\(4g - 7c + 3g\)
simplify by combining like terms​

Here are the steps to simplify the expression \(\sf\:5x\sqrt{3x} - 2x\sqrt{3x} - x\sqrt{3x} \\\):

1. Combine like terms that have the same radical term \(\sf\:\sqrt{3x} \\\):

\(\sf\:(5x - 2x - x)\sqrt{3x} \\\)

2. Simplify the coefficients:

\(\sf\:2x\sqrt{3x} \\\)

Therefore, \(\sf\:5x\sqrt{3x} - 2x\sqrt{3x} - x\sqrt{3x}\) simplifies to \(\sf 2x\sqrt{3x} \\\).

Answer:

Linear, equation: y = -2x + 1

The coefficient of \(x^{7}\) is 16796160.

For this, we have to find the coefficient of \(x^{7}\) in \((3x+4)^{10}\)

General Term: This term symbolizes all of the terms in the binomial expansion of (x + y)^n.

The general term in the binomial expansion of (x + y)^n is

T(r+1) = nCr x^(n-r)y^r.

Here the r-value is one less than the number of the term of the binomial expansion. Also, nCr is the coefficient, and the sum of the exponents of the variables x and y is equal to n.

We can use the general term for this.

\(T_{r+1} = (nCr) a^{n-r} x^{r}\)

Since we have to find  \(x^{7}\),

\(T_{3+1} = (10C3)(3x)^{7} 4^{3} \\T_{3+1} = [(10C3)3^{7} 4^{3} ]x^{7}\)

This is the coefficients of \(x^{7}\)

Calculating,

10C3 = 120 (using combinations)

\(3^{7} = 2187\\4^{3} = 64\)

Therefore, multiplying the 3,

Coefficients of \(x^{7}\) = 120 * 2187 *64

= 16796160

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Answer:

8

Step-by-step explanation:

By the property of intersecting tangent and secant outside of a circle.

\((4x + 2) \degree = \frac{1}{2} \{(22x + 14) \degree - 122 \degree) \} \\ \\2 (4x + 2) \degree = \{(22x + 14) \degree - 122 \degree) \} \\ \\ (8x + 4) \degree = (22x + 14 - 122) \degree \\ \\ (8x + 4) \degree = (22x - 108) \degree \\ \\8x + 4 = 22x - 108 \\ \\ 4 + 108 = 22x - 8x \\ \\ 112 = 14x \\ \\ x = \frac{112}{14} \\ \\ x = 8\)

Step-by-step explanation:

First, 40 percent of 1250 = 750

20 percent of 750 = 600

I don't know if this is correct I just did what my mind said sooo

Answer:

B) in the modern art section of an art museum

Step-by-step explanation:

Hope it helps! =D

D. I and IV are the quadrants the cosine function is positive

To determine in which quadrants the cosine function is positive, we need to consider the signs of cosine in different quadrants of the Cartesian coordinate system.

The unit circle is a useful tool to understand the behavior of trigonometric functions. In the unit circle, the x-coordinate represents the cosine value, while the y-coordinate represents the sine value. The cosine function is positive in the quadrants where the x-coordinate is positive.

Quadrant I is the top-right quadrant, where both the x and y coordinates are positive. In this quadrant, cosine is positive because the x-coordinate is positive.

Quadrant II is the top-left quadrant, where the x-coordinate is negative, but the y-coordinate is positive. In this quadrant, cosine is negative because the x-coordinate is negative.

Quadrant III is the bottom-left quadrant, where both the x and y coordinates are negative. In this quadrant, cosine is negative because the x-coordinate is negative.

Quadrant IV is the bottom-right quadrant, where the x-coordinate is positive, but the y-coordinate is negative. In this quadrant, cosine is positive because the x-coordinate is positive.

Based on this analysis, we can conclude that cosine is positive in Quadrant I and Quadrant IV. Therefore, the correct answer is D. I and IV.

It's important to note that this applies to the standard unit circle and the principal values of cosine. When considering periodicity and multiple revolutions around the unit circle, the positive regions of cosine will repeat every 360 degrees or 2π radians.

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On factoring the polynomial 6z² + 6z the values for length and width are obtained as 6z and z + 1.

What is a polynomial?

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

We can factor the polynomial 6z² + 6z by taking out the greatest common factor, which is 6z -

6z² + 6z = 6z(z + 1)

This means that the area of the wall is equal to 6z(z + 1) square meters. Since the area of a rectangle is given by the product of its length and width, we can write -

6z(z + 1) = length × width

Therefore, the possible expressions for the length and width of the wall are -

length = 6z

width = z + 1

or

length = z + 1

width = 6z

Both of these expressions give a product of 6z(z + 1), which is equal to the area of the wall.

We can switch the roles of length and width, so there are two possible expressions for the dimensions of the wall.

Therefore, the length is 6z and width is z + 1.

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Complete Question

Suppose that the amount of time teenagers spend weekly working at part-time jobs is normally distributed with a standard deviation of 40 minutes. A random sample of 15 teenagers was drawn and each reported the amount of the time spent at part-time jobs (in minutes). These are listed here 180, 130, 150, 165, 90, 130, 120, 60, 200, 180, 80, 240, 210, 150, 125. Determine the 95% confidence interval estimate of the population mean.

Answer:

The 95% confidence interval is  \( 127.09  <  \mu <  167.57 \)

Step-by-step explanation:

From the question we are told that

   The standard deviation is  \(\sigma = 40\)

   The sample size is  n  = 15

     The data given is   180, 130, 150, 165, 90, 130, 120, 60, 200, 180, 80, 240, 210, 150, 125

Generally the sample mean is mathematically represented as

             \(\= x = \frac{ \sum x_i}{n }\)

=>          \(\= x = \frac{ 130 + 150 + \cdots + 125 }{ 15 }\)

=>          \(\= x = 147.33\)

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as  

      \(E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }\)

=>     \(E = 1.96  *  \frac{40}{\sqrt{15} }\)

=>     \(E =20.24 \)

Generally 95% confidence interval is mathematically represented as  

      \( 147.33 -20.24<  \mu <  147.33 + 20.24 \)

      \( 127.09  <  \mu <  167.57 \)

20.124

Step-by-step explanation:

remember the pythagoream theurm states a^{2} + b^{2} =c^{2} so

9 x 9 = 81

18 x 18 = 324

324+81 = 405

now you have to sq root it (20.1246)

Answer: y = 5/14x + 5/7

Step-by-step explanation: write in slope intercept form y =mx + b

The slope-intercept equation is y = 4x + 2 when the slope is 4 and y-intercept is at (0, 2).

We are given that:

We have to find the slope-intercept equation.

As we have slope and a y-intercept, let us find the slope-intercept form of the given equation.

Slope-intercept form → \(y=mx+b\)

Where m is slope and b is the y-intercept of the equation.

Here, in our problem, \(\text{m}=4 \ \text{and} \ \text{b}=(0,2)\)

Now, we get

\(\text{y} = 4\text{x} + \text{b}\)

\(\text{y} = 4\text(0) + \text{b}\)

\(4=0 + \text{b}\)

\(\text{b}=2\)

\(\rightarrow\bold{ y = 4x + 2 }\)

Hence, the slope-intercept equation is y = 4x + 2.

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According to the information, the missing number from the box is number 40.

To find the missing number of the table we must take into account different elements. In particular we must look at the totals and the columns and rows in which the empty space is. Once we identify the totals we can subtract the other values from the total and find the missing number in the table.

According to the above we can infer that the missing number is 40.

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Joey's actual speed is 143.59 mph, and his actual direction is slightly west of northwest.

Given that Joey's aircraft speed: 188 mph

Wind speed: 60 mph

Wind direction: 150 degrees (measured clockwise from due north)

We can consider the wind as a vector, which has both magnitude (speed) and direction.

The wind vector can be represented as follows:

Wind vector = 60 mph at 150 degrees

We convert the wind direction from degrees to a compass bearing.

Since 150 degrees is measured clockwise from due north, the compass bearing is 360 degrees - 150 degrees = 210 degrees.

Joey's aircraft speed vector = 188 mph at 0 degrees (due northwest)

Wind vector = 60 mph at 210 degrees

To find the resulting velocity vector, we add these two vectors together. This can be done using vector addition.

Converting the wind vector into its x and y components:

Wind vector (x component) = 60 mph × cos(210 degrees)

= -48.98 mph (negative because it opposes the aircraft's motion)

Wind vector (y component) = 60 mph×sin(210 degrees)

= -31.18 mph (negative because it opposes the aircraft's motion)

Now, we can add the x and y components of the two vectors to find the resulting velocity vector:

Resulting velocity (x component) = 188 mph + (-48.98 mph) = 139.02 mph

Resulting velocity (y component) = 0 mph + (-31.18 mph) = -31.18 mph

Magnitude (speed) = √((139.02 mph)² + (-31.18 mph)²)

= 143.59 mph

Direction = arctan((-31.18 mph) / 139.02 mph)

= -12.80 degrees

The magnitude of the resulting velocity vector represents Joey's actual speed, which is approximately 143.59 mph.

The direction is given as -12.80 degrees, which indicates the deviation from the original northwest direction.

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Answer:

-4

Step-by-step explanation:

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9514 1404 393

Answer:

  add the subtrahend to the difference

Step-by-step explanation:

The usual way to check a subtraction problem is to add the subtrahend to the difference to see if you get the minuend as a result.

Paloma can add 5/8 to her result to see if she gets 1 3/4.

__

She can also perform the subtraction using decimal fractions to see if she gets the same result.

  1.750 -0.625 = 1.125

Linear equations are typically organized in slope-intercept form:

\(y=mx+b\)

Perpendicular lines have slopes that are negative reciprocals.

We're given:

1) Determine the slope

Let's first rearrange this equation into slope-intercept form:

\(4x-5y=-10\\-5y=-4x-10\\\\y=\dfrac{4}{5}x+2\)

Notice how \(\dfrac{4}{5}\) is in the place of m in y = mx + b. This is the slope of the give line.

Since perpendicular lines are negative reciprocals, we know the slope of the other line is \(-\dfrac{5}{4}\). Plug this into y = mx + b:

\(y=-\dfrac{5}{4}x+b\)

2) Determine the y-intercept

We're also given that the line passes through (6,3). Plug this point into our equation and solve for b:

\(y=-\dfrac{5}{4}x+b\\\\3=-\dfrac{5}{4}(6)+b\\\\b=3+\dfrac{5}{4}(6)\\\\b=\dfrac{21}{2}\)

Plug this back into our original equation:

\(y=-\dfrac{5}{4}x+\dfrac{21}{2}\)

\(y=-\dfrac{5}{4}x+\dfrac{21}{2}\)

The instantaneous rate of change at x = 2 is equal to the derivative, which is 2.

The derivative of f(x) = 2x - 5 with respect to x can be found by applying the power rule of differentiation, which states that the derivative of x^n is n*x^(n-1).

Taking the derivative of f(x) = 2x - 5:

f'(x) = 2 * (d/dx)(x) - (d/dx)(5)

= 2 * 1 - 0

= 2.

The derivative of f(x) with respect to x is a constant, 2, indicating that the function has a constant slope.

Therefore, the instantaneous rate of change at x = 2 is equal to the derivative, which is 2.

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Hey there! I'm happy to help!

Let's pretend that we are building a small sundae. We have 3 choices of ice cream flavors.

Now, we want to pick a topping. We have 4 choices here.

After we choose a topping, we can pick another. We only have 3 choices now because we need different toppings, and we already used one.

We want to find how many possible combos we can make. What we do is multiply all of these numbers of choices, and this will show us how many possible sundaes there are.

3×4×3=36

Therefore, there are 36 different sundaes that can be made.

Have a wonderful day! :D

To determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle, we can compare the given information with the formulas for each law.

The Law of Sines states:

a / sin(A) = b / sin(B) = c / sin(C)

The Law of Cosines states:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, we are given the lengths of all three sides of the triangle (a = 6.0, b = 7.7, c = 13.6). Therefore, we have enough information to use the Law of Cosines to solve the triangle.

Using the Law of Cosines, we can find the measures of the angles:

c^2 = a^2 + b^2 - 2ab * cos(C)

(13.6)^2 = (6.0)^2 + (7.7)^2 - 2 * 6.0 * 7.7 * cos(C)

184.96 = 36 + 59.29 - 92.4 * cos(C)

184.96 = 95.29 - 92.4 * cos(C)

92.67 = -92.4 * cos(C)

cos(C) ≈ -1

Since the cosine of an angle cannot be greater than 1 or less than -1, it is not possible for the given triangle to have an angle with a cosine of -1. Therefore, the triangle is not solvable with the given side lengths.

In this case, the Law of Cosines is needed, but the triangle cannot be solved with the given information.

Answer:

C.) The relationship is proportional

Step-by-step explanation:

If D is true, then it is not proportional, constants of proportionality must not include multuplting or subtracting from anything.

Also quick way to tell— the line doesn’t start from 0,0

Answer:

By using the formula down below you can find the area of a trapezoid

A = \(\frac{a+b}{2}\)h

↑ Area

A = Base

B = Base

H = Height

Example.

A = 12

B = 4

H = 2

First “ A “ + “ B “ =

12 + 4 = 16

16 / 2 = 8

8 x “ h “

8 x 2 = 16

Answer is 16

Thus the answer is, above

So if you look that up then it will show you how to find the area of a trapizoid

The limit of the function As x → - ∞, f(x) → 2.

The limit of a function is the value the function tends to as the independent variable tends to a given value.

Given the graph of the function above, to find the limit of the function As x → -∞, f(x) →? We proceed as follows

Looking at the graph, we see that f(x) has a horizontal asymptote at y = 2. Now, we see that As x → -∞, f(x) approaches 2.

So, As x → - ∞, f(x) → 2.

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The quotient is 32 and the remainder is 6.

i.e,

32 R6

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

774 ÷ 24

24 ) 774 ( 32

      768

           6

The quotient is 32 and the remainder is 6.

Now,

We can write in this form,

(Quotient) R(remainder)

Thus,

The quotient is 32 and the remainder is 6.

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Answer:

862

Step-by-step explanation:

Answer:

At the time the ball was thrown, it was 8 feet above the ground.

h'(x) = -32x + 64 = 0, so x = 2

The ball reaches its maximum height after 2 seconds.

The vertices of the rectangular garden is plotted on the graph

Given data .

Let the rectangular garden be represented as ABCD

Now , the vertices of the garden is

A ( 4 , 3 ) , B ( 6 , 3 ) , C ( 6 , 9 ) and D ( 4 , 9 )

On plotting the coordinates on the graphical plane , we get

So , the perimeter of the garden is P = 2 ( 2 + 6 )

P = 16 units

And , area of garden is A = 12 units²

Hence , the vertices of the garden is plotted

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Answer:

Step-by-step explanation:

\(A = lw \nl\frac{\dA}{\dt}\) =\(\frac{\dA}{\text{d}l}\frac{\text{d}l}{\dt} + \frac{\dA}{\text{d}w}\frac{\text{d}w}{\dt}\) =\(w\frac{\text{d}l}{\dt} + l\frac{\text{d}w}{\dt}\) \(\nll = 20 \text{ cm}\) \;\; \(\frac{\text{d}l}{\dt} = 8 \text{ cm/s}\) \;\;w = 10 \text{ cm}, \;\;  \(]\frac{\text{d}w}{\dt} = 3 \text{ cm/s}\) \(\nl\frac{\dA}{\dt} =(  10 \text{ cm} )( 8 \text{ cm/s} ) + (  20 \text{ cm} )( 3 \text{ cm/s} )  =140 \text{ cm}^2\!\text{/s} \)

Given :

To find :-

Solution :-

As we know that :-

To find the rate :-

Differenciate :-

Substitute :-