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2 years ago

Find a solution of the linear inequality. y ≥ 4x – 5 a. (1, 1) b. (2, 1) c. (3, 4) d. (3, 0)

Mathematics

2 answers:

frez [133]2 years ago

7 0

Answer:

$A(1,1)$

Step-by-step explanation:

we have

$y\geq 4x-5$

we know that

If a ordered pair is a solution of the inequality

then

the ordered pair must be located on the shaded area of the solution of the inequality

Using a graphing tool

Graph the inequality and plot the points

$A(1,1),B(2,1),C(3,4),D(3,0)$

see the attached figure

The point A is located on the shaded area

therefore

the point A is a solution of the inequality

FromTheMoon [43]2 years ago

5 0

Just a matter of subbing in ur answer choices to see which is correct.

(1,1)...x = 1 and y = 1
1 > = 4(1) - 5
1 > = 4 - 5
1 > = -1 (correct)

so ur answer is (1,1)

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = $21m^3$

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

<em>Using the volume formula of a cylinder</em>

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

$V = \frac{4}{3}\pi r^3$

Divide both sides by r

$\frac{V}{r} = \frac{4}{3r}\pi r^3$

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

$V = 14$

Hence, the volume of the sphere is 14m³

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for events A and B, P(A)= 3/14 and P(B)= 1/5. Also, P(A and B)= 3/65. Are A and B independent events?

Lady_Fox [76]

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Step-by-step explanation:

Let us study the meaning independent probability

Two events are independent if the result of the second event is not affected by the result of the first event
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