Solve the system y = 3x + 2 and 3y = 9x + 6 by using graph paper or graphing technology. What is the solution to the system?

Answer:

x = 4

Step-by-step explanation:

Step 1: Combine like terms

9x + 6 = 42

Step 2: Isolate x by subtracting 6 on both sides

9x = 36

Step 3: Isolate x by dividing by 9 on both sides

x = 4

3x+6+6x=42

9x+6=42

9x+6-6=42-6

9x= 36

Divide by 9 for 9x and 36

9x/9=36/9

x=4

Check answer by using substitution method

3(4)+6+6(4)=42

12+6+24=42

42=42

Answer is x=4

Answer:

The direction that the paraboa y=-4x^2-8x-13 open is

Down

5 1/2 weeks. you divide 85 1/4 by 15 1/2 to get the answer

Ryan will take 5 weeks and 5 days to complete the tree house.

'The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.'

According to the given problem,

Time taken by Ryan to complete building the tree house = 85[tex]\frac{1}{4}[/tex] hours

                                                                                               = [tex]\frac{341}{4}[/tex] hours

Hours he work on the tree house = 15[tex]\frac{1}{2}[/tex] hours

                                                        = [tex]\frac{31}{2}[/tex]

Weeks taken by Ryan to complete building = [tex]\frac{341}{4}[/tex] ÷ [tex]\frac{31}{2}[/tex]

                                                                        = 5.5 weeks

                                                                        = 5 weeks 5 days

Hence, we can conclude that Ryan is going to take 5 weeks and 5 days to complete building the tree house.

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Answer:

64

Step-by-step explanation:

To do this they have 4 options for each so to get the answer do 4*4*4

Answer: 64

Step-by-step explanation:

So you have a to choose a language, an elective and a science class, each of them has 4 options to choose.

The total combination is the product of all the options.

it is 4 languages * 4 electives * 4 science = 4*4*4 combinations = 64.

So you have 64 possible combinations.

Answer:

The function f(x) = 5(0.8)x is located in the first quadrant, forming a increasing curve. Imagine the reflection of the graph of the function. It is located in the fourth quadrant, forming a decreasing curve.

The graph that shows reflection is just the negative of the function. So the answer is (x) = –5(0.8)x

Step-by-step explanation:

ANSWER

A. No because f(c)=-30

EXPLANATION

The given polynomial is

[tex]f(x) =2x^3-9x^2+13x-6[/tex]

If x+1 is a factor , then f(-1) must evaluate to zero.

[tex]f( - 1) =2( - 1)^3-9( - 1)^2+13( - 1)-6[/tex]

[tex]f( - 1) =2( - 1)-9( 1)+13( - 1)-6[/tex]

[tex]f( - 1) = - 2-9 - 13-6[/tex]

[tex]f( - 1) = -11 - 19[/tex]

[tex]f( - 1) = - 30[/tex]

Since f(-1) is not equal to zero, x+1 is not a factor of

[tex]f(x) =2x^3-9x^2+13x-6[/tex]

Answer: fixed costs of production

The business application that would utilize the slope-intercept form of a linear equation is 1."break-even analysis." therefore, option 1.break-even analysis is correct.

In break-even analysis, you are trying to find the point at which your total revenue equals your total costs, resulting in zero profit (break-even point). This analysis often involves linear equations, and the slope-intercept form (y = mx + b) is commonly used to represent cost and revenue functions. The slope (m) represents the variable cost per unit, and the y-intercept (b) represents the fixed costs.

The other options, "fixed cost of production," "scheduling employee vacation," and "scheduling of employee," may involve mathematical modeling and equations, but they do not typically use the slope-intercept form of a linear equation for the primary analysis. Instead, these applications may involve other types of equations or mathematical models.

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Answer:

360

Step-by-step explanation:

Write and solve an equation:

(1/6)(1/3)(1/4)n = 5

Multiplying the left side by (6)(3)(4), or 72, an

Multiply both sides by 6.  The resulting equation will still be true, but not have 6 in the denominator:

(1)(1/3)(1/4)n = 5(6) = 30

Mult both sides by 12.  The resulting equation will still be true, but not have (3)(4) in the denominator:

   (1)(1)(1)n = 360

Then n = 360.

Check:  Does (1/6)(1/3)(1/4)(360) = 5?

Yes.  This confirms that the unknown number n is 360.

Let us find the number step by step.
Let the unknown number be represented by 'x'.
We are given that one-sixth of one-third of one-fourth of this number is equal to five.
Let's break this down:
One-fourth of x is represented by x/4.
Now, we take one-third of that amount, which means we multiply (x/4) by 1/3, giving us (x/4) * (1/3).
Finally, we take one-sixth of the result from the previous step, so we then multiply by 1/6, yielding (x/4) * (1/3) * (1/6).
The expression we have is:
(x/4) * (1/3) * (1/6) = 5
To solve for x, we must clear the fractions by performing the multiplications:
(x/4) * (1/3) * (1/6) can be simplified before we do anything else:
* 1 * 1 = x
--
4 * 3 * 6   72
So we have:
x/72 = 5
To solve for x, multiply both sides of the equation by 72:
x = 5 * 72
Now, let's do the multiplication:
x = 360
Therefore, one-sixth of one-third of one-fourth of 360 is equal to five.

Answer:

2i√3

Step-by-step explanation: Simplify the radical by breaking the radicand up into a product of known factors.

Hope this helps! :) ~Zane

For this case we must find an expression equivalent to:

[tex]\sqrt {-12}[/tex]

Then, rewriting:

[tex]\sqrt {-1 (12)} =\\\sqrt {-1} * \sqrt {12} =[/tex]

We know that:

[tex]i = \sqrt {-1}\\12 = 4 * 3 = 2 ^ 2 * 3[/tex]

Then we have:

[tex]i * \sqrt {2 ^ 2 * 3} =\\i * 2 \sqrt {3} =[/tex]

Finally we have:

[tex]2i \sqrt {3}[/tex]

Answer:[tex]2i \sqrt {3}[/tex]

Answer:

6. an odd-degree polynomial function.

    f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞

7. Length =x+10=8+10=18 inches

   Width=x=8 inches

Step by step explanation;

6. The graph represent an odd-degree polynomial function.

The graph enters the graphing box from the bottom and goes up leaving through the top of the graphing box.This is a positive polynomial whose limiting behavior is given by;

f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞

7.

The area of a rectangle is given by l×w, where l is length and w is the width

Let=w=x  , l=x+10  and A=144 in² then;

l×w=144

(x+10) × x = 144

x²+10x =144......................complete squares on both sides

x²+10x+25=144+25

x²+10x+25=144+25................factorize

(x+5)²=169.......................square root the right-hand side

x+5= ±√169

x+5=±13.

x+5=13⇒⇒⇒x=8

x+5=-13⇒⇒⇒x= --18

x=8 inches....................value of width should be positive

Length =x+10=8+10=18 inches

Width=x=8 inches

Answer:

6. Since, by given graph,

The end behavior of the function f(x),

[tex]f(x)\rightarrow -\infty\text{ if }x\rightarrow -\infty[/tex]

[tex]f(x)\rightarrow +\infty\text{ if }x\rightarrow +\infty[/tex]

Thus, the function f(x) must has odd number of roots ( where the graph of a function intersects the x-axis )

⇒ The function must has odd number of solutions,

Again by the graph,

Graph of the function intersects the x-axis 5 times ( it touches the origin so it have the repeated root of x = 0 ),

Hence, the total number of real solution of f(x) is 5.

7. Let x represents the width of the rectangle( in inches ),

Given,

The length is 10 inches longer than the width,

⇒ Length of the rectangle = ( x + 10 ) inches

Thus, the area of the rectangle,

A = length × width = x(x+10)

According to the question,

A = 144 in²

⇒ x(x+ 10) = 144

[tex]x^2+10x=144[/tex]

[tex]x^2+10x-144=0[/tex]

[tex]x^2+18x-8x-144=0[/tex]  ( Middle term splitting )

[tex]x(x+18)-8(x+18)=0[/tex]

[tex](x+18)(x-8)=0[/tex]

⇒ x = -18 or x = 8    ( By zero test property )

The width can not be negative,

Hence, the width of the rectangle would be 8 inches.

Answer:

graph?

Step-by-step explanation:

Answer:CUB

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

it is 189ft² just trust me

Answer:

a

Step-by-step explanation:

Hello! :)

Since there is one value of y for every value of x in ( − 4 , 3 ) , ( − 2 , 3 ) , ( − 1 , 2 ) , ( 2 , 5 ) , ( 3 , 2 ) ( - 4 , 3 ) , ( - 2 , 3 ) , ( - 1 , 2 ) , ( 2 , 5 ) , ( 3 , 2 ) , this relation is a function. The relation is a function.

Hope I helped and wasn’t too late in answering!

Have fun and good luck!

~ Destiny ^_^

the correct answer is a) Function 1 only.

To determine which relations are functions from the given sets, we need to check if each element of the domain (the first number in each ordered pair) is mapped to only one element in the range (the second number in each ordered pair).

Set 1: {(-4, 3), (-2, 3), (-1, 2), (2, 5), (3, 2)}

Set 2: {(-4, 1), (-2, 3), (-2, 1), (-1, 5), (3, 2)}

Set 3: {(-4, 1), (-2, 3), (-1, 2), (3, 5), (3, 2)}

Set 4: {(-4, 1), (-2, 3), (-1, 1), (-1, 5), (3, 2)}

Analyzing each set:

Set 1 is a function because each domain value is unique and pairs with only one range value.

Set 2 is not a function because the domain value -2 is mapped to two different range values (3 and 1).

Set 3 is also not a function because the domain value 3 is mapped to two different range values (5 and 2).

Set 4 is not a function because the domain value -1 is mapped to two different range values (1 and 5).

Therefore, the correct answer is a) Function 1 only.

Answer:

The constant of proportionality is y/x so the rate us 35

Step-by-step explanation:

Answer:

(g ° h)(-3) = 8/5 ⇒ first answer

Step-by-step explanation:

* Lets explain the meaning of the composition of functions

- Composition of functions is when one function is inside of an another

 function

# If g(x) and h(x) are two functions, then (g ° h)(x) means h(x) is inside

  g(x) and (h ° g)(x) means g(x) is inside h(x)

* Now lets solve the problem

∵ g(x) = [tex]\frac{x+1}{x-2}[/tex]

∵ h(x) = 4 - x

∵ (g ° h)(x) means h(x) is inside g(x)

- Find (g ° h)(-3) means find h(-3) at first and then replace the value of

 h(-3) by the x of g(x)

* Lets find h(-3)

∵ h(x) = 4 - x

- Replace the x by -3

∴ h(-3) = 4 - (-3) = 4 + 3 = 7

- Now find g(7), means replace x by 7

∵ g(x) = [tex]\frac{x+1}{x-2}[/tex]

∴ g(7) = [tex]\frac{7+1}{7-2}=\frac{8}{5}[/tex]

∴ (g ° h)(-3) = 8/5

Answer:

∠C and ∠R

Step-by-step explanation:

The ASA postulate represents angle / side / angle

where the included side is the side between the vertices of the two angles.

∠H and ∠I and the sides HC and IR are the AS

The required angles would be ∠C and ∠R for ASA

Answer:

Decimal point

Definition:

A decimal point is the symbol that is used to make the separation between the whole part and the fractional part of a number. Currently, not only is a point used to separate both parts, but the comma can also be used.

Example:

The number 39.847, in which 39 is the whole number, while 847 is the decimal part where 8 represent tenths, 4 hundredsths, and 7 thousandths.

Answer:

p(v(t))=40m/t

Step-by-step explanation:

Answer: The answer is A

Step-by-step explanation:

Yes

Answer:

x^2+5x-6

a = 1  b = 5 and c = -6

Using the quadratic formula:

x = [-5 +- sq root (25 -4 * 1 *-6) ] / 2 * 1

x = [-5 +- sq root (49)] / 2

x = [-5 +- 7] / 2

x1 = 1

x2 = -6

Step-by-step explanation:

Answer:

 [tex]y_1=-\frac{1}{2}\\\\y_2=-\frac{3}{2}[/tex]

Step-by-step explanation:

The Quadratic formula is:

[tex]y=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]

Given the equation [tex]4y^2+ 8y +7 =4[/tex], you need to subtract 4 from both sides:

[tex]4y^2+ 8y +7 -4=4-4[/tex]

[tex]4y^2+ 8y +3 =0[/tex]

Now you can identify that:

[tex]a=4\\b=8\\c=3[/tex]

Then you can substitute these values into the Quadratic formula. Therefore, you get these solutions:

[tex]y=\frac{-8\±\sqrt{8^2-4(4)(3)} }{2(4)}[/tex]

[tex]y_1=-\frac{1}{2}\\\\y_2=-\frac{3}{2}[/tex]

Answer:

The solutions are y=-1/2 and y=-3/2

Step-by-step explanation:

Ok, for this problem we need to use the quadratic formula:

For [tex]ax^{2} +bx+c=0[/tex]

The values of x which are the solutions of the equation:

[tex]x=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex]

In this case your variable is y, so:

[tex]ay^{2} +by+c=0[/tex]

[tex]y=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex]

So, a=4, b=8 and c=3

[tex]y=\frac{-(8)+-\sqrt{(8)^{2}-4(4)(3) } }{2(4)}[/tex]

[tex]y=\frac{-(8)+-\sqrt{(16)}}{8}[/tex]

[tex]y=\frac{-8+4}{8}[/tex] and [tex]y=\frac{-8-4}{8}[/tex]

The solutions are

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

Answer:

[tex]\frac{(3x)^{12} }{(3x)^{4} } =(3x)^{8}[/tex]

Step-by-step explanation:

As we are dividing by powers, we can just subtract the powers as they have the same base. As 12-4=8 the answer would be

[tex]\frac{(3x)^{12} }{(3x)^{4} } =(3x)^{8}[/tex]

Answer:

[tex] (3 x )^ 8 [/tex]

Step-by-step explanation:

We are given the following expression which we are to multiply or divide as indicated:

[tex] \frac { ( 3 x ) ^ { 1 2 } } { ( 3 x ) ^ 4 } [/tex]

We know that if the bases are same and they are divided, then the exponent of the denominator is subtracted from the exponent of the numerator. So we get:

[tex] ( 3 x ) ^ { 1 2 - 4 } =( 3 x )^ 8 [/tex]

Answer:

The horizontal cross-sections of the pyramid and the cone at the same height must have the same area.

Step-by-step explanation:

We are given that a pyramid and a cone are both 10 centimeters tall and have the same volume and we are to determine a statement which must be true for both the solids.

The horizontal cross-sections of the pyramid and cone at the same height must have the same area.

This is because

Answer:

Tbase area is same for both pyramid and cone

And cross section at same height the cross sectional area is same

Step-by-step explanation:

Points to remember

Volume of pyramid = (a²h)/3

Where a -  side of base

h - height of pyramid

Volume of cone = (πr²h)/3

Where r - Radius of cone and

h - Height of cone

To find the correct answer

We have height of pyramid and cone is 10 cm

(a²h)/3 = (πr²h)/3

(a² * 10)/3 = (πr² * 10)/3

10a² = 10πr²

From this we get base area is same for both pyramid and cone

And cross section at same height the cross sectional area is same

Answer:

-8

Step-by-step explanation:

-1-7 = -8

-8.

-1 - 7 would be adding because when subtracting negatives you always change the sign and a trick i know is that negatives are referred to as “hate” and positives are referred to as “love”. therefore if you do a negative minus a positive you will get a negative. so the answer here is -8.

Answer:

acute

Step-by-step explanation:

Answer:

• 800 pavilion seats

• 800 lawn seats

Step-by-step explanation:

Let p represent the number of pavilion seats sold. Then 1600-p is the number of lawn seats sold. Total revenue is ...

25p +20(1600 -p) = 36000

5p + 32000 = 36000

5p = 4000

p = 800 . . . . . . . . . . number of pavilion seats sold

1600-p = 800 . . . . . number of lawn seats sold

_____

You can work these problems in your head. Consider that all seats were sold at the lower price. Then revenue would be 1600·20 = 32000. It was 36000 -32000 = 4000 more than that. The difference in ticket price is 25 -20 = 5 dollars, so there must have been 4000/5 = 800 higher-priced tickets sold. (Compare this working to the math above. You will find it substantially similar.)

A. n+4=5  

Hope this helps

Based on the analysis of the residual plots, Runner B's data is best fit by the regression line. This means that Runner B kept the most consistent pace throughout the race.

Analyze the residual plots to determine the best-fit regression line and identify the runner with the most consistent pace.

Observations from the Residual Plots:

- Runner A: The residual plot shows a clear U-shaped pattern, indicating a non-linear relationship and a poor fit for the regression line.

- Runner B: The residual plot exhibits a relatively random scatter of points around zero, suggesting a better fit for the regression line compared to Runner A.

- Runner C: The residual plot displays a distinct downward trend, also indicating a non-linear relationship and a poor fit for the regression line.

Conclusion:

Based on the analysis of the residual plots, Runner B's data is best fit by the regression line. This means that Runner B kept the most consistent pace throughout the race, as their actual pace closely aligned with the predicted pace from the linear model.

Therefore, the answer is B. Runner B.

The correct option is A. A. Runner A because if Runner A’s residual plot fits the criteria of a good linear fit.

To determine which runner kept the most consistent pace based on their residual plots, you need to understand the interpretation of residual plots in the context of linear regression.

Understanding Residual Plots

1. Residuals are the differences between the observed values and the values predicted by the regression line.

2. A residual plot displays these residuals on the vertical axis and the corresponding explanatory variable on the horizontal axis.

3.Consistency in Pace: For a runner to have a consistent pace, the residuals should be randomly scattered around zero with no discernible pattern. This indicates that the linear model is a good fit.

Interpreting Residual Plots

- Runner A: If the residuals for Runner A are randomly scattered around zero with no pattern, it means Runner A's data is well-fitted by the regression line, indicating a consistent pace.

- Runner B: If Runner B's residual plot shows a pattern (e.g., residuals increase or decrease systematically), it suggests that the regression line does not fit Runner B's data well, indicating inconsistency in pace.

- Runner C: Similarly, if Runner C's residual plot shows randomness around zero with no pattern, it means Runner C's data is well-fitted by the regression line, indicating a consistent pace.

Decision

Given the prompt, if you have residual plots for each runner:

1. Look for the plot with residuals randomly scattered around zero.

2. This runner’s data is best fit by the regression line and indicates the most consistent pace.

- Choose Runner A if Runner A’s residual plot shows randomly scattered residuals around zero.

- Choose Runner B if Runner B’s residual plot shows randomly scattered residuals around zero.

- Choose Runner C if Runner C’s residual plot shows randomly scattered

Since the question prompt explicitly mentions Runner A, the implication is that Runner A has the most consistent pace if their residual plot indeed shows a good fit with no pattern. Thus, based on the information given and assuming the residual plots for Runner A are the best fit, the answer would be:A. Runner A

The complete questionis:

Three runners competed in a race. Data were collected at each mile mark for each runner. If the runner ran at a constant pace, the data would be linear. A regression line was fitted to their data. Use the residual plots to decide which data set is best fit by the regression line, and then identify the runner that kept the most consistent pace.

A. Runner A

B. Runner B

C. Runner C

ANSWER

No, there is no constant ratio.

EXPLANATION

We want to determine whether the sequence

4, 16, 36, 64

is geometric.

We need to find out if there is a common ratio between the consecutive terms.

[tex] \frac{16}{4} = 4[/tex]

[tex] \frac{36}{16} = \frac{9}{4} [/tex]

[tex] \frac{64}{36} = \frac{16}{9} [/tex]

Since the ratio is not the same for the consecutive terms, the sequence is not geometric.

4, 16, 36, 64 is a geometric sequence with a common ratio of 4.

Yes, 4, 16, 36, 64 is a geometric sequence.

Answer:

about 27% likely I think......

Answer:

13%

Step-by-step explanation:

You would take 100% and subtract 87%. That will equal 13%. So it is 13% likely that we will win.