50+50+100+80+50+50+
50+20+50+60+100+40+
25+60+100+25+50+50+
20+40+40+60+100+100+
100+50+200+80+50+50
+40+25+50+50+50+50+
20+25+125+150+0.04=

[tex]\text{L.H.S}\\\\=\dfrac{\sin^4 A - \cos^4 A}{ \sin A + \cos A}\\\\\\=\dfrac{(\sin^2 A)^2-(\cos^2 A)^2}{\sin A + \cos A}\\\\\\=\dfrac{(\sin^2 A + \cos^2 A)(\sin^2 A-\cos^2 A)}{\sin A + \cos A}\\\\\\=\dfrac{1\cdot(\sin A+\cos A)(\sin A - \cos A)}{\sin A +\cos A}\\\\\\=\sin A - \cos A\\\\\\=\text{R.H.S}~~~ \\\\\text{Proved.}[/tex]

Answer:

heya! ^^

[tex] \\ \frac{ \sin {}^{4} (A) - \cos {}^{4} (A) }{ (\sin \: A + \cos \: A) } = ( \: sin \: A\: - \: cos \: A \: )\\[/tex]

[tex] \\LHS = \frac{ \sin {}^{4} (A) - \cos {}^{4} (A) }{ (\sin \: A + \cos \: A) } \\ \\ \frac{( \sin {}^{2} \: A + \cos {}^{2} \: A)( \sin {}^{2} A - \cos {}^{2} A) }{ (\sin \: A + \cos \: A) } \\ \\ we \: know \: that \: - \: sin {}^{2} A + cos {}^{2} A = 1 \\ \\ \therefore \: \frac{(1)(\sin {}^{2} \: A - \cos {}^{2} \: A)}{(\sin \: A + \cos \: A)} [/tex]

now , we're well aware of the algebraic identity -

[tex]a {}^{2} - b {}^{2} = (a + b)(a - b)[/tex]

using the identity in the equation above ,

[tex]\dashrightarrow \: \frac{(sin \:A - \: cos \: A)\cancel{(sin \:A + \: cos \: A )}}{\cancel{(sin \: A\: + \: cos \: A)}} \\ \\ \dashrightarrow \: (sin \: A \: - \: cos \: A) = RHS[/tex]

hence , proved ~

hope helpful :D

Answer:

Step-by-step explanation:

r (2 x + 8) - x - 4

(2 r - 1) x + 8 r - 4

Start at 3 and multiply by -4 each time.

Answer:

look at pic

Step-by-step explanation:

In the given case, the value of "x" in the given isosceles triangle is 18 degrees.

The given triangle is an isosceles triangle, which means that it has two equal sides. Let's denote the length of each equal side as "x".

To find the value of "x", we need to use the properties of an isosceles triangle. In an isosceles triangle, the base angles (the angles opposite to the equal sides) are congruent (equal in measure).

Since the base angles are congruent, we can set up the following equation: 2x + 3x + 5x = 180 degrees

Combining like terms, we have: 10x = 180 degrees

To solve for "x", we divide both sides of the equation by 10: x = 18 degrees

Therefore, the value of "x" in the given isosceles triangle is 18 degrees.

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Answer:

That's cool

Step-by-step explanation:

Answer:

Thats cool and all but whats the wuestion

Step-by-step explanation:

Answer:

yoo :)

Step-by-step explanation:

(-1,-2)

x= -1

y= -2

Have a wonderful day :)

APR= (interest + fees/ loan amount) / no. of days ×355 ×10

= 5000/226 / 24 × 365 × 10

= 33640.83

= 33640.83/365

= 93%

Answer:

False

Step-by-step explanation: Matter All was take up place

Applying the combination formula, the number of ways there are is: 66.

Combination is a technique in maths used in selecting objects from a group of objects in a way that the order in which they are selected does not matter.

Combination formula is given as:

[tex]nC_r = \frac{n!}{r(n - r)!}[/tex]

Given the following:

Plug in the values:

[tex]12C_2 = \frac{12!}{2(12 - 2)!}\\\\12C_2 = \frac{12!}{2(10)!}\\\\12C_2 = \frac{12 \times 11}{2(1)}[/tex]

[tex]\mathbf{12C_2 = 66}[/tex]

Therefore, applying the combination formula, the number of ways there are is: 66.

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Answer:

[tex]y-7=\frac{4}{3} (x+3)[/tex]

Step-by-step explanation:

Hi there!

We are given the point (-3, 7)

We want to write the equation of the line containing that point, in point slope-form, and that is also parallel to 4x-3y=7

Parallel lines contain the same slope

So first, let's find the slope of 4x-3y=7

To do that, we can convert the line from standard form (ax+by=c) to slope-intercept form (y=mx+b, where m is the slope, and b is the y intercept)

To do that, we need to isolate y on one side

So start by subtracting 4x from both sides

4x-3y=7

-4x      -4x

________________

-3y=-4x+7

Divide both sides by -3

y=[tex]\frac{4}{3}x[/tex]- [tex]\frac{7}{3}[/tex]

Since 4/3 is in the place of where m should be, the slope of the line is 4/3

It is also the slope of our new line, which we are trying to find

As stated earlier, we want to write this line in point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point

This is where the point we were given earlier comes in. We simply need to substitute our values (of the point and the slope) into the formula to find the equation.

First, with the slope; substitute 4/3 as m in the equation

[tex]y-y_1=\frac{4}{3} (x-x_1)[/tex]

Now substitute -3 as [tex]x_1[/tex] in the equation

[tex]y-y_1=\frac{4}{3} (x--3)[/tex]

We can simplify this to:

[tex]y-y_1=\frac{4}{3} (x+3)[/tex]
Now substitute 7 as [tex]y_1[/tex] into the equation

[tex]y-7=\frac{4}{3} (x+3)[/tex]

Hope this helps!

Answer:

40

Step-by-step explanation:

angle AOB= 2x=80

x=80/2

x=40

Answer:

1,2, and 5

Step-by-step explanation:

The statements about the function that are correct are:

The volleyball reached its maximum height at 3 seconds.
The maximum height of the volleyball was 23 feet.

We have,

The function h(t) = -2(t - 3)2 + 23 represents the height, in feet, t seconds after a volleyball is served.

Let's analyze each statement:

The volleyball reached its maximum height at 3 seconds.

This statement is correct.

The function h(t) is a quadratic function, and its graph is a parabola that opens downwards.

The vertex of the parabola represents the maximum height of the volleyball.

In this case, the vertex occurs when t = 3 seconds.

The maximum height of the volleyball was 23 feet.

This statement is also correct.

We can see from the function that the maximum height occurs at t = 3 seconds, and substituting t = 3 into the function gives:

h(3) = -2(3 - 3)2 + 23 = 23 feet.

If the volleyball is not returned by the opposing team, it will hit the ground in 5.5 seconds.

This statement is incorrect.

To find when the volleyball hits the ground, we need to find when h(t) = 0. Solving -2(t - 3)2 + 23 = 0 gives t = 3 ± √(23/2).

Since the vertex is at t = 3 seconds, the volleyball will hit the ground at the same height it was served, which is h(0) = -2(0 - 3)2 + 23 = 5 feet.

So the time it takes for the volleyball to hit the ground is when h(t) = 0, which occurs at t = 3 ± √(23/2), not 5.5 seconds.

The graph that models the volleyball's height over time is exponential.

This statement is incorrect.

The function h(t) is a quadratic function, not an exponential function.

The volleyball was served from a height of 5 feet.

This statement is also incorrect.

The function h(t) gives the height of the volleyball above the ground, not above the height it was served.

However, we can see from the function that h(0) = -2(0 - 3)2 + 23 = 5 feet, so the volleyball was served from a height of 5 feet above the ground.

Thus,

The statements about the function that are correct are:

The volleyball reached its maximum height at 3 seconds.
The maximum height of the volleyball was 23 feet.

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[tex]f(x) = \frac{3 + x}{x - 3} [/tex]

[tex]f(a + 2) = \frac{3 + a + 2}{a + 2 - 3} = \frac{a + 5}{a - 1} [/tex]

we know that the multiplication comes first in the family then we start from left to right

4 x 5= 20

9-20 = -11

-11 + 6 = -5

there you go!

[tex]9 - 4 \times 5 + 6[/tex]

[tex]9 - 20 + 6[/tex]

[tex] - 11 + 6[/tex]

[tex] - 5[/tex]

Answer:

13/5

Step-by-step explanation:

Given:

Substitute the values into the expression:

⇒ 1/2(m ÷ 3) + n

⇒ 1/2(12 ÷ 3) + 3/5

Simplify the expression:

⇒ 1/2(12 ÷ 3) + 3/5

⇒ 1/2(4) + 3/5

⇒ 1/2 x 4 + 3/5

⇒ 2 + 3/5

Make common denominators:

⇒ 2 + 3/5

⇒ (2 x 5/1 x 5) + 3/5

⇒ 10/5 + 3/5

Simplify by adding:

⇒ 13/5

Answer:

B. 60 cm²

Step-by-step explanation:

The formula for the area of a trapezoid is: [tex]\frac{1}{2}(b_{1} + b_{2} )h[/tex]

Plugging in the given values, we can solve:

[tex]\frac{1}{2} (13+7)(6)\\\\\frac{1}{2}(20)(6)\\\\10(6)\\\\= 60[/tex]

hope this helps!

Answer:

  √5

Step-by-step explanation:

The distance from the given point to the curve can be found using the distance formula. The resulting expression can be minimized to find the minimum distance.

  d = √((x2 -x1)² +(y2 -y1)²)

__

A point on the parabola can be described by ...

  x -y² = 0

  x = y² . . . . . add y²

Then a point on this curve is ...

  (y², y)

The distance to it from (0, 3) is ...

  d = √((0 -y²)² +(3 -y)²) = √(y⁴ +y² -6y +9)

The distance will be minimized when the derivative of the radical expression is zero:

  d(y⁴ +y² -6y +9)/dy = 0 = 4y³ +2y -6

  0 = 2y³ +y -3 . . . . . . . . remove a factor of 2

This will have a rational root in the set {±1, ±3}.

Trial and error shows that y=1 is the only real solution to this equation.

__

Then the minimum distance is ...

  d = √(1⁴ +1² -6·1 +9) = √5

_____

Additional comment

The attached graph shows that a circle with radius √5 centered at (0, 3) will intersect the parabola at exactly one point. That confirms our solution.

[tex]~~x^2+16\\ \\=x^2-(-16)\\\\=x^2-(4i)^2\\\\=(x+4i)(x-4i)[/tex]

Answer:

Step-by-step explanation:

Given expression:

Clearly, 16 is a perfect square as 4 x 4 is 16.

Thus, this expression can be written as:

Using the formula "a² + b² = (a + b)(a + b)"

The value of x given the perimeter of the square is 6.

The first step is to determine the perimeter of the square.

Perimeter of the square = 4 x length

4 x 2.5x = 10x yards

The perimeter of the triangle is equal to the sum of the three side lengths

2x + 4x - 2 + 2x + 14 = 10x

Combine similar terms

14 - 2 = 10x - 2x - 4x - 2x

Add similar terms

12 = 2x

Divide both sies by 2

x = 6

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Answer:

it is 6

Step-by-step explanation:

i did it in class and the teacher siad it ws right

Answer:

what??? I can't understand you sorry

Answer:

254.4 in²

Step-by-step explanation:

Area of a circle is given by the formula:

[tex]\pi r^{2}[/tex]

Our radius is 9 so we substitute this into the equation:

π(9)² = 81π

81π = 254.4 in²

Answer:

254 cm^2.

Explain:

The area of a circle is given by pi r squared. Pi has a constant value of 3.14. And the radius of the circle is 9 cm. The area equals pi R² equals 3.14 × 9² CM squared. 3.14 × 81 = 2.54.34cm^2 equals 254cm^2.

Answer:

4 < x < 12

Step-by-step explanation:

Given:

[tex]\displaystyle \large{9|x-8| < 36}[/tex]

Divide both sides by 9:

[tex]\displaystyle \large{|x-8| < 4}[/tex]

Theorem:

For [tex]\displaystyle \large{|x-a| < b}[/tex], since absolute is less than a constant, the interval or solution is:

[tex]\displaystyle \large{-b < x-a < b}\\\displaystyle \large{-b+a < x < b+a}[/tex]

Therefore:

[tex]\displaystyle \large{|x-8| < 4 \to -4 < x-8 < 4}\\\displaystyle \large{-4+8 < x < 4+8}\\\displaystyle \large{4 < x < 12}[/tex]

Therefore, the solution is 4 < x < 12

Answer:

4 < x < 12

Step-by-step explanation:

9|x - 8| < 36

Divide both sides by 9:

|x - 8| < 4

Solution 1

(x - 8) < 4

Add 8 to both sides:

x < 12

Solution 2

-(x - 8) < 4

-x + 8 < 4

Subtract 8 from both sides:

-x < -4

Divide both sides by -1 (remembering to change the direction of the sign):

x > 4

Therefore, the solution to the inequality is   4 < x < 12

Answer:

m<RUS = 65°

m<UST = 15°

Step-by-step explanation:

Hi there!

We are given circle O, with a diameter of US

The measure of arc RU is 50°, and the measure of arc UT is 30°

We want to find the measure of <RUS and <UST

First, let's start with <RUS
As stated before, we were given the diameter of a circle - that is segment US

Notice how ΔRUS (which contains <RUS) contains the diameter US - this means that the portion of the circle that contains ΔRUS is a semicircle.
If that portion is a semicircle, then that means that m<URS is 90°

Next, we know that the measure of arc RU is 50°

Notice how <RSU is an inscribed angle, meaning that it is created by 2 chords, and that its vertex is on the circle itself

Inscribed angles are half the measure of the arcs they intercept. The arc that <RSU intercepts is arc RU, which means that the measure of <RSU is 25°

Now, to find m<RUS, you can do m<URS - m<RSU, as the acute angles in a right triangle add up to 90°

In that case:

m<RUS = m<URS - m<RSU

via substitution, m<RUS = 90° - 25°

m<RUS = 65°

Now we need to find the measure of <UST

Notice how m<UST is also an inscribed angle

The arc it intercepts is arc UT, which we were given has a measure of 30 degrees

Therefore, m<UST = half of the measure of arc UT

Via substitution,

m<UST = 1/2 * 30

m<UST = 15°

Hope this helps!

Answer:

i think c

Step-by-step explanation:

i hope this helped

Answer:

c

Step-by-step explanation:

Answer:

[tex]\tt B)\;93^o[/tex]

Step-by-step explanation:

[tex]\tt 2(19x+1)+(19x+1)+15x=360[/tex]

[tex]\tt 38x+2+19x-2+15x=360[/tex]

[tex]\tt 38x+19x+15x+2-2=360[/tex] (Add similar elements)

[tex]\tt 72x+2-2=360[/tex] (2-2=0)

[tex]\tt 72x=360[/tex]

[tex]\tt \cfrac{72x}{72}=\cfrac{360}{72}[/tex] ( Divide both sides by 72)

[tex]\tt x=5[/tex]

Now,

m∠km:-

[tex]\tt 19x-2[/tex]

[tex]\tt 19(5)-2[/tex] (Multiply 19*5= 95)

[tex]\tt =95-2[/tex] (Subtract)

[tex]\tt = 93[/tex]

Therefore, m∠km=93° is the answer.

_____

Answer:  b) 160 c) 1500

Step-by-step explanation: b) 50 + 50 + 30 + 30 = 160 c) 50 x 30 = 1500

Step-by-step explanation:

[tex]length \: of \: a \: field \: = 50m[/tex]

[tex]breadth \: of \: a \: field \: = 30m[/tex]

[tex]Perimeter \: of \: a \: field \: = ? [/tex]

We know,

Perimeter ( p ) = 2 ( l + b )

= 2 ( 50m + 30m )

= 2 × 80 m

= 160 m

The length of a wire required to fence it thrice

= 3 × 160 m

= 480 m

Area ( A ) = l × b

= 50 × 30 m

[tex] = {1500m}^{2} [/tex]

Answer:

Alright! So, the formula is

x+x+1+x+2+x+3+x+4....x+24

You can do 25x+300=1000

25x=700

x=28