MATHEMATICS HIGH SCHOOL

I am about to fail this math class. I would like to verify that my answers are right. Please help.Find the distance from the given point to the vertical axis.
(7, −6)

Determine the value of k such that the points whose coordinates are given lie on the same line.
(k, 0), (0, −1), (10, −11)

Find the slope of the line containing the given points.
P1(5, −9), P2(1, 7)

Find the equation of the line that passes through the midpoint of the line segment between
P1(4, 1) and P2(−2, 3) and has slope of 3.
Let y be the dependent variable and let x be the independent variable.

Find the equation of the line that contains the given point and has the given slope.
P(0, 6), m = 1

Suppose a ball is being twirled at the end of a string and the center of rotation is the origin of a coordinate system. If the string breaks, the initial path of the ball is on a line that is perpendicular to the radius of the circle. Suppose the string breaks when the ball is at the point whose coordinates are P(3, 9). Find the equation of the line on which the initial path lies

During one month, a homeowner used 500 units of electricity and 100 units of gas for a total cost of $331. The next month, 400 units of electricity and 250 units of gas were used for a total cost of $326. Find the cost per unit of gas.

Answers

Answer 1

Answer:

Answer:

1) 7 2) (-1,0) 3) m=-4 4) y=3x-4 5) y=x+6 6)

g(x)=-1/3x+10 7) y= $0.36

Step-by-step explanation:

These questions are all about Cartesian Geometry.

1) The Distance from point (7,-6) to vertical axis (0,-6) is measured with a straight line, between point (7,-6) and nearer point (0,-6)

d=|7-0|=7

2) To determine the value of k, let's determine the function with the two known points: (0, −1), (10, −11).

$m=(y_(2)-y_(1))/(x_(2)-x_(1))\Rightarrow m=(-11+1)/(10-0)\Rightarrow m=-1\n-11=-1*(10)+b\therefore b=-1\Rightarrow f(x)=-x-1\nf(k)=-k-1\n0=-k-1\therefore k=-1$

So (k,0)=(-1,0)

3) To find the slope of the line, we must apply that formula used above.

$m=(y_(2)-y_(1))/(x_(2)-x_(1))\Rightarrow m=(7+9)/(1-5)\Rightarrow m=(16)/(4)=-4$

4) To find the equation of the line which the midpoint (2,2) since Midpoint is given by

$Midpoint=((x_(1)+x_(2))/(2)+(y_(1)+y_(2))/(2))\n$

And the slope is 3, then m=3. Notice the formula is the same to calculate the slope, but we will only pick one point. Since (2,2) ∈ to the function let's use this point, as initial value (x0,y,0)

$m(x-x_(0))=y-y_(0)\n3(x-2)=y-2\n3x-6=y-2\Rightarrow 3x-y=6-2\Rightarrow -y=4-3x\Rightarrow y=3x-4$

5) Similarly to the previous one:

$m(x-x_(0))=y-y_(0)\n(x-0)=y-6\nx=y-6\Rightarrow -y=-x-6\Rightarrow y=x+6$

6) A ball being twirled. The center of the rotation is the origin of Coordinate System (0,0) when the string breaks at point (3,9)

If the line was straight from the origin to point (3,9) $m=(9-0)/(3-0)\Rightarrow m=3\therefore 9=3(3)+b\Rightarrow b=0\Rightarrow f(x)=3x$

But the point (3,9) ∈ to a tangent line to the circumference described by the twirling.

Since it is perpendicular instead of m=3 it is -1/m i.e. -1/3, also the circumference intercepts the y-axis in ≈10

g(x)=-1/3x+10

7) In this case, we must also find the function.

x=units of electricity, y=units of gas |

500x+100y=331

400x+250y=326

The cost per unit of gas is y. Finding out the unit value for y

$100y=331-500x\rightarrow y=(331-500x)/(100)\n500x=331-100y\nx=(331-100y)/(500)\n400((331-100y)/(500))+250y=326\n52.96-80y+250y=326\Rightarrow y=(9)/(25) \,and \,x=(59)/(100)$

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You can buy 2 songs on I-Tunes for $ 2.58, or 3 songs for $ 3.87. Write an equation to show the relationship between the number of songs, s, and the total cost, c.

Answers

Answer:

for the first pack, 1 Itune song would be 1.29 and for the other pack, for one Itune song would be 1.29 also, the relationship between these problem is that they are the same price for 1 song. The total cost for 1 is $1.29 hope this helps, have a great day! ツ

Step-by-step explanation:

This is all about matrices, I don't really get them. Any help is great.

Answers

See Explanation

Step-by-step explanation:

$\begin{bmatrix} - 3 & 5 & 6\n-3 & 0 & - 3\end{bmatrix} -\begin{bmatrix} 6 & - 1& 1\n0& - 4& - 5\end{bmatrix} \n\n=\begin{bmatrix} - 3-6 & 5-(-1) & 6-1\n-3-0 & 0-(-4) & - 3-(-5)\end{bmatrix} \n\n=\begin{bmatrix} - 3-6 & 5+1 & 6-1\n-3-0 & 0+4 & - 3+5\end{bmatrix} \n\n=\begin{bmatrix} - 9 & 6 & 5\n-3 & 4 & 2\end{bmatrix} \n\n$

$\begin{bmatrix} 4 & - 6 \n-3 & - 6\n2 & 6 \end{bmatrix} + \begin{bmatrix} 5 & 3 \n-5 & 5\n 4 & - 5\end{bmatrix} \n\n= \begin{bmatrix} 4 +5& - 6+3 \n-3+(-5) & - 6+5\n2+4 & 6+(-5) \end{bmatrix} \n\n= \begin{bmatrix} 4 +5& - 6+3 \n-3-5 & - 6+5\n2+4 & 6-5 \end{bmatrix} \n\n= \begin{bmatrix} 9& - 3 \n-8 & - 1\n6 & 1\end{bmatrix} \n\n$

Graphing recorded data from a chart or table would be helpful for interpreting trends or patterns. Please select the best answer from the choices provideda. True
b. False

Answers

The best answer to the question that is being presented above would be true. It is deemed true that graphing recorded data from a chart or table would be helpful for interpreting trends or patterns. This is because the graph shows the distribution of data and has an overall picture on how the data moves.

True;
The data points the changes occurring at different points on the graph.

Evaluate e^4 to one decimal place.

Answers

Answer:

The $e^(4)$ to one decimal is 54.6

Step-by-step explanation:

we need to calculate $e^(4)$ to one decimal.

Since, $e^(x)=1+(1)/(x!)+(x^(2))/(2!)+(x^(3))/(3!)+......$ ....(1)

To calculate $e^(4)$ , put x=4 in equation (1)

$e^(4)=1+(1)/(4!)+(4^(2))/(2!)+(4^(3))/(3!)+......$

$e^(4)=1+(1)/(24)+(16)/(2)+(64)/(6)+......$

simplify the above expression

$e^(4)=1+(1)/(24)+(16)/(2)+(64)/(6)+(256)/(24)+(1024)/(120)......$

calculate with the scientific calulator

< 0.1 =54.6

Hence, $e^(4)$ to one decimal is 54.6

The answer is going to be the general form for e^x = 1 + x/(1!) + + x^2/(2!) + x^3/(3!) +.....,. till infinity so : e^4 = 1 + 4/1 + 16/ 2 + 64/6 + 256/24 + 1024/ 120 + 4096/720 + 16384/5040 +...till the fraction is<0.1 = 54.6

I hope this helps!

Which of the following diagrams includes a centroid? In order: A, B, C, D

Answers

Answer:

Figure A

Step-by-step explanation:

First let's see what a centroid of a triangle is.

In a triangle there are three vertices. We draw a line segment from each vertices to the median of the opposite sides. The median of each vertices intersect in a point inside the triangle. That point is called the centroid of the triangle.

That is also called the center of gravity of the triangle.

By looking at the given figures,

The figure A is the correct answer.

There each line segments drawn from the vertices intersect the opposite side at the median. The point E is the centroid of the triangle.

Therefore, the answer is figure A.

The answer is A.......

Can someone pls help?

Answers

Answer: x = 4

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Explanation:

Use the remote interior angle theorem. This says a pair of interior angles always add to the measure of the exterior angle that is not adjacent to any of the interior angles, so basically what your diagram is showing.

(interior angle C) + (interior angle D) = exterior angle

(46) + (-1+8x) = 18x+5

8x+45 = 18x+5

8x-18x = 5-45

-10x = -40

x = -40/(-10)

x = 4

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