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2 years ago

Can someone help me out with this?

Mathematics

1 answer:

dexar [7]2 years ago

4 0

Answer:

-7.5x -12.5, x < -1
7.5x +2.5, x ≥ -1

Step-by-step explanation:

The absolute value function changes slope at its vertex. Here, that vertex is translated to x = -1. To the left of that point, the function is equivalent to one that negates its argument:

|x| = -x . . . for x < 0

|x| = x . . . for x ≥ 0

y = -7.5(x +1) -5 = -7.5x -12.5

y = 7.5(x +1) -5 = 7.5x +2.5

This means we can write the piecewise function as ...

$y=\begin{cases}-7.5x-12.5,&\text{if }x$

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Find the distance between the two points in simplest radical form.<br> (-1,9) and (4, -3)

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Answer:

GIVEN BY POINTS :-

( -1, 9) , ( 4 , -3)

Here ,

$\bullet \: \: x _{1} = - 1 \\ \bullet \: \: x _{2} = 4 \\ \bullet \: \: y _{1} = 9 \\ \bullet \: \: y _{2} = - 3 \\$

Using Distance formula :

$= > \sf d = \sqrt{( {x _{2} - x _{1}) }^{2} + {( {y _{2} - y _{1}) }^{2} } } \\ \\ = > \sf d = \sqrt{ ({ 4 + 1)}^{2} + { ( - 3 - 9)}^{2} } \\ \\ = > \sf d = \sqrt{ {5}^{2} + {( - 12)}^{2} } \\ \\ = > \sf d = \sqrt{25 + 144} \\ \\ = > \sf d = \sqrt{169} \\ \\ = > \boxed{ \sf{ d = 13\:units }}\\$

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3 years ago

3 less than m is greater than 9

Artist 52 [7]

Answer:

m-9 = 3 is the required expression

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3 years ago

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Rasek [7]

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3 years ago

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a company promises to release model every month. each model's battery life will be 6% longer than the previous model's. if the c

Ratling [72]

The number of months that it will take the latest model's battery life to reach 1,008.9 minutes is; 8 months

<h3>How to solve geometric progression?</h3>

Each month, there is an increase by a factor of 0.06 of the previous months model.

From geometric sequence formula of aₙ = ar^(n - 1),

where;

a is first term

r is common ratio

aₙ is nth term

we have;

1,008.9 = 671 * 1.06^(n - 1)

1008.9/671 = 1.06^(n - 1)

In 1.504 = (n - 1) In 1.06

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Read more about geometric sequence at; brainly.com/question/24643676

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1 year ago

Question 8 Find the unit vector in the direction of (2,-3). Write your answer in component form. Do not approximate any numbers

slamgirl [31]

Answer:

The unit vector in component form is $\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)$ or $\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j$ .

Step-by-step explanation:

Let be $\vec u = (2,-3)$ , its unit vector is determined by following expression:

$\hat {u} = \frac{\vec u}{\|\vec u \|}$

Where $\|\vec u \|$ is the norm of $\vec u$ , which is found by Pythagorean Theorem:

$\|\vec u\|=\sqrt{2^{2}+(-3)^{2}}$

$\|\vec u\| = \sqrt{13}$

Then, the unit vector is:

$\hat{u} = \frac{1}{\sqrt{13}} \cdot (2,-3)$

$\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)$

The unit vector in component form is $\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)$ or $\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j$ .

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2 years ago