Find the solution to the system of equations. You can use the interactive graph below to find the solution. {y=-x+2 {y=3x-4

show that the sum of the x- and y- intercepts of any tangent line to the curve sqrt(x) sqrt(y) = sqrt(c) is equal to c.

expeople1 [14]

The answer is √x + √y = √c 
=> 1/(2√x) + 1/(2√y) dy/dx = 0 
=> dy/dx = - √y/√x 

Let (x', y') be any point on the curve 
=> equation of the tangent at that point is 
y - y' = - (√y'/√x') (x - x') 

x-intercept of this tangent is obtained by plugging y = 0 
=> 0 - y' = - (√y'/√x') (x - x') 
=> x = √(x'y') + x' 

y-intercept of the tangent is obtained by plugging x = 0 
=> y - y' = - (√y'/√x') (0 - x') 
=> y = y' + √(x'y') 

Sum of the x and y intercepts 
= √(x'y') + x' + y' + √(x'y') 
= (√x' + √y')^2 
= (√c)^2 (because (x', y') is on the curve => √x' + √y' = √c) 
= c. hope this helps :D

5 0

3 years ago

Mason opens a savings account by making a $165.85 deposit. Every week, he deposits another $20.50 in the account. The following

alina1380 [7]

Answer:

$370.85

Step-by-step explanation:

sub the 10 for the x

370.85

6 0

3 years ago

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What two numbers multiply and get 100 and add and get -29??

butalik [34]

X, y - the numbers

The numbers multiply to 100.
$xy=100$

The numbers add up to -29.
$x+y=-29 \\
y=-x-29$

Substitute -x-29 for y in the first equation:
$x(-x-29)=100 \\
-x^2-29x=100 \\
-x^2-29x-100=0 \\
-x^2-4x-25x-100=0 \\
-x(x+4)-25(x+4)=0 \\
(-x-25)(x+4)=0 \\
-x-25=0 \ \lor \ x+4=0 \\
x=-25 \ \lor \ x=-4 \\ \\
y=-x-29 \\
y=-(-25)-29 \ \lor \ y=-(-4)-29 \\
y=25-29 \ \lor \ y=4-29 \\
y=-4 \ \lor \ y=-25 \\ \\
(x,y)=(-25,-4) \hbox{ or } (x,y)=(-4,-25)$

The numbers are -4 and -25.

6 0

3 years ago

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A recipe requires 3.5 teaspoons of sugar to make a tart. which equation shows the number of teaspoons of sugar, y, needed to mak

tresset_1 [31]

x = 3.5y equation shows the number of teaspoons of sugar, y, needed to make x tarts.

What is the linear equation in two variable?

Any equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called linear equation in two variable.

According to the given question

A recipe require 3.5 teaspoons of sugar to make a tart.

y represents the number of teaspoons of sugar.

x represents the number of tarts.

Now, for x tart 3.5y teaspoons of sugar required.

⇒ x = 3.5y

Hence, the linear equation in two variable that shows the number of teaspoons of sugar y, needed to make x number or tarts is x = 3.5y.

Learn more about linear equation in two variable.

brainly.com/question/24085666

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8 0

2 years ago

A square has a perimeter of 48 m. What is the length of each side?

zysi [14]

Answer: 12cm is the answer

Step-by-step explanation:

You just divide 48 divided by 4 because I square has 4 equal sides.

4 0

3 years ago

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