Factor the trinomial. Factor out the GCF first.
11x^2 + 33x + 22

Answer:

B

Step-by-step explanation:

Took the test edge2021

The function g(x) = 4(x + 3)² - 68 is the function which is mapped to 32 at x = 2 option (B) g(x) = 4(x + 3)² - 68 is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

A function which is at x = 2 mapped to 32

The above statement means that at x = 2

The value of the function will be 32

The given functions:

f(x) = -3x² - 4

Plug x = 2

f(2) = -3(2)² - 4

f(2) = -16

g(x) = 4(x + 3)² - 68

Plug x =2

g(2) = 4(2 + 3)² - 68

g(2) = 100 - 68

g(2) = 32

Thus, the function g(x) = 4(x + 3)² - 68 is the function which is mapped to 32 at x = 2 option (B) g(x) = 4(x + 3)² - 68 is correct.

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The peak of the mountain has a height of 14805 feet.

In this problem we find the case of an exponential function for atmospheric pressure (p), in pounds per square inch, in terms of height (x), in miles, whose expression is introduced below:

\(p(x) = 14.7 \cdot e^{- 0.21\cdot x}\), for x ≥ 0.

If we know that p(x) = 8.164 lb / in², then the height of the peak of a mountain is:

\(8.164 = 14.7\cdot e^{-0.21 \cdot x}\)

\(0.555 = e^{-0.21\cdot x}\)

Then, by relationship between exponential and logarithmic functions and logarithm properties:

㏑ 0.555 = - 0.21 · x · ㏑ 1

㏑ 0.555 = - 0.21 · x

x = - (1 / 0.21) · ㏑ 0.555

x ≈ 2.804

Finally, convert miles into feet:

x = 2.804 mi × (5,280 ft / 1 mi)

x = 14805.12 ft

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The slope of a line is positive with a value of 3/2 or 1.5.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

The slope of a line is used to describe the steepness and direction of the line.

Mathematically, the formula for the slope of a line is given as;

slope = Δy / Δx

where;

The slope equation is expanded as follows;

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

From the graph, the values of x and y is determined as;

( x₁, y₁ ) = ( - 2, 0 )

( x₂, y₂) = ( 0, 3 )

The slope of the line is calculated as follows;

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 3 - 0 ) / ( 0 - - 2)

m = 3 / 2

m = 1.5

Thus, the line has a positive slope.

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The complete question is below:

What is the slope of the line? type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Answer:

-600

Step-by-step explanation:

-3 x 2 is -6

then add the zeros

The graph which best represents the new function is: Y. a linear function on a coordinate plane that passes through (1, 3), (0, 0), and (-1, -3).

First of all, we would determine the slope of the linear function as follows:

\(Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\\\\Slope, m = \frac{2\;-\;3}{0\;-\;(-3)}\)

Slope, m = -⅓.

Multiplying by -9, the new slope is:

Slope = -⅓ × -9

Slope = 3.

For the equation of this line, we have:

y - y₁ = m(x - x₁)

y - 3 = -⅓(x - (-3))

y - 3 = -⅓x - 1

y = -⅓x - 1 + 3

y = -⅓x + 2

Increasing the y-value by 2, we have:

y + 2= -⅓x + 2

y = -⅓x + 2 - 2

y = -⅓x.

Therefore, we would have a linear function on a coordinate plane that passes through (1, 3), (0, 0), and (-1, -3).

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Answer

Options A and C are correct.

The triangle is a Scalen triangle and it is also an Acute triangle.

Explanation

To answer this question, we first explain what these type of triangles are

According to side lengths,

- Scalene triangle has none of its three sides having the same length as another. All the three sides have different lengths. To use angle to know this, all the three angles of a Scalene triangle have different values.

- Isoscelles triangle has two of its sides with the same lengths. In terms of angles, an Isoscelles triangle has two of its angles equal to each other.

- Equilateral triangle has all of its sides equal to one another. In terms of angles, all of the angles of an Equilateral triangle are equal to one another. Each of the angle is equal to 60°.

According to the angles,

- Acute triangle has all of the angles in the triangle being less than 90 degrees.

- Right angle triangle has one of the angles in the triangles being equal to 90 degrees.

- Obtuse triangle has one of the angles in the triangle being greater than 90 degrees but obviously less than 180 degrees.

For this triangle,

We can see that all of its sides have different lengths. Hence, the triangle is a Scalene triangle.

Also, each of the angles of the triangle is less than 90 degrees. Hence, the triangle is an Acute triangle.

Hope this Helps!!!

Answer:

\(f''(x)=36x^2+4\)

Step-by-step explanation:

Let's start by finding the first derivative of \(f(x)= 3x^4+2x^2-8x+4\). We can do so by using the power rule for derivatives.

The power rule states that:

This means that if you are taking the derivative of a function with powers, you can bring the power down and multiply it with the coefficient, then reduce the power by 1.

Another rule that we need to note is that the derivative of a constant is 0.

Let's apply the power rule to the function f(x).

Bring the exponent down and multiply it with the coefficient. Then, reduce the power by 1.

Simplify the equation.

Now, this is only the first derivative of the function f(x). Let's find the second derivative by applying the power rule once again, but this time to the first derivative, f'(x).

Simplify the equation.

Therefore, this is the 2nd derivative of the function f(x).

We can say that: \(f''(x)=36x^2+4\)

Answer:

\(y = f(x) = 3 {x}^{4} + 2 {x}^{2} - 8x + 4 \\ \frac{dy}{dx} = 12 {x}^{3} + 4x - 8 \\ \frac{d {}^{2} y}{dx {}^{2} } = 36 {x}^{2} + 4 \\ \boxed{\frac{d {}^{2} y}{dx {}^{2} } = 4(9 {x}^{2} + 1)}\)

The ordered triple representing \(3u - 2v\) is \((13, -8, 5)\).

To find an ordered triple representing \(3u - 2v\),

where \(u = (5, -2, 3)\) and \(v = (1, 1, 2)\),

we can perform the following operations:

\(3u = 3(5, -2, 3)\)

\(3u = (15, -6, 9)\)

\(2v = 2(1, 1, 2)\)

\(2v = (2, 2, 4)\)

Now, subtracting 2v from 3u gives:

\(3u - 2v = (15, -6, 9) - (2, 2, 4)\)

\(3u - 2v = (15-2, -6-2, 9-4)\)

\(3u - 2v = (13, -8, 5)\)

Therefore, the ordered triple representing 3u - 2v is (13, -8, 5).

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The domain of the function B(d) is from d = 0 to the number of days the account was open will be 0 ≤ d ≤ 21.

The range is the set of values the bank balance might have. We know the minimum is 0 and the maximum is 400 0 ≤ B ≤ 400.

The balance on day 12 is B(12). We're told it is zero, so  B(12) = 0 The 4th segment of the graph is at B(d) = 0.

In this context, it is reasonable to assume the vertical scale starts at 0 at the horizontal axis. We are told that (12, 0) is a point on the graph.

It is consistent with this assumption that slightly more than halfway through the graphed domain, the graph meets the horizontal axis. The graph stays at the horizontal axis for segment 4.

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Slope intercept form is written as follows:

\(y=mx+b\)

With this information, isolate y on the left side of the provided equation:

\(4y=10x-14\)

Now, divide both sides of the equation by 4:

\(y=\frac{10}{4} x-\frac{7}{2}\)

This equation cannot be simplified anymore, and is therefore the answer!

\(y=\frac{10}{4} x-\frac{7}{2}\)

Answer:

y = (5/2)x - (7/2)

Step-by-step explanation:

–10x + 4y + 14 = 0

                 -14     -14

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

-10x + 4y = -14

+10x                 + 10x

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

4y = 10x - 14

÷4    ÷4     ÷4

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

y = (10/4)x - (14/4)

simplified

y = (5/2)x - (7/2)

I hope this helps!

Answer:

i got u

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

6^2 plus 3^2 = 324, square root 324 =18

Answer:

\(\sqrt{45}\)

Step-by-step explanation:

The line represents the hypotenuse of a right triangle with legs 6 and 3. For any right triangle, the Pythagorean Theorem states that \(a^2+b^2=c^2\), where \(a\) and \(b\) are two legs of the triangle and \(c\) is the hypotenuse.

Therefore, we have:

\(6^2+3^2=c^2,\\c^2=36+9,\\c=\boxed{\sqrt{45}}\)

At a price of $3, the total revenue will be the greatest, and the company will sell 3 units at that price.

To find the total revenue at each price, we can multiply the price by the corresponding quantity.

Price        Quantity          Total Revenue

$6                0                      $0

$5                 1                       $5

$4                 2                       $8

$3                 3                        $9

$2                 4                         $8

$1                  5                          $5

To find the price at which total revenue is the greatest, we look for the highest value in the Total Revenue column.

In this case, the highest total revenue is $9, which occurs when the price is $3.

At a price of $3, the company will sell 3 units (as indicated in the Quantity column).

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The probability that either event will occur is 0.33

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 8 + 7 + 30

Evaluate

Total = 45

So, we have

P(A) = 8/45

P(B) = 7/45

For either events, we have

P(A or B) = 8/45 + 7/45

P(A or B) = 15/45

Evaluate

P(A or B) = 0.33

Hence, the probability that either event will occur is 0.33

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The gym's regular monthly rate, r, is $18.50.

Amount is the term used to describe a quantity or size of something. It will stop to used to refer to a numbers of object items or people as well as the measure of money, time and distance.

To solve this problem, we first need to calculate the total amount of money Malik paid for the 3 months. This equals $49.50. We then divide this amount by the number of months that Malik received a discount, which is 3. This yields the discounted monthly rate of $16.50.

Now, we need to find the regular monthly rate, which is equal to the discounted monthly rate plus the amount of the discount. Therefore, the regular monthly rate, r, is equal to $16.50 + $2, or $18.50.

Therefore, the gym's regular monthly rate, r, is $18.50.

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1. The possible amounts of time for which the chemistry club could rent the meeting room are 1 to 5 hours.

2. Solving the inequality for t is 39 + 6.80t ≤ 73, where the maximum time is 5 hours.

Inequality is a mathematical statement that two or more mathematical expressions are unequal.

Inequalities are depicted using the following symbols:

The total budget of the chemistry club for renting a meeting room = $73.60

The reservation fee charged by the college = $39

The additional fee (variable cost) per hour = $6.80

The number of hours the club can rent the meeting room = t

The inequality representing the situation is:

39 + 6.80t ≤ 73.

39 + 6.80t ≤ 73

6.8t ≤ 73 - 39

6.8t ≤ 34

t ≤ 5 (34/6.8)

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The equation y = \(-0.024x^2\) + 0.0791x + 4.873 represents a quadratic function with a downward-opening parabol

The given expression is a quadratic equation in the form y = -0.024x^2 + 0.0791x + 4.873. Let's analyze its components and characteristics.

The equation represents a quadratic function, where x is the independent variable and y is the dependent variable. The coefficients in front of each term determine the shape, position, and direction of the graph.

The term with the highest power of x is -0.024x^2, which indicates a downward-opening parabola. The coefficient -0.024 determines the steepness of the curve. A negative coefficient means the parabola is concave down.

The term 0.0791x is the linear term and determines the slope of the line. A positive coefficient indicates an upward or positive slope. It affects the overall direction and position of the graph.

The constant term 4.873 is the y-intercept. It indicates the point at which the graph intersects the y-axis when x = 0.

To analyze the graph of the quadratic equation further, we can calculate the vertex. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients of x^2 and x, respectively. In this case, a = -0.024 and b = 0.0791. Substituting these values into the formula, we have x = -0.0791 / (2 * -0.024) ≈ 1.643. By substituting this x-coordinate into the equation, we can find the y-coordinate of the vertex.

Overall, the equation y =\(-0.024x^2 + 0.0791x\) + 4.873 represents a quadratic function with a downward-opening parabola. The specific properties, such as the vertex and other key points, can be determined by further calculations and analysis of the equation.

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Answer:

-1,000

Step-by-step explanation:

Answer:

The answer is -1,000 > -999

Step-by-step explanation:

That is because the more further you go away from the zero into the negatives on a number line graph, the bigger the number with a negative sign is, that considered smaller

Answer:

  1/60 gallon

Step-by-step explanation:

You want to know what is left of 4/5 gallon of paint if 3/4 gallon was used to paint a doghouse, and 2/3 of the remaining amount was used to paint a door.

To find the amount remaining we subtract the amount used for the doghouse from the original amount:

  4/5 -3/4 = (16 -15)/20 = 1/20 . . . . . gallon

2/3 of that was used, so 1/3 of it remains:

  (1/3)(1/20 gallon) = 1/60 gallon

There is 1/60 of a gallon of paint left in the can.

__

Additional comment

In a standard size gallon paint can, that's about 0.11 inches of paint in the bottom.

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If λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.

The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.

Then, we have:

Av = λv

Taking transpose on both sides we have:

\(v^T A^T = \lambda v^T\)

The above equations thus relates transpose of vector and transpose of A to λ.

Now, consider a matrix:

\(\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right]\)

Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.

The eigenvectors are:

\(v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T\)

Now, for transpose of A:

\(A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right]\)

The eigen vectors are:

\(u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T\)

Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

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Kary's outfit is 3/7 sewn

Step-by-step answer:

Step 1: Moving up 3 units.

- Before: \(f(x) = x + 1\)

- After: \(f(x) = x + 4\)

Step 2: Reflect f (x) over the y-axis.

- Before: \(f(x) = x + 4\)

- After: \(f(x) = -x + 4\)

Hope this help!

in the isosceles triangle, the two angles opposite to equal lengths are equal .

so, in the triangle we have angles,

61 , 61 , x

a

Step-by-step explanation:

If 10 students are taking algebra and drafting  and 24 are taking algebta, then 24 - 10 = 14 are taking algebra only.

So   11 + 14 = 25 are taking algebra and drafting, but not both.

hope it helps!

\(\large{\underline{\underline{\pmb{\sf {\color {blue}{Solution:}}}}}}\)

Since, we know that in Elimination method we have to first the value of "x" or either "y". For that we have to multiply a number which makes the both equation's "x" or "y" equal so that we cut cancel it and find the solution.

Here's an example:

Like, in here

Equation 1: - 2x + 3y = 9

Equation 2: - 8x - 7y = 10

We can see that in "Equation 1" the first number is "- 2x" and in "Equation 2" the first number is "-8x". So, what we do in Elimination method is that we have to make the first number of both the equations equal or same.

Eg:

- 2x + 3y = 9.

- 8x + 7y = 10--(ii)

Now,we can see that in "Equation 2" the first number is "8x" whereas in "Equation 1" the first number is "-2x". We have to multiply with any number that makes the both the first number of equation is same.

So, I'm taking the number "4" to multiply it with equation 1, which gives us the result,

\(4( - 2x + 3y) = 9 \times 4 \\ \\ \leadsto - 8x + 12y = 36\)

Now, we've subtract both the equation to get the results.

\( \boxed{ \frak \red{brainlysamurai}}\)

This example demonstrates a two-step inequality where we first express the savings equation and then solve for the variable 'w' to determine the number of weeks needed to reach the savings goal.

Liam is saving money to buy a new video game console. He has already saved $50 and is saving $10 per week from his allowance. He wants to determine how many weeks it will take for his savings to reach at least $150.

Let:

number of weeks Liam saves = w

total amount of money he saves = S

Step 1: Express the first step of the problem as an inequality.

Liam saves $10 per week, so the amount of money he saves after w-weeks is 10w. We can write the first step of the inequality as:

10w + 50 ≥ 150

Step 2: Solve the inequality.

To isolate 'w', we can subtract 50 from both sides of the inequality:

10w ≥ 150 - 50

10w ≥ 100

Finally, divide both sides of the inequality by 10 to solve for 'w':

w ≥ 10

Therefore, it will take Liam at least 10 weeks to save enough money to reach $150 for the video game console.

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Answer:Subtract 8 from both sides of the inequality. Divide both sides of the inequality by 3-- A

Step-by-step explanation:

Step 1

In solving 3b + 8 ≥ 14

we first  subtract both sides by 8, which will give

3b+ 8 -8 ≥ 14-8

3b  ≥ 6

Step 2

Then, divide both sides  by 3----Since  we are multiplying by a positive number, 3, the inequalities sign  will not change but will still remain the same.

3b/3  ≥ 6/3

To give answer as b ≥ 2.

Answer:

A

Step-by-step explanation:

The answer is a mode, median, and mean.

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The complete question is :

A distribution is positively skewed. Which is the most probable order, from largest to smallest, for three measures of central tendency?