42-2x=5x
what’s x in this equation

The augmented matrix for the system of equations is given as follows:

[tex]\left[\begin{array}{cccc}9&4&-2&0\\4&0&6&-2\\0&-3&2&2\end{array}\right][/tex]

A system of equations is when multiple variables are related, and equations are constructed to find the values of each variable. There are multiple ways to solve a system, and one of the most usual is in a matricial way, as the augmented matrix of the system is constructed.

In standard notation, the system is given by:

The augmented matrix for a system with variables x, y and z is constructed as follows:

Hence for this system, the matrix is given by:

[tex]\left[\begin{array}{cccc}9&4&-2&0\\4&0&6&-2\\0&-3&2&2\end{array}\right][/tex]

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Answer:

[tex]\left|2x-6\right|<4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:1<x<5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(1,\:5\right)\end{bmatrix}[/tex]

Therefore, the 3rd graph represents the solutions to inequality.

Please also check the graph below.

Step-by-step explanation:

Given the expression

[tex]|2x\:-\:6|\:<\:4[/tex]

[tex]\mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a[/tex]

[tex]-4<2x-6<4[/tex]

[tex]2x-6>-4\quad \mathrm{and}\quad \:2x-6<4[/tex]

condition 1

[tex]2x-6>-4[/tex]

Add 6 to both sides

[tex]2x-6+6>-4+6[/tex]

[tex]2x>2[/tex]

Divide both sides by 2

[tex]\frac{2x}{2}>\frac{2}{2}[/tex]

[tex]x>1[/tex]

condition 2

[tex]2x-6<4[/tex]

Add 6 to both sides

[tex]2x-6+6<4+6[/tex]

[tex]2x<10[/tex]

Divide both sides by 2

[tex]\frac{2x}{2}<\frac{10}{2}[/tex]

[tex]x<5[/tex]

combine the intervals

[tex]x>1\quad \mathrm{and}\quad \:x<5[/tex]

Merging overlapping intervals

[tex]1<x<5[/tex]

Thus,

[tex]\left|2x-6\right|<4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:1<x<5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(1,\:5\right)\end{bmatrix}[/tex]

Therefore, the 3rd graph represents the solutions to inequality.

Please also check the graph below.

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:

In this exercise, you're required to describe the score which this ski jumper must earn on the second jump to beat his or her competitor. Therefore, let x represent the score of his or her second acrobatic ski jump.

Based on the competitor's score of 119.8 in the second jump, this ski jumper must earn the following score represented by this inequality:

x > 119.8

From the table (see attachment), we can logically deduce that the competitor's score in the first ski jump is equal to 117.1. This ultimately implies that, the ski jumper's score can be modeled by this inequality:

x > 117.1

In this context, we can reasonably infer and logically deduce that both the coach and the teammate are correct because a score of "118.4" and "117.5" are greater than a score of "117.1."

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Complete Question:

MAKING AN ARGUMENT

In an aerial ski competition, you perform two acrobatic ski jumps. The scores on the two jumps are then added together.

a. Describe the score that you must earn on your second jump to beat your competitor.

b. Your coach says that you will beat your competitor if you score 118.4 points. A teammate says that you only need 117.5 points. Who is correct? Explain.

Answer:

C

Step-by-step explanation:

Senators don't need to be born in the United States. They only need nine years of U.S. citizenship to qualify for office.

Answer:

its c cause its cool

Step-by-step explanation:

Answer:

42,183

Step-by-step explanation:

We will use the Continuous Compounding Interest since a regular interval was not stated.

P(t) = Pe^(rt)

We will plug in the variables to the formula

P(t) = 31250 * e^(.12 * 2.5)

We can simplify and evaluate the compound interest.

P(t) = 42183.08

1 pound = 16 ounces (general knowledge)

270 calories divided 5 ounces

1 ounce= 54 calories

2 pounds = 32 ounces

32 ounces × 54 calories = 1728

2 pounds = 1728 calories

Yes, it is a right-angled triangle.

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Answer:

43%

Step-by-step explanation:

There are 39 girls. 21 of them like biology. 11 out of 34 who like chemistry are girls.

No. of girls who prefer biology = 21

There are (100-39) boys. 16 of them like physics. (34-11) of them like chemistry.

No. of boys who prefer biology = 100-39-16-34+11

                                                    = 22

Percentage of students who prefer biology = [tex]\frac{21+22}{100}[/tex] × 100%

                                                                        = [tex]\frac{43}{100}[/tex] × 100%

                                                                        = 43%

Answer:

D

Step-by-step explanation:

If the percent change is 30 to 36 you can already see that it is an increase

here is the work

36 - 30

30

x 100% = 20%

Answer:

20% increase, which corresponds to the light

Step-by-step explanation:

(y - x)/x * 100

(36 - 30)/30 * 100

(6 * 100)/30

600/30

20% increase

Answer:

a) 25

b) 59

c) Too lazy

Step-by-step explanation:

If 30% were to be a decimal, it would be 0.3 because 30% of 1 is 0.3. We will use this to figure out how many purple skittles there are.

A) To find the amount of purple skittles we must multiply the total number of skittles by the percent (in this case 0.3). Equation = (84*0.3=25.2) You can't really have 0.2 of a skittle so we would round down to the whole number (25).

B) Knowing the number of purple skittles, finding the number of non-purple skittles is straightforward. All you have to do is subtract the # of purple skittles from the total amount of skittles (84-25=59).

C) Kinda forgot how to do this but good luck

Answer:

The amount is $25.4

Step-by-step explanation:

There are 109 students to attend the science workshop.

Number of erasers needed is 109, but whole packages of erases can be bought which consist 12 erasers. The total packages of erasers needed would be 10.

The cost of 10 packages of erasers = $0.75 x 10

                                  = $7.5

The cost of 109 folders = 109 x $0.10

                                  = $10.9

Number of pencils needed is 109, but whole packages of pencils can be bought which consist 8 pencils. The total packages of pencils needed would be 14.

The cost of 14 packages of pencils = $0.50 x 14

                                  = $7.0

Total cost = $7.5 + $10.9 + $7.0

                = $25.4

The amount that would be spent by the school is $25.4

Answer:

25.4

Step-by-step explanation:

Answer:

(3,22.50)

(6, 33)

Rise/Run using two points

33-22.50/ 6-3

10.5/3

Rate = 3.5

Answer:

15

Step-by-step explanation:

Hypotenuse: 17ft long

Height: 8ft long

17^2 = 8^2 + b^2

b^2 = 17^2 - 8^2

b = √225

b = 15

Answer:

[tex]1\frac{5}{9}[/tex]

Step-by-step explanation:

This is the answer because:

1)  Reduce the expression, if possible, by cancelling the common factors.

2) You can also find the reciprocal of 1 1/2 = 3/2 while dividing the expression:

1. Convert both fractions into improper fractions:

[tex]2\frac{1}{3} = \frac{7}{3}[/tex]

[tex]1\frac{1}{2} = \frac{3}{2}[/tex]

2. Divide both fractions:

[tex]\frac{7}{3}[/tex] ÷ [tex]\frac{3}{2}[/tex] = [tex]\frac{7}{3}[/tex] x [tex]\frac{2}{3}[/tex] = [tex]\frac{14}{9}[/tex] = [tex]1\frac{5}{9}[/tex]

Therefore, the answer is [tex]1\frac{5}{9}[/tex]

Hope this helps! :D

Answer:= x +27 Solve for x x = 326 = 8 32 ≈ 8.666666667

Answer:

3

Step-by-step explanation:

Answer: Answer is D

Step-by-step explanation:

I just did the question

Answer:

28 mph

Step-by-step explanation:

1h = 60m

45m --- 21 miles

60m --- [tex]\frac{60}{45}[/tex] × 21 miles = 28 miles

Thus, his average speed is 28 mph.

Hi there!

The error in using the diagram to find x in the solving is that they only picked two angles and equated to 180° which is wrong. You'll find out that their final value for x contains a decimal point which should never be in angles.

The above diagram is a revolution (360°) or angle at a point, so all the angles have to be considered and equated to 360° and NOT 180°

Below is the corrected solving.

[tex]13x + 45 + 12x - 40 + 19x + 3 + 6x + 2 = 360[/tex]

(reason: angles at a point = 360°)

Collect like terms, and make x the subject of formula.

[tex]⟹50x + 10 = 360[/tex]

[tex]⟹50x = 360 - 10[/tex]

[tex]⟹50x = 350[/tex]

Now, divide both sides by 50 to find the value of x.

[tex] \frac{50x}{50} = \frac{350}{50} [/tex]

Therefore:

[tex]x = 7[/tex]

Answer:

P" = (-2, -1)

Step-by-step explanation:

When a point P(x, y) is rotated 180° clockwise or anticlockwise the coordinates of the new point P'(x', y') become (-x, -y). The rotated point has coordinates which are negative of the original coordinates

When a point is translated (a, b) then new coordinates become (x + a,, y + b)

Here point P is (1, -1)

Rotation by 180° ⇒ rotated point P'(-1, 1)

If we translate P' by (-1, -2) translated point

P" has coordinates x" = -1 -1 = -2 and y" = 1 -2 = -1

So coordinates of P" are (-2, -1)

Answer:

The probability is 8/48

Step-by-step explanation:

There is a total of 48 marbles and 8 of them are blue.

Answer:a

Step-by-step explanation:

Answer:

2x-1

Step-by-step explanation:

hope you get help from me

Answer: D I think?

Step-by-step explanation:

By using logarithm properties and arithmetic operations, the approximate value of the logarithm of base 4 of 100 is approximately equal to 3.3.

In this problem we find two approximate value of two natural logarithms and we are asked to find the value of a logarithm of base 10 in terms of the two natural logarithms, whose approximate values are given. This can be done by using logarithm properties, especially the base change property:

㏒₄ 100, ㏑ 4, ㏑ 100                                      Given                                              

㏑ 100 / ㏑ 4                                                   Base change property of logarithms

4.6 / 1.4                                                            Substitution of each logarithm (Step 1)

23 / 7                                                               Amplification of fraction / Definition of multiplication

3.286                                                               Definition of division / Result

The approximate value of the logarithm of base 4 of 100 is approximately equal to 3.3.

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Answer:   [tex]\frac{14y}{25x^2}[/tex]

====================================================

Work Shown:

First calculate [tex]\frac{dy}{dx}[/tex] through the use of implicit differentiation.

Don't forget about the chain rule.

[tex]y^5 = x^7\\\\\frac{d}{dx}\left[y^5\right] = \frac{d}{dx}\left[x^7\right]\\\\5y^4\frac{dy}{dx} = 7x^6\\\\\frac{dy}{dx} = \frac{7x^6}{5y^4}\\\\[/tex]

Go back to line 3, shown above, and apply the derivative to both sides.

You'll be using the product rule.

[tex]5y^4\frac{dy}{dx} = 7x^6\\\\\frac{d}{dx}\left[5y^4\frac{dy}{dx}\right] = \frac{d}{dx}\left[7x^6\right]\\\\\frac{d}{dx}\left[5y^4\right]*\frac{dy}{dx}+5y^4*\frac{d}{dx}\left[\frac{dy}{dx}\right] = 42x^5\\\\20y^3*\frac{dy}{dx}*\frac{dy}{dx}+5y^4*\frac{d^2y}{dx^2}=42x^5\\\\20y^3*\left(\frac{dy}{dx}\right)^2+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\[/tex]

Use substitution and isolate [tex]\frac{d^2y}{dx^2}[/tex] to get the following:

[tex]20y^3*\left(\frac{dy}{dx}\right)^2+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\20y^3*\left(\frac{7x^6}{5y^4}\right)^2+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\\frac{196x^{12}}{5y^5}+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\\frac{196x^{12}}{5x^7}+5y^4\frac{d^2y}{dx^2} = 42x^5\\\\[/tex]

[tex]\frac{196x^5}{5}+5y^4*\frac{d^2y}{dx^2}=42x^5\\\\5y^4*\frac{d^2y}{dx^2}=42x^5-\frac{196x^5}{5}\\\\5y^4*\frac{d^2y}{dx^2}=\frac{210x^5-196x^5}{5}\\\\5y^4*\frac{d^2y}{dx^2}=\frac{14x^5}{5}\\\\[/tex]

[tex]\frac{d^2y}{dx^2}=\frac{14x^5}{5}*\frac{1}{5y^4}\\\\\frac{d^2y}{dx^2}=\frac{14x^5}{25y^4}\\\\\frac{d^2y}{dx^2}=\frac{14x^5*x^2}{25y^4*x^2}\\\\\frac{d^2y}{dx^2}=\frac{14x^7}{25y^4*x^2}\\\\\frac{d^2y}{dx^2}=\frac{14y^5}{25y^4*x^2}\\\\\frac{d^2y}{dx^2}=\frac{14y}{25x^2}\\\\[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

We cannot tell what kind of proportionality to assume here.

If x and y are directly proportional, multiplying one by a factor will multiply the other by the same factor.

If x and y are inversely proportional, multiplying one by a factor will divide the other by the same factor.

__

1. Given (x, y) = (2, 24). Direct: y = 9/2(24) = 108.

  Inverse: y = 2/9(24) = 16/3

__

2. Given (x, y) = (25, 18). Direct: y = 30/25(18) = 108/5.

  Inverse: y = 25/30(18) = 15.

__

3. Given (x, y) = (1, 10). Direct: y = 20/1(10) = 200.

  Inverse: y = 1/20(10) = 1/2.

__

4. Given (x, y) = (21, 10). Direct: x = 35/10(21) = 147/2.

  Inverse: x = 10/35(21) = 6.

Answer: slope is 5/4 and y intercept is -7

Y=mx(slope)+b(y-intercept)

Answer: C. 3x^2 + 7x - 6

Step-by-step explanation:

3x^2 + 9x -2x -6

3x^2 + 7 - 6

Hope you got it.

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