1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
irina1246 [14]
2 years ago
8

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
No body helped me :'(
ziro4ka [17]
What was your question that was never answered?
6 0
3 years ago
Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x&gt;1
Lera25 [3.4K]
Assuming the function is

f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}

For f(x) to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)
\iff\displaystyle\lim_{x\to1}2x=\lim_{x\to1}(bx^2+cx)
\iff2=b+c

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

f'(x)=\begin{cases}2&\text{for }x1\end{cases}

\displaystyle\lim_{x\to1^-}2=\lim_{x\to1^+}(2bx+c)
\iff2=2b+c

Now we solve for b and c:

\begin{cases}b+c=2\\2b+c=2\end{cases}\implies b=0,c=2
5 0
3 years ago
Factorise the following 27 x minus 9 y​
dangina [55]

Answer:

27x-9y

3(9x-3y)

Step-by-step explanation:

please mark me as brainlest

4 0
2 years ago
Write a quadratic equation for a parabola with roots at (-2, 0) &amp; (4,0) and a y-intercept at ( 0, -16) Write your answer in
meriva

9514 1404 393

Answer:

  y = 2(x +2)(x -4)

Step-by-step explanation:

The y-intercept will be a constant times the product of the roots. Here, the product of the roots is (-2)(4) = -8, so the constant of interest is -16/-8 = 2. That constant is the coefficient of the leading term of the quadratic, so is a multiplier of the factored form.

  y = 2(x +2)(x -4)

__

For root p, (x-p) is a factor in the factored form.

8 0
3 years ago
How do you determine if polygons are similar?
Vikentia [17]

Answer:

  a) corresponding angles of similar polygons are congruent

  b) corresponding sides of similar polygons are proportional

  c) a triangle is a polygon

Step-by-step explanation:

By <em>definition</em>, similar polygons have congruent corresponding angles and proportional corresponding sides.

A triangle is a polygon, so two triangles will be similar if they have congruent corresponding angles and proportional corresponding sides.

___

For an n-sided polygon, one only needs to show the conditions are met for n-1 angles and sides. Those will determine the measures of the final angle/side.

8 0
3 years ago
Other questions:
  • Explain how you can determine if 1/3 and 4/12 are equivalent fractions
    12·2 answers
  • Can someone please help me!!! thanks
    10·2 answers
  • What is m CGD = 4x + 2, m DGE = 3x - 5, m EGF = 2x + 10
    9·2 answers
  • What is 1/2 to the fifth power in fraction form?
    5·2 answers
  • It took a car 6 hours to cover the distance between points A and B with the speed of 50 mph. How long will it take a bus to cove
    5·1 answer
  • Joe solved this linear system correctly.
    10·1 answer
  • Square Root Functions
    7·1 answer
  • Choose the more precise measurement.<br><br> 37 T <br><br> 56 lb
    12·1 answer
  • Pls Help! the question is down below
    11·1 answer
  • Jane Rose’s semimonthly salary is $750. Her yearly salary is A.$9000 B. $12,500 C. $18,000 D. $19,500 E. $21,000
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!