At least 350 students attended the band concert friday night

Answers

Answer 1

Answer: Yes 350 people attended the Friday concert

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Plz halp i need to get this right.

Help asap please!Add 4p^2+6 / 4p^2 + 2p-2 / 10p

Which statements are true about adding the rational expressions? Check all that apply

The least common denominator is 20p
.
The first fraction rewritten with the LCD is 20p^2+30 / 20p^2

The second fraction rewritten with the LCD is 4p - 4 / 20p

The sum is 24p^2-,4p+30 / 20p^2 = 12p-2p+15 / 10p^2

The sum is a rational expression.

Answers

I have to rewrite the expressions because they look very confusing.

1) The given fractions to add are:

4p² + 6        2p - 2
------------ + ------------
     4p²             10p²

2) The statements to asses are:

A) The least common denominator is 20p
.
B) The first fraction rewritten with the LCD is (20p² +30) / 20p²

C) The second fraction rewritten with the LCD is (4p - 4) / 20p

D) The sum is (24p² -4p +30 ) / 20p² = (12p-2p+15) / 10p^2

E) The sum is a rational expression.

This is the result for each statement.

A) The least common denominator is 20p

FALSE: THE LCD IS 20p², because it the least expression that contains all the prime factors of both denominators: 4p² and 10p.

See that you cannot divide 20p by 4p² but you can divide 20p² by 4p² and 10 p. So, 20p is not a common denominator.
.
B) The first fraction rewritten with the LCD is (20p² +30) / 20p²

TRUE: you get this expression from the first fraction by multiplying both numerator and denominator by 20p² / 4p² = 5:

(4p² + 6)×5 = 20p² + 30

(4p²)×5 = 20p²

=>

20p² + 30
--------------
      20p²

C) The second fraction rewritten with the LCD is (4p - 4) / 20p

FALSE: you have to multiply both numerator an denominator by 20p² / 10p = 2p

(2p - 2) × 2p = 4p² - 4p

10p × 2p = 20p²

So, the second fraction rewritten with the LCD is:

4p² - 4p
-----------
    20p²

D) The sum is (24p² - 4p +30 ) / 20p² = (12p-2p+15) / 10p²

TRUE

20p² + 30        4p² - 4p         24p² - 4p + 30
-------------- +   --------------- = ----------------------
      20p²              20p²                    20p²

And when you simplify the last fraction dividing by 2 you get:

12p² - 2p + 15
-----------------------
          10p²

E) The sum is a rational expression.

TRUE:

The sum of rational number has the closure property which means that by adding rational expression you will always ge a rational expression.

the 2nd, 4th, and 5th statements are correct. Let me know if you have questions on how to do the problem..

By first calculating the size of angle LMN,calculate the area of triangle MNL.
You must show all your working.
ML is 4.8cm
LN is 7.2 cm
angle N is 38 degrees

Answers

9514 1404 393

Answer:

16.66 cm² or 8.49 cm²

Step-by-step explanation:

The law of sines is useful for this.

sin(N)/LM = sin(M)/LN

M = arcsin(sin(N)×LN/LM) = arcsin(sin(38°)×7.2/4.8)

M =67.44° or 112.56°

Angle L is the remaining angle, so will have one of two measures:

L1 = 180° -38° -67.44° = 74.56°

The area of that triangle is ...

A = (1/2)LM×LN×sin(74.56°) ≈ 16.66 . . . . cm²

or ...

L2 = 180° -38° -112.56° = 29.44°

The area of that triangle is ...

A = (1/2)LM×LN×sin(29.44°) ≈ 8.49 . . . . cm²

Final answer:

To calculate the area of triangle MNL, first calculate the size of angle LMN using the Cosine Rule. Then use that angle and the known side lengths in the formula for the area of a triangle (Area = 0.5 * a * b * sin(C)) to find the area.

Explanation:

To solve this, you need to first calculate the size of angle LMN. This can be done using the Cosine Rule, which states that cos(C) = (a² + b² - c²) / 2ab, where a and b are the sides enclosing angle C. Here, angle C would be LMN, and sides a and b would be ML and LN.

Applying the values from your question, the cosine of LMN would be cos(LMN) = (4.8² + 7.2² - 38²) / (2 * 4.8 * 7.2). After calculating the cosine of the angle, you can find the angle itself using the inverse cosine function, or arccos.

Once you have the size of angle LMN, you can calculate the area of the triangle using the formula Area = 0.5 * a * b * sin(C), where a and b are sides of the triangle and C is the included angle. So, the area of triangle MNL would be Area = 0.5 * ML * LN * sin(LMN).

Learn more about Triangle Area Calculation here:

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it is 10 3\5 miles from Alston to Barton and 12 1/2 from Barton to Chester.the distance from Alston to Durban,via BARTON and Chester,is 35 miles.how far is it from Chester to Durban.

Answers

Answer:

Distance from Chester to Dublin is $11(9)/(10)$ miles

Step-by-step explanation:

Given :

Distance from Alston to Barton (A to B)= $10(3)/(5)=(53)/(5)$ miles

Distance from Barton to Chester (B to C)= $12(1)/(2)=(25)/(2)$ miles

Distance from Alston to Dublin via Barton and Chester(A to D) = 35 miles

Let the distance from Chester to Durban(C to D) = x

Refer the attached figure.

Therefore,

Total distance(A to D)= distance (A to B)+distance (B to C)+distance (C to D)

Putting values , we get

$35=(53)/(5)+(25)/(2)+x$

$35-(53)/(5)-(25)/(2)=x$

$35-10.6-12.5=x$

$11.9=x$

or $x=11(9)/(10)$

Distance from Chester to Dublin is $11(9)/(10)$ miles.

Final answer:

To find the distance from Chester to Durban, add the distances from Alston to Barton and Barton to Chester, and subtract this total from the given distance from Alston to Durban.

Explanation:

To find the distance from Chester to Durban, we need to determine the distance from Alston to Durban. We can start by finding the distance from Alston to Chester by adding the distances from Alston to Barton and from Barton to Chester. The total distance is 10 3/5 miles + 12 1/2 miles = 23 1/10 miles. Now, to find the distance from Alston to Durban, we subtract this total distance from the given distance from Alston to Durban via Barton and Chester: 35 miles - 23 1/10 miles = 11 9/10 miles. Therefore, it is 11 9/10 miles from Chester to Durban.

Learn more about Distance Calculation here:

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A rotating light on top of a lighthouse sends outrays of light in opposite directions. As the beacon
rotates, the ray at an angle 8 makes a spot of light
that moves along the shore. The lighthouse is
located 500 m from the shoreline and makes
one complete rotation every 2 min.
Determine the equation that expresses the
distance, d, in metres, as a function
of time, t, in minutes.

Answers

Answer:

$\sf d = 500 \cdot (\theta(t))$

Step-by-step explanation:

The equation can be derived using the following trigonometric identity:

That is:

$\sf tan(\theta) =( opposite )/( adjacent)$

In this case, the opposite side is the distance from the lighthouse to the shoreline and the adjacent side is the distance from the lighthouse to the spot of light on the shoreline (500m)

The angle is equal to the angle of the light beam.

It is changeable according to the time. so,

$\sf \theta \textsf{ will be } \theta t$

Substituting these values into the trigonometric identity gives us the following equation:

$\sf tan(\theta t) = (d)/(500)$

Solving for d gives us the following equation:

$\sf d = 500 \cdot (\theta(t))$

Therefore, the equation to express the distance, d, in metres, as a function of time, t, in minutes is:

$\sf d = 500 \cdot (\theta(t))$

Mario has a business selling muffins. Let x be the price of a muffin. Then, the profit P for Mario’s business is given by p(x)=-100x2+350x-150 Choose the inequality that shows the business will make a positive profit.