What is the answer ?

You have a 40% coupon, what will the price be of shoes that cost 45

Bond [772]

Answer:

20.25

Step-by-step explanation:

45x.40=20.25

4 0

3 years ago

Someone please help me on this math problem!

Galina-37 [17]

Look at the picture.

Therefore we have the equation:

10y - 29 = 7y + 19 add 29 to both sides

10y = 7y + 48 subtract 7y from both sides

3y = 48 divide both sides by 3

y = 16

3x + 7 = 5x - 21 subtract 7 from both sides

3x = 5x = -28 subtract 5x from both sides

-2x = -28 divide both sides by (-2)

x = 14

3 0

3 years ago

Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)

ELEN [110]

Question:

Find the point (,) on the curve $y = \sqrt x$ that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

Step-by-step explanation:

$y = \sqrt x$ can be represented as: $(x,y)$

Substitute $\sqrt x$ for $y$

$(x,y) = (x,\sqrt x)$

So, next:

Calculate the distance between $(x,\sqrt x)$ and $(3,0)$

Distance is calculated as:

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

So:

$d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}$

$d = \sqrt{(x-3)^2 + (\sqrt x)^2}$

Evaluate all exponents

$d = \sqrt{x^2 - 6x +9 + x}$

Rewrite as:

$d = \sqrt{x^2 + x- 6x +9 }$

$d = \sqrt{x^2 - 5x +9 }$

Differentiate using chain rule:

Let

$u = x^2 - 5x +9$

$\frac{du}{dx} = 2x - 5$

So:

$d = \sqrt u$

$d = u^\frac{1}{2}$

$\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}$

Chain Rule:

$d' = \frac{du}{dx} * \frac{dd}{du}$

$d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}$

$d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}$

$d' = \frac{2x - 5}{2\sqrt u}$

Substitute: $u = x^2 - 5x +9$

$d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}$

Next, is to minimize (by equating d' to 0)

$\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0$

Cross Multiply

$2x - 5 = 0$

Solve for x

$2x =5$

$x = \frac{5}{2}$

Substitute $x = \frac{5}{2}$ in $y = \sqrt x$

$y = \sqrt{\frac{5}{2}}$

Split

$y = \frac{\sqrt 5}{\sqrt 2}$

Rationalize

$y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$y = \frac{\sqrt {10}}{\sqrt 4}$

$y = \frac{\sqrt {10}}{2}$

Hence:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

3 0

3 years ago

Is the point (5,-1) a solution of y=2x-11

Nataly [62]

if the given point satisfies this equation then it would be its solution

(-1)=2(5)-11

-1=10-1

-1=-1

lHS=RHS

Hence (/,-1) is the solution of y=2x-11

3 0

3 years ago

Determine an equation of a Quadratic function

Pepsi [2]

Answer:

y = -4x² + 32x - 48

Step-by-step explanation:

The standard form of a quadratic equation is

y = ax² + bx + c

We must find the equation that passes through the points:

(2, 0), (6,0), and (3, 12)

We can substitute these values and get three equations in three unknowns.

0 = a(2²) + b(2) + c

0 = a(6²) + b(6) + c

12 = a(3²) + b(3) + c

We can simplify these to get the system of equations:

(1) 0 = 4a + 2b + c

(2) 0 = 36a + 6b + c

(3) 12 = 9a + 3b + c

Eliminate c from equations (1) and (2). Subtract (1) from (2).

(4) 0 = 32a + 4b

Eliminate c from equations (2) and (3). Subtract (3) from (2).

(5) -12 = 27a - 3b

Simplify equations (4) and (5).

(6) 0 = 8a + b

(7) -4 = 9a - b

Eliminate b by adding equations (6) and (7).

(8) a = -4

Substitute (4) into (6).

0 = -32 + b

(9) b = 32

Substitute a and b into (1)

0 = 4(-4) + 2(32) + c

0 = -16 + 64 + c

0 = 48 + c

c = -48

The coefficients are

a= -4, b = 32, c = -48

The quadratic equation is

y = -4x² + 32x - 48

The diagram below shows the graph of your quadratic equation and the three points through which it passes.

4 0

3 years ago