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3 years ago

Graph the solution set of this inequality: 5x − 4y > 20.

Mathematics

1 answer:

Yanka [14]3 years ago

3 0

Answer:

Step-by-step explanation:

Solve the inequality 5x − 4y > 20 for y, as follows: Subtract 5x from both sides, obtaining:

-4y > 20 - 5x;

Then divide all terms by -4:

y < -5 +(5/4)x, where the direction of the inequality sign has been reversed because of division by a negative quantity.

Temporarily replace the < symbol with = obtaining y = -5 +(5/4)x. Now choose at least three x values and find the corresponding y values. For example:

x y = -5 +(5/4)x

0 -5

4 0

-8 -15

Now plot these three points (0, -5), (4, 0) and (-8, -15). Draw a dashed line through them. Because of the < symbol in y < -5 +(5/4)x, shade the area underneath the dashed line.

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The maximum value of 12 sin 0-9 sin²0 is: -

jeka57 [31]

Answer:

Step-by-step explanation:

The question is not clear. You have indicated the original function as 12sin(0) - 9sin²(0)

If so, the solution is trivial. At 0, sin(0) is 0 so the solution is 0

However, I will assume you meant the angle to be $\theta$ rather than 0 which makes sense and proceed accordingly

We can find the maximum or minimum of any function by finding the first derivate and setting it equal to 0

The original function is

$f(\theta) = 12sin(\theta) - 9 sin^2(\theta)$

Taking the first derivative of this with respect to $\theta$ and setting it equal to 0 lets us solve for the maximum (or minimum) value

The first derivative of $f(\theta)$ w.r.t $\theta$ is

$12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right)$

And setting this = 0 gives

$12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right) = 0$

Eliminating $cos(\theta)$ on both sides and solving for $sin(\theta)$ gives us

$sin(\theta) = \frac{12}{18} = \frac{2}{3}$

Plugging this value of $sin(\theta)$ into the original equation gives us

$12(\frac{2}{3}) - 9(\frac{4}{9} ) = 8 - 4 = 4$

This is the maximum value that the function can acquire. The attached graph shows this as correct

3 0

1 year ago

How to solve it?........................

Feliz [49]

5x+4=114
5x= 110
X=22

114+ 3(22)-24=156
180-156=24
2y=24
Y=12

5 0

3 years ago

You have 800 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. What are the larg

katovenus [111]

Problema Solution

You have 800 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. What are the largest dimensions of this enclosure that you could build?

Answer provided by our tutors

Make a drawing and denote:

x = half of the length of the enclosure

2x = the length of the enclosure

y = the width of the enclosure

P = 800 ft the perimeter

The perimeter of the two enclosures can be expressed P = 4x + 2y thus

4x + 3y = 800

Solving for y:

........

click here to see all the equation solution steps

........

y = 800/3 - 4x/3

The area of the two enclosure is A = 2xy.

Substituting y = 800/3 - 4x/3 in A = 2xy we get

A = 2x(800/3 - 4x/3)

A =1600x/3 - 8x^2/3

We need to find the x for which the parabolic function A = (- 8/3)x^2 + (1600/3)x has maximum:

x max = -b/2a, a = (-8/3), b = 1600/3

x max = (-1600/3)/(2*(-8/3))

x max = 100 ft

y = 800/3 - 4*100/3

y = 133.33 ft

2x = 2*100

2x = 200 ft

3 0

3 years ago

Exactly 120 tickets were sold for a concert. The tickets cost $12 each for adults, $10 each for seniors, and $6 each for childre

Gemiola [76]

A=adult tickets
c=chlderenticekts
s=sinior tickets

a=c

a+c+s=120
2a+s=120

total made is 1100
12a+6c+10s=1100
sub
a=c
12a+6a+10s=1100
add
18a+10s=1100

multiply first equation by -9 and add to other equation

-18a-9s=-1080
18a+10s=1100 +
0a+s=20

s=20
20 senior tickets were sold

answer is B

5 0

3 years ago

Can someone please help me? I’ll give brainliest to the first person who gets it right

Pavlova-9 [17]

Answer:

128 degrees

Step-by-step explanation:

B = D

B = 128

Therefore, D = 128

3 0

2 years ago

Read 2 more answers