The diagram below shows the partial construction of which shape?

Recall the Pythagorean identity,

[tex]\sin^2(x) + \cos^2(x) = 1[/tex]

Then we can rewrite the equation as

[tex]\sin(3x) + 2 \cos^2(3x) = 1[/tex]

[tex]\sin(3x) + 2 (1 - \sin^2(3x)) = 1[/tex]

[tex]1 + \sin(3x) - 2 \sin^2(3x) = 0[/tex]

Factorize the left side.

[tex](1 + 2 \sin(3x)) (1 - \sin(3x)) = 0[/tex]

Then we have

[tex]1 + 2\sin(3x) = 0 \text{ or } 1 - \sin(3x) = 0[/tex]

[tex]\sin(3x) = -\dfrac12 \text{ or } \sin(3x) = 1[/tex]

Solve for [tex]x[/tex]. We get two families of solutions:

[tex]3x = \sin^{-1}\left(-\dfrac12\right) + 2n\pi \text{ or } 3x = \pi - \sin^{-1}\left(-\dfrac12\right) + 2n\pi[/tex]

[tex]\implies 3x = -\dfrac\pi6 + 2n\pi \text{ or } 3x = \dfrac{7\pi}6 + 2n\pi[/tex]

[tex]\implies \boxed{x = -\dfrac\pi{18} + \dfrac{2n\pi}3} \text{ or } \boxed{x = \dfrac{7\pi}{18} + \dfrac{2n\pi}3}[/tex]

and

[tex]3x = \sin^{-1}(1) + 2n\pi[/tex]

[tex]\implies 3x = \dfrac\pi2 + 2n\pi[/tex]

[tex]\implies \boxed{x = \dfrac\pi6 + \dfrac{2n\pi}3}[/tex]

(where [tex]n[/tex] is any integer)

The required equation is g+300-900-900=1300.

The value of g is 2800 pounds.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Initially, there is a mound of g pounds of gravel, then 300 pounds are added, and then two orders of 900 pounds are sold. At the end of the day, the mound has 1,300 pounds of gravel.

The equation for the given information is formed as follows:

g+300-900-900=1300

Solve the equation to find the value of g,

g+300-1800=1300

g-1500=1300

g=1300+1500

g=2800

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Formula:

[tex]\frac{1}{2}(Big Arc- Small Arc)[/tex]

[tex]\frac{1}{2} (118-26)[/tex]

[tex]\frac{1}{2}(92)\\[/tex]

=46

m∠DPR = 46°

I hope it helps! :)

First of all, a pair of angles that are complementary means that they add up to 90 degrees. In this case, angle b + 63 degree = 90 degree (because they are complementary), which mean angle b = 90 - 63 = 27 degree.

Answer: 27°

Step-by-step explanation:

Hello.

Complementary angles add up to 90°

Therefore,

63° + ? = 90°

Now we can subtract!

90° - 63° = 27°

Hope this helps and have a nice day :)

33) [tex]AC=6[/tex] and [tex]BD=6[/tex], so [tex]AC/BD=1[/tex]

34) By the distance formula,

[tex]AE=\sqrt{(-2-4)^2 + (8-0)^2 }=10\\[/tex]

Also, EC = 8. So, [tex]AE/EC = 5/4[/tex].

35) [tex]\frac{8-0}{4-2}=4[/tex]

36) [tex]\frac{8-0}{4-8}=-2[/tex]

The value of a is (c) 86

The given parameter is:

Angle C = 86

By vertical angle theorem, we have:

Angle A = Angle C = 86

This implies that:

Angle A = 86

The arc A subtends angle A

This means that:

Arc A = 86

Hence, the value of a is (c) 86

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The points where both coordinates are integers lie within the intersection of these circles, including its boundary are 8 points.

To answer the question, we need to find the equation of the circles.

The equation of a circle with center (h, k) and radius r is

(x - h)² + (y - k)² = r²

Given that the first circle has

Its equation is

(x - 0)² + (y - 0)² = 5²

x² + y² = 25  (1)

Given that the second circle has

Its equation is

(x - 8)² + (y - 0)² = 5²

x² - 16x + 64 + y² = 25  (2)

To find the point of intersection of both circles, subtracting (1) from (2), we have

x² - 16x + 64 + y² = 25  (2)

-

x² + y² = 25  (1)

-16x + 64 = 0

-16x = -64

x = -64/-16

x = 4

Substituting x = 4 into (1), we have

x² + y² = 25

4² + y² = 25

16 + y² = 25

y² = 25 - 16

y² = 9

y = ±√9

y = ±3

So, the circles intersect at (4,-3) and (4, 3).

So, all the points that lie within their points of intersection where both coordinates are integers including their points of intersection are

So, there are 8 points.

So, all the points where both coordinates are integers lie within the intersection of these circles, including its boundary are 8 points.

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Answer:

'A prime number is a number which has exactly two factors i.e. '1' and the number itself. A composite number has more than two factors, which means apart from getting divided by 1 and the number itself, it can also be divided by at least one positive integer.'

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the definition of prime & composite numbers?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

A prime number can be evenly divided by 1 and itself. These are its only two factors.

A composite number can be evenly divided by 1, itself, and something else. In other words, composite numbers have more than 2 factors.

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

              [tex]\bf{\begin{cases}\bf{Primes\;have\;only\;2\;factors} \\ \bf{Composites\;have\;3\;or\;more\;factors} \end{cases}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta l}}[/tex]

Answers:

====================================================

Explanation:

Here are all the ways to multiply to 18 when using integers only:

Sum each pair of factors to find out a possible value of b.

Therefore, the possible values of b are

which are the final answers.

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

An example:

Let's say b = 11. This would mean [tex]x^2+bx+18[/tex] becomes [tex]x^2+11x+18[/tex]

It would factor to [tex](x+2)(x+9)[/tex] since it was stated earlier that:

2+9 = 11

2 * 9 = 18

You can use the FOIL rule, distributive property, or the box method to confirm that [tex]x^2+11x+18 = (x+2)(x+9)[/tex] is a true equation for all real numbers x.

This same idea applies for the other values of b.

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

If you're curious why this works, consider multiplying the two factors (x+p) and (x+q)

Use the FOIL rule to get [tex](x+p)(x+q) = x^2+qx+px+pq = x^2+(p+q)x + pq[/tex]

The middle term [tex](p+q)x[/tex] has the components add to the coefficient, while those same two components multiply to get the last term. This is why when factoring we're looking for two numbers that multiply to 18, and also add to the value of b (which in the case of the last example was 11).

The value of x is 103.

The value of x is 59.

The value of x is 134.

The value of x is 12

The value of x is 50

The value of x is 135

The sum of angles on a straight line add up to 180 degrees.

180 - 77 = 103

180 - 121 = 59

180 - 46 = 134

12 x + 36 = 180

12x = 180 - 36

12x = 144

x = 12

24 + 3x + 6 = 180

3x = 180 - 24 - 6

3x = 150

x - 50

[tex]\frac{x}{3}[/tex] + 99 + 36 = 180

[tex]\frac{x}{3}[/tex] = 180 - 36 - 99

[tex]\frac{x}{3}[/tex] = 45

x = 45 x 3

x = 135

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Answer:

Step-by-step explanation:

Answer: m=-1.

Step-by-step explanation:

[tex]Q(x)=x^2+mx-12\ \ \ \ Q(-3)=0\ \ \ \ \ m=?\\Q(-3)=(-3)^2+m*(-3)-12=0\\9-3m-12=0\\-3m-3=0\\3m=-3\ |:3\\m=-1.[/tex]

Answer:

y is the variable in that expression.

Answer:

C. 2y²

Step-by-step explanation:

[tex] \sf{( {3}^{0}y) {}^{2} \times 2(xy {)}^{0} = }[/tex]

[tex]\sf{ = (\red{1} \times y)^{2} \times (2 \times \red{1}) }[/tex]

[tex]\sf{ = (y)^{2} \times 2 }[/tex]

[tex]\sf{ =2 {y}^{2} }[/tex]

Answer:

[tex]\textsf{C.} \quad 2y^2[/tex]

Step-by-step explanation:

Given:

[tex](3^0y)^2 \times 2(xy)^0[/tex]

[tex]\textsf{Apply exponent rule} \quad a=a^1:[/tex]

[tex](3^0y^1)^2 \times 2(x^1y^1)^0[/tex]

[tex]\textsf{Apply exponent rule} \quad(a^n)^c=a^{nc} \implies (a^nb^n)^c=a^{nc}b^{nc}:[/tex]

[tex]\implies 3^{(0 \times 2)}y^{(1 \times 2)} \times 2 \left(x^{(1 \times 0)}y^{(1 \times 0)} \right)[/tex]

[tex]\implies 3^0y^2 \times 2\left(x^0y^0\right)[/tex]

[tex]\textsf{Apply exponent rule} \quad a^0=1:[/tex]

[tex]\implies (1)y^2 \times 2\left(1 \times 1 \right)[/tex]

Simplify:

[tex]\implies (1)y^2 \times 2(1)[/tex]

[tex]\implies y^2 \times 2[/tex]

[tex]\implies 2y^2[/tex]

Using the Central Limit Theorem, the percentage that is expected to be the closest to the actual percentage is:

A. The Tribune, at 68%.

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard error [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].

From this, a larger sample size leads to a smaller error estimate. Since the Tribune had the largest sample size, option A is correct.

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Answer:

In slope-intercept form:

[tex]y = - \frac{1}{4} x - 5[/tex]

In standard form:

[tex]x + 4y = - 20[/tex]

Step-by-step explanation:

[tex] - 3 = - \frac{1}{4} ( - 8) + b[/tex]

[tex] - 3 = 2 + b[/tex]

[tex]b = - 5[/tex]

[tex]y = - \frac{1}{4} x - 5[/tex]

[tex] - 4y = x + 20[/tex]

[tex] - x - 4y = 20[/tex]

[tex]x + 4y = - 20[/tex]

Answer:

Hence the expression [tex]$$(a+b)(2a+3b)=2a^2+5ab+3b^2$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{matrix}{} & {} & {} & {} & a & + & b \\ \times & {} & {} & {} & 2a & + & 3b \\ \end{matrix}$$[/tex]

___________________

[tex]$$\begin{matrix}{} & {} & {} & {} & 3ab & + & 3{{b}^2} \\ {} & {} & 2{{a}^2} & + & 2ab & {} & {} \\ \end{matrix}$$[/tex]

___________________

[tex]$$\begin{matrix}{} & {} & 2{{a}^2} & + & 5ab & + & 3{{b}^2} \\ \end{matrix}$$[/tex]

Answer:

Step-by-step explanation:

Answer:

Volume = 64

Step-by-step explanation:

To find the volume of the cube use the formula.

Formula: l×b×h

l=length

b=base

h=height

Use the information given to solve using the formula.

4×4×4=64

The volume of this cube is 64.

Hope this helps!

If not, I am sorry.

Step-by-step explanation:

the sum of all angles in a triangle is always 180°.

so,

180 = 60 + 45 + angle4 = 105 + angle4

75° = angle4

Answer:

Step-by-step explanation:

1/2 pi is an angle ( in radians)

in degrees its 90 degrees.

cos 90 = 0.

3:8:1

3/12 x 144= 36

8/12 x 144= 96

96+36= 132

144-132= 12

12/12=1

Therefore, the ratio of Alyssa's nickels to dimes to quarters is 3:8:1

Hello !

[tex]a_{n} = a_{1} + (n - 1) \times d[/tex]

[tex]a_{39} = - 28 + (39 - 1) \times ( - 4) = - 28 + 38 \times ( - 4) = - 180[/tex]

The required a39 of the arithmetic sequence is -180.

Given that,
To find a39 of the arithmetic sequence given a1 = -28 and d = - 4.

Arithmetic progression is the series of numbers that have common differences between adjacent values.

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

The nth term of an arithmetic sequence is given as
an = a1 + (n - 1) * d
for term n = 39
a39 = -28 + (39 - 1) * -8
a39 = -28 - 152
a39 = - 180

Thus, the required a39 of the arithmetic sequence is -180.

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Step-by-step explanation:

ATTACHED IS THE SOLUTION!!

Answer: after t hours, the distance d between the hikers is

d^2 = (.24t)^2 + (.17t)^2 - 2(.24t)(.17t)cos109.167°

so, find t when d = 0.0568182

Step-by-step explanation:

Answer:

20cm

Step-by-step explanation:

You divide by 12

Answer:

(×-4) (x + 4)

Step-by-step explanation:

first of all, recognize that the polynomial expression is a difference of two squares.

thus

X^2-16

(x -4)(x+4)

⊱________________________________________________________⊰

[tex]\\[/tex][tex]\\[/tex]

Answer:

Step-by-step explanation:

[tex]\large\begin{gathered} \sf{To \ factor \ this \ polynomial, \ we \ must \ first \ recognise \ it. \ Isn't \ it \ the \ difference} \\ \sf{of \ two \ squares?} \\ \rm{It \ is! } \\ \sf{Polynomials \ like \ (a^2-b^2) are \ factored \ like \ this\!\!:} \\ \sf{(a+b)(a-b).} \\ \sf{Similarly, \ (x^2-16) \ is \ factored \ as \ (x+4)(x-4). \end{gathered}[/tex]

Done!!

⊰_____________________________________________________⊱

[tex]\\[/tex][tex]\\[/tex]

[tex]\boldsymbol{\rm{\triangleright\overbrace{C}\triangleleft\underbrace{A}\triangleright\overbrace{L}\triangleleft\underbrace{L}}\triangleright\overbrace{\stackrel\bigstar{I}}\triangleleft\underbrace{G}\triangleright\overbrace{R}\triangleleft\underbrace{A}\triangleright\overbrace{P}\triangleleft\underbrace{H}\triangleright{Y}}}[/tex]

Based on the information provided and the requirements to organize the students, Jon most likely has 23 students.

In general, Jon will need a number that is not prime as this type of number will not allow him to complete all the grid.

20 = A rectangular grid of 5 x 4 seats can be arranged

21= A rectangular grid of 7 x 3 can be arranged

22 = A rectangular grid of 2 x 11 can be arranged

23 = It is impossible to organize 23 seats in a rectangular grid without gaps

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Jon has 23 students in his class.

Number of students = Least 20 and most 28

In this case, we are getting a 1 * x rectangle of desks, which is the only possible arrangement.

'x' is a prime number.

Since his classes can't have less than 20 and more than 28, it means we are  looking out for a prime number between 20 and 28.

Let's sort out a prime number between the numbers, 20 and 28

20: 1,2,4,5,10,20

21: 1,3,7,21

22: 1,2,11,22

23: 1,23

24: 1,2,3,4,6,8,12,24

25: 1,5,25

26: 1,2,13,26

27: 1,3,9,27

28: 1,2,4,7,14,28

From what we have, 23 is a prime number because it is only divisible by one and itself.

Therefore, Jon has 23 students in his class.

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The population of viruses in the dish A is 3,391 viruses.

Population density measures the amount of organisms in 1 square millimeters of a place (in this case the dish)

Population density = population / area

Population = population density x area

1.2 x 2826 = 3,391 viruses

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Answer:

Yes, because they are congruent by AAS (angle angle side)

Step-by-step explanation:

One of the congruence theorem is AAS. If you follow the sides of the triangle, you will see that they are marked with an angle, another angle, and a side being congruent. I hope this helps!