(a) What is the coefficient of x^4y^{12} in the expansion of (-4x+2y)^{16}
(b) What is the coefficient of x^4y^8z^7 in the expansion of (-4x+2y-1z)^{19}?

The value of the angle ∠U using the exterior angle theorem is calculated as; D: 34°

An exterior angle of a triangle is created by extending one side of the triangle. Now, the theorem of exterior angle of a triangle is that If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

Now, since we are given that m∠V = 95°, and m∠Z = 129°, then it means we can say that;

∠X, ∠Y = ∠Z

Similarly;

∠U + ∠V = ∠W

By congruency and external angles theorem, we can say that;

∠U + ∠V = ∠Z

Thus;

∠U +  95° = 129°

Thus;

∠U = 129 - 95

∠U = 34°

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Answer:

See below

Step-by-step explanation:

The chi-squared analysis aims to check whether observed frequencies in one or more categories match up with expected frequencies. I don't see any answer choices, but hopefully this short explanation will help!

To solve this equation, we need to get x by itself on one side of the equation. To do this, we can start by adding 8 to both sides of the equation to get:

2/3 x - 8 + 8 = 24 + 8

This simplifies to:

2/3 x = 32

Then, we can divide both sides of the equation by 2/3 to get:

(2/3) / (2/3) * x = 32 / (2/3)

This simplifies to:

x = 48

So the solution to this equation is x = 48.

The correct answer is 7.07 and 8.43 units, so option C is correct and 8.43 units. This can be calculated using trigonometry.

The two sides of the triangle are referred to as the opposite side and adjacent side. The adjacent side is the side of the triangle adjacent to the angle, and the opposite side is the side opposite to the angle. The adjacent side is calculated using the cosine of the angle multiplied by the hypotenuse, which in this case is 11.

Cos 40° multiplied by 11 gives a value of 7.07 units for the adjacent side.

Cos40×11= 7.07

The opposite side is calculated using the sine of the angle multiplied by the hypotenuse, which gives a value of 8.43 units.

Sin40×11= 8.43

Therefore, the lengths of the two sides of the right triangle are 7.07 units and 8.43 units.

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Answer:

16

Step-by-step explanation:

I had this on my test and got correct

The total number of different 4-digit numerals that can be written using the 10 digits is 7.

Numbers are represented by digits, which include 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. A group of digits known as numerals is used to represent a number. 1234 2314 56111, for example, are numerals.

The number of different permutations of 4 digits can be calculated using the formula nPr = n! / (n-r)!.

2. In this case, n = 10 and r = 4, so nPr = 10! / (10-4)! = 10! / 6! = 5040 / 720 = 7!.

Since each digit can only be used once, there are no duplicate combinations. Therefore, the total number of different 4-digit numerals that can be written using the 10 digits is 7!

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Answer

[tex]\sqrt[3]{4^{2} }[/tex]

Step-by-step explanation:

The answer to the given equation is 240.

We can con solve the equation in the following ways:

6 f(x) dx = 6 * (4x) dx for x ≥ 4

Here, we will do the derivative and integration of the given equations as required. That will take us to the simplified statement. Note: we need to take into consideration the greater than equal  sign as it will directly affect the result of the equation.

= 24 * ∫x dx from 4 to 6

= 24 * (x^2/2)|4 to 6

= 24 * (6^2/2 - 4^2/2)

= 24 * (18 - 8)

= 24 * 10

= 240

Therefore, The answer to the given equation is 240.

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Answer: I don’t know

Step-by-step explanation:

The extraneous solution of the equation x - 1 = √x + 1 is x = 0

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

x - 1 = √x + 1

Take the square of both sides

So, we have

x² - 2x + 1 = x + 1

Evaluate the like terms

x² - 3x = 0

So, we have

x(x - 3) = 0

Solving for x, we have

x = 3 and x = 0

Substitute x = 3 and x = 0 in x - 1 = √x + 1

3 - 1 = √3 + 1

2 = 2 ---- true

0 - 1 = √0 + 1

-1 = 1 ---- false

Hence, the extraneous solution is x = 0

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Answer:

Step-by-step explanation:

point form:

(-24,-13)

Equation form:

x = -24  y = -13

The value of [tex]x[/tex] and [tex]y[/tex] is [tex]x=-24[/tex] and [tex]y=-13[/tex]

The two given equation are

                       [tex]2x-3y=-9\\x-5=-29[/tex]

We need to find [tex]x[/tex] and [tex]y[/tex]

 that is ,

           [tex]x=-29+5\\x=-24[/tex]

We can substitute the value of [tex]x[/tex] in equation [tex]2x-3y=-9[/tex]

       that is ,

                      [tex]2(-24)-3y=-9\\-48-3y=-9\\-3y=-9+48\\-3y=39\\y=-13[/tex]

The value of [tex]x=-24,y=-13[/tex]

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The complete question is , Find the value of [tex]x[/tex] and [tex]y[/tex] if [tex]2x-3y=-9 , x-5=-29[/tex] in the substitution form.

Answer:

Eden planted 2 basil plants and 8 mint plants.

Step-by-step explanation:

Here's one possible way to write a system of equations to represent the information given in the problem:

Let x be the number of basil plants and y be the number of mint plants.

The first equation represents the total number of plants:

x + y = 10 (because Eden is planting a total of 10 herbs)

The second equation represents the total cost of all the plants:

x* $0.50 + y* $0.25 = $3

Elimination Method:

Multiply the first equation by $0.50

x* $0.50 + y* $0.50 = $5

subtracting this equation from the second equation

y* $0.25 = $3-$5 = -$2

y = 8

then substitute the value of y in first equation

x + 8 = 10

x = 2

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The value of the variable based on the triangle given is 5.5 units.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.

Add each side of the triangle.

3z + z + 1 + 4z - 3 = 8z - 2

8z - 2 is equivalent to the  perimeter.

Since you know the perimeter is 38 units, you can set 8z-2 to 38.

8z -2 = 38

Solve for z. Subtract 2 from each side.

8z = 36

Divide each side by 8.

z = 4.5

Now solve for side WX.

WX = z + 1

WX = 4.5 + 1

WX = 5.5

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Each of Liam, Anika, and Sai is figuring out the identical equation for x. 12x+4=20x-12 in the original equation. 12x+16=20x was the outcome of Sai's initial action.

Getting the variable on one side is the first step in solving an equation with a variable on both sides once it has been simplified. To do this, one of the words with the variable's addition or subtraction is reversed.

12 x + 4 = 20 x - 12 x 4 = 20 x - 12 x - 12 x 4 = 8x - 12

The linear term was then simply merged.

12 on each side is added. Consequently, 12 x + 16 = 20 x. 12 x + 4 + 12 = 20 x

12 x + 4 = 20 x - 12 is the analysis.

12 on each side added

Consequently, 12 x + 16 = 20 x. 12 x + 4 + 12 = 20 x

12 x from both sides 16 = 20 x - 12 x 16 = 8x x = 2.

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Answer:

-45, -46

Step-by-step explanation:

-45 + (-46) = -91

The equation of the line that passes through these points X -2,0,2,3 and Y -17, -5, 7, 13 is given by y = 6x - 30

The slope, m of the linear function is calculated using the points on the form the table (0, -5) and  (2, 7)

m = (y₀ - y₁) / (x₀ - x₁)

m = (-5 - 7) / (0 - 2)

m = (-12) / (-2)

m = 6

equation passing through point (0, 5)

(y - y₁) = m (x - x₁)

y - 0 = 6 (x - 5)

y = 6x - 30

The equation of the line for the table is solved to be  y = 6x - 30

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Answer:

y = -0.2x + 4.6

Step-by-step explanation:

We can set up a point-slope form to calculate for the equation:

y - y1 = m (x - x1)

Before we plug the coordinate into the formula, we need m, the slope of L, we know that L is perpendicular to the straight line, and the slope of the straight line is 5:

Perpendicular slope form is: opposite reciprocal of m, which is:

-1/5 or -0.2

Now we plug all the numbers into the previous equation:

y - 5 = -0.2 (x + 2)

y = -0.2 (x + 2) + 5

y = -0.2x + -0.4 + 5

y = -0.2x + 4.6

Now this is a slope-intercept form.

Its speed of Rachel would be 30 meters per second.

Given that,

Stunt driver Rachel is trying to get out of a building that is going to blow up.

Here, the equation is,

[tex]d = - 38t + 220[/tex]

Where, variable d models Rachel's distance from her exit (in meters) t seconds after the cameras began recording the stunt.

Now, Velocity is the rate at which a distance changes over time.

[tex]d = - 38t + 220[/tex]

[tex]\dfrac{d(d)}{dt} = - 38[/tex]

Hence, Speed is the magnitude of velocity.

[tex]|- 38| = 38[/tex]

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Answer:

x < -2  or  x > 4

Step-by-step explanation:

This is an absolute value inequality of the form

|X| ≥ b

where X is an expression with a variable, and b is a non-negative number.

An absolute value inequality of this form is solved by changing the form into a compound inequality using the word "or."

To solve

|X| ≥ a,

solve the compound inequality

X < - a or X > a

In other words, when the absolute value of an expression is greater than (or greater than or equal to) a number, rewrite the absolute value inequality as

expression < -number or expression > number

In your problem, you have

|2x - 2| ≥ 6

The expression is 2x - 2.

The number is 6.

You change the absolute value inequality to the following compound inequality:

2x - 2 ≤ -6  or  2x - 2 > 6

Now you solve each inequality always keeping the word "or" in between them.

2x - 2 ≤ -6  or  2x - 2 > 6

2x < - 4  or  2x > 8

x < -2  or  x > 4

I hope you understand the solution and explanation. If you have any questions, ask in the comments.

The matching of the first row of expressions with the second row of expressions are;

1) 2√(3x²y) → x√(12y)

2) 2x√(6xy²) → y√(24x³)

3) 2y√(2x⁴) → x²√(8y²)

4) 3x²√(2y⁴) → xy√(18x²y²)

1) 2√(3x²y)

This can be broken down into the expression;

2x√(3y)

2) 2x√(6xy²)

This can broken down into;

2xy√(6x)

3) 2y√(2x⁴)

This can be simplified into;

2x²y√2

4) 3x²√(2y⁴)

This can be simplified into;

3x²y²√2

The second row of expressions are simplified as;

xy√(18x²y²)

= 3x²y²√2

x√(12y)

= 2x√3y

x²√(8y²)

= 2x²y√2

y√(24x³)

= 2xy√6x

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In order to solve problems involving triangles that require constructions, you can use a straightedge and compass.

Here are the steps you can follow:

First, identify the information that is given in the problem and what you need to find.

Draw a diagram of the triangle, including any given segments or angles.

Use the given information to construct any points or lines that are required.

Use the straightedge to draw any necessary lines, and use the compass to construct any circles or arcs that are required.

Use the properties of triangles and the given information to solve for the unknown quantity. It's important to note that not all problems involving triangles can be solved using constructions. In some cases, you may need to use other techniques, such as the Pythagorean Theorem or the Law of Sines.

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Answer:

600

Step-by-step explanation:

To determine how well Daniel must score on Exam B in order to do equivalently well as he did on Exam A, we can use the concept of standard scores or z-scores. A z-score indicates how many standard deviations away from the mean a score is.

First, we need to convert Daniel's score on Exam A to a z-score:

z = (18 - 28) / 5 = -2

This tells us that Daniel's score on Exam A is 2 standard deviations below the mean.

We can then use this z-score to find Daniel's equivalent score on Exam B. To do this, we can use the formula:

x = z * σ + μ

Where x is the equivalent score on Exam B, z is the z-score from Exam A, σ is the standard deviation of Exam B, and μ is the mean of Exam B.

x = (-2) * 40 + 700

x = 600

Therefore, Daniel must score 600 on Exam B in order to do equivalently well as he did on Exam A.

Keep in mind that this calculation assumes that the scores on each exam are normally distributed, which may or may not be the case. It also assumes that the two exams are of similar difficulty, which also may not be the case.

Root x = 2 is an extraneous solution for radical equation √(4 · x - 7) - √(2 · x) = 1, whose roots are 2 and 8, respectively.

In this problem we find the definition of a radical equation, whose roots must be found by combining algebra properties and power properties. A root is an extraneous solution if the result lead to an absurdity. (i.e. 1 = 0).

First, write the complete expression:

√(4 · x - 7) - √(2 · x) = 1

Second, apply algebraic substitution formula u = 2 · x to simplify the model:

√(2 · u - 7) - √u = 1

Third, use algebra properties to clear square roots:

√(2 · u - 7) = 1 + √u

Fourth, square both sides of the expression:

2 · u - 7 = (1 + √u)²

2 · u - 7 = 1 + 2 · √u + u

u - 7 = 1 + 2 · √u

u - 2 · √u - 8 = 0

Fifth, use algebraic substitution k = √u and solve the quadratic-like equation by factorization:

k² - 2 · k - 8 = 0

(k - 4) · (k + 2) = 0

k₁ = 4 or k₂ = - 2

Sixth, find the values of x by reversing algebraic substitutions:

√u₁ = 4 or √u₂ = - 2

u₁ = 4² or u₂ = (- 2)²

2 · x₁ = 4² or 2 · x₂ = (- 2)²

x₁ = 8 or x₂ = 2

Seventh, look for any extraneous solution:

x₁ = 8

√(4 · 8 - 7) - √(2 · 8) = 1

√25 - √16 = 1

5 - 4 = 1

1 = 1

x₂ = 2

√(4 · 2 - 7) - √(2 · 2) = 1

√1 - √4 = 1

1 - 2 = 1

- 1 = 1 (CRASH!)

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Brandon ' s rate of change , give the graph on the amount of savings per period, is C. 75

The rate of change can be found by the formula :

= Rise / Run

The rise can be found by subtracting an earlier value of the amount in savings, from a later value of the amount in savings .

The run can be found by subtracting an earlier value in periods from a later value in periods . Therefore , the first step is to pick two points on the graph.

Points picked are ( 2 , 150 ) and ( 4 , 300 )

The rise is :

= 300 - 150

= 150

The run is :
= 4 - 2

= 2

The rate of change is :
= 150 / 2

= 75

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It should be noted that (2,3) is not a solution to a the equation y = x + 1.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

No, (2,3) is not a solution to the equation y = x + 1. If we substitute 2 for x and 3 for y, we get 3 = 2 + 1 which is not true.

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Answer:

Use the Cosine Rule to find unknown sides and angles

Step-by-step explanation

If Jordan is taking out a 2-week payday loan for $600. He will be charged $95 interest for the 2-week loan. The APR for this loan is 412.8%.

Using this formula to find the Annual percentage rate (APR)

APR =Loan interest /loan amount ÷ Number of loan length / 365

Let plug in the formula

APR = 95/600 ÷ (2 × 7 days)/365 days

APR = 95/600 ÷ 14 days/365 days

APR = 4.1279 × 100

APR = 412.8% ( Approximately)

Therefore we can conclude that the APR is 412.8%.

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Answer:

x = 15

Step-by-step explanation:

[tex]\sqrt[3]{2x-3}[/tex] = 3 ( cube both sides to clear the radical )

( [tex]\sqrt[3]{2x-3}[/tex] )³ = 3³

2x - 3 = 27 ( add 3 to both sides )

2x = 30 ( divide both sides by 2 )

x = 15

Answer:

7 1/2

Step-by-step explanation:

9 4/5 - 2 3/10 =

(9 + 4/5) - (2 + 3/10) =

(9 + 4/5) - 2 - 3/10 =  ==> distribute the minus sign to 2 and 3/10

9 + 8/10 - 2 - 3/10 =  ==> change 4/5 to 8/10 to have common denominators

9 - 2 + 8/10 - 3/10 =  ==> combine like terms

7 + 5/10 = ==> simplify

7 + 1/2 = 7 1/2