Solve for x
7(x-2) < 2x +3
Give your answer as an improper fraction in its simplest form.

Answer: [tex]x=-3z+4, y=-2z+1, z=z[/tex]

Step-by-step explanation:

We have the system:

[tex]x-2y-z=2\\\\-x+3y+3z=-1\\\\-x+4y+5z=0[/tex]

Adding the first and second equations yields [tex]y+2z=1[/tex].

Adding the first and third equations yields [tex]2y+4z=2[/tex].

We know that there are infinitely many solutions, so [tex]y=1-2z[/tex].

Substituting this result back into the first equation,

[tex]x-2(1-2z)-z=2\\\\x-2+4z-z=2\\\\x+3z-2=2\\\\x=-3z+4[/tex]

The solution in term of z variable is; x = 4 - 3z

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We have the linear system:

x - 2y - z = 2

-x + 3y + 3z = -1

-x + 4y + 5z = 0

Adding the first and second equations;

y + 2z = 1

Now Adding the first and third equations yield;

2y + 4z = 2

We know that there are infinitely many solutions, so;.

y = 1-2z

Then Substituting this result back into the first equation;

x - 2y - z = 2

x - 2( 1-2z) - z = 2

x - 2 + 4z - z = 2

x -4 + 3z = 0

x = 4 - 3z

The solution in term of z variable is; x = 4 - 3z

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ1

The fraction which shows what part of packages they have eaten is 3/5.

What is fraction?

A fraction is characterized as a portion of something larger. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.

Main Body:

Total no. of boxes of cereals in a package = 10

Total no. of boxes eaten by family = 6

Fraction  can be calculated by directly by diving the values.

Fraction ⇒ 6/10

dividing by 2 on both denominator and numerator

hence, Simple fraction is 3/5.

to learn more about fraction click on ythe link  below

https://brainly.com/question/17220365

#SPJ9

The solution is

1) Angles 7 and 6 are Vertical angles

2) Angles 1 and 8 are Alternate exterior angles

3) Angles 4 and 5 are Alternate interior angles

4) Angles 2 and 6 are Corresponding angles

5) Angles 6 and 8 are Complementary angles

What are angles in parallel lines?

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.

We can conclude three factors determining parallel lines ,

Given data ,

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.

Each pair of alternate angles around the transversal are equal to each other.

The pairs of angles formed on the same side of the transversal that are either both obtuse or both acute and are called corresponding angles and are equal in size.

Each pair of corresponding angles on the same side of the intersecting transversal are equal to each other.

Co-interior angles on the same side of an intersecting transversal add to 180°

Hence , the angles are

1) Angles 7 and 6 are Vertical angles

2) Angles 1 and 8 are Alternate exterior angles

3) Angles 4 and 5 are Alternate interior angles

4) Angles 2 and 6 are Corresponding angles

5) Angles 6 and 8 are Complementary angles

To learn more about angles in parallel line click :

https://brainly.com/question/27400033

#SPJ1

Step-by-step explanation:

girls:boys

3:1

total=400

1/3 × 400

400/3

=133.33

to whole number

=133 boys

Answer:

The correct answer is 100

The grid has 100 squares and each exercise will be represented by the following percentages:

Percentages refer to the ratio or proportion of a value when compared to the whole.

Percentages are fractional values, computed as a quotient of the part with respect to the whole, and usually expressed over 100.

The percentage sign (%) is used to depict values in percentages.

Exercise          Minutes   Percentage

Endurance:          8                 20% (8/40 x 100)

Strength:            16                 40% (16/40 x 100)

Balance:              4                  10% (4/40 x 100)

Flexibility:          12                 20% (12/40 x 100)

Total                 40                100% (40/40 x 100)

Thus, the percentage representation of the exercises on the grid shows that Endurance occupies 20%, Strength 40%, Balance 10%, and Flexibility 30%.

Learn more about percentage representations at https://brainly.com/question/28515981

#SPJ1

In the grid below, represent the percentage of each exercise.

Answer:

v = 7

Step-by-step explanation:

42 = v + 35

-35        -35

7 = v

The answer is D. 7

I took the quiz and got it right

The age of  Mark and Lynne’s house right now, given the number of years left till the mortgage is paid off is 4 years.

Mark and Lynne’s house is currently aged such that in 20 years when the mortgage is paid off, it will be five times as old as it is now.

Assuming the age of the house right now is x, the age of the house can be shown in an equation as:

20 years = 5x

The age of the house now is therefore:

x = 20 / 5

x = 4 years

Find out more on houses at https://brainly.com/question/27894340

#SPJ1

Answer:

5.39

Step-by-step explanation:

Answer: 9.09%

that is the answer

Step-by-step explanation:

When dealing with transversals, most angles either add to 180 or equal to each other. These angles form a linear pair so they add to 180

[tex](x + 1) + 4x - 36 = 180[/tex]

[tex]5x - 35 = 180[/tex]

[tex]5x = 215[/tex]

[tex]x = 43[/tex]

So

[tex]x + 1 = 43+ 1 = 44[/tex]

[tex]4(43) - 36 = 136[/tex]

Answer:

x + 1 = 44 degrees

4x - 36 = 136 degrees

Step-by-step explanation:

Since the lines are parallel, the angles are same-side-interior angles, which means they are supplementary and add up to 180:

x + 1 + 4x - 36 = 180

5x - 35 = 180

5x = 180 + 35

5x = 215

x = 43

x + 1 = 43 + 1 = 44 degrees

4x - 36 = 4(43) - 36 = 136 degrees

If the length of HJ is 7 unit then the length of EI is 14 unit.

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

We are given a circle with center H.

Therefore, the radius of the circle is found as; HJ

Then the Diameter is the line from one point in the circle to the other point through the center of the circle.

Diameter of the circle = EI

Since we know that One of the theorems of a circle states that the angles in the same segments or on the same chord are equal.

Then the name of the chord is FG.

If the length of HJ is 7 unit then the length of EI is;

EI = 2 HJ

EI = 14 unit.

Learn more about circumference here;

brainly.com/question/12512221

#SPJ1

Considering the function C = 5 + 4e, it is found that:

a. The situation represents a linear function, as the increase in the price is constant for each kwh hour used.

b. The continuous domain of the function is: e ≥ 0.

c. The graph of the function is given by the image shown at the end of the answer.

A linear equation is a special function that has the format of the equation given as follows:

y = mx + b.

The coefficients of the equation y = mx + b are given as follows:

For this problem, the function is:

C(e) = 5 + 4e.

Which is a linear function, as it follows the same format of the general linear function, with a constant cost of 4 per each kwh used.

The domain of the function contains the set of all possible input values of the function. Hence, in this problem, it is composed by the amounts of kwh used, which:

Hence the domain is:

e ≥ 0.

A similar problem, also featuring linear functions, is presented at https://brainly.com/question/24808124

#SPJ1

Answer:

D: x≤-4

Step-by-step explanation:

If its not just reply to me and i will re asses

Answer:

3

Step-by-step explanation:

The value of ex = e2x + 5 is -5.

The mathematical expression f(x)=exp or ex denotes the exponential function. Unless otherwise stated, the term typically refers to the positive-valued function of a real variable. it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.

Given ,

[tex]e^x=e^{2 x}+5[/tex]

By simplifying the exponential rule we get

x= -5

Therefore the value of [tex]e^x=e^{2 x}+5[/tex] is -5

To learn more about exponential function refer to:

https://brainly.com/question/2456547

#SPJ1

Answer:

p = 1

Step-by-step explanation:

Given equation,

→ -8(1 + 4p) + 7p = -25 - 8p

Let's solve for the value of p,

→ -8(1 + 4p) + 7p = -25 - 8p

→ -8 - 32p + 7p = -25 - 8p

→ -32p + 7p + 8p = -25 + 8

→ -17p = -17

→ p = (-17)/(-17)

→ [ p = 1 ]

Hence, the value of p is 1.

For the given points S(2,-9), 7(6, -6), U(9,-7), and V (6, y), the value of y such that ST is perpendicular to UV is -3.

What is the slope of a line?

A line's slope, also known as its gradient, is defined as the value of a line's steepness or direction in a coordinate plane. Slope can be calculated using various methods given a line equation or the coordinates of points on a straight line.

If P(a, b) and Q(c, d) are two given points on a coordinate plane, then the slope of line PQ can be computed using the formula

                        [tex]Slope(m) = \frac{d-b}{c-a}[/tex]

The slope of two perpendicular lines:

If two perpendicular lines are given then the product of their slopes will be equal to -1.

The given points are S(2,-9), 7(6, -6), U(9,-7), and V (6, y).

The slope of line ST   [tex]=\frac{-6-(-9)}{6-2}[/tex]

                                    [tex]= \frac{-6+9}{4}\\ = \frac{3}{4}[/tex]----------------(I)

Now, finding the slope of line UV,

The slope of line UV [tex]=\frac{y-(-7)}{6-9}[/tex]

                                  [tex]=\frac{y+7}{-3}[/tex]  ---------------(II)

Now, by using the property of slopes of two perpendicular lines, we can write

    Slope of line ST × Slope of line UV = -1

                                [tex]\frac{3}{4} *\frac{y+7}{-3}=-1 \\y+7=4\\y=4-7\\y=-3[/tex]

Hence, For the given points S(2,-9), 7(6, -6), U(9,-7), and V (6, y), the value of y such that ST is perpendicular to UV is -3.

To learn more about the slope of two perpendicular lines visit:

https://brainly.com/question/17448083

#SPJ13

Answer:

the answer is that there is 8 percent that they all will spend an hour on the internet.

Step-by-step explanation:

Let W=width of wing

The ratio (Length/Width) is given and is constant, so you can set ratios equal (this is a proportion):

      Length / Width = 8/1 = 32.3/W

 (1) cross-multiply, (2) invert both sides, multiply both sides by one of the denominators ... any legal operation of algebra in order to isolate W.

multiply both sides by (W/8):

                      W = 32.3/8 = 4.04

The equation represents the relationship between the x and y values is y = 2.75x

The first point = (0,0)

The second point = (4,11)

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where m is the slope of the line

[tex](x_1,y_1)[/tex] is the coordinates of the first point

[tex](x_2,y_2)[/tex] is the coordinates of the second point

Substitute the values in the equation

The slope of the line m = (11-0) / (4-0)

= 11 / 4

= 2.75

The slope intercept form is

y = mx + b

m is the slope of the line

b is the y intercept

The equation will be

y = 2.75x

Hence, the equation represents the relationship between the x and y values is y = 2.75x

Learn more about slope intercept form here

brainly.com/question/9682526

#SPJ1

Answer:

[tex]x + 3y = -30:[/tex] Perpendicular to line a

[tex]y = \frac{1}{3} x + 1 :[/tex] Neither Parallel nor Perpendicular to line a

[tex]-3x + y = -2 :[/tex] Parallel to line a

Explanation:

[tex]-3x + y = -4\\y = 3x - 4[/tex]

[tex]x + 3y = -30\\3y = x - 30\\y = \frac{1}{3} x - 10[/tex]

[tex]y = \frac{1}{3} x + 1[/tex]

[tex]-3x + y = -2\\y = 3x - 2[/tex]

Answer:

86

Step-by-step explanation: 89+92+81+x=total score=262+x

avg score = 87= (262+x)/4

262+x=348

.

x=86

.

Check,,,(89,92,81,86)/4 = 87

Answer: 86

Step-by-step explanation:

Answer:

it is £16490.36

Step-by-step explanation:

since £156.78 is 100%, £16470.45 by 3.5 is £16490.36

Answer:

it's 17,046.92

Step-by-step explanation:

that's what my calculations said

Answer:

233 is a Fibonacci number

Step-by-step explanation:

The radius is the distance from the center to a point on a circle.

The diameter is twice the radius.

1. 3 yd, 6 yd

2. 46 in, 92 in

3. 23 ft, 46 ft

Answer:

when x = 3

8(3)

8*3=24

all you have to do is to substitute x into the expression

Answer:

---------------------

Initial number of pairs of shoes is 20.

To achieve 50 pairs Mindy needs 30 more pairs.

Each week 2 pairs added but 1 removed. It makes total of 1 pairs addition.

After 28 weeks Mindy will have 20 + 28 = 48 pairs of shoes.

The next week he will purchase 2 more pairs and get 50 pairs in total.

The number of weeks it will take for her closet to have 50 pairs of shoes would be = 30 weeks.

A purchase price is the amount of money that was use to obtain a valuable.

The number of shoes owned by Mindy = 20 pairs

The number of shoes Mindy purchases per week = 2 pairs

The number of shoes Mindy destroys = 1 pair.

Therefore, in a week Mindy has an additional 1 pair of shoe.

The number of pairs she needs extra = 50-20 = 30

Since 1 pair of shoe = 1 week, she will require 30 weeks to purchase additional 30 pairs making it up to 50 pairs of shoes she owns.

Learn more about purchase here:

https://brainly.com/question/27975123

#SPJ1

Kevin needs to read 57 novels in 19 months.

Given,

The number of novels Kevin needs to read in a month = 3

N = Number of novels Kevin needs to read in M months.

Write an equation with M and N.

That is,

Kevin needs to read 3 novels in one month.

So, number of novels, N Kevin reads in M months,  3M = N

The equation is;

3M = N

Now,

The number of months Kevin needs to read the novels = 19

Then,

The number of novels Kevin reads in 19 months;

3M = N

3 × 19 = 57

That is,

Kevin needs to read 57 novels in 19 months.

Learn more about number of novels here;

brainly.com/question/14329352

#SPJ1

The number of degrees does it move in 2 1/5 hours is -66°.

From the information given, it was illustrated that the hour hand of a clock moves −30° every hour.

Therefore, to calculate the degree for a number of hours, we simply have to multiply.

In this case, to get the degree for 2 1/5 hours will be:

= Degree every hour × Number of hours

= -30° × 2 1/5

= -30° × 2.2

= -66°

Learn more about time on:

brainly.com/question/26046491

#SPJ1

Answer:

9.995%

Step-by-step explanation:

principal-10760

n(time)-17

rate-?

amount-54343

[tex]a = p(1 + \frac{r}{100} ) {}^{n} [/tex]

54343=10760(1+(r/100))^17

5.05=(1+(r/100))^17

1.09995=1+(r/100)

0.09995=r/100

r=9.995%

Answer: First, I substituted x for 11. -2 times 11 = -22. -22 + 5 equals -17. Therefore, f(11) or y, is equal to -17.

Step-by-step explanation:

The total pay change for each issue of Math is Fun sold by Carlos is $110. If he doesn't sell copies of Math is Fun, Carlos's gross wages are $2500 for him.

Given that:

x represents the number of copies of Math is Fun he sells. Suppose that x and y are related by the equation 2500 + 110x = y.

Equation: The equation is the values of two expressions that are equal.

Here,

For equation,

y = 2500 + 110x

The change in Carlos's total pay for each copy of Math is Fun he sells,

Differentiate the equation,

dy/dx = 110

The total pay for each copy of Math is Fun he sells is $110.

Carlos's total pay if he doesn't sell any copies of Math is Fun,

x = 0

y = 2500

Carlos's total pay if he doesn't sell any copies of Math is Fun is $2500.

Thus, the change in Carlos's total pay for each copy of Math is Fun he sells is $110. Carlos's total pay if he doesn't sell any copies of Math is Fun is  $2500.

Learn more about the equation here:

brainly.com/question/10413253

#SPJ1