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Write the linear function for the given function values.<br> f(-2)=9 and f(6)=7

BigorU [14]

Answer:

$y = -\frac14x + 8.5$

Step-by-step explanation:

Hello!

A linear function is written in the form of $y = mx + b$ , where m is the slope and b is the y-intercept.

Each of these expressions can be converted to coordinate form, (-2,9) and (6,7).

<h2>Slope</h2>

Slope can be calculated by the difference in the x-values divided by the difference in the y-values.

Solve

$\frac{9 - 6}{-2 - 6}$
$\frac{2}{-8}$
$-\frac14$

The slope is -1/4.

<h2 /><h2>Y-intercept</h2>

The y-intercept is found by plugging in the x and y values of a coordinate and the slope and then solving for b.

Solve

$y = mx + b$
$9 = -\frac14(-2) + b$
$9 = 0.5 + b$
$8.5 = b$

<h2>Equation</h2>

We can find the equation by simply plugging in all the values that we found.

Equation: $y = -\frac14x + 8.5$

6 0

2 years ago

Solve: 2cos(x)-square root 3=0 for 0 less than x less than 2 pi

Leona [35]

Answer:

The general solution of $cos x = cos(\frac{\pi }{6})$ is

x = 2nπ± $\frac{\pi }{6}$

The general solution values

$x = - \frac{\pi }{6} and x = \frac{\pi }{6}$

Step-by-step explanation:

Explanation:-

Given equation is

$2cosx-\sqrt{3} =0 for 0$

$2cosx =\sqrt{3}$

Dividing '2' on both sides, we get

$cos x =\frac{\sqrt{3} }{2}$

$cos x = cos(\frac{\pi }{6})$

<em>General solution of cos θ = cos ∝ is θ = 2nπ±∝</em>

<em>Now The general solution of </em> $cos x = cos(\frac{\pi }{6})$ <em> is </em>

put n=0

$x = - \frac{\pi }{6} and x = \frac{\pi }{6}$

Put n=1

$x = 2\pi +\frac{\pi }{6} = \frac{13\pi }{6}$

$x = 2\pi -\frac{\pi }{6} = \frac{11\pi }{6}$

put n=2

$x = 4\pi +\frac{\pi }{6} = \frac{25\pi }{6}$

$x = 4\pi -\frac{\pi }{6} = \frac{23\pi }{6}$

And so on

But given 0 < x< 2π

The general solution values

$x = - \frac{\pi }{6} and x = \frac{\pi }{6}$

6 0

3 years ago

Which one is right triangle angle <br>a. 45, 55 and 35<br>b. 52, 48 and 20

Gemiola [76]

<h2>option b. 52, 48 and 20</h2>

Step-by-step explanation:

<u>let's solve:-</u>

To test whether given this triangle is right triangle or not, we can use the Pythagorean Theorem .

soo

Pythagorean Theorem=

$\bold \green{(leg1)^{2} +(leg2)^{2} =(hypotenuse)^{2} }$

Here:-

$\bold \blue{leg \: 1 = 48} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \bold \blue{ leg2 = 20} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \bold\blue{hypotenuse = 52}$

Putting values:-

${48}^{2} + {20}^{2} = {52}^{2} \: \: \: \: \: \: \\ \\ 2304 + 400 = 2704 \\ \\ 2704 = 2704 \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

4 0

2 years ago

In imaginary numbers can you multiply two radicals that have negative values under them that do not square to whole numbers

ElenaW [278]

Yes, you can; based on the inherent assumption that the "two radicals that have negative values" are, in fact, "imaginary numbers" .

Take, for example, the commonly known "imaginary number": "i" ; which represents the "imaginary number" ; " √-1 " .

Since: "i = √-1" ;

Note that: " i² = (√-1)² = √-1 * √-1 = √(-1*-1) = √1 = 1 .
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7 0

3 years ago

Read 2 more answers

Help me through this

NikAS [45]

Monday= 13.45
Tuesday=9.5
wednesday/Friday= x/3

1st. you add Monday and Tuesday
2nd. you subtract the total 42.6 with added numbers of step one
3rd. finally you divided the total of step 2 by 3

finally you shall receive your answer.

6 0

3 years ago