What is the solution to -2|x − 1| = -4? A. x = 3 B. x = -1 or x = 3 C. x = 1 or x = 3 D. No solutions exist.

[tex]\boxed{\sf x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}}[/tex]

Explanation:

Given expression: (ab)x^2 + (b^2 - ac)x + (-bc) = 0

Here given:

Apply quadratic formula:

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \ ax^2 + bx + c = 0[/tex]

Insert values:

[tex]\sf x = \dfrac{-(b^2 - ac) \pm \sqrt{(b^2 -ac)^2-4(ab)(-bc)} }{2(ab)}[/tex]

[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2-ac\right)^2+4abbc} }{2ab}[/tex]

[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{b^4+2b^2ac+a^2c^2} }{2ab}[/tex]

[tex]\sf x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2+ac\right)^2} }{2ab}[/tex]

[tex]\sf x = \dfrac{-b^2 + ac \pm( b^2+ac )}{2ab}[/tex]

[tex]\sf x = \dfrac{-b^2 + ac +( b^2+ac )}{2ab} \quad or \quad \dfrac{-b^2 + ac -( b^2+ac )}{2ab}[/tex]

[tex]\sf x = \dfrac{2ac}{2ab} \quad or \quad \dfrac{-2b^2}{2ab}[/tex]

[tex]\sf x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}[/tex]

Apply quadratic formula:

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex]\\ \sf\Rrightarrow x = \dfrac{-(b^2 - ac) \pm \sqrt{(b^2 -ac)^2-4(ab)(-bc)} }{2(ab)}[/tex]

[tex]\\ \sf\Rrightarrow x= \dfrac{-b^2 + ac \pm \sqrt{\left(b^2-ac\right)^2+4abbc} }{2ab}[/tex]

[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm \sqrt{b^4+2b^2ac+a^2c^2} }{2ab}[/tex]

[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm \sqrt{\left(b^2+ac\right)^2} }{2ab}[/tex]

[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac \pm( b^2+ac )}{2ab}[/tex]

[tex]\\ \sf\Rrightarrow x = \dfrac{-b^2 + ac +( b^2+ac )}{2ab} \quad or \quad \dfrac{-b^2 + ac -( b^2+ac )}{2ab}[/tex]

[tex]\\ \sf\Rrightarrow x = \dfrac{2ac}{2ab} \quad or \quad \dfrac{-2b^2}{2ab}[/tex]

[tex]\\ \sf\Rrightarrow x = \dfrac{c}{b} \quad or \quad \dfrac{-b}{a}[/tex]

Step-by-step explanation:

Brackets is the bigger version of parentheses, you first solve the questions inside the parentheses, then move onto brackets.

For example, this question:

[tex]x=-1\\y=-2\\z=3[/tex]

[tex]5x-y[7-4(z-y)][/tex]

plug in x, y, and z.

[tex]5(-1)-(-2)[7-4(3-(-2))][/tex]
[tex]5(-1)-(-2)[7-4(5)][/tex]

[tex]5(-1)-(-2)[7-20][/tex]

[tex]5(-1)-(-2)[-13][/tex]

[tex]-5-(-2)[-13][/tex]

[tex]-5-26[/tex]

[tex]-31[/tex]

I hope you understand better now.

Answer:

142 506

Step-by-step explanation:

here the order does not matter

Then

we the number of sets is equal to the number of combinations.

Using the formula :

the number of sets is 30C5

[tex]C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}[/tex]

      [tex]=142506[/tex]

There are 142506 ways in which 5 students can be selected out of 30 students.

The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.

By using the formula:

[tex]\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}[/tex]

where;

[tex]\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}[/tex]

[tex]\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}[/tex]

[tex]\mathbf{^nC_r = 142506}[/tex]

Learn more about combination here:

https://brainly.com/question/11732255

#SPJ11

Answer:

195

Step-by-step explanation:

87+38+40=165

360-165=195

Hope this helps!

If not, I am sorry.

Assuming the dilation is centered at the origin, the scale factor is 1/3.

This means the coordinates of the point (8,4) are [tex]\boxed{\left(\frac{8}{3}, \frac{4}{3} \right)}[/tex]

Answer:

pounds (£)

Step-by-step explanation:

pounds are used in countries such as the UK and South Georgia

The molarity of the resulting solution is 3.99 × 10⁻⁴ M. The correct option is the third option 3.99 × 10⁻⁴ M

From the question, we are to determine the molarity of the resulting solution

From the given information,

Number of moles = 5.99 × 10⁻⁶ mol

Volume = 1.50 × 10⁻² L

Using the formula,

Molarity = Number moles / Volume

∴ Molarity = (5.99 × 10⁻⁶) / (1.50 × 10⁻²)
Molarity = 3.99 × 10⁻⁴ M

Hence, the molarity of the resulting solution is 3.99 × 10⁻⁴ M. The correct option is the third option 3.99 × 10⁻⁴ M

Learn more on Calculating molarity here: https://brainly.com/question/23051191

#SPJ1

Answer:

The answer is 3.99 × 10–4 M

Step-by-step explanation:

I just did the assignment on Edge :)

Answer:

I exactly don't have or know the answer

Answer:

4 secs

Step-by-step explanation:

Since they have to be synchronized, their parabolic equations must be equal to one another

3(t^2 + 9 - 6t) - (t^2 + 25 - 10t) - t + 2 = 0

2t^2 - 9t + 4

(2t - 1)(t - 4) = 0

t = 1/2, 4

From the options, the answer is 4

The gymnasts will be at the same height during their flips at two different times: 1/2 seconds and 4 seconds.

so, correct option is: C.

Here, we have,

To determine when the gymnasts will be at the same height during their flips, we need to find the time (x) at which the equations for y are equal.

The given equations are:

y = –(x – 5)² + 3

y = –3(x – 3)² + x + 1

Setting the two equations equal, we have:

–(x – 5)² + 3 = –3(x – 3)² + x + 1

Expanding the squared terms:

–(x² – 10x + 25) + 3 = –3(x² – 6x + 9) + x + 1

Simplifying the equation:

–x² + 10x – 25 + 3 = –3x² + 18x – 27 + x + 1

Combining like terms:

–x² + 10x – 22 = –3x² + 19x – 26

Rearranging the equation:

2x² - 9x + 4 = 0

To solve this quadratic equation, we can factor it:

(2x - 1)(x - 4) = 0

Setting each factor equal to zero:

2x - 1 = 0 or x - 4 = 0

Solving for x:

2x = 1 or x = 4

Dividing by 2:

x = 1/2 or x = 4

Therefore, the gymnasts will be at the same height during their flips at two different times: 1/2 seconds and 4 seconds.

To learn more on equation click:

https://brainly.com/question/14468218

#SPJ2

Answer:

the answer will be 36

Step-by-step explanation:

if you divide 24 by 8 it will be 3 so then you multiply 12 times 3 and it's 36

Answer:

-3/2

Step-by-step explanation:

First, you divide by taking the reciprocal of -2/5 which is -5/2.

Second, you get the answer which is -5/4.

Add that with -1/4 and you will get -6/4.

Simplify to get the answer which is -3/2.

Answer:

[tex]-\dfrac{3}{2}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{\dfrac{1}{2}}{-\dfrac{2}{5}}+\left(-\dfrac{1}{4}\right)[/tex]

To divide fractions, flip the second fraction (make the numerator the denominator, and the denominator the numerator) then multiply it by the first fraction:

[tex]\implies \dfrac{1}{2} \times -\dfrac{5}{2}+\left(-\dfrac{1}{4}\right)[/tex]

To multiply the fractions, multiply the numerators and multiply the denominators:

[tex]\implies \dfrac{1 \times (-5)}{2 \times 2} +\left(-\dfrac{1}{4}\right)[/tex]

[tex]\implies -\dfrac{5}{4} +\left(-\dfrac{1}{4}\right)[/tex]

Apply the rule -a + (-b) = -a - b :

[tex]\implies -\dfrac{5}{4} -\dfrac{1}{4}[/tex]

As the denominators are the same, subtract the numerators and put the answer over the same denominator:

[tex]\implies \dfrac{-5-1}{4}[/tex]

[tex]\implies -\dfrac{6}{4}[/tex]

Simplify by dividing the numerator and denominator by the highest common factor:

[tex]\implies -\dfrac{6 \div 2}{4 \div 2}[/tex]

[tex]\implies -\dfrac{3}{2}[/tex]

The probability of selecting a jack, replacing the card, and then selecting a king is 1/169

In a standard deck of cards, we have:

Total = 52

Jack = 4

King = 4

The probability of each is:

P(Jack) = 4/52

P(King) = 4/52

So, we have:

P = 4/52 * 4/52

Simplify

P = 1/13 * 1/13

Evaluate

P = 1/169

Hence, the probability is 1/169

Read more about probability at:

https://brainly.com/question/25870256

#SPJ1

Answer: [tex]f(x)=-\frac{1}{2}x+1[/tex]

Step-by-step explanation:

The slope is [tex]\frac{-1-1}{4-0}=-\frac{1}{2}[/tex], which matches the second option.

Linear function that is represented by the graph is f(x)= -1/2 x+1.

Here, we have,

From the graph,

y - intercept of the linear function is 1 , i.e. c = 1

and there are two points on the line (-4, 3), (4, -1)

We can get the equation of line by applying slope-intercept formula,

Slope of the line,

m = y₂ -y₁ / x₂-x₁

so, we get,

m = -1 -3 / 4 + 4

   = -4/8

   = -1/2

Now applying slope-intercept formula,

y = mx+c

Putting the values,

=> y = -1/2 x + 1

=>f(x) = -1/2 x + 1.

Therefore, linear function that is represented by the graph is

f(x) = -1/2 x + 1.

To learn more on slope click:

brainly.com/question/3605446

#SPJ5

can u please tell if the figure is a right angled triangle??...cuz in order to find the perimeter, Pythagoras theorem must be applied but it's only for right angled triangle...so specify please

Answer:

6 to 9 meals

Step-by-step explanation:

9 If he feeds 2 pounds per meal. 18÷2 =9

6 if he feeds 3 pounds per meal. 18÷3=6

Answer:

Area of a triangle = 1/2 * base * height

here ,

base = 120 ft

height = 25 ft

Area = 1/2* 120*25

= 60 * 25

= 1500 ft²

Answer 2

Answer:

1/2 * base * height

so 1/2 * 25 * 120

= 1500

Answer:

$6847.955

Explanation:

Use the compound interest formula, but the value decreases over time.

[tex]\sf A = P(1 - \dfrac{r}{100} )^t[/tex]

where 'A' is final amount, r is rate, t is time

Inserting P = $15,000, r = 23, t = 3 years

[tex]\sf A = 15000(1- \dfrac{23}{100} )^3[/tex]

[tex]\sf A = 6847.995[/tex]

Hence the value of truck after three years will be $6847.955.

Answer:

Step-by-step explanation:

Answer:

25 < t < 350

Step-by-step explanation:

The mean lifetime of a bulb ranges from 25 to 350 hrs but the question is unclear.

Answer:

x = 9

Step-by-step explanation:

x-2 = 7

you solve by adding 2 to both sides to maintain equality. and you add by 2 to cancel out the -2 to isolate the x.

x = 9

Step-by-step explanation:

area of rectangle= 12×6

=72ft^2

A2=9ft^2 whereby the base of the hole is 3ft

height is 6ft

therefore the square is 18 ft

Answer:

answer= 3

hope this helps if not I'll try to do it again

Answer:

4^-3*(1/4)^2

(1/64)*(1/16)

=(1/1024)

Answer:

0.00025

Step-by-step explanation:

hope it'll help I'll ask . if you feel that it's not that correct please comment so that I can ask my sister who I'm sure she'll help although she's far good day.

Answer:

B or 40.67mph

Step-by-step explanation:

To solve we will use formula distance over total time, so are distance is 183miles and are time is 4 hours and 30 minutes. If we put that in hours we get 4.5 hours. Now we simply divide 183/4.5 to get about 40.67 .

The given statement is false.

What is the effect of a row operation on a determinant?

The factor by which a row operation intends to change the determinant is not equal to the determinant of the elementary matrix corresponding to that row operation. Rather, when a row is scaled up by a factor in a matrix, the determinant of that matrix also scales up by that factor.

Similarly, the factor by which a row operation changes the determinant is equal to the factor times the determinant of the elementary matrix corresponding to that row operation.

Learn more about a matrix here:

https://brainly.com/question/9967572

#SPJ4

Total number of multiple-choice questions that Desiree has to answer in Aptitude test = 50

Points given for every correct Answer = +3

Points deducted for every Incorrect Answer = -1

For every question unanswered ,

points Deducted = -0.5

Total Points Obtained by Desiree after Answering all the questions = 110

Number of Answers that Desiree answered correctly = x questions

Number of Incorrect Answers = (50 - x) questions

Then,the Equation representing above situation

→ 3 × x + ( -1 ) × ( 50 - x ) = 110

⇒3x - 50 + x = 110 ----------- equation that represents the given situation

⇒ 4x - 50 = 110

Adding 50, on both sides

→ 4x - 50 + 50 = 110 + 50

⇒ 4x = 160

Dividing both sides by, 4 we get

x = 40

Number of correct answers given by Desiree= 40 questions

Number of Incorrect Answers = 50 - 40

= 10 Questions .

Answer:

Desiree is given an aptitude test with 50 multiple-choice questions. For every correct answer, Desiree will get 3 points. For every wrong answer, 1 point will be deducted. For every question unanswered, 0.5 points is deducted. Desiree did not leave any questions unanswered and gets 110 points on the test.

If x is the number of questions Desiree answered correctly, then the equation that represents the given situation is

3(50 - x) + x = 110

and the equation will have

no solution

.

Step-by-step explanation:

Answer:

The second option

Step-by-step explanation:

If you look at the graph, it appears that from negative infinity to 0, the line is just constant, so the range of that would simply be the constant value or in this case 4. from 0 to infinity it appears the line is decreasing at a constant rate and should go towards negative infinity as x goes towards infinity. So the range would be -infinity < f(x) <= 4

The fraction of their student loan will be left to spend is half of their loan.

A number expressed quotient, in which numerator is divided by denominator is called a fraction.

Let the loan amount be $100.

Expenses for food is given that two fifths of their loan

i.e.

= 2/5 × 100

= $40

Now,

Remaining part will be = $100- $40 = $60

So,

Expenses for travel are given that one sixth of their loan,

i.e.

= 1/6 × 60

= $10

So,

Remaining part will be = $60 - $10 = $50

Hence, the fraction of their student loan will be left to spend is half of their loan.

Learn more about fraction here:

https://brainly.com/question/415517

#SPJ10