Ask question

Ask question

All categories

Veseljchak [2.6K]

3 years ago

11

How many answers are in each of these three questions: 1. x squared minus three x plus four equals zero 2. Two x squared plus fo

ur x minus five equals zero 3. X squared plus eight x plus sixteen equals zero

1 answer:

vaieri [72.5K]3 years ago

6 0

1. No solutions ( no answers) 2 . 2 answers 3. 1 answer

You might be interested in

Chris runs 6 miles in 50 minutes. At the same rate, how many miles would he run in 35 minutes?

Nataly_w [17]

You could either find how far Chris can run in 60 minutes, or write an equation of ratios:

x 35 min
--------- = --------------
6 mi 50 min

Solving for x: 50x = 210; x = 4.2 miles (answer)

4 0

3 years ago

Can you answer these please! I really need help! And I'm so not even joking only 16 17 18 and 19

frozen [14]

16.) 38.25= 4.25h
divide by 4.25 on both sides
h=9
17.)214= 1/3x
divide by 1/3 on both sides
x= 642
18.)70= 2x
divide by 2 on both sides
x=35
19.)18.69= 5.25+1.68x
subtract 5.25 on both sides
13.44=1.68x
divide by 1.68 on both sides
x=8

4 0

3 years ago

look at pic 10 pts will mark brainilest hhhionnia

-BARSIC- [3]

30 because 18 and the plain goes into 12 which is 30
I think

7 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

Please help me with this math problem

goldfiish [28.3K]

If you look at the graph you can tell the graph is increasing before x = -2.

From x = -2 to x = 0, it's decreasing.

Then it's increasing again from x = 0 to x = 2, then decreasing after x = 2

So answer is the last one
It is increasing before x = -2 and from x = 0 to x = 2

3 0

3 years ago