Write the following as an algebraic expression. Simplify if possible.
Add 9x - 8 to 4x - 1.

The required reverse Euclidean algorithm is the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

Given that (5*x) mod 91 =32.

To solve the modular equation (5*x) mod 91 =32 using reverse Euclidean algorithm is to find the modular inverse of 5 modulo 91.

Consider  (5*x) mod 91 =32.

5x = 32(mod 91)

Apply the Euclidean algorithm to find GCD of 5 and 91 is

91 = 18 * 5 + 1.

Rewrite it in congruence form,

1 = 91 - 18 *5

On simplifying the equation,

1 = 91 (mod 5)

The modular inverse of 5 modulo 91 is 18.

Multiply equation by 18 on both sides,

90x = 576 (mod91)

To obtain the smallest positive  solution,

91:576 = 6 (mod 91)

Divide both sides by the coefficient of x:

x = 6 * 90^(-1).

Apply the Euclidean algorithm,

91 = 1*90 + 1.

Simplify the equation,

1 + 1 mod (90)

The modular inverse of 90 modulo 91 is 1.

Substitute the modular inverse in the given question gives,

x = 6*1(mod 91)

x= 6 (mod91)

Therefore, the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

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Answer:

b = 21 ft is the answer.

Step-by-step explanation:

a = 28 ft

b = ?

c = 35 ft

According to the Pythagoras theorem,

a² + b² = c²

28² + b² = 35²

784 + b² = 1225

b² = 1225 - 784

b² = 441

b = 21 ft

∴ b = 21 ft is the length of the missing leg.

The situation Veronica receives $21 for babysitting, and then spends the same amount, $21, on a new shirt quantities combine to make 0.The correct answer is option C.

When we add +21 (the money she receives) and subtract -21 (the money she spends), the result is 0. This means that the net change in Veronica's money is zero, indicating that the quantities combine to make 0.

In situations A, B, and D, the quantities do not combine to make 0. In situation A, the player earns 4 points for getting an answer right and then earns an additional 4 points for making it around the board.

The total points earned in this situation would be 8, which is not equal to 0.

In situation B, the car is initially filled with 10 gallons of gas, but then half of that, which is 5 gallons, is used on a day's drive. The remaining fuel in the car would be 5 gallons, which is also not equal to 0.

In situation D, the bird flies 25 feet up in the air and then 25 feet across to its nest. The total distance traveled by the bird would be 50 feet, which is not equal to 0.

Therefore, only in situation C, where Veronica receives and spends the same amount of money, do the quantities combine to make 0.

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The probable question may be:

In which of these situations do the quantities combine to make 0?

A. A player a game earns 4 points for getting an answer right. She then earns 4 points for making it around the board.

B. A car is filled with 10 gallons of gas. Half of the 10 gallons are then used on a day's drive.

C. Veronica receives $21 for babysitting. She then spends $21 on a new shirt.

D. A bird flies 25 feet up in the air. It then flies 25 feet across to its nest.

Answer:

46 boxes

Step-by-step explanation:

1012 / 22 = 46

D 231 = 46w can be used to solve for w, the number of white eggs used last week.

Let f(x) = -5x – 1 and g(x)=x2- 3.

Find (fog)(1).

Remember that

(fog)(x)=f(g(x))

so

f(g(x))=-5(x^2-3)-1

(fog)(1).=f(g(1))=-5(1^2-3)-1=-5(-2)-1=9

therefore

f(g(x)

Answer:

The ratio for the first print job is 150/30 = 5 pages per second.

The ratio for the second print job is 130/20 = 6.5 pages per second.

Since the ratios are different, the data do not represent a proportional relationship. In a proportional relationship, the ratio between two variables remains constant.

Step-by-step explanation:

Answer:

y=4

Step-by-step explanation:

5x4=20

20x4=80

80x4=320

and so on

Answer:

y = 5 * 4^x

Step-by-step explanation:

For each iteration of x, the output of y is increased by a multiple of 4.

So we can write the equation y = 5*4^x

Cheers.

Rita worked for 2 1/2 hours more during the second week

The first step is to write out the parameters given in the question

Rita works 12 3/4 hours in her first week at a new job

She works 15 1/4 hours in the second week

The number of hours that she worked longer during the second week can be calculated by subtracting the number of hours worked in the second week from the number of hours worked during the first week of the job

= 15 1/4 - 12 3/4

= 61/4 - 51/4

= 10/4

= 5/2

= 2 1/2

Hence Rita worked  2 1/2 hours longer during the second week

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Answer: :P

Step-by-step explanation:

Answer: 3.14159

Step-by-step explanation:

something

The true expression about the account is D.) It is the sum of the initial amount and the additional amount after d days.

The answer is D because it represents the sum of the initial amount and the additional amount after d days. The initial amount is $10 and Owen adds $0.50 to the account each day for a number of days, represented by d.

By subtracting 1 from d, the expression ensures that on the first day (when d=1), only the initial $10 is counted. On each subsequent day, the additional amount of $0.50 is added to the total. Therefore, the expression 10+0.5(d−1) gives the amount of money in Owen's account after d days.

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The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.

(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.

There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.

Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.

(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:

⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Recall that (a-b)(a+b) = a^2 - b^2

So,

(x-2i)(x+2i) = x^2 - (2i)^2 = x^2+4

(x+i-i)(x+1+i) = (x+1)^2 + 1 = x^2 + 2x + 2

(x-2+2i)(x-2-2i) = (x-2)^2 + 4 = x^2 - 4x + 8

According to the question there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.

A website is a collection of related web pages, images, videos, and other digital assets that are hosted on a web server and can be accessed by users over the internet. A website is typically identified by a unique domain name and can be accessed by typing the URL into a web browser.

Using the formula for calculating the number of combinations of size k from a set of size n (n choose k), we can calculate the number of distinct website graphics that can be created by using at least four of seven different bitmap images as follows:

n = 7 (7 different bitmap images)
k = 4 (at least 4 of the 7 bitmap images)
Number of distinct website graphics = (7 choose 4) = 35
Therefore, there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.

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The values of f(0) that can be read from (a similar question in part (a) and (c)) the table, functions, and graph in the question are;

(a) f(0) = 1

(b) f(0) = 12

(c) f(0) = -2

Part of the question appears missing. From a similar question online, we have;

(a) A table of values;

x: -1, 0, 1, 2, 3

y: 7, 1, 6, -3, -4

Taking the function, f(x) = y, we have;

From the above values in the table, when x = 0, y = f(0) = 1

Therefore;

(b) y = 12 - 2•x²

Taking the function, f(x) = y, we have;

At x = 0, y = f(0) = 12 - 2 × 0² = 12

Therefore;

(c) A graph of a parabola passing through the points (-1, 3), (2, -6), (5, 3)

Let f(x) = a•x² + b•x + c, represent the function, we have;

f(-1) = 3 = a•(-1)² + b•(-1) + c = a - b + c

f(2) = -6 = a•(2)² + b•(2) + c = 4•a + 2•b + c

f(5) = 3 = a•(5)² + b•(5) + c = 25•a + 5•b + c

Solving the system of linear equations, (1), (2), (3) using a graphing calculator gives;

a = 1, b = -4, c = -2

Which gives;

f(x) = x² - 4•x - 2

Therefore;

f(0) = 0² + 4×0 - 2 = -2

Which gives;

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Answer:

x = 67

y = 169

Step-by-step explanation:

We know that (x-1) + 52 + (y-7) = 180 because they're all on the same straight line. We also know that x-1 = 66, because they are alternate interior angles.

Solve for x:

x-1 = 66

x = 67

Now solve for y:

(67-1) + 52 + (y-7) = 180

y = 169

The profit will be $181.25 if the price is $40 for the given quadratic function.

To find the profit, you need to determine the value of x that gives the maximum profit. To do this, you can use the formula for the vertex of a quadratic function.

The vertex form of a quadratic function is given by:

f(x) = a(x - h)²+ k

where (h, k) is the vertex of the parabola.

As per the question, the quadratic function is given by:

f(x) = (x - 34)(61 - x)

To put this function in vertex form, you can expand the product and rearrange the terms to get:

f(x) = x² - 95x + 2214

Comparing this to the general form of a quadratic function, we can see that a = 1, h = 95/2, and k = 2214.

Therefore, the vertex of the parabola is (47.5, 2214). This is the point at which the profit is maximized.

To find the profit at this point, you just need to substitute x = 47.5 into the original function:

f(47.5) = (47.5 - 34)(61 - 47.5) = 13.5 x 13.5 = 181.25

Thus, the maximum profit is $181.25.

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The domain and range of the given piecewise function are (-∞, ∞) and [-10, ∞) respectively.

Given a function shown in the graph.

We have to find the domain and the range of the function.

Domain is the set of all x values for which the  function is defined.

Range is the set of all the y values for the x values in the domain.

Here the function is quadratic.

The function is defined for all the real numbers.

Domain is thus (-∞, ∞).

y values ranges down from ∞ to -10 and then again goes up to ∞.

So range = [-10, ∞)

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This set {σ ∈ S4 : σ(1) = 3} contains the following elements of S4: (13), (23), (34), (24), (14), (12)(34), (13)(24), (14)(23) and  {σ ∈ S4 : σ(2) = 2} this set contains the following elements of S4: (12), (21), (13)(24), (24)(13).

The group S4 is the symmetric group on 4 elements and has 24 elements. We can list all of its subgroups as follows:

Now, let's consider the sets (a) and (b) and see if they are subgroups of S4:

(a) {σ ∈ S4 : σ(1) = 3}

This set contains the following elements of S4: (13), (23), (34), (24), (14), (12)(34), (13)(24), (14)(23). We can check that this set is not a subgroup of S4 because it is not closed under composition. For example, (13)(14) = (134) is not in the set.

(b) {σ ∈ S4 : σ(2) = 2}

This set contains the following elements of S4: (12), (21), (13)(24), (24)(13). We can check that this set is a subgroup of S4. It is closed under composition, inverses, and contains the identity element e. Therefore, it is a subgroup of S4 and is isomorphic to the cyclic group of order 2.

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Answer:

≈ 404.6666667

Step-by-step explanation:

70 - 8 ÷ 6 + 8 x 42

70 - 1.33333333 + 8 x 42

70 - 1.33333333 + 336

68.6666667 + 336

404.6666667

A statement that describes the median of a triangle include the following: A. a segment drawn from a vertex to the midpoint of the opposite side.

In Mathematics and Geometry, a triangle is a two-dimensional geometric shape that comprises three sides, three vertices and three angles only.

In Mathematics and Geometry, the median of a triangle can be defined as a line segment with end points that is typically drawn from a vertex to the midpoint of the opposite side of the triangle.

In this context, we can logically deduce that a line segment with end points at the vertex and the midpoint of the triangle's opposite side simply refers to the median of a triangle.

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The solution for this inequality x is x ≤ 256 and x ≥ -128

This inequality can be resolved by multiplying x by 256 and by -128. We must first isolate x on one side of the inequality before we can solve for it. In this situation, 3(1/4)x1 192.

We can start by making the expression on the inequality's left side simpler:

3(1/4)x = (3/4)x

We can now take away 1 from both sides:

(3/4)

x -1 ≤ 192-1\s(3/4)x ≤ 191

Now we may divide both sides by (191*4/3) x (3/4), which is 256.

Now we also need to think about the opposite answer to x. We also need to determine the answer when the inequality is flipped and the sign is "greater than or equal to" x -(191*4/3) = -128

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Answer:

multipicton of -x on both sides

Step-by-step explanation:

Answer: 3y + 10z - 13

Step-by-step explanation:

Answer:

10^4

Step-by-step explanation:

Answer:

12/15

Step-by-step explanation:

3x5=15

4x3=12

15-12=3

Therefore the answer is 12 over 15

Answer:She can use these 120 pounds of flour for 30 months, if that's what you are asking.

Step-by-step explanation:  

120÷4=30