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3 years ago

Which graph best represents the solution set of 2/3 x + y ≤ − 2?

Mathematics

1 answer:

aliina [53]3 years ago

4 0

Answer:

<u>Option D</u>

Step-by-step explanation:

The given inequality 2/3 x + y ≤ − 2

Need to find x-intercept and y-intercept of the line 2/3 x + y = − 2

x-intercept ⇒ y = 0 ⇒ 2/3 x = − 2 ⇒ x = -3

y-intercept ⇒ x = 0 ⇒ y = -2

Compare the results with the graphs

The answer is option D

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

Note:

The shade area represents the solution of an inequality

The shaded area over a solid line if the the sign is ≥

The shaded area below a solid line if the the sign is ≤

The shaded area over a dashed line if the the sign is >

The shaded area below a dashed line if the the sign is <

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melamori03 [73]

Answer:

500+4=504

Step-by-step explanation:

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3 years ago

Find the y value for point I such that DI and EI form a 3:5 ratio.

Pachacha [2.7K]

The y value of I is (5(2) + 3(5))/(3 + 5) = (10 + 15)/8 = 25/8 = 3.125

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3 years ago

A rectangle with a length of L and a width of W has a diagonal of 10 inches. Express the perimeter P of the rectangle as a funct

KatRina [158]

<h2>Answer:</h2>

The expression which represents the perimeter P of the rectangle as a function of L is:

$Perimeter=2(L+\sqrt{100-L^2})$

<h2>Step-by-step explanation:</h2>

The length and width of a rectangle are denoted by L and W respectively.

Also the diagonal of a rectangle is: 10 inches.

We know that the diagonal of a rectangle in terms of L and W are given by:

$10=\sqrt{L^2+W^2}$

( Since, the diagonal of a rectangle act as a hypotenuse of the right angled triangle and we use the Pythagorean Theorem )

Hence, we have:

$10^2=L^2+W^2\\\\i.e.\\\\W^2=100-L^2\\\\W=\pm \sqrt{100-L^2}$

But we know that width can't be negative. It has to be greater than 0.

Hence, we have:

$W=\sqrt{100-L^2}$

Now, we know that the Perimeter of a rectangle is given by:

$Perimeter=2(L+W)$

Here we have:

$Perimeter=2(L+\sqrt{100-L^2})$

7 0

4 years ago

What is the solution of x-1/1-x < 0?

kykrilka [37]

Option C is correct option.

Step-by-step explanation:

We need to find the solution of $\frac{x-1}{1-x}$

The given inequality becomes undefined when x = 1 because the denomiator is: 1-x and if x = 1 then it becomes 1-1 = 0 and anything divided by zero is undefined.

So, all values other than 1 are included in the solution of the given inequality.

So, solution is: x<1 or x>1 but x≠1

So, Option C is correct because all numbers are included in number line except 1. An unfilled circle on 1 shows that it is not included in the solution. Rest of numbers are included.

Option C is correct option.

Keywords: Solving inequalities

Learn more about Solving inequalities at:

#learnwithBrainly

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4 years ago

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Luba_88 [7]

Answer:

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