I) state the

A line intersects the points (6, -12) and (15, -3). What is the slope intercept equation for this line?

Korolek [52]

Let's say that the unknown value here is c. Although we are given two points on the line, it is only necessary to use one as there is only one unknown value, so let's say we choose the point (6, -12) and substitute this into the equation:

-12 = 1(6) - c
-12 - 6 = -c
-18 = -c
c = 18

Thus the equation for the line is y = 1x - 18

8 0

3 years ago

A box contains 35 gems, of which 10 are real diamonds and 25 are fake diamonds. Gems are randomly taken out of the box, one at a

Sonja [21]

Answer:

Step-by-step explanation:

The total number of ways of selecting 3 gems of any kind without replacement is 35 * 34 * 33 = 39270

Now selecting 2 gems from 25 is 25C2

25 C 2 = 25 * 24/2 = 300

Selecting one good gem is 10

Total selection = 300 * 10 = 3000

P(gems) = 3000 / 39270

P(gems) = 300/3927

P(gems) = 100/1309

6 0

2 years ago

Tell whether the lines through the given points are parallel, perpendicular, or neither.

antoniya [11.8K]

Answer:

The Slope of Line 1 is -> $-\frac{2}{9}$

The Slope of Line 2 is -> $-\frac{9}{2}$

These two lines are - > Perpendicular

Step-by-step explanation:

To find the slope of line one, you follow these steps:

First Coordinate 10 -> x1, 5 -> y1

Second Coordinate -8 -> x2, 9 -> y2

Then insert the assigned values into this equation: $\frac{y2-y1}{x2-x1}$ -> $\frac{9-5}{-8-10}$ which equals $\frac{4}{-18}$ which simplifies to $-\frac{2}{9}$

Then do the same process to find the slop of line 2:

First Coord: 2 -> x1, -4 -> y1

Second Coord: 11 -> x2, -6 -> y2

Then insert the values into this equation: $\frac{y2-y1}{x2-x1}$ -> $\frac{11-2}{-6-(-4)}$ which equals $\frac{9}{-2}$ .

We know the lines are perpendicular by:

a. Typing the equations of the lines into a graphing calculator and observing the graph

b. Looking at the slopes. By looking at the slopes, we see that the slope of line 1 is the reciprocal of line 2, and vice versa. Since reciprocal slopes indicate perpendicular lines, the lines 1 and 2 are perpendicular to each other.

Hope this helps!

5 0

2 years ago

What weight of dry substance is in 150g of a 3% substance solution? What weight of an 8% solution can we have with the same weig

Pavlova-9 [17]

The answers are: 4.5 g and 56.25 g respectively.

Since the first type of measurement in this question is weight or mass, I'll suppose that the percentage concentration is % mass/mass. For that type of concentration measurement, just multiply the percentage by the total mass to get the mass of the wanted material.
So 150 g * 3% = 150 g * 0.03 = 4.5g

For the 8% solution with the same amount of dry substance, use the ratio of percentages, multiplied by the mass of the first solution to get the wanted amount of new solution:
3/8 * 150 g = 56.35 g

5 0

2 years ago

At Costco, you can buy a ten-pound bag of Halloween candy for $23.99. Kroger is running a special on the same brand of candy: bu

kirill [66]

Answer:

A. 2.40

B. 4

C. Costco is the better deal

Step-by-step explanation:

23.99/10= 2.399 (rounded to 2.40)

10/2.5 lbs (16 oz = 1 lb) = 4

6 0

3 years ago