Find the midpoint of the line segment with the endpoints (-6, -8) and (-2, -6)

Simplify 12 + 16 ÷ 4 · 5 - 8

elena55 [62]

Step-by-step explanation:

12 + 16 ÷ 4 × 5 - 8

12 + 4 × 5 - 8

12 + 20 - 8

32 - 8

24

7 0

3 years ago

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Find the domain and range of f(x)= 2|x+2|-8

nordsb [41]

Answer:

Domain (-∞,∞)

Range: [-8,∞)

3 0

3 years ago

Determine if the table shows a linear or an exponential function

____ [38]

Answer:

The table shows an exponential function

Step-by-step explanation:

Linear vs Exponential Functions

A linear function is written as:

$y=mx+b$

where m and b are constants.

If a table contains a linear function, then for each pair of ordered pairs (x1,y1) and (x2,y2), the value of m must be constant.

The slope can be calculated as:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

An exponential function is written as:

$y=y_o.r^x$

Where r is the ratio and yo is a constant.

If a table contains an exponential function, for two ordered pairs (x1,y1) and (x2,y2), the value of r must be constant.

The ratio can be calculated as:

$\displaystyle r=\sqrt[x2-x1]{\frac{y2}{y1}}$

Calculate the slope for (0,4) and (1,2):

$\displaystyle m=\frac{2-4}{1-0}=-2$

Calculate the slope for (1,2) and (2,1):

$\displaystyle m=\frac{1-2}{2-1}=-1$

Since the slope is not the same, the function is not linear.

Now calculate the ratio for (0,4) and (1,2)

$\displaystyle r=\sqrt[1-0]{\frac{1}{2}}$

The radical of index 1 is simply equal to its argument:

$\displaystyle r=\frac{1}{2}$

Now calculate the ratio for (0,4) and (2,1)

$\displaystyle r=\sqrt[2-0]{\frac{1}{4}}$

$\displaystyle r=\sqrt{\frac{1}{4}}$

$\displaystyle r=\frac{1}{2}$

Testing other points we'll find the same ratio, thus the table is an exponential function

4 0

3 years ago

Read 2 more answers

Help: <img src="https://tex.z-dn.net/?f=1.%5C%20%26x%5E4-61x%5E2%2B900%3D0%20%5C%5C%202.%20%5C%20%26%20x%5E4-25x%5E2%2B144%3

yawa3891 [41]

$\bf{1) \ x^4-61x^2+900=0 }$

Applying the factorization method, for example:

$\bf{ 0=(x^2)^2-61(x^2)+900=(x^2-36)(x^2-25)}$

$\bf{\\ &=(x+6)(x-6)(x+5)(x-5); }$

$\bf{ x_1=6 \quad x_2=-6 \quad \ \ \ x_3=5 \quad x_4=5 }$

$\bf{2) \ x^4-25x^2+144=0 }$

Applying the factorization method:

$\bf{0&=(x^2)^2-25(x^2)+144=(x^2-16)(x^2-9) }$

$\bf{ =(x-4)(x+4)(x-3)(x+3); }$

$\bf{ x_1=4 \quad x_2=-4 \quad x_3=3 \quad x_4=-3 }$

7 0

2 years ago

What is the equation of the line that passes through the points (1, −10) and (−4, −7)?

nignag [31]

Hi there! :)

First, let's find the slope using this formula:

m= $\frac{y2-y1}{x2-x1}$

m= $\frac{-7-(-10)}{-4-1} \\\frac{-7+10}{-5} \frac{3}{-5} =-\frac{3}{5}$

Now, use the Point-Slope formula:

y-y1=m(x-x1)

y-(-10)=-3/5(x-1)

y+10=-3/5x+3/5

y=-3/5x+3/5-10

y=-3/5x-9.4

Hope this helps..

~Just an emotional teen who listens to "Try Everything"

$SilentNature$

4 0

2 years ago