I have a lot of algebra problems. Someone help me even with this one please!

Observe that

5/12 = 1/4 + 1/6

so that

tan(5π/12) = tan(π/4 + π/6)

Then

tan(5π/12) = sin(π/4 + π/6) / cos(π/4 + π/6)

… = (sin(π/4) cos(π/6) + cos(π/4) sin(π/6)) / (cos(π/4) cos(π/6) - sin(π/4) sin(π/6))

… = (cos(π/6) + sin(π/6)) / (cos(π/6) - sin(π/6))

(since sin(π/4) = cos(π/4) = 1/√2)

… = (√3/2 + 1/2) / (√3/2 - 1/2)

… = (√3 + 1) / (√3 - 1)

… = (√3 + 1) / (√3 - 1) × (√3 + 1) / (√3 + 1)

… = (√3 + 1)² / ((√3)² - 1²)

… = ((√3)² + 2√3 + 1²) / (3 - 1)

… = (3 + 2√3 + 1) / 2

… = (4 + 2√3) / 2

… = 2 + √3 … … … (C)

If you insist on using the half-angle identity, recall that

sin²(x) = (1 - cos(2x))/2

cos²(x) = (1 + cos(2x))/2

==>   tan²(x) = (1 - cos(2x)) / (1 + cos(2x))

Let x = 5π/12. The angle x lies in the first quadrant, so we know tan(x) is positive.

==>   tan(x) = +√[(1 - cos(2x)) / (1 + cos(2x))]

We also know

cos(2x) = cos(5π/6) = -√3/2

which means

tan(x) = tan(5π/12) = √[(1 - (-√3/2)) / (1 + (-√3/2))]

… = √[(1 + √3/2) / (1 - √3/2)]

… = √[(2 + √3) / (2 - √3)]

… = √[(2 + √3) / (2 - √3) × (2 + √3) / (2 + √3)]

… = √[(2 + √3)² / (2² - (√3)²)]

… = √[(2 + √3)² / (4 - 3)]

… = √[(2 + √3)²]

… = 2 + √3

Answer:

The fraction of the pocket money she left is 1/8.

Step-by-step explanation:

Let the total pocket money is p.

Spent on Monday = p/2

Amount left = p - p/2 = p/2  

Spent on Tuesday = 2/3 of p/2 = p/3

Amount left = p/2 - p/3 = p/6

Spent on Wednesday = 1/4 of p/6 = p/24

Amount left = p/6 - p/24 = p/8

So, the fraction of the pocket money she left is 1/8.  

Answer:

21/13

Step-by-step explanation:

3 1/2 = 7/2

2 1/6 = 13/6

7/2 divided by 13/6

7/2 X 6/13 = 42/26 = 21/13

Answer:

Step-by-step explanation:

3 1/2 = 7/2 and 2 1/6 = 13/6

7/2 divided by 13/6 = 7/2 x 6/13

42/26

21/13 is your final answer.

Answer:

B is the answer because the graph is translated 2 down. the translation cannot be included within the radical sign, so it can't be C

Answer:

2/60 = 1/30 = 3.3%

Step-by-step explanation:

Answer:

[tex]P(x = 3) = 0.048[/tex]

Step-by-step explanation:

Given

[tex]n = 10[/tex]

[tex]p=59\% = 0.59[/tex]

Required

[tex]P(x = 3)[/tex] --- probability that 3 are afflicted

This question illustrates binomial probability and it is calcuated using:

[tex]P(x) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]

So, we have:

[tex]P(x = 3) = ^{10}C_3 * 0.59^3 * (1 - 0.59)^{10-3}[/tex]

[tex]P(x = 3) = ^{10}C_3 * 0.59^3 * 0.41^7[/tex]

[tex]P(x = 3) = 120 * 0.59^3 * 0.41^7[/tex]

[tex]P(x = 3) = 0.048[/tex]

Answer:

p = 0

Step-by-step explanation:

1 - 4p - 2p = 1 - 5p

-6p + 1 = -5p + 1

-p + 1 = 1

-p = 0

p = 0

Answer:

Moving 4 to the right on the x axis

Answer:

x^4+4x^3+6x^2+7x+2

Given:

The dotted boundary line passes through the points (-3,-8), (1,-2) and (9,10).

Above line is shaded.

To find:

The inequality for the given graph.

Solution:

Consider any two points on the line. Let the two points are (1,-2) and (9,10). So, the equation of the line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-(-2)=\dfrac{10-(-2)}{9-1}(x-1)[/tex]

[tex]y+2=\dfrac{10+2}{8}(x-1)[/tex]

[tex]y+2=\dfrac{12}{8}(x-1)[/tex]

[tex]y+2=\dfrac{3}{2}(x-1)[/tex]

Multiply both sides by 2.

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

[tex]2y+4=3x-3[/tex]

[tex]2y-3x=-3-4[/tex]

[tex]-3x+2y=-7[/tex]

Above line is shaded and the boundary line is a dotted line. So, the sign of inequality must be >.

[tex]-3x+2y>-7[/tex]

This inequality is not in the equations. So, multiply both sides by -1 and change the inequality sign.

[tex](-3x+2y)(-1)<-7(-1)[/tex]

[tex]3x-2y<7[/tex]

Therefore, the correct option is D.

Answer:

31

Step-by-step explanation:

[tex]3+7[/tex] × 4        Multiply first

3 + 28           Then add

31

Answer:

a)

x=4, y=-2

b)

x=2, y=2

c)

x=0, y=0

d)

x=1, y=1

e)

x=3, y=3

f)

x=4, y=4

Step-by-step explanation:

a) (x,-2) = (4,y)

x=4

y=-2

b) (3x, 4) = (6, 2y)

3x=6 => x=2

2y=4 => y=2

c) (2x-1, y + 2) = (-1,2)

2x-1 =-1 => x=0

y+2 = 2 => y=0

d) (2x + 4, y + 5) = (3x + 3,6)

2x+4 = 3x+3 => x=1

y+5 = 6 => y=1

e) (x + y,y + 3) = (6, 2y)

x+y = 6 => x+3 = 6 => x=3

y+3 = 2y => y=3

f) (x + y, x - y) - (8,0)​

x+y = 8 => 2x=8 => x=4

x-y = 0 => x=y => y=4

Answer:

54°

Step-by-step explanation:

Here :-

Measure of 6 :-

Answer:

m<6 = m<2 = 54º

Step-by-step explanation:

13x + 9 + 5x + 9 = 180

18x + 18 = 180

18x = 180 - 18

18x = 162

x = 162 / 18

x = 9

13x + 9

13(9) + 9

126

180 - 126

54

m<6 = m<2 = 54º

[tex]\large {\text {$ \sf \cfrac{1}{2x^2} -2 = 0 $}}[/tex]

[tex]\large {\text {$ \sf \cfrac{1}{2x^2}\cdot \:2x^2-2\cdot \:2x^2=0\cdot \:2x^2 $}[/tex]

                 [tex]\searrow[/tex]

                     [tex]\large {\text {$ \sf 1-4x^2=0$}}[/tex]

[tex]\large {\text {$ \sf -4x^2+1 = 0 $}}[/tex]

[tex]\large {\text{$\sf x=\cfrac{-b\pm\sqrt{b^2-4ac}}{2a} \quad\rightarrow\quad x=\cfrac{-0\pm\sqrt{0^2-4\cdot (-4) \cdot1} }{2\cdot (-4) } \:\rightarrow\:\: x=\cfrac{-0^2 \pm4}{2 \cdot(-4)} $}}[/tex]  

                                                             [tex]\huge {\text {$ \sf \downarrow$}}[/tex]

           [tex]\large {\text {$\sf {\bf x_1} = \cfrac{-0+4}{2\left(-4\right)}= \cfrac{-1}{2} $}}[/tex]                        [tex]\large {\text {$\sf {\bf x_2 }=\cfrac{-0-4}{2\left(-4\right)} = \cfrac{1}{2} $}}[/tex]

[tex]\large {\boxed {\boxed { \bf x_1 + x_2= -\cfrac{1}{2}+ \cfrac{1}{2} = 0} }}[/tex]

                                           [tex]\huge {\text {$ \it Alternative \: A $}}[/tex]

Answer:

A: The y-intercept of f(x) is equal to the x-intercept of g(x)

Step-by-step explanation:

From the equation of f(x) given, we have;

f(x) = -4(1.09)^(x)

Now,the y-Intercept will be the point where x = 0.

Thus;

f(0) = -4(1.09)^(0)

f(0) = -4

Now,from the table given for g(x), we can see that at x = 0,g(x) = -4.

Thus,it means that the y-intercept of f(x) is equal to the x-intercept of g(x)

Answer:

The equation of the line is, y = x

Step-by-step explanation:

The constraints of the required linear equation are;

The point through which the line passes = (2, 2)

The line to which the required line is parallel = y = x + 4

Two lines are parallel if they have the same slope, therefore, we have;

The slope of the line, y = x + 4 is m = 1

Therefore, the slope of the required line = 1

The equation of the required lime in point and slope form becomes;

y - 2 = 1 × (x - 2)

∴ y = x - 2 + 2 = x

The equation of the required line is therefore, y = x

Answer:

1/2×d1×d2

=1/2× (4+4)(6+3)

=36

Answer:

See below

Step-by-step explanation:

Let side AB equal x. Since triangle ABC is equilateral, sides AB, BC, and Ac are all the same length, x. In any isosceles triangle(equilateral is a type of isosceles triangle) the median is the same as the altitude and angle bisector. This means we can say that AD is also a median. A median splits a side into two equal sections, so we can say BD = DC = x / 2. We are given that DC = CE, so we can also say CE = DC = x / 2. Now, we can use the pythagorean theorem to find the length of AD. So we get the equation:

AB^2 - BD^2 = AD^2

We have the values of AB and BD, so we can substitute them and solve for AD:

x^2 - (x/2)^2 = AD^2

x^2 - x^2 / 4 = AD^2

AD^2 = 3x^2 / 4

AD = x√3 / 2

DE is equal to the sum of DC and CE because of segment addition postulate, so we can say DE = DC + CE = x / 2 + x/ 2 = x. We can again use the pythagorean theorem to find the length of AE:

AD^2 + DE^2 = AE^2

(x√3 / 2)^2 + x^2 = AE^2

3x^2 / 4 + x^2 = AE^2

AE^2 = 7x^2 / 4

AE = x√7 / 2

Now, we know(from before) that AE squared is 7x^2 / 4. We can say EC squared is x^2 / 4 because EC is x / 2 and x / 2 squared is x^2 / 4. We can also notice that AE squared is 7 times EC squared because 7x^2 / 4 = 7 * x^2 / 4

Therefore, we can come to the conclusion AE^2 = 7 EC^2

Answer:

C

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original, so

scale factor = [tex]\frac{XY}{AB}[/tex] = [tex]\frac{9}{45}[/tex] = [tex]\frac{1}{5}[/tex] → C

The scale factor will be equal to 1 / 5. the correct option is C.

The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

In the given image all the angles are the same and the sides are dilated so the scale factor will be calculated as below,

Scale factor = Original size / dilated size

Scale factor = XY / AB

Scale factor = 9 / 45

Scale factor = 1 / 5

Therefore, the scale factor will be equal to 1 / 5. the correct option is C.

To know more about scale factors follow

https://brainly.com/question/25722260

#SPJ2

Answer:

The probability that they each will catch 3 fish is 0.000063956

Step-by-step explanation:

The hyper geometric distribution is used to solve this as it has a population, a sample , number of successes  for both the population and sample.

Here

Population size= N =200

Sample size= n =9= (3*3)

Number of successes in population = k = 3 hours

Number of successes in sample = x= 3

Applying the hyper geometric distribution

P (x=3) = kCx *(N-k) C (n-x)/ N Cn

   = 3 C 3 * 197 C 6/ 200 C 9

    =0.000063956

The probability that they each will catch 3 fish is 0.000063956

Step-by-step explanation:

=> (3x-12) =(x+6)

or,3x - x = 6 + 12

or,2x = 18

or,x = 18/2

•: x=9#

Given:

For en exponential function f(a):

[tex]f(-3)=18[/tex]

[tex]f(1)=59[/tex]

To find:

The value of f(0).

Solution:

The general form of an exponential function is:

[tex]f(x)=ab^x[/tex]          ...(i)

Where, a is the initial value and b is the growth/ decay factor.

We have, [tex]f(-3)=18[/tex]. Substitute [tex]x=-3,f(x)=18[/tex] in (i).

[tex]18=ab^{-3}[/tex]            ...(ii)

We have, [tex]f(1)=59[/tex]. Substitute [tex]x=1,f(x)=59[/tex] in (i).

[tex]59=ab^{1}[/tex]            ...(iii)

On dividing (iii) by (ii), we get

[tex]\dfrac{59}{18}=\dfrac{ab^{1}}{ab^{-3}}[/tex]

[tex]3.278=b^{1-(-3)}[/tex]

[tex]3.278=b^{4}[/tex]

[tex](3.278)^{\frac{1}{4}}=b[/tex]

[tex]1.346=b[/tex]

Substituting the value of b in (iii).

[tex]59=a(1.346)^1[/tex]

[tex]\dfrac{59}{1.346}=a[/tex]

[tex]43.83358=a[/tex]

[tex]a\approx 43.83[/tex]

The initial value of the function is 43.83. It means, [tex]f(0)=43.83[/tex].

Therefore, the value of f(0) is 43.83.

Answer:

The circumference of Earth's equator is 40,080 km.

Step-by-step explanation:

Given that every 24 hours, Earth makes a full rotation around its axis, and Earth's speed of rotation at the equator is 1,670 km per hour, to determine what is the circumference of Earth's equator the following calculation must be performed:

24 x 1,670 = X

40,080 = X

Therefore, the circumference of Earth's equator is 40,080 km.

Answer:

condition

Step-by-step explanation:

An experiment can be defined as an investigation which typically involves the process of manipulating an independent variable (the cause) in order to be able to determine or measure the dependent variable (the effect).

This ultimately implies that, an experiment can be used by scientists to show or demonstrate how a condition causes or gives rise to another i.e cause and effect, influence, behavior, etc in a sample.

On the other hand, an observational study can be defined as a type of study in which a researcher observes and measures the effect of a diagnostic test, risk factors, or treatments on individuals without intervening, changing or manipulating who are or aren't exposed to it (controlled conditions).

Hence, the main purpose of doing an experiment over an observational study is to learn whether a certain condition causes a certain response.

Cause and effect can be defined as the relationship between two things or events in which an occurrence of one (cause) leads to the occurrence of another (effect).

Answer:

b. remains unchanged

Step-by-step explanation:

Formula for standard error of mean is;

SE = σ/√n

From the above, we can see that the standard error of mean is independent of the confidence coefficient as it doesn't affect the SE.

Now, we are given that;

random sample; n = 100

Standard deviation; σ = 1

Thus;

SE = 1/√100

SE = 1/10

Now, even if the confidence coefficient is reduced, we can see that it has no impact on the standard error of mean.

Thus, SE remains unchanged.

Step-by-step explanation:

Cos A = 40^2 + 25^2- 34^2 ÷ (2×40×25)

= 200+625-1156 ÷ (2000)

= 1069 ÷2000

Cos A = 0.5345

A= cos inverse 0.5345

A = 57.7

Answer:

57.7

Step-by-step explanation:

took the test

Answer:

36π mm²

Step-by-step explanation:

Formula: πr²

r=radius

r=6

π6²=36π

Answer:

x = 3

Step-by-step explanation:

2(5x - 3) = 24

Divide both sides by 2.

5x - 3 = 12

Add 3 to both sides.

5x = 15

Divide both sides by 5.

x = 3