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3 years ago

Given the original statement "lf a number is negative, the additive inverse is positive," what is true

1 answer:

8 0

Yes the additive inverse in postive,because the opposite of negative is postive and the opposite of subtraction is addition

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How many solution does this have and how do you solve it

Vadim26 [7]

Answer:

Infinite solutions

Step-by-step explanation:

To determine the number of solutions a system has, you need its slope. If the slopes are the same, check if the equations are equivalent or not.

To find the slope, rearrange the equation to isolate "y", which makes it slope-intercept form y = mx + b.

"x" and "y" represent points on the line.

"m" represents the slope, which is how steep a line is.

"b" represents the y-intercept (where the graph hits the y-axis).

Isolate "y" in both equations:

x + 3y = 0

3y = -x Subtract 'x' from both sides

y = -x/3 Divide both sides by 3.

y = $-\frac{1}{3}x$

The slope is -1/3.

9y = -3x

y = -3x/9 Divide both sides by 9

y = $-\frac{3}{9}x$ Reduce the fraction to lowest terms

y = $-\frac{1}{3}x$

The slope is -1/3, but the two equations are the same.

Since the equations are the same, or <u>equivalent</u>, the two lines are always touching. The solution of a system means where two lines intersect, or meet. Therefore, <u>there are infinite solutions</u>.

5 0

3 years ago

10. A box contains five and two-thirds cups of rice. If three fourths of the rice will

sweet [91]

Answer:

5 2/3 - 3/4

5 8/12 - 9/12

4 20/12 - 9/12

4 11/12

4 0

3 years ago

Name the line and plane shown in the diagram. A.AB and plane ABD B.BA and plane DC C.AC and plane ABD D.AB and plane DA

elena-14-01-66 [18.8K]

Answer: The line is AB and the plane is ABD, the first option is the correct one.

Step-by-step explanation:

Ok, first some definitions.

A line is any line that crosses two colinear points. Particularly, you can see in the graph that the line crosses through A and B, so the line is AB.

A plane needs 3 non-colinear points (if the points where colinear, then the points may define a line). Other definition of plane is "a line and a point that is not in the line"

So, if our line is AB, then the possible planes are:

ABC and ABD.

then the correct option is:

Line AB and plane ABD, so the correct option is the first one.

6 0

3 years ago

find the volume of a solid that is generated by rotating around the indicated axis the plane region bounded by the giveb curves:

Fofino [41]

Assuming the area below the line y=0 (i.e. x>1) does NOT count, the area to be rotated is shown in the graph attached.

A. Again, using Pappus's theorem,
Area, A = (2/3)*1*(1-(-1))=4/3 (2/3 of the enclosing rectangle, or you can integrate)
Distance of centroid from axis of rotation, R = (2-0) = 2
Volume = 2 π RA = 2 π 2 * 4/3 = 16 π / 3 (approximately = 16.76 units)

B. By integration, using the washer method
Volume = $2\pi\int_{-1}^1(1-x^2)(2-x)dx$
$=2\pi\int_{-1}^1(x^3-2x^2-x+2)dx$
$=2\pi[x^4/4-2x^3/3-x^2/2+2x]_{-1}^{1}$
$=2\pi([1/4-2/3-1/2+2]-[1/4+2/3-1/2-2])$
$=2\pi(8/3)$
= 16 π /3 as before

3 0

3 years ago

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distrib

uysha [10]

Answer:

Step-by-step explanation:

Given that that (X) the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.

i.e. X is normal with mean = 15 and unknown std deviation $\sigma$

Given that $P(X$

i.e. P( $z$

z=-1.475 (from normal table)

Hence $\frac{13-15}{\sigma}=-1.475\\\sigma = 1.356$

Using this we find P(X>17) = $P(Z>\frac{17-15}{1.356} \\=P(Z>1.475)\\=0.5-0.428\\=0.072$

6 0

3 years ago