MATHEMATICS HIGH SCHOOL

Jane worked 32 hours in one week. If she worked the same number of hours each day for 4 days, how many hours a day did she work? A. 8
B. 6
C. 10
D. 4

Answers

Answer 1
Answer: 4x=32⇒ x=32/4⇒ x=8

the answer is A. 8
Answer 2
Answer: You need to divide, so 32/4=8, so your answer is A.8

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M(5, 7) is the midpoint of mc140-1.jpg. The coordinates of S are (6, 9). What are the coordinates of R? (4, 5) (7, 11) (5.5, 8) (10, 14)

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.
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Find the equation of the line that passes through the midpoint of the line segment between
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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.
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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) 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)

A point moves on the x-axis in such a way that its velocity at time t (t>0) is given by v=lnt/t. At which value of t does v attain its maximum? (A) 1
(B) e^(1/2)
(C) e
(D) e^(3/2)
(E) There is no maximum value for v.

Answers

(D) e^(3/2)

v = ln(t) / t 

max of v when dv/dt = 0 
dv/dt = (t/t - ln(t))/t² 
= [1 - ln(t)]/t² = 0 
ln(t) = 1 
t = e (option C) 

check this is a max and not a min 
d²v/dt² = [t²(-1/t) - 2t(1 - ln(t))]/t^4 
= [-1 - 2t + 2t ln(t)]/t^4 

= [-1 - 2e + 2e ln(e)]/e^4 
= [-1 - 2e + 2e]/e^4 
= -1/e^4 < 0 so it is a max 

The formula below is the general form of which of the following formulas?X= -b+-(√b^2 - 4ac)
/2a
A. Distance formula
B. Discriminant formula
C. Quadratic formula
D. Slope formula

Answers

C- quadratic formula

Translate the phrase into a math expression.15 divided by a number, then decreased by 2

A.
(15 ÷ n) + 2

B.
(15 ÷ n) – 2

C.
15 ÷ (n – 2)

D.
15 ÷ (n + 2)

Answers

B. (15/n) – 2

Because you have to divide the 15 and the number first then "decrease" it by 2

The mean radius of earth is 6,371.0 kilometers and the mean radius of earths moon is 1,737.5 kilometers. What is the approximate difference in the mean conferences, in kilometers, of earth and earths moon? Round your answer to the nearest tenth of a kilometer.

Answers

6,371.0- 1,737.5 = 4,633.5 kilometres.
the approximate difference is 4,633.5 kilometres

A concert hall has seven sections. Each section has 23 rules. Please roll has 14 seats. If the theater sells out pretty particular performance, how many people attended? If the average ticket sold for $20, how much was collected at the box office? Need to write an equation. Thanks

Answers

Answer:

The number of people that attended the performance = 2,254

Amount collected at box office = $45,080

Step-by-step explanation:

For the theater to sell out a performance, it means it was filled to the brim( completely filled)

We have 7 sections, with 23 rows each

The total number of rows will be 23 * 7 = 161 rows

Since each row has 14 seats, the total number of seats will be 161 * 14 = 2,254 seats

Secondly we want to know how much was collected at the box office given the average ticket price

The amount collected at the box office = Number of seats * average ticket price = 2,254 * 20 = $45,080
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