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2 years ago

Donnie writes an absolute value equation to determine the values that are 0.8 units from 3.5.

Mathematics

1 answer:

enot [183]2 years ago

4 0

Answer:

Step-by-step explanation:

0.4 out of the 0.8/ for the 3.5 it should be 1.5

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What is he value of F(-3)

PolarNik [594]

The correct answer is: " 10 " .

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→ " f(-3) = 10 " .

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Explanation:

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Given:

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f(x) = 7 − x ; if: x ≤ -3 ;

f(x) = x + 4 ; if: x > -3 ;

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Find: " f(-3) " :

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Note: " f(x) = f(-3) " ; → " x = - 3 " ;

Since " x = - =3 " ; → x is NOT greater than "-3" ;

→ So; " f(x) does NOT equal " x + 4" ;

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Consider our other option given:

We have "x = -3 " .

We our given: If " x ≤ -3 " ; {that is; if "x" is less than or equal to "-3" };

→ then: " f(x) = 7 − x " .

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Since: " x = - 3 " ;

→ then " x ≤ -3 " ; and:

→ f(x) = 7 − x ;

THEN:

→ f(-3) = 7 − (-3) ; → Note: Plug in "-3" for the value(s) of "x" in the equation;

and solve:

→ = 7 + 3 ;

= 10 .

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→ f(-3) = 10 .

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The answer is: " 10 " .

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Hope this answer — and explanation — is helpful to you.

Best wishes in your academic pursuits!

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5 0

4 years ago

Find the six trig function values of the angle 240*Show all work, do not use calculator

-BARSIC- [3]

Solution:

Given:

$240^0$

To get sin 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, sin 240 will be negative.

$sin240^0=sin(180+60)$

Using the trigonometric identity;

$sin(x+y)=sinx\text{ }cosy+cosx\text{ }siny$

Hence,

$\begin{gathered} sin(180+60)=sin180cos60+cos180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\ \\ Thus, \\ sin180cos60+cos180sin60=0(\frac{1}{2})+(-1)(\frac{\sqrt{3}}{2}) \\ sin180cos60+cos180sin60=0-\frac{\sqrt{3}}{2} \\ sin180cos60+cos180sin60=-\frac{\sqrt{3}}{2} \\ \\ Hence, \\ sin240^0=-\frac{\sqrt{3}}{2} \end{gathered}$

To get cos 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, cos 240 will be negative.

$cos240^0=cos(180+60)$

Using the trigonometric identity;

$cos(x+y)=cosx\text{ }cosy-sinx\text{ }siny$

Hence,

$\begin{gathered} cos(180+60)=cos180cos60-sin180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\ \\ Thus, \\ cos180cos60-sin180sin60=-1(\frac{1}{2})-0(\frac{\sqrt{3}}{2}) \\ cos180cos60-sin180sin60=-\frac{1}{2}-0 \\ cos180cos60-sin180sin60=-\frac{1}{2} \\ \\ Hence, \\ cos240^0=-\frac{1}{2} \end{gathered}$

To get tan 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, tan 240 will be positive.

$tan240^0=tan(180+60)$

Using the trigonometric identity;

$tan(180+x)=tan\text{ }x$

Hence,

$\begin{gathered} tan(180+60)=tan60 \\ tan60=\sqrt{3} \\ \\ Hence, \\ tan240^0=\sqrt{3} \end{gathered}$

To get cosec 240 degrees:

$\begin{gathered} cosec\text{ }x=\frac{1}{sinx} \\ csc240=\frac{1}{sin240} \\ sin240=-\frac{\sqrt{3}}{2} \\ \\ Hence, \\ csc240=\frac{1}{\frac{-\sqrt{3}}{2}} \\ csc240=-\frac{2}{\sqrt{3}} \\ \\ Rationalizing\text{ the denominator;} \\ csc240=-\frac{2}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\ \\ Thus, \\ csc240^0=-\frac{2\sqrt{3}}{3} \end{gathered}$

To get sec 240 degrees:

$\begin{gathered} sec\text{ }x=\frac{1}{cosx} \\ sec240=\frac{1}{cos240} \\ cos240=-\frac{1}{2} \\ \\ Hence, \\ sec240=\frac{1}{\frac{-1}{2}} \\ sec240=-2 \\ \\ Thus, \\ sec240^0=-2 \end{gathered}$

To get cot 240 degrees:

$\begin{gathered} cot\text{ }x=\frac{1}{tan\text{ }x} \\ cot240=\frac{1}{tan240} \\ tan240=\sqrt{3} \\ \\ Hence, \\ cot240=\frac{1}{\sqrt{3}} \\ \\ Rationalizing\text{ the denominator;} \\ cot240=\frac{1}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\ \\ Thus, \\ cot240^0=\frac{\sqrt{3}}{3} \end{gathered}$

5 0

1 year ago

Does 6 3/8 - 4 3/4 = 4 3/4

UNO [17]

Answer:

no it doesnt

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

A rectangle park measures 300 ft by 400 ft. A sidewalk runs diagonally from one comer to the opposite corner. Find the length o

DochEvi [55]

The length of side walk is 500 feet

Solution:

Given that, A rectangle park measures 300 ft by 400 ft

Length = 300 feet

Width = 400 feet

A sidewalk runs diagonally from one comer to the opposite corner

We have to find the length of side walk

Which means, we have to find the length of diagonal of rectangle

The diagonal of rectangle is given by formula:

$d = \sqrt{w^2+l^2}$

Where,

d is the length of diagonal

w is the width and l is the length of rectangle

Substituting the values in formula, we get

$d = \sqrt{400^2+300^2}\\\\d = \sqrt{160000+90000}\\\\d = \sqrt{250000}\\\\d = 500$

Thus length of side walk is 500 feet

5 0

4 years ago

A hospital prepares a 100mg supply of technetium-99m which has a half-life of 6 hours. what is the decay factor?

SashulF [63]

For a half- life, the formula is
A(t) = A0(0.5)^( t / t_0.5)
where A(t) is the amount of substance at time t
A0 is the initial amount of subtance
t_0.5 is the time it will reduce its amount to half
t is the time

substitute the given to the formula
A(t) = 100(0.5)^( t/6 )
so the decay factor is 0.5^( t/6 )

6 0

3 years ago