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saul85 [17]
3 years ago
11

I need help solving a system of linear equation, and it says to solve it by Substitution.

Mathematics
2 answers:
Nata [24]3 years ago
7 0
First solve for x in the second equation (x=-6y+18).then substitute -6y+18 in the first equation and solve for y.after solving for y then substitute it in one of the equation and then solve for x.
2x-3y=-25
x+6y=18

x=-6y+18
2(-6y+18)-3y=-24
-12y+36-3y=-24
-15y+36=-24
-15y=-24-36
-15y=-60
y=4

x+6(4)=18
x+24=18
x=18-24
x=-6

y=4,x=-6
olga_2 [115]3 years ago
6 0
2x - 3y = -24
x+ 6y = 18

you solve the first one by the x:

2x = -24 + 3y

x = (-24+3y)/2

then you substitute what you found in the other equation and you solve by y

(-24+3y)/2 + 6y = 18                   multiply everything by 2

-24 + 3y + 12y = 36

3y + 12y = 36 + 24

15y = 60

y = 60/15

y = 4

Good job! You found your y! :D

Now let's substitute the y in the first equation with 4:

2x - 3(4) = -24

2x - 12 = -24

2x = -24 + 12

2x = -12

x = -12/2

x= -6

Done!! ;) <span />
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A committee of 15 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the pr
Igoryamba

Answer:

0.006% probability that the final vote count is unanimous.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Random voting:

So 50% of voting yes, 50% no, so p = 0.5

15 members:

This means that n = 15

What is the probability that the final vote count is unanimous?

Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So

p = P(X = 0) + P(X = 15)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{15,0}.(0.5)^{0}.(0.5)^{15} = 0.00003

P(X = 15) = C_{15,15}.(0.5)^{15}.(0.5)^{0} = 0.00003

So

p = P(X = 0) + P(X = 15) = 0.00003 + 0.00003 = 0.00006

0.006% probability that the final vote count is unanimous.

7 0
2 years ago
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tatuchka [14]

You weren't clear on instructions

7 0
3 years ago
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in order for an object to begin to move. stop moving, or change direction, which of the following must be present?​
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Answer:

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6 0
3 years ago
show that the sum of the x- and y- intercepts of any tangent line to the curve sqrt(x) sqrt(y) = sqrt(c) is equal to c.
expeople1 [14]
The answer is <span>√x + √y = √c </span>
<span>=> 1/(2√x) + 1/(2√y) dy/dx = 0 </span>
<span>=> dy/dx = - √y/√x </span>

<span>Let (x', y') be any point on the curve </span>
<span>=> equation of the tangent at that point is </span>
<span>y - y' = - (√y'/√x') (x - x') </span>

<span>x-intercept of this tangent is obtained by plugging y = 0 </span>
<span>=> 0 - y' = - (√y'/√x') (x - x') </span>
<span>=> x = √(x'y') + x' </span>

<span>y-intercept of the tangent is obtained by plugging x = 0 </span>
<span>=> y - y' = - (√y'/√x') (0 - x') </span>
<span>=> y = y' + √(x'y') </span>

<span>Sum of the x and y intercepts </span>
<span>= √(x'y') + x' + y' + √(x'y') </span>
<span>= (√x' + √y')^2 </span>
<span>= (√c)^2 (because (x', y') is on the curve => √x' + √y' = √c) </span>
<span>= c.  hope this helps :D</span>
5 0
3 years ago
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