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12 days ago

6

Which graph shows the solution to the system of linear inequalities? x – 4y < 4 y < x + 1 Image for option 1 Image for opt

ion 2 Image for option 3 Image for option 4

1 answer:

Inessa [3.9K]12 days ago

7 0

Answer:

The graph provided in the accompanying figure

Step-by-step explanation:

we have

$x-4y$ ----> inequality A

solving for y

$-4y$

$4y>x-4$

$y> (x/4)-1$

The shaded area above the dashed line denotes the solution for inequality A

The slope of the dashed line is positive

The y-intercept corresponds to the point $(0,-1)$

The x-intercept corresponds to the point $(4,0)$

$y< x+1$ ----> inequality B

The solution for inequality B is represented by the shaded area below the dashed line

The slope of the dashed line is positive

The y-intercept corresponds to the point $(0,1)$

The x-intercept corresponds to the point $(-1,0)$

Using a graphing tool

This illustrates the solution for the system of inequalities in the provided figure

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A solid oblique cone with a slant length of 17 units is placed inside an empty cylinder with a congruent base of radius 8 units

PIT_PIT [3919]

Step $1$

Calculate the volume of a cylinder

We understand that

the volume of a cylinder can be expressed as

$V1=\pi r^{2} h$

In this scenario

$r=8\ units \\ h=15\ units$

Insert the values

$V1=\pi 8^{2} 15$

$V1=960\pi\ units^{3}$

Step $2$

Calculate the volume of a cone

We are aware that

the volume of a cone equals

$V2=\frac{1}{3}\pi r^{2} h$

In this example

$r=8\ units \\ l=17\ units \\ h=?$

Use the Pythagorean Theorem to determine the height h

$h^{2} =l^{2}-r^{2}\\ h^{2} =17^{2}-8^{2}\\ h^{2}=225\\ h=15\ units$

$V2=\frac{1}{3}\pi 8^{2} 15\\ \\ V2=320\pi \ units^{3}$

Step $3$

Calculate the empty volume inside the cylinder

$V1-V2=960\pi -320\pi =640\pi \ units^{3}$

Thus

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8 days ago

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What is the value of n? 9x27+2x31-28= n

Svet_ta [4321]

n equals 277

9 multiplied by 27 plus 2 multiplied by 31 minus 28 gives n

243 plus 62 minus 28 results in n

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which means 277 is n

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11 days ago

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A recipe calls for 400 grams of flour. if leena makes one quarter of the recipe, how many kilograms of flour will she need?

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Additional 300 grams of flour will be required.

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Part A: Rhett made $250 washing cars with his mobile car wash company. He charges $70 per car and earned $50 in tips. Write an e

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Conclusion:

Please refer to the explanation provided.

Detailed explanation:

Starting with these facts:

Total revenue = $250

Fee charged = $70 per car

Tips received = $50

Equation 1 representing the above:

(Fee per car × number of cars) + tips = total revenue

Let the number of cars be c.

Thus, we have:

$70c + $50 = $250

Part B:

Total revenue = $250

Fee charged = $75 per car

Tips received = $35

Supplies cost per car washed = $5

Equation 2:

(Fee per car × number of cars) + tips - (supplies cost × number of cars) = total revenue

$75c + $35 - $5c = $250

$70c + $35 = $250

Part C:

Equation 1 does not factor in costs associated with washing the car, while equation 2 does incorporate costs, which are deducted from the amount charged per car. Additionally, tips in equation 1 total $50 compared to a $35 fee in equation 2.

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which is linear. Shift the $x$ term to the right side, then multiply both sides by $e^{3t/10}$ :

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Next, integrate both sides and solve for $x$ :

$e^{3t/10}x=50e^{3t/10}+C$

$\implies x(t)=50+Ce^{-3t/10}$

Initially, the tank contains 5 g of salt at time $t=0$ , so we have

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