What is tan 30°?
1
60°
90°
√3
2
30°
OA. √2
B. √3
O C. √√3
OD. √3
2
O E 1
OF.
F. 7/3

[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 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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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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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:

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

Answer:

-6/11

Step-by-step explanation:

please follow me to mark me on brainliest

Answer: 175

Step-by-step explanation:

7 x 1 x 5^2

7 x 1 x 25

7 x 25

175

Answer:

175

Step-by-step explanation:

Since we have 7ca^2 and since we know a = 5 and c = 1, we can just plug in these values for a and c and follow the order of operations:

[tex]7ca^2\\7(1)(5)^2\\7(1)(25)\\7*25=175[/tex]

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 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 polynomial of p(x) is 20/13(x³+4x²-9x-36) with the satisfying's conditions degree 3.

Given that,

An nth degree polynomial p meets the requirements listed below:

p is of degree 3.

-3 is a multiplicity 1 zero of p.

-4 is a zero, with multiplicity 1, of p.

3 is a root, with multiplicity 1, of p.

p(-2)=-40

We have to determine an nth degree polynomial that satisfier the conditions.

Let the polynomial be p(x) whose zero are -3,-4 and 3.

a be the coefficient.

p(x)=a(x+3)(x+4)(x-3)

p(x)=a(x²-3²)(x+4)

p(x)=a(x²-9)(x+4)

p(x)=a(x³+4x²-9x-36)

Now, take x=-2

p(-2)=a((-2)³+4(-2)²-(-2)-36)

-40=a(-8+16+2-36)

-40=a(-26)

a=-40/-26

a=40/26

a=20/13

We get,

p(x)=20/13((x+3)(x+4)(x-3))

p(x)=20/13(x³+4x²-9x-36)

Therefore, the polynomial of p(x) is 20/13(x³+4x²-9x-36) with the satisfying's conditions degree 3.

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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:

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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Answer:

48000

Step-by-step explanation:

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

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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[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]

Answer:

false

Step-by-step explanation:

25% is equivalent to 0.25

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 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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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  :)

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:

A or C

Step-by-step explanation:

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:

-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

All that apply are:

The slope is 0.

The y-intercept is -2

The line is horizontal.

The equation of the line is Y = -2.

Given points:

(1,-2) and (4,-2)

slope m = -2-(-2) / 4 - 1

= -2+2/3

= 0

so slope is 0

y = mx + c

(1,-2) passes

-2 = 0*1 + c

c = -2

y = 0*x + -2

y = -2

so the line is horizontal and equation of the line is y = -2.

The y-intercept is -2.

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Answer:

3.1

Step-by-step explanation:

23.5-6.8x

x=3

first put 3 in for x

23.5-6.8(3)

now solve the expression

23.5-20.4

3.1

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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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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Answer:

y=-5x+19

Step-by-step explanation:

yeah -ya...... right?