Please show work and thank you

solve |5x - 1| < 1 a. {x|0 < x < 2/5} b. {x|x < 0 or x > 2/5} c. {x|-2/5 < x < 2/5}

aliina [53]

|5x - 1| < 1
-1 < 5x - 1 < 1
-1 + 1 < 5x < 1 + 1
0 < 5x < 2
0/5 < x < 2/5
0 < x < 2/5

8 0

3 years ago

Find the measure of the the sides of DEF then classify it by it sides. D(8,-6) E(-1,-3) F(-2,5)

Mama L [17]

Answer:

Part a) The measure of the sides of triangle DEF are

$d_D_E=\sqrt{90}\ units$

$d_E_F=\sqrt{65}\ units$

$d_D_F=\sqrt{221}\ units$

Part b) Is a scalene triangle

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have the coordinates

D(8,-6) E(-1,-3) F(-2,5)

step 1

Find the length side DE

D(8,-6) E(-1,-3)

substitute in the formula

$d=\sqrt{(-3+6)^{2}+(-1-8)^{2}}$

$d=\sqrt{(3)^{2}+(9)^{2}}$

$d_D_E=\sqrt{90}\ units$

step 2

Find the length side EF

E(-1,-3) F(-2,5)

substitute in the formula

$d=\sqrt{(5+3)^{2}+(-2+1)^{2}}$

$d=\sqrt{(8)^{2}+(-1)^{2}}$

$d_E_F=\sqrt{65}\ units$

step 3

Find the length side DF

D(8,-6) F(-2,5)

substitute in the formula

$d=\sqrt{(5+6)^{2}+(-2-8)^{2}}$

$d=\sqrt{(11)^{2}+(-10)^{2}}$

$d_D_F=\sqrt{221}\ units$

step 4

Classify the triangle by the measure of its sides

we have

$d_D_E=\sqrt{90}\ units$

$d_E_F=\sqrt{65}\ units$

$d_D_F=\sqrt{221}\ units$

so

Is a scalene triangle, because is a triangle in which all three sides have different lengths.

6 0

3 years ago

PLS HELP ME ASAP FOR ALL 6!! (SHOW WORK!!) + LOTS AND LOTS OF POINTS!!! *GIVING THANKS!!*

aleksandr82 [10.1K]

This is the answer for #1

4 0

3 years ago

The equations -6x + 3y = 6 and x² + y = 10 intersect at the

eimsori [14]

The values of the letters in coordinates (a, b) and (c,d) are;

a = -4

b = -6

c = 2

d = 6

We are given two equations;

-6x + 3y = 6 ---(eq 1)

x² + y = 10 ---(eq 2)

We are told that they intersect at coordinates; (a, b) and (c, d).

Let us make y the subject in eq 2 to get;

y = 10 - x² --(eq 3)

Let us put 10 - x² into eq 1 to get;

-6x + 3(10 - x²) = 6

expanding further gives;

-6x + 30 - 3x² = 6

rearranging gives;

3x² + 6x - 24 = 0

Using online quadratic equation solver, we have;

x = -4 and x = 2

Putting x = -4 into eq 3 gives;

y = 10 - (-4)²

y = 10 - 16

y = -6

Putting x = 2 into eq 3 gives;

y = 10 - (2)²

y = 10 - 4

y = 6

Thus, the coordinates are; (-4, -6) and (2, 6)

Comparing with (a, b) and (c,d), we have;

a = -4

b = -6

c = 2

d = 6

Read more at; brainly.com/question/15165519

5 0

2 years ago

If q, s, and t are all different numbers, is q < s < t ?

inessss [21]

It very well could be, but not necessarily. What if q = 10, s = 8, and t = 6?

The statement is that q is less than s, and s is less than t (which therefore also means q is less than t).

However, when we substitute (replace) all the letters with the values we assigned them, we can find that the expression becomes:

10 < 8 < 6

This clearly isn’t right, as 10 is the greatest number there, and 8 is definitely less than 10 and greater than 6.

7 0

3 years ago