MATHEMATICS HIGH SCHOOL

|h-8|=|h+10| What is h

Answers

Answer 1
Answer: Your answer is h= -1
Answer 2
Answer:

Final answer:

The value of h that satisfies the equation |h-8|=|h+10| is -1.

Explanation:

To solve the equation |h - 8| = |h + 10|, we need to consider two cases based on the absolute values.

  • First, when h - 8 is positive, we can rewrite the equation as h - 8 = h + 10. Simplifying this equation, we find that -18 = 0, which is not true.
  • Second, when h - 8 is negative, we rewrite the equation as -(h - 8) = h + 10.
  • Simplifying this equation, we get -h + 8 = h + 10.
  • Combining like terms, we have 2h = -2.
  • Dividing both sides by 2, we find that h = -1.

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The system of equations below has exactly one (x, y) pair for its solution.4x+6y=244x+6y=242x+y=82x+y=8If we double each side of the second equation, 2x+y=82x+y=8, we have 4x+2y=164x+2y=16. Explain why the same pair that is the solution to the system is also a solution to this new equation.If needed, you can support your explanation with hanger diagrams (upload a picture), or by inventing a situation that the equations represent.If we add the two equations in the original system, we have 6x+7y=326x+7y=32. Explain why the same (x, y) pair is also a solution to this equation.Again, you can support your explanation with diagrams or a situation, if needed.
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Find the missing endpoint given one endpoint and midpoint2)
endpoint- ( -4,1) midpoint-(-1,3)

Answers

endpoint: \ ( x_(2),y_(2))= (-4,1) , \n midpoint : \(x,y)=(-1,3) \n\nMindpoint \ Formula : \n (x,y)=\left ( (x_(1)+x_(2) )/(2), \frac{y_ {1}+y_(2) }{2} \right )\n\n(-1,3)=\left ( (x_(1)-4 )/(2), \frac{y_ {1}+1 }{2} \right )

\begin{cases} (x_(1)-4 )/(2)= -1 \ \ /\cdot 2 \n \frac{y_ {1}+1 }{2} =3 \ \ / \cdot 2 \end{cases}\n\n\begin{cases} x_(1)-4 =-2 \n y_ {1}+1 =6\end{cases}\n \n\begin{cases} x_(1) =-2+4 \n y_ {1} =6-1 \end{cases}\n \n\begin{cases} x_(1) =2\n y_ {1} =5 \end{cases} \n \nAnswer : \ second \ endpoint : \ (x_(1),y_(1))=(2,5)

choose the equation below that represents the line that passes through the point (−2, −1) and has a slope of 5. (5 points) y − 1 = 5(x − 2) y 1 = 5(x 2) y 2 = 5(x 1) y − 2 = 5(x − 1)

Answers

Equation of a line;
y=mx+c
m=5
y=5x+c
Replacing for x and y using point (-2, -1)
-1=5(-2)+c
-1=-10+c
c=-1+10
c=9
y=5x+9

Sixteen is fourteen less than the product of a number and five. What is the number?

Answers

16=5x-14
+14 +14
30=5x
/5 /5
6=x
X=6
5*?=?-14=16
5*6=30
30-14=16

An order of 12 dozen rollerball pens and 5 dozen ballpoint pens cost $116. A later order 8 dozen rollerball pens and 12 dozen ballpoint pens cost $112. What was the cost of 1 dozen of pens?And how much does 1 dozen pencils cost?

Answers

r=cost per dozen rollerball pens
b=cost per dozen ballpoint pens
p=cost per dozen pencils
???

ignore pencils

12r+5b=116
8r+12b=112

eliminate
simplify last equation by dividing by 4
2r+3b=28

eliminate r's
multiply 2r+3b=28 by -6 and add to top equation

-12r-18b=-168
12r+5b=116 +
0r-13b=-52

-13b=-52
divide both sides by -13
b=4

plug back in
2r+3b=28
2r+3(4)=28
2r+12=28
minus 12
2r=16
divide by 2
r=8



ballpoint=pencils

1dozen pencils=$4
1dozen rollerbladepens=$8

Two systems of equations are shown below:System A:
6x+y=2
-x-y=-3
System B:
2x-3y=-10
-x-y=-3
Which of the following statements is correct about the two system equations?

A) The value of x for System B will be 4 less than the value of x for System A because the coefficient of x in the first equation of System B is 4 less than the coefficient of x in the first equation of System A.

B) They will have the same solution because the first equations of both the systems have the same graph.

C) They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 4 times the second equation of System A.

D) The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding -4 to the first equation of System A and the second equations are identical.

Answers

System A:
6x + y = 2
-x - y = -3

System B:
2x - 3y = -10
-x-y = -3

Solve:
System A:
6x + y = 2
y = 2 - 6x
-x - (2-6x) = -3
-x - 2 + 6x = -3
5x = -3 + 2
5x = -1
x = -1/5
y = 2 - 6(-1/5)
y = 2 + 6/5
y = 2 + 1.2
y = 3.2     System A: x = -1/5 or -0.2  ; y = 3 1/5 or 3.2

System B:
2x - 3y = -10
2x = -10 + 3y
x = -5 + 1.5y
-x - y = -3
-(-5 + 1.5y) -y = -3
5 - 1.5y - y = -3
-2.5y = -3 - 5
-2.5y = -8
y = 3.2
x = -5 + 1.5(3.2)
x = -5 + 4.8
x = -0.2   System B: x = -0.2 ; y = 3.2

B) They will have the same solution because the first equations of both the systems have the same graph.

Answer: I just took the test and got it wrong when I put B, the correct answer is C.

Step-by-step explanation:

There are 2,100 bacteria in a circular petri dish. The dish has a radius of 40 millimeters. What is the approximate population density? (Use 3.14 for π)

Answers

A petri dish is simply a circle; thus, we use the formula of the area of the circle which is πr^2. 
Given r = 40 mm
A = π(40)^2 = 5026.55 sq. mm

Population density = bacteria count / area
PD = 2,100 / 5026.55
PD = 0.417782 bacteria / mm sq.

Therefore, the answer is approximately 0.418 bacteria per square millimeter.
Determine the area of the circular petri dish through the equation, A = πr^2. Substituting the radius to the equation and solving for area gives, 5024 mm^2. The population density is obtained by dividing the population with the calculated area. Thus, the population density is approximately 0.418 bacteria per mm^2. 
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