Graph the following system of equations.

y = 3x + 9
6x − 2y = 6

What is the solution to the system?

A There is no solution.
B There is one unique solution (−1, −6).
C There is one unique solution (0, −3).
D There are infinitely many solutions.

[tex]\huge\begin{array}{ccc}\left(\frac{f}{g}\right)(x)=x\sqrt{3x+3};&x\in[-1,\ \infty)\end{array}[/tex]

We have:

[tex]f(x)=\sqrt{3x+3}[/tex]

and

[tex]g(x)=\dfrac{1}{x}[/tex]

Create the domains:

[tex]D_f:\\\\3x+3\geq0\\\\3x+3-3\geq0-3\\\\3x\geq-3\\\\\dfrac{3x}{3}\geq\dfrac{-3}{3}\\\\\boxed{x\geq-1\to x\in[-1,\ \infty)}[/tex]

[tex]D_g:\\\\x\neq0\\\\\boxed{x\in\mathbb{R}-\{0\}}[/tex]

Solution:

[tex]\left(\dfrac{f}{g}\right)(x)=\dfrac{\sqrt{3x+3}}{\frac{1}{x}}=\sqrt{3x+3}\cdot\dfrac{x}{1}=x\sqrt{3x+3}[/tex]

Answer:

its 2 i think

Step-by-step explanation:

Answer: Infinite number of solutions

Step-by-step explanation: The graph has arrows at the end indicating it will go to infinity.

The answers are a) (f+g)x = 4x+15, b) 39 and c) the animals adopted in 6 months are 24 and there were already 15 animal at the shelter.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) is called a function.

Given that, the function f(x) = 3x + 10 represents the number of animals adopted at one shelter, and the function g(x) = x + 5 represents the number of animals adopted at another shelter, where x is the number of months.

a) (f+g)x = f(x) + g(x)

= 3x+10 + x+5

= 4x+15

∴ (f+g)x = 4x+15

b) (f + g)(6)

Put x = 6 in (f+g)x = 4x+15

∴ (f + g)(6) = 4(6)+15

= 24+15

= 39

c) It means, the animals adopted in 6 months are 24 and there were already 15 animal at the shelter.

Hence, the answers are a) (f+g)x = 4x+15, b) 39 and c) the animals adopted in 6 months are 24 and there were already 15 animal at the shelter.

Learn more about functions, click;

https://brainly.com/question/12431044

#SPJ1

Answer:

Step-by-step explanation:

Part A: (f + g)(x) = 4x + 15.

My work for Part A:

Step 1: Write the functions without the parentheses: x + 5 + 3x + 10 .

Step 2: Rewrite the function so like terms are next to each other: x + 3x + 5 + 10.

Step 3: Combine like terms: x + 3x = 4x, and 5 + 10 = 15.

Step 4: Write the final function in standard form: (f + g)(x) = 4x + 15.

Part B: (f + g)(6) = 39.

My work for Part B:

Step 1: Write the first function substituting x for 4: f(6) = 6 + 5.

Step 2: Solve the function: f(6) = 6 + 5 = 11.

Step 3: Write the final answer for the first function: f(6) = 11.

Step 4: Write the second function substituting x for 4: g(4) = 3 x 6 + 10.

Step 5: Solve the function: g(4) = 3 x 6 = 18, and 18 + 10 = 28.

Write the final answer for the second function: g(4) = 28.

Step 6: Add the output answers together: 11 + 28 = 39.

Step 7: Write the final output answer for both functions: (f + g)(4) = 39.

Part C: 39 represents the total number of animals adopted at two shelters in 6 months.

The area of a circle is [tex]A = πr2[/tex], where A is the area, π is 3.14, and r is the radius of the circle.

Prefix: Self - referring to one's self or own self;

Suffix: -produce - to create, make or cause something;

Word Root: Color - the sensation of light that is seen by the eye;

Prefix: Both/Double - referring to two or more;

Suffix: -single - indicating one only;

Prefix: Without/Lack of/Not - indicating the absence of something;

Word Root: Body - referring to the physical structure or anatomy of a living organism;

Word Root: Chromosomes - a thread-like structure made up of DNA found in the nucleus of cells;

Suffix: -small - indicating a size that is lesser than the average.

For example, let's say we want to calculate the area of a circle. We can use the formula [tex]A = πr2[/tex], where A is the area, π is 3.14, and r is the radius of the circle. We can plug in the numbers to calculate the area: [tex]A = 3.14 × 42 = 50.24 cm2[/tex]. This formula allows us to calculate the area of the circle with accuracy, and also allows us to use it for different shapes

The formula and calculation used to calculate the area of a circle is [tex]A = πr2[/tex], where A is the area, π is 3.14, and r is the radius of the circle.

Learn more about area of the circle here:

https://brainly.com/question/27251790

#SPJ4

All the roots of the function will be -5, 5, and -10. Then the correct option is D.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The function is given below.

f(x) = x³ + 10x² - 25x - 250

Factorize the equation, then we have

f(x) = x³ + 10x² - 25x - 250

f(x) = x²(x + 10) - 25(x + 10)

f(x) = (x² - 5²)(x + 10)

f(x) = (x + 5)(x - 5)(x + 10)

Then the roots of the function are given as,

f(x) = 0

(x + 5)(x - 5)(x + 10) = 0

x = -5, -10, 5

All the roots of the function will be -5, 5, and -10. Then the correct option is D.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ1

The simplest form of the ratio is given as 15 cm : 106 mm

We would have to divide the values by  a factor that is common to both the numerator and the denominator.

Hence we would have to divide through both sides of the equation by 10

150 / 10 : 1060 / 10

= 15 : 106

The ratio 150 cm: 1060 mm can be written as 15:106 in its simplest form. To simplify the ratio, both numbers are divided by the greatest common factor which is 10 in this case.

Read more on ratios here:https://brainly.com/question/12024093

#SPJ1

Answer:

10

Step-by-step explanation:

find GCF for both numbers

150=2*3*5*5

1060=2*2*5*53

multiply all common ones:2*5=10

Mean is 121.4, standard ,the deviation is 13. 21, variance is 175.47, minimum is 95, median is 118.

Here is an estimate of the order of a given intelligence level:

a. mean (normal):

mean can be found by including all scores and dividing by the number of scores:

mean = (141 + 139 + 126 + 122 + 125 + 130 + 95 + 110 + 118 + 118)/10 = 121.4

center:

b. median

if the scores are ordered ascending, center is the center score:

95, 110 , 118, 118, 122 , 125, 126, 130, 139, 141

Median = 118

c. Standard Deviation:

The standard deviation indicates how spread out the information is. Here's a recipe for finding the standard deviation:

Standard Deviation = sqrt(Variance)

d. Variation:

Variation is the proportion of variation in the set of information. The recipe for determining the change is:

Variance = (amount of ((each score - average)^2)/(number of scores - 1)

connect the numbers obtained:

Variance = (( ( amount of each score - ) 121.4)^2)/(10 - 1)

Variance = 1579.

24/9 = 175.47

standard deviation = sqrt(variance) = sqrt(175.47) = 13.21

e. minimum:

base is information gathering minimum:

minimum = 95

so, mean is 121.4, standard The deviation is 13. 21, difference is 175.47, base is 95, middle is 118

To learn more about statistics and probability, refer:

https://brainly.com/question/26146867

#SPJ4

The complete question is:

Below are the iq test scores of 10 randomly chosen fifth-grade students. 141 139 126 122 125 130 95 110 118 118. calculate a. mean b. median c. standard deviation d. variance e. minimum.

The  probability that they both take shapes 3 / 8.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that there are five shapes, Four of the shapes are squares and one of the shapes is a circle, One square is black, three squares are white, circle is black.

Jasmine takes a shape at random from the bag 150 times

3 / 5 ×150 = 90 times.

If Alec takes a shape at random from the bag and does not replace it, there are now 4 shapes left in the bag.

The probability that they both take a square is 3 / 4 × 3 / 3 = 3 / 4.

The probability that Bashir takes a square is 2 / 4 = 1 / 2.

If Alec takes a circle, the probability that Bashir takes a square is 3 / 4. The overall probability that they both take shapes

(3 / 4) × (1 / 2) + (1 / 4)× (3 / 4) = 3 / 8.

Hence, the  probability that they both take shapes 3 / 8.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ1

The angle ∠Bm is equal to the measure of the angle in degrees rounded to the nearest degree.

The angle is the amount of deviation from a straight line. It is measured in degrees, with a full circle being 360 degrees. Angles can be either acute, obtuse, right, or reflex. An acute angle is less than 90 degrees, an obtuse angle is greater than 90 degrees but less than 180 degrees, a right angle is exactly 90 degrees, and a reflex angle is greater than 180 degrees but less than 360 degrees. Angles can be used in a variety of ways, from measuring distances and directions to constructing shapes and figures. They are an important part of mathematics and can provide a useful way of understanding the world around us.

To find this, calculate the measure of the angle in degrees and then round it to the nearest degree.

To learn more about angle visit :-

brainly.com/question/25716982

#SPJ1

Find m∠B

Note that

m∠B is acute. Round to the nearest degree.

The value of x in parallelogram ABCD is equal to 7.

In Mathematics, a parallelogram simply refers to a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

In this context, we can reasonably infer and logically deduce that this parallelogram has both pairs of opposite sides being parallel to each other and the opposite angles (vertical angles) are equal and congruent:

x + 3 = 2x - 4

2x - x = 3 + 4

x = 7.

Read more on a parallelogram here: brainly.com/question/19196707

#SPJ1

Answer:

The first five terms of the recursive sequence are:

an = 3an-1 + 3

a1 = 9

a2 = 3a1 + 3 = 3 * 9 + 3 = 30

a3 = 3a2 + 3 = 3 * 30 + 3 = 93

a4 = 3a3 + 3 = 3 * 93 + 3 = 282

a5 = 3a4 + 3 = 3 * 282 + 3 = 849

So the first five terms are: 9, 30, 93, 282, 849.

Step-by-step explanation:

a) The probability that the married couples will have 0, 1, 2, 3, or 4 preferences in common is as follows:

b) Yes, the probabilities add up to 1.

c) The above result does make sense. The table values add up to 375 as the probabilities sum up to 1.

d) The sample space in this problem is C. 0, 1, 2, 3, 4 personality preferences in common.

Probability refers to the odds, chance, or likelihood of an expected outcome occurring given many possible outcomes.

Probability is a fractional value, lying between 0 and 1, in most instances, except when it is 100% uncertain or certain.

Random Sample = 375 married couples

Number of Similar     Number of              Probability of

  Preferences        Married Couples   Common Preferences

     All four                        26                       6.93% (26/375)   or 0.07

     Three                         120                    32.00% (120/375) or 0.32

     Two                            113                     30.13% (113/375)   or 0.30

     One                             61                     16.27% (61/375)     or 0.16

    None                           55                     14.67% (55/375)    or 0.15

Total                               375                     100%                      or  1  

Learn more about probabilities at https://brainly.com/question/13604758

#SPJ1

The variance of P + Q or  Var(P + Q) for given random variables is 14.

Since X and Y are independent N(0,1) random variables, we have Variance of X = 1 and Variance of Y = 1.

Given, P = 3X + XY

Variance of P = Variance of 3X + Variance of XY

= 9 + Variance of X * Variance of Y + 2 * Covariance(X,Y)

= 9 + 1 * 1 + 2 * Covariance(X,Y)

= 10

Given, Q = 2X

Variance of Q = Variance of 2X

= 4 * Variance of X

= 4

Variance of P + Q = Variance of P + Variance of Q

= 10 + 4

= 14

Therefore, the variance of P + Q = 14.

Learn more about Variance here:

https://brainly.com/question/9304306

#SPJ4

[tex]\cfrac{4}{5}\div\cfrac{3}{4}\implies \cfrac{4}{5}\cdot \cfrac{4}{3}\implies \cfrac{16}{15}[/tex]

Answer:

Second choice

0.23

Step-by-step explanation:

Total number of students = 1 + 8 + 2 + 5 + 9 + 7 + 3 =35

Out of these 35 students, 8 studied for exactly one hour

P(a randomly picked student studied for exactly 1 hour
= 8/35

= 0.22857

= 0.23 rounded to nearest hundredth

This is the second choice among those provided

Answer:

The probability that a student studied for exactly 1 hour is 0.38. This is calculated by dividing the number of students who studied for 1 hour (8) by the total number of students surveyed (35).

Probability = Number of successful outcomes / Total number of outcomes

= 8 / 35

= 0.23

The solution is Option C.

The value of the equation is -6 + 3x = 2 + 4x

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Elena and Kiran play a card game. Every time they collect a pair of matching cards, they earn x points.

At one point in the game, Kiran has -6 points and Elena has 2 points.

After Elena collects 3 pairs and Kiran collects 4 pairs, they have the same number of points

-6 + 2 ( x ) pairs = 2 + 4 ( x ) pairs

Therefore , the equation is x = -8

Hence , the equation is -6 + 3x = 2 + 4x

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

The value of x and y from the given right triangle are 13 units and 18.38 units respectively.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

We know that, cosθ= Base/Hypotenuse and sinθ= Perpendicular/Hypotenuse

Now, cos45°= 13/y

0.7071= 13/y

y =13/0.7071

y =18.38 units

Here, sin45°= x/y

0.7071=x/18.38

x= 18.38×0.7071

x= 12.99

x≈13 units

Therefore, the value of x and y are 13 units and 18.38 units respectively.

Learn more about the trigonometric ratios here:

brainly.com/question/25122825.

#SPJ1

The factors of the cubic function f(x) = 27x³ + 8 are ( 3x + 2) and ( 9x² - 6x + 4 ).

Given the function in the question;

f(x) = 27x³ + 8

To determine the factors, first rewrite 27x³ as (3x)² and 8 as 2³

27x³ + 8

(3x)² + 2³

Since both terms are perfect cubes, factor using the sum of cubes formula.

a³ + b³ = (a+b)(a² - ab + b² )

Here, a = 3x and b = 2

Plug in these values

(a+b)(a² - ab + b² )

( 3x + 2)( (3x)² - (3x)×2 + 2² )

Simplify

( 3x + 2)( (3x × 3x) - (3x)×2 + 2² )

( 3x + 2)( 9x² - 6x + 4 )

Therefore, the factors are ( 3x + 2) and ( 9x² - 6x + 4 ).

Learn more about sum of cubes formula here: https://brainly.com/question/10367382

#SPJ1

Answer:

162

Step-by-step explanation:

Systematic sampling involves selecting every nth item from a list, potentially with bias and non-random results, so choose carefully.

The method used to choose the sample in this study is called "systematic sampling". This involves selecting a starting point (in this case using a random number generator) and then selecting every nth item (in this case, every 3rd person) from a list to form the sample. This type of sampling can introduce biases in the sample if the list has some pattern or structure, so it's important to be aware of these potential issues when using this method.

In systematic sampling, the selection of each member of the sample is based on a fixed and systematic rule. The advantage of this method is that it is easy to implement and cost-effective. The disadvantage is that if the list has any pattern or structure, such as alternation or clustering, the sample may not be representative of the population. It's important to carefully consider the list and choose an appropriate starting point and interval to reduce the potential for bias.

It's also worth noting that systematic sampling may not result in a random sample, as the sample members may not be independent of each other. This can have implications for the validity of inferences made from the sample to the population. Therefore, it's important to carefully consider the properties of the population and the goals of the study when choosing a sampling method.

Learn more about systematic sampling here:

https://brainly.com/question/28454088

#SPJ4

The rearrangement of Tue following words to make a meaningful sentence is as follows:

A sentence is defined as the a group of words that is made up of a subject, a verb and punctuation marks which are used to create a meaning to the sentence.

The restructuring of the given sentence above would be shown below as follows:

Learn more about sentence here:

https://brainly.com/question/27275966

#SPJ1

The equation representing the number of beads varies directly with the number of inches of the string is y = 9x.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

Given, The number of beads varies directly with the number of inches of string.

Therefore, y ∝ x.

y = kx.

From the table,

18 = 2k.

k = 9.

So, y = 9x.

learn more about proportion here :

https://brainly.com/question/7096655

#SPJ1

X + Y is continuous with density function fx+y(t) = |sx.x(8,6-u)|dxdy.

Let X and Y be jointly continuous random variables with joint density function fx,y(x,y). The density function of the sum of X and Y, X + Y, is given by the convolution of fx,y(x,y) and is denoted by fx+y(t). The convolution of fx,y(x,y) is calculated as follows:

fx+y(t) = ∫∫infinityfX,Y(x,y)dydx

= ∫∫∞fX,Y(x,y)dxdy

= ∫∫∞fX,Y(x,y)sx.(x(8,6-u))dxdy

= ∫∫∞|sx.x(8,6-u)|dxdy

Hence, X + Y is continuous with density function fx+y(t) = |sx.x(8,6-u)|dxdy.

Learn more about continuous here:

https://brainly.com/question/12970235

#SPJ4

Answer:

Let y be the amount of money in the bank account after t years, where t >= 0.

The exponential function for this situation is:

y = 5000 * (1 + 0.027)^t

This function models the amount of money in the bank account after t years, given the initial deposit of $5,000 and an annual interest rate of 2.7%.

Step-by-step explanation:

Answer:

The formula for calculating the sum of the interior angles of a polygon is (n - 2) * 180, where n is the number of sides.

Since an octagon has 8 sides, Shane needed to use the formula (8 - 2) * 180 to get 1080.

The only way Shane could have gotten 1440 is by inputting 10 for n since (10 - 2) * 180 = 1440.

The number of frophs on the farm is 21 frophs.

First we need to determine the ratio of frophs to umpts and then multiply that ratio by the number of umpts on the farm.

The ratio of frophs to umpts is 5 frophs per 12 umpts, which can be simplified to 5/12 frophs per umpt.

If farmer Pisquet has 50 umpts on her joogh farm, then the number of frophs on the farm is:

50 umpts * (5/12 frophs per umpt) = 20.83 frophs

Rounding to the nearest whole number, the number of frophs on the farm is 21 frophs.

Learn more about simplified here: brainly.com/question/28780542

#SPJ1