coin pulled at random from the jar will not be a dime or penny is 20 or 13.

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Answer:

Step-by-step explanation:

Answer:

Mean: 6.6

Mode: 5

Median: 5.5

Answer:

c

Step-by-step explanation:

hope this hellpppeedd

He also added lettuce, tomatoes, and cheese. Kenneth also made sure to put plenty of condiments like mayonnaise and mustard on each sandwich.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.


Kenneth's family was excited to get to the beach. When they arrived, they set up their umbrellas and beach chairs and found a spot to settle down. After they were all settled, Kenneth passed out the sandwiches he had made. Everyone was satisfied with the delicious sandwiches Kenneth had created.

Kenneth's family enjoyed their day at the beach. They swam in the ocean, built sandcastles, and played volleyball. They even laid out and got a nice tan. As the day got hotter, Kenneth's family got hungrier. Fortunately, they still had the sandwiches Kenneth had made. Everyone was thankful for the delicious sandwiches that Kenneth had prepared for them.

After a fun day at the beach, Kenneth's family packed up their things and headed home. Kenneth was happy that he could provide for his family and make their day even better. He was grateful for the opportunity to make the sandwiches for his family and make their day at the beach even more enjoyable.

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Answer:

-11

Step-by-step explanation:

9+35=44. 34+21=55. - each other=-11

Answer:

can u plz rewrite the question

Answer:

I think it’s 56

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ralph reads 7 pages. Lily reads 8 times as Ralph reads.

Lily reads 7*8=56 pages.

C.) right and isosceles, but not equilateral

Answer:

C.) right and isosceles, but not equilateral

Step-by-step explanation:

Step-by-step explanation:

Bagong balita tungkol sa corona virus 19 sa Pilipinas, Ayon sa WHO at DOH mayroong 2.5M na vaccine na ang pinangangasiwaan ang Pilipinas at naitala ring mayroon ng 2.02M ang na bakunahan na indibiduwal.

Answer: The diagram shows a rectangle.

Step-by-step explanation:

A rectangle Expression for "a": a = 12b - 30,Expression for "b": b = (12b² - 30b) / (12b - 30),Length of the rectangle: Length = a = 12b - 30,Perimeter of the rectangle: Perimeter = 2 × (13b - 30)

Let's break down the given information step by step:

The area of the rectangle is given as 12b² - 30b.

The expression for "a":

The area of a rectangle is equal to its length (a) multiplied by its width (b). So, set up the following equation:

Area = Length ×Width

12b² - 30b = a × b

To find the expression for "a," divide both sides of the equation by "b":

a = (12b² - 30b) / b

Simplify the expression for "a":

a = 12b - 30

The expression for "b":

From the same equation as above,  that:

Area = Length × Width

12b² - 30b = a × b

To find the expression for "b," divide both sides of the equation by "a":

b = (12b² - 30b) / a

Substitute the value of "a" from the previous expression:

b = (12b² - 30b) / (12b - 30)

The length of the rectangle:

The length of the rectangle is represented by "a," so the expression for the length is: a = 12b - 30

The perimeter of the rectangle:

The perimeter of a rectangle is given by the formula: Perimeter = 2 ×(Length + Width)

Since the rectangle has two pairs of equal sides (opposite sides are equal in a rectangle), the expression for the perimeter will be:

Perimeter = 2 × (a + b)

Substitute the value of "a" from the expression we found earlier:

Perimeter = 2 × ((12b - 30) + b)

Simplify the expression for the perimeter:

Perimeter = 2 ×(13b - 30)

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the general solution of the differential equation is given by cos y = C√(x^2 + 1) The correct option is (d) None of these.

We are given the differential equation:

(x^2 + 1) tan y dy/dx = x

We can solve this equation by separation of variables. We begin by multiplying both sides by dx/tan y:

(x^2 + 1) dy/tan y = x dx

Next, we can use the substitution u = x^2 + 1, which implies du/dx = 2x:

dy/tan y = (x du)/(2u - 2)

We can separate the variables as follows:

(tan y) dy = (x du)/(2u - 2)

We can integrate both sides:

∫(tan y) dy = (1/2)∫(x du)/(u - 1)

Using the substitution v = u - 1, which implies du = dv, we get:

∫(tan y) dy = (1/2)∫x dv/v

Integrating the right-hand side using ln |v| as the antiderivative, we get:

∫(tan y) dy = (1/2) ln |v| + C

Substituting back for v, we get:

∫(tan y) dy = (1/2) ln |u - 1| + C

Substituting back for u and simplifying, we get:

∫(tan y) dy = (1/2) ln |x^2 + 1| + C

Integrating the left-hand side using ln |cos y| as the antiderivative, we get:

ln |cos y| = (1/2) ln |x^2 + 1| + C

Simplifying and exponentiating both sides, we get:

cos y = ±C√(x^2 + 1)

Therefore, the general solution of the differential equation is given by:

cos y = C√(x^2 + 1)

where C is an arbitrary constant. Hence, the correct option is (d) None of these.

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The solution to the given system of linear equations using the five methods is x₁ = -2, x₂ = -1, and x₃ = -4.

Here is the step-by-step explanation using each method:

1. Gaussian Elimination:

  - Rewrite the system in matrix form: [2 -6 -1; -8 1 -2] * [x₁; x₂; x₃] = [-38; -20].

  - Perform row operations to eliminate variables: Row₂ = Row₂ + 4 * Row₁

2. Gauss-Jordan Elimination:

  - Augment the coefficient matrix with the column vector of constants.

  - The rightmost column will contain the solutions x₁, x₂, and x₃.

3. LU Factorization:

  - Decompose the coefficient matrix A into LU form, where L is a lower triangular matrix and U is an upper triangular matrix.

  - Solve Lc = b, where c is a vector containing intermediate solutions.

  - Solve Ux = c to obtain the final solution.

4. Inverse Matrix:

  - Rewrite the system in matrix form: AX = B, where A is the coefficient matrix, X is the vector of variables, and B is the vector of constants.

  - Find the inverse matrix A⁻¹.

  - Multiply both sides of the equation by A⁻¹ to obtain X = A⁻¹B.

5. Cramer's Rule:

  - Divide the determinant of the modified A by the determinant of A to find x₁.

  - Repeat the process for x₂ and x₃, replacing the respective columns of A with B.

Note: Due to the limited word count, the step-by-step explanations provided here may not be comprehensive. It's recommended to consult a textbook or online resources for detailed instructions on each method.

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Answer:

Hey!

Your Answer Is,

No Triangles: A, C

One Triangle, F, D

Many Triangles: B,E

I hope this helps you!

Step-by-step explanation:

To find ANOVA df: find N to get dftotal=N-1, calculate Ybar and group means to get dfbetween=k-1, and use dfwithin=N-k. Without Ybar1, Ybar2, and Ybar3, only dftotal and dfwithin can be calculated.

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The statement is proven true by induction: for any positive integer n, the sum of (2i - 1)³ from i = 1 to n is equal to n²(2n² - 1).

To prove the statement using mathematical induction, we need to establish two conditions: the base case and the inductive step.

Base Case:

Let's start with the base case, where n = 1.

When n = 1, we have p₁ ∑ (2i - 1)³ = 1³ = 1.

On the right-hand side, we have 1 * (2 * 1² - 1) = 1.

Since the statement holds true for n = 1, the base case is satisfied.

Inductive Step:

Next, we assume that the statement holds true for some positive integer k, i.e., pₖ ∑ (2i - 1)³ = k²(2k² - 1).

Now, we need to prove that the statement also holds for n = k + 1, i.e., pₖ₊₁ ∑ (2i - 1)³ = (k + 1)²(2(k + 1)² - 1).

Starting with the left-hand side:

pₖ₊₁ ∑ (2i - 1)³ = (pₖ ∑ (2i - 1)³) + (2(k + 1) - 1)³

                 = k²(2k² - 1) + (2k + 1)³ (using the inductive hypothesis)

                 = 2k⁴ - k² + 8k³ + 12k² + 6k + 1

Simplifying the right-hand side:

(k + 1)²(2(k + 1)² - 1) = (k² + 2k + 1)(2k² + 4k + 2 - 1)

                         = 2k⁴ + 4k³ + 2k² + 4k³ + 8k² + 4k + 2k² + 4k + 2 - k² - 2k - 1

                         = 2k⁴ + 8k³ + 12k² + 6k + 1

Comparing the left-hand side and right-hand side, we can see that they are equal.

Therefore, by the principle of mathematical induction, the statement is proven true for all positive integers n.

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Answer:

Step-by-step explanation:

the x-axis really runs left and right, and the _y-axis_  runs up and down.

Answer:

4. h=9in

5. 150.8\(m^{2}\)

6. 301.6\(in^{2}\)

Step-by-step explanation:

4.

Surface area of a rectangular prism form : A=2(wl+hl+hw)

Substitute in values from the question: 558=2[(9)(11)+h(11)+h(9)]

Multiply where applicable: 558=2[(99)+11h+9h]

Combine like terms: 558=2[(99)+20h]

Divide both sides by 2: 279=(99)+20h

*note- This step can also be seen as multiplying the right side by 2 without messing with the left at all (558=(198)+40h) then you would solve in the same fashion as I will from here just with the alternative numbering*

Subtract to isolate the h: 180=20h

Divide both sides to isolate the h: 9=h

Now we see that the missing dimension h=9in

*note- I did not bold the equations with squares so please don't be confused by that*

5.

Surface area of a cylinder form: A=2πrh+2π\(r^{2}\)

Substitute in values from the question: A=2π(3)(5)+2π\(3^{2}\)

Multiply were applicable: A≈94.2+56.5

Add remaining values: A≈150.8

Now we see that the total surface area is 150.8\(m^{2}\)

*note- whenever we solve for volume or SA of a figure we square the unit (\(m\)➞\(m^{2}\))*

6.

Surface area of a cylinder form: A=2πrh+2π\(r^{2}\)

Substitute in values from the question: A=2π(6)(2)+2π\(6^{2}\)

*note- we use 6 instead of the given value 12 because the equation calls for the radius and not the diameter*

Multiply were applicable: A≈75.2+226.2

Add remaining values: A≈301.6

Now we see that the total surface area is 301.6\(in^{2}\)

*note- whenever we solve for volume or SA of a figure we square the unit (\(in\)➞\(in^{2}\))*

Hope this helps :)

The probability that X=5 is 0.16. This is calculated by looking at the probability distribution table, which shows that the probability of X=5 is 0.16.

To find the probability of X=5, we first look at the discrete probability distribution given. This tells us the probability of each of the possible values that X can take on. In this case, there are four possible values (0, 1, 2, and 5). We can see that the probability of X=5 is 0.16.

In general, when given a discrete probability distribution, we can calculate the probability of any event (such as X=5) by looking at the probabilities listed in the table. All we need to do is find the value we are looking for (in this case, 5) and then look at the corresponding probability listed in the table.

It is important to note that when dealing with discrete probability distributions, the probabilities must always add up to 1. In this example, we can verify that the probabilities add up to 1 (0.25 + 0.16 + 0.08 = 0.49, which is equal to 1).

In conclusion, the probability that X=5 is 0.16. This was found by looking at the given discrete probability distribution table.

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The measure of angles:

∠S = 72

∠Q = 72

∠R = 180

In the given trapezium

∠P  = 108 degree

We know that for a trapezium,

The sum of the angles of two adjacent sides = 180°.

Therefore,

∠S + 108 = 180

⇒       ∠S = 72 degree

And

∠Q + 108 = 180

⇒        ∠Q = 72 degree

Now.

  ∠S + ∠R = 108

⇒ 72 + ∠R = 180

⇒         ∠R = 108 degree

Hence,

∠S = 72

∠Q = 72

∠R = 180

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