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tino4ka555 [31]
3 years ago
7

Tom keeps all of his favorite marbles in a special leather bag. right know five red marbles four marbles and three marbles are i

n the bag .
part A:if he randomly chooses one marbles to give to a friend what is the probability that it is blue.

part B: tom does not really want to give away blue marbles and would like to change the probability that he choose a blue marble to 1/10. how many marbles that are not blue could he add to the bag so that the probability of choosing a blue marble becomes 1/10
Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
5 0
Part a: seven to five because there it says that there is five red marbles but it doesn't say any other colors for and if the other marbles so weave to assume that the rest are blue

Part b: tom could add 70 other color marbles because it is equivalent to 1/10 and it would happen with out taking any marbles out of the bag
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Find the distance from point A(−9,−3) to the line y = x−6. Round your answer to the nearest tenth.
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The distance from point A(−9,−3) to the line y = x−6 is 8.5 units

<u>What is slope ?</u>

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

step 1

Find the slope of the perpendicular line to the given line

y=x-6 ---> given line

The slope is m=1

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

m1*m2 = -1

we have

m1=1

substitute

(1)*m2 = -1

so

m2 = -1

step 2

Find the equation of the perpendicular line to the given line

The equation in point slope form is

y-y1=m(x-x1)

we have

m=-1

(x1,y1)=(−9,−3)

substitute

y+3=-1(x+9)--> equation in point slope form

y+3= -x-9

y= -x-12---> equation in slope intercept form

step 3

Find the intersection point between the given line and the perpendicular line to the given line

we have the system of equations

y = x−6.

y= -x-12

Solve the system by graphing

The intersection point is (-3,-9)

see the attached figure

step 4

we know that

The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6

the formula to calculate the distance between two points is equal to

d=√[(y2-y1)² + (x2-x1)²]

substitute the values

d=√[(-9+3)² + (-3+9)²]

d= √72 units

simplify

d= 6√2 = 8.5 units

To learn more about the slope from the given link

brainly.com/question/16949303

#SPJ1

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