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
My name is Ann [436]
3 years ago
11

Solve |p + 2| = 10Solve |p + 2| = 10 {-12} {-8, 8} {-12, 8}

Mathematics
1 answer:
valentinak56 [21]3 years ago
3 0

By definition, we have

|p+2| = \begin{cases} p+2 &\text{ if } p+2 \geq 0 \\-p-2 &\text{ if } p+2 < 0 \end{cases}

So, we have to solve two different equations, depending of the possible range for the variable. We have to remember about these ranges when we decide to accept or discard the solutions:

Suppose that p+2\geq 0 \iff p \geq -2

In this case, the absolute value doesn't do anything: the equation is

p+2 = 10 \iff p = 10-2 = 8

We are supposing p \geq -2, so we can accept this solution.

Now, suppose that p+2 < 0 \iff p < -2. Now the sign of the expression is flipped by the absolute value, and the equation becomes

-p-2 = 10 \iff -p = 12 \iff p = -12

Again, the solution is coherent with the assumption, so we can accept this value as well.

You might be interested in
Find the absolute maximum and minimum values of f(x,y)=xy−4x in the region bounded by the x-axis and the parabola y=16−x2.
skad [1K]

Answer:

The absolute maximum and minimum is 20\; \text{and} -20.

Step-by-step explanation:

We first check the critical points on the interior of the domain using the

first derivative test.

f_x=y-4=0

f_y=x=0

The only solution to this system of equations is the point (0, 4), which lies in the domain.

f_{xx}=0, \;f_{yy}=0\; \text{and}\; f_{xy}=-1

\Rightarrow f_{xx}f_{yy}-f_{xy}=o-1=-1

\therefore (0,4) is a saddle point.

Boundary points -  (4,0),  (-4,0), (0,16)

Along boundary  y=16-x^2

   f=x(16-x^2)-4x

=16x-x^3-4x

\Rightarrow f^'=16-3x^2-4=0

\Rightarrow 3x^2=12

\Rightarrow x=\pm2,\;\;y=14

Values of f(x) at these points.

\begin{array}{}(4,0)=-16\\(-4,0)=16\\(0,16)=0\\(2,14)=20\\(-2,14)=-20\end{array}

Therefore, the absolute maximum and minimum is 20\; \text{and} -20.

6 0
3 years ago
Angle 3 is a supplement of angle 4. If the m of angle 3 is 100 degrees, what is the m of angle 4?
Triss [41]

Answer: 80

Step-by-step explanation: Supplements mean they add up to 180. is m of 3 is 100, then m of 4 must be 80 to add up to 180. Hope this helps!

7 0
3 years ago
Can someone help me pls
Andrej [43]

Answer:

x=78

Step-by-step explanation:

q is 90 degrees since it is a right angle,

p=12

90 plus 12 =102

x=180-102

x=78

3 0
3 years ago
Read 2 more answers
Find the equation of a line that passes through points (1,8) and (4,4).​
daser333 [38]

Step-by-step explanation: Using the equation, y = mx + b, the slope-intercept form, plug in the values you have and solve for b. (m is the slope.) You have y = -8 and x = 4 and m = 1/2.

3 0
2 years ago
Construct x such that a/x= x/b
jenyasd209 [6]
\frac{a}{x} =  \frac{x}{b}

From there we can see that because x equals both to a and b, it must be that a = b.
8 0
3 years ago
Other questions:
  • What is the diameter of a sphere with a volume of 4397\text{ m}^3,4397 m
    7·2 answers
  • Find all the points having an x coordinate of 1 whose distance from the point (-2,-3) is 5
    15·1 answer
  • Explain how 2 different squares can be made using the number 9.
    8·1 answer
  • 5 hours 18 minutes equals
    11·1 answer
  • How much would I have to deposit now in order to have 150,000 in 18 years
    5·1 answer
  • What ratios are equivalent to 7:3|. 12:9, 14:6, 11:7, 4:2,| PLZ HELP
    14·2 answers
  • 4. What is the equation of the x-axis?<br> (1) x=0<br> (2) y=-mx+b<br> (3) y=mx+b<br> (4) y=0
    13·1 answer
  • The following triangle is and .
    8·1 answer
  • Eli buys milk and lemons at the store.
    5·1 answer
  • 3. If there are 104 ounces in 2 quarts, how many quarts are there in 260 ounces?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!