the terminal side of an angle in standard position passes through P(-3,-4). what’s the value of tan(Theta)

Answer:

Yes

Both equilateral and equiangular triangles

Step-by-step explanation:

The AA (Angle-Angle) similarity states that if two pairs of corresponding angles are congruent, then the triangles are similar

In equilateral triangles, all angles are equal.The corresponding sides of two equilateral triangles are congruent thus they will be similar. An Equiangular triangle is also an equilateral triangle because its interior angles are the same and add up to 180°.

Both equilateral and equiangular triangles are similar by the Angle-Angle Similarity Postulate because they each have two congruent angles with any other triangle of the same type.

The Angle-Angle (AA) Similarity Postulate states that two triangles are similar if two angles of one triangle are congruent to two angles of the other triangle. Equilateral triangles are similar by AA postulate because all angles in any equilateral triangle measure 60 degrees, thus any two will be congruent with any two angles in another equilateral triangle. Equiangular triangles are also similar by the AA postulate, as all their corresponding angles are equal. Consequently, both equilateral and equiangular triangles are similar according to the AA Similarity Postulate.

Answer:

The independent variable is the time (variable x)

The dependent variable is the number of cars he washes (variable y)

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In this problem

The relationship between the number of cars he washes and the time it takes  him to wash those cars represent a a proportional variation

Let

y -----> the number of cars he washes

x -----> the time

The linear equation is [tex]y=kx[/tex]

The independent variable is the time x

The dependent variable is the number of cars he washes y

Answer:

y-7 = -5(x+2)

or

y = -5x-3

Step-by-step explanation:

We can use the point slope form of the equation

y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point

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

y-7 = -5(x+2)

If we want the equation in slope intercept form

Distribute

y-7 = -5x-10

Add 7 to each side

y-7+7 = -5x-10+7

y = -5x-3

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

We know that the slope of the line (m)  will be -5

y = -5x + b

Now we must find b

To do that you must plug in the point the line goes through in the x and y of the equation.

(-2, 7)

7 = -5(-2) + b

7 = 10 + b

-3 = b

y = -5x - 3

Hope this helped!

~Just a girl in love with Shawn Mendes

The total distance from Chicago to New Orleans is calculated by adding the distances from Chicago to Memphis and then from Memphis to New Orleans, which totals to 921.2 miles.

In order to calculate the total distance from Chicago to New Orleans, we simply need to add the given distances. The distance from Chicago to Memphis is 527.4 miles and from Memphis to New Orleans is 393.8 miles. Hence, the total distance from Chicago to New Orleans would be 527.4 miles + 393.8 miles = 921.2 miles. So, the total travel distance from Chicago to New Orleans is 921.2 miles.

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Answer:

Median: 4.5

Mode: 4

Mean: 6.7

Step-by-step explanation:

First lets find the median, the number in the middle. To do this we need to put this data set in ascending order

1,4,4,4,4,5,7,8,15,15

The two numbers in the middle are 4 and 5. Now we must add these two numbers together and then divide by 2.

[tex]\frac{4+5}{2} =\frac{9}{2} =4.5[/tex]

Nexte lets find the mode, the number that occurs the most. 4 appears 4 times, which is the greatest amount.

Now lets find the mean. First we need to find the sum of these 10 numbers

[tex]1+4+4+4+4+5+7+8+15+15=67[/tex]

Next we have to divide by the number of data points, which is 10

[tex]\frac{67}{10} =6.7[/tex]

Answer:

C

Step-by-step explanation:

Given

x² = 7x - 3 ( subtract 7x - 3 from both sides )

x² - 7x + 3 = 0 ← in standard form

with a = 1, b = - 7, c = 3

Using the quadratic formula to solve for x

x = ( - (- 7) ± [tex]\sqrt{(-7)^2-(4(1)(3)}[/tex] ) / 2

  = ( 7 ± [tex]\sqrt{49-12}[/tex] ) / 2

  = [tex]\frac{7+/-\sqrt{37} }{2}[/tex] → C

Answer:

[tex]\frac{dy}{dx}=\frac{4y-2x}{y-4x}[/tex]

Step-by-step explanation:

[tex]\frac{d}{dx}(2x^2)=4x[/tex]

[tex]\frac{d}{dx}(y^2)=2y\frac{dy}{dx}[/tex]

[tex]\frac{d}{dx}(8xy)[/tex]

[tex]=8\frac{d}{dx}(xy)[/tex]

[tex]=8(\frac{d}{dx}(x)y+x\frac{d}{dx}(y))[/tex]

[tex]=8[1y+x\frac{dy}{dx}][/tex]

[tex]=8y+8x\frac{dy}{dx}[/tex]

Let's put it altogether now:

[tex]2x^2+y^2=8xy[/tex]

Differentiating both sides gives:

[tex]4x+2y\frac{dy}{dx}=8y+8x\frac{dy}{dx}[/tex]

We are solving for dy/dx so we need to gather those terms on one side and the terms without on the opposing side:

I'm going to first subtract 4x on both sides:

[tex]2y\frac{dy}{dx}=8y-4x+8x\frac{dy}{dx}[/tex]

I'm not going to subtract 8xdy/dx on both sides:

[tex]2y\frac{dy}{dx}-8x\frac{dy}{dx}=8y-4x[/tex]

It is time to factor the dy/dx out of the two terms on the left:

[tex]\frac{dy}{dx}(2y-8x)=8y-4x[/tex]

Divide both sides by (2y-8x):

[tex]\frac{dy}{dx}=\frac{8y-4x}{2y-8x}[/tex]

Reduce right hand side fraction:

[tex]\frac{dy}{dx}=\frac{4y-2x}{y-4x}[/tex]

Answer:

[tex]\frac{8y-4x}{2y-8x}[/tex]

Step-by-step explanation:

Differentiate implicitly with respect to x

noting that

[tex]\frac{d}{dx}[/tex] (y² ) = 2y[tex]\frac{dy}{dx}[/tex]

Differentiate 8xy using the product rule

Given

2x² + y² = 8xy, then

4x + 2y[tex]\frac{dy}{dx}[/tex] = 8x[tex]\frac{dy}{dx}[/tex] + 8y

Collect terms in [tex]\frac{dy}{dx}[/tex]

2y[tex]\frac{dy}{dx}[/tex] - 8x[tex]\frac{dy}{dx}[/tex] = 8y - 4x

[tex]\frac{dy}{dx}[/tex] (2y - 8x) = 8y - 4x

[tex]\frac{dy}{dx}[/tex] = [tex]\frac{8y-4x}{2y-8x}[/tex]

Answer:

In order:

2nd step

1st step

3rd step

4th step

Step-by-step explanation:

The checking part comes last.

Before you can determine the solution, your lines need to be graphed.

To graph your lines, they have to be in a form for you to determine how to graph them.

So the first step here is

"Write each equation in a form that is easy to graph"

The second step is:

To graph them

Third step is:

To see where they cross

The last step:

(Some people don't do it but should is check it).

The recursive formula for the sequence -16, -33, -50, -67, .... is  f(n) = f(n - 1) - 17, f(1) = -16

Finding the recursive formula for the sequence

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

-16, -33, -50, -67, ....

In the above sequence, we can see that -17 is added to the previous term to get the new term

This means that

First term, a = -16

Common difference, d = -17

The recursive formula for the sequence is then represented as

f(n) = f(n - 1) - 17, f(1) = -16

Final answer:

The annualized ROI is calculated by dividing the total ROI, which is 150%, by the number of years, which is 5, resulting in an annualized ROI of 30%. The correct answer is option (C).

Explanation:

To calculate the annualized ROI, we first determine the total ROI by using the formula:

Total ROI = (final value – initial value) / initial value × 100

Substituting the given values:

Total ROI = ($25,000 – $10,000) / $10,000 × 100 = $15,000 / $10,000 × 100 = 150%

As this ROI was achieved over a period of 5 years, to find the annualized ROI, we divide the total ROI by the number of years:

Annualized ROI = Total ROI / number of years

Annualized ROI = 150% / 5 = 30%

Therefore, the correct answer is C. 30%.

Answer:

  A. 50%

Step-by-step explanation:

You want the annualized ROI represented by a profit of $25,000 over a period of 5 years on a $10,000 investment.

Your formula seems to be ...

  [tex]\text{annualized ROI}=\dfrac{\text{final value}-\text{initial value}}{(\text{initial value})(\text{number of years})}\times100\%[/tex]

The profit is the difference between final value and initial value, so this becomes ...

  [tex]\text{annualized ROI}=\dfrac{\text{profit}}{(\text{initial value})(\text{number of years})}\times100\%\\\\\\\text{annualized ROI}=\dfrac{25000}{(10000)(5)}\times100\%=50\%[/tex]

The annualized ROI in this scenario is 50%, choice A.

__

Additional comment

The annualized ROI is effectively the "internal rate of return" for a given set of cash flows. If we assume $10,000 is paid at the beginning of year 1, and $5000 is received at the end of each of 5 years followed by repayment of the initial $10,000 investment along with the last dividend, then the IRR is exactly 50%.

If the total profit of $25000 is distributed differently in time, then the rate of return is different. For example, if $35,000 is received at the end of 5 years, the IRR is about 28.47%.

Answer:

-3

Step-by-step explanation:

a₁ = a₂/r = 3/(-1)=-3

a₉ = a₁ · r⁸ = -3 · (-1)⁸ = -3 · 1 = -3

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x-2y=-26\\x-y=-2&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}x-2y=-26\\-x+y=2\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-y=-24\qquad\text{change the signs}\\.\qquad\qquad y=24\\\\\text{Put the value of y to the second equation:}\\\\x-24=-2\qquad\text{add 24 to both sides}\\x=22[/tex]

Answer:

The mean is equal to the median.

Step-by-step explanation:

Median is the middle value of a given data set. In a symmetric distribution, the data on the left side of the median is equal to the data on the right side of the median. Therefore, the mean of that data is equal to the median of the symmetric distribution.

Answer:

the mean is less than the explanation

Step-by-step explanation:

I just checked

Answer: the actual answer is triangle b and triangle f

Triangle B and triangle F are not congruent with any other given triangles

So we are left with triangle B and triangle F.

The size and shapes of these triangles does not matches with any other triangles.

So  triangle B and triangle F are not congruent with any other given triangles.

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[tex]2\cdot50+2\cdot100=100+200=300[/tex]

300ft of fencing is required to enclose the whole yard.

Hope this helps.

r3t40

Answer:

300

Step-by-step explanation:

l + l + w + w

50 + 50 + 100 + 100 = 300

Answer:

The volume of the pyramid is [tex]V=\frac{1}{3}(x^{2})(y)\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the pyramid is equal to

[tex]V=\frac{1}{3}BH[/tex]

where

B is the area of the base

H is the height of pyramid

we know that

The area of the base is

[tex]B=x^{2}\ cm^{2}[/tex]

The height is equal to

[tex]H=y\ cm[/tex]

substitute

[tex]V=\frac{1}{3}(x^{2})(y)\ cm^{3}[/tex]

Answer:

A. 30 meters

Step-by-step explanation:

Let's find the answer.

The problem established a quadratic relationship between height (h) and time (t), then we can establish:

h(t)=K*t where 'K' is a coefficient.

Because an experiment was done, we can find 'K' as follows:

h(t)=K*t

90meters=K*(3seconds)

90meters/3seconds=K

30m/s=K

Now we can solve the problem, so for 2 seconds:

h(t)=K*t

h(t)=(30m/s)*(2s)

h(t)=60m

But notice that the obtained 60 meters are the distance traveled in 2 seconds from the top the building to the ground. So 'how far from the ground' can be calculated as:

(far from the ground) = (total building height) - (distance traveled in 2s)

(far from the ground) = 90m - 60m = 30m

In conclusion, after 2 seconds, the ball is 30 meters far from the ground. The answer in then A. 30 meters.

Answer:

40 meters

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 9.81 m/s²

[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow u=\frac{s-\frac{1}{2}at^2}{t}\\\Rightarrow u=\frac{90-\frac{1}{2}\times 9.81\times 3^2}{3}\\\Rightarrow u=15.285\ m/s[/tex]

u = 15.285 m/s

[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow s=15.285\times 2+\frac{1}{2}\times 9.81\times 2^2\\\Rightarrow s=50.19\ m[/tex]

The ball has fallen 50.19 m from the top of the building.

So, the ball is 90-50.19 = 39.81 = 40 meters off the ground

Answer:

90

Step-by-step explanation:

Alright first step what is the degree measure of LN.

A full rotation is 360 degrees so LN=360-270=90.

So angle M is half the difference of the intercepted arcs:

[tex]\frac{1}{2}(270-90)=\frac{1}{2}(180)=90[/tex]

The measure of the vertex angle from the given geometry figure is 90 degrees

The given circle is made up of arc and angles. In order to determine the value of <M, we will use the theorem

"The half of the difference between the arc is equal to the angle at the vertex

1/2(270 - (360 - 270)) = <M
<M = 1/2 (270 -90)

<M = 1/2(180)

<M = 90degrees

Hence the measure of the vertex angle from the given geometry figure is 90 degrees

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Answer:

C. supplementary angles

D. straight angle

The given angles ABD and DBC lies on a straight line. So they are straight angle.

We know that the sum of the straight angles is = 180 degrees. If the sum of two angles is 180 degrees, then they are also called supplementary angles.

It means the shown angles are also supplementary angles.

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Answer:

D and C

Step-by-step explanation:

Answer:

x=-1, y = 2, z = 1

Step-by-step explanation:

We are given with three equations and we are asked to find the solution to them.

2x + 2y + 3z = 5  ------------- (A)

6x + 3y + 6z = 6  --------------(B)

3x + 4y + 4z = 9 ---------------(C)

Step 1 .

multiplying equation (A) by 3 and subtracting B from the result

6x + 6y + 9z = 15

6x + 3y + 6z = 6

-     -       -       = -

_______________

3y+3z=9

y+z=3

y=3-z  ----------------- (C)

Step 2.

Substituting this value of y in equation B and C

6x + 3(3-z) + 6z = 6  

6x+9-3z+6z=6

6x+3z=-3

2x+z=-1 ----------------(D)

3x + 4(3-z) + 4z = 9

3x+12-4z+4z=9

3x=-3  

x=-1 ------------ (E)

Putting this value f x in (D)

2(-1)+z=-1

-2+z=-1

z=1

Now we put this value of z in equation (C)

y=3-z

y=3-1

y=2

Hence we have

x=-1, y=2 and z=1

Answer:

Degree is 2 so it is a quadratic.

The number of terms is 2 so it is a binomial.

It is a binomial quadratic.

Step-by-step explanation:

Let's find the degree of the polynomial first. I'm going to consider first the degrees of 5x^2 and 3.

The degree of the monomial 5x^2 is 2 because x is the only variable and it's exponent is 2.

The degree of the monomial 3 is 0 because there is no variable.

The degree of 5x^2+3 is therefore 2 because that is the highest degree of the monomials contained with in this polynomial 5x^2+3.

Degree 2 has a special name.

The special name for a degree 2 polynomial is quadratic.

Let's look at the number of terms in 5x^2+3.

Terms are separated by addition and subtraction symbols so there are two terms.

There is a special name for a two-termed polynomial, it is binomial.

So this is the following information I collected on our given polynomial:

Degree is 2 so it is a quadratic.

The number of terms is 2 so it is a binomial.

It is a binomial quadratic.

Answer:

x=61

Step-by-step explanation:

In a triangle all measure add up to 180 degrees, therefore

52+67=119

180-119=61

This means we have 61 degrees remaining to complete the triangle

Answer:

[tex]x=61^{\circ}[/tex]

Step-by-step explanation:

We have been that B is 67 degrees and angle C is 52 degrees. We are asked to find the value of x of angle A.

We will use angle sum property to solve our given problem.

Angle sum property of triangle states that sum of all angles of a triangle is equal to 180 degrees.

Using angle sum property, we can set an equation as:

[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]

Upon substituting our given values in above equation, we will get:

[tex]x+67^{\circ}+52^{\circ}=180^{\circ}[/tex]

[tex]x+119^{\circ}=180^{\circ}[/tex]

[tex]x+119^{\circ}-119^{\circ}=180^{\circ}-119^{\circ}[/tex]

[tex]x=61^{\circ}[/tex]

Therefore, the value of x is 61 degrees.

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 12x + 7 ← is in this form

with m = 12 and c = 7

y = 12x + 2 ← is also in this form

with m = 12 and c = 2

Since the slopes are equal the lines are parallel

c = 7 → c = 2 is a vertical translation of 5 units down

In comparison the line y = 12x + 2 is parallel to y = 12x + 7

and translated < 0, - 5 >

Answer:

D. (-7/2, 3/2)

Step-by-step explanation:

x = (-6+(-1))/2 = -7/2

y = (-2+5)/2 = 3/2

Answer:  D.

[tex](\dfrac{-7}{2},\ \dfrac{3}{2})[/tex]

Step-by-step explanation:

The coordinates of mid point (x,y) of a line joining points [tex](x_1 , y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by :-

[tex]x=\dfrac{x_1+x_2}{2},\ y=\dfrac{y_1+y_2}{2}[/tex]

From the given graph , we can see that the line is joining two points (-6,-2) and (-1,5) .

Then, the mid point of the line is given by :-

[tex]x=\dfrac{-6+(-1)}{2},\ y=\dfrac{-2+5}{2}[/tex]

[tex]x=\dfrac{-6-1}{2},\ y=\dfrac{5-2}{2}[/tex]

[tex]x=\dfrac{-7}{2},\ y=\dfrac{3}{2}[/tex]

Hence, the midpoint of the given segment = [tex](\dfrac{-7}{2},\ \dfrac{3}{2})[/tex]

Answer:

(2, -16).

Step-by-step explanation:

(x - 6)(x + 2)

Convert to vertex form:

Expanding the parentheses we have:

x^2 + 2x - 6x - 12

= x^2 - 4x - 12

Completing the square:

= (x - 2)^2 - 4 - 12

= (x - 2)^2 - 16

So the vertex is (2, -16),

To estimate the age of the skull, we can use the concept of radioactive decay of carbon-14. We can set up an equation to find the original amount of C-14, and then calculate the number of half-lives that have occurred to determine the age of the skull.

The age of the skull can be estimated using the concept of radioactive decay of carbon-14 (C-14). The half-life of C-14 is approximately 5730 years, which means that after 5730 years, half of the original amount of C-14 will remain. Since the skull contains 32% of its original amount of C-14, we can estimate that 68% has decayed. To find the age of the skull, we can set up the following equation:

0.68 * original amount = current amount

Solving for the original amount gives us:

original amount = current amount / 0.68

Now, we just need to divide the age of the skull by the half-life of C-14 to find the number of half-lives that have occurred. We can then multiply this by 5730 years to get the approximate age of the skull to the nearest year.

Answer:

The center of this circle is at (6, 1).

Step-by-step explanation:

Rewrite x^2+y^2-12x-2y+12=0 by grouping like terms.  Then:

x^2+y^2-12x-2y+12=0 becomes x^2 - 12x +y^2 - 2y + 12=0.

Next, complete the squares:

x^2 - 12x + 36 - 36 + y^2 - 2y + 1 - 1 + 12 = 0.

Rewriting the two perfect squares as squares of binomials, we get:

(x - 6)^2 - 36 + (y - 1)^2 - 1 + 12 = 0

Moving the constants to the right side:

(x - 6)^2     + (y - 1)^2   = 36 + 1 - 12 = 25

Then the desired equation is:

(x - 6)^2 + (y - 1)^2 = 5^2.  The center of this circle is at (6, 1).

Answer:

The top one

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x + 1 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex] and y- intercept c = + 1

Since m > 0 then graph slopes upwards from left to right

That indicates the top or bottom graphs

The bottom one has a y- intercept of c = - 1

While the top one has a y- intercept of c = + 1

Hence the top graph is the graph of y = [tex]\frac{1}{2}[/tex] x + 1

Hence, the graph of f(x) = 2x is A.

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

On plotting the graph of f(x) = [tex]\frac{1}{2}x + 1[/tex],

we observe that it is coincident to option A.

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Answer:

1.6 m

Step-by-step explanation:

The side of the sign, the ground, and the wire form a right triangle where the wire is the hypotenuse.

The angle of depression plus the upper interior angle of the triangle add to 90 degrees. That means that the upper acute angle of the triangle measures 90 - 28 = 62 deg.

Call the upper acute angle of the triangle Angle A and the height of the sign h.

tan A = opp/adj

tan 62 = 3/h

h tan 62 = 3

h = 3/tan 62

h = 1.6

Answer: 1.6 m

Answer:

The tall of the sign board is 1.6 m.

Step-by-step explanation:

Let's draw a diagram to represents the given situation.

In the diagram, the base of the festival sign to the ground forms 90°. So it is right triangle.

The angle of depression is 28°. The angle of the upper interior angle = 90° - 28° = 62°.

Now we can use the trigonometric ration "tan = [tex]\frac{Oppsoite}{Adjacent}[/tex]" and the height of the sign board.

Let's take "h" be the height/tall of the sign board.

As you can see in the diagram, the opposite side = 3m

Now plug in the given values in the tan ratio, we get

tan 62° = [tex]\frac{3}{h}[/tex]

The value of tan 62° = 1.88

So, 1.88 =  [tex]\frac{3}{h}[/tex]

h =  [tex]\frac{3}{1.88}[/tex]

h = 1.595

We are asked to round of the nearest tenths place.

So, h = 1.6 m

Therefore, the tall of the sign board is 1.6 m.

Answer:

The smallest integer = 49

Step-by-step explanation:

It is given that, the sum of five consecutive odd integers is 265

To find the smallest integer

Let 'x' be the smallest odd  integer, the other integers are,

(x + 2), (x + 4), (x + 6), and (x + 8)

x + x + 2 + x + 4 + x + 6 + x + 8 = 265

5x + 20 = 265

5x = 245

x = 245/5 = 49

Therefore the smallest integer = 49

Answer:

49,50,51,52,53

Step-by-step explanation: