Pls help
Am not very good at this​

The solution for the given equation √2x - 7 = 1 is  extraneous .

Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Solve for x , √2x - 7 = 1

1x − 2+1x + 2=4(x − 2)(x + 2) .

1x − 2+1x + 2=4(x − 2)(x + 2)

(x − 2)(x + 2)(x − 2)+(x − 2)(x + 2)(x + 2)=4(x − 2)(x + 2)(x − 2)(x + 2)

(x−2)+(x+2)=4

2x=4

x=2

However, since division by zero is prohibited, the number 2 is not included in the range of the original equation because it would reduce one of the fractions' denominators to zero.

As a result, it can't be one of the roots of the initial equation.

2 is therefore an erroneous solution. As a result, the equation has no answers.

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The solution to the equation is x = -1.

The given equation is log6(x + 4) + log6(x + 3) = 1. Using the logarithmic identity logb(x) + logb(y) = logb(xy), we can simplify the given equation to log6((x + 4)(x + 3)) = 1. Now we can write the equation as 6¹ = (x + 4)(x + 3). Simplifying further, we get x² + 7x + 12 = 6.

Therefore, x² + 7x + 6 = 0.

Factoring the equation, we get:

(x + 6)(x + 1) = 0.

So, the solutions are x = -6 and x = -1. However, we need to check the solutions to ensure that they are valid. If x = -6, then log6(-6 + 4) and log6(-6 + 3) are not defined, which is not a valid solution. If x = -1, then we get:

log6(3) + log6(2) = 1,

which is true.

Therefore, the solution to the equation is x = -1.

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Answer:

1/6 of the bread

Step-by-step explanation:

Given data

Let the amount of the loaf of bread be 1

But they are expected to share half

hence the amount to be shared is= 1/2 bread

The number of children is 3

Hence

=1/2/3

=1/2*1/3

=1/6 bread

Hence each child will get 1/6 of the bread

The average velocity of Gwen over the time interval 0 < t is zero. We need to solve the equation:250sin(πt/45) = 0Solving for t, we get:πt/45 = nπwhere n is an integer.

Given that Gwen runs back and forth along a straight track and her velocity, in feet per second, is modeled by the function v(t) during the time interval 0 < t < 45 seconds; We are to determine the first time at which Gwen changes direction and find her average velocity over the time interval 0 < t.Firstly, we know that velocity is a vector quantity and has both magnitude and direction.

Since she is running back and forth along a straight track, her displacement at any given time t is given by the function s(t), which is the integral of her velocity function v(t).That is, s(t) = ∫v(t)dtWe can find the displacement by taking the definite integral of v(t) from 0 to t. Since Gwen is running back and forth, her displacement will be zero at the times when she changes direction.

Therefore, we need to solve the equation:250sin(πt/45) = 0Solving for t, we get:πt/45 = nπwhere n is an integer. Therefore,t = 45n/πwhere n is an integer. Since we are looking for the first time at which Gwen changes direction, we need to take the smallest positive value of n, which is n = 1.

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The person will have to place the compasses 6 feet away from the point they want the arch to start, and draw the arch with a radius of 9 feet.

The radius of the arch is 9 feet.

The formula for calculating the radius of an arch is \(R = (width / 2) / sin(90°)\).

Therefore, the radius of the arch is:

R = (18 ft / 2) / sin(90°) = 9 ft

To calculate the radius of the arch he needs to draw, the person can use the formula R = (width / 2) / sin(90°). In this case, the width of the arch is 18 feet, so the radius of the arch is 9 feet, calculated as R = (18 ft / 2) / sin(90°). The person will have to place the compasses 6 feet away from the point they want the arch to start, and draw the arch with a radius of 9 feet.

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Answer:

b on edge 2020

Step-by-step explanation:

The probability of the event occuring is 29/51

When we talk about probability, we are essentially trying to measure the likelihood of an event occurring. One way to do this is by using the ratio of the number of favorable outcomes to the total number of outcomes.

In this case, the odds for a certain event are given as 29 to 22. This means that for every 29 favorable outcomes, there are 22 unfavorable outcomes. So, the total number of outcomes can be calculated as the sum of the favorable and unfavorable outcomes, which is 29 + 22 = 51.

To calculate the probability of the event occurring, we need to divide the number of favorable outcomes by the total number of outcomes. In this case, the number of favorable outcomes is 29, so the probability can be calculated as:

Probability = 29 / 51

This can be simplified by dividing both the numerator and denominator by the greatest common factor, which is 1 in this case. So the final answer is:

Probability = 29/51

This means that if we were to repeat the event many times, we would expect the event to occur approximately 29/51 or 56.86% of the time.

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Explanation is\(^{}\) in a file

bit.\(^{}\)ly/3gVQKw3

The store's expected profit from a random shipment of 500 pounds of oranges is approximately $400.88.

Here, we have,

To calculate the store's expected profit from a random shipment of 500 pounds of oranges, we need to consider the probabilities and prices associated with each quality category of oranges.

Let's break down the calculations step by step:

High Quality Oranges:

Probability: 40% of the time

Purchase price: $0.52 per pound

Selling price: $1.99 per pound

Expected profit per pound: $1.99 - $0.52 = $1.47

The expected profit from high-quality oranges per pound is $1.47.

To calculate the expected profit from high-quality oranges in the entire shipment, we multiply the expected profit per pound by the total weight of high-quality oranges:

Expected profit from high-quality oranges = 0.4 * $1.47 * (0.8 * 500) = $235.20

Low Quality Oranges:

Probability: 55% of the time

Purchase price: $0.52 per pound

Selling price: $1.49 per pound

Expected profit per pound: $1.49 - $0.52 = $0.97

The expected profit from low-quality oranges per pound is $0.97.

To calculate the expected profit from low-quality oranges in the entire shipment, we multiply the expected profit per pound by the total weight of low-quality oranges:

Expected profit from low-quality oranges = 0.55 * $0.97 * (0.65 * 500) = $165.68

Rotten Fruit:

Probability: 5% of the time

The store cannot sell any rotten fruit, so the expected profit from rotten fruit is $0.

Now, let's calculate the total expected profit from the entire shipment of oranges:

Total expected profit = Expected profit from high-quality oranges + Expected profit from low-quality oranges + Expected profit from rotten fruit

= $235.20 + $165.68 + $0

= $400.88

Therefore, the store's expected profit from a random shipment of 500 pounds of oranges is approximately $400.88.

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Answer:

The Lower Left Option

Step-by-step explanation:

The upper-left graph is neither increasing or decreasing, it's slope is infinite

The upper-right graph decreases, then increases slightly, and increases again

The last graph increases then decreases

======================================================

Explanation:

To get the 6th term, we multiply the fifth term by the common ratio

6th term = (fifth term)*(common ratio)

6th term = 162*3

6th term = 486

The 7th term is found by tripling 486, and so on.

To get the fourth term, we go in reverse of this process. We'll divide 162 by 3 to get 162/3 = 54

The third term is then going to be 54/3 = 18

The second term is 18/3 = 6

The first term is 6/3 = 2

-----------------------

Here's another way we can solve this question.

The nth term of a geometric sequence is a*(r)^(n-1)

We know that the common ratio is 3, so r = 3.

The 5th term is 162, meaning plugging n = 5 into that expression above leads to 162, so,

a*(r)^(n-1)

a*(3)^(n-1)

a*(3)^(5-1) = 162

a*(3)^4 = 162

a*81 = 162

81a = 162

a = 162/81

a = 2 is the first term

-----------------------

The first five terms of the geometric sequence are:

2, 6, 18, 54, 162

Each time we go from left to right, we're multiplying by 3. Going in reverse (right to left), we divide by 3.

Multiplying by 1/3 is the same as dividing by 3.

Answer: 1/6

Step-by-step explanation:

5/6 - 4/6 = 1/6

Answer:

1

-

6

Step-by-step explanation:

the contribution margin for the braised greens is $2.68.

The correct option is a. $2.68.

the contribution margin, we subtract the cost of goods sold (COGS) from the selling price. In this case, the cost of ingredients for the braised greens is $1.32, and the selling price is $4.

Contribution Margin = Selling Price - COGS

Contribution Margin = $4 - $1.32

Contribution Margin = $2.68

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Answer:

x < 10

set builder notation: (-∞ , 10)

Step-by-step explanation:

2(x - 4) < 12

multiply left side out:

2x - 8 < 12

add 8 to both sides:

2x - 8 + 8 < 12 + 8

2x < 20

divide both sides by 2:

2x/2 < 20/2

x < 10

in set builder notation: (-∞ , 10)

Yes, that is correct. The notation P(z < a) represents the probability that a standard normal distribution variable Z is less than a particular value "a".

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to happen. The probability of an event A is typically denoted as P(A) and is calculated as the number of ways that event A can occur divided by the total number of possible outcomes. Probability is used in a wide range of fields, including mathematics, statistics, physics, finance, and engineering.

what is statistics?

Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data. It includes a variety of methods for collecting data, such as surveys, experiments, and observational studies. Statistical methods are used to summarize and analyze the data, and to draw conclusions and make predictions about the population from which the data is sampled. The results of statistical analyses can be used in a variety of fields, including business, social sciences, natural sciences, and engineering.

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Answer:

Approximately 120.31 people per square mile

Step-by-step explanation:

1) The population density can be found by dividing the whole population over the area.

2) Since the NH map is modeled like this triangle, let's firstly calculate its area.

3) Based upon the original picture, and tracing it on we can easily see that the y coordinate is little bit over 200, precisely 220. Each mark on the original y-axis count as 20 miles. That'll give us the height.

The base of the triangle is 100 miles for F(100,0). Plugging that information on the formula:

\(\bigtriangleup_{area}=\frac{b*h}{2}\rightarrow \frac{220*100}{2}=11,000 \:sq. \:miles\)

4) The Population density:

\(Pop. \:density=\frac{1,323,459}{11,000}=120.31 \:people\:per\:square\:mile\)

Step-by-step explanation:

The answer:

147 persons/mi^2

Remember that using radical notation, fractionary exponents can be represented as follows:

On the other hand, when the index of a radical does not appear, we understand that it is equal to 2:

Rewrite each of the radical factors of the given expression using fractionary exponents:

To simplify the expression, use the following rule of exponents:

Then:

To simplify the expression, solve the addition with fractions:

Simplify the fraction 4/2 as 2/1:

The leas common denominator for these fractions is 5. Rewrite 2/1 as 10/5 and add the fractions:

Then:

Therefore, the final expression in rational form, is:

Answer: \(m=\frac{360^{\circ}}{n}\)

Step-by-step explanation:

This is a standard result.

The second option is the segment addition postulate.

The third option is the sum of the angles of a polygon with n sides.

The fourth option is the measure of each interior angle of a regular polygon with n sides.

The fifth option is the angle addition postulate.

According to the statement the distance from the plane to the top of the larger sphere is 3 + 2 = 5 units.

The distance from the plane to the top of the larger sphere can be found by considering the arrangement of the spheres.

We have three smaller spheres of radius 1 that are mutually tangent to each other and the plane.

On top of them, there is a larger sphere of radius 2.
Let's denote the distance from the plane to the center of the larger sphere as h.

Since the spheres are tangent to each other, the distance from the plane to the top of the larger sphere will be equal to the sum of the radii of the smaller spheres (3 x 1 = 3) plus the radius of the larger sphere (2).
Therefore, the distance from the plane to the top of the larger sphere is 3 + 2 = 5 units.

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The area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

To solve this problem, we can use the formula for the volume of a hexagonal prism:

V = (3√3/2) * a^2 * h

where V is the volume, a is the length of one side of the hexagonal base, and h is the height of the prism.

We are given that the height of the prism is 4 units and the volume is 98 units^3. Plugging these values into the formula, we can solve for the length of one side of the base:

98 = (3√3/2) * a^2 * 4
a^2 = 98 / (12√3)
a ≈ 2.95

Now that we know the length of one side of the base, we can find the area of the hexagon by using the formula:

A = (3√3/2) * a^2

where A is the area of one of the bases. Plugging in the value we found for a, we get:

A = (3√3/2) * (2.95)^2
A ≈ 7.39

Therefore, the area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

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ANSWER

EXPLANATION

We want to find the inverse of the function given:

f(x) = 12x - 3

First, replace f(x) with y:

y = 12x - 3

Now, make x the subject of the function:

y + 3 = 12x

Now, replace x with f-1(x) and y with x:

That is the inverse function.

Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

The given statement "if you try to match a slope and an intercept at the same time, their mistakes will be related" is TRUE.

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis.

This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y.

These points satisfy x = 0 because of this.

The errors of a slope and an intercept will be connected if you fit them simultaneously.

By changing Y to 0 in the equation and figuring out X, you can always determine the X-intercept.

Similarly, by putting X to 0 in the equation and solving for Y, you can always determine the Y-intercept.

Therefore, the given statement "if you try to match a slope and an intercept at the same time, their mistakes will be related" is TRUE.

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Answer:

D, -6 and -4 only​

Explanation:

Given the inequality:

First, subtract 3 from both sides:

Next, multiply both sides by -2.

Note that when inequality is multiplied by a negative number, the inequality sign is reversed.

Therefore, the values from the set (-6. -4, -3, -1, 0, 2) that satisfy this inequality are: -6 and -4 only​

Answer:( 3, 4)

Step-by-step explanation: :)

Answer:

d

Step-by-step explanation:

Here's a Python program that solves the simultaneous equations given the coefficients a, b, c, d, e, and f:

def solve_simultaneous_equations(a, b, c, d, e, f):

   determinant = a * e - b * d

   if determinant == 0:

       print("The equations have no unique solution.")

   else:

       x = (c * e - b * f) / determinant

       y = (a * f - c * d) / determinant

       print("The solutions are:")

       print("x =", x)

       print("y =", y)

# Accept coefficients from the user

a = float(input("Enter coefficient a: "))

b = float(input("Enter coefficient b: "))

c = float(input("Enter coefficient c: "))

d = float(input("Enter coefficient d: "))

e = float(input("Enter coefficient e: "))

f = float(input("Enter coefficient f: "))

# Solve the simultaneous equations

solve_simultaneous_equations(a, b, c, d, e, f)

```

In this program, the `solve_simultaneous_equations` function takes the coefficients `a`, `b`, `c`, `d`, `e`, and `f` as parameters. It first calculates the determinant of the coefficient matrix (`a * e - b * d`). If the determinant is zero, it means the equations have no unique solution. Otherwise, it proceeds to calculate the solutions `x` and `y` using the Cramer's rule:

```

x = (c * e - b * f) / determinant

y = (a * f - c * d) / determinant

```

Finally, the program prints the solutions `x` and `y`.

You can run this program and enter the coefficients `a`, `b`, `c`, `d`, `e`, and `f` when prompted to find the solutions `x` and `y` for the given simultaneous equations.

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It is not possible to determine the level of water in the tank using only the given information. To determine the level of water in the tank, we need to know either the height of the water column or the total pressure at the bottom of the tank, which includes the pressure due to the water column and the pressure due to the atmosphere.

Therefore, we can't fill the blank with any value since the problem does not provide any information regarding it. In order to find the level of water in the tank, we need to know either the height of the water column or the total pressure at the bottom of the tank, which includes the pressure due to the water column and the pressure due to the atmosphere.

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