Simplify.
8.4c-4.3c.

The expression that must be equivalent to the one give must be 1/3x - 2

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable. Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

In this problem, we just need to simply the expression to get the answer to this.

1/3(x + 6) - 4

Step 1 : Expand or open the bracket

1/3x + 2 - 4

Step 2: Simplify the expression.

1/3x + 2 - 4 = 1/3x - 2

The equivalent expression must be 1/3x - 2

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[tex]\displaystyle \lim_{\theta \to 0}\cfrac{\tan^2(\theta )-\sin(\theta )}{\theta 4}\implies \stackrel{\textit{\Large L'Hopital's rule}}{\lim_{\theta \to 0}\cfrac{\frac{d}{d\theta }[\tan^2(\theta )-\sin(\theta )]}{\frac{d}{d\theta }[\theta 4]}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{d}{d\theta }[\tan^2(\theta )-\sin(\theta )]\implies \cfrac{d}{d\theta }[[\tan(\theta )]^2-\sin(\theta )]\implies \stackrel{chain~rule}{2\tan(\theta )\cdot \sec^2(\theta )} ~~ -\cos(\theta ) \\\\\\ 2\tan(\theta )\cdot \cfrac{1}{\cos^2(\theta )}-\cos(\theta )\implies \cfrac{~~ \frac{2\sin(\theta) }{\cos(\theta) } ~~}{\cos^2(\theta )}~~ -\cos(\theta ) \\\\\\ \cfrac{2\sin(\theta) }{\cos^3(\theta) }~~ -\cos(\theta )\implies \cfrac{2\sin(\theta)-\cos^4(\theta)}{\cos^3(\theta)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{d}{d\theta}[4\theta]\implies 4 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\displaystyle \lim_{\theta \to 0}\cfrac{\tan^2(\theta )-\sin(\theta )}{\theta 4}\implies \lim_{\theta \to 0}\cfrac{ ~~ \frac{2\sin(\theta)-\cos^4(\theta)}{\cos^3(\theta)} ~~ }{4}\implies \lim_{\theta \to 0}\cfrac{2\sin(\theta)-\cos^4(\theta)}{4\cos^3(\theta)} \\\\\\ \displaystyle \lim_{\theta \to 0}\cfrac{2\sin(0)-\cos^4(0)}{4\cos^3(0)}\implies \lim_{\theta \to 0}\cfrac{2(0)-1^4}{4(1^3)}\implies {\Large \begin{array}{llll} -\cfrac{1}{4} \end{array}}[/tex]

The total cost of the shoes after tax is 105.84 dollars.

Sales tax is a tax on goods and services purchased and is normally a percentage added to the buyer's cost.

Jaclyn bought new shoes priced at $98 and sales tax is 8%. The total cost of the shoes after tax can be calculated as follows;

Therefore, the cost after tax is the sum of the cost and the sales tax.

Hence,

sales tax = 8% of 98

sale tax = 8 / 100 × 98

sales tax = 784 / 100

sales tax = $7.84

Hence,

total cost after tax = 7.84 + 98 = 105.84 dollars

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The correct statements regarding the functions are given as follows:

Regarding the type of function, we have that:

The y-intercepts are the values of y for which x = 0, hence they are given as follows:

Hence function g(x) starts less than f(x), but it eventually exceeds function f(x), as it is exponential, meaning that it has a greater average rate of change.

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There are total 4*5*3 = 60 ways of wearing one each.

What is Fundamental Counting Principle?

A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle.

Solution:

Let,

for three events A, B, and C, number of outcomes be a,b, and c respectively.

So, the total number of outcomes is given by the product of outcomes of all the events i.e. by using Fundamental Counting Principle.

In the question mentioned,

a = 4

b = 5

c = 3

So, total outcomes = 4*5*3 = 60 ways

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Answer:

y=-5x+19

Step-by-step explanation:

yeah -ya...... right?

The required equation is y = - 3.5x + 8.5 (in slope-intercept form) of the line passing through the points with the given coordinates.

The slope of a line is defined as the gradient of the line.

Given that the line that passes through two points (1,5), and (3,−2)

Let the required equation of the line will be as :

y - 5 = [(-2 - 5)/(3-1)](x - 1)

y - 5 = (-7/2)(x - 1)

y - 5 = - 3.5(x - 1)

y - 5 = - 3.5x + 3.5

y = - 3.5x + 3.5 + 5

y = - 3.5x + 8.5

Thus, the required equation is y = - 3.5x + 8.5 (in slope-intercept form) of the line passing through the points with the given coordinates.

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The number of minutes that the executive use the phone is 131 minutes.

From the information, the cellular phone service for a business executive is $35 per month plus $0.40 per minute of phone use.

Let the number of minutes be m.

This will be illustrated as:

35 + 0.40m = 87.80

Collect like terms

0.40m = 87.80 - 35

0.40m = 52.80

Divide

m = 52.40 / 0.40

m = 131

The number of minute is 131 minutes.

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It is a rhombus kind of quadrilateral.

What is quadrilateral?

A quadrilateral has four sides, is two-dimensional (flat), closed (the lines join up), and has straight sides.

A rhombus is a four-sided quadrilateral with all of the features of a parallelogram.

A rhombus has three more characteristics: consecutive sides that are congruent; diagonals that bisect pairs of opposite angles; and diagonals that are perpendicular to one another.

Moving clockwise, beginning at point A in the top left corner of a hypothetical rhombus ABCD, you can see that side AB is congruent to side BC and side CD is congruent to side DA.

Additionally, you can see that diagonals AC and DB are perpendicular to one another and that the rhombus' diagonals split pairs of opposing angles.

Hence, It is a rhombus kind of quadrilateral.

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[tex]\cfrac{5x^6 5x^{-2}125x 2x^4 2x^{-5}}{2x^5 5x^{-3} 2x^6}\implies \cfrac{5\cdot 5\cdot 125\cdot 2\cdot 2}{2\cdot 5\cdot 2}\cdot \cfrac{x^6 x^{-2}x x^4 x^{-5}}{x^5 x^{-3} x^6} \\\\\\ \cfrac{ 5\cdot 125}{1}\cdot \cfrac{x^{6-2+1+4-5}}{x^{5-3+6}}\implies 125\cdot \cfrac{x^4}{x^8}\implies 125\cdot \cfrac{1}{x^8 x^{-4}}\implies \cfrac{125}{x^{8-4}}\implies {\Large \begin{array}{llll} \cfrac{125}{x^4} \end{array}}[/tex]

The equation of a line in y = mx + b form that passes through (5,-5) and (-5, -3) is y = (-1/5)x - 4.

The formula to calculate the slope between two points is equal to

[tex]m = y2-y1/(x2-x1)[/tex]

Find the slope of Line a

We have the points

(5,-5) and (-5, -3)

Substituting the value in the formula

[tex]m = -3 - (-5)/(-5-5)\\m = (-3 + 5)/(-10)\\m = 2/-10\\m = -1/5[/tex]

The slope is -1/5.

Finding the y-intercept from the below-given equation:

y = mx + b ...... (1)

Putting value of y = - 5, x = 5, m = -1/5

-5  = (-1/5) x (5) + b

-5 = - 1 + b

=> b = - 4

Putting the value of b = - 4 and m = -1/5 in equation (1). We get,

y = (-1/5)x - 4

Hence, the equation of the line is y = (-1/5)x - 4.

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Answer:

-15530

Step-by-step explanation:

plug it in to a calculator

why so random numbers

Answer:

Step-by-step explanation:

2(5+777x60/6x(-1))

2(5-7770)

2x(-7765)

-15530

Value of x rounded to nearest tenth is 25.5 units.

Given in question,

Right angled triangle CDE

θ = 20°

CD = perpendicular = 24 units

CE = Hypotenuse = x

Therefore,

cosθ = Perpendicular/Hypotenuse

cos 20 = 24/x

0.9397 = 24/x

         x = 24/0.9397

            = 25.54

Hence, value of x rounded to nearest tenth is 25.5 units.

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Answer:

Step-by-step explanation:

The factored form of 8x²⁴-27⁶ is (2x⁸-3y²)(4x¹⁶+6x⁸y²+9y⁴)

Equations may be solved and x-intercepts can be found very quickly when a quadratic expression is in factored form and equal to 0. You may also find vertices and maximum and minimum values of the expression.

The four main methods of factoring are the Grouping method, Difference in Two Squares, Sum or Difference in Cubes, and Greatest Common Factor (GCF).

It is referred to as being in factored form when a quadratic expression is represented as the sum of two linear factors plus a constant. Examples of factors include ((5x + 2)(3x-1)) and ((2(x-1)(x+3)).

Given,

8x²⁴-27⁶

=(2x⁸)³-(3y²)³

=(2x⁸-3y²)((2x⁸)²+2x⁸×3y²+(3y²)²

=(2x⁸-3y²)(4x¹⁶+6x⁸y²+9y⁴)

Therefore, the factored form of 8x²⁴-27⁶ is (2x⁸-3y²)(4x¹⁶+6x⁸y²+9y⁴)

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The drug administered to the patient by the doctor has a half-life of 5 hours

Half-life is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential decay.

The formula is given as;

T1/2 = ln2 / λ

Where;

But λ = 15% = 0.15/hr

t1/2 = ln2 / 0.15

T1/2 = 0.693/0.15

T1/2 = 4.62 = 5 hours.

The drug has an half-life of approximately 5 hours

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The coordinates of the starting point is  (12, 5)

Ordered pairs refers to the arrangement of 2 numbers in the form (a, b)

The rule to move ordered pair one unit left 1 will be subtracted in the x coordinates

(5, 5) → one unit left → ( 5 - 1, 5 ) = (4, 5)

The rule to move ordered pair 8 units left, 8 will be added in the x coordinates

(4, 5) → one unit left → ( 4 + 8, 5 ) = (12, 5)

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Answer:

Step-by-step explanation:

This is a simple linear equation.

Y=12x + 43

The 12x represents the money he makes hourly, as x represents each hour he works

+43 represents the amount of money in tips he made since this was added on top of the hourly pay he was making.

Answer:

your welcome

Step-by-step explanation:

42+43=85$

to get the 42 you have to do 83-43 and that leaves you with 42

In terms of fractions, 2/5 of the icicle was eaten by the boy.

In mathematical term:

A boy ate three fifth of an icicle = 3/5

A boy gave = 1/3

So, Icicle eaten by the boy = 3/5 - 1/3

= (9 - 3) / 15

= 6/15

= 2/5

Hence, In terms of fractions 2/5 of the icicle was eaten by the boy.

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The largest possible total area of the three pens is 15312.5sq.units.

What is a rectangular area?

The quantity of space occupied by a flat surface with a specific shape is referred to as the area.

Area of a Rectangle = (Length × Breadth) square units.

Here,

We let x be the length and y be the breadth of a rectangle area.

Given equation : 2y + 4x = 700

y + 2x  = 350

y = 350 - 2x .......(1)

Area of rectangular field (A)= xy

A = x(350 - 2x)

A = 350x - 2x²

Differentiating w.r.t x we get,

A' = 350 - 4x

Again, differentiating w.r.t x we get,

A" = -4

Let A' = 0

350 - 4x = 0

4x = 350

x = 87.5

A is maximum at 87.5feets.

Hence, the largest possible total area of the three pens = XY = 87.5×175 = 15312.5 sq. units.

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The value of (y-x) when (x-y) = 3 is -3.

According to the question,

We have the following equation:

x-y = 3

Now, we have to find the value of (y-x). We can easily do this by multiplying both sides of this equation by -1.

We know that the multiplication of two negative integers always gives us the positive results and the multiplication of one negative and one positive integer give us the negative results.

So, we will have the following expression:

-x+y = -3

It can rewritten as follows:

y-x = -3

Hence, the value of (y-x) when (x-y) = 3 is -3.

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Answer: The pickles are $3.99

Step-by-step explanation:For percents,this is always done by simply dividing the percent (in this case 15%) by 100%. So, the conversational term "15%" becomes 15% / 100% = 0.15 in terms of a real mathematical number. 0.15 x $152.00=$3.99

The vertex form of Parabola is y= 1/4(x + 2)² -4 .

The general equation of a parabola is given by y = a(x – h)² + k or

x = a(y – k)² +h. Here (h, k) is vertex.

Given:

focus at (–2,–3) and a directrix at y = –5.

We know, the standard form is (x - h)² = 4p (y - k),

where the focus is (h, k + p) and the directrix is y = k - p

So, (h, k + p) = (-2, -3)

h = -2, k + p = -3

Directrix is y = k - p:

k - p = -5

k + p = -3

so, 2k = -8

k = -4

and, p = -3+ 4 = 1

Thus, the vertex is at (-2, -4) and p = 1, the equation is:

(x + 2)² = 4(y+  4)

1/4(x + 2)² =  y+4

y= 1/4(x + 2)² -4

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Answer:

Step-by-step explanation:

do you happen to know the formula for finding the area of a cone?

V=π*[tex]r^{2}[/tex]*h/3

does that formula look familiar?

we know the radius ,  r,  is 18 and the height, h is 6  :)  can you figure this out now?   just plug those into the formula above  :)

Answer: How many cards are there tho?

Step-by-step explanation:

Answer:

A or C

Step-by-step explanation:

Answer: x - 2y = -10.

Step-by-step explanation:

The value of x is x=p(m-n).

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Given expression: m=n+(x/p)

To find: Make x the subject.

To make x the subject we have to separate the x to one side.

Expression m=n+(x/p)

Take n to another side,

(x/p)=m-n

Cross multiply,

x=p(m-n)

Therefore, the value of x is x=p(m-n).

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Answer:

48000

Step-by-step explanation:

I multiplied the length times width time height (20x40x60) to get 48000.