The slope of the line below is -3 which of the following is the point-slope form of the line? (2, -2)

A foam toy is 2 inches wide. It doubles in size for every minute it is in water. Write an expression for the width of the toy af

Solnce55 [7]

it would be 2(2^5), which is two times two to the fifth power. you take the original size and double it for every minute, which is like squaring it, but to the power of five, because it doubles once every minute for five minutes. i hope this makes sense!:)

7 0

3 years ago

Use a benchmark fraction to compare 7 10 ths and 5 12 ths. Explain how you found the answer

elixir [45]

<span>Benchmark fractions are created when we make two different fractions have the same numerator or denominator. In thisi case, we will produce the same denominator. The LCM of 10 and 12 is 60. So the fractions become 42/60 and 25/60. Since the fraction with the larger numerator has a larger value when the denominators are the same, 7/10 is larger than 5/12.</span>

5 0

2 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

Math help please right answer

kvasek [131]

Answer:

135°

Step-by-step explanation:

The sum of interior angles in this rectangle is equal to 720

Two of the angles are right (has 90°)

so 4x + 180 = 720 subtract 180 from both sides

4x = 540 divide both sides by 4

x = 135°

6 0

3 years ago

Holly earns $30 for babysitting 5 hours. She earns $28 when she does chores for 4 hours. Which compares the unit

zhenek [66]

Answer:

The unit rate for doing chores is $1 per hour more than the unit rate for babysitting

Step-by-step explanation:

30 / 5 = 6

28 / 4 = 7 the person above me was right

8 0

2 years ago

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