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The measure of the angle that would maximize the area of this isosceles trapezoid is equal to 0.4395 rad.

Given the following data:

Mathematically, the area of a trapezium is given by this formula:

A = ½ × (a + b) × h

A = ½ × (12 + 2l) × h

A = h(6 + l)

Next, we would derive a mathematical expression for A in terms of h as follows;

A = (6 + 4sin(θ)) × 4cosθ

In order to determine the value of θ for which the area of this isosceles trapezoid is maximized, we would differentiate the area (A) with respect to angle (θ):

Note: sin²θ + cos²θ = 1   ⇒ cos²θ = 1 - sin²θ.

[tex]\frac{dA}{d\theta} =16 cos^{2} \theta - 4sin \theta(6+4sin \theta)\\\\\frac{dA}{d\theta} = 16 cos^{2} \theta - 16 sin^{2} \theta - 24sin\theta\\\\\frac{dA}{d\theta} =16(1-sin^{2} \theta)- 16 sin^{2} \theta - 24sin\theta\\\\\frac{dA}{d\theta} = - 32 sin^{2} \theta - 24sin\theta+16\\\\32 sin^{2} \theta + 24sin\theta-16=0[/tex]

Next, we would use the quadratic formula to solve for the value of sinθ.

Mathematically, the quadratic formula is given by this equation:

[tex]sin\theta = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Where:

Substituting the parameters into the formula, we have;

[tex]sin\theta = \frac{-24\; \pm\; \sqrt{24^2 - 4(32)(-16)}}{2(32)}\\\\sin\theta = \frac{-24\; \pm\; \sqrt{2624}}{64}\\\\sin\theta = \frac{-24\; \pm\; 51.23}{64}\\\\sin\theta = \frac{-24\;+\; 51.23}{64}\\\\sin\theta = \frac{27.23}{64}\\\\sin\theta = 0.4255\\\\\theta = sin^{-1}(0.4255)[/tex]

θ = 0.4395 rad.

Note: We would only consider the positive value of the quadratic root.

For the obtuse interior angles of the trapezoid, we have [tex](\frac{\pi}{2} +0.4395)[/tex]

Similarly, the measure of the acute interior angles of the trapezoid is [tex](\frac{\pi}{2} -0.4395)[/tex]

Read more on isosceles trapezoid here: https://brainly.com/question/4758162

Answer:

Line 2

Step-by-step explanation:

When factoring the second bracket, 1 x -8 is -8.

Answer:

4

Step-by-step explanation:

For one year, plan B would be recommended, because it would be cheaper.

An equation is an expression that shows the relationship between two or more numbers and variables.

The cost of plan A is given by f(x) = 50x + 199 and the cost of plan B is given by g(x) = 90x + 50

For one year, plan B would be recommended, because it would be cheaper.

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Answer: Plan A

Step-by-step explanation:

f(x) = 50x + 199 = A

g(x) = 90x + 50 = B

Plan A = (1,249) (2, 299) (3,349) (4,399) (5,449) (6,499)

Plan B = (1, 140) (2, 230) (3, 320) (4,410) (5, 500) (6, 590)

Plan A would be recommended because plan A you pay the least amount = 499 dollars over 6 months versus 590 dollars over 6 months with plan B.  

Answer:

8

Step-by-step explanation:

[tex]\hookrightarrow 18 - [5 + 1 + (4 - 2 + 2)]\\\\\hookrightarrow 18-[5+1+(6-2)]\\\\\hookrightarrow 18-[5+1+4]\\\\\hookrightarrow 18-10\\\\\hookrightarrow 8[/tex]

Answer:

Acc to ques

7x-3x = 60

x = 15

so they made total of 10x = 150

Using a system of equations, it is found that the equation that could be used to find the value of b is given by:

3×4−8=b

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

Fatima has 3 packs of batteries. Each pack contains 4 batteries, hence:

b = 3 x 4

She gives her brother 8 batteries to put in his toy robot, hence:

b = 3 x 4 - 8

Which means that the first expression is correct.

More can be learned about a system of equations at https://brainly.com/question/24342899

Answer:

a set of numbers that are used to find the hypotenuse

Step-by-step explanation:

brainliest

The integer solutions to the Pythagorean theorem, are called Pythagoras triples.

The integer solutions to the Pythagorean theorem, [tex]a^{2} +b^{2} =c^{2}[/tex] are called Pythagorean triples which contains three positive integers a, b and c.

For example:

(3, 4, 5)

By evaluating we get

[tex]3^{2} +4^{2} =5^{2}[/tex]

⇒ 9 + 16 = 25

Hence, 3, 4 and 5 are Pythagorean triples.

Learn more about Pythagorean Triples here:

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Answer:

D should be the answer because the rate of Mason and Evan is 3 pages per a minute because three goes into both like so 30÷10=3 and 12÷4=3. Which is why D is your answer.

Answer:

Step-by-step explanation:

Scale:- 1box=1units

So

Take one side of each

Scale factor(A to B)

[tex]\\ \rm\rightarrowtail \dfrac{6}{10}=\dfrac{3}{5}[/tex]

#6

Scale factor (A to B)

[tex]\\ \rm\rightarrowtail \dfrac{12}{6}=2[/tex]

Scale factor (B to A)

[tex]\\ \rm\rightarrowtail \dfrac{6}{12}=0.5[/tex]

Answer:

g< 0.0153

Step-by-step explanation:

0.08g +0.2 < 5

0.08g < 5 + 0.2

0.08g < 5.2

g< 0.0153

Answer:

Step-by-step explanation:

Let the width of the rectangle = x

As length is 5 inches longer than width, we have to add 5 to width

Length = x + 5

Perimeter of ractangle = 56 in

2* (length + width) = 56

2*( x + 5 + x) = 56

2* (2x + 5)    = 56

Use distributive property: a*(b +c) =(a*b) + (a * c)

2*2x + 2*5   = 56

4x  + 10 = 56

Subtract 10 from both sides

4x = 56- 10

4x = 46

Divide both sides by 4

x = 46/4

x = 11.5

Width = 11.5 in

length = 11.5 + 5

            = 16.5 in

Answer:

h=9

g=61

Step-by-step explanation:

16-h=7

g+4=65

&

Opposite angles and sides are equal in a paralleogram

Amd

Answer:

54

Step-by-step explanation:

9x6=54

Answer:

x=17.771mm

Step-by-step explanation:

given a right triangle

to find vslue of x

solution (perpendicular) ² + (base) ² =(hypotenus) ²

using pythagorus theorem

(16.5)²+(6.6)²=(x)²

272.25+43.56=(x)²

315.81=(x)²

√315.81=x

x=17.771mm

Answer:

By Pythagoras theorem

H^2=P^2+B^2

x^2=(6.6)^2+(16.5)^2

x^2=43.56+272.25

x^2=315.81

x=√315.81

x=17.771mm

Answer:

[tex] \displaystyle{ \sqrt{ \frac{1 + cos \: {30}^{ \circ} }{1 - cos \: {30}^{ \circ} } } = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} }[/tex]

[tex]LHS = \displaystyle{ \sqrt{ \frac{1 + cos \: {30}^{ \circ} }{1 - cos \: {30}^{ \circ} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{1 + \frac{ \sqrt{3} }{2} }{1 - \frac{ \sqrt{3} }{2} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{ \frac{2 + \sqrt{3} }{2} }{ \frac{2 - \sqrt{3} }{2} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{(2 + \sqrt{3} {)}^{2} }{4 - 3} } }[/tex]

[tex] \displaystyle{2 + \sqrt{3} }[/tex]

[tex]RHS = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} [/tex]

[tex] = 2 + \sqrt{3} [/tex]

[tex] \rm\therefore{LHS=RHS,proved. }[/tex]

so we know that 40% for the rent payment is for food, and we also know that those 40% are really 200 bucks, so what would it be for the 100%?

[tex]\begin{array}{ccll} \%&amount\\ \cline{1-2} 40 & 200\\ 100& x \end{array} \implies \cfrac{40}{100}=\cfrac{200}{x}\implies \cfrac{2}{5}=\cfrac{200}{x} \\\\\\ 2x=1000\implies x=\cfrac{1000}{2}\implies x=500[/tex]

Answer:

half a circle

Answer:

[tex]\displaystyle \textcolor{black}{4.}\:[-3, -5][/tex]

[tex]\displaystyle \textcolor{black}{3.}\:[8, -1][/tex]

[tex]\displaystyle \textcolor{black}{2.}\:[4, -7][/tex]

[tex]\displaystyle \textcolor{black}{1.}\:[3, -2][/tex]

Step-by-step explanation:

When using the Elimination method, you eradicate one pair of variables so they are set to zero. It does not matter which pair is selected:

[tex]\displaystyle \left \{ {{2x - 3y = 9} \atop {-5x - 3y = 30}} \right.[/tex]

{2x - 3y = 9

{⅖[−5x - 3y = 30]

[tex]\displaystyle \left \{ {{2x - 3y = 9} \atop {-2x - 1\frac{1}{5}y = 12}} \right. \\ \\ \frac{-4\frac{1}{5}y}{-4\frac{1}{5}} = \frac{21}{-4\frac{1}{5}} \\ \\ \boxed{y = -5, x = -3}[/tex]

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

[tex]\displaystyle \left \{ {{x - 2y = 10} \atop {x + 3y = 5}} \right.[/tex]

{x - 2y = 10

{⅔[x + 3y = 5]

[tex]\displaystyle \left \{ {{x - 2y = 10} \atop {\frac{2}{3}x + 2y = 3\frac{1}{3}}} \right. \\ \\ \frac{1\frac{2}{3}x}{1\frac{2}{3}} = \frac{13\frac{1}{3}}{1\frac{2}{3}} \\ \\ \boxed{x = 8, y = -1}[/tex]

_______________________________________________

[tex]\displaystyle \left \{ {{y = -3x + 5} \atop {y = -8x + 25}} \right.[/tex]

{y = −3x + 5

{−⅜[y = −8x + 25]

[tex]\displaystyle \left \{ {{y = -3x + 5} \atop {-\frac{3}{8}y = 3x - 9\frac{3}{8}}} \right. \\ \\ \frac{\frac{5}{8}y}{\frac{5}{8}} = \frac{-4\frac{3}{8}}{\frac{5}{8}} \\ \\ \boxed{y = -7, x = 4}[/tex]

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

[tex]\displaystyle \left \{ {{y = -x + 1} \atop {y = 4x - 14}} \right.[/tex]

{y = −x + 1

{¼[y = 4x - 14]

[tex]\displaystyle \left \{ {{y = -x + 1} \atop {\frac{1}{4}y = x - 3\frac{1}{2}}} \right. \\ \\ \frac{1\frac{1}{4}y}{1\frac{1}{4}} = \frac{-2\frac{1}{2}}{1\frac{1}{4}} \\ \\ \boxed{y = -2, x = 3}[/tex]

_______________________________________________

I am joyous to assist you at any time.

Answer:

Step-by-step explanation:

B) 9 and 36

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

9 is a common factor of

9 and 36.

Here's why:

6 is not evenly divisible by 9

16 is not divisible evenly by 9 (it is divisible by 8)

All the other numbers are divisible by 9.

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

Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer. :)

Answer:

9 doller

Step-by-step explanation:

we will find 20 percent of 46.69

is=pxw divided by 100

=9.338

or 9 doller

Answer:

A. 3.    B. 20

Step-by-step explanation:

2 divided by 2/3 is 2/ 2/3 or  6/2   which is 3.

3 divided by 1/10 is  3/ 1/10 or 30.

Answer:

80 Percent

Step-by-step explanation:

Since she has done 6/30 pages, she has 24/30 more pages to complete. Convert 24/30 to a decimal by dividing 24 by 30 to get the percentage, which is 80 percent

Hopefully this helps - let me know if you have any questions!

Answer: 15

Step-by-step explanation:

Answer:

50°

Step-by-step explanation:

In a parallelogram opposite angles have the same measure. Angle ABC has then the same measure of angle ADC, which is 38°+12°=50°

Answer:

[tex] \displaystyle{ \frac{x + 4}{x - 4} + \frac{x - 4}{x + 4} = 3 \frac{1}{3} }[/tex]

[tex]\displaystyle{ \frac{ {(x + 4) }^{2} + {(x - 4)}^{2} }{(x + 4)(x - 4)} = \frac{10}{3} }[/tex]

[tex]\displaystyle{ \frac{ {x}^{2} + 8x + {4}^{2} + {x}^{2} - 8x + {4}^{2} }{ {x}^{2} - {4}^{2} } = \frac{10}{3} }[/tex]

[tex]\displaystyle{ \frac{ {2x}^{2} + 16 + 16 }{ {x}^{2} - 16 } = \frac{10}{3} }[/tex]

[tex]\displaystyle{3( {2x}^{2} + 32) = 10( {x}^{2} - 16) }[/tex]

[tex]\displaystyle{ {6x}^{2} + 96 = {10x}^{2} - 160 }[/tex]

[tex]\displaystyle{ {10x}^{2} - 160 = {6x}^{2} + 96 }[/tex]

[tex]\displaystyle{ {10x}^{2} - {6x}^{2} - 160 - 96 = 0 }[/tex]

[tex]\displaystyle{ {4x}^{2} - 256 = 0}[/tex]

[tex]\displaystyle{4( {x}^{2} - 64) = 0}[/tex]

[tex] {x}^{2} - {8}^{2} = \displaystyle{ \frac{0}{4} }[/tex]

[tex]\displaystyle{(x + 8)(x - 8) = 0}[/tex]

[tex]\displaystyle{ \rm{either, \: x + 8 = 0............(1) }}[/tex]

[tex] \rm{or ,\: x - 8 = 0...............(2)}[/tex]

From equation (1)

[tex]x + 8 = 0[/tex]

[tex]x = - 8[/tex]

From equation (2)

[tex]x - 8 = 0[/tex]

[tex]\displaystyle{x = 8}[/tex]

[tex] \therefore{x=±8}[/tex]

In order to balance the equation, John should multiply the second side of the equation by s.

Why?

Remember the Golden Rule of Algebra:-

[tex]\bigstar{\boxed{\sf{Whatever~you~do~to~one~side,~you~do~to~the~other.}}[/tex]

So if you multiply 1 side of the equation by s, you multiply the second side by s.

Please tell John about the Golden Rule of Algebra ;)

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)