MATHEMATICS HIGH SCHOOL

What is the slope between the points (7,4) and (-5, -6)?a.) 5/6
b.) -5/6
c.)6/5

Answers

Answer 1

Answer:

Answer:

b.) -5/6

Step-by-step explanation:

m = -10/-12 = -5/-6

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A certain microscope is able to magnify an object up to 100,000 times its original size. In scientific notation, 100,000 is _____.

Answers

Answer: In scientific notation, 100,000 is $1.0*10^5$

Step-by-step explanation:

We know that the scientific notation is a technique to describe a very large or a very small number in the product of a decimal form of number [generally between 1 and 10] and powers of ten.

The given number = 100,000

Here the number of zeroes = 5

Then, in scientific notation, 100,000 = $1.0*10^5$

shift 5 decimal places to the left, so the exponent for base 10 is 5. Therefore, the number in scientific notation is:
1.0 x 105

The cost C, in dollars, of building m sewing machines at Sienna’s Sewing Machines is given by the equation: C(m) = 20m^2 - 830m + 15,000
(a) Find the cost of building 75 sewing machines.
(b) How many sewing machines should the company manufacture
to minimize the cost C?

Answers

OK. So the cost to manufacture any number 'm' machines is

   C(m) = 20m^2 - 830m + 15,000 .

Whatever number of machines you're interested in, you write
that number in place of 'm', and this equation tells you the cost
for that many.

Examples:

-- The cost to manufacture zero sewing machines ... what the
company had to invest in equipment and building space before
they could even start manufacturing anything:

C(m) = 20m^2 - 830m + 15,000

C(0) = 20(0)² - 830(0) + 15,000 = 15,000 .

-- The cost to manufacture one sewing machine ... buy the
building, set up the manufacturing equipment, and turn out
the first one:

C(m) = 20m^2 - 830m + 15,000

C(1) = 20(1)² - 830(1) + 15,000 = 14,190 .

Now, part-a) wants to know the cost to build 75 sewing machines.
If you've been paying attention so far, you know you have to take
the same equation, and write '75' in place of 'm'.

   C(m) = 20m^2 - 830m + 15,000

   C(75) = 20(75)² - 830(75) + 15,000

   = 20(5,625) - 830(75) + 15,000

   = 112,500 - 62,250 + 15,000 = 65,250 .
===================

Now you need to find the number of sewing machines
that can be built for the lowest total cost.

I'm sure you noticed that the equation for the cost C(m) is a
quadratic equation. So if you drew it on a graph, it would be
a parabola. It would have a minimum value at some 'm', and
for greater 'm', it would start going up again.

(Why should your cost start increasing past some number of
sewing machines ? Well, maybe the manufacturing equipment
is starting to wear out, and needs repair more often. All of that
is actually built into the equation for C(m) . )

Now, I'm not sure what method you've learned for finding the
minimum value of a parabola (quadratic equation). Here are
the two ways I know:

Way #1). If you've had some pre-calculus, then you'll take the
derivative of the equation, set the derivative equal to zero, and
that leads you to the minimum:

The equation:    C(m) = 20m^2 - 830m + 15,000

Its first derivative:       C'(m) = 40m - 830

'C'; is minimum when C'=0 : 40m - 830 = 0

Add 830 to each side: 40m = 830

Divide each side by 40 : m = 20.75

The number of sewing machines manufactured for the
minimum total cost is 20 or 21 .

Way #2). Really the same as Way-#1 but it's not called 'derivative'.

I looked online for rules of parabolas, and found the one that
you may have learned to use:

   For the quadratic expression Ax² + Bx + C ,
   the axis (midline) of the parabola is at
   x = - B / 2A .

That's exactly what we need.
Our equation is C(m) = 20m^2 - 830m + 15,000

so the axis of the parabola is at m = - (-830)/2(20)

   = 830/40 = 20.75 .

Same as Way-1 .

so basically function of m (f(m) or in this case C(m)) means the price
so just input the value you put for m for all the other m's in the problem
ex. if you had f(x)=3x and you wanted to find f(4) then you replace and do f(3)=3(4)=12 so f(3)=12 and so on

A. cost of 75 sewing machines
75 is the number you replace m with
C(75)=20(75)^2-830(75)+15,000
simplify
20(5625)-62250+15000
112500-47250
65250
the cost for 75 sewing machines is $65,250

B. we notice that in the equation, that the only negative is -830m
so we want anumber that will be big enough to make -830m destroy as much of the other posities a possible

-830m+20m^2+15000
try to get a number that when multiplied by 830, is almost the same amount as or slightly smaller than 20m2+15000 so we do this
830m<20m^2+15000
subtract 830m from both sides
0<20m^2-830m+15000
factor using the quadratic equation which is
(-b+ the square root of (b^2-4ac))/(2a) or (-b- the square root of (b^2-4ac))/(2a)
in 0=ax^2+bx+c so subsitute 20 for a and -830 for b and 15000 for c
you will get a non-real result I give up on this meathod since it gives some non real numbers so just guess

after guessing and subsituting, I found that the optimal number was 21 sewing machines at a cost of 6420

Can someone please help I really need help

Answers

Answer:

see below

Step-by-step explanation:

Each point and line moves to half its previous distance from the center of dilation, the origin. So, the point (-10, -10) moves to (1/2)(-10, -10) = (-5, -5). The dilation factor applies in the same way to other coordinates.

I find it easy enough just to spot the points on the graph and draw the lines between them.

Find the slope between the two points (-5,5) and (3,-5)

Answers

the formula is y2 minus y1 over x2 minus x1 or rise (y) over run (x). So you would do (-5) - (5) over (3) - (-5). that would equal -10 over 8, or -5/4 when you simplify. your slope would be -5/4

What is the answer for 4⁴÷4³=

Answers

Answer:

Step-by-step explanation:

4^4 = 256

4^3 = 64

256/64

Which strategie would eliminate a variable in the system of equations? −x+6y=8 7x−y=−2

Answers

Answer:

substitution (or addition)

Step-by-step explanation:

A simple strategy for this system is to use substitution. The first equation is easily solved for x, so you could substitute that into the second equation:

x = 6y -8

7(6y -8) -y = -2 . . . . . x variable eliminated

The second equation is easily solved for y, so you could substitute that into the first equation.

y = 7x +2

-x +6(7x +2) = 8 . . . . . y-variable eliminated

The "addition" method is always a good way to eliminate a variable.

When the coefficient of a variable in one equation is a divisor of the coefficient of that variable in the other equation, a simple multiplication and addition will do.

To make the coefficient of x in the first equation the opposite of the coefficient of x in the second, multiply the first equation by 7. Adding that result to the second equation will eliminate x:

7(-x +6y) +(7x -y) = 7(8) +(-2)

42y -y = 56 -2 . . . . . . x-variable eliminated

Likewise, the second equation can be multiplied by 6 and added to the first to eliminate the y-variable:

(-x +6y) +6(7x -y) = (8) +6(-2)

-x +42x = -4 . . . . . . . . y-variable eliminated

It is often the case that using either substitution or "addition" requires about the same amount of work.

Here, the solutions are (x, y) = (-4/41, 54/41).

Final answer:

To eliminate a variable in the given system of equations, you can use the elimination method. By multiplying the equations by suitable numbers and adding them, you can cancel out one of the variables, simplifying the process to solve for the other variable.

Explanation:

You can eliminate a variable in the given system of equations: −x+6y=8 and 7x-y=−2 by using either the substitution method or the elimination method. For this scenario, the elimination method will work best.

Strategy:

To eliminate x, you should first multiply the first equation by 7 and the second by 1, resulting in the equations: -7x+42y=56 and 7x-y=-2
Adding these two equations together, the x terms (-7x and 7x) cancel out, giving us: 41y=54.
Finally, you divide both sides by 41 to solve for y. This process effectively eliminates the variable x from the equation, providing a solution for y.

This variable eliminationstrategy lets you solve one equation for one variable, simplifying the process of finding solutions for a system of equations.