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3 years ago

Compare and contrast the solution of |2x + 8| > 6 and the solution of |2x + 8| < 6.

Mathematics

1 answer:

svet-max [94.6K]3 years ago

3 0

Answer:

The solution of |2x + 8| > 6 includes all values that are less than –7 or greater than –1.

The solution of |2x + 8| < 6 includes all values that are greater than –7 and less than –1.

Step-by-step explanation:

You can find the solution by "unfolding" the absolute value, then dividing by 2 and subtracting 4:

-6 > 2x +8 > 6 . . . . . read this as -6 is less than 2x+8 or 2x+8 is greater than 6

-3 > x +4 > 3 . . . . . . .divide by 2

-7 > x > -1 . . . . . . . . . solution to the first inequality: x is less than -7 or greater than -1.

___

The solution to the other inequality is identical, except the direction of the comparison is reversed. It is read differently, because the segments overlap, rather than being disjoint.

-7 < x < -1 . . . . . . . . solution to the second inequality: x is greater than -7 and less than -1.

These descriptions match choice B.

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Can someone explain me how to solve this?

sesenic [268]

Answer:

X=12

Step-by-step explanation:

since it is an isosceles triangle opposite sides are congruent which means 7x+24=13x-48 you then would need to subtract either the whole numbers or the variables from each side so add 48 on each side it equals to 7x+72=13x then subtract 7x from 13x and you get 72=6x divide both sides 6/6=x, 72/6 Therefore x=12 HOPE that helped mark me brainiest pls

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3 years ago

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Can someone help me with these problems step by step? It’s pre-algebra so it’s not rlly that hard.

gtnhenbr [62]

Answer:

Step-by-step explanation:

√121=11 so right answer is B

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3 years ago

What is the value of x?<br> Enter your answer in the box.

loris [4]

Answer:

Step-by-step explanation:

Since all the angles are the same in this triangle, all the sides should be the same too.

Hence, 3x - 5 = 4x - 30

5 + -1x = -30

-1x = -35

x = 35

Hope this helped!

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3 years ago

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Determine if the segment lengths form a triangle. If so, would the triangle be acute, right, or obtuse? 4.1, 8.2, 12.2

goldfiish [28.3K]

Three line segments can form a triangle if the length of the longest segment is greater than the sum of the lengths of the shorter segments.

$4.1 + 8.2 \ \textgreater \ 12.2 \\
12.3 \ \textgreater \ 12.2 \\
true$
They can form a triangle.

Now if c is the length of the longest side and a and b are the lengths of the shorter sides, then:
- if $c^2=a^2+b^2$ , the triangle is right
- if $c^2\ \textless \ a^2+b^2$ , the triangle is acute
- if $c^2\ \textgreater \ a^2+b^2$ , the triangle is obtuse

$4.1^2+8.2^2=16.81+67.24=84.05 \\
12.2^2=148.84 \\ \\
148.84\ \textgreater \ 84.05$
The triangle is obtuse.

The answer is D.

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3 years ago

You have fit a regression model with two regressors to a data set that has 20 observations. The total sum of squares is 1000 and

Llana [10]

Answer:

Hence the adjusted R-squared value for this model is 0.7205.

Step-by-step explanation:

Given n= sample size=20

Total Sum of square (SST) =1000

Model sum of square(SSR) =750

Residual Sum of Square (SSE)=250

The value of R ^2 for this model is,

R^2 = \frac{SSR}{SST}

R^2 = 750/1000 =0.75

Adjusted $R^2$ :

$Adjusted R^2 =1- \frac{(1-R^2)\times(n-1)}{(n-k-1)}$

Where k= number of regressors in the model.

$Adjusted R^2 =1-(19\times 0.25/((20-2-1)) = 0.7205$

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3 years ago