All categories

2 years ago

Determine the solution to the system of equations graphed below and explain

Mathematics

1 answer:

lawyer [7]2 years ago

7 0

If x - 4 ≥ 0, then |x - 4| = x - 4, so

G(x) = F(x) ⇒ 3x + 2 = (x - 4) + 2

⇒ 3x + 2 = x - 2

⇒ 2x = -4

⇒ x = -2

Otherwise, if x - 4 < 0, then |x - 4| = -(x - 4), so

G(x) = F(x) ⇒ 3x + 2 = -(x - 4) + 2

⇒ 3x + 2 = -x + 6

⇒ 4x = 4

⇒ x = 1

However,

• when x = -2, we have

G(-2) = 3(-2) + 2 = -4

F(-2) = |-2 - 4| + 2 = 8

• when x = 1, we have

G(1) = 3(1) + 2 = 5

F(1) = |1 - 4| + 2 = 5

so only x = 1 is a solution to G(x) = F(x).

You might be interested in

Patrick made a cake for his mother's birthday. He started making the

zlopas [31]

Answer: 11:15 AM

Step-by-step explanation:

9:00 plus an hour and 15 minutes (75 minutes) makes it 10:15. Then bake for an hour (60 minutes), makes it 11:15

4 0

3 years ago

Tina is saving to buy a notebook computer. She has two options. The first option is to put $500 away initially and save $30 ever

Jlenok [28]

First option:
y=money saved
x=number of months

y=30x+500

Second option:

y=50x+200

We have this system of equations:

y=30x+500
y=50x+200

We can solve this system of equations by equalization method
30x+500=50x+200
30x-50x=200-500
-20x=-300
x=-300/-20
x=15

so;
y=30x+500
y=30(15)+500
y=450+500
y=950

Answer; after 15 months, she would save the same amount using either option, the amount saved in either option will be $950.

3 0

3 years ago

Suppose you want to represent a triangle with sides 12 feet, 16 feet, and 18 feet on a drawing where 1 inch = 2 feet. How long s

slega [8]

Answer:

The correct answer is C. 6, 8 and 9 inches.

Step-by-step explanation:

1. Let's review all the information provided for answering the questions properly:

Length of the sides of the triangle = 12 feet, 16 feet and 18 feet.

Scale used : 1 inch = 2 feet.

2. How long should the sides of the triangle be in inches?

For calculating the length of the sides of the triangle in the draw, we use the scale this way:

1st Side = 12 feet

12 feet/2 = 6 inches

2nd Side = 16 feet

16 feet/2 = 8 inches

3rd Side = 18 feet

18 feet/2 = 9 inches

The correct answer is C. 6, 8 and 9

8 0

3 years ago

A group of 100 people is divided into 2 teams with 45 people in team A and 55 people in team B.

Zepler [3.9K]

Team A) 45 people
Team B) 55 people

A)There are two ways to solve this problem, finding the number of combinations possible for Team B, or the number of combinations possible for Team A.
Team A
It's a given that 20 mathematicians are on team A, which leavs the other 25 people for team A to be chosen from a pool of 80 (100- 20 mathletes)
80-C-25 = 80! / (25!/(80-25)!) =363,413,731,121,503,794,368
or 3.63 x 10^20
Solving using Team B
Same concept, but choosing 55 from a pool of 80 (mathletes excluded)
80-C-25 = 80! / (55!(80-55!) = 363,413,731,121,503,794,368
or 3.63 x 10^20

As you can, we get the same answer for both.

B)
If none of the mathematicians are on team A, then we exclude the 20 and choose 45:
80-C-45 = 80! / (45!(80-45)!) = 5,790,061,984,745,3606,481,440
or 5.79 x 10^22

Note that, if you solve from the perspective of Team B (80-C-35), you get the same answer

7 0

2 years ago

(1 point) The length of an insect (L, in mm) is a function of the temperature during development (T , measured in ∘C according t

lawyer [7]

Answer:

$M(T)=1.1(7(8+T^{10})^{3})$ and $M(T)=1.1(7(8+22^{10})^{3})=1.44\time10^{41}$