Determine the LCM of the following monomials listed below.

If sin(x) = 3a/2 and 0 ≤ x ≤ π/2, then x = arcsin(3a/2). The condition on x here is useful because it makes the sin and arcsin functions exacts inverses of one another: if y = sin(x), then arcsin(y) = x.

Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

Also because 0 ≤ x ≤ π/2, we know both sin(x) > 0 and cos(x) > 0. So from the Pythagorean identity, it follows that

sin²(x) + cos²(x) = 1

==>   cos(x) = √(1 - sin²(x)) = √(1 - 9a ²/4) = 1/2 √(4 - 9a ²)

Then we have

x/4 - sin(2x) = x/4 - 2 sin(x) cos(x)

… = 1/4 arcsin(3a/2) - 2 (3a/2) (1/2 √(4 - 9a ²))

… = 1/4 arcsin(3a/2) - 3a/2 √(4 - 9a ²)

Answer:

Step-by-step explanation:

The radius of the whole figure: 14 : 2 = 7 (cm)

The area of the whole figure: 7 x 7 x 3.14 = 153.86 (cm2)

The area of the unshaded region:  3.5 x 3.5 x 3.14 = 38.465 (cm2)

The area of the shaded region: 153.86 - 38.465 =  115.395 (cm2)

Answer: 115.395 cm2.

Hope it helps!

Answer: 4.5cm

Step-by-step explanation:

From the information given in the question, we are informed that an airport runway measuring 450 m is drawn to a scale of 1 cm represent 100m, then the length in the drawing will be calculated thus:

Let the length be represented by x. Therefore, we'll have:

1/x = 100/450

Cross multiply

(100 × x) = (1 × 450)

100x = 450

x = 450/100

x = 4.5

Therefore, the length in the drawing is 4.5cm

Answer:

X = 32 meters.

Step-by-step explanation:

Given the following data;

To find how many meters he would cover in four hours;

1 hour = 8 meters

4 hours = X meters

Cross-multiplying, we have;

X = 8 * 4

X = 32 meters.

Answer:

3x (3x-1)-10 (3x-1)

9x2-3x-30x+10 (the 2 in 9x2 is the square ok)

9x2-33x+10 Ans..

I hope this will help you

If this is incorrect forgive meplz

Answer:

= 8:00 A.M.

Step-by-step explanation:

▪You first find the total time taken which will be :

2 hrs 55 min + 25 min

= 3 hrs 20 min + 25 min

= 3 hrs 45min

▪ Beginning time = Arrival time - Time taken

= 11:45 - 3:45

= 8:00 am

¿

Answer:

x = 130 degrees

Step-by-step explanation:

ok so first find all the interior angles of the triangle before using the supplementary angle rule to find x.

the interior angle A = 20 degrees, so the interior angle B must be 50 degrees (since there can only be 180 degrees in a triangle). So, since B is 50 degrees and x is 180-50, we know that x = 130 degrees

Step-by-step explanation:

the answer is in the image above

Answer:

No! 20% does not correspond to a central angle 20°.

Step-by-step explanation:

The central angle for pie chart is 360°.

So, a category represents 20% is 20%(360) for central angle.

Let's simplify it to get the angle,

[tex]\frac{20}{100} * 360[/tex]

Simplify it,

72°

So, 20% does not correspond to a central angle 20°.

Answer:

A)let x be the length of one side , 6 × x= peri.

B)6 × 11 = 66

Answer: 39 pages

Step-by-step explanation:

x = the amount of pages Tom read

[tex]2x+12=90\\2x=78\\\frac{2x}{2}=\frac{78}{2}\\x=39[/tex]

If Sue read 90 pages, which is 12 more than twice the amount, subtract 12 from 90, then divide the result by 2, boom, you got your answer. Which should be 39

Answer:

[tex]\displaystyle c = \frac{20}{3}[/tex]

Step-by-step explanation:

According to Rolle's Theorem, if f(a) = f(b) in an interval [a, b], then there must exist at least one c within (a, b) such that f'(c) = 0.

We are given that g(5) = g(8) = -9. Then according to Rolle's Theorem, there must be a c in (5, 8) such that g'(c) = 0.

So, differentiate the function. We can take the derivative of both sides with respect to x:

[tex]\displaystyle g'(x) = \frac{d}{dx}\left[ -7x^3 +91x^2 -280x - 9\right][/tex]

Differentiate:

[tex]g'(x) = -21x^2+182x-280[/tex]

Let g'(x) = 0:

[tex]0 = -21x^2+182x-280[/tex]

Solve for x. First, divide everything by negative seven:

[tex]0=3x^2-26x+40[/tex]

Factor:

Zero Product Property:

[tex]x-2=0 \text{ or } 3x-20=0[/tex]

Solve for each case. Hence:

[tex]\displaystyle x=2 \text{ or } x = \frac{20}{3}[/tex]

Since the first solution is not within our interval, we can ignore it.

Therefore:

[tex]\displaystyle c = \frac{20}{3}[/tex]

Answer:

[tex]\#\text{ of 8-onion bags: }4,\\\#\text{ of 3-onion bags: }3[/tex]

Step-by-step explanation:

Let [tex]a[/tex] be the number of bags with 8 onions and let [tex]b[/tex] be the number of bags with 3 onions. We have the following system of equations:

[tex]\begin{cases}a+b=7,\\8a+3b=41\end{cases}[/tex]

Subtracting [tex]b[/tex] from both sides of the first equation, we get [tex]a=7-b[/tex]. Substitute this into the second equation:

[tex]8(7-b)+3b=41,\\56-8b+3b=41,\\56-5b=41,\\-5b=-15,\\b=\boxed{3}[/tex]

Therefore, the number of 8-onion bags is:

[tex]a=7-b,\\a=7-3,\\a=\boxed{4}[/tex]

Thus, the chef got 4 8-onion bags and 3 3-onion bags.

Answer: 25 in.

Step-by-step explanation:

Answer:

x(x+5)^2

Step-by-step explanation:

x^3 + 10x^2 + 25x

Factor out x

x(x^2+10x+25)

What 2 numbers multiply to 25 and add to 10

5*5 = 25

5+5 =10

x(x+5)(x+5)

x(x+5)^2

Answer:

D

Step-by-step explanation:

Given

x³ + 10x² + 25x ← factor out x from each term

= x(x² + 10x + 25) ← perfect square

= x(x + 5)²

Answer:

Step-by-step explanation:

The equation for this free fall problem is

[tex]h(t)=-16t^2+1296[/tex] where h(t) is the height of the pebble from the ground at any time t. If we are looking for the time it takes the pebble to hit the ground, knowing that at ground level the height is 0, we set the quadratic equal to 0 and solve for t:

[tex]-16t^2+1296=0[/tex] and

[tex]-16t^2=-1296[/tex] and

[tex]t^2=81[/tex] so

t = -8, 8

Since time will never be negative,

t = 8 seconds

Answer:

21 inches

Step-by-step explanation:

We can write a ratio to solve

7 inches        x inches

-------------  = -------------------

1 bracelet      3 bracelets

Using cross products

7*3 = 1x

21 = x

21 inches

Answer:

21 inches

Step-by-step

This can be solved two ways: addition or multiplication.

Addition: Since there are three bracelets you could add 7 three times

                 7+7+7

             = 14+7

             = 21

Multiplication: Simply multiply 7 x 3= 21

Answer:

Based on two Pythagorean Identities:

sec²θ(1 - cot²θ)

= sec²θ - sec²θ · cot²θ

[tex]=\frac{1}{cos ^{2} \theta} -\frac{1}{cos ^{2}\theta }*\frac{cos ^{2}\theta}{sin^{2} \theta}\\\\=\frac{1}{cos ^{2}\theta }-\frac{1}{sin^{2}\theta }\\\\=sec^{2}\theta-csc^{2}\theta\\\\=1+tan^{2}\theta-(1+cot^{2}\theta)\\\\=1+tan^{2}\theta-1-cot^{2}\theta\\\\=tan^{2}\theta-cot^{2}\theta[/tex]

Answer:

∠? = 76°

Step-by-step explanation:

The two lines on the sides of the triangle indicate that this is an isosceles triangle. An isosceles triangle has 2 congruent sides and one side that is different. The same goes for its angles. The angle opposite to these same sides are also the same. So if one angle = 76°, then ∠? = 76° as well.

Hope this helps! Best of luck <3

Answer:

True

Step-by-step explanation:

The answer is "True". Let me explain.

Let's say that we have a line segment which we will call AB, construct a perpendicular bisector. The following steps will be taken;

1) Draw a semi circle with its centre at point A and passing through point B.

2) Draw a semi circle with its centre at point B and passing through point A.

3) The two semicircles will intersect at two points with one being above and the other being below the straight line segment AB. Now, a line will have to be drawn that passes through those two intersecting points. This drawn line is called the perpendicular bisector for line segment AB.

Answer:

True

Step-by-step explanation:

Make sure you’re paying attention to if your question says “were able to” or “were not able to”.

Answer:

Perimeter of original triangle: 6+8+10=24 cm

Perimeter of new triangle: 3+4+5=12 cm (You get 3, 4, and 5 from dividing 6, 8. and 10 by 2.)

Ratio of original to new is 24 to 12, simplified to 2 to 1.  

The ratio of the perimeter is the ratio of the corresponding sides, as the original measurements are two times the length of the new measurements.

Area of original triangle: (6x8)/2=24 cm^2

Area of new triangle: (3x4)/2=6 cm^2

Ratio of original to new is 24 to 6, simplified to 4 to 1.

Answer:

47

Your answer is this.

Hope it will help you

Answer:

sas

Step-by-step explanation:

dide angle side is correct

def=149

gef=5x-13

deg=x

5x-13+x=149

6x=162

x=27

plug the x back in

5(27)-13=122

The value of <GEF is 122

In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle. Let us read about the different parts of an angle.

Parts of an Angle

There are two main parts related to an angle - the arms and the vertex.

Arms of the Angle

The two rays which join at a common point to form the angle are called the arms of the angle. Observe the figure given below which shows that OA and OB are the arms of the angle AOB.

<DEF=149

let <DEG be x

So,<GEF = 5x-13

Now

5x-13+x=149

6x=162

x=27

Hence, <GEF = 5(27)-13= 122

Learn more about angle here:

https://brainly.com/question/13954458

#SPJ2

Answer:

B is the answer

Step-by-step explanation:

The intercept is at x = 0 then y = 21 or (0,21) so A and D drop out.

The vertex (-5, -4) satisfies the equation but (-4,-5) does not so C drops out leaving B.

Answer:

B.

Step-by-step explanation:

B.

Answer:

2 standard deviations of the mean. so, 41 to 65

Step-by-step explanation:

from the empirical rule we know that for 95% we are in 2 standard deviations of the mean. so:

53- 6- 6 = 41

*2 minus 6s because 2 standard dev. with the mean

53 + 6 + 6 = 65

Answer:

A.

The y-intercept of m is less than the y-intercept of n.

Step-by-step explanation:

y-intercept of a function:

The y-intercept of a function is the value of y when [tex]x = 0[/tex]

Function n represents a cubic function that passes through the points (-1,0) and (0,2).

When [tex]x = 0, y = 2[/tex], and thus, the y-intercept is y = 2.

Function m:

When [tex]x = 0, y = -6[/tex], and thus, the y-intercept is y = -6, which is a smaller number than 2, so the y-intercept of m is less than the y-intercept of n, and the correct answer is given by option A.

Answer:

Step-by-step explanation:

Look at the photo