2/5of a number is 80. What is 3/4of the same number?

A circle has a diameter with endpoints at (6, 5) and (8, 5). Write the equation for the circle.

mario62 [17]

Answer:

$(x-7)^2+(y-5)^2=1$

Step-by-step explanation:

The two things that are required to formulate the equation of the circle is the center coordinate and the radius of the circle!

Center of the circle:

The center of the circle always lies at the midpoint of the endpoints of its diameter: Let's call the endpoints A(6,5) and B(8,5).

Using the midpoint formula we'll get:

$(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$(x_m, y_m) = \left(\dfrac{6+8}{2},\dfrac{5+5}{2}\right)$

$(x_m, y_m) = (7,5)$

This is the center coordinate of our circle.

Radius:

The radius of the circle is the distance from the center of the circle to any of the endpoints of the diameter (A or B)

We can use the distance formula:

$r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$r = \sqrt{(x_1-x_m)^2+(y_1-y_m)^2}$

$r = \sqrt{(6-7)^2+(5-5)^2}$

$r = \sqrt{1^2}$

$r = 1$

Equation of the circle:

The equation is written as:

$(x-a)^2+(y-b)^2=r^2$

here, (a,b) are the center points of the circle

in our case this is $(a,b)=(x_m,y_m)=(7,5)$

and r = 1

$(x-7)^2+(y-5)^2=1^2$

$(x-7)^2+(y-5)^2=1$

This is the equation of the circle!

3 0

3 years ago

4.89 is this a rational or a irrational

worty [1.4K]

Answer:

Rational because it isn't a repeating decimal

Step-by-step explanation:

7 0

3 years ago

Need help ASAP! Giving Brainliest!

allsm [11]

ok thats cool ig what do you need help with

4 0

3 years ago

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A manufacturing company produces 3 different products A, B, and C. Three types of components, i.e., X, Y, and Z, are used in the

Murljashka [212]

Answer:

Step-by-step explanation:

Using the Excel Formula:

Decision Variable Constraint Constraint

A 65 65 100

B 80 80 80

C 90 90 90

14100 300 300

= (150 *B3)+(80*B4) +(65*B5)-(100-B3+80-B4+90-B5)*90

Now, we have:

Suppose A, B, C represent the number of units for production A, B, C which is being manufactured

A B C Unit price

Need of X 2 1 1 $20

Need of Y 2 3 2 $30

Need of Z 2 2 3 $25

Price of

manufac - $200 $240 $220

turing

Now, for manufacturing one unit of A, we require 2 units of X, 2 units of Y, 2 units of Z are required.

Thus, the cost or unit of manufacturing of A is:

$20 (2) + $30(2) + $25(2)

$(40 + 60 + 50)

= $150

Also, the market price of A = $200

So, profit = $200 - $150 = $50/ unit of A

Again;

For manufacturing one unit of B, we require 1 unit of X, 3 units of Y, and 2 units of Z are needed and they are purchased at $20, $30, and 425 each.

So, total cost of manufacturing a unit of B is:

= $20(1) + $30(3) + $25(2)

= $(20 + 90+50)

= $160

And the market price of B = $240

Thus, profit = $240- $160

profit = $80

For manufacturing one unit of C, we have to use 1 unit of X, 2 unit of Y, 3 units of Z are required:

SO, the total cost of manufacturing a unit of C is:

= $20 (1) + $30(2) + $25(3)

= $20 + $60 + $25

= $155

This, the profit = $220 - $155 = $65

However; In manufacturing A units of product A, B unit of product B & C units of product C.

Profit --> 50A + 80B + 65C

This should be provided there is no penalty for under supply of there is under supply penalty for A, B, C is $40

The current demand is:

100 - A

80 - B

90 - C respectively

So, the total penalty

${(100 - A) + (80 - B) +(90 - C) } + \$40$

This should be subtracted from profit.

So, we have to maximize the profit

$Z = 50A + 80B + 65C = {(100 -A) + (80 - B) + (90 - C)};$

Subject to constraints;

we have the total units of X purchased can only be less than or equal to 300 due to supplies capacity

Then;

$2A + B +C \le 300$ due to 2A, B, C units of X are used in manufacturing A, B, C units of products A, B, C respectively.

Next; demand for A, B, C will not exceed 100, 80, 90 units.

Hence;

$A \le 100$

$B \le 80$

$C \le 90$

and $A, B, C \ge 0$ because they are positive quantities

The objective is:

$\mathbf{Z = 50A + 80B + 65 C - (100 - A + 80 - B + 90 - C) * 40}$

A, B, C $\to$ Decision Varaibles;

Constraint are:

$A \le 100 \\ \\ B \le 100 \\ \\ C \le 90 \\ \\2A + B + C \le 300 \\ \\ A,B,C \ge 0$

6 0

3 years ago

Given f(x) = 10 -2xfind f(7). –4 3 7 56

strojnjashka [21]

Answer: $f(7)=-4$

Step-by-step explanation:

1. You have the following function given in the problem:

$f(x)=10-2x$

2. Then, to find $f(7)$ asked in the exercise, you only need to substitute $x=7$ (which is the input value) into the given function.

3. Therefore, keeping the above on mind, you obtain that $f(7)$ is:

$x=7$

$f(7)=10-2(7)$

$f(7)=10-14$

$f(7)=-4$

3 0

3 years ago

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