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3 years ago

How many solutions does the system of equations have?

Mathematics

2 answers:

Fynjy0 [20]3 years ago

4 0

No solution. These lines are parallel meaning they will never intersect

shepuryov [24]3 years ago

3 0

C. it has no solution because the solution is the coordinate points intersect

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Let T:R²->R² be a linear transformation ,and assume that T (1,2)=(-1,1) and T(1,-1)=(2,3)

zavuch27 [327]

Answer:

(-4,-1)

Step-by-step explanation:

We are given T(1,2)=(-1,1) and T(1,-1)=(2,3) and T is a linear transformation.

This implies for scalars a and b that

T(a(1,2)+b(-1,1))=aT(1,2)+bT(-1,1)

T((a,2a)+(-b,b))=a(-1,1)+b(2,3)

T((a-b,2a+b))=(-a,a)+(2b,3b)

T((a-b,2a+b))=(-a+2b,a+3b)

This means we should be able to solve the system below to find a and b for T(3,3):

a-b=3 and 2a+b=3

Add equations to eliminate b and solve for a:

3a=6

Divide 3 on both sides:

a=2

If a-b=3 and a=2, then b=-1.

Plug in a=2, b=-1:

T((a-b,2a+b))=(-a+2b,a+3b)

T((2--1,2×2+-1)=(-2+2×-1,2+3×-1)

T(3,3)=(-4,-1).

4 0

2 years ago

A hose fills an empty fish tank with 24 gallons of water in 8 minutes. At that same rate, how many minutes will it take the hose

kolezko [41]

Answer:

$\frac{8}{24} = \frac{x}{60}$

24x = 8*60

24x = 480

x = 20

Step-by-step explanation:

3 0

2 years ago

Is (x+1) a factor off (x)=x3+x2−4x−4? <br><br> A) Yes<br> B) No

satela [25.4K]

Remainder theorem again...

$p(x)=x^3+x^2-4x-4$

$p(-1)=(-1)^3+(-1)^2-4(-1)-4=0$

So Yes, $x+1$ is a factor.

4 0

3 years ago

Read 2 more answers

Part A: Consider the equation x + 7 = 16. Which number from the set {5, 7, 9, 11} makes the equation true?

wel

Part A: Substitute/plug in each number into the equation to see which number will make the equation true.

x + 7 = 16 Plug in 5 into "x"

5 + 7 = 16

12 = 16 5 doesn't make the equation true because it equals 12 not 16

x + 7 = 16 Plug in 7 into "x"

7 + 7 = 16

14 = 16 7 doesn't make the equation true because it equals 14 not 16

x + 7 = 16 Plug in 9 into "x"

9 + 7 = 16

16 = 16 9 makes the equation true because it equals 16

Part B: Plug in 9 into "x" in the inequality to see if it still makes it true.

x + 7 < 16 [x plus 7 is less than 16]

9 + 7 < 16

16 < 16 [16 is less than 16] The same number would not make the inequality true because 16 can't be less than itself.

To figure out which numbers satisfy the inequality, plug it into the inequality:

x + 7 < 16 Plug in 5 into "x"

5 + 7 < 16

12 < 16 5 does satisfy the inequality because 12 is less than 16

x + 7 < 16 Plug in 7 into "x"

14 < 16 7 does satisfy the inequality because 14 is less than 16

x + 7 < 16 Plug in 11 into "x"

11 + 7 < 16

18 < 16 11 doesn't satisfy the inequality because 18 isn't less than 16

3 0

2 years ago

ANWSER THE TWO BOTTEM

svp [43]

a) 2/5(n)=6 n=15

b) 4/7(x)=16/3 x=28/3 x=9.33333 x=9 1/3

any option for b works

i hope this is right and helps

3 0

3 years ago