MATHEMATICS HIGH SCHOOL

Which values, when placed in the box, would result in a system of equations with no solution? Check all that apply.y = –2x + 4

6x + 3y =


A: –12

B: –4

C: 0

D: 4

E: 12

Answers

Answer 1
Answer:

For this case we have the following system of equations:

Rewriting equation 1 we have:

Therefore, the equivalent system is:

The system will have no solution, if we write equation 2 as a linear combination of equation 1.

Therefore, since both lines have the same slope, they are parallel.

Parallel lines do not intersect when they have different cut points.

Therefore, there is no solution for:

-12, -4, 0, 4

The system has inifinites solutions for:

12

This is because the lines intersect at all points in the domain.

Answer:

The values, when placed in the box, would result in a system of equations with no solution are:

A: -12

B: -4

C: 0

D: 4
Answer 2
Answer:

Answer:

Thus, option (a), (b) , (c) , (d) are correct.

The system will have no solution for all values except 12.

Step-by-step explanation:

 Given a system of equation y = –2x + 4  and 6x + 3y = ?

We have to check for which value the '?'  would result in a system of equations with no solution.

Consider a system of equation  a_1x+b_1y+c_1=0 \n\na_2x+b_2y+c_2=0

For the system to have no solution the condition is,

(a_1)/(a_2)=(b_1)/(b_2)\neq (c_1)/(c_2)

For the given system of equation ,

Let unknown quantity be v.

y = –2x + 4   ⇒ 2x +y - 4 = 0  

and 6x + 3y = v ⇒  6x + 3y - v =0

On comparing, we get,

a_1=2 , b_1=1,c_1=-4\n\n\a_2=6,b_2=3,c_3=-v

Substitute the values in condition for no solution , we get ,

(2)/(6)=(1)/(3)\neq (-4)/(-v)

Consider second and third ratio, we get,

(1)/(3)\neq (-4)/(-v)

Solve for v , we get,

(1)/(3)\neq (-4)/(-v) \n\n \Rightarrow v \neq 12  

Thus, for all values v except v = 12

The system will have no solution

at v = 12 the system will have infinite many solution.

Thus, option (a), (b) , (c) , (d) are correct.

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If your class wins the contest, then the class will receive a pizza party. Brooke’s class won the contest. What conclusion can you make from the statements above? Which law did you use to come up with your conclusion?


A.
Brooke’s class will have fun eating pizza.
law of syllogism
B.
Brooke’s class will have wings with their pizza.
law of detachment
C.
Brooke’s class will have a pizza party.
law of syllogism
D.
Brooke’s class will have a pizza party.
law of detachment

Answers

Answer:

The correct answer is D. Brooke’s class will have a pizza party by the law of detachment.

Step-by-step explanation:

By definition, the lay of detachment establishes if these two statements are true:

  • If p, then q.
  • p.

Then:

  • q is true.

In this case:

If your class wins the contest, then the class will receive a pizza party.

P: If your class wins the contest.

Q: The class will receive a pizza party.

Using P for Brooke's class:

P: If Brooke’s class wins the contest.

Q: Brooke’s class will have a pizza party.
the answer to your question is D

85% of what number equals 17

Answers

percent means parts out of 100
85%=85/100=0.85
'of' means multiply

therefor
85% of x equals 17 means
0.85 times x=17
divide both sides by 0.85
x=20



the number is 20

26 × 73? a. (80 × 26) - (80 × 7) =
b. (80 × 26) - (7 × 26) =
c. (20 73) - (6 73) =
d. (20 × 73) (6 × 73) =

Answers

26 x 73 = (20 + 6) x 73 = (20 x 73) + (6 x 73)

From the digits 9, 8, 7, 5, 3, and 1, find the number of positive even integers each consisting of three digits.a)36
b)25
c)3

Answers

even integers
they alwasy end with an even number
the only listed one is 8

find how may 2 number combos you can make with remaining 5 numbers
assuming you can repeat number
5 options, 2 slots
5*5=25

25 ways

answe ris B

The correct answer is 36.

Simplify the expression 18 + 12xa 2 (9 + 5x )
b 3(6 +3x)
c 6 ( 3 + x)
d (3 + 2x)
​

Answers

Answer:

c:) 6(3 + 2x)

Step-by-step explanation:

The given expression is 18 + 12x. To simplify this expression, we can first look for any common factors that can be factored out. In this case, we can factor out 6, which gives:

18 + 12x = 6(3 + 2x)

So, the simplified expression 18 + 12x is 6(3 + 2x).

A bank pays 5% interest compounded annually. What principal will grow to $12,000 in 10 years.

Answers

Answer: 7366.96 dollars

========================================================

Use the compound interest formula:

A = P(1+r/n)^(n*t)

where in this case,

A = 12000 = amount after t years

P = unknown = deposited amount we want to solve for

r = 0.05 = the decimal form of 5% interest

n = 1 = refers to the compounding frequency (annual)

t = 10 = number of years

-------

Plug all these values into the equation, then solve for P

A = P(1+r/n)^(n*t)

12000 = P(1+0.05/1)^(1*10)

12000 = P(1.05)^(10)

12000 = P(1.62889462677744)

12000 = 1.62889462677744P

1.62889462677744P = 12000

P = 12000/1.62889462677744

P = 7366.95904248911

P = 7366.96
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