Solve the equation.
1/3 (
(9x + 3) = 3x + 1

The length of the side RS in triangle RST as required to be determined in the task content is; 12 units.

The distance between two points defined by pairs of coordinates on the Cartesian plane can be determined by a modification of the Pythagoras theorem.

Hence, the distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is:

AB= √{(y₂ - y₁)² + (x₂ - x₁)²}

Given that the vertices R and S of the triangle is at R(−3,3), S(-3,-9), hence:

RS= {( -9-3 )² + ( -3-(-3))² } = 12 units.

The length of the side RS in triangle RST is 12 units.

Read more on distance between points:

https://brainly.com/question/24578913

#SPJ1

log₄x²y³ = log x² + log y² is solution of this logarithmic function.

What is an example of a logarithmic function?

What distinguishes exponential from logarithmic growth?

we use property [ log ( mn) = log +  log n ] in equation -

log₄x²y³ = log x² + log y²

Learn more about exponential functions

brainly.com/question/11487261

#SPJ4

x = 4 is an extraneous solution.

√(5-x) -√x=1

√(5-x) = 1 + √x

Squaring both sides of the equations, we get

(√(5-x))² = (1 + √x)²

5 - x = 1 + x + 2√x

4 - 2x = 2√x

Squaring again both sides of the equations, we get

(4 - 2x)² = (2√x)²

16 + 4x² - 16x = 4x

4x² - 20x + 16 = 0         ...(1)

By middle term splitting equation (1) can be written as

4x² - 16x - 4x + 16 = 0  

4x(x - 4) -4(x - 4) = 0  

(x - 4) (4x - 4) = 0

4x - 4 = 0 and x - 4 = 0

x = 1 and 4

Check for Extraneous solution by putting value of x in the original equation -

Let x = 1

√(5-1) -√1=1

√4 - 1 = 1

2 -1 = 1

1 = 1

Since, LHS = RHS, so, x = 1 is not an extraneous solution

Let x = 4

√(5-4) -√4=1

√1 - 2 = 1

1 - 2 = 0

-1 = 0

which is a contradiction, so, x = 4 is an extraneous solution.

Know more about extraneous solution:

brainly.com/question/1511979

#SPJ4

2nm = 2e-7 cm or written out 0.0000002 cm

To convert nm to cm, you have to divide the value by 1e+7 (10000000).

Two parallel lines have equal slope.

Therefore, slope of line y = -2/9x + 6 is equal to the slope of the line joining the points (3,2).

Slope of line is given by :

m= -[(coefficient of x) / (coefficient of y)]

Where m= slope,

Slope of line y = -2/9x + 6

2/9x + y = 6

(m1) slope of equation g = -x/y

                                     = -(2/9)/1

                                     = -2/9

Since equation h is parallel to g

So, m1=m2

That is slope of equation h=slope of equation g

We know,

Equation of the line h having slope=m2= -2/9

passing through the slope of the point (3,2) is,

       y-y1=m(x-x1)

Replace with values x1,y1=(3,2) and m=-2/9

      y-2=(-2/9)(x-3)

We can solve it :      

       9y-18=-2x+6

       2x+9y=6+18

       2x+9y=24

       2x+9y-24=0

Hence,

     2x+9y-24=0 is the equation of h.

Therefore,

Line g has an equation of y = -2/9x + 6. Parallel to line g is line h, which passes through the point (3, 2), then the numbers in the equation of line h is 2x+9y-24=0

Learn more about event correlation here: brainly.com/question/15935155

#SPJ9

Answer:

the answer is false

Step-by-step explanation:

this is an example: 22+1=23  23 is not an even number

Answer:

B. False

Step-by-step explanation:

Let the even number be x_e and odd be x_o

[tex]{ \tt{ = x _{e} + 1}}[/tex]

Assume the range is 2 ≤ x ≤ 4

[tex]{ \tt{x _{2} = 2 + 1}} \\ { \tt{x_{2} = 3 \: (odd)}}[/tex]

[tex]{ \tt{ x_{4} = 4 + 1}} \\{ \tt{x _{4} = 5 \: (odd)}}[/tex]

Therefore:

[tex]{ \tt{x _{n + 1} = x _{e} + n \: \: gives \: odd}}[/tex]

Hence;

[tex]{ \tt{ x_{e} + 1 = x _{o} }}[/tex]

Answer:

2. 7x^2 + 4x + 2x

4. -x - 6

6. 4x^2

8. 7x - 2

10. 10x^2 + 5

PLEASE MARK AS BRAINLIEST!!!

Answer:

-3.625 < -3.62

Step-by-step explanation:

Answer: Yes √35 +5 is a rational number

Step-by-step explanation:

A rational number is any number that is a fraction, decimal, repeating decimal, or negative decimal.

Answer:

75% filled

Step-by-step explanation:

Each triangle is 50%.

Half of 50% is 25%.

One full triangle, 50%, plus one half triangle, 25%, add up to 75% percent of the two triangles being filled.

The standard deviation of the response time is 1.2755 minutes.

Based on the information, the response times for a certain ambulance company are normally distributed with a mean of 12.5 minutes. Ninety-five percent of the response times are between 10 and 15 minutes.

The standard deviation of the response time will be illustrated thus:

It should be noted that the area under the one tailed standard normal curve is given as:

P(0 <= Z <= 1.96) = 0.475

The standards deviation will be:

= 2.5 / 1.96

= 1.2755

Learn more about normal distribution on:

brainly.com/question/4079902

#SPJ1

The response times for a certain ambulance company are normally distributed with a mean of 12.5 minutes. Ninety-five percent of the response times are between 10 and 15 minutes. What is the standard deviation of the response time?

If the equation 8x+7y=6 is a true equation, then  the value of the equation 5+8x+7y is 11

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The equation is given as

8x + 7y = 6

The above equation is said to be true

The next step is to add 5 to both sides of the equation 8x + 7y = 6

So, we have

5 + 8x + 7y = 6 + 5

Evaluate the sum of the like terms

So, we have

5 + 8x + 7y = 11

Hence, if the equation 8x+7y=6 is a true equation, then  the value of the equation 5+8x+7y is 11

Read more about linear equations at

https://brainly.com/question/14323743

#SPJ1

Answer: Papst blue ribbon

Step-by-step explanation:

Ryan lives in a trailer park. He likes to drink papst blue ribbon and not wear satin robes.

Since the difference between consecutive terms is the same, the sequence is an arithmetic sequence, hence Mai is correct.

The sequence is missing, and has these following information:

We also have that:

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

From the values os the function, we have that:

The rate of change is the same, hence sequence is an arithmetic sequence, and Mai is correct.

More can be learned about arithmetic sequences at https://brainly.com/question/6561461

#SPJ1

The best there terms of the sequence will be:

a. 10, 16

b. 211, 311

c. 10 , 12.5

d. -13, -22

It should be noted that in an arithmetic sequence, there is a constant difference, which is the difference between a term and the previous term.

We find the constant difference for each sequence, and we add it to the second term to find the third term. Then we add the constant difference to the third term to find the fourth term.

a. 4 - (-2) = 6

3rd term: 4 + 6 = 10

4th term: 10 + 6 = 16

b. 111 - 11 = 100

3rd term: 111 + 100 = 211

4th term: 211 + 100 = 311

c. 7.5 - 5 = 2.5

3rd term: 7.5 + 2.5 = 10

4th term: 10 + 2.5 = 12.5

d. -4 - 5 = -9

3rd term: -4 + (-9) = -13

4th term: -13 + (-9) = -22

Learn more about sequence on

https://brainly.com/question/6561461

#SPJ1

Here are the first two terms of some different arithmetic sequences:

a. -2,4

b. 11, 111

C. 5, 7.5

d. 5,-4

What are the next three terms of each sequence?

Answer:

0.119

Step-by-step explanation:

Based on the concept of conditional probability, the probability that the first iPod is defective and the others are not defective is approximately 0.1842

Conditional Probability is a term that is used to describe the chances that some outcome occurs given that another event has also occurred.

Generally, the functional probability is often stated as the probability of B given A and is written as P(B|A), where the probability of B depends on that of A happening

In this case, to find the answer we break down the problem step by step:

Step 1: Find the probability that the first iPod is defective.

Since there are 3 defective iPods out of 20 total the probability of selecting a defective iPod on the first draw is 3/20.

Step 2: Find the probability that the second and third iPods are not defective.

After selecting a defective iPod there are 19 remaining iPods in the box out of which 17 are not defective.

Hence, the probability of selecting a non-defective iPod on the second draw is 17/19.

Also, given that the probability of selecting a non-defective iPod on the third draw (assuming the previous two iPods were not defective) is 16/18.

Step 3: Finding the overall probability.

The overall probability of the first iPod being defective and the second and third iPods being non-defective can be computed by multiplying the probabilities of each step:

Probability = (3/20) * (17/19) * (16/18)

= (51/380) * (16/18)

= 0.1842105

Therefore, in this case, it is concluded that the correct answer is approximately 0.1842 or 18.42%.

Learn more about Conditional Probability here: https://brainly.com/question/10739997

#SPJ2

The solution of the system of equation by elimination method is (-3, 3)

The system of equation can be solved using substitution, elimination and graphical method.

But we are asked to use elimination method.

Therefore,

2x + 6y = 12

2x - 3y=  - 15

Subtract equation(i) from equation(ii)

Therefore,

6y - (-3y) = 12 - (-15)

6y + 3y = 12 + 15

9y = 27

y = 27 / 9

y = 3

Therefore,

2x - 3y =  - 15

2x - 3(3) = - 15

2x - 9 = - 15

2x  = - 15 + 9

2x  = -6

divide both sides by 2

x = - 6 / 2

x = -3

Therefore, the solution of the system of equation by elimination method is (-3, 3)

learn more on system of equation here: https://brainly.com/question/26450455

#SPJ1

Answer:

112

Step-by-step explanation:

Find the lowest common multiple of 14 and 16.

To find the lowest common multiple:

1) Break the numbers down into their prime factors.

14 = [tex]2^{1}[/tex] x [tex]7^{1}[/tex]

16 = 2 x 8 = 2 x 2 x 4 = 2 x 2 x 2 x 2 =  [tex]2^{4}[/tex]

2) Multiply the highest power of each prime number.

We have three numbers, but only two are unique:  [tex]2^{1}[/tex] , [tex]7^{1}[/tex] and  [tex]2^{4}[/tex]

  [tex]2^{4}[/tex] >  [tex]2^{1}[/tex] , so we will use  [tex]2^{4}[/tex]

[tex]7^{1}[/tex] x  [tex]2^{4}[/tex] = 7 x 16 = 112

The constant of variation is 3.6

The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity. That means, we can say that if one values will increase then other will automatically decrease and vice versa.

Let say if x and y are two values and k is a constant value, then

According to inverse variation

k = xy or y = k/x

In the given question,

Take the order pair (0.9,4)

As it is an inverse variation, we can substitute it

y=k/x  

Now find the constant of variation

4=k/0.9

K=3.6

Therefore, constant of variation is 3.6

To know more about inverse variation and values, visit :

brainly.com/question/14632732

#SPJ4

The simplest form of the expression [tex]\frac{5+\sqrt{3} }{2-\sqrt{3} }[/tex] is [tex]13+7\sqrt{3}[/tex].

The simplest form of a fraction is one with a reasonably prime denominator and numerator. It indicates that, except for 1, there is no common factor between the fraction's numerator (upper portion or top) and denominator (lower part or bottom).

In elementary algebra, the procedure of rationalization is performed to get rid of the irrational number in the denominator. There are several methods for rationalizing the denominator.

An expression comprises a variable, a number, or a combination of a number, a variable, and operation symbols. An equation is created by joining two expressions with an equal sign.

Consider the expression,

[tex]\frac{5+\sqrt{3} }{2-\sqrt{3} }[/tex]

Rationalizing the denominator,

[tex]\frac{5+\sqrt{3} }{2-\sqrt{3} } = \frac{5+\sqrt{3} }{2-\sqrt{3} } \times \frac{2+\sqrt{3} }{2+\sqrt{3}}[/tex]

[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} =\frac{(5+\sqrt{3})(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3})}[/tex]

Using the identity,

( a + b )( a - b ) = a² - b²

Therefore,

[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} =\frac{5 \times 2 + 5 \times \sqrt{3} + \sqrt{3} \times 2 + (\sqrt{3} )^{2}}{(2)^{2}-(\sqrt{3} )^{2}}[/tex]

[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = \frac{10+7\sqrt{3}+3}{4-3}[/tex]

[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = \frac{13+7\sqrt{3}}{1}[/tex]

[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = 13+7\sqrt{3}[/tex]

Learn more about expression here:

https://brainly.com/question/4344214

#SPJ9

The value of m<1 is 65 degrees

From the diagram shown, we have that;

It is important to note that angles on a straight line sum up to 180 degrees

Also, corresponding angles are equal

Then, we have that;

m<2 + m<3 = 180°

Substitute the values

9x + 7 + 5x + 5 = 180

collect like terms

14x = 180 - 12

14x = 168

Make 'x' the subject

x = 168/ 14

x = 12

We have that;

m<3 = 5x + 5 = 5(12) + 5 = 60 + 5 = 65

But m<3 = m<1

m<1 = 65

Thus, the value of m<1 is 65 degrees

Learn more about corresponding angles here:

https://brainly.com/question/2009183

#SPJ1

Answer:

The larger figures are 3 times the size of the smaller figures.

Scale factor = 3?

Step-by-step explanation:

Answer:

The scale factor is 3 :)

Step-by-step explanation:

The smaller figure multiplied by 3 is the larger figure.

The true statement about the graph of the parabola inequality given as y < x^2 + 2x - 6 is (b) the vertex is located at (-1,-7)

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The parabola inequality is given as

y < x^2 + 2x - 6

Next, we plot the graph of the parabola inequality

To plot this graph, we simply enter the inequality y < x^2 + 2x - 6 in a graphing calculator

From the attached graph, we can see that the vertex of the parabola inequality is at (-1, -7)

Hence, the true statement about the graph of the parabola inequality given as y < x^2 + 2x - 6 is (b) the vertex is located at (-1,-7)

Read more about parabola at

https://brainly.com/question/1480401

#SPJ1

The result of simplifying the number 32¹.² using the exponent rules is 1024

To solve this exercise we have to resolve algebraic operations following the exponent rules.

Note the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:

(32¹)²

32⁽¹*²⁾ =

32² =

32 * 32 =

1024

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

Learn more about exponent at: brainly.com/question/847241

#SPJ4

The domain and the range are  −∞ < x < ∞ and −∞ < y < ∞ while the intercept is (2, 0)

The domain of the function is the set of input values of the graph

The range of the function is the set of input values of the graph

The function is given as

g(x) = 3x + 6

The above function is a linear function

This means that the domain and the range of the function are the set of all real values

i.e. −∞ < x < ∞ and −∞ < y < ∞

Calculate x when g(x) = 0 to determine the x-intercept

So, we have

3x + 6 = 0

Divide through by 3

x + 2 = 0

This gives

x = -2

Hence, the domain and the range are  −∞ < x < ∞ and −∞ < y < ∞ while the intercept is (2, 0)

Read more about domain and range at

https://brainly.com/question/2264373

#SPJ1

Answer:

10m + 100 = 15m

20 movies

Step-by-step explanation:

Hello!

Let the number of movies watched be m.

The equation for the first movie club would be 10m + 100, as you pay 10 dollars per movie (10*m) and you add the original membership fee (100).

The equation for the second movie club is 15m, 15 dollars per movie. Set the equations equal to each other and solve for m, the number of movies, so the price would be equal.

Therefore, you would need to watch 20 movies in each movie club for the total price to be equal.

In linear equation , the car y's price changes the most.

What are a definition and an example of a linear equation?

According to the question

a)  Car x : £ 10320  ≈  £ 10300        10320 - 10300 = 20

    Car y  : £ 15430 ≈ £ 15400          15430 - 15400 = 30

    Car z   :  £ 17490 ≈  £ 17500        17490 - 17500  = 10

                   10 < 20 < 30

so the car y's price changes the most.

b) this car's price change £ 30

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

Answer:

D) 7

Step-by-step explanation:

The answer is D because A, B, and C are not considered numbers that are natural, whole, integers, or fractional. Irrational numbers are numbers that cannot be quantified any other way, do not have repeating decimals, and never end. A good example of this is π or 3.14159265.... you get the picture.

Hope this helps!

The inequality is: 14.2 + 14.2 + x < 51.3

x < 22.9

We are given the following:

Perimeter of the triangle < 51.3 in.

The sides are 14.2 in., x in., and 14.2 in.

Therefore, we would have the following inequality:

14.2 + 14.2 + x < 51.3

Solve for x

28.4 + x < 51.3

x < 51.3 - 28.4

x < 22.9

Learn more about inequality on:

https://brainly.com/question/11613554

#SPJ1