1.)24:56=X:46

How many solutions are there to the equation below? |x| = -31

ella [17]

Break down the problem into these two equations;

x = -31

-x = -31

Solve for the 1st equation; x = -31

x = -31

Solve for the 2nd equation; -x = -31

x = 31

Collect all solutions

x = ±31

Check the solution

When x = -31, the original equation; |x| = -31 does not hold true. Thus, we will drop x = -31 from the solution set.

Check the solution again;

When x = 31, the original equation |x| = -31 does not hold true as well. Thus we will drop x = 31 from the solution set.

Therefore,

<u>No solution exists to this equation. </u>

5 0

3 years ago

Read 2 more answers

What is the square root

shusha [124]

Answer:

Step-by-step explanation:

Trying to factor as a Difference of Squares :

1.1 Factoring: r2-96

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 96 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step 1 :

r2 - 96 = 0

Step 2 :

Solving a Single Variable Equation :

2.1 Solve : r2-96 = 0

Add 96 to both sides of the equation :

r2 = 96

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

r = ± √ 96

Can √ 96 be simplified ?

Yes! The prime factorization of 96 is

2•2•2•2•2•3

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 96 = √ 2•2•2•2•2•3 =2•2•√ 6 =

± 4 • √ 6

The equation has two real solutions

These solutions are r = 4 • ± √6 = ± 9.7980

Two solutions were found :

r = 4 • ± √6 = ± 9.7980

Processing ends successfully

4 0

3 years ago

Can someone help me plssss???

mote1985 [20]

Yes the answer is 10

6 0

3 years ago

Which pairs of points would result in a line with a rate of change of 2:1? Select all that apply.

Helen [10]

Answer:

Options A, C, D are true.

Step-by-step explanation:

We have to choose the pair of points from that given in the attached file which will result in a line with a rate of change i.e. slope of 2:1 i.e. 2.

A. The points are (-4,-11) and (-2,-7).

Then the slope of the joining line is $\frac{-7-(-11)}{-2-(-4)} =2$

B. The points are (5,6) and (-5,12).

Then the slope of the joining line is $\frac{12-6}{-5-5} =-\frac{3}{5}$

C. The points are (0,-3) and (-4,-11).

Then the slope of the joining line is $\frac{-11-(-3)}{-4-0} =2$

D. The points are (0,-3) and (5,7).

Then the slope of the joining line is $\frac{7-(-3)}{5-0} =2$

Therefore, options A, C, D are true. (Answer)

7 0

3 years ago

In a survey at a local college, 18% of students reported that they do not own a mobile device with internet capabilities. if 20

Sholpan [36]

Answer:

0.64

Step-by-step explanation:

The probability that randomly selected student doesn't own a mobile device with internet capabilities is $p=0.18$ and the probability that randomly selected student owns a mobile device with internet capabilities is $q=1-p=1-0.18=0.82.$

If 20 students are selected at random, the probability that at most 5 students (0 students, 1 student, 2 students, 3 students, 4 students or 5 students) don't own a mobile device with internet capabilities is

$Pr=C_{20}^0p^0q^{20}+C_{20}^1p^1q^{19}+C_{20}^2p^2q^{18}+C_{20}^3p^3q^{17}+C_{20}^4p^4q^{16}+C_{20}^5p^5q^{15}=q^{20}+20pq^{19}+190p^2q^{18}+1,140p^3q^{17}+4,875p^4q^{16}+15,504p^5q^{15}\approx 0.6405021423\approx 0.64.$

3 0

3 years ago