Consider the function f(x) = 3x + 1 and the graph of the function g(x) shown below.

A coordinate plane linear graph function shows a line intersecting Y-axis at minus 5 and X-axis at 1.5.
The graph g(x) is the graph of f(x) translated units , and g(x) =

Answer:

step one needs to be fixed... you are supposed to subtract 10 from both sides of the equation.

Step-by-step explanation:

STEP 1: Move all terms not containing n to the right side of the equation.

\(2n=-12\)

STEP 2: Divide each term by 2 and simplify.

\(n=-6\)

Answer:

7 child tickets

14   adult tickets

Step-by-step explanation:

Let a = the number of adult tickets

Let c = the number of child tickets

16a + 16c + 672

2c = a  Substitute 2c for a

15a + 16c = 672

16(2a) + 16c = 672

32a + 16c = 672  Combine like terms

48a = 672  Divide both sides by 48

a = 14

2c = a

2c = 14  Divide both sides by 2

c = 7                                                                                                  

Given:

The equation is:

\(\dfrac{x-3}{x+2}+\dfrac{3x-3}{(x+1)(x+2)}=\dfrac{x}{x+1}-\dfrac{x-2}{x+2}\)

To find:

The solution for the given equation.

Solution:

We have,

\(\dfrac{x-3}{x+2}+\dfrac{3x-3}{(x+1)(x+2)}=\dfrac{x}{x+1}-\dfrac{x-2}{x+2}\)

Taking LCM on both sides, we get

\(\dfrac{(x-3)(x+1)+3x-3}{(x+1)(x+2)}=\dfrac{x(x+2)-(x+1)(x-2)}{(x+1)(x+2)}\)

\((x-3)(x+1)+3x-3=x(x+2)-(x+1)(x-2)\)

\(x^2+x-3x-3+3x-3=x^2+2x-(x^2-2x+x-2)\)

\(x^2+x-6=x^2+2x-x^2+2x-x+2\)

On further simplification, we get

\(x^2+x-6=3x+2\)

\(x^2+x-6-3x-2=0\)

\(x^2-2x-8=0\)

Splitting the middle term, we get

\(x^2-4x+2x-8=0\)

\(x(x-4)+2(x-4)=0\)

\((x+2)(x-4)=0\)

\(x=-2,4\)

But \(x\neq -2\) because for \(x=-2\) the given equation is not defined.

Therefore, the only solution of the given equation is \(x=4\).

The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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Answer:

Simplest form of expression:

-3+2x

Answer:

2x - 3 (or) -3 + 2x

Step-by-step explanation:

Given equation,

→ (-+ 3) - 2 (-x)

The simplest form will be,

→ (-+ 3) - 2 (-x)

→ -3 + (-2 × -x)

→ -3 + 2x

→ 2x - 3

Thus, the answer is 2x - 3.

Answer:

2

Step-by-step explanation:

   1/2x4=2

Answer:

7.745

Step-by-step explanation:

Square root of 60 equals X.

The algebraic property illustrated is the commutative property of multiplication

The properties of algebra are those properties mostly used in simplifying algebraic expressions.

Algebraic properties are:

From the expression given we have

4/5 • 5/4 = 1

= 4/ 5 × 5/ 4

= 1

Thus, the algebraic property illustrated is the commutative property of multiplication

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\(\left(\dfrac{5}{n+1}\right) \left( \dfrac{n+1}{n+3} \right)\\\\\\=\dfrac{5(n+1)}{(n+1)(n+3)} \\\\\\=\dfrac{5}{n+3}\)

Answer:

x=7

m∠T=80

Step-by-step explanation:

The interior angles of a quadrilateral add up to 360.

Set up all the angles to equal 360.

95+80+12x-4+15x=360

Solve.

171+27x=360

27x=189

x=7

Answer:

134 children and 120 adult plates were served

Step-by-step explanation:

let the children mean be x

Let the adult meal be y

If fourteen less children’s meals were served than adult meals at a barbecue, then;

y = x - 14 .... 1

IF Children plate were 1.50 each and adult plates were 2.00 each with a total of 441 in amount then;

1.5x + 2y = 441 .... 2

Substitute 1 into 2;

1.5x + 2(x-14) = 441

1.5x+2x-28 = 441

3.5x = 441+28

3.5x = 469

x = 469/3.5

x = 134

Recall that y = x - 14

y = 134-14

y = 120

Hence 134 children and 120 adult plates were served

Answer:

Xavier's age = 23

Yifei's age = 27

Step-by-step explanation:

Represent Yifei's age with Y and Xavier's age with X;

Given that the sum of their ages is 124;

X + Y = 124

Also, given that Yifei is 4 years older

Y = X + 4

Required

Find their age when they got married

From the parameters above, we've been able to form a simultaneous equation

\(X + Y = 124\)

\(Y = X + 4\)

Substitute X + 4 for Y in the first equation

\(X + X + 4 = 124\)

\(2X + 4=124\)

Subtract 4 from both sides

\(2X + 4 - 4 = 124 - 4\)

\(2X = 120\)

Divide both sides by 2

\(\frac{2X}{2} = \frac{120}{2}\)

\(X = 60\)

Substitute 60 for X in the second equation

\(Y = X + 4\) becomes

\(Y = 60 +4\)

\(Y = 64\)

To get their ages when they got married; we simply subtract 37 from their current ages

Xavier's age = 60 - 37

Xavier's age = 23

Yifei's age = 64 - 37

Yifei's age = 27

The equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle, and r is its radius.

We have given that circle having radius of 8 units. Thus, r = 8.

Since we know that circle having the center (10,−7).

Thus, the equation of the circle, with a radius of 8 units is;

(x - h)² + (y - k)² = r²

(x - 10)² + (y + 7)² = 8²

Thus, the equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²

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One of the Possible values of length and width of the prism are 15 cm and 0.5 cm

In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.

Given here: The volume of the prism is 2¹/₂=2.5 cm³

And the height is 1/3 cm

let the length and breadth of the prism is x and y respectively.

We know the volume of the prism as

1/3 × x×y=2.5

x×y=7.5

Thus possible values of length and breadth are the factors of 7.5

out of which one of the pair whose length is 15 cm and width 0.5 cm

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Answer:

Step-by-step explanation:

slope intercept form is y = mx + b

b is the y intercept ( crossing y axis value)....     by inspection   b = 5

m is the slope of the line, the slope equals the 'rise' over 'run'  

if the line moves up the slope is positive, if the line moves down the slope is negative

the rise is how many y units does the line go 'up' or 'down'

the run is how many x units does the line go 'left' or 'right'

By inspection the line moves up to the right, it rises ONE Y unit for every THREE X units (the run)   so m = rise/run    m = 1/3

so        Y = (1/3)X + 5      Answer

try this one method. I hope it will help a little

Answer:

\(\Huge \boxed{\boxed{ x = 1}}\)

Step-by-step explanation:

Isolate the variable on one side of the equation before trying to solve it. It means that you should only have constants (numbers) on the other side of the equal sign and the variable alone on the one side.

To do this, you can add, subtract, multiply, divide, or use any other operation to both sides of the equation as long as you do the same thing on both sides.

Your final step depends on the equation and how you've simplified it. In general, you want to figure out how you arrived at the final equation by working backwards from it. You'll isolate the variable in the last action you took.

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

Step1: Subtract \(\bold{2x}\) from both sides

Step 2: Subtract 3 from both sides

Step 3: Divide both sides of the equation by 6

So the solution to the equation \(\bold{8x + 3 = 2x + 9}\) is \(\bold{x = 1}\).

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

Answer:

19

Step-by-step explanation:

BODMAS

Brackets.

Of

Division

Multiplication

Addition and

Subtraction

go according to the BODMAS rule and solve the division first

24-(16÷4)×2+3

Then solve the multiplication part

24-(4×2)+3

Now solve like a regular sum

24-8+3

16+3

19

None of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

To find the slope of the red line given that it is perpendicular to the green line with a slope of 2, we can use the property that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the green line is 2. To find the slope of the red line, we take the negative reciprocal of 2. The negative reciprocal is obtained by taking the reciprocal (flipping the fraction) and changing the sign.

Reciprocal of 2: 1/2

Negative reciprocal: -1/2

Therefore, the slope of the red line is -1/2.

However, none of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

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Answer:

Step-by-step explanation:

You want to identify the graphs that go with each of these functions, along with a particular point on the curve.

The equations are written here in standard form, factored form, and vertex form. (The "factored form" is sometimes called "intercept form.") Each of these forms can be analyzed for characteristics relevant to identifying the corresponding graph.

In general, we can readily identify the opening direction, based on the sign of the leading coefficient. Depending on the form, we can also identify zeros, the vertex, and the y-intercept.

The line of symmetry (x-coordinate of the vertex) of the equation in the form ax² +bx +c is x = -b/(2a). That is, it will be left of the y-axis when the coefficients 'a' and 'b' have the same sign.

The graph of equation A will be graph 4, the only one with its vertex left of the y-axis. The y-intercept is the constant: point S = (0, 9).

Equation B has a positive leading coefficient, so opens upward. The zeros of the factors are -3 and +9, so identify the places where the graph crosses the x-axis. Graph 3 is the only one that opens upward and has x-intercepts. Point R is (9, 0).

The vertex form of a quadratic is ...

  y = a(x -h)² +k . . . . . . . vertex (h, k); leading coefficient 'a'

Equation C has its vertex at (h, k) = (3, 9) and opens upward (a>0). Graph 1 is the only one matching those characteristics. Point P is the vertex, so point P is (3, 9).

Equation D is the same as equation B, but with a negative leading coefficient. That is, it opens downward and crosses the x-axis in two places, at x = -3 and x = 9. Graph 2 is matches this description. The left zero is point Q, (-3, 0).

<95141404393>

9514 1404 393

Answer:

Step-by-step explanation:

Formula:

To solve the formula for height, multiply both sides by the inverse of the coefficient of h.

  \(\left(\dfrac{3}{\pi r^2}\right)\cdot V=\left(\dfrac{3}{\pi r^2}\right)\cdot\left(\dfrac{\pi r^2}{3}\right)\cdot h\\\\\boxed{h=\dfrac{3V}{\pi r^2}}\)

__

Height:

Fill in the given values and do the arithmetic.

  \(h=\dfrac{3\cdot 32\pi\text{ cm$^3$}}{\pi(4\text{ cm})^2}=\boxed{6\text{ cm}}\)

Answer:

1 x= 23°

2 x= 148°

3 x= 106°

4 x=17.3°

5 x=25°

6 x=30°

7 x=45°

8 x=48°

9 x=44°

The trapezoids in the picture follow the next proportion:

Replacing with data and solving for PU,

Answer:

Here are the steps for conducting a survey in your school to find out which mode of transportation students prefer the most, arranged in order from start to finish:

1) Define the objective: Clearly define the objective of the survey, which is to determine the preferred mode of transportation among students in your school.

2) Determine the sample size: Decide on the number of students you want to include in your survey. This will depend on factors such as the size of your school and the resources available for conducting the survey.

3) Design the survey questionnaire: Create a well-designed survey questionnaire that includes relevant questions about different modes of transportation. Ensure that the questions are clear, unbiased, and cover all the necessary aspects.

4) Seek necessary permissions: If required, seek permission from school authorities or relevant individuals to conduct the survey on school premises and to involve students.

5) Pre-test the survey: Before distributing the survey to the entire student population, pre-test the questionnaire on a small group of students to identify any potential issues or areas for improvement.

6) Distribute the survey: Once the questionnaire has been finalized and pre-tested, distribute it to the selected sample of students. Ensure that the survey is distributed in a fair and unbiased manner, taking into account the diversity of the student population.

7) Collect the survey responses: Set a specific timeframe for students to complete the survey and collect the responses. Consider using a combination of online platforms and physical collection methods to maximize participation.

8) Analyze the data: Once you have collected all the survey responses, analyze the data to determine the preferred mode of transportation among students. Use appropriate statistical tools and techniques to interpret the results accurately.

9) Present the findings: Prepare a report or presentation summarizing the survey findings. Include key insights, trends, and any significant findings related to the preferred mode of transportation among students.

10) Share the results: Share the survey results with the school community, including students, teachers, and administrators. This can be done through presentations, newsletters, or other suitable communication channels.

By following these steps, you will be able to conduct a comprehensive survey to determine the preferred mode of transportation among students in your school.

Hope this helps!

I can not do it for you but I can give you what you should do

Explanation: take a survey

Answer:

20x + 8

Step-by-step explanation:

5*4x + 5*5 -17

20x +25 -17

20x + 8

Answer:

2. is b

3.is d

4.is b

5

Step-by-step explanation:

I've done these before

have a good grade

Answer:

Step-by-step explanation:

- The domain of (f+g)(x) is all real numbers.

- The domain of (g-f)(x) is all real numbers.

- The domain of (f⋅g)(x) is all real numbers.

- The domain of (g/f)(x) is all real numbers except x ≠ 0 and x ≠ -2.

(f+g)(x) = (x^2 + 2x) + (5 - x) = x^2 + x + 5

Domain: The domain of (f+g)(x) is all real numbers since there are no restrictions on x.

(g-f)(x) = (5 - x) - (x^2 + 2x) = -x^2 - 3x + 5

Domain: The domain of (g-f)(x) is all real numbers since there are no restrictions on x.

(f⋅g)(x) = (x^2 + 2x) * (5 - x) = -x^3 + 3x^2 + 5x

Domain: The domain of (f⋅g)(x) is all real numbers since there are no restrictions on x.

(g/f)(x) = (5 - x) / (x^2 + 2x)

Domain: The domain of (g/f)(x) is all real numbers except x ≠ 0 and x ≠ -2, because the denominator (x^2 + 2x) cannot be equal to zero.

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