$\displaystyle\bf 3x+7\geq 52 \ ; \ x>15 \\\\3x\geq 45\\\\x\geq 15 \ \ \ and \ \ \ x>15$ here is a contradiction because in one inequality x can be equal to 15 ; and in the other it cannot

6 0

3 years ago

Kate is constructing an equilateral triangle. She has already used her straightedge to construct the line segment shown. A line

gavmur [86]

<span>Given that Kate is constructing an equilateral triangle and she has already used her straightedge to construct a line segment AB.

What Kate should do for her next step is "</span><span>Place the point of the compass on point A and draw an arc, using AB as the width for the opening of the compass".</span>

4 0

3 years ago

Three cube-shaped boxes are stacked one above the other. The volumes of two of the boxes are 1,331 cubic meters each, and the vo

blsea [12.9K]

The volume of a box with dimensions x by x by x is $x^{3}$ .

So if we are given the volume V of a cube-shaped box, the side length of thit is $\sqrt[3]{V}$ .

So we calculate the cubic roots of the volumes we have, and we add their heights.

To calculate the cubic root of 729, we can factorize it, and group the perfect cubes together, as follows:

$\frac{729}{3}= \frac{600}{3} + \frac{120}{3} + \frac{9}{3}=200+40+3=243$

$\frac{243}{3}= \frac{240}{3}+ \frac{3}{3}=80+1=81$ , which we recognize as $3^{4}$

so $729=3*3* 3^{4}= 3^{6}= ( 3^{2} )^{3}= 9^{3}$

similarly 1,331 can be found to be $11^{3}$ .

Thus we have 2 boxes with side length equal to 11 m and one with side length equal to 9 m.

Answer: h= 11+11+9 = 31 (meters)

7 0

3 years ago

Read 2 more answers

What is the first term of the geometric sequence presented in the table below?

Rina8888 [55]

176 = a1 * r^4
704 = a1 * r^6

dividing:-

r^2 = 706/174 = 4 so r = +/- 2

a1 = 176 / 2^4 = 176/16 = 11

So 11 is the first term

8 0

3 years ago