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3 years ago

Determine which system below will produce infinitely many solutions.

Mathematics

2 answers:

ddd [48]3 years ago

7 0

Answer:

i think its a

Step-by-step explanation:

options are

-6x + 3y = 18

4x − 3y = 6

2x + 4y = 24

6x + 12y = 36

3x − y = 14

−9x + 3y = −42

5x + 2y = 13

−x + 4y = −6

mariarad [96]3 years ago

4 0

A system that will produce infinitely many solutions will have the property where all the equations overlap. That means they will have the same slope and y-intercept.

An easy way to determine if they will produce infinitely many solutions is to put all the equations into $y=mx+b$ form. If everything is the same, you know it will have infinite solutions.

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An urn contains 3 red and 7 black balls. Players A and B take turns (A goes first) withdrawing balls from the urn consecutively.

andrey2020 [161]

Answer:

The probability that A selects the first red ball is 0.5833.

Step-by-step explanation:

Given : An urn contains 3 red and 7 black balls. Players A and B take turns (A goes first) withdrawing balls from the urn consecutively.

To find : What is the probability that A selects the first red ball?

Solution :

A wins if the first red ball is drawn 1st,3rd,5th or 7th.

A red ball drawn first, there are $E(1)= ^9C_2$ places in which the other 2 red balls can be placed.

A red ball drawn third, there are $E(3)= ^7C_2$ places in which the other 2 red balls can be placed.

A red ball drawn fifth, there are $E(5)= ^5C_2$ places in which the other 2 red balls can be placed.

A red ball drawn seventh, there are $E(7)= ^3C_2$ places in which the other 2 red balls can be placed.

The total number of total event is $S= ^{10}C_3$

The probability that A selects the first red ball is

$P(A \text{wins})=\frac{(^9C_2)+(^7C_2)+(^5C_2)+(^3C_2)}{^{10}C_3}$

$P(A \text{wins})=\frac{36+21+10+3}{120}$

$P(A \text{wins})=\frac{70}{120}$

$P(A \text{wins})=0.5833$

6 0

3 years ago

What is the answer. Shawn pays $1.75 for a school lunch on days when he doesn't bring his own lunch to school. One week he bough

katen-ka-za [31]

Answer:

C. 3.50

Step-by-step explanation:

He bought a lunch two times, so $1.75*2 = 3.50.

5 0

3 years ago

A store manager is accepting applications for part-time workers. he can hire no more than 14 people. so far,he has hired 9 peopl

Lorico [155]

The manager already hired 9 people. Let $x$ be the number of people he still can hire. Since these people will add to the 9 he already hired, when the hiring campaign will be over he will have hired $9+x$ people. We know that he can't hire more than 14 people, so the number of people hired must be less than or equal to 14:

$9+x \leq 14$

If we subtract 9 from both sides, we have

$x \leq 14-9=5$

so, the manager can hire at most 5 other people

6 0

3 years ago

A runner passes the 12-mi point after 2 hours and reaches the 15-mi point 30 minutes later. Assuming a constant rate, find th

Arturiano [62]

Answer:

6 mph

Step-by-step explanation:

Difference in distance

= 15 - 12

= 3 mi

time taken

= 30 mins

= 1/2 hour

Speed

= 3 ÷ 1/2

= 6 mph

8 0

3 years ago

When Rafael emptied his pockets, e found he had a total of $3.50 in quarters and nickels. If he had 8 more quarters that nickels

jasenka [17]

You can use systems of equations for this one.

We are going to use 'q' as the number of quarters Rafael had,
and 'n' as the number of nickels Rafael had.

You can write the first equation like this:
3.50=0.05n+0.25q
This says that however many 5 cent nickels he had, and however many
25 cent quarters he had, all added up to value $3.50.
Our second equation is this:
q=n+8
This says that Rafael had 8 more nickels that he had quarters.

We can now use substitution to solve our system.

We can rewrite our first equation from:
3.50=0.05n+0.25q
to:
3.50=0.05n+0.25(n+8)

From here, simply solve using PEMDAS.

3.50=0.05n+0.25(n+8)     --Distribute 0.25 to the n and the 8
3.50=0.05n+0.25n+2     --Subtract 2 from both sides
1.50=0.05n+0.25n     --Combine like terms
1.50=0.30n     --Divide both sides by 0.30
5=n     --This is how many NICKELS Rafael has.

We now know how many nickels he has, but the question is asking us
how many quarters he has.

Simply substitute our now-known value of n into either of our previous
equations (3.50=0.05n+0.25q or q=n+8) and solve.

We now know that Rafael had 13 quarters.

To check, just substitute our known values for our variables and solve.
If both sides of our equations are equal, then you know that you have
yourself a correct answer.

Happy math-ing :)

5 0

3 years ago