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[tex]\textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(255^o)\implies sin(135^o+120^o) \\\\\\ sin(135^o)cos(120^o)~~ + ~~cos(135^o)sin(120^o) \\\\\\ \left( \cfrac{\sqrt{2}}{2} \right)\left( -\cfrac{1}{2} \right)~~ + ~~\left( -\cfrac{\sqrt{2}}{2} \right)\left( \cfrac{\sqrt{3}}{2} \right)\implies -\cfrac{\sqrt{2}}{4}~~ - ~~\cfrac{\sqrt{6}}{4}\implies \cfrac{-2-\sqrt{6}}{4}[/tex]

Answer:

18 grams,160 grams,2,100 grams,2 kilograms,17 kilograms,208 kilograms.

The measure from least to greatest is 18 gm < 10 gm< 17 Kg < 2Kg < 2300 gm < 208 Kg.

The arrangement of numbers or other things in increasing order from least to greatest is known as ascending order. Ascending order is demonstrated by numbers on a number line, which are listed from left to right.

Given:

18gm, 17 Kg, 100 gm, 2 Kg, 2300 gm, 208 Kg

Converting all the units into gram we have

18 , 1700,  100, 2000, 2300, 208000

So, the mass from least to greatest.

18 < 100 < 1700< 2000< 2300 < 208000

Hence, 18 gm < 10 gm< 17 Kg < 2Kg < 2300 gm < 208 Kg.

Learn more about Ascending order here:

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Answer:

A). thickness are correct

Step-by-step explanation:

Range -6

Range is a higherd number

10-4=6

Answer:

Step-by-step explanation:

In a regular pentagon, all the angles and sides are equal. So, to find an angle, divide 540 by 5.

Sum of all angles of regular pentagon = 540

measurement of one angle = 540 ÷ 5

                                             = 108°

∠N = 108°

Answer:

B

Step-by-step explanation:

[tex] \Large \bold{SOLUTION\ 1:} [/tex]

[tex] \small \begin{array}{l} \text{First, we need to check if the given differential} \\ \text{equation is exact.} \\ \\ (1-xy)^{-2} dx + \big[y^2 + x^2 (1-xy)^{-2}\big]dy = 0 \\ \\ \dfrac{dx}{(1-xy)^2} + \left[y^2 + \dfrac{x^2}{(1-xy)^2}\right]dy = 0 \\ \\ \quad M(x, y) dx + N(x, y) dy = 0 \end{array} [/tex]

[tex] \small \begin{array}{l l}\tt\: M(x,y) = \dfrac{1}{(1 - xy)^2}, & N(x,y) = y^2 + \dfrac{x^2}{(1-xy)^2}\\ \\\tt \dfrac{\partial M}{\partial y} = \dfrac{-2(-x)}{(1 - xy)^3}, & \dfrac{\partial N}{\partial x} = \dfrac{2x}{(1 - xy)^2} + \dfrac{-2(-y)x^2}{(1 - xy)^3} \\ \\\tt \dfrac{\partial M}{\partial y} = \dfrac{2x}{(1 - xy)^3}, & \dfrac{\partial N}{\partial x} = \dfrac{2x(1 - xy)+2x^2y}{(1 - xy)^3} \\ \\\tt \: & \dfrac{\partial N}{\partial x} = \dfrac{2x}{(1 - xy)^3} \end{array} [/tex]

[tex] \small \begin{array}{l} \tt\dfrac{\partial M}{\partial y} = \dfrac{\partial N}{\partial x} \implies \text{Differential equation is exact.} \\ \\\tt \dfrac{\partial F}{\partial x} = M(x, y) = \dfrac{1}{(1 - xy)^2} \\ \tt\displaystyle F(x, y) = \int \dfrac{1}{(1 - xy)^2} \partial x = -\dfrac{1}{y} \int \dfrac{1}{(1 - xy)^2}(-y)\partial x \\ \\ \tt\:F(x, y) = \dfrac{1}{y(1 - xy)} + h(y) \\ \\ \tt\dfrac{\partial F}{\partial y} = N(x, y) = y^2 + \dfrac{x^2}{(1-xy)^2} \\ \\\tt \dfrac{\partial}{\partial y}\left[\dfrac{1}{y(1 - xy)} + h(y)\right] = y^2 + \dfrac{x^2}{(1-xy)^2} \\ \\ \tt-\dfrac{1 - xy + y(-x)}{y^2(1 - xy)^2} + h'(y) = y^2 + \dfrac{x^2}{(1-xy)^2} \\ \\ \tt-\dfrac{1 - 2xy}{y^2(1 - xy)^2} + h'(y) = y^2 + \dfrac{x^2}{(1-xy)^2} \\ \\ h'(y) = y^2 + \dfrac{x^2}{(1-xy)^2} + \dfrac{1 - 2xy}{y^2(1 - xy)^2} \\ \\ \tt\:h'(y) = y^2 + \dfrac{x^2y^2 - 2xy + 1}{y^2(1-xy)^2} = y^2 + \dfrac{1}{y^2} \\ \\ h(y) = \dfrac{y^3}{3} - \dfrac{1}{y} + C \\ \\ \tt\text{Substituting to }F(x,y),\text{we get} \\ \\ \dfrac{1}{y(1 - xy)} + \dfrac{y^3}{3} - \dfrac{1}{y} = C \\ \\ \quad \quad \text{or} \\ \\ \tt\red{\boxed{\dfrac{x}{1 - xy} + \dfrac{y^3}{3} = C} \Longleftarrow \textit{Answer}} \end{array} [/tex]

[tex] \Large \bold{SOLUTION\ 2:} [/tex]

[tex] \small \begin{array}{l} \tt\text{Since we already know that the equation is exact,} \\ \text{we can then continue solving for the solution by} \\ \text{inspection method or by algebraic manipulation.} \\ \\ \tt(1-xy)^{-2} dx + \big[y^2 + x^2 (1-xy)^{-2}\big]dy = 0 \\ \\ \tt\dfrac{dx}{(1-xy)^2} + \left[y^2 + \dfrac{x^2}{(1-xy)^2}\right]dy = 0 \\ \\ \tt\dfrac{dx}{(1-xy)^2} + y^2 dy + \dfrac{x^2}{(1-xy)^2} dy = 0 \\ \\ \tt\dfrac{dx + x^2dy}{(1-xy)^2} + y^2 dy = 0 \\ \\ \tt\text{Divide both numerator and denominator of the} \\ \tt\text{fraction by }x^2. \end{array} [/tex]

[tex] \small \begin{array}{c}\tt \dfrac{\dfrac{1}{x^2}dx + dy}{\dfrac{(1-xy)^2}{x^2}} + y^2 dy = 0 \\ \tt\\ \tt\dfrac{\dfrac{1}{x^2}dx + dy}{\left(\dfrac{1}{x}-y\right)^2} + y^2 dy = 0 \\ \\ \tt-\dfrac{\left(-\dfrac{1}{x^2}dx - dy\right)}{\left(\dfrac{1}{x}-y\right)^2} + y^2 dy = 0 \\ \\ \tt\displaystyle {\large{\int}} -\frac{d\left(\dfrac{1}{x}-y\right)}{\left(\dfrac{1}{x}-y\right)^2} + \int y^2 dy = \int 0 \\ \\ \tt\implies\tt \dfrac{1}{\dfrac{1}{x}-y} + \dfrac{y^3}{3} = C \\ \\\text{or} \\ \\ \tt\red{\boxed{\dfrac{x}{1 - xy} + \dfrac{y^3}{3} = C} \Longleftarrow \textit{Answer}} \end{array} [/tex]

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Answer:

B

Step-by-step explanation:

bbbbbb brainless me

Answer:

When it's negative when it goes to the other side it becomes a positive.....

Y=(x-4)(x-1)

Make y 0 when your calculating for x

Make x 0 when your calculating for y

0=(x-4)(x-1)

Therefore x=4 or x=1

Step-by-step explanation:

1 kilometer

thank you very much

Answer:

Option 3 is the correct answer.

Answer: The number of tickets sold is the independent variable because it affects the amount of money earned.

Step-by-step explanation: I just took test got 100%

The number of tickets sold is the independent variable because it affects the amount of money earned.

Using Chebyshev's Theorem, considering a standard deviation of 40, we have that at least 75% of the students scored between 360 and 520.

When we have no information about the population distribution, Chebyshev's Theorem is used. It states that:

In this problem, considering a standard deviation of 40, we have that:

440 - 2 x 40 = 360.

440 + 2 x 30 = 520.

Within 2 standard deviations of the mean, no information about the distribution, hence, at least 75% of the students scored between 360 and 520.

More can be learned about Chebyshev's Theorem at https://brainly.com/question/25303620

Answer:

226.19 in.

Step-by-step explanation:

circumference = πd

circumference = 3.14159 × 12 in.

circumference = 37.70 in.

In one revolution of the wheel, the unicycle travels a distance equal to the circumference of the wheel, or 37.70 in.

In 6 revolutions, the unicycle travels 6 times the circumference of the wheel.

6 × circumference = 6 × 37.70 in. = 226.19 in.

Answer: 226.19 in.

Answer:

D) none of the above

Step-by-step explanation:

16+20+30+30=96

96/4 =24

Let's see

LHS

Keep it stay

RHS

Use distributive law

Hence proved

Answer:

24.

Step-by-step explanation:

Solution,

By Prime Factorisation method,

576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

576 = (2)² × (2)² × (2)² × (3)²

Now,

By Taking square roots on both the sides,

√576 = √ (2)² × (2)² × (2)² × (3)²

√576 = 2 × 2 × 2 × 3

√576 = 24.

How to determine the total amount of rainfall

From the dot plot, we have the following frequency table

Rainfall    Frequency

0                  4

1/8               5

1/4               1

3/8              2

1/2               1

1 1/4             1

= 3/8 inches

The amount of oxygen in the flask through the intake tube illustrates proportions

The flask 99.35% will contain of oxygen after 5L have passed through the intake tube

To do this, we make use of the following representations

So. we have the following derivative

dP = dV - P * dV

Divide through by dV

dP/dV  = 1 - P

Next, we set up the integral

[tex]\int\limits^x_{0.040} \frac {1}{1 - P}dP= \int\limits^5_0 {dV}[/tex]

Integrate both sides

[tex]-\ln(|P - 1|)|\limits^x_{0.04} = 5[/tex]

Expand

-ln(|x - 1|) + ln(|0.04 - 1|) = 5

Evaluate the difference

-ln(|x - 1|) + ln(|-0.96|) = 5

Express as a fraction

ln(0.96/|x - 1|) = 5

Express both sides as exponents with a base of 2

e^ln(0.96/|x - 1|) = e^5

Solve for x

x = 1 - 0.96/e^5

Evaluate the difference

x = 0.9935

Express as percentage

x = 99.35%

Hence, the flask 99.35% will contain of oxygen after 5L have passed through the intake tube

Read more about proportions at:

https://brainly.com/question/1781657

Answer:

139600

Step-by-step explanation:

just dived all the numbers

In the given histogram, the correct option regarding the representation of the fourth bin is:

at least 12 pounds but less than 16 pounds.

An histogram is a graph that shows the number of times each element of x was observed. The lower bound is inclusive, while the upper bound is exclusive.

Hence, considering the inclusiveness and exclusiveness of the bounds, the correct option regarding the fourth bin, given by [12, 16) is:

at least 12 pounds but less than 16 pounds.

More can be learned about histograms at https://brainly.com/question/25836450

Answer:

The answer is "at least 12 pounds but less than 16 pounds"

Explanation:

I took the quiz! Hope this helps! :)

Answer:

Step-by-step explanation:

The equation factors into

(x^2 + 14x + 49) =16                      Factor

(x + 7)^2 = 16                                 Take the square root of both sides

√(x + 7)^2 = √16

x + 7 = +/- 4

x + 7 = + 4                                      Subtract 7 from both sides

x  = 4 - 7

x = - 3

x + 7 = - 4                                      Subtract 7 from both sides.

x = - 4 - 7

x = - 11

x1 = -11

x2 = - 3

Answer:

x = 5

Step-by-step explanation:

3^2 + 4^2 = x^2

9 + 16 = x^2

25

Now we need to find the square root of 25 :)

The answer is 5

X = 5

Have a great day!!

Please rate and mark brainliest!!

Step-by-step explanation:

the inverse of 2x-3 is

[tex] \frac{1}{2x - 3} [/tex]

if this helped pls give brainliest

Answer:

it matters how many colors are there

[tex]\dfrac 6p = x+a\\\\\implies \dfrac 6p \times\dfrac 16 = (x+a) \times\dfrac 16 ~~~~~~;\left[\text{Multiply both sides by}~ \dfrac 16 \right]\\\\\implies \dfrac 1p = \dfrac{x+a}6\\\\\implies p= \dfrac{6}{x+a}~~~~~~~~~~~~~~~~~~~~;[\text{Cross multiply}][/tex]

Answer:

The graph should look almost exactly like this. I used a virtual graphing chart to assist, since it is capable of showing more than paper alone.

Answer:

Here is your answer.

Step-by-step explanation:

Answer:

the answer will be 5

Step-by-step explanation:

Answer:

20π

Step-by-step explanation:

Area = πr^2

100π = πr^2

solve for r and r = 10

circumference of a circle is 2πr

therefore 2π×10=20π in

Answer:

Step-by-step explanation:

7 hours and 37 minuties

Answer:

5 hours

Step-by-step explanation:

it lasted 5 hours for the tournament

Answer:

z=3t

Step-by-step explanation:

multiply it by 3