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3 years ago

Which graph represents the solution to the compound inequality? –6 < 3x – 12 ≤ 9

Mathematics

1 answer:

andrey2020 [161]3 years ago

4 0

Answer:

second graph

Step-by-step explanation:

Solving the inequality

- 6 < 3x - 12 ≤ 9 ( add 12 to all 3 intervals )

6 < 3x ≤ 21 ( divide the intervals by 3 )

2 < x ≤ 7

The graph has an open circle at 2 and a closed circle at 7

This is represented on the second graph

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What is 449,650 rounded to the nearest ten thousand?

Alona [7]

Answer:

450,000

Step-by-step explanation:

The ten thousand digit is 4 and if we compare it to 9, it is bigger then 5 therefore it is rounded up and you get the answer of 450,000

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2 years ago

Why did my dad hasn't come back with the milk after ten years?

adoni [48]

Answer: gta wasted

Step-by-step explanation: your dad left for milk

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3 years ago

. Given ????(5, −4) and T(−8,12):

damaskus [11]

Answer:

a) $y=\dfrac{13x}{16}-\dfrac{129}{16}$

b) $y = \dfrac{13x}{16}+ \dfrac{37}{2}$

Step-by-step explanation:

Given two points: $S(5,-4)$ and $T(-8,12)$

Since in both questions,a and b, we're asked to find lines that are perpendicular to ST. So, we'll do that first!

Perpendicular to ST:

the equation of any line is given by: $y = mx + c$ where, m is the slope(also known as gradient), and c is the y-intercept.

to find the perpendicular of ST <u>we first need to find the gradient of ST, using the gradient formula.</u>

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

the coordinates of S and T can be used here. (it doesn't matter if you choose them in any order: S can be either x_1 and y_1 or x_2 and y_2)

$m = \dfrac{12 - (-4)}{(-8) - 5}$

$m = \dfrac{-16}{13}$

to find the perpendicular of this gradient: we'll use:

$m_1m_2=-1$

both $m_1$ and $m_2$ denote slopes that are perpendicular to each other. So if $m_1 = \dfrac{12 - (-4)}{(-8) - 5}$ , then we can solve for $m_2$ for the slop of ther perpendicular!

$\left(\dfrac{-16}{13}\right)m_2=-1$

$m_2=\dfrac{13}{16}$ :: this is the slope of the perpendicular

a) Line through S and Perpendicular to ST

to find any equation of the line all we need is the slope $m$ and the points $(x,y)$ . And plug into the equation: $(y - y_1) = m(x-x_1)$

side note: you can also use the $y = mx + c$ to find the equation of the line. both of these equations are the same. but I prefer (and also recommend) to use the former equation since the value of 'c' comes out on its own.

$(y - y_1) = m(x-x_1)$

we have the slope of the perpendicular to ST i.e $m=\dfrac{13}{16}$

and the line should pass throught S as well, i.e $(5,-4)$ . Plugging all these values in the equation we'll get.

$(y - (-4)) = \dfrac{13}{16}(x-5)$

$y +4 = \dfrac{13x}{16}-\dfrac{65}{16}$

$y = \dfrac{13x}{16}-\dfrac{65}{16}-4$

$y=\dfrac{13x}{16}-\dfrac{129}{16}$

this is the equation of the line that is perpendicular to ST and passes through S

a) Line through T and Perpendicular to ST

we'll do the same thing for $T(-8,12)$

$(y - y_1) = m(x-x_1)$

$(y -12) = \dfrac{13}{16}(x+8)$

$y = \dfrac{13x}{16}+ \dfrac{104}{16}+12$

$y = \dfrac{13x}{16}+ \dfrac{37}{2}$

this is the equation of the line that is perpendicular to ST and passes through T

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3 years ago

In anova, by dividing the mean square between groups by the mean square within groups, a(n) _____ statistic is computed.group of

jek_recluse [69]

In anova, by dividing the mean square between groups by the mean square within groups, a(n) Analysis of variance statistic is computed.

What is Analysis of variance ?

With the help of the statistical analysis approach known as ANOVA, apparent aggregate variability within a data set is explained by separating systematic components from random factors.
Systematic influences, but not random ones, statistically affect the data set that is being presented.

What are some instances where ANOVA has been applied?

An ANOVA demonstrates the link between the dependent variable and the level of the independent variable.
For illustration: In order to determine whether there is a difference in the number of hours of sleep each night as your independent variable, you divide the groups into low, medium, and high social media use categories.

Learn more about Analysis of variance

brainly.com/question/28274784

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2 years ago

Kinda stuck and would like help

Stella [2.4K]

Answer: See below

Explanation:

8x + 14 = 10x - 10 (alt. exterior angle)
8x - 10x = -10 - 14
-2x = -24
x = -24/-2
x = 12

Now plug x = 12 in 10x - 10 to find the angle:

10(12) - 10 = 120 - 10 = 110 degree

6 0

3 years ago

Read 2 more answers