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3 years ago

Solve x(x-1) (X-5) <=O

Mathematics

1 answer:

lara [203]3 years ago

8 0

Answer:

x <= 0 or 1 = < x <= 5.

Step-by-step explanation:

First we find the critical points:

x(x - 1)(x - 5) = 0

gives x = 0, x = 1 and x = 5.

Construct a Table of values:

x < 0 x = 0 0< x < 1 1 =< x <= 5 x = 5

x <0 0 >0 <0 0

x - 1 <0 -1 >0 <0 0

x - 5 < 0 0 > 0 <0 0

x(x-1)(x-5) < 0 0 >0 <0 0

So the answers are x =< 0 or 1 =< x <= 5.

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Dmitrij [34]

Answer:

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Step-by-step explanation:

There are 10 numbers so the median is 4 and 5 which makes the median 4.5.

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3 years ago

Read 2 more answers

Enrique left the study group traveling 20 mph. Then, 2 hours later, Tevin left traveling the same direction at 28 mph. How long

nadya68 [22]

Answer:

After 7 hours Tevin will catch Enrique

Step-by-step explanation:

We have given speed of Enrique is 20 mph

Tevin left traveling after 2 hours of Enrique

Speed of Tevin is 28 mph

When Tevin catches Enrique will cover same distance

Let Enrique is traveling for t hours

Then Tevin will travel for t-2 hours

We know that distance = speed × time

So $20\times t=28\times (t-2)$

$20t=28t-56$

$8t=56$

t = 7 hours

So after 7 hours Tevin will catch Enrique

4 0

4 years ago

Oliver has created a plot of his backyard on the given coordinate plane, so that each unit length is one yard. He wants to desig

Karolina [17]

Answer:

The possible locations are;

(3, 4), (3, 12), (7, 4), and (7, 12)

Please find attached the plot of the points created with Microsoft Excel

Step-by-step explanation:

The given parameters of the plot of Oliver's backyard are;

The area of the right triangular plant bed Oliver wants to design, A = 8 yd²

The length of a/each unit of the plot = 1 yard

The location of one of the vertex of the right triangular area = (3, 8)

The location of the other vertex of the right triangular area = (7, 8)

We note that the area of a triangle, A = 1/2 × Base length, B × Height, h

Let the distance between the two plotted point represent the base length, 'B', therefore;

B = 7 - 3 = 4 (We subtract only the x-values (7 and 3) given that the y-values (8 and 8) are the same;

Therefore, the base length, B = 4 yards

A = 1/2 × B × h

∴ A = 8 yd.² = 1/2 × 4 yd. × h

h = 8 yd.²/ 2 yd. = 4 yd.

The height of the right triangle, h = 4 yd.

Therefore the possible locations of the last vertex the right triangle on the coordinate plane, given that the first two points are parallel with the x-axis, are points 4 units above or the y-axis value of the plotted points with the x-value of the last vertex being either 3, or 7 as follows;

(3, 8 ± 4) or (7, 8 ± 4) which give points, (3, 4), (3, 12), (7, 4), and (7, 12).