please help me !! :)

sin(x+y) - sin(x-y) - 1 = cos(2x)

sin(90) - sin(x-y) - 1 = cos(2x)

1 - sin(x-(90-x)) - 1 = cos(2x)

-sin(2x-90) = cos(2x)

-1*(sin(2x)cos(90) - cos(2x)sin(90)) = cos(2x)

-1*(sin(2x)*0 - cos(2x)*1) = cos(2x)

-1*(0 - cos(2x)) = cos(2x)

-1*(-cos(2x)) = cos(2x)

cos(2x) = cos(2x)

This confirms the identity is true.

Notice that throughout this proof, I only changed the left hand side.

On the 5th line, I used the identity sin(A-B) = sin(A)cos(B)-cos(A)sin(B).

9514 1404 393

Answer:

  60

Step-by-step explanation:

Let m represent the mark Cheryn scored on her first quiz. Then her average is ...

  (m +76 +89)/3 ≥ 75

  m +165 ≥ 225 . . . . . . . . multiply by 3

  m ≥ 60 . . . . . . . . . . . . subtract 165

Cheryn scored a minimum of 60 marks on her first quiz.

Answer:

Plot the coordinates on a graph and join them to form a triangle. After doing that, you can count the length of each triangular side and find the sum of the 3 sides. That will be your answer.

Answer:

Solution

= -7 (x2 -6) +2y

= -7 ( 2*2 - 6 ) + 2 * 6

= -7 ( 4 - 6) + 12

= -7 - 2 + 12

= - 9 + 12

= 3

I hope this help u :)

Use distributive law

[tex]\boxed{\sf a(b+c)=ab+ac}[/tex]

Now

[tex]\\ \sf\longmapsto 2x(x-y)+3y(x-y)[/tex]

[tex]\\ \sf\longmapsto 2x^2-2xy+3xy-3y^2[/tex]

[tex]\\ \sf\longmapsto 2x^2-3y^2-2xy+3x^2[/tex]

[tex]\\ \sf\longmapsto 2x^2-3y^2+xy[/tex]

Taking common

Answer: 2x (x-y) + 3y (x-y)

             = ( x-y ) ( 2x-3y )

Step-by-step explanation:

45 >= 4x + 5

40 >= 4x

10 >= x (x <= 10)

and

53 > 4x + 5

48 > 4x

12 > x (x < 12)

so, both conditions need to be true (that is the meaning of "and").

how can that be achieved ? well, the harder, narrower condition beats any other.

so, when x <= 10, then it is automatically also smaller than 12.

so, the solution (inequality notation) is

x <= 10

and the graph just shows a line that starts at 10 (with a full, black dot at 10, as the point is included) and goes all the way to the left (to infinity and beyond ...)

Answer:

The height of the triangle is four meters.

Step-by-step explanation:

We are given that the area of a triangle is 12 square meters. The base is two meters longer than the height, and we want to determine the height of the triangle.

Recall that the area of a triangle is given by:

[tex]\displaystyle A = \frac{1}{2}bh[/tex]

Since the area is 12 square meters:

[tex]\displaystyle 12 = \frac{1}{2}bh[/tex]

The base is two meters longer than the height. In other words, we can write that:

[tex]b = h + 2[/tex]

Substitute:

[tex]\displaystyle 12=\frac{1}{2}(h+2)h[/tex]

Solve for h. Multiply both sides by two:

[tex]24 = (h+2)h[/tex]

Distribute:

[tex]h^2+2h=24[/tex]

Isolate:

[tex]h^2+2h-24=0[/tex]

Factor:

[tex](h+6)(h-4)=0[/tex]

Zero Product Property:

[tex]h + 6 = 0\text{ or } h -4 =0[/tex]

Solve for each case:

[tex]h = -6\text{ or } h = 4[/tex]

Since the height cannot be negative, we can ignore the first solution.

Thus, the height of the triangle is four meters.

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION..

hey, can i please get your intro? would you like to be my friend?

Myself Ojasvi

Class 8, 13

India

Answer: c

Step-by-step explanation:

The correct answer is option C i.e. all of the options

Question : Why did I choose the answer as option C

Reason : To assure it we'll match all the options with the figure

First of all in the given figure all the sides and angles are equal hence, we can refer it as regular

Secondly, It is convex because all the parts are pointing outwards and inner ones are not more than 180°

Finally, As it has 8 sides it is an octagon

Now, we can see all the three options are matching leaving C which states all of these options, hence C is correct

1) What is Octagon ?

ans :- Octagon is an 8 sided polygon

2) What is a regular polygon ?

ans :- Any polygon which has equal angles and sides is known as a regular polygon.

3) What is convex ?

ans :- A convex is a shape where all the parts points outwards and interior angles are not more than 180°

Answer:  y = (-4/3)*sqrt(2/3)

This is the same as writing [tex]y = -\frac{4}{3}\sqrt{\frac{2}{3}}[/tex]

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Explanation:

The phrasing "where the absolute value of the slope is minimized" is an interesting way of saying "the tangent slope is 0". This is because absolute values are never negative, so the smallest it can get is 0.

Your teacher has given you

y = x^3 - 2x

which differentiates into

dy/dx = 3x^2 - 2

after using the power rule

The derivative function lets us determine the slope of the tangent. The slope is the dy/dx value. Since we want a slope of 0, we'll set 3x^2-2 equal to zero and solve for x. So you have the correct idea, but you won't involve the second derivative.

dy/dx = 0

3x^2 - 2 = 0

3x^2 = 2

x^2 = 2/3

x = sqrt(2/3)

Notice how I'm ignoring the negative version of this root. This is due to the fact that [tex]x \ge 0[/tex]

-------------------------

Now plug this x value back into the original equation to find its corresponding y coordinate.

y = x^3 - 2x

y = x(x^2 - 2)

y = sqrt(2/3)*( 2/3 - 2 )

y = sqrt(2/3)*( -4/3 )

y = (-4/3)*sqrt(2/3)

Note that x = sqrt(2/3) leads to x^2 = 2/3 after squaring both sides.

-------------------------

Therefore, the equation of this tangent line is y = (-4/3)*sqrt(2/3)

All horizontal lines are of the form y = k, for some constant k. This constant value is basically what number you want the horizontal line to go through on the y axis. That number would be (-4/3)*sqrt(2/3).

Fred's age is 13 years

Let

Fred's age = x

Jack's age = 2x + 4

After 8 years:

= 2x + 12

Sum of their ages = Fred's age + Jack's age

59 = (x + 8) + (2x + 12)

59 = x + 8 + 2x + 12

59 = 3x + 20

59 - 20 = 3x

39 = 3x

x = 39/3

x = 13 years

Therefore, Fred's age = 13 years

https://brainly.com/question/24371832

Answer:

3.75%

Step-by-step explanation:

The percent that are broken is the number broken over the total * 100%

3/80 * 100%

.0375 * 100%

3.75%

Answer:

3.75% of the glass are broken

Step-by-step explanation:

3/80 × 100 = 3.75

I hope this helps.

Answer:

[tex]T_{n}[/tex] = 3n + 1

Step-by-step explanation:

There is a common difference between consecutive terms, that is

7 - 4 = 10 - 7 = 13 - 10 = 3

This indicates the sequence is arithmetic with nth term

[tex]T_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 4 and d = 3 , then

[tex]T_{n}[/tex] = 4 + 3(n - 1) = 4 + 3n - 3 = 3n + 1

Step-by-step explanation:

sinx = p/h = 7/25

so

p = 7

h = 25

now

h^2 = p^2 + b^2

25^2 = 7^2 + b^2

or, 625 = 49 + b^2

or, 625-49 = b^2

or, 576 = b^2

or,  b = [tex]\sqrt{576}[/tex]

so, b = 24

so

cosx = b/h = 24/25

tanx = p/b = 7/24

Answer:

80 grades is the answer.

Step-by-step explanation:

72° into grades

1° = 10/9 grades

72° = 10/9 × 72grades

= 720/9 grades

= 80 grades

Answer:

80 grades

Step-by-step explanation:

72° into grades  

=>1° = 10/9 grades

=>72° = 10/9 × 72 grades  

=>72° = 720/9 grades

=>72° = 80 grades

21) Angle 4

Angle 5

Angle GVH

Angle GVI

Angle HVI

22) Area of parallelogram = [tex]bh[/tex]

     A = 9 × 4 = [tex]36mi^2[/tex]

23) Area of a triangle = [tex]\frac{1}{2} bh[/tex]

     A =    [tex]\frac{1}{2} (12)(7.3)[/tex]

     A = [tex]43.8m^2[/tex]

24) Distance between each pair of point:

Distance between two points = [tex]\sqrt{(x_{B}-x_{A} )^2+(y_{B}-y_{A} )}[/tex]

Add the values in the formula & solve:

[tex]=\sqrt{(-2-0)^2+(2--4)^2}[/tex]

[tex]=\sqrt{(-2)^2+6^2}[/tex]

[tex]=\sqrt{4+36}[/tex]

[tex]=\sqrt{40}=6.3246[/tex]

25) Midpoint [tex](x_{M},y_{M} )=(\frac{x_{A} -x_{B} } {2} ,\frac{y_{A}+y_{B} }{2} )[/tex]

                                    [tex]=(\frac{10+0}{2},\frac{6+7}{2} )[/tex]

                                    [tex]=(\frac{10}{2} ,\frac{13}{2} )[/tex]

Midpoint of a line segment [tex](x_{M},y_{M} )=(5,6.5)[/tex]

I hope this helps....

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Explanation:

Let's square both sides and do a bit of algebra to get the following.

[tex]\sin(x) + \cos(x) = 1/5\\\\\left(\sin(x) + \cos(x)\right)^2 = \left(1/5\right)^2\\\\\sin^2(x) + 2\sin(x)\cos(x) + \cos^2(x) = 1/25\\\\\sin^2(x) + \cos^2(x) + 2\sin(x)\cos(x) = 1/25\\\\1 + 2\sin(x)\cos(x) = 1/25\\\\\sin(2x) = 1/25 - 1\\\\\sin(2x) = 1/25 - 25/25\\\\\sin(2x) = -24/25\\\\[/tex]

Now apply the pythagorean trig identity to determine cos(2x) based on this. You should find that cos(2x) = -7/25

This then means tan(2x) = sin(2x)/cos(2x) = 24/7.

From here, you'll use this trig identity

[tex]\tan(2x) = \frac{2\tan(x)}{1-\tan^2(x)}\\\\[/tex]

which is the same as solving

[tex]\tan(2x) = \frac{2w}{1-w^2}\\\\[/tex]

where w = tan(x)

Plug in tan(2x) = 24/7 and solve for w to get w = -4/3 or w = 3/4

So either tan(x) = -4/3 or tan(x) = 3/4.

If we were to numerically solve the original equation for x, then we'd get roughly x = 2.21; then notice how tan(2.21) = -1.345 approximately when your calculator is in radian mode.

Since tan(x) < 0 in this case, we go for tan(x) = -4/3

Answer:

Step-by-step explanation:

According to intersecting secants theorem we have the following equation:

Solve it for k:

Answer:

1. mean-The mean is the average value of the data you collect. In statistics, you find the mean of your sample. Then you use that mean to approximate the mean of the entire population. If you want the mean of the data to be a good approximation of the mean of the entire population, your need to make sure that you collect a random sample. To find the mean, you find the sum of the data points you collected and divide it by the number of data points in the set. For example, if the data you collected was {3, 3, 6}. Then the mean would be (3 + 3 + 6) ÷ 3 = 12 ÷ 3 = 4. It's important to note that the mean does not have to be a data point in your set. You can generalize the formula as well. If you collect n data points {d1, d2, d3, … dn}, then the mean of your data set is . The Greek letter μ—pronounced "mu"—is used because the word "mean" begins with the letter "m." It is important that you divide by the number of data points in your set, n.

2. Population-A population is the entire group you want to understand. So, in a certain sense, you can think of the population as the "opposite" of the sample because a sample is not the entire population. A sample is chosen subset upon that you use to draw conclusions about the entire population.

3. Experiment-An experiment is a well-defined procedure under controlled conditions designed to gather data that tests a hypothesis. For example, you want to test the hypothesis that flowers grow faster when they are watered every other day as opposed to every day. Then you could water one set of plants every day and another set of plants every other day. What data would you collect? The height of each plant once a day. What conditions would you need to control? You would need to make sure that the groups of plants are treated the same in every other way by getting the same amount of sun and being maintained at the same temperature, etc.

4. Sample-A sample is a subset chosen from a population. In most cases, you want a random sample. Why? A random sample has the best chance of accurately representing the entire population.

5. Bais-Bias is the preference for a particular group or subset. In the example above, the bias was toward viewers who like sports. When your sample is not chosen at random, you introduce bias into your study. So, in a certain sense, a biased sample is the opposite of a random sample. Why? In a biased sample, some members of the population are more likely to be chosen than others. In a random sample, every member of the population is equally likely to be chosen. Bias may also occur in surveys. See "survey" below for more information on this type of bias.

6. Survey-A survey is the means of collecting a sample. In statistics, a survey is often a question or set of questions. It is critical that the questions, like the sample itself, be free from bias. Bias in a question tends to favor one response. As an extreme example of a biased question about colors might be, "Don't you think blue is beautiful and yellow is yucky?" An unbiased form of the question might be, "Which color do you prefer, blue or yellow?" Though careful, statisticians might be concerned about the order in which the colors are offered, so that might further simplify the question to, "What is your favorite color?" This type of question is most free from bias because it does not suggest a response and therefore does not favor a response.

7. Random-Random means free from bias. So, if you choose a random sample from a population, every member of the population has an equal chance of being chosen. It should be pointed out that this "true randomness" is an ideal which is difficult to achieve in real world experiments conducted on real world populations. That is why statisticians make every effort to ensure their samples chosen as free from bias as is possible, that is, as randomly as possible under real world conditions.

Step-by-step explanation:

It says what each of them are in each paragraph, you just need to match them up.

Hope this helps :)

Answer:

119.43 cm²

Step-by-step explanation:

The shaded area (A) is calculated as

A = area of rectangle - area of circle

   = (11 × 12) - π × 2²

  = 132 - 4π

  ≈ 119.43 cm² ( to the nearest hundredth )

Answer:

427.09

Step-by-step explanation:

(2.75 x 107) + (1.23 x 108)

294.25 + 132.84 = 427.09

Answer:

x = 110

y = 15

Step-by-step explanation:

AB is parallel to CD

angle B and angle D are alternate and they are equal

106-2x = 3x-4

106 + 4 = 3x - 2x

110 = x

same goes for y

7y + 13 = 10y - 32

13 + 32 = 10y - 7y

45 = 3y divide both sides by 3

15 = y

Answer:

an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable is called polynomial. A polynomial with real coefficients is a product of irreducible polynomials of first and second degrees.

Answer:

4%  = 0.04

4000 = 0.04

6 years = 0.04

Step-by-step explanation:

Hope this helps!

Answer:

The p is 4

Step-by-step explanation:

Answer:

$118

Step-by-step explanation:

First, find how much money you had after going to the bank:

100 + 30

= $130

Find how much money you spent at the store by subtracting 12 from 130:

130 - 12

= 118

So, you spent $118

Answer:

10cm

Step-by-step explanation:

Assuming the shape is a rectangle since it's already stated that it's a parallelogram, and the area is stated, we can use the Pythagorean theorem to find the length

[tex]a^{2} +b^2=c^2[/tex], where c will be the length

isolate c

[tex]c^2=a^2+b^2[/tex]

[tex]c=\sqrt{a^2+b^2}[/tex]

substitute for a and b

[tex]c=\sqrt{8^2+6^2}[/tex]

[tex]c=\sqrt{64+36}[/tex]

[tex]c=\sqrt{100}[/tex]

[tex]c=10[/tex]

take the help of the attachments.

here is your answer hope you will understand it

Answer:

21 1/6 ft

Step-by-step explanation:

Add the lengths together

12 1/2 + 8 2/3

Get a common denominator of 6

12 1/2 *3/3  + 8 2/3 *2/2

12 3/6 + 8 4/6

20 7/6

20 +6/6+1/6

21 1/6