Choose the equation that represents a line that passes through points (-6,0) and (2,0).

Answer:

a=2*n*pi where n is an integer

Step-by-step explanation:

[tex]\frac{\cos^2(a)}{1-\tan(a)}+\frac{\sin^3(a)}{\sin(a)-\cos(a)}[/tex]

The denominators are different here so I'm going to try to make them the same.

I'm going to write everything in terms of sine and cosine.

That means I'm rewriting tan(a) as sin(a)/cos(a)

[tex]\frac{\cos^2(a)}{1-\frac{\sin(a)}{\cos(a)}}+\frac{\sin^3(a)}{\sin(a)-\cos(a)}[/tex]

I'm going to multiply top and bottom of the first fraction by cos(a) to clear the mini-fraction from the bigger fraction.

[tex]\frac{\cos^2(a)}{1-\frac{\sin(a)}{\cos(a)}} \cdot \frac{\cos(a)}}{\cos(a)}+\frac{\sin^3(a)}{\sin(a)-\cos(a)}[/tex]

Distributing and Simplifying:

[tex]\frac{\cos^3(a)}{\cos(a)-\sin(a)}+\frac{\sin^3(a)}{\sin(a)-\cos(a)}[/tex]

Now I see the bottom's aren't quite the same but they are almost... They are actually just the opposite. That is -(cos(a)-sin(a))=-cos(a)+sin(a)=sin(a)-cos(a).

Or -(sin(a)-cos(a))=-sin(a)+cos(a)=cos(a)-sin(a).

So to get the denominators to be the same I'm going to multiply either fraction by -1/-1... I'm going to do this to the second fraction.

[tex]\frac{\cos^3(a)}{\cos(a)-\sin(a)}+\frac{\sin^3(a)}{\sin(a)-\cos(a)} \cdot \frac{-1}{-1}[/tex]

[tex]\frac{\cos^3(a)}{\cos(a)-\sin(a)}+\frac{-\sin^3(a)}{\cos(a)-\sin(a)}[/tex]

The bottoms( the denominators) are the same now.  We can write this as one fraction, now.

[tex]\frac{\cos^3(a)-\sin^3(a)}{\cos(a)-\sin(a)}[/tex]

I don't know if you know but we can factor a difference of cubes.

The numerator is in the form of a^3-b^3.

The formula for factoring that is (a-b)(a^2+ab+b^2).

[tex]\frac{(\cos(a)-\sin(a))(\cos^2(a)+\cos(a)\sin(a)+\sin^2(a)}{\cos(a)-\sin(a)}[/tex]

There is a common factor of cos(a)-sin(a) on top and bottom you can "cancel it".  

So we now have

[tex]\cos^2(a)+\cos(a)\sin(a)+\sin^2(a)[/tex]

We can actually simplify this even more.

[tex]\cos^2(a)+\sin^2(a)=1[/tex] is a Pythagorean Identity.

So we rewrite [tex]\cos^2(a)+\cos(a)\sin(a)+\sin^2(a)[/tex]

as [tex]1+\cos(a)\sin(a)[/tex]

So that is what we get after simplifying left hand side.

So I guess we are trying to solve for a.

[tex]1+\cos(a)\sin(a)=\sin(a)+\cos(a)[/tex]

Subtract sin(a) and cos(a) on both sides.

[tex]\cos(a)\sin(a)-\sin(a)-\cos(a)+1=0[/tex]

This can be factored as

[tex](\sin(a)-1)(\cos(a)-1)=0[/tex]

So we just need to solve the following two equations:

[tex]\sin(a)-1=0 \text{ and } \cos(a)-1=0[/tex]

[tex]\sin(a)=1 \text{ and } cos(a)=1 \text{ I just added one on both sides}[/tex]

Now we just need to think of the y-coordinates on the unit circle that are 1

and the x-coordinates being 1 also (not at the same time of course).

List thinking of the y-coordinates being 1:

a=pi/2 , 5pi/2 , 9pi/2 , ....

List thinking of the x-coordinates being 1:

a=0, 2pi, 4pi,...

So let's come up with a pattern for these because there are infinite number of solutions that continue in this way.

If you notice in the first list the number next to pi is going up by 4 each time.

So for the first list we can say a=(4pi*n+pi)/2 where n is an integer.

The next list the number in front of pi is just even.

So for the second list we can say a=2*n*pi where n is an integer.

So the solutions is a=2*n*pi   ,    a=(4pi*n+pi)/2

We really should make sure if this is okay for our original equation.

We don't have to worry about the second fraction because sin(a)=cos(a) only when a is pi/4 or pi/4+2pi*n OR (pi+pi/4) or (pi+pi/4)+2pi*n.

Now the second fraction we have 1-tan(a) in the denominator, and it is 0 when:

tan(a)=1

sin(a)/cos(a)=1                       =>              sin(a)=cos(a)

So the only thing we have to worry about here since we said sin(a)=cos(a) doesn't hurt our solution is the division by the cos(a).

When is cos(a)=0?

cos(a)=0 when a=pi/2 or any rotations that stop there (+2npi thing) or at 3pi/2 (+2npi)

So the only solutions that work is the a=2*n*pi where n is an integer.

Answer:

[tex]\large\boxed{a=2k\pi\ for\ k\in\mathbb{Z}}[/tex]

Step-by-step explanation:

[tex]\bold{a=x}[/tex]

[tex]\text{The domain:}\\\\1-\tan x\neq0\ \wedge\ \sin x-\cos x\neq0\ \wedge\ x\neq\dfrac{\pi}{2}+k\pi\ (from\ \tan x)\\\\\tan x\neq1\ \wedge\ \sin x\neq\cos x\\\\x\neq\dfrac{\pi}{4}+k\pi\ \wedge\ x\neq\dfrac{\pi}{4}+k\pi\ for\ k\in\mathbb{Z}[/tex]

[tex]\dfrac{\cos^2x}{1-\tan x}+\dfrac{\sin^3x}{\sin x-\cos x}=\sin x+\cos x[/tex]

[tex]\text{Left side of the equation:}[/tex]

[tex]\text{use}\ \tan x=\dfrac{\sin x}{\cos x}\\\\\dfrac{\cos^2x}{1-\tan x}=\dfrac{\cos^2x}{1-\frac{\sin x}{\cos x}}=\dfrac{\cos^2x}{\frac{\cos x}{\cos x}-\frac{\sin x}{\cos x}}=\dfrac{\cos^2x}{\frac{\cos x-\sin x}{\cos x}}=\cos^2x\cdot\dfrac{\cos x}{\cos x-\sin x}\\\\=\dfrac{\cos^3x}{\cos x-\sin x}\\\\\dfrac{\cos^2x}{1-\tan x}+\dfrac{\sin^3x}{\sin x-\cos x}=\dfrac{\cos^3x}{\cos x-\sin x}+\dfrac{\sin^3x}{\sin x-\cos x}\\\\=\dfrac{\cos^3x}{\cos x-\sin x}+\dfrac{\sin^3x}{-(\cos x-\sin x)}[/tex]

[tex]=\dfrac{\cos^3x}{\cos x-\sin x}-\dfrac{\sin^3x}{\cos x-\sin x}\\\\=\dfrac{\cos^3x-\sin^3x}{\cos x-\sin x}\qquad\text{use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\=\dfrac{(\cos x-\sin x)(\cos^2x+\cos x\sin x+\sin^2x)}{\cos x-\sin x}\qquad\text{cancel}\ (\cos x-\sin x)\\\\=\cos^2x+\cos x\sin x+\sin^2x\qquad\text{use}\ \sin^2x+\cos^2x=1\\\\=\cos x\sin x+1[/tex]

[tex]\text{We're back to the equation}[/tex]

[tex]\cos x\sin x+1=\sin x+\cos x\qquad\text{subtract}\ \sin x\ \text{and}\ \cos x\ \text{from both sides}\\\\\cos x\sin x+1-\sin x-\cos x=0\\\\(\cos x\sin x-\sin x)+(1-\cos x)=0\\\\\sin x(\cos x-1)-1(\cos x-1)=0\\\\(\cos x-1)(\sin x-1)=0\iff \cos x-1=0\ or\ \sin x-1=0\\\\\cos x=1\ or\ \sin x=1\\\\x=2k\pi\in D\ or\ x=\dfrac{\pi}{2}+2k\pi\notin D\ for\ k\in\mathbb{Z}[/tex]

Answer:(7,52)

Step-by-step explanation:plug those values into the equation.

52<8(7)+3.

52<59.

Answer:

d =12

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

Substituting what we know

36 pi = pi r^2

Divide each side by pi

36 pi/pi = pi r^2/pi

36 = r^2

Taking the square root of each side

sqrt(35) = sqrt(r^2)

6 =r

We want the diameter

d = 2r

d = 2(6)

d = 12

D. 103 12/13 or about 104

First sort the data into two sets of points, (1989,2881), (2002, 4232).

Now use the slope equation with your numbers.

(y2-y1)/(x2-x1)

(4232-2881)/(2002-1989)

1351/13=

103 12/13 or about 104

The y-intercept would elevate up the y-axis by 3

This is because the y-intercept in y= -4x+2 is 2 and when you change it to y= -4x+5 you are moving the intercept to a y of 5.

Answer:

The HCF = 3.

Step-by-step explanation:

The prime factors of

234 = 2*3*3*13,

and of 111 = 3*37.

The only common factor is 3.

Answer:

(- 9 × 234 ) + (19 × 111 )

Step-by-step explanation:

Using the division algorithm to find the hcf

If a and b are any positive integers, then there exists unique positive integers q and r such that

a = bq + r → 0 ≤ r ≤ b

If r = 0 then b is a divisor of a

Repeated use of the algorithm allows b to be found

here a = 234 and b = 111

234 = 2 × 111 + 12 → (1)

111 = 9 × 12 + 3 → (2)

12 = 4 × 3 + 0 ← r = 0

Hence hcf = 3

We can now express the hcf (d) as

d = ax + by where x, y are integers

From (2)

3 = 1 × 111 - 9 × 12

From (1)

3 = 1 × 111 - 9( 1 × 234 - 2 × 111)

   = 1 × 111 - 9 × 234 + 18 × 111

   = - 9 × 234 + 19 × 111 ← in required form

with x = - 9 and y = 19

Answer:

=14

Step-by-step explanation:

In a rhombus, opposite angles are equal.

In the one provided in the question, 5x° is opposite the angle 70°

Let us equate the two.

5x=70

x=70/5

=14°

The value of x in the figure is 14°

Answer:

B

Step-by-step explanation:

1/2x < -3

Multiply each side by 2

1/2x *2 < -3*2

x < -6

Since x is less than -6, there is an open circle at -6

Less than means the line goes to the left

Answer:

The distance between (-3, 2) and (0,3) is √10.

Step-by-step explanation:

As we go from (-3,2)  to  (0,3), x increases by 3 and y increases by 1.

Think of a triangle with base 3 and height 1.  Use the Pythagorean Theorem to find the length of the hypotenuse, which represents the distance between the points (-3, 2) and (0, 3):

distance = √(3² + 1²) = √10

The distance between (-3, 2) and (0,3) is √10.

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]

We have the following points:

[tex](x_ {1}, y_ {1}): (- 3,2)\\(x_ {2}, y_ {2}) :( 0,3)[/tex]

Substituting:

[tex]d = \sqrt {(0 - (- 3)) ^ 2+ (3-2) ^ 2}\\d = \sqrt {(3) ^ 2 + (1) ^ 2}\\d = \sqrt {9 + 1}\\d = \sqrt {10}[/tex]

Answer:

The distance between the points is [tex]\sqrt {10}[/tex]

Answer:

$3.49

12 quarters,4 dimes,1 nickle, 4 pennies

Step-by-step explanation:

First remember that;

Quarter=25 pennies

Dime=10 pennies

Nickel =4 pennies

I cent =0.01$

Given the amount as $3.50

Assume you use 4 quarters, this means a whole dollar, so it will be;

1 dollar = 4quarters

3 dollars=?

cross multiply

3×4=12 quarters

The remaining $0.49

Here identify 40 cents, which is 40 pennies

But 10 pennies=1 dime

so 40 pennies=?

cross-multiply

(40×1)÷10=4 dimes

and a nickel for 4 pennies.

Answer:

B

Step-by-step explanation:

Factor the numerator, that is

x² + 6x + 8 = (x + 4)(x + 2), now

f(x) = [tex]\frac{(x+4)(x+2)}{x+4}[/tex]

Cancel the factor (x + 4) on the numerator/ denominator, leaving

f(x) = x + 2 ← simplified version

Cancelling the factor x + 4 leaves a discontinuity ( a hole ) at

x + 4 = 0 ⇒ x = - 4 and f(- 4) = x + 2 = - 4 + 2 = - 2

There is a discontinuity at (- 4, - 2 )

To find the zero let f(x) = 0, that is

x + 2 = 0 ⇒ x = - 2

The zero is (- 2, 0 )

Answer:

y=2x-2

Step-by-step explanation:

in slope intercept form we need make in this formula..

y=Mx+c

Answer:

y = 2x - 2

Step-by-step explanation:

Given

y + 6 = 2(x + 2) ← distribute

y + 6 = 2x + 4 ( subtract 6 from both sides )

y = 2x - 2 ← in slope- intercept form

Answer:

The value of y = 4.3

Step-by-step explanation:

It is given that,

5/7 = y/6

To find the value of y

We have, 5/7 = y/6

(5 * 6) = (y * 7)

y * 7 = 5 * 6

y = (5 * 6)/7

 = 30/7

 = 4.29

 ≈ 4.3

Therefore the correct answer, the value of y = 4.3

Answer:

y=2

Step-by-step explanation:

8 - y = 9 - 3

Combine like terms

8 - y = 6

Subtract 8 from each side

8-8 - y = 6-8

-y = -2

Multiply each side by -1

-1 * -y = -2 *-1

y =2

Answer:

c. when all angles are right angles

Step-by-step explanation:

Answer:

[tex]A=\frac{225t^2}{\pi}[/tex] given the circumference is 30t.

Step-by-step explanation:

The circumference of a circle is [tex]C=2\pi r[/tex] and the area of a circle is [tex]A=\pi r^2[/tex] assuming the radius is [tex]r[/tex] for the circle in question.

We are given the circumference of our circle is [tex]2 \pi r=30t[/tex].

If we solve this for r we get: [tex]r=\frac{30t}{2\pi}[/tex].  To get this I just divided both sides by [tex]2\pi[/tex] since this was the thing being multiplied to [tex]r[/tex].

So now the area is [tex]A=\pi r^2=\pi (\frac{30t}{2 \pi})^2[/tex].

Simplifying this:

[tex]A=\pi (\frac{30t}{2 \pi})^2[/tex].

30/2=15 so:

[tex]A=\pi (\frac{15t}{\pi})^2[/tex].

Squaring the numerator and the denominator:

[tex]A=\pi (\frac{(15t)^2}{(\pi)^2}[/tex]

Using law of exponents or seeing that a factor of [tex]\pi[/tex] cancels:

[tex]A=\frac{(15t)^2}{\pi}[/tex]

[tex]A=\frac{15^2t^2}{\pi}[/tex]

[tex]A=\frac{225t^2}{\pi}[/tex]

Answer:

red: 9/20, 0.45, 45%

White: 15%, 0.15, 3/20

Blue: 0.4, 2/5, 40%

Step-by-step explanation:

For red: you start with 9/20. It’s best to get to a denominator of 10. So divide each number by 2. You would get 4.5/10. Then change to a percent by moving the decimal of the numerator one to the right and changing it to percent. 4.5 -> 45. -> 45%. Then for the decimal, divide 45 by 100. 45/100 = 0.45.

For white: you start with 15%. Divide by 100. 15/100=0.15. Put into a fraction with a denominator of 100. It would be 15/100. Simplify. Each number can be divided by 5, so your fraction would be 3/20.

For blue: you start with 0.4. Turn this into a fraction. Since there is one decimal place, it can have a denominator of 10. The fraction is 4/10, simplified to 2/5. Using the fraction 4/10, the percent would be 40%.

I hope this helps!

Answer:

d=-4

Step-by-step explanation:

20 = –d + 16

Subtract 16 from each side

20-16 = –d + 16-16

4 = -d

Multiply each side by -1

-1 *4 = -1 * -d

-4 =d

Answer:

P(x) is the profit amount from selling tickets.

P(100) = $160

Step By Step Explanation:

First, plug in r(x) and c(x) into the p(x) equation:

p(x) = r(x) - c(x)

p(x) = (10x) - (8x+40)

Then simplify it:

p(x) = 10x - 8x - 40 {just distribute a +1 into the parentheses}

p(x) = 2x - 40 {combine like terms}

Now substitute 100 for x:

p(100) = 2(100) - 40

Then solve:

p(100) = 200 - 40

p(100) = 160

Answer:

x = -4 and x=1

Step-by-step explanation:

The solutions to the equation x^2 +3x -4 = 0 will be given by the points at which the graph intercepts the x-axis.

By looking at the graph, we can clearly see that the graph intercepts the x-axis at x=-4 and x=1.

One of the roots is located between -4 and -3, and the other one between 0 and 1.

Answer:

B.

I ignored the extra y= part in each equation.

Step-by-step explanation:

The line given is in slope-intercept form, y=mx+b where m is slope and b is y-intercept.

Parallel lines have the same slope.

So the slope of y=(2/5)x+9 is m=2/5.

So we are looking for a line with that same slope.

In slope-intercept form the line would by y=(2/5)x+b where we do not know b since we weren't given a point.

So all of the choices are written in standard form ax+by=c where a,b, and c are integers.

We want integers so we want to get rid of that fraction there.  To do that we need to multiply both sides of y=(2/5)x+b for 5.  This gives us:

5y=2x+5b

Subtract 2x on both sides:

-2x+5y=5b

Now of the coefficients of x in your choices is negative like ours is. So I'm going to multiply both sides by -1 giving us:

2x-5y=-5b

Compare

2x-5y=-5b to your equations.

A doesn't fit because it's left hand side is 5x+2y.

B fits because it's left hand side is 2x-5y.

C doesn't fit because it's left hand side is 5x-2y.

D doesn't fit because it's left hand side is 2x+5y.

I ignored all the extra y= parts in your equations.

Answer:

27

Step-by-step explanation:

The range is the greatest value subtract the smallest value

greatest value = 50 and smallest value = 23, so

range = 50 - 23 = 27

Answer:

27

Step-by-step explanation:

23,32,37,40,41,41,41,42,43,48,49,49,50.

Range=50-23=27

Answer:

8.4

Step-by-step explanation:

the equation 4x+8y -40 can be written as 4x-8y-40=0, this represents a line in a space of two dimensions.

solving for x when y=0.8 we have the equation below>

[tex]4x+8*0,8-40=0[/tex]

Which gives that x=42/5, or in more simpler terms, 8.4

Answer:

c 5.1

Step-by-step explanation:

The diameter of the circle is 102.

The radius is half of the diameter

r =d/2

r =10.2 /2 =5.1

Option C ,

40 degrees

Because angle Z was 70 (isosceles triangle)

Then 180-140=40 degrees

Answer:

15

Step-by-step explanation:

The formula for factoring a sum of cubes is:

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]

We have a=3f and b=5g here.

So a*b in this case is 3f*5g=15fg.

The ? is 15.

The value of the missing coefficient in the factored form of the sum of cubes 27f³ + 125g³ is 15, resulting in the complete factorization being (3f+5g)(9f² -15fg+25g²).

The expression 27f³ + 125g³ can be factored using the sum of cubes formula, which is a³ + b³ = (a + b)(a² - ab + b²).

Given [tex]27f^3+125g^3[/tex], we have [tex]a=3f[/tex] and [tex]b=5g[/tex]

Applying the sum of cubes formula, we get:

[tex]27f ^3+125g ^3 =(3f+5g)((3f) ^2 -(3f)(5g)+(5g)^ 2 )[/tex]

[tex]27f ^3 +125g ^3=(3f+5g)(9f ^2-15fg+25g ^2 )[/tex]

So, the missing coefficient in the factored form is 15.

Therefore, the factored form is,

[tex]27f ^3+125g ^3[/tex] is [tex](3f+5g)(9f^ 2-15fg+25g ^2 )[/tex]

The complete question is:

Find the value of the missing coefficient in the factored form of 27f³ + 125g³ .

27f³ + 125g³ =(3f+5g)(9f² -?fg+25g² )

The value of ? =

Answer:

A, C and E are true.

Step-by-step explanation:

The domain is a set of natural numbers.

The recursive formula is correct:

When x = 1, f(x) = 4 and f(x + 1) = f(2) = 3/2 f(x) = 3/2 * 4 = 6.

It is also true for the other points on the graph.

D is  incorrect.

E is correct exponential growth with the formula  4(3/2)^(x-1).

Answer:

A and C

Step-by-step explanation:

10/3 x 6/5 is 4                                                                                                                      

It can be represented using the formula f(x + 1) = Six-fifths(f(x)) when f(1) = Ten-thirds

It can be represented using the formula f (x) = ten-thirds (six-fifths) Superscript x minus 1. edge 2020-2021

Answer:

x = ±3

Step-by-step explanation:

x^2 +3 = 12

Subtract 3 from each side

x^2 +3-3 = 12-3

x^2 = 9

Take the square root of each side

sqrt(x^2) =±sqrt(9)

x = ±3

Answer:

Part 1) The measure of angle A is [tex]A=80\°[/tex]

Part 2) The length side of a is equal to [tex]a=10.9\ units[/tex]

Part 3) The length side of b is equal to [tex]b=6.3\ units[/tex]

Step-by-step explanation:

step 1

Find the measure of angle A

we know that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

[tex]A+B+C=180\°[/tex]

substitute the given values

[tex]A+35\°+65\°=180\°[/tex]

[tex]A+100\°=180\°[/tex]

[tex]A=180\°-100\°=80\°[/tex]

step 2

Find the length of side a

Applying the law of sines

[tex]\frac{a}{sin(A)}=\frac{c}{sin(C)}[/tex]

substitute the given values

[tex]\frac{a}{sin(80\°)}=\frac{10}{sin(65\°)}[/tex]

[tex]a=\frac{10}{sin(65\°)}(sin(80\°))[/tex]

[tex]a=10.9\ units[/tex]

step 3

Find the length of side b

Applying the law of sines

[tex]\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

substitute the given values

[tex]\frac{b}{sin(35\°)}=\frac{10}{sin(65\°)}[/tex]

[tex]b=\frac{10}{sin(65\°)}(sin(35\°))[/tex]

[tex]b=6.3\ units[/tex]

Answer:

17.009 in

Step-by-step explanation:

For a normal distribution with mean of 15.2 in and standard deviation of 1.1 inches, we finnd that 5% are excluded when the width of the seats are greater than 17.009 inches.

Therefore, the seat should have a width of 17.009 in.

To accommodate 95% of women based on hip breadth, airline seats should be designed at least 17.015 inches wide, calculated using the given mean of 15.2 inches, a standard deviation of 1.1 inches, and the z-score for the 95th percentile.

To determine the width of airline seats that would accommodate 95% of women, the airline needs to calculate the 95th percentile of women's hip breadths, modeled by a normal distribution.

Using the provided mean of 15.2 inches and a standard deviation of 1.1 inches, we find the z-score that corresponds to the 95th percentile. In normal distribution, the z-score for the 95th percentile is approximately 1.65.

Using the z-score formula Z =(X - μ / Σ, where Z is the z-score, X is the value we seek, μ is the mean, and Σ is the standard deviation, we can set Z to 1.65 and solve for X:

1.65 = (X - 15.2) / 1.1

X = 1.65 * 1.1 + 15.2

X = approx. 1.815 + 15.2

X = approx. 17.015 inches

Therefore, to exclude only the 5% of women with the widest hips, the airline should design seats that are at least 17.015 inches wide.